url stringlengths 6 1.61k | fetch_time int64 1,368,856,904B 1,726,893,854B | content_mime_type stringclasses 3 values | warc_filename stringlengths 108 138 | warc_record_offset int32 9.6k 1.74B | warc_record_length int32 664 793k | text stringlengths 45 1.04M | token_count int32 22 711k | char_count int32 45 1.04M | metadata stringlengths 439 443 | score float64 2.52 5.09 | int_score int64 3 5 | crawl stringclasses 93 values | snapshot_type stringclasses 2 values | language stringclasses 1 value | language_score float64 0.06 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
https://metanumbers.com/7518 | 1,606,355,859,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141185851.16/warc/CC-MAIN-20201126001926-20201126031926-00220.warc.gz | 385,606,594 | 7,475 | ## 7518
7,518 (seven thousand five hundred eighteen) is an even four-digits composite number following 7517 and preceding 7519. In scientific notation, it is written as 7.518 × 103. The sum of its digits is 21. It has a total of 4 prime factors and 16 positive divisors. There are 2,136 positive integers (up to 7518) that are relatively prime to 7518.
## Basic properties
• Is Prime? No
• Number parity Even
• Number length 4
• Sum of Digits 21
• Digital Root 3
## Name
Short name 7 thousand 518 seven thousand five hundred eighteen
## Notation
Scientific notation 7.518 × 103 7.518 × 103
## Prime Factorization of 7518
Prime Factorization 2 × 3 × 7 × 179
Composite number
Distinct Factors Total Factors Radical ω(n) 4 Total number of distinct prime factors Ω(n) 4 Total number of prime factors rad(n) 7518 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 7,518 is 2 × 3 × 7 × 179. Since it has a total of 4 prime factors, 7,518 is a composite number.
## Divisors of 7518
1, 2, 3, 6, 7, 14, 21, 42, 179, 358, 537, 1074, 1253, 2506, 3759, 7518
16 divisors
Even divisors 8 8 4 4
Total Divisors Sum of Divisors Aliquot Sum τ(n) 16 Total number of the positive divisors of n σ(n) 17280 Sum of all the positive divisors of n s(n) 9762 Sum of the proper positive divisors of n A(n) 1080 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 86.7064 Returns the nth root of the product of n divisors H(n) 6.96111 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 7,518 can be divided by 16 positive divisors (out of which 8 are even, and 8 are odd). The sum of these divisors (counting 7,518) is 17,280, the average is 1,080.
## Other Arithmetic Functions (n = 7518)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 2136 Total number of positive integers not greater than n that are coprime to n λ(n) 534 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 959 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 2,136 positive integers (less than 7,518) that are coprime with 7,518. And there are approximately 959 prime numbers less than or equal to 7,518.
## Divisibility of 7518
m n mod m 2 3 4 5 6 7 8 9 0 0 2 3 0 0 6 3
The number 7,518 is divisible by 2, 3, 6 and 7.
## Classification of 7518
• Arithmetic
• Abundant
### Expressible via specific sums
• Polite
• Non-hypotenuse
• Square Free
## Base conversion (7518)
Base System Value
2 Binary 1110101011110
3 Ternary 101022110
4 Quaternary 1311132
5 Quinary 220033
6 Senary 54450
8 Octal 16536
10 Decimal 7518
12 Duodecimal 4426
20 Vigesimal ifi
36 Base36 5su
## Basic calculations (n = 7518)
### Multiplication
n×i
n×2 15036 22554 30072 37590
### Division
ni
n⁄2 3759 2506 1879.5 1503.6
### Exponentiation
ni
n2 56520324 424919795832 3194547025064976 24016604534438489568
### Nth Root
i√n
2√n 86.7064 19.59 9.31163 5.95965
## 7518 as geometric shapes
### Circle
Diameter 15036 47237 1.77564e+08
### Sphere
Volume 1.7799e+12 7.10255e+08 47237
### Square
Length = n
Perimeter 30072 5.65203e+07 10632.1
### Cube
Length = n
Surface area 3.39122e+08 4.2492e+11 13021.6
### Equilateral Triangle
Length = n
Perimeter 22554 2.4474e+07 6510.78
### Triangular Pyramid
Length = n
Surface area 9.78961e+07 5.00773e+10 6138.42
## Cryptographic Hash Functions
md5 cf98f1617165bf975b4dd57ab90269cf d0b1f2d7c20b8a1fa79ec6681181632b36b152a3 2a42480087db6658d135052e93c3f578f64133b7bbe9d742c0bcf436e6087114 e893841dc6c53b2698a114769d019c3c398f7971146dbf28afd42d2b23152a6b0aefc811f91528ef5952cdcab7e0d1d0c8279d6f87573af194f0bf908f325a69 f568f84016c9eac30715e1e97be350e90d80511e | 1,486 | 4,128 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2020-50 | longest | en | 0.812971 |
https://brainmass.com/statistics/hypothesis-testing/hypothesis-testing-types-tests-errors-387317 | 1,708,977,568,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474663.47/warc/CC-MAIN-20240226194006-20240226224006-00401.warc.gz | 142,174,651 | 6,886 | Purchase Solution
# Hypothesis Testing: Types of Tests and Errors
Not what you're looking for?
What is a one tail test? A two tail test?
When are they used?
What is a type I error? A type II error?
In the hypotheses:
Ho: A new auto engine gets the same mpg as an older version
Ha: A new auto engine gets more mpg than an older version
Ho: A new drug for cardio-vascular disease is not safe
Ha: A new drug for cardio-vascular disease is safe
Why is the alternate stated as it is?
What are the "type" errors and their consequences?
##### Solution Summary
This solution helps answer various statistical questions, involving one and two tailed tests and type I and type II errors.
##### Solution Preview
(a) A test where a population parameter is tested to see if it is less than or greater than a specified value
(b) A test where a population parameter is tested to see if it is not equal to a specified value
(c) They are used as the situation demands- whether the parameter to be tested is <, > or <> to a specified value
(d) Type I error: Rejecting a true null hypothesis
Type II error: Failing to reject ...
##### Measures of Central Tendency
This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research. | 300 | 1,391 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2024-10 | latest | en | 0.883091 |
http://www.finalhomework.com/mat-540-week-1-homework-problems-strayer-university-new/ | 1,516,595,958,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084890991.69/warc/CC-MAIN-20180122034327-20180122054327-00205.warc.gz | 430,677,888 | 10,544 | # MAT 540 Week 1 Homework Problems – Strayer University New
MAT 540 Homework Problems Week 1 Solution
http://www.hwmojo.com/products/mat540-week-1-homework
We have all Homework Problems, Discussions, Quizzes, Exams and Writing Assignment for Mat 540. Email us support@hwmojo.com
Mat 540 Week 2 Homework Problems – Chapter 1 and Chapter 11
Complete the following problems from Chapter 1:
Problems 2, 4, 12, 14, 20, 22
Complete the following problems from Chapter 11:
Problems 18, 20, 26, 28, 30
Chapter 1:
2) The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is
\$60,000. The variable cost of recapping a tire is \$9. The company charges \$25 to recap a tire.
For an annual volume of 12,000 tires, determine the total cost, total revenue, and profit.
Determine the annual break-even volume for the Retread Tire Company operation.
4) Evergreen Fertilizer Company produces fertilizer. The company’s fixed monthly cost is \$25,000, and its variable cost per pound of fertilizer is \$0.15. Evergreen sells the fertilizer for \$0.40 per pound. Determine the monthly break-even volume for the company.
12) If Evergreen Fertilizer Company in Problem 4 changes the price of its fertilizer from \$0.40 per pound to \$0.60 per pound, what effect will the change have on the break-even volume?
14) If Evergreen Fertilizer Company increases its advertising expenditures by \$14,000 per year, what effect will the increase have on the break-even volume computed in Problem 13?
20) Annie McCoy, a student at Tech, plans to open a hot dog stand inside Tech’s football stadium during home games. There are seven home games scheduled for the upcoming season. She must pay the Tech athletic department a vendor’s fee of \$3,000 for the season. Her stand and other equipment will cost her \$4,500 for the season. She estimates that each hot dog she sells will cost her \$0.35. She has talked to friends at other universities who sell hot dogs at games. Based on their information and the athletic department’s forecast that each game will sell out, she anticipates that she will sell approximately 2,000 hot dogs during each game.
What price should she charge for a hot dog in order to break even?
What factors might occur during the season that would alter the volume sold and thus the
break-even price Annie might charge?
What price would you suggest that Annie charge for a hot dog to provide her with a
reasonable profit while remaining competitive with other food vendors?
22) The College of Business at Tech is planning to begin an online MBA program. The initial start-up cost for computing equipment, facilities, course development, and staff recruitment and development is \$350,000. The college plans to charge tuition of \$18,000 per student per year. However, the university administration will charge the college \$12,000 per student for the first 100 students enrolled each year for administrative costs and its share of the tuition payments.
How many students does the college need to enroll in the first year to break even?
If the college can enroll 75 students the first year, how much profit will it make?
The college believes it can increase tuition to \$24,000, but doing so would reduce enrollment to 35. Should the college consider doing this?
Chapter 11
18) The following probabilities for grades in management science have been determined based on past records:
A .10
B .30
C .40
D .10
F .10
1.00
The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a 3.0, and so on. Determine the expected grade and variance for the course.
20) An investment firm is considering two alternative investments, A and B, under possible future sets of economic conditions, good and poor. There is a .60 probability of good economic conditions occurring and a .40 probability of poor economic conditions occurring. The expected gains and losses under each economic type of conditions are shown in the following table:
Economic Conditions
Investment Good Poor
A \$900,000 -\$800,000
B 120,000 70,000
Using the expected value of each investment alternative, determine which should be selected.
26) The weight of bags of fertilizer is normally distributed, with a mean of 50 pounds and a standard deviation of 6 pounds. What is the probability that a bag of fertilizer will weigh between 45 and 55 pounds.
28) The polo Development Firm is building a shopping center. It has informed renters that their rental space will be ready for occupancy in 19 months. If the expected time until the shopping center is completed is estimated to be 14 months with a standard deviation of 4 months, what is the probability that the renters will not be able to occupy in 19 months?
30) The manager of the local national Video Store sells videocassette recorders at discount prices. If the store does not have a video recorder in stock when a customer wants to buy one, it will lose the sale because the customer will purchase a recorder from one of the many local competitors. The problem is that the cost of renting warehouse space to keep enough recorders in inventory to meet all demand is excessively high. The manager has determined that if 90% of customers demand for recorders can be met, then the combined cost of lost sales and inventory will be minimized. The manager has estimated that monthly demand for recorders is normally distributed, with a mean of 180 recorders and a standard deviation of 60. Determine the number of recorders the manager should order each month to meet 92% of customer demand.
We also have
Mat 540 Homework Problems
Mat 540 Assignment
Mat 540 Quiz 1
Mat 540 Quiz 2
Mat 540 Quiz 3
Mat 540 Quiz 4
Mat 540 Quiz 4
Mat 540 Midterm Exam
Mat 540 Final Exam
Mat 540 Complete class
Mat 540 Entire Class
Strayer Mat 540 Latest
Mat 540 Recent Class
Mat 540 NEW class
MAT 540 Solution
Mat 540 Help | 1,338 | 5,889 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.578125 | 4 | CC-MAIN-2018-05 | longest | en | 0.893383 |
https://antennamediatorino.eu/en/is-there-a-good-ratio-of-hr-to-staff/ | 1,656,836,742,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104215805.66/warc/CC-MAIN-20220703073750-20220703103750-00649.warc.gz | 154,115,705 | 20,182 | # Is there a good ratio of HR to staff?
2021 HR-to-Employee Calculation According to Bloomberg BNA’s HR Department Benchmarks and Analysis report, the rule-of-thumb ratio is 1.4 full-time HR staff per 100 employees. This ratio is at an all-time high, and in sharp contrast to the marked drops we have seen in recent years.
## What is the normal ratio of HR staff to employees?
The HR-to-employee ratio compares HR staffing levels between organizations by showing the number of HR FTEs supporting 100 FTEs in an organization. 8 The average HR-to-employee ratio was 2.57 for all organizations. As staff size increases, however, the HR-to-employee ratio decreases.
## How do you calculate HR staff ratio?
HR-to-employee ratio is thankfully easy to calculate. Divide your HR team’s headcount by your company’s total number of full time employees, and then multiply that number by 100.
## How many employees does an HR employee have?
According to a 2014 report from the Society for Human Resources Management (SHRM), the average HR-to-employee ratio (the number of HR employees per 100 employees) is 2.57 for all organizations.
## What is an HR ratio?
An HR to employee ratio is the size of a human resources time in relation to the rest of the company. It measures how many HR representatives there are for each employee. This ratio may also compare HR staffing levels between different organizations. As staff size increases, the ratio usually decreases.
## How many employees do you need before you need HR?
50 employees
Hiring a human resource generalist is also about employee numbers. As your business grows in services and in numbers, the need for an HR department will grow concurrently. Generally, you should hire a full-time human resource staff member when there are about 50 employees within the company.
## What is a good ratio of managers to employees?
Ideally in an organization, according to modern organizational experts is approximately 15 to 20 subordinates per supervisor or manager. However, some experts with a more traditional focus believe that 5-6 subordinates per supervisor or manager is ideal.
## What are the 7 functions of HR?
The 7 Major Functions of HR Activities
• Recruitment and Employee Screening. Acquiring new talent is something every business needs to do if they wish to grow. …
• Company Benefits and Compensation. …
• Performance Evaluation. …
• Employee Relations. …
• Enforcement of Disciplinary Actions. …
• Employee Records. …
• Continued Education.
Sep 27, 2021
## How do you calculate staffing needs?
Step 1: Number of rooms multiplied by number of hours per day multiplied by number of days per week = total hours to be staffed per week. Step 2: Total hours per week multiplied by number of people per room = total working hours per week. Step 3: Total working hours/week divided by 40 hours worked/week = basic FTE.
## How many employees should a HR business Partner support?
According to a PwC Saratoga survey, which includes organizations of all sizes and industries, the average HRBP FTE ratio is . 184 per 100 employees or 1:1,016. This implies in an organization size of 30,000 employees, there would be 30 HRBPs supporting the business.
## How do you structure an HR team?
3 Steps To Evaluate Your HR Department Structure
1. Identify Critical Issues. List all the tasks you need to take care of in the future and assign priorities to the tasks (1-5, let’s say). …
2. Define HR Processes. Now comes the hard part. …
3. Implement An HR Software.
## How do you calculate employee to supervisor ratio?
A management to staff ratio is calculated by dividing the number of managers in a company or department by the number of employees working in it.
## How many direct reports is ideal?
Seven
Seven is the optimal number of direct reports
Responses spanned startups, public companies, and not-for-profits, with the largest segment being “growth stage” startups.
## What percentage of workforce are managers?
Workforce Manager Gender By Year
Year Male Female
2015 62.92% 37.08%
2016 63.83% 36.17%
2017 61.16% 38.84%
2018 61.07% 38.93% | 916 | 4,111 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2022-27 | latest | en | 0.960681 |
http://catalog.century.edu/preview_course_nopop.php?catoid=7&coid=12290 | 1,600,475,881,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400189264.5/warc/CC-MAIN-20200918221856-20200919011856-00721.warc.gz | 22,526,361 | 17,875 | Sep 18, 2020
2019-2020 Course Catalog
Select a Catalog 2020-2021 Course Catalog 2019-2020 Course Catalog [ARCHIVED CATALOG] 2018-2019 Course Catalog [ARCHIVED CATALOG] 2017-2018 Course Catalog [ARCHIVED CATALOG]
HELP 2019-2020 Course Catalog [ARCHIVED CATALOG] Print-Friendly Page (opens a new window)
ECAD 2053 - Introduction to SolidWorks
Credits: 3
Hours/Week: Lecture 1 Lab 4
Course Description: Students will use SolidWorks software to sketch, create, edit, and dimension 3D solid models, as well as create 2D drawings from these models. Assembly modeling and 2D & 3D printing are also covered. A hands-on approach is used in this class in an effort to build a foundation for continued training and self-instruction.
MnTC Goals
None
Prerequisite(s): ECAD 1020 or ENGR 1020 or instructor consent.
Corequisite(s): None
Recommendation: ECAD 1070 and course placement into MATH 0070 /MATH 1015 or above or completion of MATH 0030 with a grade of C or higher.
Major Content
1. Assembly drawings
2. Associative Functionality
3. Auxiliary and section views
4. Constructive Solid Geometry Concepts
5. Dimensioning and Notes
6. Geometric construction tools
7. Multi-view drawings
8. Overview of solid modeling
9. Part Drawing
10. SolidWorks Feature Design Tree
11. SolidWorks user interface
12. Templates and plotting
Learning Outcomes
At the end of this course students will be able to:
1. create orthographic drawings from 3D models.
2. create intermediate 3D solid models.
3. analyze various properties of 3D models.
4. explain feature-based parametric solid modeling.
5. modify models.
6. explain softwares user interface.
7. create simple 3D solid models.
8. compare 2D vs. 3D design process.
9. manipulate 3D solid models using basic SolidWorks tools.
10. describe 3D coordinate systems and depth concept.
11. compare 3D model types.
12. analyze advanced theory and analysis.
13. add dimensions and notations to drawings.
14. create assembly drawing with a Bill of Materials.
15. create assembly models.
16. create section and auxiliary views.
17. plot drawings in 2D and one in 3D.
Competency 1 (1-6)
None
Competency 2 (7-10)
None | 574 | 2,148 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2020-40 | latest | en | 0.735942 |
https://cs.stackexchange.com/questions/168412/analog-computers-more-powerful-than-turing-machines | 1,726,607,314,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651835.53/warc/CC-MAIN-20240917204739-20240917234739-00655.warc.gz | 162,834,413 | 41,850 | Analog computers more powerful than turing machines?
Ignoring quantum mechanics for a moment, is it true that analog computers are more powerful than turing machines? for example an analog computer can add two irrational numbers together, but a turing machine cannot.
but if one were to take quantum mechanics into account, I still think it's reasonable to redefine effective computation based off the power of analog computers since although the real world is technically discretized, it is also the case that you cannot build unbounded machines in the real world.
• In what sense can an analog computer "add two irrational numbers together" that a Turing machine can't? Commented Jun 3 at 20:22
• @NaïmFavier Turing machines can't add irrational numbers together with perfect precision in finite time Commented Jun 4 at 15:00
• I guess my point is that a model of computation requires specifying input and output encodings. If your analog computer can add real numbers instantly with infinite precision but you can only read finite amounts of the result in finite time, then what's the point? Commented Jun 4 at 15:16
As far as anyone can tell, no, analog computers are not more powerful than Turing machines. In practice, they run into problems with errors accumulating rapidly.
It's also worth pointing out that specifying how to provide information as an input, and how to read it from the output is not entirely trivial. For instance, if I gave you an irrational number, how would you encode it as a stick of that length, or a bucket of water of that volume? It's basically not possible. If the output is a stick of some length, or a jug of water of some volume, how would you measure its length or volume to sufficient precision to distinguish between rational vs irrational numbers? You can't. You can only measure to finite accuracy, and the time it takes to measure is (at least) proportional to the number of digits of precision needed (and probably much more).
So it is widely believed that there is no free lunch here.
See also the extended Church-Turing hypothesis, which proposes that no realizable computation method is faster (by more than polynomially) than a Turing machine. See especially https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis#Variations.
• This is a good answer. To put it in perspective, the smallest possible measurement scientists believe can exist, is a planck length. Which is 10 ^ -35 meters. Which is 35 zeroes after the fullstop. Any modern computer could easily calculate something accurately to 35 decimal places. But 2 sticks that are 10 ^ -35 meters long each, can't be added together to get 2 * the plank length. And I don't think something like this is feasible even with analog electronics like resistors. Though I think there might exist cases where an analog computer could be better over a normal digital one. Commented Jun 4 at 6:25
• "if I gave you an irrational number, how would you encode it as a stick of that length," well you would give it to me as, for example, the charge on a capacitor. Not sure what you mean Commented Jun 4 at 15:01
• @JobHunter69, if I have an input of $x=\sqrt{23}+\cos(\pi/17)$ (some irrational number) that I want to provide to an analog computer, how do I arrange to charge up a capacitor so it has charge $x$?
– D.W.
Commented Jun 4 at 17:02
• @D.W. The input comes in the form of the capacitor. A counter question is, if I have a capacitor of irrational charge x, how do I arrange a digital computer to input this number? Commented Jun 4 at 18:22
• @JobHunter69, under the ordinary understanding of a computer, if I have some data I want to compute on, there has to be some way to provide that to the computer as input. For a digital computer, the answer is that you cannot provide irrational numbers as input. You suggested that a Turing machine cannot take irrational numbers as input but an analog computer can, and I'm pointing out there are some flaws in that statement. Even if you ignore that, there still remain the issues with reading off the output and with noise accumulation.
– D.W.
Commented Jun 4 at 20:59 | 920 | 4,124 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2024-38 | latest | en | 0.944392 |
http://www.wwnorton.com/college/soc/introductiontosociology8/ch/08/dataminingexer.aspx | 1,467,294,949,000,000,000 | text/html | crawl-data/CC-MAIN-2016-26/segments/1466783398869.97/warc/CC-MAIN-20160624154958-00153-ip-10-164-35-72.ec2.internal.warc.gz | 985,356,867 | 22,054 | ## Data Mining Exercises
### WHAT CONTRIBUTES TO THE SOCIAL CLASS IN COMMUNITIES?
As you learned in Chapter 7, stratification exists among different groups of individuals and has important consequences. These structured inequalities influence opportunities for achieving economic prosperity, referred to as life chances by sociologists. As the authors of your textbook point out, in our society the social class of the family into which people are born and the community in which they grow up affect their life chances. Regardless of their own social class, individuals living in upper-class or upper-middle-class communities have many more resources and opportunities than individuals living in lower-middle-class or lower-class communities. In this exercise we will look at how communities in this country differ in terms of the income, wealth, education, and occupation of the residents of the community. You will also analyze the social class of your own community.
Four communities will be profiled in this exercise. Darien, CT, is a community of 20,732 people located in the New York City metropolitan area; Naperville, IL, is a suburb in the Chicago metropolitan area with population of 141,853; Oakland, CA, is part of the San Francisco metropolitan area with a population of 390,724; and Camden, NJ, with a population of 77,344, lies within the Philadelphia metropolitan area. If you are not already familiar with these communities, you might want to browse their respective Web sites in order to learn more about each. The data on income, wealth, education, and employment for these four communities was obtained at the U.S. Census Web site. Before you start the data analysis, go to the U.S. Census Web site, and discover the wide range of statistical information about the U.S. population available there.
Part I
Wealth, defined as all of the assets an individual owns, is difficult to measure because many times it is hidden. Here we will use the median value of homes and the degree to which this value appreciates over time as approximate measures of wealth. At the time the census was done in 2000, the median value of homes for the United States as a whole was \$119,600; however, housing values reflect local markets, so we can expect to see wide variations in the communities we are researching. Table 1 provides information on housing values for the four communities we are investigating.
Table 1. Wealth (as measured by housing values), 2000
Darien, CT Naperville, IL Oakland, CA Camden, NJ Median housing value \$711,000 \$254,200 \$235,500 \$40,700 % valued at less than \$200,000 2.2 27.2 43.1 99.5 % valued between \$200,000 and \$499,999 27.1 68.0 43.3 0.5 % valued at \$500,000+ 70.8 4.6 13.6 0.0 Source: American Fact Finder, Fact Sheet, "Housing Characteristics," U.S. Census 2000.
Writing Assignment 1
After comparing these communities, summarize the differences among them, as well as how each stands in relation to the national median housing values.
As a generator of wealth, housing is important if it increases in value over time. Table 2 provides you with information on the housing values for these same communities in both 1990 and 2000, as well as the percentage change in the values between these two points in time (the percentage change was calculated by subtracting the value in 2000 from the value in 1990, dividing this amount by the 1990 value, then multiplying by 100).
Table 2. Housing Values in 1990 and 2000 and the Percentage Change in These Values
1990 Housing Value 2000 Housing Value Change, 1990–2000 Darien, CT \$460,100 \$711,000 54% Naperville, IL \$176,200 \$254,200 44% Oakland, CA \$172,100 \$235,500 37% Camden, NJ \$ 31,100 \$ 40,700 30% Source: U.S. Census 1990 and 2000.
Writing Assignment 2
Which of the communities had the greatest appreciation in housing values over the ten -year period? Overall, what was the pattern of change? What can you conclude about the accumulation of wealth by individuals within these four communities?
Finally, before we turn to some of the other indicators of social class, look at the patterns of home ownership among these communities. Table 3 presents information on the percentage of housing units that are owner occupied as well as those that are renter occupied. As you can see, our four communities differ in terms of these two types of households. Using concepts associated with stratification, how can you explain this pattern of differences?
Table 3. Percent of Households Living in Different Types of Housing Units for Selected Communities, 2000
Darien, CT Naperville, IL Oakland, CA Camden, NJ Owner occupied 88 83 46 41 Renter occupied 12 17 54 59 Source: American Fact Finder, U.S. Census 2000.
We will now investigate the differences in median and mean income, as well as the way in which income is distributed among the residents of the community. Income refers to the wages and salaries earned from paid labor, plus unearned money from investments. Without a doubt, income and wealth are related; those with higher incomes have more money with which to invest in property as well as other forms of wealth. For the United States as a whole, the median household income in 2000 was \$41,994. You will analyze the incomes of households living within each of these communities.
Table 4. Income Characteristics of Households in Selected Communities, 2000
Darien, CT Naperville, IL Oakland, CA Camden, NJ Median income \$146,755 \$88,771 \$40,055 \$23,421 Mean income (with earnings) \$225,316 \$101,169 \$57,924 \$23,201 % of with income of less than \$15,000 3.3 3.8 19.8 34.7 % with income between \$15,000 and \$35,999 7.0 9.7 24.5 31.9 % with income between \$35,000 and \$74,999 17.0 26.1 32.0 27.6 % with income between \$75,000 and \$149,999 23.5 42.4 17.9 5.1 % with income of \$150,000 or more 49.2 18.0 5.9 0.6 Source: American Fact Finder, Fact Sheet, "Economic Characteristics," U.S. Census 2000.
Writing Assignment 3
As you look at the numbers, what can you conclude about the differences in income levels between these communities? How do differences in income levels and distribution impact the overall quality of life? Go back and explore the Web sites for each of these communities and see if you can find some evidence of difference.
Let’s try to further penetrate the social class differences between the individuals living in these places. Specifically, let us look at their educational differences and the kinds of jobs they hold.
Table 5. Educational and Occupational Characteristics for Selected Communities, 2000
Darien, CT Naperville, IL Oakland, CA Camden, NJ Educational attainment of population aged 25+ (percentage) < than high school diploma 4.3 3.7 26.1 49.9 High school diploma only 10.6 11.6 17.7 28.6 Some college 10.5 17.9 19.9 14.5 A.A. 4.2 6.1 5.5 2.5 B.A. 40.2 37.0 18.0 3.5 Graduate or professional 30.3 23.7 12.9 1.9 Occupational category of population aged 16+ (percentage) Management/professional 59.6 56.0 39.2 16.8 Services 6.3 7.5 15.8 25.5 Sales and offices 29.4 28.0 25.1 25.1 Farming, fishing, forestry 0.0 0.0 0.2 0.3 Construction, extraction, maintenance 3.0 3.6 7.4 6.7 Production, transportation, material moving 1.6 4.7 12.3 25.7 Source: American Fact Finder, Fact Sheet, "Social and Economic Characteristics," U.S. Census 2000.
Writing Assignment 4
How would you characterize the patterns of educational attainment for each of these communities? How about their occupational structures? What conclusions can you draw about the relationships between education, occupation, and income?
Part II
Now let us examine the differences between these four places in terms of a few other social attributes. We suspect that a community’s patterns of income, wealth, education and occupation would be influenced by several other factors as well. There are a number of different hypotheses that we could test. For instance, a community with a high percentage of middle-aged residents is likely to be wealthier than a community with a higher percentage of children and/or old people. Having higher percentages of children or elderly reduces the potential work force. Given the patterns of discrimination found within our society (something about which you will learn more in subsequent chapters), we are likely to find that concentrated "minority" communities have more concentrated poverty. Also, a community with a higher percentage of foreign-born residents is likely to be poorer than one composed of predominantly native-born residents.
The following table contains information taken from the 2000 Census and found on the U.S. Census Web site.
Table 6. Selected Community Attributes, 2000
Darien, CT Naperville, IL Oakland, CA Camden, NJ Age Distribution (percentage) 19 and under 33.5 34.0 27.4 38.2 20–64 53.9 59.8 62.0 54.0 65 and older 12.5 6.2 10.5 7.6 Median Age 38.0 34.2 33.3 27.2 Race and Ethnicity (percentage)1 White 96.7 86.2 34.7 19.0 Black or African American 0.6 3.3 37.6 55.3 American Indian or Alaska Native 0.2 0.3 1.7 1.2 Asian 2.9 10.3 16.6 3.0 Native Hawaiian or Other Pacific Islander 0.1 0.1 0.8 0.3 Other 0.5 1.1 14.1 25.4 Hispanic (any race) 3.2 21.9 38.8 Place of birth (percentage) Born in U.S. 87.9 87.6 72.4 76.5 Born outside the United States in U.S. territory 1.5 0.8 1.1 14.6 Foreign born 10.5 11.7 26.6 8.9 Source: American Fact Finder, Fact Sheet, "General Characteristics," U.S. Census 2000. 1 In combination with one or more other races listed on the 2000 Census form. The percentages add to more than 100 percent because individuals may have reported more than one race and the "Hispanic" category includes individuals of any race.
Writing Assignment 5
Having examined the information in the table, consider whether the hypotheses are supported. Are there other attributes of socioeconomic status that contribute to the socioeconomic differences between communities? Try generating some hypotheses and testing them with data from the U.S. Census Web site, using the American Fact Finder.
Overall, how would you classify these four communities within the U.S. social class system? You might want to refer back to the discussion in your textbook of the characteristics of the four social classes —upper, middle, working, and lower class— to help you determine the social class character for each of them.
Part III
Your final project is to research your own community and compare it with the communities you’ve been working with up to this point. If you haven’t been to the U.S. Census Web site yet, you will need to go there now in order to complete the assignment. You will be using the American Fact Finder
• First, click on the light-blue box on the left-side of the page labeled "Geographies." A new window will pop up. Click on the tab labeled "address," enter your home address, and click "GO." From the list that appears, look in the right-hand column labeled "Geography Type" and find the one labeled "Place." Click on the name of your hometown located in the left-hand column across from the geography type labeled "Place." Close the pop-up window. Your hometown will now appear in the upper left-hand box labeled "Your Selections."
• Next, find the "Search within Results for…" box on the left-hand side of the page, which is located just underneath the "Your Selections" box. In that box, type "DP-1: Profile of General Demographic Characteristics: 2000" and then click the gray-box labeled "GO." In the right-hand column labeled "Dataset," find the file labeled "2000 SF4 Sample Data" and click on the title to the left. Review this data, taking notes as appropriate. When you are finished browsing the data, click on the gray box labeled "back to search" in the upper left-hand corner of the screen.
• Repeat the previous steps three more times, substituting the following selections for "DP-1…": "DP-2: Profile of Selected Social Characteristics: 2000," "DP-3: Profile of Selected Economic Characteristics: 2000," and "DP-4: Profile of Selected Housing Characteristics: 2000." Make sure that in the box labeled "Your Selections," you click on the red "X" next to the "DP" file that you previously selected, otherwise the new dataset will not load. Browse this data to get a sense of the demographic, social, economic, and housing characteristics of your hometown.
Writing Assignment 6
Based on what you found, how would you rate your community, as mostly upscale, mostly middle class (upper or lower), or mostly working class? What did you learn about social stratification in America and in your community from this assignment?
Part IV
Writing Assignment 7/Essay
Based on what you have learned in this activity regarding the social class characteristics of communities, write an essay in which you discuss how our individual opportunities for economic success are affected by the wider social environment in which we live. Use some of the evidence that was provided in this exercise in making your case. | 3,157 | 12,956 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2016-26 | longest | en | 0.946102 |
https://discuss.kotlinlang.org/t/new-conditional-operator-a-equals-b-and-or-c/18726 | 1,618,142,193,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038062492.5/warc/CC-MAIN-20210411115126-20210411145126-00019.warc.gz | 316,907,264 | 6,045 | # New conditional operator: a equals b and/or c
``````if (a == b || a == c)
``````
do this:
``````if (a == b | c)
``````
also works with ‘and’. instead of this:
``````if (a == b && a == c)
``````
do this:
``````if (a == b & c)
``````
More examples:
``````(a != b || a != c) -> (a != b | c)
(a != b && a != c) -> (a != b & c)
(a == b && a == c && a == d) -> (a != b & c & d)
(a == x || b == x || a == y || b == y) -> (a | b == x | y)
(a == b && a != c) -> (a == b !& c)
(a != b || a == c) -> (a != b !| c)``````
If you need the `||` case a lot (which I think few of us do), you can already do:
``````if (a in setOf(b, c))
``````
(Preferably storing that set in a field somewhere to avoid creating a new copy each time. And probably being more efficient than multiple equality checks, especially if the set is large.)
Or:
``````when (a) {
b, c ->
}
``````
The `&&` case is harder (e.g. `if (setOf(b, c).all{ a == it })`) – but I’m struggling to think of any realistic situation where you’d want to do that…
Neither seem to justify new syntax. Especially as the syntax gets ambiguous pretty quickly. (For example, if `c` is Boolean, then that syntax already has a valid meaning, which is incompatible.)
And your more complex cases just look confusing to me! I’d hate to have to read code written that way. (But that wouldn’t be likely, seeing how rarely that sort of situation occurs.)
What makes Kotlin such a great language isn’t the number of operators, nor the complexity of its syntax. Quite the reverse: it’s the simplicity and regularity. Every feature, every keyword, every syntactic element has been carefully chosen to give the most benefit for the least complexity. Even if Kotlin were young enough to be considering lots of new syntax (which it’s not), IMO these operators simply don’t give enough benefit often enough to be justified.
8 Likes
You can pretty much do it yourself with infix functions.
Take a look at this simple example:
``````open class ValueSet<T> : TreeSet<T>() {
fun add(v1: T, v2: T) {
}
fun add(v1: ValueSet<T>, v2: T) {
}
}
class AndSet<T> : ValueSet<T>()
class OrSet<T> : ValueSet<T>()
infix fun <T> T.equals(list: ValueSet<T>): Boolean {
if (list is OrSet<*>) return this in list
if (list is AndSet<*>) return list.find { it != this } == null
error("Unsupported set type: \${list::class.simpleName}")
}
infix fun <T> T.or(second: T) = OrSet<T>().also { it.add(this, second) }
infix fun <T> OrSet<T>.or(second: T) = OrSet<T>().also { it.add(this, second) }
infix fun <T> T.and(second: T) = AndSet<T>().also { it.add(this, second) }
infix fun <T> AndSet<T>.and(second: T) = AndSet<T>().also { it.add(this, second) }
fun main() {
val test1 = "a"
val test2 = "b"
val test3 = "c"
val test4 = "d"
println(test1 equals ("b" or "c" or "d")) // Prints: false
println(test2 equals ("b" or "c" or "d")) // Prints: true
println(test3 equals ("b" or "c" or "d")) // Prints: true
println(test4 equals ("b" or "c" or "d")) // Prints: true
val test5 = "a"
val test6 = "a"
val test7 = "a"
val test8 = "b"
println("a" equals (test5 and test6 and test7)) // Prints: true
println("a" equals (test5 and test6 and test8)) // Prints: false
}
``````
It can be polished and made much better; this is just a quick idea. Maybe, you can introduce operator overloading for even shorter syntax and a negation with `!` operator.
3 Likes
I don’t really see a need for this as when is usually a better alternative, but syntax-wise this is not a good choice and I’m sure would lead to ambiguities. You would need a slight variation on the syntax like using another character in the operator to distinguish it from the regular operator
if (a == b |= c) | 1,086 | 3,692 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2021-17 | latest | en | 0.930305 |
https://www.gradesaver.com/textbooks/math/algebra/introductory-algebra-for-college-students-7th-edition/chapter-5-section-5-7-negative-exponents-and-scientific-notation-exercise-set-page-409/77 | 1,537,564,112,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267157569.48/warc/CC-MAIN-20180921210113-20180921230513-00167.warc.gz | 753,995,043 | 14,323 | ## Introductory Algebra for College Students (7th Edition)
Published by Pearson
# Chapter 5 - Section 5.7 - Negative Exponents and Scientific Notation - Exercise Set - Page 409: 77
#### Answer
$\dfrac{y^{9}}{x^{6}}$
#### Work Step by Step
Using the laws of exponents, the given expression, $\left( \dfrac{x^2}{y^3} \right)^{-3} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{x^{2(-3)}}{y^{3(-3)}} \\\\= \dfrac{x^{-6}}{y^{-9}} \\\\= \dfrac{y^{9}}{x^{6}} .\end{array}
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 201 | 642 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2018-39 | longest | en | 0.688125 |
https://snowfestival.se/sa8m2bed/page.php?tag=d3bf4f-statistics-for-economics-class-11-chapter-3-ppt | 1,623,684,278,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487612537.23/warc/CC-MAIN-20210614135913-20210614165913-00381.warc.gz | 501,738,875 | 30,347 | # statistics for economics class 11 chapter 3 ppt
Check out the latest CBSE NCERT Class 11 Economics Syllabus. Classification Univariate Distribution The frequency distribution of a single variable is called a univariate distribution. Hope given Statistics for Economics Class 11 Solutions Chapter 4 are helpful to complete your homework. Raw Data A mass of data in its crude form is called raw data. Chapter 1 Indian Economy on the Eve of Independence Class 11 Notes Chapter 2 Indian Economy 1950 – 1990 Class 11 Notes Chapter 3 Liberalisation, Privatisation and Globalisation : An Appraisal Class 11 Notes Chapter 4 Statistics for economics concerns itself with the collection, processing, and analysis of specific economic data. 2. Distinguish between univariate and bivariate frequency distribution. The items assume a range of values and are placed within the limits is called class interval. Classification makes the raw data comprehensible by summarising them into groups. Download Notes For Class 11 Chapter Wise Free Download Maths, Physics, Chemistry, Biology, Account, Eco ... ☞ Class 12 Solved Question paper 2020 ☞ Class 10 Solved Question paper 2020 NCERT Solutions for Class 15Statistics Chapter 5 Measures Of Central Tendency – Here are all the NCERT solutions for Class 11 Statistics Chapter 5. Also after the chapter, you can get links to Class 11 Economics Notes, NCERT Solutions, Important Question, Practice Papers etc. Which of the following alternatives is true? students are advised to check out the complete syllabus and exam pattern with the marking scheme. Chronological Classification When data are classified on the basis of time, it is known as chronological classification. Classification is done to group things in such a way that each group consists of similar items, e.g., we classify our wardrobe into different types of clothes or dresses according to the occasions on which they are to be worn. Here you can read Chapter 3 of Class 11 Economics NCERT Book. Answer: Discrete varibles increase in finite jumps from one value to another and cannot take any intermediate value between them. It not only save our time but also our energy, which would otherwise be utilised in searching from entire things. (d) the class mid-points Which of the following alternatives is true? Synopsis 1. What is loss of information’ in classified data? (i) The class mid-point is equal to (a) the average of the upper class limit and the lower class limit (b) the product of upper class limit and the lower class … Answer: The range is the difference between the largest and the smallest values of the variable. Statistics for Economics Class 11 Notes CBSE Chapter Wise July 5, 2019 by Veerendra Chapter Wise CBSE Statistics for Economics Class 11 Quick Revision Notes and Key Points in English an Hindi Pdf free download was designed by expert teachers from latest edition of NCERT books to get good marks in board exams. Highest Value = 5090 (b) Bivariate Distribution Free PDF download of Important Questions with Answers for CBSE Class 11 Indian Economic Development Chapter 3 - Liberalisation, Privatisation and Globalisation: An Appraisal prepared by expert Economics teachers from latest edition of CBSE(NCERT) books. Question 6. On the other hand “bi” means two and a Bivariate Frequency Distribution is the frequency distribution of two variables, e.g., the frequency distribution of two varibles, e.g., like price of good and sales of the good is a bivariate distribution. Class Mid-Point or Class Mark = $$\frac{\text { (Upper Class Limit + Lower Class Limit) }}{2}$$. Link to download Class 11 Economics Syllabus is given at the end of this article. Scroll down for Skip to content NCERT Solutions PDF CBSE Notes - Books - Guide Select Class Home Class 6 Class 7 Class 8 Class … (a) the upper class limit of a class is excluded in the class interval If you present them as a table, they may appear something like Table 3.1. Question 10. (d) The class mid-points of each class is used to represent the class and therefore, it is used in further calculations after the raw data are grouped into classes. The raw data is usually large and fragmented and it is very difficult to draw any meaningful conclusion from them. Qualitative Classification This classification is according to qualities or attributes of the data. Consumption “Consumption is the process of using up utility value of goods and services for the […] Geographical Classification This classification of data is based on the geographical or locational differences of the data. Concept of Variable A characteristic or a phenomenon which is capable of being measured and changes its value overtime is called a variable. (b) Number of hoseholds whose monthly expenditure on food is more than ₹ 3000 (c) the lower class limit of a class is excluded in the class interval Ohri Books for 11th Class Statistics for Economics Subject. (b) the product of upper class limit and the lower class limit (ii) Divide the range into appropriate number of class intervals and obtain the frequency distribution of expenditure. Collection of Data - Class 11 - Statistics 1. PPT is a short and … Exclusive Series It is that series in which every class-interval excludes items corresponding to its upper limit. It lies halfway between the lower class limit and the upper class limit of a class and is calculated as Continuous Variable Variable that assume a range of values or increase not in jumps but continuously or in fractions are called continuous variables. Classification of data as a frequency distribution summarises the raw data making it concise and comprehensible but it does not show the details that are found in raw data. (d) the lower class limit of a class is included in the class interval 24 STATISTICS FOR ECONOMICS students of your school. Answer: NCERT Solutions Class 11 Economics PDF Free Download. = 13 + 6= 19. According to this method, an observation that is exactly equal to the upper class limit would not be included in that class but would be included in the next class. Explain the ‘exclusive’ and ‘inclusive’ methods used in classification of data. Do you agree that classified data is better than raw data? Discrete Series or Frequency Array It is that series in which data are presented in way that exact measurement of items are clearly shown. NCERT Books for Class 11 Statistics – Hindi Medium Chapter 1 Introduction Chapter 2 Collection of Data Chapter 3 Organisation of Data Chapter 4 Presentation of Data Chapter 5 Measures of Central Tendency Chapter CBSE Class 11-commerce Statistics for Economics Get sample papers, syllabus, textbook solutions, revision notes, test, previous year question papers & videos lectures online for CBSE Class 11-commerce Statistics for Economics on TopperLearning. Mathematical techniques used for this include mathematical analysis, linear algebra, stochastic analysis, differential equation and measure-theoretic probability theory. (a) The class mid-point is the middle value of a class. CBSE Class 11 … Consumer “A consumer is one who consumes goods and services for the satisfaction of his wants”. Classification refers to arranging or organising similar things into groups or classes. etc. Question 4. Let us understand this in some detail. Register for Online tuition on Vedantu.com to score more marks in CBSE examination. It helps us understand and analyze economic theories and denote correlations between variables such as demand, supply, price, output etc. Key terms 2. NCERT Solutions for Class 11 Commerce Statistics for economics Chapter 3 Organisation Of Data are provided here with simple step-by-step explanations. (c) Number of households whose expenditure on food is between ₹ 1500 and ₹ 2500 (b) Bi means two and hence the frequency distribution of two variables is known as Bivariate Distribution. Organisation of Data (a) Under the exclusive method we form classes in such a way that the lower limit of a class coincides with the upper class limit of the previous class. On the other hand, if it were equal to the lower class limit then it would be included in that class, e.g., if the class intervals are 0-5, 5-10, 15¬20 and so on, a value of 10 would be included in the 10-15 and not in the interval 5-10. (a) the actual values of observations Continuity of the data is maintained in this method. NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12, Question 1. = 20 + 13 = 33 (d) None of the above Explain with an example from your daily life. Examples-number of workers in a factory, number of residents in a colony, etc. Free pdf download of class 12 micro economics chapter 2 theory of consumer behaviour revision notes short key notes prepared by our expert economics teachers from latest edition of cbsencert books. Classification Classification is the process of arranging things in groups or […] Answer: Question 7. NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12. Collection of Data Statistics Class - XI 2. 2 4 2 7 4 2 4 3 4 2 0 3 1 4 3 Chapter 3 Economics of Regional and Community Growth - Title: Chapter 1 Introduction to Real Estate Decision Making Author: College of Business Last modified by: Auburn University Created Date: 6/14/2000 11:46:04 PM (i) The class mid-point is equal to So, Range = 5090 – 1007 = 4083, (iii) (a) Number of households whose monthly expenditure on food is less than ₹ 2000 (c) Multivariate Distribution 20–30 3 0.55 30–40 61 11.25 40–50 132 24.35 50–60 153 28.24 60–70 140 25.83 70–80 51 9.41 80–90 2 0.37 All 542 100.00 Source: Assembly election Patna central constituency 2005, … Frequency Distribution It is that series in which items cannot be exactly measured. (c) average of the largest and the smallest observations We put party wears, school uniform, casual daily wears and night wears separately. (i) Range = Largest Value – Smallest Value Inclusive Method The inclusive method does not exclude the upper class limit in a class interval. Lowest Value = 1007 Answer: RD Sharma Class 11 Solutions Free PDF Download, NCERT Solutions for Class 12 Computer Science (Python), NCERT Solutions for Class 12 Computer Science (C++), NCERT Solutions for Class 12 Business Studies, NCERT Solutions for Class 12 Micro Economics, NCERT Solutions for Class 12 Macro Economics, NCERT Solutions for Class 12 Entrepreneurship, NCERT Solutions for Class 12 Political Science, NCERT Solutions for Class 11 Computer Science (Python), NCERT Solutions for Class 11 Business Studies, NCERT Solutions for Class 11 Entrepreneurship, NCERT Solutions for Class 11 Political Science, NCERT Solutions for Class 11 Indian Economic Development, NCERT Solutions for Class 10 Social Science, NCERT Solutions For Class 10 Hindi Sanchayan, NCERT Solutions For Class 10 Hindi Sparsh, NCERT Solutions For Class 10 Hindi Kshitiz, NCERT Solutions For Class 10 Hindi Kritika, NCERT Solutions for Class 10 Foundation of Information Technology, NCERT Solutions for Class 9 Social Science, NCERT Solutions for Class 9 Foundation of IT, PS Verma and VK Agarwal Biology Class 9 Solutions, Statistics for Economics Class 11 NCERT Solutions, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, Periodic Classification of Elements Class 10, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16, CBSE Previous Year Question Papers Class 12, CBSE Previous Year Question Papers Class 10. Get step by step NCERT solutions for Class 11 economics-statistics-for-economics Chapter 3 - Organisation of Data. Different varibles vary differently and depending on the way they vary, they are broadly classified into two types. Continuous variables can take any conceivable value and can be broken into infinite gradations. T.R. These series may be presented in two ways, Frequency Series Frequency series may be of two types. First, of all check the CBSE Class 11 Economics Exam Pattern . Inclusive Series An inclusive series is that series which includes all items upto its upper limit. (v) Range is the Jain and V.K. Answer: These solutions for Collection Of Data are extremely popular among Class 11 Science students for Economics Collection Of Data Solutions come handy for quickly completing your homework and preparing for exams. Introduction to Economic Notes class 11 Download in PDF IMPORTANT CONCEPTS 1. Discrete Variable These are those variables that increase in jumps or in compete numbers. At BYJU'S, it is available for free download here. Distinguish between a discrete and a continuous variable. A measurable characteristic which takes different values at different points of time and in different circumstance is called a variable as it keeps varying. Chapter 3 PDF Chapter 4 PDF Chapter 5 PDF Chapter 6 PDF Chapter 7 PDF Chapter 8 PDF Chapter 9 PDF NCERT Books For Class 11 Statistics For Economics PDF Free Download. First, of all check the The syllabus is for the academic year 2020-21 session. CBSE Class 11 Economics Revision Notes Introduction Points to Remember Economics is a science that studies human behavior which aims at allocation of scarce resources in such a way that consumer can maximise their satisfaction, producers can maximise their profits and society can maximise its social welfare. (b) the upper class limit of a class is included in the class interval Quantitative or Numerical Classification Data are classified in to classes or groups on the basis of their numerical values. Question 8. Answer: Nov 29,2020 - Chapter 1 - Introduction to Microeconomics Economics Class 11 is created by the best Commerce teachers for Commerce preparation. Prepare a frequency distribution by inclusive method taking class interval of 7 from the following data These solutions for Organisation Of Data are extremely popular among (b) the upper class limits Under this method, the upper class limit is excluded but the lower class limit of a class is included in the interval. It will be helpful for students preparing for exams and for the teachers to use it as a teaching aid. You just clipped your first slide! (a) Univariate Distribution (ii) The frequency distribution of two variables is known as Cumulative frequencies may be expressed on the basis of upper class limits of the class-intervals. NCERT Solutions for Class 11 … CBSE Class 11 Economics Syllabus 2019-20 PDF is available here. Open End Series An open end series is that series in. 3 3 2 3 2 2 6 1 6 2 1 5 1 5 3 CBSE Guide Organisation of Data class 11 Notes CBSE guide notes are the comprehensive notes which covers the latest syllabus of CBSE and NCERT. For the advantage of Plus Two students, subjects like Physics, Chemistry, Mathematics, Economics, Accountancy etc are included in this hand book. Ohri Solutions for Class 11 Statistics Economics Chapter 8 - Arithmetic Line- Graphs or Time Series Graphics, covers all the questions provided in T.R. Answer: (iv) Under exclusive method, Statistics for Economics Class 11 NCERT Solutions Chapter 3 Organisation of Data Question 1. Jain and V.K. NCERT-Solutions.com try to provide online tutoring for you. It inlcludes the upper class in a class. (a) the average of the upper class limit and the lower class limit CBSE School Educational Study Material. Sources of data 3. NCERT Solutions for Class 11 Science Economics Chapter 2 Collection Of Data are provided here with simple step-by-step explanations. (c) the lower class limits Answer: Question 9. Meaning of Statistics in Plural Sense :– It deals with the collection, presentation, analysis and interpretation of quantitative information. Individual Series These are those series in which the items are listed singly. Use the data in Table 3.2 that relate to monthly household expenditure (in ₹) on food of 50 households and Class 11 Economics notes on Chapter 3 Organisation of Data class 11 Notes Economics are also available for download in CBSE Guide website. NCERT Solutions for Class 11 Economics - Chapter 3 - Liberalisation, Privatisation and Globalisation: An Appraisal Revision Notes CBSE Class 11 Indian Economic Development Revision Notes Chapter 2 - Indian Economy 1950-1990 (a) The variation in variable’s value are captured by its range. (d) None of the above (a) difference between the largest and the smallest observations Thus, it is evident that classification saves time and labour and helps to produce the desired results. This solution contains questions, answers, images, explanations of the complete chapter 5 titled Measures Of Central Tendency taught in Class 11… Question 5. Cumulative Frequency Series It is that series in which the frequencies are continuously added corresponding to each class-interval in the series. (c) the ratio of the upper class limit and the lower class limit (iii) Statistical calculation in classified data are based on The pdf form of Higher Secondary Plus Two Economics Study Notes (Mikavu 2014) is given below. (i) Obtain the range of monthly household expenditure on food. Frequency distribution is also known as continuous series or series with class-intervals, or series of grouped data. When facts of similar characteristics are placed in the same class, it enables one to locate them easily, analyse them, make comparison and draw inferences. The term “uni” stands for one and thus the frequency distribution of a single variable is called a Univariate Distribution, e.g., the fequency distribution of age of students in a class is univariate as its gives the distribution of a single variable i.e., age. 1 3 2 2 2 2 1 2 1 2 2 3 3 3 3 A discrete variable can take only whole numbers. Under the method, the upper class limit is excluded but the lower class limit of a class is included in the interval. Answer: In a city, 45 families were surveyed for the number of domestic appliances they used. Answer: RD Sharma Class 11 Solutions Free PDF Download, NCERT Solutions for Class 12 Computer Science (Python), NCERT Solutions for Class 12 Computer Science (C++), NCERT Solutions for Class 12 Business Studies, NCERT Solutions for Class 12 Micro Economics, NCERT Solutions for Class 12 Macro Economics, NCERT Solutions for Class 12 Entrepreneurship, NCERT Solutions for Class 12 Political Science, NCERT Solutions for Class 11 Computer Science (Python), NCERT Solutions for Class 11 Business Studies, NCERT Solutions for Class 11 Entrepreneurship, NCERT Solutions for Class 11 Political Science, NCERT Solutions for Class 11 Indian Economic Development, NCERT Solutions for Class 10 Social Science, NCERT Solutions For Class 10 Hindi Sanchayan, NCERT Solutions For Class 10 Hindi Sparsh, NCERT Solutions For Class 10 Hindi Kshitiz, NCERT Solutions For Class 10 Hindi Kritika, NCERT Solutions for Class 10 Foundation of Information Technology, NCERT Solutions for Class 9 Social Science, NCERT Solutions for Class 9 Foundation of IT, PS Verma and VK Agarwal Biology Class 9 Solutions, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, Periodic Classification of Elements Class 10, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16, CBSE Previous Year Question Papers Class 12, CBSE Previous Year Question Papers Class 10. Prepare a frequency array based on their replies as recorded below. Answer: The syllabus is for the academic year 2020-21 session. What is a variable? Class 11 Math Chapter 15 Statistics Formulas & Notes - PDF Download Statistics Class 11 Formulas & Notes are cumulated in a systematic manner which gets rid of confusion among children regarding the course content since CBSE keeps on updating the course every year. Question 3. (b) difference between the smallest and the largest observations If you have any doubts, please comment below. TABLE 3.1 Marks in Mathematics Obtained by 100 Students in an Examination 47 45 10 60 51 (iii) Find the number of households whose monthly expenditure on food is, Answer: In this series there are no class intervals and a particular item in the series. Bivariate Distribution A bivariate distribution is the frequency distribution of two variables. All exercise questions are solved by experts as per NCERT (CBSE) guidelines. Can there be any advantage in classifying things? (d) ratio of the largest to the smallest observation Classification is the process of arranging things in groups or classes according to their resemblances and affinities and gives expression to the unity of attributes that may exist amongst a diversity of individuals. Mathematical statistics is the application of Mathematics to Statistics, which was originally conceived as the science of the state — the collection and analysis of facts about a country: its economy, and, military, population, and so forth. Cbse revision notes for class 11 economics ncert chapter wise notes of 11th economics cbse key points and chapter summary for 11 economics all chapters in pdf format for free download. A continuous variable can take any numerical value. Statistics for Economics Class 11 Notes Chapter 1 Introduction Economics by Alfred Marshall, “The study of man in the ordinary business of life”. Once, the data are grouped into classes, an individual observation has no significance in further statistical calculations. Question 2. Answer: = 2 + 1 + 2 + 0 + 1 = 6 Thus, both class limits are parts of the class interval, e.g., the class intervals of 0-5, 6-10, 11-15, and so on are inclusive. Quantitative classification is also called classification by variables. Types of Statistical Series Statistical series are of two types. This helps us in an orderly arrangement of clothes and we can easily fetch the clothes we want at a particular time without searching through the whole wardrobe. Cumulative frequencies may b expressed on the basis of lower class limits of the class-intervals. Meaning of Statistics in plural sense :– It is a collection of numerical facts. Statistics for Economics Class 11 Notes Chapter 3 Organisation of Data Organisation of Data Organisation of data refers to the arrangement of figures in such a form that comparison of the mass of similar data may be facilitated and further analysis may be possible. A large range indicates that the values of the variable are widely spead. Those series in which the frequencies are continuously added corresponding to its upper.! Exclusive series it is that series in agree that classified data data is large... Appear something like table 3.1 school uniform, casual daily wears and night wears separately limit is excluded the... And ‘ inclusive ’ methods used in classification of data is maintained in this.. Or in compete numbers of items are clearly shown covers the latest syllabus of CBSE and NCERT the range appropriate... Notes which covers the latest CBSE NCERT class 11 Notes Economics are also available for in... Of Higher Secondary Plus two Economics Study Notes ( Mikavu 2014 ) is given at end! 11Th class Statistics for Economics concerns itself with the collection, processing, and analysis specific. Like table 3.1 price, output etc … introduction to economic Notes class 11 in... Between the largest and the smallest values of the data value and can take! Higher Secondary Plus two Economics Study Notes ( Mikavu 2014 ) is given at the of! ‘ inclusive ’ methods used in classification of objects or things saves our valuable and! Raw data is maintained in this method stochastic analysis, differential equation and measure-theoretic probability theory and are placed the... Is that series in which the items are clearly shown open end series is that series in which items! The smallest values of the Variable differential equation and measure-theoretic probability theory items assume a range of values or not! Which items can not be exactly measured ‘ inclusive ’ methods used in classification of data class Science... Supply, price, output etc increase not in jumps but continuously or in numbers! Demand, supply, price, output etc collection, processing, and analysis of specific economic data frequency... Limits of the data is better than raw data is usually large and fragmented and it is that series which... 'S, it is known as chronological classification When data are grouped into classes An! The frequencies are continuously added corresponding to each class-interval in the interval things saves valuable! Labour and helps to produce the desired results syllabus and Exam Pattern with the collection processing! Class 11 Solutions Chapter 4 are helpful to complete your homework no class intervals obtain! Statistics - class 11 download in CBSE examination workers in a colony, etc conceivable and. A factory, number of domestic appliances they used items assume a range of or... The complete syllabus and Exam Pattern continuous variables things saves our valuable time and labour helps... Conceivable value and can be broken into infinite gradations depending on the basis their... 11 Science Economics Chapter 2 collection of numerical facts overtime is called a.... From entire things between the largest and the smallest values of the data are provided here with step-by-step! Ohri Books for 11th class Statistics for Economics class 11 Economics syllabus is for the academic year 2020-21 session on... Are solved by experts as per NCERT ( CBSE ) guidelines covers the latest syllabus CBSE... Classification refers to arranging or organising similar things into groups or classes classified on the of! Notes Economics are also available for free download here series of grouped data and effort the! Classification saves time and effort which the frequencies are continuously added corresponding to its upper limit daily wears and wears... Not only save our time but also our energy, which would otherwise utilised. And for the teachers to use it as a table, they may appear something table. Vary, they may appear something like table 3.1 indicates that the values of the are. Organisation of statistics for economics class 11 chapter 3 ppt Question 1 this method, output etc NCERT ( CBSE guidelines. The inclusive method does not exclude the upper class limit of a class is included in series! Are presented in way that exact measurement of items are clearly shown ’. Between the largest and the smallest values of the data are classified on the geographical or locational of! Widely spead a short and … introduction to Statistics - class 11 Commerce Statistics for Subject. Consumer “ a consumer is one who consumes goods and services for the academic year 2020-21.. Any conceivable value and can not be exactly measured of two types Chapter 2 collection data... Labour and helps to produce the desired results the end of this article ’ in classified is. Pdf Important CONCEPTS 1 for Economics class 11 Economics syllabus Guide Notes are the comprehensive Notes covers! A Variable series there are no class intervals and a particular item in interval... Very difficult to draw any meaningful conclusion from them for Online tuition Vedantu.com. They vary, they are broadly classified into two types characteristic or a phenomenon which is of... By summarising them into groups given at the end of this article broken into gradations... Continuous variables jumps but continuously or in fractions are called continuous variables can take any intermediate value between.. 11 and 12, Question 1 economic theories and denote correlations between variables such as,! Per NCERT ( CBSE ) guidelines check the CBSE class 11 - Statistics.... Have any doubts, please comment below series is that series in which the items assume a of... Variable is called a univariate distribution When data are provided here with simple step-by-step explanations are. Colony, etc things saves our valuable time and effort bivariate distribution a bivariate distribution is the difference the... Equation and measure-theoretic probability theory desired results as a teaching aid of Variable a characteristic or a phenomenon which capable! Jumps but continuously or in fractions are called continuous variables two ways, series... Differences of the class-intervals called class interval its statistics for economics class 11 chapter 3 ppt overtime is called class interval such as demand,,... Helps us understand and analyze economic theories and denote correlations between variables such as demand supply. Organising similar things into groups or classes one who consumes goods and services for the to... A bivariate distribution a bivariate distribution is also known as continuous series or series of grouped data - 11! 3 Organisation of data are provided here with simple step-by-step explanations workers in factory... Recorded below, etc of domestic appliances they used for students preparing exams! With class-intervals, or series with class-intervals, or series with class-intervals, series. Also available for free download here ( ii ) Divide statistics for economics class 11 chapter 3 ppt range appropriate. Have any doubts, please comment below covers the latest CBSE NCERT class 11 Commerce Statistics for Economics Subject into... And helps to produce the desired results in its crude form is called a Variable are spead. A collection of numerical facts there are no class intervals and a particular item in the series CBSE 11. Univariate distribution frequency Array based on their replies as recorded below vary differently and on. That classification saves time and labour and helps to produce the desired results appear something like table.... Two types in compete numbers the largest and the smallest values of the Variable simple step-by-step explanations inclusive... Variable Variable that assume a range of values or increase not in jumps but or... One who consumes goods and services for the academic year 2020-21 session appear something like 3.1! Concepts 1 objects or things saves our valuable time and labour and helps produce. Stochastic analysis, differential equation and measure-theoretic probability theory output etc, please below... Otherwise be utilised in searching from entire things prepare a frequency Array it is series! Theories and denote correlations between variables such as demand statistics for economics class 11 chapter 3 ppt supply,,! Is usually large and fragmented and it is that series which includes all items upto its upper...., Important Question, Practice Papers etc of his wants ” with simple step-by-step explanations and... In CBSE examination for class 11 Economics syllabus is for the academic year 2020-21.. Wears separately are broadly classified into two types series with class-intervals, or series with class-intervals, or series grouped... And can be broken into infinite gradations BYJU 'S, it is that series in which the assume! Crude form is called raw data comprehensible by summarising them into groups is maintained in this method the... Marking scheme denote correlations between variables such as demand, supply, price, output etc economic data the..., Practice Papers etc characteristic or a phenomenon which is capable of being measured and changes its value is! Lower class limit in a factory, number of class intervals and the... Meaning of Statistics in plural sense: – it deals with the collection,,! Of CBSE and NCERT download here: the raw data comprehensible by summarising them into groups produce the desired.. And can be broken into infinite gradations Statistical series Statistical series Statistical series Statistical series are of two.! ’ and ‘ inclusive ’ methods used in classification of data are provided here with simple step-by-step.... For Economics class 11 … NCERT Solutions for class 6, 7 8... The teachers to use it as a teaching aid into appropriate number of domestic appliances used., school uniform, casual daily wears and night wears separately Higher Secondary Plus Economics... Our valuable time and effort class 11 Economics syllabus is given below ’... Is that series which includes all items upto its upper limit is in... Classes or groups on the basis of upper class limit in a,! From one value to another and can not take any intermediate value between them way they vary, they appear... Something like table 3.1, of all check the the syllabus is for the year. Are classified on the basis of upper class limits of the data marking scheme table, they are classified! | 6,948 | 33,093 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2021-25 | longest | en | 0.881337 |
https://codereview.stackexchange.com/questions/32751/counting-perfect-squares | 1,718,746,170,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861794.76/warc/CC-MAIN-20240618203026-20240618233026-00755.warc.gz | 146,601,523 | 40,559 | # Counting perfect squares
Below is the code I have written for counting perfect squares between a given lower and upper bound.
I am using the following concept to solve this:
Starting with 1, there are $\sqrt{m}$ square numbers up to and including $m$.
public static int CountPerfectSquares(long A, long B)
{
int count = 0;
//Proceed if lowerbound is less than upperbound
if (A < B)
{
//negative numbers are not perfect squares
if (A < 0 && B < 0) return count;
//Reset lowerbound if required
if (A <= 0) A = 1;
//Find number of squares between A & B (INCLUSIVE lower and upperbound)
//count = (int)Math.Sqrt(B) - (int)Math.Sqrt(A); //Giving wrong count when LowerBound value is a whole square (For exp. CountPerfectSquares(1, 25))
int sqrtA = (int)Math.Sqrt(A);
int sqrtB = (int)Math.Sqrt(B);
count = sqrtB - sqrtA;
//To handle the case when lowerbound value is a perfect square number
if (A == sqrtA * sqrtA)
{
count++;
}
}
return count;
}
Can you please help me make this more efficient, if possible?
Is there any other way of handling the case when the lower bound value is a perfect square number, so that I don't have to do an extra count++?
• you are over thinking this one.
– Malachi
Commented Oct 16, 2013 at 17:00
• you can just return the Square root of the larger Number as the count, if you don't give the application perfect squares then that is a different issue
– Malachi
Commented Oct 16, 2013 at 17:02
If A was not included in the observed range, you wouldn't need the if (A == sqrtA * sqrtA) part, right? So, let's use that: instead of checking the range {A,A+1,...,B}, check the range {A-1,A,...,B}. Since you're working with integers, the two are the same:
int sqrtA = (int)Math.Sqrt(A-1);
int sqrtB = (int)Math.Sqrt(B);
count = sqrtB - sqrtA;
A minor detail: when returning a predefined constant, I prefer writing the constant itself, not a variable initialized to that value:
if (A < 0 && B < 0) return 0;
It seems more readable to me.
Also, I would replace two main if-s with if (B < 0 || B < A) return 0. This gives the same result, but in a cleaner way.
So, my version would be:
public static int CountPerfectSquares(long A, long B)
{
// Return zero if there are obviously no perfect squares
if (B < 0 || B < A) return 0;
// Reset the lower bound if required
if (A <= 0) A = 1;
// Find the number of perfect squares between A & B (INCLUSIVE)
return (int)Math.Sqrt(B) - (int)Math.Sqrt(A-1); // Now giving the correct count, even when the lower bound value is a whole square (for exp. CountPerfectSquares(1, 25))
}
• +1. You could refactor this even further: public static int CountPerfectSquares(long A, long B) { if (A <= 0) A = 1; return B < 0 || B < A ? 0 : (int)Math.Sqrt(B) - (int)Math.Sqrt(A-1); } Commented Oct 16, 2013 at 12:11
• @DeeMac This would reduce readability, with no benefits (at least obvious to me). Btw, you could replace B < 0 || B < A with B < A, since you've already changed A. ;-) Commented Oct 16, 2013 at 12:14
• Nice! Fair point about the readability. Commented Oct 16, 2013 at 12:15
• really if you are being inclusive as you are, you can just return the Square root of the larger Number as the count. if you are going to give the application perfect squares and you are not going into imaginary numbers and you count 1.
– Malachi
Commented Oct 16, 2013 at 16:57
• @Vedran, Thanks a lot for the review and also for pointing out returning constant value. It does improve readability :-) Commented Oct 16, 2013 at 20:46 | 987 | 3,516 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5625 | 4 | CC-MAIN-2024-26 | latest | en | 0.850368 |
https://www.turtlediary.com/quiz/subtracting-money.html | 1,720,869,132,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514493.69/warc/CC-MAIN-20240713083241-20240713113241-00558.warc.gz | 821,422,912 | 31,772 | # Subtracting Money
Rate 0 stars
Quiz size:
Message preview:
Someone you know has shared quiz with you:
To play this quiz, click on the link below:
https://www.turtlediary.com/quiz/subtracting-money.html
Hope you have a good experience with this site and recommend to your friends too.
Login to rate activities and track progress.
Login to rate activities and track progress.
Subtracting money is same as subtracting numbers.
For example: Let's find the difference of \$46 and \$13.
First, subtract the ones.
4 6 – 1 3
3
Now, subtract the tens.
4 6 – 1 3
3 3
So, \$46 \$13 = \$33.
ds
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z | 189 | 653 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2024-30 | latest | en | 0.878172 |
http://physics.stackexchange.com/questions/21818/the-dual-cloud-chamber-paradox?answertab=active | 1,462,472,762,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461860127878.90/warc/CC-MAIN-20160428161527-00142-ip-10-239-7-51.ec2.internal.warc.gz | 221,422,068 | 28,183 | # The Dual Cloud Chamber Paradox
Two 10m diameter spheres $A$ and $B$ of very cold, thin gas have average atomic separations of 1nm. Their atoms are neutral, but ionize easily and re-radiate if a relativistic ion passes nearby. Both clouds are seeded with small numbers of positive and negative ions. The clouds collide at a relative speed of $0.994987437c$, or $\gamma=10$. Both are sparse enough to minimize collisions and deceleration. Both show passage of each other's ions. (a) What do distant observers moving parallel to $A$ and $B$ observe during the collision? (b) Are their recordings of this event causally consistent?
The answer to (a) requires only straightforward special relativity, applied from two perspectives. For the traveler moving in parallel to cloud $A$, cloud $B$ should appear as a Lorentz contracted oblate spheroid with one tenth the thickness of cloud $A$, passing through cloud $A$ from right to left. If you sprinkled cloud $A$ with tiny, Einstein-synchronized broadcasting clocks, the $A$-parallel observer would observe a time-stamped and essentially tape-recording like passage of the $B$ spheroid through cloud $A$.
The $B$-parallel observer sees the same sort of scenario, except with cloud $A$ compressed and passing left-to-right through cloud $B$. If $B$ is sprinkled with its own set of Einstein synchronized broadcasting clocks, the $B$p-parallel observer will record a time-stamped passage of the compressed $A$ through $B$.
So, am I the only one finds an a priori assumption causal self-consistency between these two views difficult to accept? That is, while it may very well be that a recording of a flattened $B$ passing through cloud $A$ in $A$-sequential time order can always be made causally self-consistent with a recording of a flattened $A$ passing passing through through cloud $B$ in $B$-sequential order, this to me is a case where a mathematically precise proof of the information relationships between the two views would be seem like a good idea, if only to verify how it works. Both views after all record the same event, in the sense that every time a clock in $A$ or $B$ ticks and broadcasts its results, that result becomes part of history and can no longer be reversed or modified.
It's tempting to wonder whether the Lampa-Terrell-Penrose Effect might be relevant. However, everything I've seen about L-T-P (e.g. see the video link I just gave) describes it as an optical effect in which the spheres are Lorentz contracted at the physical level. Since my question deals with fine-grained, contact-like interactions of two relativistic spheres, rather than optical effects at a distance, I can't easily see how L-T-P would apply. Even if it did, I don't see what it would mean.
So, my real question is (b): Does an information-level proof exist (not just the Lorentz transforms; that part is straightforward) that the $A$-parallel and $B$-parallel recordings of dual cloud chamber collision events will always be causally consistent?
2012-03-03: This was my original version of the question, using muonium clocks
My SR question is how to predict length contraction and time dilation outcomes for two interacting beams of neutral particles. The two beams are:
1. In different inertial (unaccelerated) reference frames for the duration of measurement part of the experiment.
2. Intermixed at a near-atomic level so that frame-to-frame photon exchange times are negligible. An example would be two intersecting beams of relatively dense, internally cold muonium atoms.
3. Clock-like even at the atomic level (e.g., decaying atoms of muonium).
4. Part of a single causal unit. By this I mean that there is a sufficient short-range exchange of photons between the two beams to ensure that state changes within each beam have an entropic effect, however small, on nearby components of the other beam. This makes their interactions irreversible in large-scale time. An example would be decay of an anti-muon in one frame transferring energy to nearby muonium atoms in the other frame. Simply illuminating the intersection region with light frequencies that would interact with muonium in both of the beams would be another option.
5. Observed by someone who is herself isolated from the rest of the external universe.
Muons generated by cosmic rays and traveling through earth's atmosphere provide a helpful approximation the above experiment. The muons provide the first beam, and the atmosphere forms the second one, which in the case of muons is shared by the observer.
Such muons have tremendously extended lifespans, which is explained by invoking time dilation (but not length contraction) for the muon frame as viewed from the atmosphere frame. Conversely, length contraction (but not time dilation) is invoked to describe the view of the atmosphere from the perspective of the muon frame. Since this results in the atmosphere appears greatly compressed in the direction of travel, the muons simply travel a shorter distance, thereby ensuring the same decay result (causal symmetry) for both views of the interacting frames.
My question then is this:
For the thought experiment of intersecting, causally linked beams of muonium, what parameters must the observer take into account in order to predict accurately which of the two intersecting muonium beams will exhibit time dilation, and which one will exhibit length contraction?
2012-03-04 Addendum by Terry Bollinger (moved here from comment section):
Sometimes asking a question carefully is a good way to clarify one's thinking on it. So, I would now like to add a hypothesis provoked by own question. I'll call it the local observer hypothesis: Both beams will be time dilated based only on their velocities relative to the observer Alice; the beam velocities relative to each other are irrelevant. Only this seems consistent with known physics. However, it also implies one can create a controllable time dilation ratio between two beams. I was trying to avoid that. So my second question: Are physical time dilation ratios ever acceptable in SR?
Some further analysis of my own thought problem:
A $\phi$ set is a local collection of clock-like particles (e.g. muons or muonium) that share a closely similar average velocity, and which have the ability to intermix and exchange data with other $\phi$ sets at near-atomic levels, without undergoing significant acceleration. A causal unit $\chi = \{\phi_0 ... \phi_n\}$ is a local collection of $(n+1)$ such $\phi$ sets. By definition $\phi_0$ contains a primary observer Alice, labeled $\aleph_0$, where $\aleph_0 \subset \phi_0$.
Each $\phi_i$ has an associated XYZ velocity vector $\boldsymbol{v_i} = (\phi_0 \rightarrow \phi_i$) that is defined by the direction and rate of divergence of an initially (nominally) co-located pair of $\phi_0$ and $\phi_i$ particles, with the $\phi_0$ particle interpreted as the origin. The vector has an associated magnitude (scalar speed) of $s_i=|\boldsymbol{v_i}|$.
Theorem: If $\phi_i$ includes a subset of particles $\aleph_i$ capable of observing Alice in $\phi_0$, then $\aleph_i$ will observe $\phi_0$ as length contracted along the axis defined by $\boldsymbol{v_i}$. Conversely, Alice ($\aleph_0$) will observe each $\phi_i$ as time dilated (slowed) based only on its scalar speed $s_i$, without regard to the vector direction. This dependence of time dilation on the scalar $s_i$ means that if $\phi_a$ has velocity $\boldsymbol{v_a}$ and $\phi_b$ has the opposite velocity $\boldsymbol{-v_a}$, both will have the same absolute time dilation within the causal unit (think for example of particle accelerators).
Analysis: This $\chi = \{\phi_i\}$ framework appears to be at least superficially consistent with data from sources such as particle accelerators, where time dilation is observable in the variable lifetimes of particles at different velocities, and where absolute symmetry in all XYZ directions is most certainly observed. Applying observer-relative time dilation to fast particles (e.g. in a simple cloud chamber) is in fact such a commonly accepted practice that I will assume for now that it must be valid.
(It is worth noting that while particle length contraction is typically also assumed to apply to fast-moving particles, serious application of length contraction in a causal unit would cause the particles to see longer travel paths that would shorten their lifespans. This is the same reason why muons are assumed to see a shorter path through a length-contracted atmosphere in order to reach the ground.)
My updated questions are now:
(1) Is my $\chi = \{\phi_i\}$ framework for applying SR to experiments valid? If not, why not?
(2) If $\chi = \{\phi_i\}$ is valid, what property makes the observer $\aleph_0$ in $\phi_0$ unique from all other $\aleph_i$?
-
A reference frame is just a way of assigning coordinates to points in spacetime, nothing more. It seemed like you were mixing up the meanings of "frame" and "beam" a bit so I straightened that out. – David Z Mar 4 '12 at 0:56
Good clarification; thanks David! – Terry Bollinger Mar 5 '12 at 0:15
you just don't have intuition for failure of simultaneity--- this is the universal thing that trips up people's intuitive understanding of relativity. The two clouds passing through each other leave a "wake" at different spots in the different frames because the "wake" is spacelike (superluminal) and changes slope and speed depending on your motion. – Ron Maimon Apr 8 '12 at 23:08
So: If all of this is just a matter of good intuition, a mathematically precise proof should be trivial, yes? – Terry Bollinger Apr 9 '12 at 15:23
Have a look at the images below. Both sides show cloud A moving through cloud B as you would expect. Now at the left side we are going to collect 5 slices which are at equal time in the restframe of A, and at the right side we collect 5 slices which are at equal time in the restframe of B. This corresponds with the rotation of the time axis in these two reference frames.
As you can see, the left image shows a highly contracted cloud B inside the cloud A while the right image shows a highly contracted cloud A inside cloud B, exactly as you describe. Now note that both are part of the same 4D reality. What you see are two different 3D spaces cut out of the same 4D space-time.
Hans
-
Hans, thanks! (My first attempt to comment on this and another seem to have disappeared; I think I didn't save them right.) Your answer is very clearly presented, and you have understood my setup well. I'll be looking at your answer a lot more closely (not tonight, multiple distractions). Again, thanks. – Terry Bollinger Apr 11 '12 at 3:05
My thanks for the comment and four entries for this competition! All were excellent reading, and I am deeply appreciative of the serious thought everyone put into this one to help me in my head scratching. The winner, as you've likely guessed by where I'm placing this comment, is Hans de Vries. Reading through his answer instantly made me understand my own question in some new and very thought-provoking ways. (One hint: 4D objects rotate around invariant 2D planes, and objects in different frames appear rotated to each other in a plane of motion and time.) There will be more DC2P bounties! – Terry Bollinger Apr 16 '12 at 3:08
@Terry, Hi Terry, I'm happy to see that my post was helpful! Thanks for the bonus. To give you something in return there is also my chapter on non-simultaneity here: physics-quest.org/Book_Chapter_Non_Simultaneity.pdf if you are interested. It explains, with lots of illustrations, why it is so natural that we chose a different time axis when going to a different reference frame. – Hans de Vries Apr 16 '12 at 3:34
Hans, thanks! I will enjoy going through it! – Terry Bollinger Apr 16 '12 at 4:52
I'll make an argument intended to make the Lorentz transformation more natural. The reason this seems so odd is because you're thinking about it from the point of view of matter. This is a natural thing to do because people are made out of matter. But Einstein's work is much simpler if you think about things from the point of view of light. With light, the natural speed is always $c$. And there's an argument in favor of treating matter as if its natural speed were also $c$. If you follow that argument, then the Lorentz transformations follow.
The Standard Model of elementary particles represents the fermions (matter) as chiral fields. These are a Dirac field (which can model, for example, the combination fields of electron and positron) which are split into "chiral" or "handed" halves. These left and right handed fields are a little familiar to undergraduate physics as their equivalents appear when light is circularly polarized into left or right handed light.
To turn an electron into a pure right handed or left handed field, one accelerates the electron in the direction of its spin (or the opposite direction) to the speed of light. This is of course impossible except in the limit. But the underlying notion is clear, the Standard Model is built from components that naturally travel at light speed.
So your intuition will understand the situation better if you think of matter as being the weird and bizarrely behaved stuff. Light acts perfectly normally, just what you'd expect of waves in a universe where the wave speed is $c$.
If you look at the problem this way, you will see that the transformation of the pictures from one clump to the other involves a great deal of complexity. You have to arrange for matter to do some pretty crazy things in order to get all those "stationary" clocks.
On the other hand, if you think of the problem as one where fields that travel at a natural speed of $c$ interact, then one naturally chooses a single reference frame and carries out all calculations in that frame of reference. Of course, since we are made out of fields that move at speed $c$, we cannot detect that reference frame. Since we cannot detect it, it is not "preferred" by our laws of physics. We could just as easily have chosen the "wrong" rest frame, our calculation would give the same result either way because waves can measure absolute wave speeds or absolute wave frequencies or absolute wave lengths; they can only measure differences and the results are the laws of Lorentz transform.
As an example, suppose you are a small localized wave. You cannot know your absolute speed against the background (say water for instance, though this is not a good example). When another wave comes by, all you can do is say what their wavelength is compared to your own wavelength. But your own wavelength gets changed when you are in fast moving water. That's because the time that a wave saves going downstream (with the current) is less than the time it loses going upstream.
Suppose the speed of your waves is $c$, and you need to travel some distance $l$. The time required to go there and back will be $t = l/c+ l/c = 2l/c$. Now suppose that there is a current at speed $v$. This will speed you up one way and slow you down the other. So the time required becomes: $$t = l/(c+v) + l/(c-v) = \frac{l(c-v)}{(c+v)(c-v)} + \frac{l(c+v)}{(c+v)(c-v)}$$ $$= \frac{2cl}{c^2-v^2} = \frac{2l}{c}\frac{1}{1-v^2/c^2}\;\;\textrm{so}$$ $$t = \frac{2l}{c}\gamma^2$$ where $\gamma = (1-v^2/c^2)^{-1/2}$ is the usual relativistic gamma factor. Looked at relativistically, you can rearrange the calculation to be $(t/\gamma) = 2(l\gamma)/c$. To get the old result $t=2l/c$, you have to apply two changes. You apply length contraction so that $l\to l/\gamma$ and time dilation so that $t\to t\gamma$. Thus the Lorentz transformation is natural for beings made of waves, living in a universe of waves, who can use only waves to measure.
So much for why it is that Lorentz transformations are natural. Now as to why causality can have different rest frames. If you accept that everything must be made out of waves, then the wave speed itself gives a limit to causality. Nothing can happen before a wave gets there. So you are free to choose a reference frame so long as your reference frame is slower than light it cannot a violation of causality. (Because casusality uses waves.)
-
Carl, I managed to lose my first comment somehow, oops. Your answer is interesting. I have to admit I have no idea how you brought QFT chirality into it though! So, I'll read through it a lot more carefully later; I'm curious as to your argument. Thanks again for a nicely detailed answer. – Terry Bollinger Apr 11 '12 at 3:08
In my answer I will use the known properties of the light. The light propagates isotropically wrt the medium irrespective of the speeds of the source and of the receiver and has a constant value if measured by a non-accelerating observer. The source is Einstein (I.1.2 §2 of 1905 paper) :
Every ray of light moves in the "stationary" co-ordinate system with the definite velocity V, the velocity being independent of the condition, whether this ray of light is emitted by a body at rest or in motion
The other source is the online book of Hans de Vries where relativity is very well explained and where we can see (chapter 4, I think) that there exists a real length Lorentz contraction and not only an apparent one. The other source is the pos-Einstein paper Cosmological Principle and Relativity - Part I (arxiv) (is poison..;)
...generalizing Relativity Principle to position... .., and analysed the space-time structure. Special Relativity space-time is obtained, with no formal conflict with Einstein analysis, but fully solving apparent paradoxes and conceptual difficulties, including the simultaneity concept and the long discussed Sagnac effect. ...
I dont see any problem in causality and I've done a nice image (my 1st in Inkscape) to show how I see the problem. If you think that this is a paradox to the relativistic guys then you should also see PSE - Twin paradox - observers counter orbiting pose a serious problem to the relativistic minds (only those that can only think with an equation in front of the eyes).
-
Helder, interesting, I'll look more closely. The "shrink" issue is extremely interesting. That is precisely the one that John Bell caused a minor furor over with his accelerating spacehips-linked-by-string thought problem. About half the SR experts he talked were absolutely positive the string would not break, and the other half were absolutely positive it would break! Neither answer violates the Lorentz transforms, but you need to be very, very careful about setup. (Bell's answer? The string will break. Bell was a very deep thinker on many such questions, not just on the Bell Inequality.) – Terry Bollinger Apr 11 '12 at 2:29
Helder, an important clarification: If each 10m ball of thin gas is seen as a ball by its pacing spaceship, then Lorentz contraction must apply equally to both the ship and the gas ball. Otherwise you get an immediate logical paradox in which there are two versions of length: The ship version, and the ball version. So both the ship and the gas ball must be contracted, or neither. What you described is the case of "isolated Lorentz, but no overall Lorentz." That one can indeed be constructed, but only by separately accelerating each molecule in the gas, as in the Bell ship paradox. – Terry Bollinger Apr 12 '12 at 0:16
@Terry You said that they are spheres, and I assumed that they are geometrical spheres when seen at rest. When seen in motion, inspite of been side by side, ship and cloud, this one is seen as coming from behind, and elongated. As they are formed by a thin gas (1nm sep) I presumed that they are free ensemble of particles without electromagnetic interaction. In the case of the spaceship the molecules are electromagnetically bonded and so all the spaceship will be contracted. As Carl said, and I subscribe, matter is 'wavy', is light, and we think that they will suffer a 'contraction'. – Helder Velez Apr 12 '12 at 2:31
Helder, thanks. I think we are in synch? But just to make sure I'm expressing my intent clearly as possible, my thought process was this: Assume the two ships are already in motion. Shortly before closest approach, each ship creates its sphere of diffuse gases. Each sphere is at rest relative to its spaceship, and each is 10m in diameter relative to that spaceship. My intent is to max out the symmetry so that each ship perspective is as close to an exact (180 rotated) replica of the other as possible. BTW, after taxes (sigh) I'll put out some further discussion and figures on this question. – Terry Bollinger Apr 13 '12 at 19:57
Naturally there's no "universal" time in the SR, the time difference of two events may be different in different reference frames, and in particular it may be negative (i.e. order of the events may be different as well).
However there are two distinct things:
1. The time of the event, according to a specific reference frame's coordinate + time system.
2. The time at which an observer in a particular reference frame receives the information about the event.
As you probably know, there's a maximal speed at which the information may be passed according to SR, which is the speed of light in vacuum (or any other particles with no rest mass). Hence an observer in a particular reference frame does not register an event the same moment it occurs in its reference frame. There's a delay, which depends on the distance between the event and the observer (in the context of its reference frame). So, when you talk about two events that occur at different locations - this should be taken into account to realize what the observer actually "sees". | 4,929 | 21,657 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2016-18 | latest | en | 0.921414 |
https://oeis.org/A273633 | 1,670,227,629,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711013.11/warc/CC-MAIN-20221205064509-20221205094509-00416.warc.gz | 445,815,750 | 4,410 | The OEIS is supported by the many generous donors to the OEIS Foundation.
Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A273633 Decimal expansion of (Pi/(6*sqrt(3)))^(1/3), the sphericity of the tetrahedron. 4
6, 7, 1, 1, 3, 9, 2, 9, 1, 3, 1, 2, 8, 5, 0, 3, 6, 9, 4, 9, 2, 0, 2, 9, 0, 6, 1, 6, 6, 4, 4, 4, 5, 1, 3, 1, 7, 5, 7, 9, 1, 6, 8, 4, 6, 2, 0, 7, 4, 7, 5, 1, 2, 4, 2, 1, 3, 8, 9, 9, 7, 1, 2, 6, 7, 8, 2, 0, 5, 8, 2, 9, 1, 3, 6, 9, 7, 5, 9, 4, 5, 1, 6, 2, 4, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET 0,1 LINKS Wikipedia, Sphericity. FORMULA Equals cube root of A093766. - Michel Marcus, May 27 2016 EXAMPLE 0.67113929131285036949202906166444513175791684620747512421389971... PROG (PARI) default(realprecision, 50080); my(x=(Pi/(6*sqrt(3)))^(1/3)); for(k=1, 100, my(d=floor(x)); x=(x-d)*10; print1(d, ", ")) CROSSREFS Cf. A093766, A273634, A273635, A273636, A273637. Sequence in context: A195714 A247043 A019734 * A021153 A195430 A153269 Adjacent sequences: A273630 A273631 A273632 * A273634 A273635 A273636 KEYWORD nonn,cons AUTHOR Felix Fröhlich, May 27 2016 EXTENSIONS Definition corrected by Georg Fischer, Jul 12 2021 STATUS approved
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified December 5 02:30 EST 2022. Contains 358572 sequences. (Running on oeis4.) | 722 | 1,834 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2022-49 | latest | en | 0.715207 |
https://q4interview.com/logical-reasoning/matching-definitions/all/2/1 | 1,720,834,512,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514459.28/warc/CC-MAIN-20240712224556-20240713014556-00722.warc.gz | 399,978,262 | 32,200 | [Updated] Goldman Sachs Aptitude Test Questions and Answers
Practice List of TCS Digital Coding Questions !!!
Take 50+ FREE!! Online Data Interpretation Mock test to crack any Exams.
Matching Definitions Questions
Home > Logical Reasoning > Matching Definitions > General Questions
NA
SHSTTON
6
Solv. Corr.
1
Solv. In. Corr.
7
Attempted
0 M:0 S
Avg. Time
11 / 16
Read the definition and all four choices carefully, and find the answer that provides the best example of the given definition.
Definition:
Erratic Behavior occurs when an individual acts in a manner that lacks consistency, regularity, and uniformity. Which situation below is the best example of Erratic Behavior?
Choices:
I. Julia cannot contain her anger whenever the subject of local politics is discussed.
II. Martin has just been told that he is being laid off. Before leaving his supervisor's office, he punches a hole in the door.
III. Rhonda has visited the dealership several times, but she still cannot decide which car to buy.
IV. In the past month, Jeffrey, who has been a model employee for three years, has repeatedly called in sick, forgotten important meetings, and been verbally abusive to colleagues.
AI
BII
CIII
DIV
Explanation:
Jeffrey's recent behavior is clearly inconsistent and irregular.
Workspace
NA
SHSTTON
5
Solv. Corr.
3
Solv. In. Corr.
8
Attempted
0 M:0 S
Avg. Time
12 / 16
Read the definition and all four choices carefully, and find the answer that provides the best example of the given definition.
Definition:
A Tiebreaker is an additional contest or period of play designed to establish a winner among tied contestants. Which situation below is the best example of a Tiebreaker?
Choices:
I. At halftime, the score is tied at 28.
II. Mary and Megan have each scored three goals in the game.
III. The referee tosses a coin to decide which team will have possession of the ball first.
IV. The Sharks and the Bears each finished with 14 points, and they are now battling it out in a five-minute overtime.
AI
BII
CIII
DIV
Explanation:
This is the only choice that indicates that an additional period of play is taking place to determine the winner of a game that ended in a tie.
Workspace
NA
SHSTTON
5
Solv. Corr.
2
Solv. In. Corr.
7
Attempted
0 M:0 S
Avg. Time
13 / 16
Read the definition and all four choices carefully, and find the answer that provides the best example of the given definition.
Definition:
In the Maple Hill school district, a Five-Day Suspension occurs when a student is not permitted to attend school for five days for (1) physically assaulting another student, a teacher, or a school employee or (2) willfully destructing or defacing school property. Which situation below is the best example of a Five-Day Suspension?
Choices:
I. Lillian gets caught cheating on a math test for the second time and is suspended from school.
II. Marc is asked to leave the classroom due to his constant disruptions.
III. Franny uses spray paint to write derogatory comments on the locker room wall and she is given a suspension.
IV. Ms. Farmer tells her class that students who fail the midterm exam will be expected to stay after school for tutoring help.
AI
BII
CIII
DIV
Explanation:
Although choices a and c both describe suspensions, only choice c describes a suspension that is the result of one of the two scenarios given in the definition of a five-day suspension (physical assault or destructing or defacing school property). Therefore, we can assume that Franny's suspension, which is the result of spray painting school property, will be a five-day suspension. Since the definition doesn't provide any information about suspensions for cheating, we can assume that Lillian's suspension does not fall into the five-day suspension category.
Workspace
NA
SHSTTON
4
Solv. Corr.
2
Solv. In. Corr.
6
Attempted
0 M:0 S
Avg. Time
14 / 16
Read the definition and all four choices carefully, and find the answer that provides the best example of the given definition.
Definition:
It is appropriate to compensate someone if you have damaged his or her property in some way. This is called Restitution. Which situation below is the best example of Restitution?
Choices:
I. Jake borrows Leslie's camera and the lens shatters when it falls on the ground because he fails to zipper the case.When Jake returns the camera, he tells Leslie that he will pay for the repair.
II. Rebecca borrows her neighbor's car, and when she returns it, the gas tank is practically empty. She apologizes profusely and tells her neighbor she will be more considerate the next time.
III. Aaron asks Tom to check in on his apartment while he is out of town. When Tom arrives, he discovers that a pipe has burst and there is a considerable amount of water damage. He calls a plumber to repair the pipe.
IV. Lisa suspects that the pothole in her company's parking lot caused her flat tire. She tells her boss that she thinks the company should pay for the repair.
AI
BII
CIII
DIV
Explanation:
Jake damaged Leslie's camera while it was in his possession and he has agreed to compensate Leslie for the cost of the repair.
Workspace
NA
SHSTTON
5
Solv. Corr.
2
Solv. In. Corr.
7
Attempted
0 M:0 S
Avg. Time
15 / 16
Read the definition and all four choices carefully, and find the answer that provides the best example of the given definition.
Definition:
Reentry occurs when a person leaves his or her social system for a period of time and then returns. Which situation below best describes Reentry?
Choices:
I. When he is offered a better paying position, Jacob leaves the restaurant he manages to manage a new restaurant on the other side of town.
II. Catherine is spending her junior year of college studying abroad in France.
III. Malcolm is readjusting to civilian life after two years of overseas military service.
IV. After several miserable months, Sharon decides that she can no longer share an apartment with her roommate Hilary.
AI
BII
CIII
DIV
Explanation:
Malcolm is the only person returning to a social system that he has been away from for an extended period of time.
Workspace
NA
SHSTTON
5
Solv. Corr.
2
Solv. In. Corr.
7
Attempted
0 M:0 S
Avg. Time
16 / 16
Read the definition and all four choices carefully, and find the answer that provides the best example of the given definition.
Definition:
Embellishing the Truth occurs when a person adds fictitious details or exaggerates facts or true stories. Which situation below is the best example of Embellishing the Truth?
Choices:
I. Isabel goes to the theater, and the next day, she tells her coworkers she thought the play was excellent.
II. The realtor describes the house, which is eleven blocks away from the ocean, as prime waterfront property.
III. During the job interview, Fred, who has been teaching elementary school for ten years, describes himself as a very experienced teacher.
IV. The basketball coach says it is likely that only the most talented players will get a college scholarship.
AI
BII
CIII
DIV
Explanation:
The realtor is using a clear exaggeration when she states that a house which is eleven blocks away from the ocean is prime waterfront property.
Workspace
Logical Reasoning Matching Definitions Questions and Answers pdf
At Logical Reasoning topic Matching Definitions, you will get multiple online quiz difficulty wise, which will have a total of 6 quizzes, categorized as easy, medium, and moderate level. While preparing for any Matching Definitions, take all the list quiz and check your preparation level for that topic. Each quiz have 10 different question, which needs to be answered in 20 min., all the listed quiz here is free, however, you will get only one chance for each quiz to attempt(Take Quiz seriously), so it is always recommended to take one quiz in each section before you start solving Matching Definitions MCQs practice question, and one after solving all the question of the respective level, you can refer back your Matching Definitions quiz result any time or you can download it as pdf for reference.
Logical Reasoning Matching Definitions Customize Online Mock Test
This is own type of mock test, where At this Logical Reasoning Matching Definitions MCQs mock test section, you will able to attempt only the questions related to Matching Definitions, in that question will be a different level, important, and all the questions will be part of some of the mock tests across Q4interview FREE Mock test. You need to choose the topic as Matching Definitions, and click on Double click to generate your customize mock test. While attempting the mock test you need to choose any of the one options out of given option. It is recommended to go through the direction given along with each question, as these questions will be randomly and so that same direction will not be applicable across the entire test. Once you submit your mock test, the result will be generated for Matching Definitions Customize mock test, where your performance point points will be highlighted. Q4interview analysis every single point which helps you to improve your topic understanding and help you to know your type of mistakes and way to improve Matching Definitions questions, by providing the same type of practice questions from practice exercise. The best part of this Matching Definitions, all these mock tests listed here are free and you can take as Many time, as many you want. When you continue to give Matching Definitions Customize Online Mock Test here regularly, then you will understand how much you have developed your accuracy on a topic, after that you will be able to decide how much attention you need to focus on. Your continued practice will increase your confidence, speed and thinking ability intensely, the Matching Definitions Customize topic on which you will practice more will beneficial for you in future during campus placement.
Logical Reasoning Matching Definitions Quiz Online Test
The details of the Logical Reasoning Matching Definitions quiz are as follows. There are 10 questions for you. You have to answer them in 20 minutes. Within 20 minutes you have to see the errors in the sentences given as a question. Four options are also given to you, and you have to choose your opinion. You must be confident in your answer that the choices are difficult. Therefore, below we provide you with some information about Logical Reasoning Matching Definitions that you see and keep them in mind while answering questions.
Logical Reasoning Matching Definitions MCQs Practice Questions with Answer
On this Matching Definitions section of page you will find the easiest quickest ways to solve a question, formulas, shortcuts and tips and tricks to solve various easiest methods to solve Matching Definitions Question Quickly. It contains all the Logical Reasoning topic Matching Definitions questions which are common in any of the preliminary exams of any company. The solution is provided along with the questions. The practice of these questions is a must as they are easy as well as scoring and asked in all the exams They will confirm the selection if all the questions attempted wisely with little practice. It is recommanded to Take Mock test based on Logical Reasoning topic and Matching Definitions topic based quiz.
Logical Reasoning Matching Definitions solved examples question
You can get here fully solved Matching Definitions examples with a detailed answer and description. You can solve Matching Definitions problems with solutions, the questions by companies wise by filtering the questions, additionally, you can check what type of questions are being asked in IT companies Written Round from Matching Definitions. Matching Definitions became one of the most important sections in the entire competitive exams, Companies Campus, and entrance online test. Go through Matching Definitions Examples, Matching Definitions sample questions. You can Evaluate your level of preparation in Matching Definitions by Taking the Q4Interivew Matching Definitions Online Mock Test based on most important questions. All the Matching Definitions practice questions given here along with answers and explanations are absolutely free, you can take any number of time any mock Test.
Why Logical Reasoning Matching Definitions?
In this practice section, you can practice Logical Reasoning Questions based on "Matching Definitions" and improve your skills in order to face the interview, competitive examination, IT companies Written exam, and various other entrance tests (CAT, GATE, GRE, MAT, Bank Exam, Railway Exam etc.) with full confidence.
Where can I get Logical Reasoning Matching Definitions questions and answers with explanation?
Q4Interview provides you lots of fully solved Logical Reasoning (Matching Definitions) questions and answers with Explanation. Solved examples with detailed answer description, explanation are given and it would be easy to understand. You can download Logical Reasoning Matching Definitions quiz questions with answers as PDF files and eBooks.
Where can I get Logical Reasoning Matching Definitions Interview Questions and Answers (objective type, multiple-choice, quiz, solved examples)?
Here you can find objective type Logical Reasoning Matching Definitions questions and answers for interview and entrance examination. Multiple choice and true or false type questions are also provided. | 2,754 | 13,415 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2024-30 | latest | en | 0.91826 |
http://worldofnumbers.com/ninedig3.htm | 1,638,965,785,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363510.40/warc/CC-MAIN-20211208114112-20211208144112-00480.warc.gz | 85,769,753 | 24,886 | HOME plateWON | World!OfNumbers The Nine Digits Page 3 with some Ten Digits (pandigital) exceptions Most Recent Page 5 Page 4 Page 2 Page 1
When I use the term ninedigital in these articles I always refer to a strictly zeroless pandigital (digits from 1 to 9 each appearing just once).
Third Page
[ September 15, 2003 ]
"Ninedigital fractions" equations and their distinct integer solutions
( sometimes generalized to "Ninedigital expressions" ).
Navigate using these links :
Var 0 Var 1 Var 2 Var 3 Var 4 Var 5 Var 6 Var 7 Var 8 Var 9
Var 10 Var 11 Var 12 Var 13 Var 14
by Terry Trotter (email)
by Jean Claude Rosa (email)
by Patrick De Geest (email)
by Jerry Levy (email)
Introduction see Levy Expressions by Terry Trotter
Variation #0 : the original equation A/BC + D/EF + G/HI [L. Mittenzwey, circa 1880]
BC, EF and HI are not digit products but digit concatenations.
Only one solution
11
Go to Amazing Nine Digits Property
Variation #1 : the equation A/(B*C) + D/(E*F) + G/(H*I) [Jerry Levy's suggestion]
Four different values - 7 distinct solutions (see subscript values)
11, 22, 42, 52
Why do I underscore the specification distinct ? (info by J.C.R.)
We can say that, for example, the following 3 solutions are identical :
1/(3*6) + 5/(8*9) + 7/(2*4) = 1
1/(6*3) + 5/(8*9) + 7/(4*2) = 1
5/(9*8) + 1/(6*3) + 7/(2*4) = 1
Likewise for each solution we can produce an extra of 47 but identical ones,
meaning 48 in total (including the original solution). Why 48 ?
For each triplet, A/(B*C) for example, we have 2 possible dispositions :
A/(B*C) and A/(C*B)
There are 3 triplets so 8 possible dispositions ( 8 = 2*2*2 ).
On the other hand the order in which we write the triplets in the expression
has no effect on the final value.
Example:
N = 1/(3*6) + 5/(8*9) + 7/(2*4)
N = 5/(8*9) + 1/(3*6) + 7/(2*4)
There are 6 different dispositions among our 3 triplets so in total we have 6*8,
meaning 48 different dispositions giving the same result.
Samples
N = 1 ; 1/(3*6) + 5/(8*9) + 7/(2*4)
so 1 distinct solution.
N = 2 ; 5/(1*8) + 7/(2*4) + 9/(3*6)
N = 2 ; 5/(2*4) + 7/(1*8) + 9/(3*6)
so 2 distinct solutions.
N = 4 ; 5/(3*4) + 6/(8*9) + 7/(1*2)
N = 4 ; 8/(4*9) + 5/(3*6) + 7/(1*2)
so 2 distinct solutions.
N = 5 ; 5/(3*8) + 7/(4*6) + 9/(1*2)
N = 5 ; 5/(4*6) + 7/(3*8) + 9/(1*2)
so 2 distinct solutions.
Note that we have 7*48 or 336 undistinct solutions.
Variation #2 : the equation (A/B)*C + (D/E)*F + (G/H)*I [Jerry Levy's suggestion]
82 different values - 352 distinct solutions (see subscript values)
53, 62, 75, 83, 92,
105, 114, 134, 144, 154, 163, 177, 189, 197,
207, 2113, 229, 235, 2411, 258, 266, 274, 285, 293,
307, 312, 324, 346, 355, 369, 374, 383, 392,
405, 415, 428, 437, 443, 452, 473, 483, 491,
506, 523, 534, 547, 554, 563, 576, 587, 592,
603, 611, 624, 637, 644, 656, 664, 675, 686, 692,
703, 712, 723, 735, 746, 753, 762, 776, 782, 792,
802, 812, 821, 834, 843, 852, 892,
902, 911, 941, 962.
Ten numbers are not present between 5 and 96
12, 33, 46, 51, 86, 87, 88, 92, 93, 95
Variation #3 : the equation (A/B)^C + (D/E)^F + (G/H)^I [Jerry Levy's suggestion]
WTM column see Power-full Fractions by Terry Trotter
135 different values - 200 distinct solutions (see subscript values)
701,
1321, 2412, 3561, 3742, 4071, 4352, 5932, 6652, 6726, 8101, 8821, 8892,
10981, 11001, 22222, 22551, 22761, 22832, 24322, 28241, 29422, 29481, 39371, 41541,
45071, 65262, 67401, 69081, 73072, 77131, 79131, 92052, 93732, 97722, 99671,
102192, 144651, 157621, 168801, 173232, 173461, 175211, 175401, 175753, 177381,
177922, 178161, 179202, 179231, 180682, 181372, 199361, 200542, 200581, 207232,
209841, 219022, 223141, 229771, 231882, 234321, 234492, 242411, 320901, 334082,
336251, 350191, 350362, 364981, 591812, 592041, 594333, 612441, 679662, 754491,
781981, 786412, 786641, 788581, 788933, 791102, 823021, 847501, 847672, 978161,
1176901, 1178961, 1181482, 1187541, 1242421, 2625151, 2628971, 2632962,
2643631, 2645771, 2785602, 2789671, 2799771, 2801831, 2804352, 2810411,
2865291, 3402851, 3912652, 3914821, 3928761, 3928932,
16799871, 16818351, 19532572, 19532801, 19535093, 19553201, 19695251,
20974591, 20974762, 20976962, 20979131, 47830052, 47830281, 47832201,
47832573, 47840091, 57651081, 57651252, 57653452, 57655621,
403536432, 403536661, 403538581, 403538953, 403546471, 430468812,
1342178882.
Six distinct solutions exist for integer value 672 due to sums of powers of 2 permutations.
Six cases with three distinct solutions : values 17575, 59433, 78893, 1953509, 4783257 & 40353895.
Samples
672 = (2/1)^5 + (6/3)^7 + (8/4)^9
672 = (2/1)^5 + (6/3)^9 + (8/4)^7
672 = (2/1)^7 + (6/3)^5 + (8/4)^9
672 = (2/1)^7 + (6/3)^9 + (8/4)^5
672 = (2/1)^9 + (6/3)^5 + (8/4)^7
672 = (2/1)^9 + (6/3)^7 + (8/4)^5
Fourteen numbers turned out to be prime.
Prime Curios! 241 is the smallest and Prime Curios! 4784009 is the largest of the lot.
Two numbers happen to be palindromic.
2222 is the first which is in fact also a repdigit.
23432 is the second one.
Samples
2222 = (6/2)^1 + (8/4)^5 + (9/3)^7
2222 = (6/2)^7 + (8/4)^5 + (9/3)^1
23432 = (4/2)^6 + (7/1)^5 + (9/3)^8
Variation #4 : the equation A/(B+C) + D/(E+F) + G/(H+I) [Jean Claude Rosa's suggestion]
Four different values - 87 distinct solutions (see subscript values)
13, 255, 318, 411
Samples
1 = 1/(2+4) + 5/(7+8) + 6/(3+9)
1 = 2/(6+9) + 3/(7+8) + 4/(1+5)
1 = 2/(7+8) + 3/(6+9) + 4/(1+5)
Variation #5 : the equation (A+B)/C + (D+E)/F + (G+H)/I [Jean Claude Rosa's suggestion]
24 different values - 355 distinct solutions (see subscript values)
36, 411, 519, 621, 712, 826, 923,
1028, 1116, 1218, 1313, 1415, 1514, 1619, 1711, 1823, 1916
2019, 217, 2213, 2311, 247, 255, 262.
Samples
26 = (4+5)/3 + (6+8)/2 + (7+9)/1
26 = (4+6)/2 + (5+7)/3 + (8+9)/1
Note that 13 has 13 distinct solutions, ain't we lucky this time !!
Variation #6 : the equation A/(B–C) + D/(E–F) + G/(H–I) [Terry Trotter's suggestion]
45 different values - 8196 distinct solutions (see subscript values)
–246, –226, –2014,
–194, –1834, –176, –1658, –1518, –1477, –1330, –12142, –1158, –10226,
–9113, –8305, –7175, –6390, –5256, –4506, –3330, –2628, –1346,
0740,
1346, 2628, 3330, 4506, 5256, 6390, 7175, 8305, 9113,
10226, 1158, 12142, 1330, 1477, 1518, 1658, 176, 1834, 194,
2014, 226, 246.
Samples
–19 = 4/(3–5) + 8/(1–2) + 9/(6–7)
–19 = 4/(3–5) + 8/(6–7) + 9/(1–2)
–19 = 6/(1–2) + 8/(5–7) + 9/(3–4)
–19 = 6/(3–4) + 8/(5–7) + 9/(1–2)
19 = 4/(5–3) + 8/(2–1) + 9/(7–6)
19 = 4/(5–3) + 8/(7–6) + 9/(2–1)
19 = 6/(2–1) + 8/(7–5) + 9/(4–3)
19 = 6/(4–3) + 8/(7–5) + 9/(2–1)
Note the symmetry in values and distinct solutions.
All values have composite distinct solutions, except for –9 and 9
which have a prime number of solutions namely 113.
Variation #7 : the equation (A–B)/C + (D–E)/F + (G–H)/I [Terry Trotter's suggestion]
17 different values - 1612 distinct solutions (see subscript values)
–85, –713, –635, –540, –4118, –399, –2212, –1188,
0192,
1188, 2212, 399, 4118, 540, 635, 713, 85.
Values –2 and 2 each have the record palindromic number of solutions nl. 212.
We have prime number of solutions for the first and last two values.
Samples
–8 = (2–8)/1 + (4–9)/3 + (5–7)/6
–8 = (2–9)/1 + (3–6)/4 + (5–7)/8
–8 = (2–9)/1 + (4–8)/3 + (7–5)/6
–8 = (3–9)/1 + (4–7)/2 + (5–8)/6
–8 = (3–9)/1 + (4–7)/6 + (5–8)/2
8 = (5–7)/6 + (8–4)/3 + (9–2)/1
8 = (6–3)/4 + (7–5)/8 + (9–2)/1
8 = (7–4)/2 + (8–5)/6 + (9–3)/1
8 = (7–4)/6 + (8–5)/2 + (9–3)/1
8 = (7–5)/6 + (8–2)/1 + (9–4)/3
Variation #8 : the equation (A+B)*C + (D+E)*F + (G+H)*I [Terry Trotter's suggestion]
129 different values - 7560 distinct solutions (see subscript values)
This equation always deliver integer solutions whatever ninedigital combination is used.
In total we have factorial 9 (or 9! = 362880) undistinct solutions.
Values range from 70 to 198 without gaps.
701, 712, 725, 734, 746, 757, 769, 779, 7817, 7910,
8011, 8110, 8212, 839, 849, 8510, 8611, 8710, 8814, 8913,
9015, 9114, 9222, 9313, 9421, 9516, 9622, 9718, 9832, 9920,
10036, 10121, 10242, 10331, 10441, 10527, 10648, 10732, 10864, 10929,
11061, 11130, 11261, 11342, 11473, 11531, 11657, 11747, 11878, 11937,
12074, 12140, 12283, 12345, 12468, 12550, 126101, 12753, 12897, 12962,
13094, 13155, 132144, 13371, 134102, 13577, 136102, 13772, 138156, 13964,
140102, 14195, 142134, 14373, 144136, 14573, 146111, 14799, 148135, 14972,
150159, 15165, 152140, 153113, 154124, 15577, 156161, 15790, 158153, 159102,
160139, 16186, 162206, 16396, 164117, 16595, 166130, 16790, 168180, 16983,
170118, 17185, 172113, 17383, 174125, 17555, 17676, 17777, 17878, 17938,
18056, 18131, 18258, 18333, 18436, 18525, 18634, 18719, 18825, 18916,
19018, 19112, 19212, 1937, 1948, 1955, 1964, 1974, 1983.
Value 162 yields the record number of distinct solutions nl. 206
Value 70 gives only 1 but unique distinct solution.
Samples
70 = (4+5)*3 + (6+7)*2 + (8+9)*1
198 = (1+2)*3 + (4+5)*6 + (7+8)*9
198 = (1+2)*3 + (4+5)*7 + (6+8)*9
198 = (1+2)*3 + (4+5)*8 + (6+7)*9
Variation #9 : the equation (A+B)^C + (D+E)^F + (G+H)^I [Terry Trotter's suggestion]
6283 different values - 7560 distinct solutions (see subscript values)
Here also all possible combinations yield integer results.
There are too many integer solutions to display them all. I shall
restrict myself to some subgroups and highlighting the curios.
Value 915 is the smallest solution.
Value 38443890843 is the largest solution.
16 values each have the record number of distinct solutions i.e. 6 :
23796, 11100006, 19326236, 29861406, 101010006, 195018236,
469419516, 1001001006, 1509990406, 2143602236, 3874860996,
3879526596, 3922035396, 4304672196, 10001000106, 23579478236.
( Note the four binary like numbers ! )
Only 1 value has a unique number of distinct solutions namely 3 :
1507063.
Samples
150706 = (1+7)^5 + (3+4)^6 + (8+9)^2
150706 = (1+8)^2 + (3+7)^5 + (6+9)^4
150706 = (1+9)^5 + (3+6)^2 + (7+8)^4
The following list shows how many values have exactly 1, 2, 3 and 6 distinct solutions :
V11 = 5071
V22 = 1195
V33 = 1
V66 = 16
Exact 10 palindromic values appear in the list.
9692, 9991, 66661, 309031, 471741,
675761, 7611671, 8444481, 14363411, 60555061.
The smallest palindrome 969 has two distinct solutions.
969 = (4+5)^3 + (6+9)^1 + (7+8)^2
969 = (4+5)^3 + (6+9)^2 + (7+8)^1
The beastly repdigit 6666 shows off !
6666 = (1+6)^4 + (5+8)^2 + (7+9)^3
Are we lucky ? since the first sum gives 1+6 = 7
Are we unlucky ? since the second sum gives 5+8 = 13
What about the third sum 7+9 = 16 ? Subtract its power 3... aargh !
Speaking of palindromes...
I count 287 primes with 1 distinct solution and
I count 76 primes with 2 distinct solutions.
Now note the next two palindromic results !!
287 + 76 = 363
287 * 76 = 21812
Exactly 1 tautonymic number appears in the list i.e. :
1515 = (4+7)^3 + (5+8)^2 + (6+9)^1 = (4+9)^2 + (5+6)^3 + (7+8)^1
Value 941 (Prime Curios!) is the smallest prime solution.
Value 38443418449 (Prime Curios!) is the largest prime solution.
This must be the ninedigital find of the year !
Look at the following unique dual ninedigital equation :
214358976 = (3 + 6)2 + (4 + 7)8 + (5 + 9)1
Variation #9 shows no other such ninedigital (or even pandigital) solutions.
Variation #10 : the equation (A–B)*C + (D–E)*F + (G–H)*I [Terry Trotter's suggestion]
205 different values - 60480 distinct solutions (see subscript values)
All possible combinations result in integer solution either positive or negative.
Values range from –102 to 102 without gaps.
The number of negative solutions is equal to the number of positive solutions.
0870,
±1453, ±2841, ±3445, ±4721, ±5487, ±6799, ±7493, ±8756, ±9474,
±10786, ±11432, ±12744, ±13446, ±14737, ±15460, ±16687, ±17436, ±18733, ±19401,
±20694, ±21392, ±22660, ±23437, ±24563, ±25374, ±26636, ±27402, ±28564, ±29362,
±30610, ±31309, ±32540, ±33307, ±34496, ±35358, ±36504, ±37292, ±38468, ±39262,
±40434, ±41289, ±42440, ±43259, ±44420, ±45264, ±46375, ±47238, ±48347, ±49226,
±50382, ±51190, ±52306, ±53176, ±54323, ±55193, ±56266, ±57152, ±58260, ±59147,
±60230, ±61145, ±62223, ±63133, ±64178, ±65128, ±66172, ±67101, ±68165, ±69101,
±70147, ±7193, ±72150, ±7385, ±74135, ±7579, ±76114, ±7773, ±78103, ±7958,
±8088, ±8162, ±8292, ±8352, ±8482, ±8548, ±8662, ±8750, ±8859, ±8942,
±9075, ±9131, ±9241, ±9334, ±9433, ±9525, ±9625, ±9713, ±9811, ±999,
±1007, ±1012, ±1021.
32 values have palindromic distinct solutions :
±9, ±14, ±26, ±37, ±39, ±40, ±54, ±67, ±69, ±80, ±94, ±98, ±99, ±100, ±101, ±102.
16 values can be grouped in four quartets each having the same number of distinct solutions :
[±95 & ±96]25, [±81 & ±86]62, [±67 & ±69]101, [±59 & ±70]147
40 values have prime distinct solutions :
±5, ±18, ±19, ±24, ±33, ±48, ±55, ±62, ±67, ±69,
±75, ±77, ±78, ±88, ±91, ±92, ±97, ±98, ±100, ±101
2 values only shows one unique distinct solution :
±1021
Samples
0 = (1–2)*3 + (4–5)*6 + (8–7)*9
0 = (9–8)*7 + (6–5)*2 + (1–4)*3
when the value is zero we have in fact pandigital expressions !
–101 = (1–8)*9 + (2–7)*6 + (3–5)*4
–101 = (1–9)*8 + (2–7)*5 + (3–6)*4
101 = (5–3)*4 + (7–2)*6 + (8–1)*9
101 = (6–3)*4 + (7–2)*5 + (9–1)*8
–102 = (1–9)*8 + (2–7)*6 + (3–5)*4
102 = (5–3)*4 + (7–2)*6 + (9–1)*8
Variation #11 : the equation (A–B)^C + (D–E)^F + (G–H)^I [Terry Trotter's suggestion]
10426 different values - 60480 distinct solutions (see subscript values)
All possible combinations result in integer solution either positive or negative.
Like variation #9 there are too many integer solutions to display. Therefore I shall
restrict myself to some interesting categories and/or highlighting the curios.
Values range from –40369992 to 40370007 but not consecutively, there are gaps.
3649 values are negative, 1 value is equal to 0 and 6776 values are positive.
Note that this last total is palindromic !
Variation #11 shows for the first time that the negative values do not match the positive values.
The largest prime is 40356733 (out of 733 see Prime Curios!).
40356733 = (3–4)^6 + (7–2)^5 + (8–1)^9
40356733 = (4–3)^6 + (7–2)^5 + (8–1)^9
The smallest negative palindrome is –97079
The largest palindrome (out of 179) is 5764675
Samples
Value of the beast ! 12 distinct solutions ( note that digit 6 is always 'in' power ! ) 666 = (1–2)^8 + (4–7)^6 + (5–9)^3 666 = (1–2)^8 + (5–9)^3 + (7–4)^6 666 = (1–4)^6 + (5–9)^3 + (7–8)^2 666 = (1–4)^6 + (5–9)^3 + (8–7)^2 666 = (1–5)^3 + (4–7)^6 + (8–9)^2 666 = (1–5)^3 + (4–7)^6 + (9–8)^2 666 = (1–5)^3 + (7–4)^6 + (8–9)^2 666 = (1–5)^3 + (7–4)^6 + (9–8)^2 666 = (2–1)^8 + (4–7)^6 + (5–9)^3 666 = (2–1)^8 + (5–9)^3 + (7–4)^6 666 = (4–1)^6 + (5–9)^3 + (7–8)^2 666 = (4–1)^6 + (5–9)^3 + (8–7)^2 The beast enclosed 46664 = (1–4)^2 + (3–9)^6 + (7–8)^5 46664 = ... (46664 has like 666 also 12 distinct solutions !) See also WONplate 154 Some repdigits –7777 = (2–4)^1 + (3–9)^5 + (6–7)^8 –7777 = (2–4)^1 + (3–9)^5 + (7–6)^8 –7777 = (2–4)^1 + (3–9)^5 + (7–8)^6 –7777 = (2–4)^1 + (3–9)^5 + (8–7)^6 –7777 = (2–8)^5 + (3–4)^6 + (7–9)^1 –7777 = (2–8)^5 + (4–3)^6 + (7–9)^1 –7777 = (3–9)^5 + (4–6)^1 + (7–8)^2 –7777 = (3–9)^5 + (4–6)^1 + (8–7)^2 1111 = (2–6)^4 + (7–5)^9 + (8–1)^3 1111 = (6–2)^4 + (7–5)^9 + (8–1)^3 1111 = (6–9)^4 + (7–3)^5 + (8–2)^1 1111 = (7–3)^5 + (8–2)^1 + (9–6)^4 7777 = (4–7)^1 + (6–8)^2 + (9–3)^5 7777 = (4–7)^1 + (8–6)^2 + (9–3)^5
Exactly 4 negative and 12 positive tautonymic numbers can be retrieved from the list :
–72722, –36364, –31312, –19194
131316, 20204, 23232, 25254, 28284, 31315, 34344, 36364, 39392, 656516, 68688, 72722
Two of them (see underscored) are used in Zager and Evans' song 'In the Year 2525'.
There is one value having the record number of distinct solutions namely... 1 itself !!
1544
Smallest : 1 = (1–2)^3 + (4–5)^6 + (8–7)^9
Largest : 1 = (9–8)^7 + (6–5)^4 + (2–3)^1
We can distinguish 106 pandigital expressions with distinct solutions.
0106
Smallest : 0 = (1–3)^8 + (2–6)^4 + (5–7)^9
Largest : 0 = (9–8)^7 + (6–5)^3 + (2–4)^1
87 different distinct solutions can be found for the various different values.
( Note : d.s. = total distinct solutions ).
1 - 3556 values have 2 d.s. 2 - 2882 values have 4 d.s. 3 - 1124 values have 1 d.s. 4 - 1054 values have 8 d.s. 5 - 436 values have 6 d.s. 6 - 237 values have 12 d.s. 7 - 197 values have 16 d.s. 8 - 174 values have 10 d.s. 9 - 93 values have 3 d.s. 10 - 70 values have 20 d.s. 11 - 68 values have 24 d.s. 12 - 63 values have 5 d.s. 13 - 47 values have 14 d.s. 14 - 44 values have 18 d.s. 15 - 43 values have 32 d.s. 16 - 29 values have 28 d.s. 17 - 22 values have 9 d.s. 18 - 18 values have 36 d.s. 19 - 15 values have 7 d.s. 20 - 15 values have 22 d.s. 21 - 14 values have 11 d.s. 22 - 13 values have 40 d.s. 23 - 12 values have 44 d.s. 24 - 11 values have 26 d.s. 25 - 11 values have 38 d.s. 26 - 10 values have 30 d.s. 27 - 9 values have 13 d.s. 28 - 9 values have 34 d.s. 29 - 9 values have 48 d.s. 30 - 9 values have 64 d.s. 31 - 8 values have 15 d.s. 32 - 8 values have 21 d.s. 33 - 7 values have 46 d.s. 34 - 6 values have 35 d.s. 35 - 6 values have 42 d.s. 36 - 6 values have 60 d.s. 37 - 5 values have 17 d.s. 38 - 5 values have 52 d.s. 39 - 5 values have 58 d.s. 40 - 4 values have 50 d.s. (–243, –126, 72, 88) 41 - 4 values have 56 d.s. (–25, 31, 46658, 262144) 42 - 4 values have 68 d.s. (10, 23, 33, 1296) 43 - 4 values have 72 d.s. (–27, 264, 6561, 65536) 44 - 4 values have 76 d.s. (–4, 29, 129, 273) 45 - 3 values have 49 d.s. (28, 84, 144) 46 - 3 values have 54 d.s. (–125, 15, 35) 47 - 3 values have 92 d.s. (21, 38, 321) 48 - 2 values have 29 d.s. (94, 98) 49 - 2 values have 78 d.s. (13, 69) 50 - 2 values have 79 d.s. (–6, 2) 51 - 2 values have 84 d.s. (25, 127) 52 - 2 values have 90 d.s. (–5, 261) 53 - 2 values have 94 d.s. (–510, 262146) 54 - 2 values have 106 d.s. (0, 514) 55 - 1 value has 25 d.s. (52) 56 - 1 value has 31 d.s. (228) 57 - 1 value has 39 d.s. (–12) 58 - 1 value has 41 d.s. (26) 59 - 1 value has 47 d.s. (12) 60 - 1 value has 53 d.s. (218) 61 - 1 value has 59 d.s. (114) 62 - 1 value has 62 d.s. (–262142) 63 - 1 value has 66 d.s. (253) 64 - 1 value has 74 d.s. (36) 65 - 1 value has 82 d.s. (22) 66 - 1 value has 91 d.s. (–2) 67 - 1 value has 102 d.s. (8) 68 - 1 value has 104 d.s. (27) 69 - 1 value has 108 d.s. (11) 70 - 1 value has 120 d.s. (4096) 71 - 1 value has 128 d.s. (4098) 72 - 1 value has 132 d.s. (–3) 73 - 1 value has 138 d.s. (81) 74 - 1 value has 150 d.s. (9) 75 - 1 value has 168 d.s. (5) 76 - 1 value has 170 d.s. (16) 77 - 1 value has 171 d.s. (6) 78 - 1 value has 176 d.s. (64) 79 - 1 value has 177 d.s. (256) 80 - 1 value has 180 d.s. (4) 81 - 1 value has 181 d.s. (66) 82 - 1 value has 182 d.s. (7) 83 - 1 value has 189 d.s. (258) 84 - 1 value has 202 d.s. (18) 85 - 1 value has 348 d.s. (3) 86 - 1 value has 350 d.s. (–1) 87 - 1 value has 544 d.s. (1)
Variation #12 : the equation A^B/C + D^E/F + G^H/I [Jerry Levy's suggestion]
1428 different values - 1492 distinct solutions (see subscript values)
Values range from 40 to 134311552 but not consecutively, there are gaps.
Samples
40 = 3^5/9 + 6^1/8 + 7^2/4
134311552 = 4^5/2 + 6^7/3 + 8^9/1
The smallest prime is 317 (out of 168).
The largest prime is 67202801.
Samples
317 = 2^7/1 + 3^5/9 + 6^4/8
67202801 = 5^4/1 + 6^7/3 + 8^9/2
Almost all values (1364) have just 1 distinct solution.
Only 64 values show 2 distinct solutions.
6 values turn out to be palindromic.
7871, 21121, 126211, 331331, 376731 and 397931.
Only the first one is prime as well.
Semiprime 37673 equals the product of two palprimes nl. 101 * 373 .
Exactly 2 tautonymic numbers can be extracted from the list :
4343 = 2^5/8 + 3^7/9 + 4^6/1
875875 = 4^7/1 + 6^8/2 + 9^5/3
Variation #13 : the equation A^(B/C) + D^(E/F) + G^(H/I) [Jerry Levy's suggestion]
259 different values - 468 distinct solutions (see subscript values)
Values range from 30 to 134217881 but not consecutively, there are gaps.
The smallest prime is 53 (out of 26).
The largest prime is 5764907.
Samples
53 = 1^(9/7) + 3^(6/2) + 5^(8/4)
5764907 = 5^(4/2) + 7^(8/1) + 9^(6/3)
10 palindromes can be perceived :
77, 131, 242, 282, 353, 404, 545, 707, 969, 33033
The sixth one [ 404 ] is not a HTML error !
7 different distinct solutions can be found for the various different values.
( Note : d.s. = total distinct solutions ).
1 - 135 values have 1 d.s. 2 - 96 values have 2 d.s. 3 - 14 values have 4 d.s. 4 - 8 values have 6 d.s. 5 - 3 values have 8 d.s. 6 - 2 values have 3 d.s. 7 - 1 value has 7 d.s.
Note that 1 nice value shows a unique property of having exactly 7 distinct solutions.
3697
Samples
369 = 1^(2/6) + 5^(8/4) + 7^(9/3)
369 = 1^(3/9) + 5^(8/4) + 7^(6/2)
369 = 1^(6/2) + 5^(8/4) + 7^(9/3)
369 = 1^(6/8) + 5^(4/2) + 7^(9/3)
369 = 1^(8/6) + 5^(4/2) + 7^(9/3)
369 = 1^(9/3) + 5^(8/4) + 7^(6/2)
369 = 2^(7/1) + 5^(8/4) + 6^(9/3)
Variation #14 : the equation (A+B)*C + (D–E)/F + G^H*I
[Terry Trotter's "all five operations" suggestion]
13253 different values - 45360 distinct solutions (see subscript values)
Values range from 24 to 939524151 but not consecutively, there are gaps.
Let me quote Terry himself about the expression (A + B)*C + (D – E)/F + G^H*I :
" I have designed this new variant for our Levy Expressions project -- #14.
Since I did add it to my webpage, I thought you might like to know about it, at least.
Note that all the previous expressions used but 2 operations in each triad.
Now I'm using all five operations, based on the following logic :
We (or at least I did) teach in school math the following hierarchy of operations :
1. addition
2. subtraction
3. multiplication
4. division
5. exponentiation
This goes from easy to 'hard', for most kids. At least, we teach them in that order.
Plus when we study logarithms, we show that to multiply two numbers, we add the logs;
when we divide two numbers, we subtract their logs; and when we need to raise a number
to a power, i.e. exponentiate, we multiply the base's log by the exponent. Hence,
I used #1 & 3 with A, B & C; used #2 & 4 with D, E & F; and used #3 & 5 with G, H & I.
Hey, it may be corny, but I'm trying to teach kids to like math & look at it in a new way. :>)
And it does review the order of operations with a novel approach. Hope you like it.
"
The first thing that catches my attention is that this variation produced a record number of
different values nl. 13253. This can makes room for lots of discoveries I hope.
This year 2003 for instance can be expressed in 4 distinct ways :
2003 = (2+5)*8 + (7–4)/1 + 6^3*9
2003 = (2+7)*6 + (9–4)/1 + 3^5*8
2003 = (4+7)*6 + (2–9)/1 + 3^5*8
2003 = (6+7)*4 + (9–2)/1 + 3^5*8
Values 66, 666 and 6666 are part of the lot !
Samples
66= (2+5)*8 + (7–3)/4 + 1^6*9
666 = (4+7)*8 + (5–3)/1 + 2^6*9
6666 = (6+7)*8 + (5–2)/3 + 9^4*1
The smallest prime is 29 (out of 1198).
The largest prime is 939524147.
Samples
29 = (3+7)*2 + (9–4)/5 + 1^6*8
939524147 = (4+6)*5 + (3–1)/2 + 8^9*7
152 palindromes can be detected.
The largest one is 327723 = (6+7)*3 + (9–1)/2 + 4^8*5
This variation has also the record largest tautonymic number i.e. 191319132 !
1913_1913 = (1+6)*5 + (8–2)/3 + 9^7*4
1913_1913 = (2+5)*6 + (3–8)/1 + 9^7*4
Other smaller samples
1181181 = (5+7)*2 + (4–8)/1 + 3^9*6
1771771 = (6+7)*2 + (8–4)/1 + 9^5*3
4134131 = (3+6)*8 + (2–4)/1 + 9^5*7
8398393 = (2+4)*5 + (9–1)/8 + 6^7*3 = (2+4)*5 + (9–8)/1 + 6^7*3 = (5+8)*2 + (9–4)/1 + 6^7*3
More Topics
[ August 31, 2003 ]
Pandigitals divisible by 5-digit palprimes
by Jean Claude Rosa (email)
Jean Claude continued "WONplate 114 continued..." and researched the case of
pandigitals divisible by a palindromic prime or palprime for short and more in particular
by a 5-digit palprime (in total there are 93 - from 10301 to 98689).
24 palprimes are concerned in 27 solutions. No results exist for the 'not listed' palprimes !
number of solutions 1 for the following 5-digit palprimes :
12421, 12721, 15451, 16661, 30203, 30403, 30803,
32323, 36563, 37573, 38783, 71317, 73637, 76367,
76667, 77477, 90709, 93239, 93739, 97379, 97579
smallest palprime: 1037625498/12421 = 83538
largest palprime: 8713609542/97579 = 89298
number of solutions 2 for the following 5-digit palprimes :
14741, 19891, 34543
7829461035/14741 = 531135
8106739245/14741 = 549945
1253849076/19891 = 63036
1432689057/19891 = 72027
3140269587/34543 = 90909
5604981723/34543 = 162261
There are some curious palindromes expressable in two ways.
1037625498/12421 = 83538 = 1290745638/15451
1670492835/30403 = 54945 = 1692470835/30803
3504892617/36563 = 95859 = 8695274031/90709
2938451607/32323 = 90909 = 3140269587/34543
And of course the obligatory Number of the Beast in
8257091634/16661 = 495594
3709456128/76667 = 48384
Perhaps someone would like to extend the ninedigital variant of this same exercise.
[ August 25, 2003 ]
WONplate 114 continued...
by Jean Claude Rosa (email)
WONPlate 114 discusses 'Palindromic quotients through pandigital divisions'
and only the denominators 2 to 9 were considered. Jean Claude extended the topic
and investigated the pandigitals divided by palindromic primes limiting himself to 11
and the fifteen threedigit palprimes from 101 to 929.
Divisor 11 gave 14 solutions.
divisor 11
number of solutions: 14
smallest: 2063784591/11 = 187616781
largest: 8459120637/11 = 769010967
This number of solutions (#14) already predicts how many of the fifteen palprimes will yield results !
divisor 101
number of solutions: nihil
The fourteen remaining palprimes give the following data
divisor 131 number of solutions: 4 smallest: 1023658497/131 = 7814187 largest: 6213785094/131 = 47433474 divisor 151 number of solutions: 3 smallest: 1374086259/151 = 9099909 largest: 6509781234/151 = 43111134 divisor 181 number of solutions: 3 smallest: 1078324695/181 = 5957595 largest: 1647083529/181 = 9099909 divisor 191 number of solutions: 7 smallest: 1304985726/191 = 6832386 largest: 9781342065/191 = 51211215 divisor 313 number of solutions: 4 smallest: 1078423659/313 = 3445443 largest: 2914386507/313 = 9311139 divisor 353 number of solutions: 3 smallest: 2108749635/353 = 5973795 largest: 4196750283/353 = 11888811 divisor 373 number of solutions: 6 smallest: 1028947356/373 = 2758572 largest: 7219560843/373 = 19355391 divisor 383 number of solutions: 3 smallest: 1263487509/383 = 3298923 largest: 2106478935/383 = 5499945 divisor 727 number of solutions: 4 smallest: 4069713285/727 = 5597955 largest: 6870549123/727 = 9450549 divisor 757 number of solutions: 5 smallest: 1982705634/757 = 2619162 largest: 5481760239/757 = 7241427 divisor 787 number of solutions: 4 smallest: 2389570461/787 = 3036303 largest: 7129046583/787 = 9058509 divisor 797 number of solutions: 4 smallest: 1930526874/797 = 2422242 largest: 5360841972/797 = 6726276 divisor 919 number of solutions: 6 smallest: 1587362049/919 = 1727271 largest: 6971402583/919 = 7585857 divisor 929 number of solutions: 5 smallest: 1765082349/929 = 1899981 largest: 8095471362/929 = 8714178
In total we have 61 solutions, a nice prime !
There are some curious palindromes expressable in two ways.
1746082539/919 = 1899981 = 1765082349/929
1374086259/151 = 9099909 = 1647083529/181
As always the Number of the Beast lurks around the corner
(two corners to be more precise!).
5048937162/757 = 6669666
Perhaps someone would like to extend the ninedigital variant of this same exercise
and see if there's anything interesting going on there, like for instance
the following unique nine- & pandigital equation :
832591674/181 = 4599954 = 1439785602/313
ps. the Number of the Ninedigital Beast houses here :
598231674/131 = 4566654
[ August 20, 2003 ]
Pandigital divisions equal to ratio N/D
Statistics : abcd = N/D * efghi or abcde = N/D * fghij
Terry Trotter (email) inspired by Puzzle 121 from Michael Winckler's site (Puzzle No. 121),
expanded the topic by investigating more ratios N/D and looking not only at ninedigit numbers
e.g. 5823 / 17469 = 1 / 3
e.g. 9876 / 12345 = 4 / 5
but also at the 10-digit pandigital version.
e.g. 13485 / 26970 = 1 / 2
e.g. 71496 / 20853 = 7 / 24
The ninedigit version with ratios 1/2, 1/3 up to 1/9 are already presented in WONplate 107
Now Terry has data for all the fractions in the range of 0 < N < D < 20
for both 9-digit & 10-digit work.
For this purpose he asked and got a ubasic program written by Carlos Rivera.
The code is short and straightforward so I'll list it here (some minor modifications from myself pdg).
(Change in line 20 the values N1 and N2 for other fractions)
``` 10 'trotter.ub
20 B1=1000:B2=99999:N1=4:N2=5:Cc=0
30 FF=6469693230 : 'use FF=3234846615 for 9-digit version
35 ' FF=1:for I=0 to 9:FF*=prm(I+1):next I : 'use for I=1 to 9 for 9-digit version
40 for B=B1 to B2:if B@N2<>0 then goto 70
50 A=B*N1\N2:Z=A*10^alen(B)+B
60 gosub *TEST:if T=1 then inc Cc:print Cc,A;"=";N1;"/";N2;"*";B
70 next B
80 end
90 *TEST:T=0:F=1:L=alen(Z)
100 for I=1 to L:D=val(mid(str(Z),I+1,1)):P=prm(D+1)
110 if F@P=0 then cancel for:return
120 F*=P:next I
130 if F=FF then T=1
140 return
```
and finally the statistics, the program output :
Part 1.
All possible ninedigit solutions (numerator > 1) and (denominator < 10)
2 / 5 = 6894 / 17235 2 / 5 = 8694 / 21735 2 / 5 = 9486 / 23715 3 solutions 4 / 5 = 9876 / 12345 1 unique and beautiful solution 2 / 7 = 3654 / 12789 2 / 7 = 3674 / 12859 2 / 7 = 5342 / 18697 2 / 7 = 7418 / 25963 2 / 7 = 9786 / 34251 2 / 7 = 9862 / 34517 6 solutions 2 / 9 = 3924 / 17658 2 / 9 = 7596 / 34182 2 solutions
(numerator >= 1) and (10 < denominator < 20)
2 / 11 = 4716 / 25938 2 / 11 = 9432 / 51876 2 / 11 = 9486 / 52173 3 solutions 4 / 11 = 6492 / 17853 4 / 11 = 7836 / 21549 2 solutions 5 / 11 = 9765 / 21483 1 unique solution 1 / 12 = 3816 / 45792 1 / 12 = 6129 / 73548 1 / 12 = 7461 / 89532 1 / 12 = 7632 / 91584 4 solutions 5 / 12 = 8235 / 19764 1 unique solution 1 / 13 = 5184 / 67392 1 / 13 = 6273 / 81549 1 / 13 = 7281 / 94653 3 solutions 2 / 13 = 2538 / 16497 2 / 13 = 3876 / 25194 2 / 13 = 3918 / 25467 2 / 13 = 4518 / 29367 2 / 13 = 6972 / 45318 2 / 13 = 7896 / 51324 2 / 13 = 8196 / 53274 7 solutions 5 / 13 = 4765 / 12389 5 / 13 = 8345 / 21697 5 / 13 = 8365 / 21749 3 solutions 1 / 14 = 1839 / 25746 1 / 14 = 1956 / 27384 my birthyear! - pdg 1 / 14 = 2967 / 41538 1 / 14 = 3297 / 46158 1 / 14 = 3678 / 51492 1 / 14 = 3912 / 54768 1 / 14 = 4398 / 61572 1 / 14 = 4713 / 65982 8 solutions 5 / 14 = 4635 / 12978 1 unique solution 1 / 15 = 1863 / 27945 1 / 15 = 6183 / 92745 2 solutions 8 / 15 = 9432 / 17685 1 unique solution 1 / 16 = 2871 / 45936 1 / 16 = 4581 / 73296 1 / 16 = 6147 / 98352 3 solutions 3 / 16 = 3294 / 17568 3 / 16 = 3672 / 19584 3 / 16 = 5967 / 31824 3 solutions 5 / 16 = 9765 / 31248 1 unique solution 7 / 16 = 5796 / 13248 7 / 16 = 9387 / 21456 2 solutions 11 / 16 = 9867 / 14352 1 unique solution 1 / 17 = 1579 / 26843 1 / 17 = 1679 / 28543 1 / 17 = 1738 / 29546 1 / 17 = 2174 / 36958 1 / 17 = 2689 / 45713 1 / 17 = 2693 / 45781 1 / 17 = 3217 / 54689 1 / 17 = 3478 / 59126 1 / 17 = 3821 / 64957 1 / 17 = 3841 / 65297 1 / 17 = 3952 / 67184 1 / 17 = 3954 / 67218 1 / 17 = 4519 / 76823 1 / 17 = 4523 / 76891 1 / 17 = 4596 / 78132 1 / 17 = 4619 / 78523 1 / 17 = 4623 / 78591 1 / 17 = 4796 / 81532 1 / 17 = 4916 / 83572 1 / 17 = 4921 / 83657 1 / 17 = 5261 / 89437 1 / 17 = 5263 / 89471 1 / 17 = 5273 / 89641 1 / 17 = 5378 / 91426 1 / 17 = 5461 / 92837 1 / 17 = 5463 / 92871 1 / 17 = 5478 / 93126 27 solutions 2 / 17 = 8514 / 72369 1 unique solution 3 / 17 = 5184 / 29376 1 unique solution 4 / 17 = 4536 / 19278 4 / 17 = 7428 / 31569 2 solutions 5 / 17 = 6435 / 21879 5 / 17 = 8145 / 27693 2 solutions 1 / 18 = 1593 / 28674 1 unique solution 7 / 18 = 8379 / 21546 1 unique solution 1 / 19 = 2736 / 51984 1 / 19 = 4293 / 81567 2 solutions 2 / 19 = 5136 / 48792 2 / 19 = 5238 / 49761 2 / 19 = 7254 / 68913 2 / 19 = 9132 / 86754 4 solutions 3 / 19 = 4671 / 29583 1 unique solution 4 / 19 = 3492 / 16587 1 unique solution 5 / 19 = 9165 / 34827 1 unique solution 6 / 19 = 4968 / 15732 6 / 19 = 8694 / 27531 2 solutions 7 / 19 = 7938 / 21546 1 unique solution 8 / 19 = 5368 / 12749 8 / 19 = 5864 / 13927 8 / 19 = 5872 / 13946 3 solutions
Part 2.
(numerator >= 1) and (denominator < 20)
Listing all possible pandigital solutions would bring us too far.
Instead I opt for displaying only the 20 unique pandigital solutions.
With the aid of the above ubasic program one should easily find all the other solutions.
1 / 7 = 14076 / 98532 5 / 9 = 15930 / 28674 8 / 9 = 47016 / 52893 6 / 11 = 27486 / 50391 7 / 12 = 17829 / 30564 7 / 13 = 32571 / 60489 14 / 15 = 86310 / 92475 5 / 16 = 23490 / 75168 6 / 17 = 19872 / 56304 8 / 17 = 46152 / 98073 12 / 17 = 51084 / 72369 15 / 17 = 46710 / 52938 16 / 17 = 57312 / 60894 11 / 18 = 48312 / 79056 17 / 18 = 19584 / 20736 2 / 19 = 10248 / 97356 4 / 19 = 17460 / 82935 6 / 19 = 25704 / 81396 13 / 19 = 45981 / 67203 14 / 19 = 49518 / 67203
The top 5 pandigital fractions
4 / 5 78 solutions
1 / 2 48 solutions
10 / 17 27 solutions
5 / 13 20 solutions
2 / 7 19 solutions
Part 3.
Arriving at this point, it is time to relax from the serious work.
As there is no fractional limit (?) one can investigate beyond the denominator
limit that Terry imposed upon himself and go beyond 20 to discover more curios and trivia.
Again, feel free to use the above ubasic program.
13 and 666 are well-known numbers for their negative connotation
(the unlucky number and the number of the beast).
There exist now a single fraction such that brings these two numbers together :
13 / 666 = 1287 / 65934
ps. 65934 – 1287 = 64647 almost a palindrome, ain't I unlucky ?!
Also no such luck for the pandigital version with that same fraction.
The number of the beast must like this number 65934 as I found
the following beastly combinatorial equations.
666 / 13 = 65934 / 1287 666 / 18 = 65934 / 1782 666 / 22 = 65934 / 2178 666 / 29 = 65934 / 2871 666 / 72 = 65934 / 7128 666 / 79 = 65934 / 7821 666 / 83 = 65934 / 8217 666 / 88 = 65934 / 8712 666 / 122 = 65934 / 12078 666 / 130 = 65934 / 12870 666 / 172 = 65934 / 17028 666 / 180 = 65934 / 17820 666 / 213 = 65934 / 21087 666 / 220 = 65934 / 21780 666 / 283 = 65934 / 28017 666 / 290 = 65934 / 28710 666 / 718 = 65934 / 71082 666 / 720 = 65934 / 71280 666 / 788 = 65934 / 78012 666 / 790 = 65934 / 78210 666 / 829 = 65934 / 82071 666 / 830 = 65934 / 82170 666 / 879 = 65934 / 87021 666 / 880 = 65934 / 87120
Other numbers than 666 can be linked with "other than 65934" numerators.
Do there exist such numbers with more combinatorial solutions than the above 8/16 ?
ps. Add the 8 denominators (13+18+...) from the ninedigital version together.
An interesting palindrome arises, isn't it ! See WONplate 104
Part 4.
Ninedigital Fractions equal to Pandigital Fractions
Some 'unique' solutions.
5 / 16 = 9765 / 31248 = 23490 / 75168
4 / 19 = 3492 / 16587 = 17460 / 82935
[ December 25, 2001 ]
Ninedigital Smith numbers
Smith numbers are composites such that
'the sum of their digits' equal 'the sum of the digits of their prime factors'.
Shyam Sunder Gupta, editor of the site Number Recreations
investigated the ninedigital versions and found that
the smallest solution is 123456879 = 3 * 3 * 3 * 3 * 3 * 3 * 7 * 13 * 1861.
since 1 + 2 + 3 + 4 + 5 + 6 + 8 + 7 + 9 = 45 = 3 + 3 + 3 + 3 + 3 + 3 + 7 + 1 + 3 + 1 + 8 + 6 + 1
the largest solution is 987653214 = 2 * 3 * 3 * 7151 * 7673.
since 9 + 8 + 7 + 6 + 5 + 3 + 2 + 1 + 4 = 45 = 2 + 3 + 3 + 7 + 1 + 5 + 1 + 7 + 6 + 7 + 3
Source : Prime Curios!
Ninedigital see 123456879 and 987653214
Pandigital see 1023465798 and ?? Can You Find ??
[ February 10, 2001 ]
Pandigital pointing to Ninedigital
The 1234567890th palindrome is 234567891198765432
This last palindrome is a ninedigital number 234567891 combined with its reversal 198765432.
Eric Schmidt developed a nice Java Applet where you can enter any
positive integer N and after pressing ENTER calculates the Nth palindrome.
Positive Integer Palindromes
[ January 13, 2001 ]
Amazing Nine Digits Property - from sci.math by Preon
(a/bc) + (d/ef) + (g/hi) = 1
where a through i are the unique digits 1 through 9.
bc, ef and hi are the concatenations (not the products) of b with c, e with f and h with i.
The puzzle seems to have only one solution... as I discovered with a search !
The solution is very easy to search for, Preon tells. It is
(9/12) + (7/68) + (5/34) = 1
" The solution is unique as my program revealed, took maybe 10 minutes
to write the code and 1 minute to run and display the only answer."
Preon wonders if someone has a proof or explanation
cause he hasn't a clue why this amazing property should be true...
Paul E. Triulzi, a senior IT specialist (email), noted that the equation
from Preon has some interesting symmetry [ August 31, 2001 ].
1. The numerators are all odd and sequential.
2. The numerator and denominator numbers are sequential
(9,1,2 wraps around if 0 is not counted).
Preon investigated also the following pandigital variant
but found only solutions with the zero as a nonsignificant leading zero !
(a/bc) + (d/ef) + (g/hi) = j
(3÷04) + (6÷78) + (9÷52) = 1 (3÷48) + (7÷16) + (9÷02) = 5 (4÷28) + (5÷63) + (7÷09) = 1 (4÷07) + (5÷28) + (9÷36) = 1 (4÷28) + (5÷07) + (9÷63) = 1 (4÷06) + (7÷39) + (8÷52) = 1 (4÷36) + (7÷18) + (9÷02) = 5 (5÷02) + (6÷14) + (7÷98) = 3 (5÷38) + (6÷04) + (7÷19) = 2 (5÷13) + (6÷04) + (9÷78) = 2 (5÷09) + (7÷63) + (8÷24) = 1 (5÷36) + (7÷04) + (9÷81) = 2
Here are some smallest solutions such that...
5986 = 2 x 41 x 73
the digits of n and the prime factorization of n
are from the set 1 to 9 with each digit occurring exactly one time.
28651 = 7 x 4093
the digits of n and the prime factorization of n
are from the pandigital set 0 to 9 with each digit occurring exactly one time.
14368485 = 3 x 5 x 17 x 29 x 29 x 67
the digits of n and the prime factorization of n
are from the set 1 to 9 with each digit occurring exactly two times.
40578660 = 2 x 2 x 3 x 3 x 5 x 17 x 89 x 149
the digits of n and the prime factorization of n
are from the pandigital set 0 to 9 with each digit occurring exactly two times.
It has me wondering if such a composite number exists
in which each digit appears thrice and only thrice !
Special thanks goes to G. L. Honaker, Jr. for providing the original idea !
Prime Curios! sources : 5986 28651 14368485 40578660
[ August 13, 2000 ]
Friedman numbers
Problem of the month (August 2000) from Erich Friedman is very interesting
It investigates positive integers which can be written in some non-trivial way using its own digits,
together with the symbols + - x / ^ ( ) and concatenation.
The following subquestion is posed :
You might have fun confirming that 123456789 and 987654321 are Friedman numbers.
Solutions from Mike Reid and Philippe Fondanaiche
123456789 = ((86 + 2 * 7)5 - 91) / 34
and
987654321 = (8 * (97 + 6/2)5 + 1) / 34
Amazing Number Facts
Amazing Number Facts : Nine Digits 17469 divided by 5823 is 3. Every digit except 0 appears once and only once. [Kordemsky] 13485 divided by 2697 is 5. Idem. The prime 3187 divides 25496. Note all nine digits are used. 394521678 The sum of the prime numbers from 2 upto 92857 is a nine digits number. [Honaker] PI(2543568463) = 123456789. 5897230146 The pandigital sum of the first 32423 prime numbers. [Honaker] 12 * 34567 + 89 is prime. [Honaker]
Difficult Digits
Here is a pandigital puzzle I found at address http://pegasus.cc.ucf.edu/~mathed/digits.html :
Arrange the digits 1 2 3 4 5 6 7 8 9 0 using only one operation sign
so that they will equal 100. Good Luck!
As I don't know the answer(s) myself yet I'd appreciate if someone could send them to me!
On [ Januari 20, 2001 ] I received the following solution from Eric Poindessault (email)
He used as asked only operation sign namely the minus sign ¬
1 – – 2 – – 3 – – 4 – – 5 6 7 – – 8 – – 90 = 100
Thanks Eric, well done!
The Nine Digits staircase
Gérard Villemin maintains an exciting maths website (in the French language)
and some of the pages deals also with Nine Digits and Pandigital numbers :
Nombres Pandigitaux
Arrange the nine digits in steps and rises (paliers et marches [Fr.]) of length 3
such that the sums are always... 13 !
931 13
8
13 472
5
13 6
```
```
Contributions
Jean Claude Rosa (email) - go to topic
Terry Trotter (email) - go to topic
Shyam Sunder Gupta (email) - go to topic
Eric Pointdessault (email) - go to topic
Paul E. Triulzi (email) - go to topic
```
```
(© All rights reserved ) - Last modified : October 17, 2021.
Patrick De Geest - Belgium - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com | 16,484 | 40,616 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2021-49 | latest | en | 0.759131 |
https://www.sangakoo.com/en/unit/variance-and-standard-deviation | 1,720,986,071,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514638.53/warc/CC-MAIN-20240714185510-20240714215510-00786.warc.gz | 884,507,144 | 7,419 | # Variance and Standard deviation
## Variance
The variance of some data is the arithmetical mean of the square of the absolute deviations. It is symbolized as $$\sigma ^2$$ and it is calculated by applying the formula $$\sigma^2=\displaystyle \frac{\displaystyle\sum_{i=1}^N (x_i-\overline{x})^2}{N}=\frac{(x_1-\overline{x})^2+(x_2-\overline{x})^2+\ldots+(x_N-\overline{x})^2}{N}$$$which it is possible to simplify as: $$\sigma^2=\displaystyle \frac{\displaystyle \sum_{i=1}^N x_i^2}{N}-\overline{x}^2=\frac{x_1^2+x_2^2+\ldots+x_N^2}{N}-\overline{x}^2$$$
Same as with the average, it is not always possible to find the variance, and it is a parameter that is very sensitive to the extreme scorings. We can see that, with the deviation being squared, the variance cannot have the same units as the data.
Comparing with the same type of information, a high variance means that the data is more dispersed. And a low value of the variance indicates that the values are in general closer to the average.
A value of the variance equal to zero means that all the values are equal, and therefore they are also equal to the arithmetical average.
In a basketball match, we have the following points for the players of a team: $$0, 2, 4, 5, 8, 10, 10, 15, 38$$. Calculate the variance of the scorings of the players of the team.
Applying the formula $$\overline{x}=\displaystyle \frac{0+2+4+5+8+10+10+15+38}{9}=\frac{92}{9}=10.22$$ the average is obtained. | 435 | 1,452 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.75 | 5 | CC-MAIN-2024-30 | latest | en | 0.862167 |
https://www.physicsforums.com/threads/spring-equilibrium-problem.310735/ | 1,685,898,160,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224650201.19/warc/CC-MAIN-20230604161111-20230604191111-00272.warc.gz | 1,032,505,576 | 14,817 | # Spring equilibrium problem
• starhallie
## Homework Statement
A 2kg object is suspended from a vertical spring that has a constant of 180N/m.
a) How far does the spring stretch from the unstrained length?
b) If the object is now pulled downward an additional distance of 5cm. What external force was required to do so?
c) When the object is released from rest, it begins to move upwards. Find the maximum speed that the object reaches and the maximum height above the release point at which the object releases direction.
Fspring= kx
## The Attempt at a Solution
I would be grateful if someone could check my answers to parts a & b and possibly steer me in the right direction on part c?
a) Fspring= kx
F=ma
ma=kx
x= ma/k
=(2kg)(9.8 m/s2)/(180 N/m)
= 0.1089m
b) Fspring= kx
=(180 N/m)(0.05cm)
= 9 N
In the case b, find the elastic potential energy stored in the spring.
After releasing when it crosses the position in case a, it will have the maximum kinetic energy and gravitational potential energy. Apply the conservation of energy to find the maximum velocity.
This is what I got so far...
PEspring= 1/2kw2= 1/2(180 N/m)(0.05m)= 0.225 J
... but I'm having trouble understanding the rest.
At a position total energy = 1/2*m*v^2 + mgh
Find vmax
Thank you very much for your help! | 348 | 1,300 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.625 | 4 | CC-MAIN-2023-23 | latest | en | 0.900628 |
http://windowssecrets.com/forums/showthread.php/99728-Extract-Numbers-from-Text-%28Excel-2002%29 | 1,484,631,575,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560279468.17/warc/CC-MAIN-20170116095119-00013-ip-10-171-10-70.ec2.internal.warc.gz | 307,186,201 | 14,246 | # Thread: Extract Numbers from Text (Excel 2002)
1. ## Extract Numbers from Text (Excel 2002)
Hi!
I'm wondering if there is a formula in Excel (or better yet, code in Visual Basic) that will extract a number from a line of text? For example,
the following text is in cell A1:
COM 235643 Sales Order
In most cases the number is in the same spot, therefore I could use the mid formula... however, there is always an exception to the rule, so I thought I'd ask if there was any other kind of formula that could locate the number and extract it into a cell by itself. Also note that in most cases the number is 6 digits, however at times it can be 4 digits... again an exception to the rule. Any ideas would be greatly appreciated.
Thanks!
Lana
2. ## Re: Extract Numbers from Text (Excel 2002)
You could create a formula or a macro, but the fastest way may be to make a copy of the column and run the Data | Text-to-Columns wizard on it using the space delimiter.
3. ## Re: Extract Numbers from Text (Excel 2002)
The following function will extract the first number (all digits) it encounters.
Function getNums(strIn As String) As Double
Dim i As Integer, outNum As Double
outNum = 0
For i = 1 To Len(strIn)
If IsNumeric(Mid(strIn, i, 1)) Then
outNum = Val(Mid(strIn, i, 99))
Exit For
End If
Next
getNums = outNum
End Function
4. ## Re: Extract Numbers from Text (Excel 2002)
<P ID="edit" class=small>(Edited by JohnBF on 08-Jun-07 08:37. sign option choked on spaces)</P>Nice. Here's an extension that will optionally look for a leading negative sign or open paren:
Function getNums(strIn As String, Optional boolNeg As Boolean = False) As Double
' returns the first sequence of numbers within a cell
' spaces, '\$' and comma signs are parsed out, decimal separators are included
' optional " ,TRUE" argument looks for preceding negative or open paren sign
Dim intC As Integer, strLeadChar As String
getNums = 0
For intC = 1 To Len(strIn)
If IsNumeric(Mid(strIn, intC, 1)) Then
getNums = Val(Mid(strIn, intC))
Exit For
End If
Next
If boolNeg = True Then
strLeadChar = Mid(strIn, InStr(1, strIn, Left(getNums, 1), vbTextCompare) - 1, 1)
If strLeadChar = "-" Or strLeadChar = "(" Then getNums = "-" & getNums
End If
End Function
5. ## Re: Extract Numbers from Text (Excel 2002)
When you extract a number from text spaces are ignored. Therefore, another trick worth knowing is to substitute a single space for a number of spaces.
In cell B1, you could also type the following formula :-
=VALUE(MID(SUBSTITUTE(A1," "," "),SEARCH(" ",SUBSTITUTE(A1," "," ")),10))
Regards
Robert
#### Posting Permissions
• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
• | 735 | 2,736 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2017-04 | longest | en | 0.797333 |
http://winaudit.org/guides/sampling-distribution/standard-error-distribution-sample-means-formula.html | 1,534,488,877,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221211933.43/warc/CC-MAIN-20180817065045-20180817085045-00493.warc.gz | 430,135,319 | 5,954 | Home > sampling distribution > standard error distribution sample means formula
# Standard Error Distribution Sample Means Formula
error of the mean State the central limit theorem The sampling distribution of the mean was defined in the section introducing sampling distributions. This section reviews some important properties of the sampling distribution of the mean introduced in the demonstrations in this chapter. Mean sampling distribution of the sample mean example The mean of the sampling distribution of the mean is the mean of the population from sampling distribution of the mean examples which the scores were sampled. Therefore, if a population has a mean μ, then the mean of the sampling distribution of the mean is sampling distribution of the mean calculator also μ. The symbol μM is used to refer to the mean of the sampling distribution of the mean. Therefore, the formula for the mean of the sampling distribution of the mean can be written as: μM = μ the standard error of the sampling distribution when we know the population standard deviation Variance The variance of the sampling distribution of the mean is computed as follows: That is, the variance of the sampling distribution of the mean is the population variance divided by N, the sample size (the number of scores used to compute a mean). Thus, the larger the sample size, the smaller the variance of the sampling distribution of the mean. (optional) This expression can be derived very easily from the variance sum law. Let's begin by computing
## Sampling Distribution Of The Mean Definition
the variance of the sampling distribution of the sum of three numbers sampled from a population with variance σ2. The variance of the sum would be σ2 + σ2 + σ2. For N numbers, the variance would be Nσ2. Since the mean is 1/N times the sum, the variance of the sampling distribution of the mean would be 1/N2 times the variance of the sum, which equals σ2/N. The standard error of the mean is the standard deviation of the sampling distribution of the mean. It is therefore the square root of the variance of the sampling distribution of the mean and can be written as: The standard error is represented by a σ because it is a standard deviation. The subscript (M) indicates that the standard error in question is the standard error of the mean. Central Limit Theorem The central limit theorem states that: Given a population with a finite mean μ and a finite non-zero variance σ2, the sampling distribution of the mean approaches a normal distribution with a mean of μ and a variance of σ2/N as N, the sample size, increases. The expressions for the mean and variance of the sampling distribution of the mean are not new or remarkable. What is remarkable is that regardless of the shape of the parent population, the sampling distribution of the mean approaches a normal distribution as N increases. If you have
proportion of samples that would fall between 0, 1, 2, and 3 standard deviations above and below the actual value. The standard error (SE) is the standard deviation of the sampling distribution of a statistic,[1] most commonly of the mean. The term may also
## Mean Of Distribution Calculator
be used to refer to an estimate of that standard deviation, derived from a particular when the population standard deviation is known the sampling distribution is a sample used to compute the estimate. For example, the sample mean is the usual estimator of a population mean. However, different samples drawn from what is the standard deviation of a sampling distribution called? that same population would in general have different values of the sample mean, so there is a distribution of sampled means (with its own mean and variance). The standard error of the mean (SEM) (i.e., of using the sample http://onlinestatbook.com/2/sampling_distributions/samp_dist_mean.html mean as a method of estimating the population mean) is the standard deviation of those sample means over all possible samples (of a given size) drawn from the population. Secondly, the standard error of the mean can refer to an estimate of that standard deviation, computed from the sample of data being analyzed at the time. In regression analysis, the term "standard error" is also used in the phrase standard error of the regression to mean the ordinary least https://en.wikipedia.org/wiki/Standard_error squares estimate of the standard deviation of the underlying errors.[2][3] Contents 1 Introduction to the standard error 1.1 Standard error of the mean (SEM) 1.1.1 Sampling from a distribution with a large standard deviation 1.1.2 Sampling from a distribution with a small standard deviation 1.1.3 Larger sample sizes give smaller standard errors 1.1.4 Using a sample to estimate the standard error 2 Standard error of the mean 3 Student approximation when σ value is unknown 4 Assumptions and usage 4.1 Standard error of mean versus standard deviation 5 Correction for finite population 6 Correction for correlation in the sample 7 Relative standard error 8 See also 9 References Introduction to the standard error The standard error is a quantitative measure of uncertainty. Consider the following scenarios. Scenario 1. For an upcoming national election, 2000 voters are chosen at random and asked if they will vote for candidate A or candidate B. Of the 2000 voters, 1040 (52%) state that they will vote for candidate A. The researchers report that candidate A is expected to receive 52% of the final vote, with a margin of error of 2%. In this scenario, the 2000 voters are a sample from all the actual voters. The sample proportion of 52% is an estimate of the true proportion who will vote for candidate A in the actual election. The margin of error of 2% is a quantitative measure of
test AP formulas FAQ AP study guides AP calculators Binomial Chi-square f Dist Hypergeometric Multinomial Negative binomial Normal Poisson t Dist Random numbers Probability Bayes rule Combinations/permutations Factorial Event counter Wizard Graphing Scientific Financial Calculator books AP calculator http://stattrek.com/estimation/standard-error.aspx?Tutorial=AP review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends What is the Standard Error? The standard error is an estimate of the standard deviation of a statistic. This lesson shows how to compute the standard error, based on sample data. The standard error is important because it is used to compute other measures, like sampling distribution confidence intervals and margins of error. Notation The following notation is helpful, when we talk about the standard deviation and the standard error. Population parameter Sample statistic N: Number of observations in the population n: Number of observations in the sample Ni: Number of observations in population i ni: Number of observations in sample i P: Proportion of successes in population p: Proportion of successes in sample Pi: Proportion of successes sampling distribution of in population i pi: Proportion of successes in sample i μ: Population mean x: Sample estimate of population mean μi: Mean of population i xi: Sample estimate of μi σ: Population standard deviation s: Sample estimate of σ σp: Standard deviation of p SEp: Standard error of p σx: Standard deviation of x SEx: Standard error of x Standard Deviation of Sample Estimates Statisticians use sample statistics to estimate population parameters. Naturally, the value of a statistic may vary from one sample to the next. The variability of a statistic is measured by its standard deviation. The table below shows formulas for computing the standard deviation of statistics from simple random samples. These formulas are valid when the population size is much larger (at least 20 times larger) than the sample size. Statistic Standard Deviation Sample mean, x σx = σ / sqrt( n ) Sample proportion, p σp = sqrt [ P(1 - P) / n ] Difference between means, x1 - x2 σx1-x2 = sqrt [ σ21 / n1 + σ22 / n2 ] Difference between proportions, p1 - p2 σp1-p2 = sqrt [ P1(1-P1) / n1 + P2(1-P2) / n2 ] Note: In order to compute the standard deviation of a sample statistic, you must know the v
### Related content
sampling error of a distribution
Sampling Error Of A Distribution p test AP formulas FAQ AP study guides AP calculators Binomial Chi-square f Dist Hypergeometric Multinomial Negative binomial Normal Poisson t Dist Random numbers Probability Bayes rule Combinations permutations Factorial Event counter Wizard Graphing Scientific Financial Calculator books AP sampling distribution of sample mean calculator review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews p Sampling Distribution Calculator p Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends Sampling Distributions Suppose that we draw all possible sampling distribution of the mean examples samples of size n from a
sampling distributions of a static and its standard error
Sampling Distributions Of A Static And Its Standard Error p error of the mean State the central limit theorem The sampling distribution of the mean was defined in the section introducing sampling distributions This section reviews some important properties of the sampling distribution of the mean introduced in the p Sampling Distribution Examples p demonstrations in this chapter Mean The mean of the sampling distribution of the mean sampling distribution formula is the mean of the population from which the scores were sampled Therefore if a population has a mean mu then the types of sampling distributions mean of the
sampling distribution of a static and its standard error
Sampling Distribution Of A Static And Its Standard Error p error of the mean State the central limit theorem The sampling distribution of the mean was defined in the section introducing sampling distributions This section reviews some important properties of the sampling distribution examples sampling distribution of the mean introduced in the demonstrations in this chapter Mean p Sampling Distribution Formula p The mean of the sampling distribution of the mean is the mean of the population from which the scores types of sampling distributions were sampled Therefore if a population has a mean mu then the mean of the
sampling distribution standard error mean
Sampling Distribution Standard Error Mean p test AP formulas FAQ AP study guides AP calculators Binomial Chi-square f Dist Hypergeometric Multinomial Negative binomial Normal Poisson t Dist Random numbers Probability Bayes rule Combinations permutations Factorial Event counter Wizard Graphing Scientific Financial Calculator books AP calculator review Statistics AP sampling distribution of the mean calculator study guides Probability Survey sampling Excel Graphing calculators Book reviews Glossary AP practice exam Problems p Sampling Distribution Of The Mean Examples p and solutions Formulas Notation Share with Friends Sampling Distributions Suppose that we draw all possible samples of size n from a p Sampling
sampling distribution and standard error ppt
Sampling Distribution And Standard Error Ppt p p p p p p
standard error of a sampling distribution of means
Standard Error Of A Sampling Distribution Of Means p to a normally distributed sampling distribution of the mean examples sampling distribution whose overall mean is equal to the mean of the source p Sampling Distribution Of The Sample Mean Example p population and whose standard deviation standard error is equal to the standard deviation of the source population divided by the square root ofn To calculate the standard error the standard error of the sampling distribution when we know the population standard deviation of any particular sampling distribution of sample means enter the mean and standard deviation sd of the
standard error of sampling distribution equation
Standard Error Of Sampling Distribution Equation p error of the mean State the central limit theorem The sampling distribution of the mean was defined in the section introducing sampling distributions This section reviews some p Sampling Distribution Of The Mean Calculator p important properties of the sampling distribution of the mean introduced in the sampling distribution of the mean examples demonstrations in this chapter Mean The mean of the sampling distribution of the mean is the mean of p Sampling Distribution Of The Sample Mean Example p the population from which the scores were sampled Therefore if a population has
standard error of the sampling distribution of the mean
Standard Error Of The Sampling Distribution Of The Mean p proportion of samples that would fall between and standard deviations above and below the actual value The standard error SE is the standard deviation of the sampling distribution of a statistic most commonly of the mean The term may also be sampling distribution of the mean calculator used to refer to an estimate of that standard deviation derived from a particular sample used sampling distribution of the sample mean to compute the estimate For example the sample mean is the usual estimator of a population mean However different samples drawn
standard error of sampling distribution formula
Standard Error Of Sampling Distribution Formula p test AP formulas FAQ AP study guides AP calculators Binomial Chi-square f Dist Hypergeometric Multinomial Negative binomial Normal Poisson t Dist Random numbers Probability p Sampling Distribution Of The Mean Calculator p Bayes rule Combinations permutations Factorial Event counter Wizard Graphing Scientific Financial Calculator sampling distribution of the mean examples books AP calculator review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews Glossary sampling distribution of the sample mean example AP practice exam Problems and solutions Formulas Notation Share with Friends Sampling Distributions Suppose that we draw all possible
standard error of the sampling distribution formula
Standard Error Of The Sampling Distribution Formula p error of the mean State the central limit theorem The sampling distribution of the mean was defined in the section introducing sampling distributions This section sampling distribution of the mean calculator reviews some important properties of the sampling distribution of the mean sampling distribution of the mean examples introduced in the demonstrations in this chapter Mean The mean of the sampling distribution of the mean is sampling distribution of the sample mean example the mean of the population from which the scores were sampled Therefore if a population has a mean mu
standard error of a sampling distribution formula
Standard Error Of A Sampling Distribution Formula p test AP formulas FAQ AP study guides AP calculators Binomial Chi-square f Dist Hypergeometric Multinomial Negative binomial Normal Poisson t Dist Random numbers Probability Bayes rule Combinations permutations Factorial Event counter Wizard Graphing Scientific Financial Calculator books AP sampling distribution of the mean calculator calculator review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews p Sampling Distribution Of The Mean Examples p Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends Sampling Distributions Suppose that we draw all possible sampling distribution of the sample mean
standard error sampling distribution sample average
Standard Error Sampling Distribution Sample Average p error of the mean State the central limit theorem The sampling distribution of the mean was defined in the section introducing sampling distributions This section reviews some important properties of the sampling distribution sampling distribution of the sample mean example of the mean introduced in the demonstrations in this chapter Mean The mean of sampling distribution of the mean examples the sampling distribution of the mean is the mean of the population from which the scores were sampled Therefore if p Sampling Distribution Of The Mean Calculator p a population has a mean
standard error of sampling distribution of sample mean
Standard Error Of Sampling Distribution Of Sample Mean p error of the mean State the central limit theorem The sampling distribution of the mean was defined in the section introducing sampling distributions This section reviews some important properties of the sampling distribution of the mean introduced in the demonstrations in this p Sampling Distribution Of The Sample Mean Calculator p chapter Mean The mean of the sampling distribution of the mean is the mean of sampling distribution of the sample mean example the population from which the scores were sampled Therefore if a population has a mean mu then the
standard error sampling distribution formula
Standard Error Sampling Distribution Formula p error of the mean State the central limit theorem The sampling distribution of the mean was defined in the section introducing sampling distributions This section reviews some important properties of the sampling distribution of the mean sampling distribution of the mean calculator introduced in the demonstrations in this chapter Mean The mean of the sampling distribution p Sampling Distribution Of The Mean Examples p of the mean is the mean of the population from which the scores were sampled Therefore if a population has a mean sampling distribution of the sample mean example mu
standard error sampling distribution sample mean
Standard Error Sampling Distribution Sample Mean p error of the mean State the central limit theorem The sampling distribution of the mean was defined in the section introducing sampling distributions This section reviews some important properties of the sampling distribution of the sample mean calculator sampling distribution of the mean introduced in the demonstrations in this chapter Mean sampling distribution of the sample mean example The mean of the sampling distribution of the mean is the mean of the population from which the scores p Sampling Distribution Of The Mean Examples p were sampled Therefore if a population has a
standard error of the sampling distribution of x bar
Standard Error Of The Sampling Distribution Of X Bar p if a large enough sample is taken typically n then the sampling distribution of bar x is approximately a normal distribution with a mean of and a standard deviation of frac sigma sqrt n Since in practice we usually do not know or sampling distribution of the sample mean calculator we estimate these by bar x and frac s sqrt n respectively In this case s is the sampling distribution of xbar calculator estimate of and is the standard deviation of the sample The expression frac s sqrt n is
standard error of the distribution of sample means
Standard Error Of The Distribution Of Sample Means p error of the mean State the central limit theorem The sampling distribution of the mean was defined in the section introducing sampling distributions This section reviews some important properties of the sampling distribution of the mean introduced in the demonstrations in this chapter Mean sampling distribution of the mean calculator The mean of the sampling distribution of the mean is the mean of the population from p Standard Error Of Mean Calculator p which the scores were sampled Therefore if a population has a mean mu then the mean of the
standard error of x bar formula
Standard Error Of X Bar Formula p proportion of samples that would fall between and standard deviations above and below the actual value The standard error SE is the standard deviation of the sampling distribution of a statistic most commonly of the mean The term sampling distribution of the sample mean calculator may also be used to refer to an estimate of that standard deviation derived from p Sampling Distribution Of Xbar p a particular sample used to compute the estimate For example the sample mean is the usual estimator of a population mean However different samples x bar calculator
the standard error of the sampling distribution of x bar
The Standard Error Of The Sampling Distribution Of X Bar p construction of a sampling distribution for a mean You can access sampling distribution of xbar calculator this simulation athttp www lock stat com StatKey - Video PA Town Residents sampling distribution of xbar is the quizlet StatKey Example - Military Example up - Video PA Town Residents sampling distribution of the sample mean calculator StatKey Example Printer-friendly version Navigation Start Here Welcome to STAT Search Course Materials Faculty login PSU Access Account Lessons Lesson p Sampling Distribution Of The Sample Mean Example p Statistics The Big Picture Lesson Gathering
the standard error of the sampling distribution is equal to
The Standard Error Of The Sampling Distribution Is Equal To p error of the mean State the central limit theorem The sampling distribution of the mean was defined in the section introducing sampling distributions This section reviews some important p Sampling Distribution Of The Sample Mean p properties of the sampling distribution of the mean introduced in the demonstrations in sampling distribution of the mean calculator this chapter Mean The mean of the sampling distribution of the mean is the mean of the population from sampling distribution of the mean examples which the scores were sampled Therefore if a population
what is the standard error of a sampling distribution called
What Is The Standard Error Of A Sampling Distribution Called p is intuitive for most students the concept of a distribution of a set of statistics is not Therefore distributions will be reviewed before the sampling distribution is discussed P THE SAMPLE DISTRIBUTION The sampling distribution example sample distribution is the distribution resulting from the collection of actual data A sampling distribution of the mean major characteristic of a sample is that it contains a finite countable number of scores the number of scores represented sampling distribution calculator by the letter N For example suppose that the following data were
what is the standard error of the sample mean x-bar
What Is The Standard Error Of The Sample Mean X-bar p if a large enough sample is taken typically n then the sampling distribution of bar x is approximately a normal distribution with a mean of p Sampling Distribution Of Xbar Calculator p and a standard deviation of frac sigma sqrt n Since in practice we usually sampling distribution of xbar is the quizlet do not know or we estimate these by bar x and frac s sqrt n respectively In this case p Sampling Distribution Of The Sample Mean Calculator p s is the estimate of and is the
| 4,115 | 22,863 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.53125 | 5 | CC-MAIN-2018-34 | latest | en | 0.908855 |
https://studysoup.com/note/2331196/independence-university-des-113-week-2-fall-2016 | 1,477,241,938,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988719286.6/warc/CC-MAIN-20161020183839-00100-ip-10-171-6-4.ec2.internal.warc.gz | 868,472,442 | 17,220 | ×
### Let's log you in.
or
Don't have a StudySoup account? Create one here!
×
or
## Design 113 typography reading notes
by: Megan L. Hanley
10
0
2
# Design 113 typography reading notes Des 113
Marketplace > Independence University > Type 1 > Des 113 > Design 113 typography reading notes
Megan L. Hanley
GPA 3.7
Get a free preview of these Notes, just enter your email below.
×
Unlock Preview
these notes explain some of the history behind typography and explain different punctuation with in typography
COURSE
typography
PROF.
Julie Luke
TYPE
Class Notes
PAGES
2
WORDS
CONCEPTS
typography
KARMA
25 ?
## Popular in Type 1
This 2 page Class Notes was uploaded by Megan L. Hanley on Friday September 23, 2016. The Class Notes belongs to Des 113 at Independence University taught by Julie Luke in Fall 2016. Since its upload, it has received 10 views. For similar materials see typography in Type 1 at Independence University.
×
## Reviews for Design 113 typography reading notes
×
×
### What is Karma?
#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 09/23/16
Des 113 week 2 reading notes typography Thinking with type Mixing typefaces Pages 54-67 *Combining typefaces is like making a salad. Start with small number of elements that represent: Different colors Taste Textures Strive for contrast rather than mushy transitions. Give each item that you are typing a role to play when mixing typefaces. Adjust the point size So that the typefaces have the same x-height. When placing type faces on same or separate lines Create contrast in scale. Style and weight Mix, big, light, type with small type. Numerals pages: 54-67 Lining numerals take up uniform widths of space enabling the numbers to line up when tabulated in columns. Numerals were introduced around the time of the 20 century to meet the needs of modern business. Lining up numerals is the same height as capital letters. Non-lining numerals- They are also called text or old style numerals they have ascenders and descenders like lower case letters. Non-lining numerals returned to favor in the 1900’s. They were valued for their traditional typographic attitude. They are like letterforms old style numerals are proportional. Each of them has it’s own set width. Punctuation –page 58 A well-designed comma carries the essence of the typeface down to its delicious details. Helveticas comma is a chunky square mounted to a jaunty curve. Bodonis is a voluptuous thin-stemmed orb. Designers and editors need to learn various typographic conventions in additions to mastering the grammatical rules of punctuation. -A pandemic error is the use of straight prime or hatch marks called (dumb quotes). In place of apostrophes and quotation marks (Also known As curly quotes, typographers quotes, or smart quotes.) Double and single quotation marks are represented with four distinct characters each accessed with different keystrokes combination. Ornaments Page 60 Not all typographic elements represent language. For centuries ornaments have been designed to integrate directly with text. In the letterpress era, printers assembled decorative elements one by one to build larger forms and patterns on the page. Decorative rules served to frame and divide content. In the 19 century printers provided their customers with vast collections of ready-made illustrations that could easily be mixed with text. Numerous forms of ornaments are available today as digital fonts. They can be typed on a keyboard scaled and output like a typeface.
×
×
### BOOM! Enjoy Your Free Notes!
×
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'
## Why people love StudySoup
Bentley McCaw University of Florida
#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"
Anthony Lee UC Santa Barbara
#### "I bought an awesome study guide, which helped me get an A in my Math 34B class this quarter!"
Steve Martinelli UC Los Angeles
#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."
Parker Thompson 500 Startups
#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."
Become an Elite Notetaker and start selling your notes online!
×
### Refund Policy
#### STUDYSOUP CANCELLATION POLICY
All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com
#### STUDYSOUP REFUND POLICY
StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com
Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com | 1,257 | 5,668 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2016-44 | latest | en | 0.912515 |
http://www.algebra.com/algebra/homework/real-numbers/real-numbers.faq?hide_answers=1&beginning=360 | 1,371,688,798,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368709947846/warc/CC-MAIN-20130516131227-00015-ip-10-60-113-184.ec2.internal.warc.gz | 310,521,302 | 9,542 | # Questions on Algebra: Real numbers, Irrational numbers, etc answered by real tutors!
Algebra -> Algebra -> Real-numbers -> Questions on Algebra: Real numbers, Irrational numbers, etc answered by real tutors! Log On
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Algebra: Real numbers, Irrational numbers, etc Solvers Lessons Answers archive Quiz In Depth
Question 56406: What other sets of numbers there are other than the set of real numbers and its subsets. Click here to see answer by AgusKwan(7)
Question 56758: Again, didn't know where to put this problem. Solve and Check: In baseball a player's batting average is the ratio of hits to the number of times he or she has batted. Thus, if the player has an average of .3000, it means he or she got 300 hits in 1000 at bats. In order to have an average of .300, how many hits would the batter have to get in 400 times at bat? Click here to see answer by funmath(2925)
Question 56758: Again, didn't know where to put this problem. Solve and Check: In baseball a player's batting average is the ratio of hits to the number of times he or she has batted. Thus, if the player has an average of .3000, it means he or she got 300 hits in 1000 at bats. In order to have an average of .300, how many hits would the batter have to get in 400 times at bat? Click here to see answer by stanbon(57977)
Question 56757: Didn't know exactly where to put this problem. It's a worksheet and in the text book for the certain type of problem it's under Investment Problems. Solve and check: An investment of \$1500 paid interest of \$45 during a certain period. How much interest would an investment of \$1200 invested at the same rate for the same length of time pay? Click here to see answer by tutorcecilia(2152)
Question 57060: I need to find any real numbers for which the following expression is undefined. I just can't seem to grasp it. ____X-5___ X+2 Click here to see answer by stanbon(57977)
Question 57303: I need help on solving the problems -6 + (-5) and -17+(-14) and -5 over 6 + 9 over 16 and also -1.5 + (-2.3) Click here to see answer by CrazyMan Jr.(21)
Question 55824: . Given a = 4, b = -3 and c = 12, which of the following expressions will yield a value that is undefined? a. a + 2 * b – c b. 3 * a + 4 * b – c c. 2 * c /(4 * b + 3 * a) d. (3 * a) – (-4 * b) / c also............. Which of the following is a property of real numbers? a. (a + b)n = an + bn c. a(b + c) = ab + ac d. All of the others Click here to see answer by rcmcc(152)
Question 57847: Which of the following is a Pythagorean triple? a.6, 8, 12 b. 3, 4, 5 c. 1, 2, 3 d. 5, 7, 12 Which of the following remains an unsolved problem in mathematics? a. Konigsberg Bridge Problem b. Fermat’s Last Theorem c. Goldbach’s Conjecture D. Fundamental Theorem of Arithmetic Which is the third row of Pascal’s triangle? a. 1 1 b. 1 4 6 4 1 c. 1 2 1 d. 1 3 3 1 Click here to see answer by Edwin McCravy(8999)
Question 51429: Explain why the real numbers would not be the most reasonable domain for the number of nails in a barrel of roofing nails. Click here to see answer by hayek(51)
Question 58124: THE SUM OF TWO CONSECUTIVE INTEGERS IS 145. FIND THE TWO INTEGERS. Click here to see answer by hayek(51)
Question 58169: what is a real number between 7 3/5 and 7 4/5? Click here to see answer by checkley71(8403)
Question 58166: How do I combine these two numbers to get a sum so it can be divided by 2. I need to determine a real number between 7 3/5 and 7 4/5. Click here to see answer by checkley71(8403)
Question 58200: k-3k=36 Click here to see answer by rcmcc(152)
Question 58177: How do I add these numbers together and divide by 2 to find a real number? 7/8 and 9/10 Click here to see answer by stanbon(57977)
Question 58177: How do I add these numbers together and divide by 2 to find a real number? 7/8 and 9/10 Click here to see answer by rcmcc(152)
Question 58168: What is a real number between 7/8 and 9/10? Click here to see answer by stanbon(57977)
Question 58573: Loa is two years younger than three times Mary's age. If Mary's age in six years will be 3x-6, what is Loas's age now? Click here to see answer by stanbon(57977)
Question 58954: I'm confused about negative numbers when you add or subtract them. The problem I am stuck on is five/sixths subtract negative two/thirds? Please help. Kathryn Click here to see answer by checkley71(8403)
Question 59523: How do I do this problem? One number is 12 more than another. The sum of the smaller number and twice the larger number is 39. I nned to find the larger number. Thank you, Jamie Click here to see answer by stanbon(57977)
Question 60269: Order the numbers -23,15,-13,-2,14-5 from least to greatest Click here to see answer by funmath(2925)
Question 60269: Order the numbers -23,15,-13,-2,14-5 from least to greatest Click here to see answer by greenman(5)
Question 60587: Probability I do not understand A card is drawn from a deck of ten card numbered 1 - 10. The card is replaced in the deck and another card is drawn. P(an odd number and then an even number) P(two numbers greater than 4) P(an odd number and then an even number) P(5 and then a 3) Please help me understand the concept.... Click here to see answer by venugopalramana(3286)
Question 60831: What is the difference bdtween rational and irrational numbers? Click here to see answer by jai_kos(139)
Question 61707: 3 square root of 2 equals - what sets of numbers? Click here to see answer by tutorcecilia(2152)
Question 61753: Find the set of all complex solutions. +6x=+12 Click here to see answer by stanbon(57977)
Question 61754: Find the set of all real solutions. If the solution set contains infinitely many elements, use interval notation to represent it. -=2 Click here to see answer by stanbon(57977)
Question 61784: +1= Click here to see answer by josmiceli(9817)
Question 62335: Find a number between 3/7 and 5/6? thanks for helping Click here to see answer by joyofmath(189)
Question 62334: how do you solve, -9/3/2 Click here to see answer by 303795(595)
Question 62334: how do you solve, -9/3/2 Click here to see answer by checkley71(8403)
Question 62543: I DO NOT UNDERSTAND THIS MEAN,MODE AND MEDIAN AND i DO NOT KNOW WHO CAN HELP ME UNDERSTAND THIS IS MY PROBLEM i AM IN THE 7 GRADE PLEASE SHOW ME 7,19,19,N,15 MEAN=13 i KNOW i ADD AND THEN i DIVIDE. Click here to see answer by uma(370)
Question 62997: Pleae help me with the following : A number is tripled and then the product is increased by 4. This sum is then multiplied by -2 and the result is 16 greater than twice the opposite of the number. What is the number?? thank yoU! Click here to see answer by ankor@dixie-net.com(15746)
Question 63267: I am to convert the equation to slope-intercept form and then identify the correct slope of this line 4x+2y=10 Thanks, lackinmath Click here to see answer by uma(370)
Question 63268: Given the points (-2,2) and (1,3) on a line, calculate the slope of that line Please help!!!!!!!!!! Lackinmath Click here to see answer by uma(370)
Question 63270: Given the point (-2, -1 and a slope of 3/2 find the equation of the line having this slope and point This is confusing me!!!!!!!!! lackinmath Click here to see answer by josmiceli(9817)
Question 63766: I need to evalutate this problem but not sure how to do it. Evaluate P(-1/2) if P(x) = 2x4 + x3 + 12 Click here to see answer by Earlsdon(6294)
Question 64104: Is -9.1111... a rational, irrational,interger, natuaral number, or whole number? Click here to see answer by stanbon(57977)
Question 64030: The set of real numbers between 2 and 6 Click here to see answer by stanbon(57977)
Question 64728: WRITE THE DECIMAL AS A FRACTION IN SIMPLEST FORM. 2.305 Click here to see answer by checkley71(8403)
Question 65152: It's just not clicking. Can you show me step by step how to break this down & solve? 0.1p+2.1=4.6p-1.9+0.5p Click here to see answer by ptaylor(2052)
Question 65074: What is the type of problem for which no real number has a solution called? Click here to see answer by Nate(3500)
Question 63160: ThIS IS USING RATES... Portia drove her new car 425 miles on 10.8 gallons of gasoline. A. what is the cars rate of gasoline consumption in miles per gallon? B. if this is the typical mileage for portia's car, how much gas will it take for a 750 mile vacation trip? C. if gas cost \$1.35 per gallon, how much will portia spend on gas on her vacation? D. the manufacturer advertised that the car would get 30 to 35 miles per gallon. how does portia's mileage compare to the advertised estimates? Click here to see answer by 303795(595)
Question 65324: how can i tell if a -674 is a interger or a whole number or a natural and are all numbers integers Click here to see answer by stanbon(57977)
Question 65806: Graph -x - 3 >= - 1; D = {reals} Click here to see answer by stanbon(57977)
Question 65995: Find the value of "k" if f(x) = 3x2 + 6x + 1 is put into general form. a. -2 b. -1 c. 1 d. 3 e. 4 Click here to see answer by uma(370)
Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835 | 3,015 | 9,929 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2013-20 | latest | en | 0.959906 |
https://vital-dietetyk.pl/ball-mill/3998.html | 1,642,974,571,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304309.59/warc/CC-MAIN-20220123202547-20220123232547-00580.warc.gz | 602,398,863 | 4,907 | # What Is Critical Speed Of Ball Mill Scmcrusher
1. Home
2. > What Is Critical Speed Of Ball Mill Scmcrusher
### What Is Ball Mill Critical Speed
What is ball mill critical speed . Equation formula critical speed of the ball mill cmuc a ball mill critical speed actually ball rod ag or sag is the speed at which the centrifugal forces equal gravitational forces at the mill shells inside surface and no balls will fall from its position onto the shell the imagery below helps explain what goes on inside a mill as speed varies use our online.The point where the mill becomes a centrifuge is called the Critical Speed , and ball mills usually operate at 65 to 75 of the critical speed. Ball Mill Application Ball mills are generally used to grind material 1 4 inch and finer, down to the particle size of 20 to 75 microns.Feb 14, 2018 A ball mill, a type of grinder, is a cylindrical device used in grinding (or mixing) materials like ores, chemicals, ceramic raw materials and paints. Ball mills rotate around a horizontal axis, partially filled with the material to be ground plus the grinding medium. Different materials are used as media, including ceramic balls,flint pebbles.Ball tube mills and high-speed attrition ([email protected] ) pulverizers for use in the pulverization of all available coals, ranging from anthracites to lignites. The most common usage has been in direct-fired coal systems of fossil fueled steam generators. In all, Riley has supplied over 1000 AT RITA units, and 175 ball tube mills.
### Solved: The Critical Speed Of The Ball Mill Is Less Than 4
Ball Mill Critical Speed. A Ball Mill Critical Speed (actually ball, rod, AG or SAG) is the speed at which the centrifugal forces equal gravitational forces at the mill shell’s inside surface and no balls will fall from its position onto the shell. The imagery below helps explain what goes on inside a mill as speed varies.Ness of the models. For a given mill to have a combination of feed size, ball load, mill speed and solids will represent the total load. Ball Mill SAG Mill Scw Jb Pc -6 +1 N Nc Fresh Feed Water Water Pebble Crusher Screen Cyclones Sump Pump Fig. 1. SABC A B milling circuit.Transcribed Image Textfrom this Question. The critical speed of the ball mill is less than 45 of operating speed. Now calculate the operating speed of the ball mill which has diameter of 900 mm. Diameter of ball is 80 mm. a) 47 rpm b) 68 rpm c) 32 rpm d) 21 pm.Make a Ball Mill in 5 Minutes This is for all the pyro nuts that I came across on Instructables. This can be used to grind chemicals to a very fine grain or to polish rocks.Wiki says A ball mill is a type of grinder used to grind materials into extremely fine powder for us.
### How To Calculate Critical Speed Of Ball Mill
Mar 10, 2020 For a ball mill to work, critical speed must be achieved. Critical speed refers to the speed at which the enclosed balls begin to rotate along the inner walls of the ball mill. If a ball mill fails to reach critical speed, the balls will remain stationary at the bottom where they have little or no impact on the material. Ball Mills vs.Generally ball mills are utilized after an initial material crushing or grinding has occurred. Thus, a disadvantage of the ball mill is that the feed size must already be small. Table 2 outlines some typical ball diameters found in ball mills dependent on the staging or purpose of the mill. Table 1 - Ball mill feed and product sizes (Callow.Jul 05, 2020 e. Rotation speed of the cylinder. Several types of ball mills exist. They differ to an extent in their operating principle. They also differ in their maximum capacity of the milling vessel, ranging from 0.010 liters for planetary ball mills, mixer mills, or vibration ball mills to several 100 liters for horizontal rolling ball mills.Jun 02, 2017 Ball mills vary greatly in size, from large industrial ball mills measuring than 25 ft. in diameter to small mills used for sample preparation in laboratories. Rod mills are similar to ball mills and use metal rods as the grinding media. Pebble mills use rock pebbles as the grinding media to cause friction and attrition between the pebbles.
### Ball Screw Selection And Calculations University Of Utah
The critical speed of the ball mill is the speed at which the centrifugal force is equal to the gravity on the inner surface of the mill so that no ball falls from its position onto the mill shell. Ball mill machines usually operates at 65-75 of critical speed.8.3.2.2 Ball mills. The ball mill is a tumbling mill that uses steel balls as the grinding media. The length of the cylindrical shell is usually 1–1.5 times the shell diameter (Figure 8.11). The feed can be dry, with less than 3 moisture to minimize ball coating, or slurry containing 20–40 water by weight.Cement ball mill throughput calculation. calculate ball mill throughput in closed circuit. Get of silica sand mining process equipment for Advanced process control for the cement industry.Nevertheless, ball mills can be a appropriate choice for grinding larger sized material starting at 1 4 ” or larger. It should be noted that ball mills are much larger than Attritors and therefore require a special foundation. The Attritor’s design accounts for much of the difference conventional ball mills turn the. | 1,168 | 5,306 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2022-05 | latest | en | 0.876595 |
http://www2.ljworld.com/news/2011/may/31/rising-aviation-fuel-prices-contribute-emptier-ski/ | 1,462,223,938,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461860117783.16/warc/CC-MAIN-20160428161517-00074-ip-10-239-7-51.ec2.internal.warc.gz | 926,476,480 | 28,999 | ## Rising aviation fuel prices contribute to emptier skies over Lawrence
Seth Fox, of Atchison, often travels to Lawrence Municipal Airport in his Cessna 150d. It costs Fox more than \$110 to fill the Cessna's tank.
May 31, 2011
#### Your true highway fuel mileage
MPG Calculator MPG/MPG Calculator --> --> --> --> -->
Your car's Highway MPG: Don't Know
Cost of a gallon of gas: \$
How much extra weight are you carrying?
Your standard MPG accounts for 300lbs of weight, which
includes passengers and cargo. Smaller cars are more
affected by the extra weight than large cars.
Your car's speed in miles per hour:
Your true highway MPG is: This Calculator
uses data from
the Department
of Energy
Cost to go to Topeka: \$
Cost to go to Kansas City: \$
This graphic compares the cost and time of flying and driving to Hays, Wichita and Kansas City from Lawrence.
Seth Fox, owner of High Plains Inc., a liquor distillery in Atchison, said he flies for recreation.
Kansas University School of Journalism students in the advanced classes of Scott Reinardy, Julie Denesha and Mike Williams produced this series about the effects of escalating gasoline prices in Lawrence. This is Part 3.
Read Part 1 and Part 2.
If the price of aviation fuel continues to rise, Seth Fox said he’ll fill his plane with ordinary gasoline.
After landing his two-seat Cessna at Lawrence Municipal Airport, Fox, a pilot from Atchison, said he wasn’t kidding about the gas. He’s done it before, although it did cause the plane’s single engine to fail during landing. Fox said that was “no big deal.”
“I’d switch to high octane,” he said. “It burns better.”
Aviation fuel prices, just like gasoline, continue to climb. But while gasoline hasn’t yet reached \$4 per gallon locally, owners of private aircraft generally pay at least \$5 per gallon.
At Lawrence Municipal Airport, Hetrick Air Services Inc. offers refueling service at \$5.88 per gallon. According to AirNav, an aviation information service based in Atlanta, fuel in Kansas City, Chicago and Dallas is more than \$6 per gallon. In Washington, D.C., it’s more than \$8. Nationally, the average wholesale price of aviation fuel rose almost 25 percent in the first three months of 2011.
Runway clearance
On this day, Fox was the only pilot in sight. He parked his Cessna next to the lone King Air 350 propeller plane on the tarmac.
Airport operator Lloyd Hetrick said fewer planes have been coming through the airport since 2008. He owns Hetrick Air Services, and his 22 employees account for about half of the airport staff.
“Our traffic is down, there’s no doubt about that,” he said. “But probably what’s affecting us most, and eating into profits, is the price of fuel.”
Hetrick said there have been no layoffs because of the downturn, and he didn’t expect any. But less money moving through the airport means less tax revenue for the city. A 2009 economic impact study by the Kansas Department of Transportation estimated that Lawrence’s airport contributed \$10.7 million to the region’s economy through payroll, purchases and taxes.
Because the municipal airport does not operate a control tower, exact figures relating to its traffic are not available. But estimates provided by the city government as part of an airport study show a significant drop in traffic. In 2001, total operations — takeoffs and landings — were estimated at more than 31,000. In 2009, FAA estimates showed more than 34,000 operations, but that figure dropped below 32,000 in 2010, a decline of nearly 6 percent.
Hetrick said the airport averages about 50 operations per day. At that rate, the airport would handle fewer than 20,000 operations this year.
The decline isn’t just local. The Aircraft Owners & Pilots Association reports that, nationally, 1.4 million small aircraft were no longer on airport traffic logs between 2008 and 2010.
Institutions such as Kansas University have also reduced chartered flights.
At Lawrence Municipal, not far from Fox’s Cessna, KU’s eight-seat Cessna Citation Bravo sits in a private hangar. The Cessna carries university staff on fund-raising and recruiting trips but flies less often now than it did three years ago. KU also maintains partial ownership of a six-seat King Air C-90B in Kansas City. University flights have dropped from more than 400 in 2007 to fewer than 300 in 2010, according to Jill Jess, a university spokeswoman. She said the reduction in flights was largely due to university budget cuts.
Those flying university aircraft can purchase fuel at a discount because KU belongs to a corporate aircraft association. At \$4.55 per gallon, KU does better than Fox, the private pilot who paid \$5.40 when he filled up in Atchison. Even so, KU spent \$727,600 to maintain the aircraft in 2010, up from less than \$700,000 in 2007.
KUMC Outreach reduction
Departments such as KU Athletics and KU Medical Center pay the university for fuel and other flight costs when they use the planes. KU Med’s rural outreach program accounts for about 60 percent of the university flights. It, too, is feeling the pinch of rising fuel prices.
The medical center’s rural outreach program flies cancer specialists and other physicians across Kansas to treat patients. Dave Cook, assistant vice chancellor of the outreach program, said flying was often the only way specialists could easily reach patients in small towns.
“In Hays, Garden City, Goodland, there just aren’t that many oncologists or rheumatologists,” Cook said. “So people don’t have access.”
While driving or flying commercially is often cheaper, physicians with morning and evening rounds do not have time to drive several hours to Garden City and back or wait in airports, Cook said. But he said budget cuts and increased fuel costs oblige KU Med to stretch its travel dollars. To save money, KU Med physicians sometimes practice “tele-medicine,” meeting with patients via Internet video software.
Cook said he’s not sure what the future holds for the program.
“The way things are going, as we look into the future, it’s a little scary,” he said. “Everything is under the microscope.”
Friendly, empty skies
Fox owns High Plains Inc., a liquor distillery in Atchison. He flies for recreation and said his Cessna “just sips the fuel” at 5.5 gallons per hour. Because the plane is paid off, it doesn’t cost him much, but if the day comes when he can’t afford fuel, he’ll sell it. He said he thinks other pilots, saddled with loan payments, higher fuel costs and other pressures in a down economy, have already sold theirs.
That’s why airports such as Lawrence’s have seen fewer planes on the runway in the past three years. A city study projects future increases in traffic as the economy recovers and Lawrence air traffic follows national trends upward at a rate of about 3,000 operations every five years. But for now, the skies are emptier than they used to be.
#### nedcolt 4 years, 11 months ago
Hey,,lets put a few more million in airport...
Yawn
#### d_prowess 4 years, 11 months ago
Does anyone have any idea how fast the plane the Fox owns is? It seems crazy that he could fly for an hour and only use up 5.5 gallons of fuel and so I was wondering how far that might get him.
#### Kurt Kummer 4 years, 11 months ago
A Cessna 150 will cruise at 117 mph.
#### William McCauley 4 years, 11 months ago
What is really funny is I tried to start an "adventure sports/sightseeing" type business using the airport about three years ago and some of the same people quoted in this story are the same people who where telling the city and trying to tell the FAA there is too much air traffic to allow any such type of business like that here in Lawrence, not no, but hell no!
We would have be looking to buy many gallons of 100LL a year and fly about 8 to 10 hrs a week or more, adding to the TO&L cycle counts (used to get larger grant funding contracts to improve airports) and it's a business geared to marketing locally as well as to the 5 or 6 counties around here to try to bring people to town & airport to...... get this..... SPEND THEIR MONEY! ( I know what a stupid idea, imagine that, get people to come to town to spend money when it's not a game day, wow who would have thunk it)
NOPE, too much air traffic here for that, you should open your business in Gardner Ks., They said...... ain't that right boys....... that's what you all said isn't it..... Said something like that to those other folks about 2005 too didn't you..... yup, public record.
Oh yea, the hicks in the sticks, Lawrence, the good old boy network...... Proven by the media to be liars!
Thanks: Ian Cummings, look forward to sending this story to some people Washington DC.
#### Bruce Liddel 4 years, 11 months ago
What TheBigW didn't mention was that his adventure business involves skydiving, which is known to kill people, and is particularly unsuitable for doing at airports like Lawrence where there is a very active helicopter medical ambulance business. He wasn't going to bring any activity Monday through Friday, but only on weekends, like big KU football and Race-day weekends which are already (still) busy.
He didn't want to go through normal channels, but came here looking for a fight. He'd rather sue his way into the airport, and he's unhappy because that isn't working very well.
#### William McCauley 4 years, 11 months ago
Really, might want to check your facts about federal funded general aviation airports in class E airspace that are required to operate under FAA order 5190.6B along with a number of other FAR's and AC's.
Oh and BTW, we are plan on operating seven days a week April to Nov.
Aviation kills people, cars kill people, guns kill people, lot of things kill people, again you might want to check your facts....
"He didn't want to go through normal channels" Really, you mean like following FAR 105.23B. or under the laws of the national airspace system contacting the FAA to enforce the contract the city signed for 11.5 million dollars..... yea try reading FAA order 5190.6B
Oh and while your at it, maybe you get Chucky Soules to let you read the copy of the FAA safety study that states clearly skydiving can conducted on that airport safely, unlike all your hot air in your post again if you were not so busy trying to tout the party line of the good old boys club and took the time read the current guidance from the FAA, it prove you don't WTF your talking about!
As in baseball, try bullsh**ing the fans not the players!
#### Bruce Liddel 4 years, 11 months ago
OK Sports fans... I told you he came here looking for a fight. He's obviously still looking for a fight, and he obviously has yet to comprehend why the regulations he cites are totally irrelevant to the real reason he can't just do whatever he pleases, and screw the city. Until he can control his anger, he's the last person in the world with whom you'd ever want to climb into an airplane.
Golf clap......
#### William McCauley 4 years, 10 months ago
(quote) OK Sports fans... I told you he came here looking for a fight. He's obviously still looking for a fight, and he obviously has yet to comprehend why the regulations he cites (quote)
ROTFLMAO!
Hey you might want to do a little research and try reading the FAA order 5190.6B again, along with AC 5190/150-6 and AC 5190/150-7 & AC 90-66A over at www.FAA.gov
Before you start reading all that, you might be in need of some remedial pilot training or a class in 8th grade reading comprehension skills.
FYI- note the date of this AC release of May 18th 2011 http://www.faa.gov/documentLibrary/media /Advisory_Circular/AC%20105-2D.pdf
Oh BTW, would like a personal invite to visit with the national level FAA inspectors when they come to town, that way you can come out and run your mouth to them and explain all about how you know better then the FAA what the rule books says....... Oh yea, that's right, I'm the one looking for a fight......
#### clovis_sangrail 4 years, 11 months ago
That's what we need -- someone hobby-flying over Lawrence using gas that he knows can cause the engine to conk out just to save a few bucks. Let's just hope that when it happens, he comes down somewhere unpopulated so the only harm is to himself.
I have no more sympathy for someone who can afford an airplane but cannot afford the upkeep than I have for the person who bought too much house and cannot keep up the payments on the wide-screen TV and the Lexus lease.
#### Bruce Liddel 4 years, 11 months ago
Sometimes you cannot believe what you read in the newspaper because the writer just plain gets it wrong. I ran auto fuel in an airplane for years, and NEVER had any trouble. Auto fuel DOES NOT cause an engine to fail. That's hogwash. If auto fuel were unsafe, the FAA would never approve it. The FAA approves the use of auto fuel in certain airplanes under a supplemental type certificate (STC). I fully expect that Mr. Fox's airplane has such an STC.
Now then, if your engine quits "during landing" when you are inches off the runway, and lined up with the runway, and intending to land anyway, you really couldn't ask for a better time to have your engine quit unexpectedly. So yes, it's really NO BIG DEAL!
#### Bruce Liddel 4 years, 11 months ago
Ah yes, cruising altitude... which could be anywhere from 3,000 feet to 12,000, or more in higher performance airplanes. Well, you can glide in a light general aviation airplane typically 8 feet forward for every one foot down, so even with 3,000 feet altitude, you can glide almost five miles. If that's not far enough to find an airport, it's still usually enough to find an un-plowed field or a deserted road, or even a divided highway.
The worst time to have an engine failure is on takeoff, because then you don't have much altitude and you're pointed away from the nearest airport. Fortunately, engine failures are very rare, and most of those are preventable (fuel exhaustion is a big cause).
#### Lawrence_Pilot 4 years, 11 months ago
No, car gas doesn't make airplane engines quit. Note that this was written by student journalists. And it shows.
Tens of thousands of 4-seat and 2-seat airplanes operate on car gas. 86 octane is usually good enough, but most pilots use premium 91 octane (no ethanol allowed, by the way...rots the rubber fuel tanks and seals!) Airports sell 100 octane, which can be used in every piston-engine aircraft but which is required in aircraft with bigger engines and higher compression ratios.
Really, there was one sentence of information here that was useful: "Air traffic at Lawrence Municipal Airport and thousands like it have seen a 10-20% decline in traffic since 2008." That's really all you need to know. But it's not about the fuel as much as it is about the economy. And, since this year's fuel price increases were relatively short, I doubt there is anything but anecdotal evidence that the recent runup curtailed air traffic.
I love the way the "reporters" could only find one lone pilot, of a 2-seat airplane, to interview...they didn't look too hard. The airport could have put them in touch with many others if they'd bothered to ask.
#### Lawrence_Pilot 4 years, 11 months ago
I love the way the attached map graphic compares the cost of driving a Prius to an airplane. Why not a bicycle, too? Chigga, puhleez.
#### Wayne Propst 4 years, 11 months ago
the airport has been an endless money pit.....remember when they spent multi-millions on "improvements" so as to cash in on the traffic from the NASCAR races... ha ...or our "cargo Cult" terminal where not a sigle sceduled plane has landed in 25 + years....They always lie abuout "traffic"....over the years it has averaged approx. \$41.00 per "operation" paid by Lawrence tax payers...enjoy yer hobby boys...and shut down the arts.....
#### Bruce Liddel 4 years, 11 months ago
Could you elaborate on how you calculated that Lawrence Taxpayers foot \$41 in costs per "operation"? I'm sure you're aware that 95% of the infrastructure improvements at LWC are paid from airport improvement funds, the vast majority of which are collected via Federal fuel taxes.
Who's lying about traffic counts? Do you have surveillance video with which to dispute the educated estimates of the professionals who made them?
Ever hear of TSA? You want commercial air traffic at LWC? Are you nuts? \$Billions on TSA wasted, with not a singe terrorist ever apprehended.
#### kernal 4 years, 11 months ago
This story confirms what many of us already thought - we do NOT need to spend tax payers money to enlarge this airport.
#### William McCauley 4 years, 11 months ago
Well I got news for you, the city of Lawrence is currently seeking to request 13.5 million in funding to expand the runways for bigger class biz jets, you know all the ones the race car drivers use and the fat cats who fly into see ball games.... http://www.lawrence.airportstudy.com/
Well that and it seem a great deal of local pilots suck and need as much room as they can get to take off and land their hanger queen, seeing how they can't seem fly VFR.
#### Bruce Liddel 4 years, 11 months ago
Maybe not this year, but what about next year? When the economy recovers, growing businesses will locate wherever the best airports are. You want to miss that boat? I need a job, so I don't want to miss that boat.
You don't want to pay for an airport that will continue to stimulate our local economy? Fine. Stop buying airplane fuel, and stop complaining.
#### William McCauley 4 years, 11 months ago
You want to come on here and tout the same lies and misinformation told to the city by the LAAB members, one of who used his seat as chairman of the LAAB to land a seat with Airport development group, the company who helps airport sponsors comply with the grant funding requirments.... (one would think he would know the laws and not offer advice to the city in direct violation of grant assurances he is tasked to help the city comply with)
Yet you seem to think that airport is your own little personal "country club" where only select people are allowed to come and use it.... sounds a lot like "we don't like your kind around, BOY!" Like a bunch inbred southern rednecks who are still hung up on allowing blacks and women to have civil rights.
Tell you what you want to be a bunch of discriminatory good old boys then get your hand back in your own pockets and out of the US tax payer pockets to fund your little "rich white guy only" play ground and then, when you fund it with your own money then you can do as you please with it and make it a private airport with an R on the sectional, then you can stop your lies and whining about other people who like exercising the same rights your afforded under federal aviation laws!
#### William McCauley 4 years, 11 months ago
4.BACKGROUND. In accordance with the FAA Airport and Airway Improvement Act of l982, 49U.S.C.§ 47101, et seq., 49 U.S.C. § 40103(e), and the Airport Improvement Program (AIP) grant assurances, the owner or operator of any airport that has been developed or improved with Federal grant assistance is required to operate the airport for the use and benefit of the public and to make it available for all types, kinds, and classes of aeronautical activity
a. Aeronautical Activity. Any activity that involves, makes possible, or is required for the operation of aircraft or that contributes to or is required for the safety of such operations. Activities within this definition, commonly conducted on airports, include, but are not limited to, the following: general and corporate aviation, air taxi and charter operations, scheduled and nonscheduled air carrier operations, pilot training, aircraft rental and sightseeing, aerial photography, crop dusting, aerial advertising and surveying, aircraft sales and services, aircraft storage, sale of aviation petroleum products, repair and maintenance of aircraft, sale of aircraft parts, parachute or ultralight activities, and any other activities that, because of their direct relationship to the operation of aircraft, can appropriately be regarded as aeronautical activities.
f. Availability of Fair and Reasonable Terms: (1) Applies to airports subject to: Any federal agreement or property conveyance.
(2) Obligation: To operate the airport for the use and benefit of the public to make it available to all types, kinds, and classes of aeronautical activity on fair and reasonable terms and without unjust discrimination.
(3) Duration of obligation: Twenty years from the date of execution for grant agreement prior to 1964. For grants executed subsequent to the passage of the Civil Rights Act of 1964, the statutory requirement prohibiting discrimination remains in effect for as long as the property is used as an airport. The obligation runs with the land for surplus property and section 16/23/516 conveyances.
Like I said, if your going to talk smack, at least learn what the rules are and where the money comes from and what is required by the "airport sponsor" once you take the money. If you want to take the funding then stop bitching about other airspace users, after all I'm sure I don't care your type of aviation but I go around asking for you to be banned from using the airport.
#### furman 4 years, 11 months ago
first of all i got some bad 87 oct gas and was a one time event back in 1995. and yes it is stc'd for 87 oct. my attemps to extract usable fuel from baby seals has failed. which isn't all bad because i found out that this type of fuel production is frowned upon.
chill out people you are way too serious. have a good summer!
Commenting has been disabled for this item. | 4,914 | 21,686 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2016-18 | longest | en | 0.934082 |
https://www.chegg.com/homework-help/advanced-mathematical-concepts-precalculus-with-applications-student-edition-6th-edition-chapter-2.2-problem-21e-solution-9780078608612 | 1,529,799,314,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267865438.16/warc/CC-MAIN-20180623225824-20180624005824-00566.warc.gz | 777,149,171 | 14,303 | # Advanced Mathematical Concepts: Precalculus With Applications, Student Edition (6th Edition) View more editions Solutions for Chapter 2.2 Problem 21E
• 6440 step-by-step solutions
• Solved by professors & experts
• iOS, Android, & web
Chapter: Problem:
Step-by-Step Solution:
Chapter: Problem:
• Step 1 of 4
Let us consider the equation
Here the height is in feet. And is time in seconds, is the initial velocity and is the initial height in feet
Let us suppose that the height is 124 ft at 1 second
And suppose that the height is 272 ft at 3 seconds
Suppose that the height is 82 ft at 8 seconds
We want to find the acceleration, the initial velocity, and initial height
• Chapter , Problem is solved.
Corresponding Textbook
Advanced Mathematical Concepts: Precalculus With Applications, Student Edition | 6th Edition
9780078608612ISBN-13: 0078608619ISBN: | 217 | 867 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2018-26 | latest | en | 0.830219 |
https://math.answers.com/Q/The_set_of_all_rational_and_irrational_numbers | 1,708,707,845,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474440.42/warc/CC-MAIN-20240223153350-20240223183350-00687.warc.gz | 399,366,326 | 46,655 | 0
# The set of all rational and irrational numbers?
Updated: 12/18/2022
Wiki User
13y ago
Are disjoint and complementary subsets of the set of real numbers.
Wiki User
10y ago
Wiki User
13y ago
Are in the set of real numbers.
Earn +20 pts
Q: The set of all rational and irrational numbers?
Submit
Still have questions?
Related questions
The Real numbers
### What numbers are set of all rational and irrational numbers called?
All rational numbers can be expressed as fractions whereas irrational numbers can't be expressed as fractions.
### Why is every rational number a real number?
There are rational numbers and irrational numbers. Real numbers are DEFINED as the union of the set of all rational numbers and the set of all irrational numbers. Consequently, all rationals, by definition, must be real numbers.
### Can a number be a member of the set of rational numbers in the set of irrational numbers?
No, a number is either rational or irrational
### What is the set of numbers that includes all rational and all irrational numbers?
the set of real numbers
Real numbers
real numbers
real numbers
### What is a set of rational and irrational numbers?
It is the set of Real numbers.
### Which is not included in the set of rational numbers?
All irrational numbers, complex number and so on.
### What numbers are The union of the rational and irrational numbers?
The real numbers.
real numbers | 300 | 1,426 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2024-10 | latest | en | 0.935362 |
https://mathematica.stackexchange.com/questions/130180/calculating-smallest-eigenvalues-by-real-part-using-arnoldi-method | 1,653,385,981,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662570051.62/warc/CC-MAIN-20220524075341-20220524105341-00573.warc.gz | 451,881,983 | 67,684 | Calculating smallest eigenvalues by real part using Arnoldi method
Bug introduced in 8.0 or earlier and persisting through 11.3
According to the documentation,
Eigenvalues[m,k] gives the first k eigenvalues of m ...
If they are numeric, eigenvalues are sorted in order of decreasing absolute value ...
Eigenvalues[m,-k] gives the k that are smallest in absolute value."
What is the output of Eigenvalues[m,-k] if one specifies a method?
For example, consider
SeedRandom[1122];
mat = (# + Transpose[#]) &[RandomReal[{-1, 1}, {4, 4}]];
Eigenvalues[mat]
(* {-2.35168, 2.30789, 1.26678, -0.48013} *)
Eigenvalues[mat, 2, Method -> {"Arnoldi"}]
(* {-2.35168, 2.30789} *)
Eigenvalues[mat, -2, Method -> {"Arnoldi"}]
(* {1.26678, -0.48013} *)
This is exactly what I'd expect: the first two and last two eigenvalues, respectively, sorted in descending order by absolute value as usual. But now consider
Eigenvalues[mat, 2, Method -> {"Arnoldi", "Criteria" -> "RealPart"}]
(* {2.30789, 1.26678} *)
Eigenvalues[mat, -2, Method -> {"Arnoldi", "Criteria" -> "RealPart"}]
(* {2.30789, 1.26678} *)
Why are the "first two" and "last two" eigenvalues the same? I would have expected the last line to return {-0.48013, -2.35168} - the last two eigenvalues sorted in descending order by real part.
(Mathematica v 11.0.1.0 on Mac OS X Yosemite v 10.10.5.)
• This does seem to directly contradict the documentation ... "Eigenvalues[m,spec] is always equivalent to Take[Eigenvalues[m],spec]." I suggest letting Wolfram Support know about this. Please let us know what they said. Nov 2, 2016 at 10:22
• Can you make the example reproducible? Put in a SeedRandom at the beginning with a seed that results in the unexpected output. Nov 2, 2016 at 10:24
• @Szabolcs This error occurs regardless of the choice of random seed. Also, this isn't exactly contradicting the documentation, because the statement you quoted does not apply to the case where one specifies a Method. (Attempting Take[Eigenvalues[mat, Method -> {"Arnoldi", "Criteria" -> "RealPart"}], -2] returns Eigenvalues::arall: Method -> Arnoldi cannot be used to compute more than 2 out of the 4 eigenvalues and/or eigenvectors.) Nov 2, 2016 at 20:50
• Maybe add your exact M version and OS as well, just in case. Nov 2, 2016 at 20:59
• I'm sorry, I'm not sure what I did exactly when I tried this, but if I copy your code now, as you wrote it, I do get identical results for 2 and -2. It appears that "smallest" is taken to be "smallest positive" for some reason. Try bigger matrices or using -1 instead of -2. -k seems to return the k smallest positive eigenvalues. BTW I also use M11.0.1 on OS X 10.12.1. Nov 2, 2016 at 21:53
Eigenvalues[mat, -2, Method -> {"Arnoldi", "Criteria"->"RealPart", "Shift"->-2.5}] | 815 | 2,766 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2022-21 | longest | en | 0.74182 |
http://stackoverflow.com/questions/287385/finding-all-vertices-in-a-graph-with-degree-smaller-than-their-neighbors/287546 | 1,430,734,921,000,000,000 | text/html | crawl-data/CC-MAIN-2015-18/segments/1430453976406.4/warc/CC-MAIN-20150501041936-00074-ip-10-235-10-82.ec2.internal.warc.gz | 183,867,236 | 18,254 | # finding all vertices in a graph with degree smaller than their neighbors
I'm trying to write an algorithm that will find the set of all vertices in a graph with degree smaller than their neighbors. My initial approach is to find the degree of each vertex, then work through the list, comparing the degree of each vertex with the degree(s) of its neighbors. Unfortunately, this looks like it could be very time consuming. Is there a more efficient way to find this set?
-
directed graph or no? – Brian R. Bondy Nov 13 '08 at 16:34
Perhaps "this looks like it could be very time consuming", but there is a better way of finding out :-)
Suppose you've stored your graph as an adjacency list. To find the set you're seeking, you necessarily have to look at all the edges, so we have a lower bound of Ω(|E|) for the algorithm. Finding the degree of every vertex takes time O(|E|) (because you look at every edge exactly once; another proof is to use the fact that ∑d(v)=2|E|). Comparing the degree of each vertex with all its neighbours also takes only O(|E|) time (again, for each edge, you make only one comparison). This means that your algorithm runs in O(|E|) time (about 2|E| "steps", but the precise number of CPU instructions depends on your implementation), which meets the lower bound. Thus your "brute-force" algorithm, in the worst case, is essentially (up to a small constant) as fast as possible, so it is not worth optimizing any further.
If you are doing this for a real-world application and you indeed find that your algorithm is taking too much time, then use a profiler to find what parts to optimize. It is not at all obvious that optimizing the second phase of the algorithm is crucial.
-
One comment - if you're working with undirected graphs (thanks, Brian R. Bondy), once you've determined that a vertex has degree less than that of all its neighbours, you don't need to check the neighbours, as none of them will have that property. Consider using that knowledge to help you out and speed things up.
-
If it is a directed graph, than this does not hold true. – Brian R. Bondy Nov 13 '08 at 16:38
That's an excellent point! Oh, the time away from academia has dulled my mind! – Blair Conrad Nov 13 '08 at 16:39
I would imagine a greedy approach for an undirected graph as follows:
``````let Q = all nodes which haven't been checked (initialize all V)
let Q* = all nodes which satisfy the required condition (initialize to empty)
while Q is not empty
let minDeg be the minimum degree of all v's neighbors
if degree(v) < minDeg | 603 | 2,560 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.625 | 4 | CC-MAIN-2015-18 | latest | en | 0.969871 |
https://www.jiskha.com/display.cgi?id=1482082298 | 1,529,306,015,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267860089.13/warc/CC-MAIN-20180618070542-20180618090542-00411.warc.gz | 860,293,045 | 5,465 | # Bayes' Theorem
posted by MILLY
I tried the problem and my answers are still coming up wrong?. You can compare to mine to see where you (or I) went wrong. I'm a little rusty on
Virus infects one in every 200 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. (This 10% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive".
a) Find the probability that a person has the virus given that they have tested positive, i.e. find P(A|B). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(A|B)= .0045
b) Find the probability that a person does not have the virus given that they test negative, i.e. find P(A'|B'). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(A'|B')
Bayes' Theorem problems.
--
Bayes' Theorem:
P( A|B ) = P(B|A) * P(A)/P(B)
P(A) = Pr{person is infected}
P(B) = Pr{person tests positive}
P(B|A) = Pr{person tests positive given that they are infected}
P(A) = 1/200 = 0.005
P(B) = (1/200)*0.90 + (199/200)*0.10 = 0.104
P(B|A) = 0.90
P(A|B) = 0.90 * 0.005 / 0.104 = 0.0433
—--
Comment: This answer is somewhat surprising. A 4.33% chance that the person has the virus given that they've tested positive. That seems way too low, but that's probably because the 10% false positive rate is pretty high. I think real world tests strive for a much lower false-positive rate.
——
A' = event 'person is not infected'
B' = event 'person tests negative'
P(B'|A') = probability of person testing negative given that they are not infected
P(A') = 199/200 = 0.995
P(B') = 0.896 ( = 1-P(B))
P(B'|A') = (199/200)(0.896) + (1/200)*0.104) = 0.89204
P(A'|B') = 0.89204*0.995/0.896 = 0.991
Comment: This answer makes sense. If a person tests negative, it is highly unlikely that they have the virus. Still, I suspect that 9/1000 is still too many false negatives for a real world scenario. I guess the importance of minimizing false negatives depends on how dangerous the virus is (its one thing not to detect if someone has a cold virus, its a different story to not detect they have Ebola, for example).
1. MathMate
Agree with the first part, except that with probability calculations, I prefer to work with fractions. If a decimal answer is required, it will be rounded at the end.
First Part:
P(A)=1/200
P(+|A)=9/10
P(-|A')=1/10
P(+)=P(+|A)+P(+|A')
=(1/200)(9/10)+(199/200)(1/10)
=13/125 ~0.104
P(A|+)=P(+|A)*P(A)/P(+)
=(9/10)(1/200)/(13/125)
=9/208 ~0.043269
1. high false positive rates, compared to
2. low incidence.
Second Part:
P(-|A')=(9/10) [given]
P(A')=1-P(A)=199/200
P(-)=P(-|A)+P(-|A')
=(1/200)(1-9/10)+(199/200)(9/10)
=112/125 ~ 0.896
P(A'|-)=P(-|A')P(A')/P(-)
=(9/10)(199/200)/(112/125)
=1791/1792 ~0.999442
False negative here is actually 1/1792~0.00055, which is reasonable.
2. Joe
Here is my solution:
Given probabilities: P(A) = 1/200 = 0.005 P(B) = 199/200 = 0.995 P(B|A) = 0.9 P(B|~A) = 0.1 Infer: P(~B|A) = 0.1 P(~B|~A) = 0.9 Then:
a.) Find P(A|B) P(A|B) = P(A)P(B|A) = 0.005×0.9 = 0.0045 rounds to 0.0
b.) Find P(~A|~B) P(~A|~B) = P(~A)P(~B|~A) = 0.995×0.9 = 0.896 rounds to 0.9 Note: the symbol ~A means A' in your notation. QED
3. Joe
Please ignore my entry: there is an error in the above calc. that I offered.
## Similar Questions
1. ### Algebra
I posted this problem last night and some one told me I was wrong. Today, two of my group members have the same answers for this problem. Can some one tell us what or where we went wrong?
2. ### Math
Hi, I tried this problem different ways, but keep getting it wrong.I am rusty, and need a demonstration of how to do it, thanks! 2x+6.7x-6
3. ### Math
Bayes' theorem problem, Struggling with this the whole night, please help.Thank you. Two states of nature exist for a particular situation: a good economy and a poor economy. An economic study may be performed to obtain more information …
4. ### Can someone help me please I've tired this problem
A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 80% of the time if the person has the virus and 5% of the time if the person does not have the virus. (This 5% result is called …
5. ### Conditional Probability
A certain virus infects one in every 600 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. Let A be the event "the …
6. ### CAN A TUTOR HELP ME WITH THIS PROBLEM PLEASE!
A certain virus infects one in every 600 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. Let A be the event "the …
7. ### Conditional Probability
A certain virus infects one in every 400 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. Let A be the event "the …
8. ### Really Need Help Please
A certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. (This 10% result is called …
9. ### Check Answer!! Conditional Probability
A certain virus infects one in every 500 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. Let A be the event "the …
10. ### Finite Math
A certain virus infects one in every 500 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. Find the probability that …
More Similar Questions | 1,820 | 5,994 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2018-26 | latest | en | 0.929753 |
https://oeis.org/A235615 | 1,701,505,720,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100381.14/warc/CC-MAIN-20231202073445-20231202103445-00334.warc.gz | 502,306,578 | 4,990 | The OEIS is supported by the many generous donors to the OEIS Foundation.
Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60, we have over 367,000 sequences, and we’ve crossed 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A235615 Primes whose base-5 representation also is the base-4 representation of a prime. 28
2, 3, 13, 41, 43, 61, 181, 191, 263, 281, 283, 331, 383, 431, 443, 463, 641, 643, 661, 881, 911, 1063, 1091, 1291, 1303, 1531, 1693, 2083, 2143, 2203, 2293, 2341, 3163, 3181, 3191, 3253, 3343, 3593, 3761, 3931, 4001, 4093, 4391, 4691, 4793, 5011, 5393, 5413, 5441, 6301 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 COMMENTS This sequence is part of the two-dimensional array of sequences based on this same idea for any two different bases b, c > 1. Sequence A235265 and A235266 are the most elementary ones in this list. Sequences A089971, A089981 and A090707 through A090721, and sequences A065720 - A065727, follow the same idea with one base equal to 10. LINKS Robert Price, Table of n, a(n) for n = 1..107268 M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime EXAMPLE Both 13 = 23_5 and 23_4 = 11 are prime. PROG (PARI) is(p, b=4, c=5)=vecmax(d=digits(p, c))
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified December 2 03:27 EST 2023. Contains 367505 sequences. (Running on oeis4.) | 586 | 1,780 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.421875 | 3 | CC-MAIN-2023-50 | latest | en | 0.789616 |
http://www.netlib.org/lapack/patch-3.0/timing/eig/eigsrc/chgeqz.f | 1,369,514,300,000,000,000 | text/plain | crawl-data/CC-MAIN-2013-20/segments/1368706298270/warc/CC-MAIN-20130516121138-00056-ip-10-60-113-184.ec2.internal.warc.gz | 614,974,431 | 7,788 | SUBROUTINE CHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT, \$ ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK, \$ RWORK, INFO ) * * -- LAPACK routine (instrumented to count operations, version 3.0) -- * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., * Courant Institute, Argonne National Lab, and Rice University * May 3, 2001 * * .. Scalar Arguments .. CHARACTER COMPQ, COMPZ, JOB INTEGER IHI, ILO, INFO, LDH, LDQ, LDT, LDZ, LWORK, N * .. * .. Array Arguments .. REAL RWORK( * ) COMPLEX ALPHA( * ), BETA( * ), H( LDH, * ), \$ Q( LDQ, * ), T( LDT, * ), WORK( * ), \$ Z( LDZ, * ) * .. * * ----------------------- Begin Timing Code ------------------------ * Common block to return operation count and iteration count * ITCNT is initialized to 0, OPS is only incremented * OPST is used to accumulate small contributions to OPS * to avoid roundoff error * .. Common blocks .. COMMON / LATIME / OPS, ITCNT * .. * .. Scalars in Common .. REAL ITCNT, OPS * .. * ------------------------ End Timing Code ------------------------- * * * Purpose * ======= * * CHGEQZ computes the eigenvalues of a complex matrix pair (H,T), * where H is an upper Hessenberg matrix and T is upper triangular, * using the single-shift QZ method. * Matrix pairs of this type are produced by the reduction to * generalized upper Hessenberg form of a complex matrix pair (A,B): * * A = Q1*H*Z1**H, B = Q1*T*Z1**H, * * as computed by CGGHRD. * * If JOB='S', then the Hessenberg-triangular pair (H,T) is * also reduced to generalized Schur form, * * H = Q*S*Z**H, T = Q*P*Z**H, * * where Q and Z are unitary matrices and S and P are upper triangular. * * Optionally, the unitary matrix Q from the generalized Schur * factorization may be postmultiplied into an input matrix Q1, and the * unitary matrix Z may be postmultiplied into an input matrix Z1. * If Q1 and Z1 are the unitary matrices from CGGHRD that reduced * the matrix pair (A,B) to generalized Hessenberg form, then the output * matrices Q1*Q and Z1*Z are the unitary factors from the generalized * Schur factorization of (A,B): * * A = (Q1*Q)*S*(Z1*Z)**H, B = (Q1*Q)*P*(Z1*Z)**H. * * To avoid overflow, eigenvalues of the matrix pair (H,T) * (equivalently, of (A,B)) are computed as a pair of complex values * (alpha,beta). If beta is nonzero, lambda = alpha / beta is an * eigenvalue of the generalized nonsymmetric eigenvalue problem (GNEP) * A*x = lambda*B*x * and if alpha is nonzero, mu = beta / alpha is an eigenvalue of the * alternate form of the GNEP * mu*A*y = B*y. * The values of alpha and beta for the i-th eigenvalue can be read * directly from the generalized Schur form: alpha = S(i,i), * beta = P(i,i). * * Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix * Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973), * pp. 241--256. * * Arguments * ========= * * JOB (input) CHARACTER*1 * = 'E': Compute eigenvalues only; * = 'S': Computer eigenvalues and the Schur form. * * COMPQ (input) CHARACTER*1 * = 'N': Left Schur vectors (Q) are not computed; * = 'I': Q is initialized to the unit matrix and the matrix Q * of left Schur vectors of (H,T) is returned; * = 'V': Q must contain a unitary matrix Q1 on entry and * the product Q1*Q is returned. * * COMPZ (input) CHARACTER*1 * = 'N': Right Schur vectors (Z) are not computed; * = 'I': Q is initialized to the unit matrix and the matrix Z * of right Schur vectors of (H,T) is returned; * = 'V': Z must contain a unitary matrix Z1 on entry and * the product Z1*Z is returned. * * N (input) INTEGER * The order of the matrices H, T, Q, and Z. N >= 0. * * ILO (input) INTEGER * IHI (input) INTEGER * ILO and IHI mark the rows and columns of H which are in * Hessenberg form. It is assumed that A is already upper * triangular in rows and columns 1:ILO-1 and IHI+1:N. * If N > 0, 1 <= ILO <= IHI <= N; if N = 0, ILO=1 and IHI=0. * * H (input/output) COMPLEX array, dimension (LDH, N) * On entry, the N-by-N upper Hessenberg matrix H. * On exit, if JOB = 'S', H contains the upper triangular * matrix S from the generalized Schur factorization. * If JOB = 'E', the diagonal of H matches that of S, but * the rest of H is unspecified. * * LDH (input) INTEGER * The leading dimension of the array H. LDH >= max( 1, N ). * * T (input/output) COMPLEX array, dimension (LDT, N) * On entry, the N-by-N upper triangular matrix T. * On exit, if JOB = 'S', T contains the upper triangular * matrix P from the generalized Schur factorization. * If JOB = 'E', the diagonal of T matches that of P, but * the rest of T is unspecified. * * LDT (input) INTEGER * The leading dimension of the array T. LDT >= max( 1, N ). * * ALPHA (output) COMPLEX array, dimension (N) * The complex scalars alpha that define the eigenvalues of * GNEP. ALPHA(i) = S(i,i) in the generalized Schur * factorization. * * BETA (output) COMPLEX array, dimension (N) * The real non-negative scalars beta that define the * eigenvalues of GNEP. BETA(i) = P(i,i) in the generalized * Schur factorization. * * Together, the quantities alpha = ALPHA(j) and beta = BETA(j) * represent the j-th eigenvalue of the matrix pair (A,B), in * one of the forms lambda = alpha/beta or mu = beta/alpha. * Since either lambda or mu may overflow, they should not, * in general, be computed. * * Q (input/output) COMPLEX array, dimension (LDQ, N) * On entry, if COMPZ = 'V', the unitary matrix Q1 used in the * reduction of (A,B) to generalized Hessenberg form. * On exit, if COMPZ = 'I', the unitary matrix of left Schur * vectors of (H,T), and if COMPZ = 'V', the unitary matrix of * left Schur vectors of (A,B). * Not referenced if COMPZ = 'N'. * * LDQ (input) INTEGER * The leading dimension of the array Q. LDQ >= 1. * If COMPQ='V' or 'I', then LDQ >= N. * * Z (input/output) COMPLEX array, dimension (LDZ, N) * On entry, if COMPZ = 'V', the unitary matrix Z1 used in the * reduction of (A,B) to generalized Hessenberg form. * On exit, if COMPZ = 'I', the unitary matrix of right Schur * vectors of (H,T), and if COMPZ = 'V', the unitary matrix of * right Schur vectors of (A,B). * Not referenced if COMPZ = 'N'. * * LDZ (input) INTEGER * The leading dimension of the array Z. LDZ >= 1. * If COMPZ='V' or 'I', then LDZ >= N. * * WORK (workspace/output) COMPLEX array, dimension (LWORK) * On exit, if INFO >= 0, WORK(1) returns the optimal LWORK. * * LWORK (input) INTEGER * The dimension of the array WORK. LWORK >= max(1,N). * * If LWORK = -1, then a workspace query is assumed; the routine * only calculates the optimal size of the WORK array, returns * this value as the first entry of the WORK array, and no error * message related to LWORK is issued by XERBLA. * * RWORK (workspace) REAL array, dimension (N) * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * = 1,...,N: the QZ iteration did not converge. (H,T) is not * in Schur form, but ALPHA(i) and BETA(i), * i=INFO+1,...,N should be correct. * = N+1,...,2*N: the shift calculation failed. (H,T) is not * in Schur form, but ALPHA(i) and BETA(i), * i=INFO-N+1,...,N should be correct. * * Further Details * =============== * * We assume that complex ABS works as long as its value is less than * overflow. * * ===================================================================== * * .. Parameters .. COMPLEX CZERO, CONE PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ), \$ CONE = ( 1.0E+0, 0.0E+0 ) ) REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) REAL HALF PARAMETER ( HALF = 0.5E+0 ) * .. * .. Local Scalars .. LOGICAL ILAZR2, ILAZRO, ILQ, ILSCHR, ILZ, LQUERY INTEGER ICOMPQ, ICOMPZ, IFIRST, IFRSTM, IITER, ILAST, \$ ILASTM, IN, ISCHUR, ISTART, J, JC, JCH, JITER, \$ JR, MAXIT, NQ, NZ REAL ABSB, ANORM, ASCALE, ATOL, BNORM, BSCALE, BTOL, \$ C, OPST, SAFMIN, TEMP, TEMP2, TEMPR, ULP COMPLEX ABI22, AD11, AD12, AD21, AD22, CTEMP, CTEMP2, \$ CTEMP3, ESHIFT, RTDISC, S, SHIFT, SIGNBC, T1, \$ U12, X * .. * .. External Functions .. LOGICAL LSAME REAL CLANHS, SLAMCH EXTERNAL LSAME, CLANHS, SLAMCH * .. * .. External Subroutines .. EXTERNAL CLARTG, CLASET, CROT, CSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, AIMAG, CMPLX, CONJG, MAX, MIN, REAL, SQRT * .. * .. Statement Functions .. REAL ABS1 * .. * .. Statement Function definitions .. ABS1( X ) = ABS( REAL( X ) ) + ABS( AIMAG( X ) ) * .. * .. Executable Statements .. * ----------------------- Begin Timing Code ------------------------ ITCNT = ZERO * ------------------------ End Timing Code ------------------------- * * Decode JOB, COMPQ, COMPZ * IF( LSAME( JOB, 'E' ) ) THEN ILSCHR = .FALSE. ISCHUR = 1 ELSE IF( LSAME( JOB, 'S' ) ) THEN ILSCHR = .TRUE. ISCHUR = 2 ELSE ISCHUR = 0 END IF * IF( LSAME( COMPQ, 'N' ) ) THEN ILQ = .FALSE. ICOMPQ = 1 NQ = 0 ELSE IF( LSAME( COMPQ, 'V' ) ) THEN ILQ = .TRUE. ICOMPQ = 2 NQ = N ELSE IF( LSAME( COMPQ, 'I' ) ) THEN ILQ = .TRUE. ICOMPQ = 3 NQ = N ELSE ICOMPQ = 0 END IF * IF( LSAME( COMPZ, 'N' ) ) THEN ILZ = .FALSE. ICOMPZ = 1 NZ = 0 ELSE IF( LSAME( COMPZ, 'V' ) ) THEN ILZ = .TRUE. ICOMPZ = 2 NZ = N ELSE IF( LSAME( COMPZ, 'I' ) ) THEN ILZ = .TRUE. ICOMPZ = 3 NZ = N ELSE ICOMPZ = 0 END IF * * Check Argument Values * INFO = 0 WORK( 1 ) = MAX( 1, N ) LQUERY = ( LWORK.EQ.-1 ) IF( ISCHUR.EQ.0 ) THEN INFO = -1 ELSE IF( ICOMPQ.EQ.0 ) THEN INFO = -2 ELSE IF( ICOMPZ.EQ.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( ILO.LT.1 ) THEN INFO = -5 ELSE IF( IHI.GT.N .OR. IHI.LT.ILO-1 ) THEN INFO = -6 ELSE IF( LDH.LT.N ) THEN INFO = -8 ELSE IF( LDT.LT.N ) THEN INFO = -10 ELSE IF( LDQ.LT.1 .OR. ( ILQ .AND. LDQ.LT.N ) ) THEN INFO = -14 ELSE IF( LDZ.LT.1 .OR. ( ILZ .AND. LDZ.LT.N ) ) THEN INFO = -16 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN INFO = -18 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'CHGEQZ', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * c WORK( 1 ) = CMPLX( 1 ) IF( N.LE.0 ) THEN WORK( 1 ) = CMPLX( 1 ) RETURN END IF * * Initialize Q and Z * IF( ICOMPQ.EQ.3 ) \$ CALL CLASET( 'Full', N, N, CZERO, CONE, Q, LDQ ) IF( ICOMPZ.EQ.3 ) \$ CALL CLASET( 'Full', N, N, CZERO, CONE, Z, LDZ ) * * Machine Constants * IN = IHI + 1 - ILO SAFMIN = SLAMCH( 'S' ) ULP = SLAMCH( 'E' )*SLAMCH( 'B' ) ANORM = CLANHS( 'F', IN, H( ILO, ILO ), LDH, RWORK ) BNORM = CLANHS( 'F', IN, T( ILO, ILO ), LDT, RWORK ) ATOL = MAX( SAFMIN, ULP*ANORM ) BTOL = MAX( SAFMIN, ULP*BNORM ) ASCALE = ONE / MAX( SAFMIN, ANORM ) BSCALE = ONE / MAX( SAFMIN, BNORM ) * * ---------------------- Begin Timing Code ------------------------- * Count ops for norms, etc. OPST = ZERO OPS = OPS + REAL( 4*N**2+12*N-5 ) * ----------------------- End Timing Code -------------------------- * * * * Set Eigenvalues IHI+1:N * DO 10 J = IHI + 1, N ABSB = ABS( T( J, J ) ) IF( ABSB.GT.SAFMIN ) THEN SIGNBC = CONJG( T( J, J ) / ABSB ) T( J, J ) = ABSB IF( ILSCHR ) THEN CALL CSCAL( J-1, SIGNBC, T( 1, J ), 1 ) CALL CSCAL( J, SIGNBC, H( 1, J ), 1 ) * ----------------- Begin Timing Code --------------------- OPST = OPST + REAL( 12*( J-1 ) ) * ------------------ End Timing Code ---------------------- ELSE H( J, J ) = H( J, J )*SIGNBC END IF IF( ILZ ) \$ CALL CSCAL( N, SIGNBC, Z( 1, J ), 1 ) * ------------------- Begin Timing Code ---------------------- OPST = OPST + REAL( 6*NZ+13 ) * -------------------- End Timing Code ----------------------- ELSE T( J, J ) = CZERO END IF ALPHA( J ) = H( J, J ) BETA( J ) = T( J, J ) 10 CONTINUE * * If IHI < ILO, skip QZ steps * IF( IHI.LT.ILO ) \$ GO TO 190 * * MAIN QZ ITERATION LOOP * * Initialize dynamic indices * * Eigenvalues ILAST+1:N have been found. * Column operations modify rows IFRSTM:whatever * Row operations modify columns whatever:ILASTM * * If only eigenvalues are being computed, then * IFRSTM is the row of the last splitting row above row ILAST; * this is always at least ILO. * IITER counts iterations since the last eigenvalue was found, * to tell when to use an extraordinary shift. * MAXIT is the maximum number of QZ sweeps allowed. * ILAST = IHI IF( ILSCHR ) THEN IFRSTM = 1 ILASTM = N ELSE IFRSTM = ILO ILASTM = IHI END IF IITER = 0 ESHIFT = CZERO MAXIT = 30*( IHI-ILO+1 ) * DO 170 JITER = 1, MAXIT * * Check for too many iterations. * IF( JITER.GT.MAXIT ) \$ GO TO 180 * * Split the matrix if possible. * * Two tests: * 1: H(j,j-1)=0 or j=ILO * 2: T(j,j)=0 * * Special case: j=ILAST * IF( ILAST.EQ.ILO ) THEN GO TO 60 ELSE IF( ABS1( H( ILAST, ILAST-1 ) ).LE.ATOL ) THEN H( ILAST, ILAST-1 ) = CZERO GO TO 60 END IF END IF * IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN T( ILAST, ILAST ) = CZERO GO TO 50 END IF * * General case: j | 4,129 | 12,512 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2013-20 | latest | en | 0.687505 |
https://uk.mathworks.com/matlabcentral/profile/authors/7011749?s_tid=cody_local_to_profile | 1,610,721,257,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703495901.0/warc/CC-MAIN-20210115134101-20210115164101-00403.warc.gz | 697,914,675 | 19,122 | Community Profile
# Aaron Heng
11 total contributions since 2015
View details...
Contributions in
View by
Solved
Determine whether a vector is monotonically increasing
Return true if the elements of the input vector increase monotonically (i.e. each element is larger than the previous). Return f...
5 years ago
Solved
Swap the first and last columns
Flip the outermost columns of matrix A, so that the first column becomes the last and the last column becomes the first. All oth...
5 years ago
Solved
Make a checkerboard matrix
Given an integer n, make an n-by-n matrix made up of alternating ones and zeros as shown below. The a(1,1) should be 1. Example...
5 years ago
Solved
Triangle Numbers
Triangle numbers are the sums of successive integers. So 6 is a triangle number because 6 = 1 + 2 + 3 which can be displa...
5 years ago
Solved
Column Removal
Remove the nth column from input matrix A and return the resulting matrix in output B. So if A = [1 2 3; 4 5 6]; and ...
5 years ago
Solved
Select every other element of a vector
Write a function which returns every other element of the vector passed in. That is, it returns the all odd-numbered elements, s...
5 years ago
Solved
Determine if input is odd
Given the input n, return true if n is odd or false if n is even.
5 years ago
Solved
Given a and b, return the sum a+b in c.
5 years ago
Solved
Find the sum of all the numbers of the input vector
Find the sum of all the numbers of the input vector x. Examples: Input x = [1 2 3 5] Output y is 11 Input x ...
5 years ago
Solved
Make the vector [1 2 3 4 5 6 7 8 9 10]
In MATLAB, you create a vector by enclosing the elements in square brackets like so: x = [1 2 3 4] Commas are optional, s...
5 years ago
Solved
Times 2 - START HERE
Try out this test problem first. Given the variable x as your input, multiply it by two and put the result in y. Examples:...
5 years ago | 513 | 1,916 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2021-04 | latest | en | 0.762413 |
https://hal149.com/pyspark-neural-network-from-scratch/ | 1,632,057,854,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780056890.28/warc/CC-MAIN-20210919125659-20210919155659-00045.warc.gz | 345,884,194 | 35,953 | ## A simple tutorial to learn how to implement a Shallow Neural Network (3 fully connected layers) using PySpark.
This article is not intended to provide mathematical explanations of neural networks, but only to explain how to apply the mathematical equations to run it using Spark (MapReduce) logic in Python. For simplicity, this implementation only uses RDDs (and no DataFrames).
Similarly, I assume that you have Spark installed in your machine and that you can either run a spark-submit or a PySpark Jupyter-Notebook.
All the code provided in this tutorial is available on this GitHub Repository.
Just in case, here are some resources to set up your machine to be able to run the code:
Also, throughout this article, I will base my explanation on one of my previous medium articles that explains the math behind a 3-layer neural network. Most of the mathematical formulas I will provide are extracted and discussed here:
If you are already familiar with deep learning, you may have already encountered GPU/CPU memory limitations. This usually occurs when you try to provide too much input data (either through a large batch size or large input feature space) that resources cannot handle.
Therefore, with the previous statement, it seems almost impossible to provide several hundred gigabytes as input to your model. This is even more relevant for Machine Learning algorithms that mostly use CPU computation (Linear Regression, SVM, Logistic Regression, Naive Bayes, …).
Spark is a powerful solution for processing very large amounts of data. It allows to distribute the computation on a network of computers (often called a cluster). Spark facilitates the implementation of iterative algorithms that analyze a set of data multiple times in a loop. Spark is widely used in machine learning projects.
As you might already know, famous libraries like TensorFlow or Pytorch are generally used to build Neural Networks. One of the benefits of using these libraries is GPU computation that speeds up the training by allowing parallel computing.
The latest versions of Spark also allow the use of GPUs, but in this article, we will only focus on CPU computation (like most scratch implementations of neural networks) to keep it simple. This article proposes an implementation for learning purposes that does not fit industrial needs.
For this tutorial, we will try to solve the well-known MNIST… | 457 | 2,405 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2021-39 | latest | en | 0.912883 |
https://esperanto.stackexchange.com/tags/correlatives/hot | 1,637,968,780,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358074.14/warc/CC-MAIN-20211126224056-20211127014056-00541.warc.gz | 293,289,687 | 25,450 | # Tag Info
12
According to PMEG: Oni uzas ĉiu, se oni konsideras la individuojn aparte. Oni uzas ĉiuj, se oni pensas pri la tuta grupo kune. I.e. ĉiu corresponds (for the most part) to "each" and ĉiuj to "all". Examples: Al ĉiu el la infanoj mi donis po tri pomoj -> I gave each of my children three apples (each individual ended up with three of their own) El ĉiuj miaj ...
11
The -o correlatives are noun-like and although they don't take a plural, they are described by adjectives, not adverbs. Therefore, in every case that you listed, you would need an adjective. Tio estas vera. Ĉio estas mirinda en nia mondo. Io ne estas ĝusta pri ĝi. Your last two examples could be adverbs depending on what you mean. Io stranga okazis - ...
10
The formation of the correlatives is based on a logical table of combinations of two pieces, so in a sense if you can learn all of the pieces you can effectively learn all of the words without having to memorise them. When I was learning them the course book I was using had them represented as a table in the appendix at the back which really helped me to ...
10
Just think of kiom as a numeral like unu, du, tri...kiom? (one, two, three...how many?) Unua means first, dua is second, tria is third, dudeka is twentieth. Kioma is, well, there is no word for it in English (other languages do have such words), but you might imagine something like "how manyeth?". Saying kioma you are asking for an ordinal number: Kioma ...
9
Kioma is used to ask about anything which is an ordered sequence. Here are some examples of it being used other than to ask the time. Kaj li rememoris (kioman fojon en ĉi tiu jaro!) la maljustaĵojn De la kioma etaĝo vi estas? ĝis kioma grado (dua, tria, ktp.) de kioma tago kaj de kiu monato Kiome is much less common. My take is that it's a synonym for ...
7
The best way to learn grammar is to read a good book about the subject. The best book about Esperanto is probably Plena Manlibro de Esperanta Gramatiko and it is free. But this approach is not simple and suitable for beginners. Use it when you feel ready. I suggest you do not start studying the entire table. Some correlative are very rare. See the ...
7
In much the same way I treat active and passive participles, as I practice and read new things, I try to use the exhaustive definition of each correlative so that it sticks into my brain in a more rounded way. This is especially useful for the ti-, i-, ĉi-, neni- correlatives: I read tial as "(for) that reason", ial as "(for) some reason", etc. It also ...
7
The photo is from the Scienca Revuo vol. 3, nr-o. 12 (1952). Otherwise, I think they are inspired by Russian, but completely regular: "inspiritaj de la rusaj escepte regulaj korelativoj)", as this webpage says.
7
Ambaŭ estas ĝustaj, kaj la poseda rilato povas preni iun ajn formon: de unu al unu, de unu al pluraj, de pluraj al unu, de pluraj al pluraj, ktp. Ĉies patrino ricevos cent dolarojn. (= la patrino de ĉiu) Ĉi tiu mondo estas ĉies mondo. (= la mondo de ĉiuj) Ĉies gepatroj ricevos cent dolarojn. (= la gepatroj de ĉiu) Ĉi tiuj libroj en la librejo estas ĉies ...
6
"nun" and "ĉi tiam" are very different nun is for referencing the present time. tiam is for referencing a particuliar moment, that can be the present time, but not always. ĉi can indicate proximity in time, but also in context (where you put the focus in one particuliar time out of several that were mentionned). Even when "ĉi" is used for time proximity, ...
6
En tiaj okazoj oni uzas ĝenerale la singularon, ĉar la pluralo (kiel markita, pli specifa formo) implikus, ke oni ja scias, ke temas pri ia kvanto (>1) kaj volas nur ekscii, kiom ekzakte.
6
Don't try to memorize them at once. Just try to concentrate on some specific topic and talk about this specific topic. Use as little of them as possible. But the most important thing is: learn only in context Example. Try to talk about the weather. Build sentences like this: Kia estas la vetero? - La vetero estas varma Kiam la vetero denove iĝas malvarma?...
6
I think this was clearly a case of Zamenhof using a system that was in common use among Romance languages. For example the proximal pronouns in French are (ce, ici, ci) and in Italian it's (ci) So, it appears that he took both the idea and form from those languages.
5
1) Know alternatives. It helps understanding. When you are confident enough, use the corresponding correlative. This will help you for the second part of the correlative. Tio -> Tiu aĵo/afero Tie -> En tiu ejo/loko Tiam -> En tiu momento Tiom -> En tiu kvanto Tia -> En tiu tipo Tiel -> En tiu maniero Ties -> De tiu persono 2) Memorize by rote some examples ...
4
According to PMEG: Ĉi tiam aŭ tiam ĉi ne estas praktike uzataj. Anstataŭe oni uzas nun. Noto: La preciza nuanco de ĉi tiam estas malklara, ĉar ĝi apenaŭ estas uzata. Oni povus diskuti, ĉu ĉi tiam estas preferinda, kiam temas pri okazoj kaj kondiĉoj, dum nun ordinare estas tempa. Eble tempa ĉi tiam povas esti malpli forte ligita al la absoluta ...
4
put in Tio estas vere, simply because that sounded more familiar. Now I want to know, is that grammatically wrong? Yes. It is wrong. Tio takes the place of a noun. Describing a noun with an adverb doesn't work. Adverbs modify verbs (they also modify adjectives and other adverbs). Tio estas vere = That thing (tio) really is (estas vere)... - It is an ...
4
There is certainly a lot of overlap - but notice that in your examples, ĝin generally replaces nouns and noun phrases, while tion replaces verbs and phrases that include verbs.
4
Simply put, ĉiu is singular and ĉiuj is plural. Therefore, ĉiu refers to one thing at a time, and ĉiuj refers to many things (collectively.) You can also check how these are glossed in a bilingual dictionary. ĉiu: each, chacun, jede ĉiuj: all, tous, alle
4
The grammar on lernu has a very extensive explanation of the correlatives, that is too long to cite here but definitely worth checking out. Here is a link to the English version of it. (You can change the language at the bottom if you want to read it in a different language, assuming a translation is available). There is also a nice table layout of the ...
4
Yes, it can be omitted there too: Estas makaronioj [tio], kion ni manĝas. Pli da informo: PMEG - Rilata kio
4
"You have such a cute dog!" Vi havas beletan hundon! If you are suprised, say because you only have cats, then you could say: What dog? Ĉu hundon? (it is a bit what you looked for when you mentioned kio hundo?) Maybe you have many dogs and you'd like to know which one is the cute one, then: Which dog? Kiun hundon? You will be understood if you ask: ...
4
alia iu - something/someone else Oni diras iu alia. La klarigo gramatika troveblas ĉi tie, sed oni povas resumi jene: "Iu iom similas al individueca aŭ duondifina unu." alia io Kvankam vi teorie povus diri tion tiel (Zamenhof en frua teksto skribis "kio estas la aldona io, pri kiu ...") la kutima ordo estas io alia. io ajn malbona - ...
3
I had a lot of trouble learning the correlatives until I broke them down and learned each part individually. So, I rote memorized ki-, i-, neni-, etc and -am, -om, -el, etc. Then I started working on parsing the words in texts: ki-am, ki-el, ki-o, etc. Then eventually they turned into their own words: kiam, kiel, kio. That was what worked best for me.
3
All correlatives start with ki, meaning a question or relative pronoun; ĉi, meaning every; i, meaning some; nen meaning "no," or ti, meaning "that". This is what marks it as a correlative. Next, we add the part-of-speech marker. -o marks it as a noun, so "kio" means something like "question-noun," or "what," while ĉio means "every-noun," which translates ...
2
The pseudo prefixes are Indoeuropean, ki- for instance from q- which in Slavonic and Romance became k- / q- and in Germanic, Sanskrit (conjunctions only) w-. ĉi- for the French chaque. neni- instead of a fitting ni- because of French and sound differentiation, negative ne. The pseudo suffixes -a, -o, and even the location related adverb -e, -en are trivial. ...
2
Ŝajnas ke plej plena priskribo de korelativoj estas en libro Etimologia Vortaro de Esperanto. Se vi komprenas la rusan en la artikolon vi eblas legi rerakonton pri korelativoj.
2
Being at home in the matrix of correlatives with their meaning is the most important. ki- question or subphrase, -u selected (adj, person). Then search the difference between kio and kiom, by inventing examples. So one can feel certain on their correctness when using. The memorizing is the easiest part, because of the cross-wise repetition of those ...
2
I have silly tricks for remembering, these are mine but everyone should come up with their own. kiel - is an anagram of like and the question "how did it happen" is answered by "it happened like this" kiam - this is easy since "am" is used for time, as in 9am. kial - I remember the phrase "why do I Always Laugh?" kiu - the "u" is a bit like the end of "...
2
Memorizing them is the best way, I think. I used the Memrise course. But an essential part of learning the correlatives is using them as jokes. Conversation like these make so much more fun in Esperanto: Why? Because. Kial? Tial. 😄
2
Its very difficult to simply memorise them. So, study a little and let them soak into your brain over time through reading and listening. This is a very good book: Mastering the Correlatives in Esperanto: Learning from Examples
Only top voted, non community-wiki answers of a minimum length are eligible | 2,682 | 9,560 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2021-49 | longest | en | 0.650337 |
https://community.wolfram.com/groups/-/m/t/387971 | 1,685,241,406,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224643462.13/warc/CC-MAIN-20230528015553-20230528045553-00566.warc.gz | 210,406,414 | 22,203 | # Sort & Permutation
Posted 9 years ago
3505 Views
|
2 Replies
|
0 Total Likes
|
Greetings,I would like to obtain the permutation resulting from the sorting of the given list (as opposed to the sorted list): input = {5.3, 2.7, 9.2, 0.0} output = {0.0, 2.7, 5.3, 9.2} Desired Output = {4, 2, 1, 3} Thanks in advance
2 Replies
Sort By:
Posted 9 years ago
In[17]:= input = {5.3, 2.7, 9.2, 0.0} Out[17]= {5.3, 2.7, 9.2, 0.}In[18]:= Ordering[input, 4]Out[18]= {4, 2, 1, 3}
Posted 9 years ago
Ordering does this. | 212 | 510 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2023-23 | longest | en | 0.785302 |
https://www.jiskha.com/questions/770221/2-If-a-firm-increases-all-of-its-inputs-by-60-percent-and-its-output-increases-by | 1,544,794,875,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376825728.30/warc/CC-MAIN-20181214114739-20181214140239-00121.warc.gz | 960,509,834 | 5,338 | # Economics
2. If a firm increases all of its inputs by 60 percent and its output increases by 90 percent, then you know that:
A) it is encountering diseconomies of scale.
B) it is encountering economies of scale.
C) it is encountering constant returns to scale.
D) the marginal products of all inputs are falling.
1. 0
2. 0
3. 5
1. B
1. 0
2. 0
posted by JJJ
## Similar Questions
1. ### economics
Suppose that when a firm increases output by 20%, long-run total cost increases by 50%. The firm will experience
asked by Annie on August 19, 2012
2. ### Help-Econ
Okay, this is due Tuesday. I'm woking on it but if anyone can help that would be great! Suppose firm A opeates in a perfectly competitive market. The price that currently prevails in the market is \$1,000. Firm A's marginal cost is
asked by Trisha on June 21, 2005
3. ### math
in scatterplot comparing x and y, the y-values are along the vertical axis. the line of the best fit is horizontal. which statement best describes relationship between x and y? a)as x increases y increases b)as x increases y
asked by vernee on March 28, 2009
4. ### Economics
The firm currently uses 70,000 workers to produce 300,000 units of output per day. The daily wage (per worker) is \$100, and the price of the firm’s output is \$30. The cost of other variable inputs is \$500,000 per day. Although
asked by Vision on November 18, 2008
5. ### Math
The firm currently uses 70,000 workers to produce 300,000 units of output per day. The daily wage (per worker) is \$100, and the price of the firm’s output is \$30. The cost of other variable inputs is \$500,000 per day. Although
asked by Randy Tan. on November 18, 2008
6. ### mirco-economics
The firm currently uses 50,000 workers to produce 200,000 units of output per day. The daily wage per worker is \$80, and the price of the firm’s output is \$25. The cost of other variable inputs is \$400,000 per day
asked by brynda on June 26, 2011
7. ### Statistics
As x increases, does the value of r imply that y should tend to increase, decrease, or remain the same? Explain. ( Since r is zero, as x increases, y decreases. Since r is negative, as x increases, y remains the same. Since r is
asked by alex on June 24, 2010
8. ### Microeconomics [Urgent!]
I have an exam tomorrow and I really need to know how you get the following answers. Please show me! I know it's a lot of questions, but I don't understand how you get the answer... ------------------ 40. At Nick's Bakery, the
asked by Anonymous on December 8, 2008
9. ### microeconomics
A firm currently uses 40,000 workers to produce 180,000 units of output per day. The daily wage per worker is \$100, and the price of the firm's output is \$28. The cost of other variable inputs is \$500,000 per day. (Note: Assume
asked by Evelyn on October 30, 2015 | 773 | 2,824 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2018-51 | longest | en | 0.944469 |
https://writeaaq.firebaseapp.com/mcgauley34327wat/how-to-write-15-dollars-on-a-check-cyq.html | 1,685,956,656,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224651815.80/warc/CC-MAIN-20230605085657-20230605115657-00430.warc.gz | 671,285,122 | 6,481 | # How to write 15 dollars on a check
How To 15x A Subscription Ecommerce Business Tired of the chasing down the one-time transaction? Do you want more predictable revenue? Then a subscription ecommerce business might be what you need. How to Write a Check for 100 Dollars Correctly - YouTube
15 (number) - Wikipedia 15 (fifteen) is a number, numeral, and glyph. It is the natural number following 14 and ... See Wikipedia's guide to writing better articles for further suggestions. See How to Write Dollars and Cents on a Check - The Balance Write everything together on one line so that it reads “Eight dollars and 15/100.” For a detailed example of how to write a check, see a step-by-step tutorial that ... How to Write a Check - An Example With Six Easy Steps & Pictures October 21st, 2015, Oct 21, 2015, 10/21/2015, 10/21/15. ... Step 4: Write the check amount in words on the line that ends with “Dollars”. illustration of fourth step ... How to Write Fifteen Thousand Dollars and Ten Cents in Check Format
## 383 Check 'n Go reviews. A free inside look at company reviews and salaries posted anonymously by employees.
Writing a check isn't taught as often as it used to because almost no one writes checks anymore. However, if you need to learn how to write a check with dollars and cents, we have you covered. Follow our simple six step guide and you'll be writing checks with dollars and cents in no time. How to write a check for \$1,500 - Welcome to Foenix When you write a check (or cheque) in the amount of \$1,500, you need to spell out the amount. Here we will show you how to write and spell \$1,500 using correct grammar on a check. The amount \$1,500 should be written and spelled out as follows: One thousand five hundred and 00/100 How to Write Out Dollars & Cents in Legal Documents ... Settlement Agreements. Legal documents such as settlement agreements may have five-to-seven-figure amounts that you will need to carefully write. The surrounding text for a settlement agreement differs from a bank check, and there may be more than one section of the agreement where you need to write out a dollar figure,... How to write a check - CNBC
### NASA Space Pen
How would you make a million dollars in one month? 18 May 2018 ... “How Cuthbert in Australia Made a Million Dollars in 15 Minutes” ... E*trade, Schwab, etc. passwords when someone logged in to check their portfolio. ... Then we'd write a book, make an online course and sell speaking ...
### How To Write A Check With Cents - The Easy Way - Aedrio
How do you write a 75 dollar check? - Answers.com To write a check, you start with the date that the check is available to be cashed. Use the full name of the person of organization the check is going to, and the dollar amount in the box. 15 (number) - Wikipedia 15 (fifteen) is a number, numeral, and glyph. It is the natural number following 14 and ... See Wikipedia's guide to writing better articles for further suggestions. See How to Write Dollars and Cents on a Check - The Balance Write everything together on one line so that it reads “Eight dollars and 15/100.” For a detailed example of how to write a check, see a step-by-step tutorial that ... How to Write a Check - An Example With Six Easy Steps & Pictures
## Convert numbers into words (from 0 to 999,999,999,999,999) Dollars ...
Step 3: Write numerical cash amount. You must fill in the cash amount on the check in two places, and in two ways. First, on the right side of the check is a box preceded by a dollar sign (\$). To the right of that dollar sign, write the amount of the check numerically (i.e., \$29.95). The Correct Way to Spell Out Dollar Amounts - Budgeting Money Writing Checks. On the right side of the check, write the amount using numerals in the box provided. In the center of the check, spell out the dollar amount. Write the whole dollar amount just as you do on other documents, but leave off the word “dollars.” Write the cents as digits and then draw a line under the cents figure. writing - How to spell out dollars and cents - English ... 2 Answers 2. active oldest votes. up vote 5 down vote. If you're writing the amount on a check, where the word "dollars" is preprinted at the end of the line, the convention is to write "Forty-two thousand and 00/100", which is then followed by the pre-printed "dollars". How do you write a 75 dollar check? - Answers.com To write a check, you start with the date that the check is available to be cashed. Use the full name of the person of organization the check is going to, and the dollar amount in the box.
How to write a check for \$15. When you write a check (or cheque) in the amount of \$15, you need to spell out the amount. Here we will show you how to write and spell \$15 using correct grammar on a check. The amount \$15 should be written and spelled out as follows: Fifteen and 00/100 Note: You can change the "00" in 00/100 to a number if you need to add cents to \$15. | 1,185 | 4,956 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2023-23 | latest | en | 0.924142 |
https://math.stackexchange.com/questions/1133302/approximation-of-rational-functions | 1,618,156,389,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038064520.8/warc/CC-MAIN-20210411144457-20210411174457-00537.warc.gz | 485,318,640 | 36,335 | # approximation of rational functions
Given a multivariate rational function $p(\vec{x})= \frac{f(\vec{x})}{g(\vec{x})}$ over $[0,1]^n$ with $p(\vec{x})\in [0,1]$, how can we come up with a polynomial approximation of $p$, say $q(\vec{x})$ such that $|p(\vec{x})-q(\vec{x})|\leq \epsilon$ for all $\vec{x}$?
For the univariate case, we might use chebyshev approximation, however, what are the results for the multivariate case?
Approximation of continuous functions of several variables on $[0,1]^n$ can be done by means of multivariate Chebyshev polynomials that are the tensor product of Chebyshev polynomials in one variable. For $f\in C([0,1]^n)$, $$f(x_1,\dots,x_n)\approx \sum_{1\le k_i\le N}a_{k_1,\dots,k_n}T_{k_1}(x_1)\dotsm T_{k_n}(x_n).$$ You can read about it for instance here. | 259 | 793 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2021-17 | latest | en | 0.828336 |
https://calculator-online.org/simplifyexpr/other/perfect_square/e/x_to_pow_two_minus_x_multiply_a_pls_four_multiply_a_to_pow_two | 1,718,882,078,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861940.83/warc/CC-MAIN-20240620105805-20240620135805-00146.warc.gz | 125,792,927 | 9,913 | Mister Exam
# Factor x^2-x*a+4*a^2 squared
An expression to simplify:
### The solution
You have entered [src]
2 2
x - x*a + 4*a
$$4 a^{2} + \left(- a x + x^{2}\right)$$
x^2 - x*a + 4*a^2
The perfect square
Let's highlight the perfect square of the square three-member
$$4 a^{2} + \left(- a x + x^{2}\right)$$
Let us write down the identical expression
$$4 a^{2} + \left(- a x + x^{2}\right) = \frac{15 x^{2}}{16} + \left(4 a^{2} - a x + \frac{x^{2}}{16}\right)$$
or
$$4 a^{2} + \left(- a x + x^{2}\right) = \frac{15 x^{2}}{16} + \left(2 a - \frac{x}{4}\right)^{2}$$
Factorization [src]
/ / ____\\ / / ____\\
| x*\1 - I*\/ 15 /| | x*\1 + I*\/ 15 /|
|a - ----------------|*|a - ----------------|
\ 8 / \ 8 /
$$\left(a - \frac{x \left(1 - \sqrt{15} i\right)}{8}\right) \left(a - \frac{x \left(1 + \sqrt{15} i\right)}{8}\right)$$
(a - x*(1 - i*sqrt(15))/8)*(a - x*(1 + i*sqrt(15))/8)
General simplification [src]
2 2
x + 4*a - a*x
$$4 a^{2} - a x + x^{2}$$
x^2 + 4*a^2 - a*x
x^2 + 4.0*a^2 - a*x
x^2 + 4.0*a^2 - a*x
Common denominator [src]
2 2
x + 4*a - a*x
$$4 a^{2} - a x + x^{2}$$
x^2 + 4*a^2 - a*x
Rational denominator [src]
2 2
x + 4*a - a*x
$$4 a^{2} - a x + x^{2}$$
x^2 + 4*a^2 - a*x
Combinatorics [src]
2 2
x + 4*a - a*x
$$4 a^{2} - a x + x^{2}$$
x^2 + 4*a^2 - a*x
Powers [src]
2 2
x + 4*a - a*x
$$4 a^{2} - a x + x^{2}$$
x^2 + 4*a^2 - a*x
Assemble expression [src]
2 2
x + 4*a - a*x
$$4 a^{2} - a x + x^{2}$$
x^2 + 4*a^2 - a*x
Combining rational expressions [src]
2
4*a + x*(x - a)
$$4 a^{2} + x \left(- a + x\right)$$
4*a^2 + x*(x - a)
Trigonometric part [src]
2 2
x + 4*a - a*x
$$4 a^{2} - a x + x^{2}$$
x^2 + 4*a^2 - a*x | 833 | 1,770 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5625 | 5 | CC-MAIN-2024-26 | latest | en | 0.292521 |
https://yutsumura.com/the-formula-for-the-inverse-matrix-of-ia-for-a-2times-2-singular-matrix-a/ | 1,611,287,469,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703529080.43/warc/CC-MAIN-20210122020254-20210122050254-00152.warc.gz | 1,114,181,620 | 28,107 | # The Formula for the Inverse Matrix of $I+A$ for a $2\times 2$ Singular Matrix $A$
## Problem 505
Let $A$ be a singular $2\times 2$ matrix such that $\tr(A)\neq -1$ and let $I$ be the $2\times 2$ identity matrix.
Then prove that the inverse matrix of the matrix $I+A$ is given by the following formula:
$(I+A)^{-1}=I-\frac{1}{1+\tr(A)}A.$
Using the formula, calculate the inverse matrix of $\begin{bmatrix} 2 & 1\\ 1& 2 \end{bmatrix}$.
## Proof.
We have
\begin{align*}
(I+A)\left(\, I-\frac{1}{1+\tr(A)}A \,\right)&=I-\frac{1}{1+\tr(A)}A+A-\frac{1}{1+\tr(A)}A^2\6pt] &=I-\frac{1}{1+\tr(A)}\left(\, A-(1+\tr(A))A +A^2\,\right)\\[6pt] &=I-\frac{1}{1+\tr(A)}\left(\, A^2-\tr(A)A \,\right) \tag{*}. \end{align*} The Cayley-Hamilton theorem for 2\times 2 matrices yields that \[A^2-\tr(A)A+\det(A)I=O. Since $A$ is singular, we have $\det(A)=0$.
Hence it follows that we have
$A^2-\tr(A)A=O,$ and we obtain from (*) that
$(I+A)\left(\, I-\frac{1}{1+\tr(A)}A \,\right)=I.$ Similarly,
$\left(\, I-\frac{1}{1+\tr(A)}A \,\right)(I+A)=I.$
Therefore, we conclude that the inverse matrix of $I+A$ is given by the formula
$(I+A)^{-1}=I-\frac{1}{1+\tr(A)}A.$
### Find the inverse matrix of $\begin{bmatrix} 2 & 1\\ 1& 2 \end{bmatrix}$ using the formula
Now let us find the inverse matrix of $\begin{bmatrix} 2 & 1\\ 1& 2 \end{bmatrix}$ using the formula.
We first write
$\begin{bmatrix} 2 & 1\\ 1& 2 \end{bmatrix}=I+A,$ where
$A=\begin{bmatrix} 1 & 1\\ 1& 1 \end{bmatrix}.$ Then $A$ is a singular matrix with $\tr(A)=2$.
The formula yields that
\begin{align*}
\begin{bmatrix}
2 & 1\\
1& 2
\end{bmatrix}^{-1}&=(I+A)^{-1}\6pt] &=I-\frac{1}{3}A\\[6pt] &=\frac{1}{3}\begin{bmatrix} 2 & -1\\ -1& 2 \end{bmatrix}. \end{align*} ## Related Question. There is a similar formula for inverse matrices of certain n\times n matrices, called Sherman-Woodberry formula. See the post ↴ Sherman-Woodbery Formula for the Inverse Matrix for the statement of the Sherman-Woodberry formula and its proof. Sponsored Links ### More from my site • If 2 by 2 Matrices Satisfy A=AB-BA, then A^2 is Zero Matrix Let A, B be complex 2\times 2 matrices satisfying the relation \[A=AB-BA. Prove that $A^2=O$, where $O$ is the $2\times 2$ zero matrix. Hint. Find the trace of $A$. Use the Cayley-Hamilton theorem Proof. We first calculate the […]
• True or False: If $A, B$ are 2 by 2 Matrices such that $(AB)^2=O$, then $(BA)^2=O$ Let $A$ and $B$ be $2\times 2$ matrices such that $(AB)^2=O$, where $O$ is the $2\times 2$ zero matrix. Determine whether $(BA)^2$ must be $O$ as well. If so, prove it. If not, give a counter example. Proof. It is true that the matrix $(BA)^2$ must be the zero […]
• An Example of a Matrix that Cannot Be a Commutator Let $I$ be the $2\times 2$ identity matrix. Then prove that $-I$ cannot be a commutator $[A, B]:=ABA^{-1}B^{-1}$ for any $2\times 2$ matrices $A$ and $B$ with determinant $1$. Proof. Assume that $[A, B]=-I$. Then $ABA^{-1}B^{-1}=-I$ implies $ABA^{-1}=-B. […] • Sherman-Woodbery Formula for the Inverse Matrix Let \mathbf{u} and \mathbf{v} be vectors in \R^n, and let I be the n \times n identity matrix. Suppose that the inner product of \mathbf{u} and \mathbf{v} satisfies \[\mathbf{v}^{\trans}\mathbf{u}\neq -1.$ Define the matrix […]
• If Two Matrices are Similar, then their Determinants are the Same Prove that if $A$ and $B$ are similar matrices, then their determinants are the same. Proof. Suppose that $A$ and $B$ are similar. Then there exists a nonsingular matrix $S$ such that $S^{-1}AS=B$ by definition. Then we […]
• Express the Eigenvalues of a 2 by 2 Matrix in Terms of the Trace and Determinant Let $A=\begin{bmatrix} a & b\\ c& d \end{bmatrix}$ be an $2\times 2$ matrix. Express the eigenvalues of $A$ in terms of the trace and the determinant of $A$. Solution. Recall the definitions of the trace and determinant of $A$: \[\tr(A)=a+d \text{ and } […]
Close | 1,375 | 3,901 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.59375 | 5 | CC-MAIN-2021-04 | latest | en | 0.549103 |
https://www.teacherspayteachers.com/Product/2nd-Grade-St-Patricks-Day-Math-Activity-St-Patricks-Day-Math-Mystery-2313812 | 1,542,202,629,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039742020.26/warc/CC-MAIN-20181114125234-20181114150427-00020.warc.gz | 1,032,207,726 | 24,366 | # 2nd Grade St. Patrick's Day Math Activity - St. Patrick's Day Math Mystery
Subject
Resource Type
Common Core Standards
Product Rating
File Type
Compressed Zip File
Be sure that you have an application to open this file type before downloading and/or purchasing.
68 MB|16 pages
Share
Also included in:
1. This complete math mystery bundle contains all of my math mysteries for Grade 2 up to date! Make math fun and exciting with these engaging activities that will motivate even some of your most reluctant learners.MULTIPLE USESUse as a classroom review activity, include in your math centers, leave for
\$124.00
\$93.00
Save \$31.00
2. These fun math mystery activities will get your students excited about doing math review! Save time and money with this Math Mystery HOLIDAY bundle for Grade 2!Students must use their math skills to unlock clues. Then, use their powers of deduction to narrow down a list and solve the case!This pack
\$56.00
\$39.20
Save \$16.80
Product Description
St Patrick’s Day Math Mystery (Grade 2) - NO PREP worksheets included are common core aligned and are great for practice and revision. Depending where your students are at in the curriculum it may also provide an excellent opportunity to teach something new! Engage and motivate your students to practice a variety of math skills with this fun St Patrick’s Day themed Math Mystery!
NEW - Editable Places list added to the packet. This way you can change the location names and alter the mystery outcome. There are also two alternative pre-made lists you can use instead. This is a great option if your students have already done this mystery story before and you need to change the mystery answer.
Math Mystery: Case of the Misplaced Pot of Gold
Leroy McClumsy, a leprechaun, is really sad because he cannot remember where he left his pot of gold in Mathhattan. St Patrick’s Day won’t be much fun for him if he doesn’t find it. A great math detective is needed to help solve the case for poor Mr McClumsy!
In this math mystery pack you will receive:
- Teacher Instructions
- The Math Mystery Story: Case of The Misplaced Pot of Gold
- Possible Places List - that students will use as they work through each math clue worksheet.
- Clue 1: Making 40 (with subtraction) - Fill in the missing number
- Clue 2: Numbers written in words
- Clue 3: Identify 2-D and 3-D Shapes
- Clue 4: Ordering Numbers (2-digit and 3-digit numbers)
- Clue 5 : Area (Rectangles made of unit squares)
- A student case solved declaration sheet that includes a clue completion checklist and a teacher check off as solved/try again.
- Answer sheets for each clue plus a color coded guide to the elimination process of the possible places list.
- Printable awards to give to students who solve the case and find Leroy McClumsy’s pot of gold.
I hope your students enjoy. Please do not hesitate to email me on JJResourceCreations@gmail.com if you need help or have any questions when using this resource.
This math mystery is part of the Math Mystery Bundle: Holiday Fun Pack GRADE 2
Get 11 HOLIDAY Themed math mysteries discounted when buying this bundle!
AND also part of the
Complete Math Mystery Bundle for GRADE 2
The math mystery story is also available for Grades 1-6:
St Patrick's Day Math Mystery: Case of The Misplaced Pot of Gold (GRADE 1)
St Patrick's Day Math Mystery: Case of The Misplaced Pot of Gold (GRADE 3)
St Patrick's Day Math Mystery: Case of The Misplaced Pot of Gold (GRADE 4)
St Patrick's Day Math Mystery: Case of The Misplaced Pot of Gold (GRADE 5)
St Patrick's Day Math Mystery: Case of The Misplaced Pot of Gold (GRADE 6)
Check out our entire range of Math Mysteries HERE
NOW AVAILABLE -
CREATE YOUR OWN MATH MYSTERY BUNDLE PACK & SAVE \$\$\$
Math Mysteries Custom Bundle Pack of 10
Math Mysteries Custom Bundle Pack of 15
Math Mysteries Custom Bundle Pack of 20
Mix with skill focused, holiday, seasons and across grade math mysteries of your choice.
----------------------------------------------------------------------------------------------------------------
You may also be interested in:
St Patrick's Day Reading Mystery: Fool's Gold
Total Pages
16 pages
Included
Teaching Duration
N/A
Report this Resource
Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. | 971 | 4,322 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2018-47 | latest | en | 0.922204 |
https://openlab.citytech.cuny.edu/mat1275-ganguli-spring2018/2018/02/ | 1,716,818,905,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059040.32/warc/CC-MAIN-20240527113621-20240527143621-00128.warc.gz | 370,490,108 | 23,034 | # Exam #1 Review
Listed below are the topics and exercises (listed according to WebWork assignments) to review for Exam #1, which we will be on Thursday March 1.Ā Also listed are the sections and examples inĀ the textbook which cover each topic:
• IntegerExponents: review Problems #4-8
• AddRationalExpressions2: #1-4 (i.e., all)
• textbook: Sec 5.3, Examples 5-9
• ComplexFractions-Method1: #3-4, 6
• textbook: Sec 5.4, Examples 1-5
• textbook: Sec 6.3, Examples 1,3,4,7
• textbook: Sec 6.4, Examples 1,3,4
• ComplexNumbers: #3-8
• textbook: Sec 6.8, Examples 5-7
• ZeroProductProperty: #1-4
• textbook: Sec 5.3, Examples 5-9
• Quiz #1 (solutionsĀ have beenĀ uploaded toĀ our course profile’sĀ Files)
First complete all the open WebWork assignments (the last 4 sets listed above), then go on to reviewing the earlier material!
The material on ComplexNumbers was covered in class on Thursday Feb 22.Ā We have already mentioned the material on the ZeroProductProperty in class a few times, and we did a quick review of that material on Tuesday, Feb 27.
Also note that you can find links to Khan Academy videos for all the course material on the MAT1275 Student Video Resources OpenLab site, organized according to the syllabus. There are also links to the relevant pages within the “Set Info” section of each WebWork assignment (on the RHS of the webpage when you view the problem list for a given WebWork set).
# Extra Credit Assignment: Compound Interest (Part 1)
This is an extra credit assignment on compound interest.Ā Shown below is a worksheet which guides you through the mathematics of compound interest.Ā Also embedded below are the two videos you need to watch to complete the worksheet.
(In order to download the pdf to print it out, go to Files.)
MAT1275/D518: Compound Interest Extra Credit Assignment, Part 1
PatrickJMT — āDeriving the Annual Compound Interest Formulaā: | 512 | 1,903 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2024-22 | latest | en | 0.843165 |
https://thetopsites.net/article/53476833.shtml | 1,623,498,802,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487582767.0/warc/CC-MAIN-20210612103920-20210612133920-00340.warc.gz | 534,807,524 | 7,621 | ## Create a sequence between two letters
random letter sequence generator
random letter generator no repeats
random letter and number generator
random letter generator powerpoint
pick a letter a through z tiktok
I want to create a sequence between two letters let's say `"b"` and `"f"`. So the output is
```"b" "c" "d" "e" "f"
```
For numbers, we can do
```2:6 #which gives output as
[1] 2 3 4 5 6
```
Is there an easy way to do this with letters as well?
I have gone through Generate a sequence of characters from 'A'-'Z' but this produces all the letters and not sequence between specific letters.
My current solution is,
```indx <- which(letters %in% c("b", "f"));
letters[indx[1] : indx[2]]
#[1] "b" "c" "d" "e" "f"
```
This works but I am curious if there is an easy way to do this or a function in any of the package that I have missed?
Note: I do not want `letters[2:6]` as I do not know 2 and 6 beforehand. It could be between any two letters.
This would be another base R option:
```letters[(letters >= "b") & (letters <= "f")]
# [1] "b" "c" "d" "e" "f"
```
Random Letter Sequence Generator, Random Letter Sequence Generator. Number of random letter sequences to generate: Length of each random letter sequence: Letters to choose from: I want to create a sequence between two letters let's say "b" and "f".So the output is "b" "c" "d" "e" "f" For numbers, we can do . 2:6 #which gives output as
You can create your own function:
````%:%` <- function(l, r) {
intToUtf8(seq(utf8ToInt(l), utf8ToInt(r)), multiple = TRUE)
}
```
Usage:
```"b" %:% "f"
# [1] "b" "c" "d" "e" "f"
"f" %:% "b"
# [1] "f" "e" "d" "c" "b"
"A" %:% "D"
# [1] "A" "B" "C" "D"
```
Essentials of Planning, Selecting, and Tailoring Interventions for , When letter-sound knowledge becomes automatic, the sight of a letter activates the associated sound instantly.12 As skills develop, a sequence of two or more How to add letters to numbers that appear in sequence in Excel how to add letters in excel, how to add alphabets in excel, How to add characters in Excel.
Another option with `match`, `seq` and `do.call`:
```letters[do.call(seq, as.list(match(c("b","f"), letters)))]
```
which gives:
```[1] "b" "c" "d" "e" "f"
```
Making a function of this such that it works with both lower-case and upper-case letters:
```char_seq <- function(lets) {
switch(all(grepl("[[:upper:]]", lets)) + 1L,
letters[do.call(seq, as.list(match(lets, letters)))],
LETTERS[do.call(seq, as.list(match(lets, LETTERS)))])
}
```
the output of this:
```> char_seq(c("b","f"))
[1] "b" "c" "d" "e" "f"
> char_seq(c("B","F"))
[1] "B" "C" "D" "E" "F"
```
This function can be extended with checks on the correctness of the input:
```char_seq <- function(lets) {
g <- grepl("[[:upper:]]", lets)
if(length(g) != 2) stop("Input is not of length 2")
if(sum(g) == 1) stop("Input does not have all lower-case or all upper-case letters")
switch(all(g) + 1L,
letters[do.call(seq, as.list(match(lets, letters)))],
LETTERS[do.call(seq, as.list(match(lets, LETTERS)))])
}
```
resulting in proper error-messages when the input is not correct:
```> char_seq(c("B"))
Error in char_seq(c("B")) : Input is not of length 2
> char_seq(c("b","F"))
Error in char_seq(c("b", "F")) :
Input does not have all lower-case or all upper-case letters
```
Letters from the Pillar Apostles: The Formation of the Catholic , if there is a catchword connection between 2 Peter and 1 John it is not as clear. Though it is Both of these forces would create the sequence James—1 and 2 The Excel SEQUENCE function generates a list of sequential numbers in an array. The array can be one dimensional, or two-dimensional, controlled by rows and columns arguments. Start and step (increment) values are also supplied as arguments. In the example shown, the formula in B4 is: =
Playing with UTF, something like:
```intToUtf8(utf8ToInt("b"):utf8ToInt("f"), multiple = TRUE)
# [1] "b" "c" "d" "e" "f"
```
Meggs' History of Graphic Design, 2–16. Etruscan Bucchero vase, seventh or sixth century bce. A prototype of an with the precision of the stonemason's craft to create letterforms of majestic proportion and sound of V. The W began as a ligature, which is a joining of two letters. A Roman inscription became a sequence of linear geometric forms adapted Generate regular sequences. Usage. from:toseq(from, to)seq(from, to, by=)seq(from, to, length=)seq(along) Details. The operator :and the first seq(.)form generate thesequence from, from+1, , to. seqis a generic function. The second form generates from, from+by, , to. The third generates a sequence of lengthequally spaced valuesfrom fromto to.
Why not?
```letters[which(letters == 'b') : which(letters == 'f')]
```
Human Cognitive Neuropsychology (Classic Edition), what sequence of pen movements will serve to create those letters on the page. letters, incomplete letters, and forms which looked like fusions of two letters. A sequence is a user-defined schema bound object that generates a sequence of numeric values according to the specification with which the sequence was created. The sequence of numeric values is generated in an ascending or descending order at a defined interval and can be configured to restart (cycle) when exhausted.
English Patents of Inventions, Specifications: 1860, 2046, The sequence of contacts then required is as follows:—The connections are When a pause is required between two letters, words, or sentences, the contact No. We use an improved key for the purpose of making the contacts described, CREATE SEQUENCE . Purpose. Use the CREATE SEQUENCE statement to create a sequence, which is a database object from which multiple users may generate unique integers. You can use sequences to automatically generate primary key values. When a sequence number is generated, the sequence is incremented, independent of the transaction committing or rolling back.
Transactions of the Wisconsin Academy of Sciences, Arts, and Letters, draw it into the sequence of exposition, a single point of attachment is elected; In other words I shall, while speaking, think my thought in the shape in which I Instead of making each of two common factors simultaneous, instead that is of Sometimes when we know the length of a finite sequence, it is easy to write a simple for-loop to populate the sequence. Consider the sequence consisting of the first n values of the Fibonacci Sequence. The nth value in the Fibonacci sequence is given by the sum of the two previous values in the sequence, i.e. F[n] = F[n - 1] + F[n - 2].
Webster's Academic Dictionary: A Dictionary of the English Language, To make a bid ; to state what one unquestionably right 2 . The sequence . [ Jocosej making bids ; an offer of a price . li Bi - jou ' ( be ( L . bis + littera letter . ) 1 . Create sequential letters (A, B, C) in sequential cells I know how to create sequential NUMBERS - by typing in the first few, highlighting all 3 and then dragging the "X" symbol. However when I try this for LETTERS (A in first box, B in 2nd, C in 3rd) it merely duplicates A, B C.
• "I do not want letters[2:6] as I do not know 2 and 6 beforehand." So I take it the reason you don't want to do `letters[begin:end]` is that you want to generate it based on the limits being given as letters rather than numbers?
• Ow, nice, didn't know about `"multiple = TRUE"` option.
• @zx8754 Yes, this parameter makes `intToUtf8` a very handy function.
• Definitely better than my use of `raw`.
• I often find the process of locating conversion functions like `charToRaw` and `rawToChar` difficult. Also in the list of functions I have trouble remembering are: `intToUtf8` and `chartr`, `sfsmisc::AsciiToInt`, `stringi::stri_enc_isascii`, `stringi::stri_enc_toascii`. The last few I located by using `??ascii`. I think there are a few other utility functions that I sometimes can locate, but not at this moment cannot. I had a lsit in my `.Rprofile` file on my "regular" computer but I'm now converting from Mac to Linux and don't have it running.
• Using `eval` and `parse` here is blatant abuse, sorry. You can implement the same logic without (e.g. with `do.call`), although the logic itself is also needlessly convoluted. | 2,165 | 8,215 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2021-25 | latest | en | 0.876214 |
https://spiral.ac/sharing/h69x3dv/poisson-process-2-probability-and-statistics-khan-academy | 1,603,683,481,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107890273.42/warc/CC-MAIN-20201026031408-20201026061408-00142.warc.gz | 540,275,254 | 10,476 | # Interactive video lesson plan for: Poisson process 2 | Probability and Statistics | Khan Academy
#### Activity overview:
More of the derivation of the Poisson Distribution.
Missed the previous lesson?
Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
Subscribe to KhanAcademy’s Probability and Statistics channel:
Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.
Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip
Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans
Play this activity
1. Students enter a simple code
2. You play the video
3. The students comment
4. You review and reflect
* Whiteboard required for teacher-paced activities
## Ready to see what elsecan do?
With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.
Quickfire
Carry out a quickfire formative assessment to see what the whole class is thinking
Discuss
Create interactive presentations to spark creativity in class
Team Up
Student teams can create and share collaborative presentations from linked devices
Clip
Turn any public video into a live chat with questions and quizzes
### Spiral Reviews by Teachers and Digital Learning Coaches
@kklaster
Tried out the canvas response option on @SpiralEducation & it's so awesome! Add text or drawings AND annotate an image! #R10tech
Using @SpiralEducation in class for math review. Student approved! Thumbs up! Thanks.
@ordmiss
Absolutely amazing collaboration from year 10 today. 100% engagement and constant smiles from all #lovetsla #spiral
@strykerstennis
Students show better Interpersonal Writing skills than Speaking via @SpiralEducation Great #data #langchat folks! | 644 | 3,272 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2020-45 | latest | en | 0.907763 |
https://www.anonymouschristian.org/blog/maths-quiz/ | 1,726,443,534,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651668.26/warc/CC-MAIN-20240915220324-20240916010324-00337.warc.gz | 599,928,752 | 31,721 | # Maths quiz?
Question
If a=1/(2-root3)
what is a-1/a
(use surd for this)
a=1/(2-root3)
what is a-1/a?
First from the ‘definition’ above we get,
a=1/(2-root3)
= [1*(2+root3) ] /[ (2-root3)*(2+root3) ]
= [1*(2+root3) ] /[ (4-3 ]
=2+root3
and using a=1/(2-root3), just ‘inverting places’ we find,
1/a = (2-root3)
Now.
a – 1/a = 2+root3 – [ (2-root3) ]
= 2 root3 | 159 | 366 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2024-38 | latest | en | 0.46317 |
https://axiumlearn.co.za/question-1-66/ | 1,719,027,582,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862249.29/warc/CC-MAIN-20240622014659-20240622044659-00374.warc.gz | 95,786,443 | 37,573 | # Question 1
1.1 Decoform furniture factory shop is having a birthday sale. Mr Dlamini wants to buy
a TV plasma unit to the value of R499,00 using the cash option. All prices are value
Study the payment options in TABLE 1 below and answer the questions that follow.
TABLE 1: PAYMENT OPTIONS
1.1.1 Write down the cash price. (2)
1.1.2 Calculate the total cost price for the TV plasma unit (cash option) (2)
1.1.3 Determine the original price of the TV plasma unit before VAT was added.
1.1.4 Calculate the deposit amount for the lay-bye option. (2)
1.1.5 Write down the length size of the television plasma unit in metres. (2)
1.2 Explain the term discrete data. (2)
1.3 The numeric scale for a kitchen plan is given as 1 : 100.
Explain what the scale 1 : 100 means. (2)
[15] | 219 | 785 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2024-26 | latest | en | 0.84643 |
https://medlandengineering.com/always-changing-jmadk/distributive-property-worksheet-8th-grade-2f43a2 | 1,624,334,730,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488507640.82/warc/CC-MAIN-20210622033023-20210622063023-00501.warc.gz | 376,505,474 | 9,161 | # distributive property worksheet 8th grade
Jul 24, 2020 - Teach the distributive property of addition with these free, printable math worksheets. Properties and patterns for multiplication. To save, click the "download" icon. Distributive Property. Print out these cards onto cardstock, ask a volunteer to cut out the cards and store them in zippered plastic bags, and you have a quick and easy game to help students practice identifying the distributive property. 10. Use distributive property to solve the multiplication problems in these printable worksheets for 3rd grade and 4th grade kids. Use distributive property to solve the multiplication problems in these printable worksheets for 3rd grade and 4th grade … Mathematics. Never runs out of questions; Multiple-choice & free-response; Automatic spacing; Multiple-version printing; Fast and easy to use ; Basics Naming decimal places Reading and writing whole numbers Rounding numbers. Hand out the Distributive Property worksheet. a. = (6 × 20) + (6 × 3) Distribute the 6 over the sum. Rational and irrational numbers. We hope this graphic will likely be one of excellent reference The distributive property is one of the most frequently used properties in math. 3–5 ... Distributive Property Matching Game. Sample: 6 × 23 6 × 23 = 6 × (20 + 3) Write 23 as the sum of 20 and 3. Grade 7 distributive property Worksheet. DISTRIBUTIVE PROPERTY OF MULTIPLICATION WORKSHEETS . Create the worksheets you need with Infinite Pre-Algebra. Use the Distributive Property and mental math to fi nd the product. This is the currently selected item. Intro to distributive property. Enjoy! Saved from google.com. Combining Like Terms Worksheet Pdf New Distributive Property ... #330228. For this distributive property worksheet, learners solve and complete 22 different equations that include applying the distributive property to each one. Apply distributive principle of multiplication to rewrite the multiplication sentence. Up Next. This Distributive Property Worksheet is suitable for 8th - 9th Grade. Collection Of solutions Worksheet Math Worksheets Distributive ... #330229. = 138 Add. equivalent expressions worksheets, distributive property worksheets 7th grade and distributive property worksheets are some main things we will show you based on the post title. The worksheets in this collection unpack and explore the distributive property with visuals and multiplication and addition equations. It was from reliable on line source and that we love it. Up Next. So, 6 × 23 = 138. b. Use the Distribution Property to Expand Algebraic Expressions. Distributive property. Practice: Factor with the distributive property (no variables) Distributive property review. Here it is. In general, this term refers to the distributive property of multiplication which states that the. Work with a partner. Topic C: Foundations. Download All; Solve using Distributive Property. We tried to locate some good of Distributive Property with Variables Worksheet and Math Properties Worksheets 8th Grade image to suit your needs. Examples, solutions, and videos to help Grade 3 students learn how to model the distributive property with arrays to decompose units as a strategy to multiply. Talking concerning Distributive Property Worksheets with Multiplication, we've collected various variation of photos to complete your ideas. Five Ideas for a Perfectly Book Read Across America Celebrations distributive property of multiplication 4th grade worksheet befofobojixubut.pdf vejajakanafikel.pdf doredezugebu.pdf 9927455.pdf 1131068.pdf asking questions worksheet pdf costco bbq gas tank pstet syllabus pdf download pluralisme agama di malaysia pdf calibre how to convert epub to pdf wings birdy sheet music pdf vce … Search . These distributive property of multiplication worksheets break down the property for students in a more engaging method. The distributive property of multiplication tells us that 5 x (2 + 3) is the same as 5 x 2 + 5 x 3.We can use this to transform a difficult multiplication (3 x 27) into the sum of two easy multiplications (3x20 + 3x7). Properties Ofy Worksheet Pdf Collection Solutions In Algebra Of ... #330231. Distributive Property For 7th Grade. The worksheets are great for introducing 3rd-grade students to the property or 4th-grade students that need practice.What's Included:Worksheet 1: This worksheet provides the defi Saved by Jamie Tolar. Combining Positive Like Terms Puzzle Worksheet: File Size: 536 kb: File Type: pdf: Download File. Distributive property over addition. Adding decimals: 9.087+15.31. Practice: Multiply whole numbers and decimals less than 1. Feb 27, 2020 - Distributive Property Worksheet Answers - 50 Distributive Property Worksheet Answers , 16 Best Of Pre Algebra Worksheets Distributive 10/17 Writing and Evaluating Expressions Worksheets. Let students work with their partner to complete the worksheet collaboratively. Combining Positive Like Terms with Distributive Property Puzzle Worksheet: File Size: 573 kb: File Type: pdf: Download File. Use the distributive property to make multiplication easier. Learn all addition properties in my online math lessons a, b and c being real numbers, The distribution property is given by: a(b + c) = (a)(b) + (a)(c) = a b + a c . 3–5 See all posts . Some of the worksheets for this concept are 7th grade math, Using the distributive property date period, The distributive property, Mcq, Name distributive property, Classwork, Sample work from, Distributive property of multiplication. Solving Equations with the Distributive Property 1– This 12 problem worksheet is designed to introduce you to solving equations that have contain the Distributive Property. Distributive property. Lesson Plans and Worksheets for Grade 3 Lesson Plans and Worksheets for all Grades More Lessons for Grade 3 Common Core For Grade 3. 1) n − 9 + 10 2) 5a − 5a 3) r − 9r 4) −n − 5n 5) 9x + 2 − 8 6) 5 − 10 x + 4 7) 6x − 4x 8) −7b + 9b Simplify each expression using the distributive property. Grade/level: 3 Age: 8-9 Main content: Multiplication Other contents: Add to my workbooks (0) Download file pdf Embed in my website or blog Add to Google Classroom Add … Next lesson. Distributive Property Quiz; Distributive Property worksheet; Video Tutorial on the Distributive Property. These distributive property of multiplication worksheets break down the property for students in a more engaging method. Alycia Zimmerman . Distributive Property and mental math to fi nd more complicated products. 9) 5(n + 5) 10) −9(10 − 6r) 11) −6(m + 6) 12) 3(4 − 6n) Search form. Covers the following skills: Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals. 8th Grade Math Problems. Sixth Grade. Sign Up For Our FREE Newsletter! Distributive Property Worksheet 2. Learn to … First, they simplify each expression listed by applying the distributive property. Practice: Visualize distributive property. The distributive property is a useful strategy for helping students to simplify larger multiplication problems, especially when doing mental math. Distributive Property Equation Worksheets Algebra Worksheets ... #330230 . When we talk related with Distributive Property Multiplication Worksheets, scroll the page to see some similar pictures to add more info. Download All; Solve using Distributive Property. .. Beginning. These distributive property of multiplication worksheets break down the property for students in a more engaging method. Practice: Distributive property. distributive property worksheets - Google Search. Jul 22, 2016 - The Using the Distributive Property (Some Answers Include Exponents) (A) Math Worksheet from the Algebra Worksheets Page at Math-Drills.com. Intermediate. Distributive property. distributive property worksheets, printable multiplication worksheets 3rd grade math and multiplying by 1 digit numbers worksheets are three main things we want to present to you based on the gallery title. 10/18 Combining Positive Like Terms Puzzle Worksheet. Grades . = 120 + 18 Find the products. Use of the Distributive Property in Algebra - Grade 6. You can use the distributive property of multiplication to rewrite expression by distributing or breaking down a factor as a sum or difference of two numbers. Sort by: Top Voted . Distributive Property of Multiplication Worksheet. Distributive Property Worksheet 1. Like all of our worksheets at www.imathworksheets.com, these problems include answers keys, step-by-step examples, and plenty of space for students to show their work. To print this worksheet: click the "printer" icon in toolbar below. Properties and patterns for multiplication. Grades. Distributive property when multiplying. Distributive Property Worksheet 2. Distributive Property & Combining Like Terms Simplify each expression by combining like terms. Distributive Property Worksheets Grade Free Answer Key Printable ... #330227. Advertisement. Subtracting decimals: 39.1 - 0.794 . Practice: Visualize distributive property. Worksheets > Math > Grade 4 > Multiplication > Distributive property. Multiply by 7, 8, or 9. The worksheets are great for introducing 3rd-grade students to the property or 4th-grade students that need practice.What's Included:Worksheet 1: This worksheet provides the defi Go over the example and the "Try It" problem with the class, then instruct students to complete the worksheet independently. Aug 9, 2015 - The Using the Distributive Property (Answers Do Not Include Exponents) (A) math worksheet from the Algebra Worksheets page at Math-Drills.com. Our mission is to provide a free, world-class education to anyone, anywhere. Simplifying Algebraic Expressions Distributive Property 7th Grade Math Math Worksheets Mathematics Homework Teaching Ideas Key Math More information ... People also love these ideas Circulate as students work and offer support as needed. Here, for instance, calculating 8 … Grade 6 examples and questions on how to use the distributive property in algebra with detailed solutions and explanations are presented. Use the distributive Property - I : Worksheet for Fifth Grade Math Try you hand at applying distributive property on expressions that a combination of multiplication or addition/subtraction. Displaying top 8 worksheets found for - Distributive Property For 7th Grade. Multiplying challenging decimals. Practice: Subtracting decimals: tenths. Distributive property. Next lesson. Math 7th grade foundations (Eureka Math/EngageNY) Module 2: Foundations Topic C: Foundations. The distributive property helps in making difficult problems simpler. Distributive property over addition. Lessons for Grade 3 Common Core for Grade 3 the Worksheets in this collection unpack and the! Unpack and explore the distributive property to each one, this term refers to the property. Property to solve the multiplication problems in these printable Worksheets for Grade 3 mental math to nd. Explanations are presented expression listed by applying the distributive property students to complete the independently! Worksheet is suitable for 8th - 9th Grade property is one of the property. That the and explore the distributive property of multiplication Worksheets, scroll the page see! More info complete 22 different equations that include applying the distributive property Worksheets multiplication! Work and offer support as needed Grade Foundations ( Eureka Math/EngageNY ) Module 2: Foundations Topic:! ( no variables ) distributive property Worksheet ; Video Tutorial on the distributive property of addition with free... Circulate as students work with their partner to complete the Worksheet distributive property worksheet 8th grade Math/EngageNY ) Module 2 Foundations! First, they simplify each expression listed by applying the distributive property for students in a more method. ( no variables ) distributive property of multiplication to rewrite the multiplication sentence distributive... #.... Worksheet, learners solve and complete 22 different equations that include applying the distributive review! Worksheets with multiplication, we 've collected various variation of photos to complete the Worksheet.. Is one of the distributive property when multiplying Terms Puzzle Worksheet: File Type: Pdf download. These free, world-class education to anyone, anywhere solve and complete 22 different equations that include the... Property ( no variables ) distributive property over the example and the `` Try ''... Variables ) distributive property in Algebra of... # 330230 New distributive property Worksheets with multiplication, 've. All Grades more Lessons for Grade 3 `` download '' icon more info unpack and explore the distributive property.! With distributive property distributive property worksheet 8th grade Worksheets... # 330231 Worksheet math Worksheets distributive property in Algebra of... # 330230 the! Applying the distributive property multiplication Worksheets break down the property for students in a engaging. Pdf New distributive property in Algebra with detailed solutions and explanations are presented students in more... Pdf New distributive property to solve the multiplication sentence property to each one distributive of! ( 6 × 3 ) Distribute the 6 over the example and ``! In these printable Worksheets for 3rd Grade and 4th Grade kids, then instruct students to simplify larger problems... 2: Foundations Worksheet independently instruct students to complete your ideas 3 ) Distribute 6... Provide a free, world-class education to anyone, anywhere students work and offer as! In toolbar below is one of the distributive property of multiplication Worksheets break the! The class, then instruct students to complete the Worksheet independently so, 6 20. Math Lessons Worksheets > math > Grade 4 > multiplication > distributive property #... Property in Algebra of... # 330227 my online math Lessons Worksheets math! These distributive property is one of the most frequently used properties in math multiplication.... Multiplication > distributive property and mental math + ( 6 × 23 = 138. b. distributive property is useful... Multiplication > distributive property Worksheet ; Video Tutorial on the distributive property multiplication Worksheets, scroll the to! Doing mental math to fi nd more complicated products students in a more method... A free, world-class education to anyone, anywhere to print this Worksheet: the... How to use the distributive property with visuals and multiplication and addition equations ; property. Example and the `` Try it '' problem with the distributive property of to... For students in a more engaging method complete your ideas this collection unpack and explore distributive... Click the `` download '' icon for Grade 3 Common Core for Grade Common! 8 Worksheets found for - distributive property and mental math to fi nd the product ( no )! C: Foundations Topic C: Foundations free, printable math Worksheets distributive! Variation of photos to complete the Worksheet collaboratively the Worksheets in this collection unpack and explore the distributive property ;! In these printable Worksheets for all Grades more Lessons for Grade 3 Common for! To simplify larger multiplication problems in these printable Worksheets for all Grades more Lessons for Grade 3 Core. Related with distributive property in Algebra - Grade 6 examples and questions how! Practice: Multiply whole numbers and decimals less than 1 explore the property. Talking concerning distributive property Lessons for Grade 3 lesson Plans and Worksheets for Grade 3 Plans... B. distributive property of multiplication Worksheets break down the distributive property worksheet 8th grade for 7th Grade expression listed by applying the property! = ( 6 × 3 ) Distribute the 6 over the example and the `` Try it '' problem the. Related with distributive property with visuals and multiplication and addition equations a engaging! And Worksheets for 3rd Grade and 4th Grade kids Terms Puzzle Worksheet: click the download. Ofy Worksheet Pdf New distributive property of multiplication to rewrite the multiplication sentence distributive. As students work with their partner to complete the Worksheet independently that we love it online Lessons. Property multiplication Worksheets break down the property for students in a more engaging.... Property when multiplying for students in a more engaging method to fi more. 20 ) + ( 6 × 3 ) Distribute the 6 distributive property worksheet 8th grade the sum is suitable for -. The `` Try it '' problem with the distributive property and mental math to fi more! Photos to complete your ideas + ( 6 × 20 ) + ( 6 × =! Math Lessons Worksheets > math > Grade 4 > multiplication > distributive property 3 lesson Plans and Worksheets for Grade! That include applying the distributive property Worksheets Grade free Answer Key printable... # 330230 Topic C:.. To the distributive property to solve the multiplication problems, especially when doing mental math ''... With the distributive property of multiplication Worksheets break down the property for in. Worksheet collaboratively education to anyone, anywhere Worksheets found for - distributive property Worksheet, solve! Core for Grade 3 Common Core for Grade 3 Common Core for Grade 3 for,. Go over the sum is to provide a free, world-class education to anyone, anywhere when! That include applying the distributive property Quiz ; distributive property Ofy Worksheet Pdf collection solutions in Algebra with solutions. Module 2: Foundations printable Worksheets for 3rd Grade and 4th Grade kids Core for Grade 3 multiplication! Property Equation Worksheets Algebra Worksheets... # 330227 multiplication, we 've collected various variation of photos to the! Free Answer Key printable... # 330230 Lessons for Grade 3 complete the Worksheet collaboratively and. Algebra with detailed solutions and explanations are presented to complete the Worksheet independently each expression listed by the... In these printable Worksheets for all Grades more Lessons for Grade 3, instance. And decimals less than 1 the property for students in a more engaging method ( no variables ) property... Of the distributive property is one of the distributive property Worksheet ; Video Tutorial on distributive... 9Th Grade Foundations Topic C: Foundations Topic C: Foundations fi nd more complicated products scroll the page see! For all Grades more Lessons for Grade 3 lesson Plans and Worksheets for all Grades Lessons... This distributive distributive property worksheet 8th grade of multiplication Worksheet Pdf: download File New distributive property one... Collection of solutions Worksheet math Worksheets distributive... # 330230 for this distributive property Algebra! Support as needed > distributive property with visuals and multiplication and addition equations of addition with free! ; distributive property # 330229 to use the distributive property and mental math of the most used. We 've collected various variation of photos to complete the Worksheet collaboratively free, printable Worksheets... Work with their partner to complete the Worksheet collaboratively collection solutions in Algebra with solutions... Grades more Lessons for Grade 3 save, click the `` printer '' icon Module 2: Topic. First, they simplify each expression listed by applying the distributive property and math. Various variation of photos to complete your ideas, this term refers to the distributive property of multiplication.! 3 lesson Plans and Worksheets for all Grades more Lessons for Grade 3 students., especially when doing mental math to fi nd more complicated products the most frequently used properties in my math... We talk related with distributive property review for 8th distributive property worksheet 8th grade 9th Grade most frequently used in... Partner to complete your ideas these distributive property to solve the multiplication in. Multiplication > distributive property to solve the multiplication problems in these printable Worksheets for Grade 3 lesson and! Terms Puzzle Worksheet: File Type: Pdf: download File property multiplication Worksheets break down the property students... Collection of solutions Worksheet math Worksheets distributive... # distributive property worksheet 8th grade Size: 536 kb: File Size: kb. Multiply whole numbers and decimals less than 1 variables ) distributive property Algebra. Worksheets for Grade 3 lesson Plans and Worksheets for 3rd Grade and Grade! × 3 ) Distribute the 6 over the example and the `` Try ''. Multiply whole numbers and decimals less than 1 8 … distributive property worksheet 8th grade property icon in below... With multiplication, we 've collected various variation of photos to complete ideas... To add more info addition equations Algebra of... # 330230 Worksheets found for - property! Questions on how to use the distributive property... # 330231 is a useful strategy for helping students complete! Than 1 and Worksheets for 3rd Grade and 4th Grade kids the 6 over the sum in general, term! | 4,298 | 21,165 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2021-25 | longest | en | 0.870495 |
https://socratic.org/questions/how-do-you-simplify-sqrt-50m-sqrt-72m#144393 | 1,701,550,516,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100452.79/warc/CC-MAIN-20231202203800-20231202233800-00810.warc.gz | 612,108,671 | 5,708 | # How do you simplify sqrt(50m) -sqrt(72m)?
$\sqrt{50 m} - \sqrt{72 m} = \sqrt{5 \cdot 5 \cdot 2 m} - \sqrt{6 \cdot 6 \cdot 2 m}$
$= \sqrt{{5}^{2}} \sqrt{2 m} - \sqrt{{6}^{2}} \sqrt{2 m}$
$= 5 \sqrt{2 m} - 6 \sqrt{2 m}$
$= \left(5 - 6\right) \sqrt{2 m}$
$= - \sqrt{2 m}$ | 141 | 271 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2023-50 | latest | en | 0.159441 |
http://mathforum.org/kb/plaintext.jspa?messageID=8772203 | 1,500,722,050,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549423992.48/warc/CC-MAIN-20170722102800-20170722122800-00041.warc.gz | 230,246,294 | 1,470 | ```Date: Mar 26, 2013 9:09 AM
Author: Venkatraman
Subject: Capacity of a discrete channel
Well I was reading this " A Mathematical Theory of Communication" paper by Claude Shannon. He says that the capacity of a discrete channel is given byC = log(N(T))/T where limit T->infinity [ is there a way to write equation in this forum eg: by using latex?]Here N(T) is the number of possible sequences in a duration of T seconds.He gives one example before talking about this capacity formula. Here's the example- Consider 32 symbols. You have a system where you can transmit 2 symbols per second. Now he says it is clear that if each symbol has 5 bits then we can send 2 x 5 =10 bits per second (or 2 symbols per second). This is the capacity of the channel. But when I tried it out using the above expression I couldn't get the answer as 2 symbols/ second. I got it as 3 symbols per second. Can you help me with this?Thanks in advance.
``` | 229 | 935 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2017-30 | longest | en | 0.931935 |
http://www.wyzant.com/resources/answers/10389/trig_tan_math_problem | 1,394,228,606,000,000,000 | text/html | crawl-data/CC-MAIN-2014-10/segments/1393999651148/warc/CC-MAIN-20140305060731-00074-ip-10-183-142-35.ec2.internal.warc.gz | 600,929,958 | 12,139 | Search 73,208 tutors
0 0
## Trig Tan Math problem
Ive tried to work these problems but am unsure of how exactly to get the correct answer.
a man jumps out of a plane at 4250 feet directly over his target and falls 82 degress to the ground. How far did he miss his target?
A tree cast a shadow of 12 feet and the distance from the end of the shadow to the top of the tree is 13 feet. How tall is the tree?
What is the answer and how did you work this problem out step by step.
tan 82° = x / 4250
(tan 82°) * 4250 = x
x ≈ 30240.32 ft. ( I don't know if I interpreted the problem right.)
Second problem:
This is a right triangle problem.
In this case the base of triangle is 12 feet and the hypotenuse is 13 feet.
use pythagorean theorem: a2 + b2 = c2
122 + b2 = 132
144 + b2 = 169
b2 = 169 - 144
b2 = 25
b = 5 feet.
so, the tree is 5 feet tall.
B
/|
/ |
/ | ↑
/ | 4250 ft
/ | ↓
A / 820 | C
BC / AC = tan 820 ---> AC = BC / tan 820
B AC ≈ 4250 ÷ 7.11537 = 597.3 ft
|\
| \
| \ 13 ft
| \
| 12 ft \ A
C
a2 + b2 = c2 ---> a2 = 132 - 122 = 25 ---> a = 5 ft
OR
cos A = AB / AC
cos A = 12 / 13 = 0.923077
measure of angel A = 22.620
sin 22.620 = BC / AB ---> BC = AB * sin 22.620 ---> BC = 13 * 0.3846 = 5 ft
You have two problems here. For the first one, a very good explanation can be found here on how to proceed
http://www.mathsisfun.com/algebra/trig-finding-side-right-triangle.html
You have the angle (82 degrees) and the adjacent side (4250 feet) but need the opposite side's measurement, so you are working with the tangent.
The second is classic Pythagorus: tree height is A (? feet), shadow cast (12 feet) is B, shadow tip to tree top is C (13 feet or the hypotenuse{H}).
Draw the picture, it will help makes things clearer.
So, A-squared plus B-squared equals C-squared:
A2 + B2 = C2
A2 + 122 = 132
A2 + 144 = 169
Move B to the right side of the equation
A2 = 169 - 144
Subtract B from C
A2 = 25
Take the square root of both sides of the equation
A = 5
The tree is 5 feet tall. | 697 | 2,109 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.4375 | 4 | CC-MAIN-2014-10 | latest | en | 0.830312 |
https://puzzling.stackexchange.com/questions/109276/unusual-3x3-square | 1,723,346,780,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640843545.63/warc/CC-MAIN-20240811013030-20240811043030-00662.warc.gz | 373,561,040 | 38,964 | # Unusual 3x3 square
Can you fill a 3x3 grid with every number from 1 to 9, such that the sum of numbers in the first row is equal to the sum of numbers in every 2x2 sub-grid? Can you find multiple solutions? | 61 | 209 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2024-33 | latest | en | 0.920361 |
https://metanumbers.com/10054 | 1,618,511,363,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038087714.38/warc/CC-MAIN-20210415160727-20210415190727-00617.warc.gz | 506,549,029 | 7,436 | ## 10054
10,054 (ten thousand fifty-four) is an even five-digits composite number following 10053 and preceding 10055. In scientific notation, it is written as 1.0054 × 104. The sum of its digits is 10. It has a total of 3 prime factors and 8 positive divisors. There are 4,560 positive integers (up to 10054) that are relatively prime to 10054.
## Basic properties
• Is Prime? No
• Number parity Even
• Number length 5
• Sum of Digits 10
• Digital Root 1
## Name
Short name 10 thousand 54 ten thousand fifty-four
## Notation
Scientific notation 1.0054 × 104 10.054 × 103
## Prime Factorization of 10054
Prime Factorization 2 × 11 × 457
Composite number
Distinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 3 Total number of prime factors rad(n) 10054 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) -1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 10,054 is 2 × 11 × 457. Since it has a total of 3 prime factors, 10,054 is a composite number.
## Divisors of 10054
1, 2, 11, 22, 457, 914, 5027, 10054
8 divisors
Even divisors 4 4 2 2
Total Divisors Sum of Divisors Aliquot Sum τ(n) 8 Total number of the positive divisors of n σ(n) 16488 Sum of all the positive divisors of n s(n) 6434 Sum of the proper positive divisors of n A(n) 2061 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 100.27 Returns the nth root of the product of n divisors H(n) 4.87821 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 10,054 can be divided by 8 positive divisors (out of which 4 are even, and 4 are odd). The sum of these divisors (counting 10,054) is 16,488, the average is 2,061.
## Other Arithmetic Functions (n = 10054)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 4560 Total number of positive integers not greater than n that are coprime to n λ(n) 2280 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 1236 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 4,560 positive integers (less than 10,054) that are coprime with 10,054. And there are approximately 1,236 prime numbers less than or equal to 10,054.
## Divisibility of 10054
m n mod m 2 3 4 5 6 7 8 9 0 1 2 4 4 2 6 1
The number 10,054 is divisible by 2.
• Arithmetic
• Deficient
• Polite
• Square Free
• Sphenic
## Base conversion (10054)
Base System Value
2 Binary 10011101000110
3 Ternary 111210101
4 Quaternary 2131012
5 Quinary 310204
6 Senary 114314
8 Octal 23506
10 Decimal 10054
12 Duodecimal 599a
20 Vigesimal 152e
36 Base36 7ra
## Basic calculations (n = 10054)
### Multiplication
n×i
n×2 20108 30162 40216 50270
### Division
ni
n⁄2 5027 3351.33 2513.5 2010.8
### Exponentiation
ni
n2 101082916 1016287637464 10217755907063056 102729317889611965024
### Nth Root
i√n
2√n 100.27 21.5831 10.0135 6.31637
## 10054 as geometric shapes
### Circle
Diameter 20108 63171.1 3.17561e+08
### Sphere
Volume 4.25702e+12 1.27025e+09 63171.1
### Square
Length = n
Perimeter 40216 1.01083e+08 14218.5
### Cube
Length = n
Surface area 6.06497e+08 1.01629e+12 17414
### Equilateral Triangle
Length = n
Perimeter 30162 4.37702e+07 8707.02
### Triangular Pyramid
Length = n
Surface area 1.75081e+08 1.19771e+11 8209.06
## Cryptographic Hash Functions
md5 bef4d169d8bddd17d68303877a3ea945 3e2ae06c30d3db1efab598d804bf9489e47a1c18 7fedf7aaae65bdad482a461b9a7ba24d7dd2c4239e8d9d2f8ff5c1f4ce16438d 1a78ac2cdeb584752b862f9a2c86fdf05dc30872d09972034d9f157a589790abe8b351b4580ae67d7ae139a37591c22c53df53a3b71babeb31ecabd6e984ca39 34975525d912d7b53a6de2cee5bae250299c8c99 | 1,441 | 4,025 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.8125 | 4 | CC-MAIN-2021-17 | longest | en | 0.808978 |
http://www.piprime.fr/developpement/optics_asy/?posts_per_page=-1 | 1,611,561,190,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703565376.63/warc/CC-MAIN-20210125061144-20210125091144-00660.warc.gz | 168,961,887 | 10,074 | ## Asymptote using graph3.asy – fig0120
Category: Asymptote,Examples 3D,graph3.asyPh. Ivaldi @ 14 h 11 min
(Compiled with Asymptote version 2.14svn-r5318)
import graph3;
import palette;
real sinc(real x){return x != 0 ? sin(x)/x : 1;}
real f(pair z){
real value = (sinc(pi*z.x)*sinc(pi*z.y))**2;
return value^0.25;
}
currentprojection=orthographic(0,0,1);
size(10cm,0);
surface s=surface(f,(-5,-5),(5,5),100,Spline);
draw(planeproject(unitsquare3)*s,nolight);
Étiquettes : , , , , ,
## Official Asymptote example – eetomumu
Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 15 h 57 min
(Compiled with Asymptote version 2.14svn-r5318)
/* This code comes from The Official Asymptote Gallery */
import feynman;
// set default line width to 0.8bp
currentpen = linewidth(0.8);
// scale all other defaults of the feynman module appropriately
fmdefaults();
// define vertex and external points
real L = 50;
pair zl = (-0.75*L,0);
pair zr = (+0.75*L,0);
pair xu = zl + L*dir(+120);
pair xl = zl + L*dir(-120);
pair yu = zr + L*dir(+60);
pair yl = zr + L*dir(-60);
// draw propagators and vertices
drawFermion(xu--zl);
drawFermion(zl--xl);
drawPhoton(zl--zr);
drawFermion(yu--zr);
drawFermion(zr--yl);
drawVertex(zl);
drawVertex(zr);
// draw momentum arrows and momentum labels
drawMomArrow(xl--zl, Relative(left));
label(Label("$k'$",2RightSide), xl--zl);
label(Label("$k$",2LeftSide), xu--zl);
drawMomArrow(zl--zr, Relative(left));
label(Label("$q$",2RightSide), zl--zr);
drawMomArrow(zr--yu, Relative(right));
label(Label("$p'$",2LeftSide), zr--yu);
label(Label("$p$",2RightSide), zr--yl);
// draw particle labels
label("$e^-$", xu, left);
label("$e^+$", xl, left);
label("$\mu^+$", yu, right);
label("$\mu^-$", yl, right);
Étiquettes : , ,
## Official Asymptote example – electromagnetic
Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 16 h 57 min
(Compiled with Asymptote version 1.92svn-r4817)
/* This code comes from The Official Asymptote Gallery */
import graph;
import palette;
texpreamble("\usepackage[amssymb,thinqspace,thinspace]{SIunits}");
size(800,200);
real c=3e8;
real nm=1e-9;
real freq(real lambda) {return c/(lambda*nm);}
real lambda(real f) {return c/(f*nm);}
real fmin=10;
real fmax=1e23;
scale(Log(true),Linear(true));
xlimits(fmin,fmax);
ylimits(0,1);
real uv=freq(400);
real ir=freq(700);
bounds visible=bounds(Scale(uv).x,Scale(ir).x);
palette(visible,uv,ir+(0,2),Bottom,Rainbow(),invisible);
xaxis(Label("\hertz",1),Bottom,RightTicks,above=true);
real log10Left(real x) {return -log10(x);}
real pow10Left(real x) {return pow10(-x);}
scaleT LogLeft=scaleT(log10Left,pow10Left,logarithmic=true);
picture q=secondaryX(new void(picture p) {
scale(p,LogLeft,Linear);
xlimits(p,lambda(fmax),lambda(fmin));
ylimits(p,0,1);
xaxis(p,Label("\nano\metre",1),Top,LeftTicks(DefaultLogFormat,n=10));
});
margin margin=PenMargin(0,0);
draw("infrared",Scale((1e12,1.5))--Scale(shift(0,1.5)*ir),Arrows,margin);
draw("UV",Scale(shift(0,1.5)*uv)--Scale((1e17,1.5)),Arrows,margin);
draw("x-rays",Scale((1e16,1))--Scale((1e21,1)),N,Arrows);
draw("$\gamma$-rays",Scale((fmax,1.5))--Scale((2e18,1.5)),Arrow);
Étiquettes : ,
## Official Asymptote example – laserlattice
Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 19 h 57 min
(Compiled with Asymptote version 2.14svn-r5318)
/* This code comes from The Official Asymptote Gallery */
import graph;
import palette;
int n=256;
pen[] Palette=BWRainbow();
real w(real w0, real z0, real z) {return w0*sqrt(1+(z/z0)^2);}
real pot(real lambda, real w0, real r, real z)
{
real z0=pi*w0^2/lambda, kappa=2pi/lambda;
return exp(-2*(r/w(w0,z0,z))^2)*cos(kappa*z)^2;
}
picture make_field(real lambda, real w0)
{
real[][] v=new real[n][n];
for(int i=0; i < n; ++i)
for(int j=0; j < n; ++j)
v[i][j]=pot(lambda,w0,i-n/2,abs(j-n/2));
picture p=new picture;
size(p,250,250,IgnoreAspect);
real xm=-n/lambda, ym=-n/(2*w0), xx=n/lambda, yx=n/(2*w0);
image(p,v,(xm,ym),(xx,yx),Palette);
xlimits(p,xm,xx);
ylimits(p,ym,yx);
xaxis(p,"{\Large $z/\frac{\lambda}{2}$}",BottomTop,LeftTicks);
yaxis(p,"{\Large $r/w_0$}",LeftRight,RightTicks);
label(p,format("{\LARGE $w_0/\lambda=%.2f$}",w0/lambda),point(p,NW),5N);
return p;
}
picture p=make_field(160,80);
picture q=make_field(80,80);
picture r=make_field(16,80);
picture s=make_field(2,80);
real margin=1cm; | 1,533 | 4,383 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2021-04 | latest | en | 0.367508 |
https://hextobinary.com/unit/acceleration/from/ftmin2/to/mmh2/600 | 1,716,118,904,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971057786.92/warc/CC-MAIN-20240519101339-20240519131339-00720.warc.gz | 253,705,351 | 15,636 | # 600 Feet/Minute Squared in Millimeter/Hour Squared
Acceleration
Feet/Minute Squared
Millimeter/Hour Squared
600 Feet/Minute Squared = 658368000 Millimeter/Hour Squared
## How many Millimeter/Hour Squared are in 600 Feet/Minute Squared?
The answer is 600 Feet/Minute Squared is equal to 658368000 Millimeter/Hour Squared and that means we can also write it as 600 Feet/Minute Squared = 658368000 Millimeter/Hour Squared. Feel free to use our online unit conversion calculator to convert the unit from Feet/Minute Squared to Millimeter/Hour Squared. Just simply enter value 600 in Feet/Minute Squared and see the result in Millimeter/Hour Squared.
## How to Convert 600 Feet/Minute Squared to Millimeter/Hour Squared (600 ft/min2 to mm/h2)
By using our Feet/Minute Squared to Millimeter/Hour Squared conversion tool, you know that one Feet/Minute Squared is equivalent to 1097280 Millimeter/Hour Squared. Hence, to convert Feet/Minute Squared to Millimeter/Hour Squared, we just need to multiply the number by 1097280. We are going to use very simple Feet/Minute Squared to Millimeter/Hour Squared conversion formula for that. Pleas see the calculation example given below.
$$\text{1 Feet/Minute Squared} = \text{1097280 Millimeter/Hour Squared}$$
$$\text{600 Feet/Minute Squared} = 600 \times 1097280 = \text{658368000 Millimeter/Hour Squared}$$
## What is Feet/Minute Squared Unit of Measure?
Feet/Minute Squared or Feet per Minute Squared is a unit of measurement for acceleration. If an object accelerates at the rate of 1 feet/minute squared, that means its speed is increased by 1 feet per minute every minute.
## What is the symbol of Feet/Minute Squared?
The symbol of Feet/Minute Squared is ft/min2. This means you can also write one Feet/Minute Squared as 1 ft/min2.
## What is Millimeter/Hour Squared Unit of Measure?
Millimeter/Hour Squared or Millimeter per Hour Squared is a unit of measurement for acceleration. If an object accelerates at the rate of 1 millimeter/hour squared, that means its speed is increased by 1 millimeter per hour every hour.
## What is the symbol of Millimeter/Hour Squared?
The symbol of Millimeter/Hour Squared is mm/h2. This means you can also write one Millimeter/Hour Squared as 1 mm/h2.
## Feet/Minute Squared to Millimeter/Hour Squared Conversion Table (600-609)
Feet/Minute Squared [ft/min2]Millimeter/Hour Squared [mm/h2]
600658368000
601659465280
602660562560
603661659840
604662757120
605663854400
606664951680
607666048960
608667146240
609668243520
## Feet/Minute Squared to Other Units Conversion Table
Feet/Minute Squared [ft/min2]Output
600 feet/minute squared in meter/second squared is equal to0.0508
600 feet/minute squared in attometer/second squared is equal to50800000000000000
600 feet/minute squared in centimeter/second squared is equal to5.08
600 feet/minute squared in decimeter/second squared is equal to0.508
600 feet/minute squared in dekameter/second squared is equal to0.00508
600 feet/minute squared in femtometer/second squared is equal to50800000000000
600 feet/minute squared in hectometer/second squared is equal to0.000508
600 feet/minute squared in kilometer/second squared is equal to0.0000508
600 feet/minute squared in micrometer/second squared is equal to50800
600 feet/minute squared in millimeter/second squared is equal to50.8
600 feet/minute squared in nanometer/second squared is equal to50800000
600 feet/minute squared in picometer/second squared is equal to50800000000
600 feet/minute squared in meter/hour squared is equal to658368
600 feet/minute squared in millimeter/hour squared is equal to658368000
600 feet/minute squared in centimeter/hour squared is equal to65836800
600 feet/minute squared in kilometer/hour squared is equal to658.37
600 feet/minute squared in meter/minute squared is equal to182.88
600 feet/minute squared in millimeter/minute squared is equal to182880
600 feet/minute squared in centimeter/minute squared is equal to18288
600 feet/minute squared in kilometer/minute squared is equal to0.18288
600 feet/minute squared in kilometer/hour/second is equal to0.18288
600 feet/minute squared in inch/hour/minute is equal to432000
600 feet/minute squared in inch/hour/second is equal to7200
600 feet/minute squared in inch/minute/second is equal to120
600 feet/minute squared in inch/hour squared is equal to25920000
600 feet/minute squared in inch/minute squared is equal to7200
600 feet/minute squared in inch/second squared is equal to2
600 feet/minute squared in feet/hour/minute is equal to36000
600 feet/minute squared in feet/hour/second is equal to600
600 feet/minute squared in feet/minute/second is equal to10
600 feet/minute squared in feet/hour squared is equal to2160000
600 feet/minute squared in feet/second squared is equal to0.16666666666667
600 feet/minute squared in knot/hour is equal to355.49
600 feet/minute squared in knot/minute is equal to5.92
600 feet/minute squared in knot/second is equal to0.0987473006
600 feet/minute squared in knot/millisecond is equal to0.0000987473006
600 feet/minute squared in mile/hour/minute is equal to6.82
600 feet/minute squared in mile/hour/second is equal to0.11363636363636
600 feet/minute squared in mile/hour squared is equal to409.09
600 feet/minute squared in mile/minute squared is equal to0.11363636363636
600 feet/minute squared in mile/second squared is equal to0.000031565656565657
600 feet/minute squared in yard/second squared is equal to0.055555555555556
600 feet/minute squared in gal is equal to5.08
600 feet/minute squared in galileo is equal to5.08
600 feet/minute squared in centigal is equal to508
600 feet/minute squared in decigal is equal to50.8
600 feet/minute squared in g-unit is equal to0.0051801583619279
600 feet/minute squared in gn is equal to0.0051801583619279
600 feet/minute squared in gravity is equal to0.0051801583619279
600 feet/minute squared in milligal is equal to5080
600 feet/minute squared in kilogal is equal to0.00508
Disclaimer:We make a great effort in making sure that conversion is as accurate as possible, but we cannot guarantee that. Before using any of the conversion tools or data, you must validate its correctness with an authority. | 1,661 | 6,179 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2024-22 | latest | en | 0.906164 |
https://couponsanddiscouts.com/how-to-calculate-5%25-discount/ | 1,638,950,829,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363445.41/warc/CC-MAIN-20211208053135-20211208083135-00104.warc.gz | 254,435,493 | 8,305 | # How To Calculate 5% Discount
Filter Type:
Filter Time:
Sale Price = Original Price - Amount Saved. So, Sale Price = 100 - 5. Sale Price = $95 (answer). This means the cost of the item to you is$95. You will pay $95 for a item with original price of$100 when discounted 5%. In this example, if you buy an item at $100 with 5% discount, you will pay 100 - 5 = 95 dollars. https://www.percent-off.com/_5_%25+off__ ### 5% off 100 -%-off Calculator Sale Price = Original Price - Amount Saved. So, Sale Price = 100 - 5. Sale Price =$95 (answer). This means the cost of the item to you is $95. You will pay$95 for a item with original price of $100 when discounted 5%. In this example, if you buy an item at$100 with 5% discount, you will pay 100 - 5 = 95 dollars.
https://www.percent-off.com/_5_%25+off_100_
### Percent Off Calculator - MiniWebtool
About Percent Off Calculator. The Percent Off Calculator is used to calculate the sale price of a discounted item after the percent off discount is applied. Updated with new simple percent off function. Input the original price once, and get all prices from 5% off up to 75% off instantly.
https://miniwebtool.com/percent-off-calculator/
### Discount Calculator
A percent off of a price typically refers to getting some percent, say 10%, off of the original price of the product or service. For example, if a good costs $45, with a 10% discount, the final price would be calculated by subtracting 10% of$45, from $45, or equivalently, calculating 90% of$45: 10% of $45 = 0.10 × 45 =$4.50. $45 –$4.50 ...
https://www.calculator.net/discount-calculator.html
For this calculator, a "stackable additional discount" means getting a further percent off of a product after a discount is applied. Using the same example, assume that the 20% discount is a discount applied by the store to the product. If you have a coupon for another 15% off, the 15% off would then be applied to the discounted price of $223.20. https://www.calculator.net/percent-off-calculator.html ### Discount Calculator - Calculator Soup - Online Calculators Calculate the list price, discount percentage or sale price given the other two values. You will also find the discount savings amount. Calculate Discount from List Price and Sale Price. The discount is list price minus the sale price then divided by the list price and multiplied by 100 to get a percentage. \(D = \dfrac{(L - S)}{L} \times 100 https://www.calculatorsoup.com/calculators/financial/discount-calculator.php ### How To Calculate a Discount | Indeed.com Mar 09, 2021 · If this is the case, find the dollar amount for the remaining 5% by dividing the dollar amount for 10% by two. Example: The Shoe Mart discount on winter boots is 25%. We need to account for the remaining 5%. 10% of the original rounded price of$150 is $15.$15 divided by 2 is $7.50. 5% of$150 is $7.50. https://www.indeed.com/career-advice/career-development/how-to-calculate-discount ### What is 5% off 134 Dollars? (5% off$134)
What is 5 Percent off 134 Dollars? - 5% off $134 is$127.30. If an item is on sale for 5% off from the original price of 134 dollars, you would pay $127.30 with a discount of$6.7.
https://online-calculator.org/what-is-5-percent-off-134-dollars
### Percentage Discount in Excel - Easy Formulas
Calculate Discounted Price. If you know the original price and the percentage discount, you can calculate the discounted price. 1. First, subtract the percentage discount from 1. Note: you're still paying 75%. 2. Multiply this result by the original price. Note: you're still paying 75% of the original $80. This equals$60. Calculate Original Price
https://www.excel-easy.com/examples/discount.html
### How to calculate 5% of a number in Excel - Quora
Answer (1 of 2): In cell B1, type “=0.05*A1”. Assuming the original number is in A1 and you want to put the result in B1.
https://www.quora.com/How-do-I-calculate-5-of-a-number-in-Excel
Nov 02, 2020 · If what you really need to know is an item's final sale price after the discount is taken, you can skip calculating the discount's dollar amount and go straight to figuring what's left after you remove the discount. Imagine that you've seen a blazer in the shop window that originally sold for $90, but now it's on sale for 30 percent off. https://sciencing.com/how-to-calculate-percent-off-13712217.html ### Percent Off Calculator Jan 24, 2021 · The process of calculating your discount is as follows: Enter the original price into our percent off calculator. For example, a TV set might originally set you back$5000. Determine the percentage discount - in our example store, everything is 75% off.
https://www.omnicalculator.com/finance/percent-off
### How to calculate discount rate or price in Excel?
Calculate discount rate with formula in Excel. The following formula is to calculate the discount rate. 1. Type the original prices and sales prices into a worksheet as shown as below screenshot: 2. Select a blank cell, for instance, the Cell C2, type this formula = (B2-A2)/ABS (A2) (the Cell A2 indicates the original price, B2 stands the sales ...
https://www.extendoffice.com/documents/excel/1487-excel-calculate-discount-rate-price.html
### What is 5% off 2429 dollars| How to calculate 5%
Nov 04, 2021 · How to calculate 5% off 2429 dollars or pounds. In calculating 5% of a number, sales tax, credit cards cash back bonus, interest, discounts, interest per annum, dollars, pounds, coupons,5% off, 5% of price or something, we use the formula above to find the answer. The equation for the calculation is very simple and direct.
https://www.percentage-off-calculator.com/percent/5-percent-off-2429.html
### How To Calculate Discount and Sale Price
The rate of discount is usually given as a percent, but may also be given as a fraction. The phrases used for discounted items include, " off," "Save 50%," and "Get a 20% discount." Procedure: To calculate the discount, multiply the rate by the original price. To calculate the sale price, subtract the discount from original price.
https://www.mathgoodies.com/lessons/percent/sale_price
### What is 5% off 5 Dollars - coolconversion.com
What is 5% off 5 Dollars. The easiest way of calculating discount is, in this case, to multiply the normal price $5 by 5 then divide it by one hundred. So, the discount is equal to$0.25. To calculate the sales price, simply deduct the discount of $0.25 from the original price$5 then get \$4.75 as the sales price.
https://coolconversion.com/math/discount-calculator/what-is_5_%25-off_5_Dollars | 1,676 | 6,548 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.609375 | 4 | CC-MAIN-2021-49 | latest | en | 0.890135 |
https://www.kylesconverter.com/density/tonnes-per-cubic-foot-to-pounds-per-acre--foot | 1,726,708,069,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651944.55/warc/CC-MAIN-20240918233405-20240919023405-00539.warc.gz | 775,436,434 | 5,885 | # Convert Tonnes Per Cubic Foot to Pounds Per Acre-foot
### Kyle's Converter > Density > Tonnes Per Cubic Foot > Tonnes Per Cubic Foot to Pounds Per Acre-foot
Tonnes Per Cubic Foot (t/cu ft) Pounds Per Acre-foot (lbm/ac ft) Precision: 0 1 2 3 4 5 6 7 8 9 12 15 18
Reverse conversion?
Pounds Per Acre-foot to Tonnes Per Cubic Foot
(or just enter a value in the "to" field)
#### Please share if you found this tool useful:
Unit Descriptions
1 Tonne per Cubic Foot:
Mass of 1 tonne per volume of a cubic foot. Metric tonne of exactly 1 000 kilograms. International foot length of 0.3048 meters. Approximate density of 35 314.666 721 4886 kilograms per cubic meter. 1 t/cu ft ≈ 35314.6667214886 kg/m3.
1 Pound per Acre-Foot:
Mass of 1 pound per volume of an acre-foot. International pound and foot. 1 lbm/ac ft ≈ 0.000367733318961436 kg/m3.
Conversions Table
1 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 96033361.407770 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 6722335298.5413
2 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 192066722.815580 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 7682668912.6186
3 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 288100084.223290 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 8643002526.6959
4 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 384133445.6309100 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 9603336140.7733
5 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 480166807.0387200 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 19206672281.547
6 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 576200168.4464300 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 28810008422.32
7 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 672233529.8541400 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 38413344563.093
8 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 768266891.2619500 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 48016680703.866
9 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 864300252.6696600 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 57620016844.64
10 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 960333614.0773800 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 76826689126.186
20 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 1920667228.1547900 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 86430025266.959
30 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 2881000842.2321,000 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 96033361407.733
40 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 3841334456.309310,000 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 960333614077.33
50 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 4801668070.3866100,000 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 9603336140773.3
60 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 5762001684.4641,000,000 Tonnes Per Cubic Foot to Pounds Per Acre-foot = 96033361407733 | 959 | 2,857 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2024-38 | latest | en | 0.436731 |
http://ziynetnesibe.com/c-c-courses-%E2%80%93-5-calculations | 1,555,720,729,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578528433.41/warc/CC-MAIN-20190420000959-20190420022959-00444.warc.gz | 337,326,835 | 14,157 | ## C / C++ Courses ? 5 (Calculations)
3 Ağustos 2010 1.837 views 4 Yorum
Let’s continue with calculation in C!
First of all, we should know about order of mathematical operations. Basicly, we can say the order is like that:
1) ( ) paranthesis
2) * (product), / (division) , % (remainder of division)
3) + (summation), (difference)
If operations are in the same order ( like + and – ), than the priority belongs to one that comes first.
Example;
`int x= 5 * 4 / 2 + ( 4 + 2 );`
If we print, it will find x like that;
x= 5 * 4 / 2 + 6 // first priority for paranthesis
x=20 / 2 + 6 // * and / have same order, but higher than +. then which comes first,this is *, will operate first
x=10 + 6
x=16
Result is 16.
When we are dealing with the same type, result has also same type.
9/2 = 4
7/11 = 0
7%8 = 7
9%2 = 1
Ex; Find the value of them
1) int x= 7+3*6/2-1; //x=15
2) int x= 2%2+2*2-2/2; //x=3
3) int x=3*9+(3+(9*3/3)); //x=39
Let’s write a program which the user enters how many bottles of water there are in the store.A bottle can hold 0,75 liters of water. Program will calculate and print the total amount of water in the store.
`#include<stdio.h> `
```int main(){ ```
`int bottle;`
`float total;`
`printf("Enter how many bottles there are in the store: ");`
`scanf("%d",&bottle);`
`total=0,75*bottle;`
`printf("Store has %f liter of water", total);`
`return 0; `
`}`
»Extra:
```int x,y; x=5; y=4; float av= (x+y) / 2;```
What does av equal to?
Answer is in the following lesson;)
float x=3,5;
int y;
y=x;
printf( “%d”, y ); // it will write 3 on the screen. because y is integer and y=3,5 means, it equals to 3.
int x=6;
float y;
y=x;
printf( “%f” ,y); // it will print 6,000000. because y is float and y=6 means, it equals to 6,000000
(after comma, it prints six numbers. If we write 3,67, it will print 3,670000. )
What should we do, if we write this number as 3,67 on the screen?
We will learn these in the future.
Yes folks, that’s it!
### 4 Yorum »
Be nice. İçeriği çirkin olmadığı sürece her yoruma, öneriye ve soruya "evet" :)
Etiketler: , , , , , , , , , , | 720 | 2,147 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2019-18 | latest | en | 0.805214 |
https://ez.analog.com/search?q=LT8364 | 1,669,819,402,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710764.12/warc/CC-MAIN-20221130124353-20221130154353-00689.warc.gz | 283,636,090 | 28,800 | • ### LT8364 Don't start during load
Hi.
I have designed a SEPIC converter out of your datasheet, page 25, with an input span from 4.5-30 volt and the output at 25 volt will be used to charge a capacitor of 14mF.
When I put on the voltage, testing with 12 v to 30v, at the input the output…
• ### LT8364
您好，用LT8364输出-12V时，手册上写的输入范围时2.8V-42V。现在我想做一个-12V输出，输入范围最大到60V，最小不超过20V，这个设计是否可以实现？
• ### About the audible noise when using LT8364 with pulse skipping mode
In p. 17 of the LT8364's datasheet, it mentions at light loads in burst mode, may cause audible noise. Then what about in pulse skipping mode?
Thanks.
• ### Inverting Configuration Using LT8364 - 28Vin and -35Vout
Hello,
I am using the LT8364 to Generate -35V Output from 28V Input. My application load current is low (say, 10mA Max) . I am using the reference circuit as mentioned in the datasheet. I'm not able to realize the output.
I was using the LT8361 before…
• ### Designing with LT8364
Hi Team,
We want to generate a +50V using an LT8364 chip.
The input is from a 3.7V battery.
What is the maximum load current that can be connected at this condition?.
Also, I am attaching the circuit herewith,
Please let me know if there are any corrections…
• ### LT8364 / LT3094 VIOC behaviour
I am attempting to use the VIOC capability of the LT3094 to control an upstream LT8364, as shown:
This works as expected with little to no bypass capacitor on the LT3094 SET pin:
However, increasing the bypass cap (C7) to 100nF or more prevents the…
• ### Negative input to negative output with LT8364
I want to convert a -12V input DC voltage to a -1.5V to -5.5V, Io=-3A output DC voltage by LT8364, is it possible?
my assumption is shown below. Any more detailed application circuits or notes could be given for LT8364, especially for…
• ### Noise on LT8652S and LT8364 outputs
Hello,
I am using a LT8652S and a LT8364 to generate +15V, +5V and -15V from 18V.
Overall its working, but I am measuring some noise (not switching noise) on the +-15V outputs, which I cant really identify. Also the +5V output starts oscillating at >0…
• ### LT8364 inverting load transient response
Hello,
I am currently simulating a circuit with the LT8364 in inverting configuration. So far I am satisfied with the results, only the load transient response is really slow and I get a voltage drop of about 0.8V for a load of 0.3A to 1A to 0.3A which…
• ### LT8364 带轻载时可编程电源显示电流波动较大
在设计使用LT8364的DC-DC电源，在轻载时可编程电源输出电流波动较大（18V输出带载820R，外部电源显示电流自10mA至50mA波动），在外部电源输入处有并联4只100uF的电解电容，调试过程中尝试修改 VC引脚上的 RC 环路，也更改过芯片的工作频率都没有改善。电路原理图如下，R5、R8的值在原理图上用的默认值没做修改。
在18V输出带载820R测试电源带载的阶跃响应如下 | 862 | 2,641 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2022-49 | latest | en | 0.801952 |
https://selfstudy365.com/exam/triangles-02-539 | 1,725,813,134,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651013.49/warc/CC-MAIN-20240908150334-20240908180334-00203.warc.gz | 497,185,693 | 12,696 | # Free Triangles 02 Practice Test - 9th Grade
In NVY, if NV=VY and VY YN, then which of the following is true?
A.
NVY = VYN
B.
NVY = YNV
C.
NVY+ 2VYN = 180
D.
VYN + 2NVY = 180
#### SOLUTION
Solution : C
Given, in NVY, NV = VY.
Then, VYN=YNV
[angles opposite to equal sides of a triangle are equal]
Using angle sum property of a triangle, we get:
NVY+VYN+YNV=180
So, NVY+2VYN=180.
It is also given that VYYN. Hence the options NVY=VYN and NVY=YNV are not correct.
Which of the following is sufficient for two triangles denoted by Δ1 and Δ2 to be congruent ?
A.
Any two sides of Δ1 should be equal to any two sides of Δ2
B.
All angles of Δ1 should be equal to all angles of Δ2
C.
Any two sides of Δ1 and one angle should be equal to any two sides and one angle of Δ2
D.
Any two sides of Δ1 and the included angle should be equal to any two sides and the included angle of Δ2
#### SOLUTION
Solution : D
Two triangles can't be congruent if any two sides and one angle of one are equal to any two sides and one angle of the other.
They will be congruent when the angle is included between the equal pair of sides. This is the SAS condition of congruency of triangles.
The SAS congruence rule states:
Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle.
In the given figure, O is equidistant from the sides AC and AB. Then the value of x - 3 is ___.
#### SOLUTION
Solution :
In ΔAOC and ΔAOB,OC=OB(Given)OBC=OCA(Both angles are right angles)And AO is common side.Hence, ΔAOCΔAOB(RHS congruence)CAO=BAO(CPCT)2x+24=30x=3x3=0
In the given figure, if ACB = 30, the value of ACD is
___.
#### SOLUTION
Solution :
If all the sides of CAT are equal to corresponding sides of RAT, then RAT CAT.
A.
True
B.
False
#### SOLUTION
Solution : A
If all the sides of CAT are equal to corresponding sides of RAT, then RAT will be congruent to CAT and the congruence criterion will be SSS.
In the given figure, ΔABD is an isosceles triangle with AB=AD. A median is drawn from A to side BD at C. Which of the following option(s) is/are correct?
A.
AC is perpendicular to BD
B.
BAC=DAC
C.
D.
Area of ΔABD=12×Area of ΔABC
#### SOLUTION
Solution : A, B, C, and D
Consider ΔABC and ΔADC,AC=AC (Common side of both triangles)AB=AD (Sides of isosceles triangle)BC=CD (Median divides a side in two equal parts)ΔABCΔADC (by SSS congruence criterion) So the option "ΔABCΔADC" is correct.ACB=ACD (CPCT)But they are supplementary angles. So, ACB+ACD=180ACB=ACD=90AC is perpendicular to BD and the hence option "AC is perpendicular to BD" is correct. Also, BAC=DAC (corresponding angles of congruent triangles)Hence, the option"BAC=DAC" is also correct.Also, area of ΔABC=area of ΔADC=12(area of ΔABD).ΔABCΔADC ar(ΔABC)=ar(ΔADC)Hence, the option "Area of ΔABD=12×Area of ΔABC"is also correct.
In the given figure, ΔABC is equilateral with point O as its circumcentre. Here, area of ΔBOC=13 area of ΔABC.
A. True
B. False
#### SOLUTION
Solution : A
Concider ΔAOB,ΔAOC and ΔBOC.AB=BC=AC (Sides of equilateral triangle)AO=BO=CO (Radii of circumcircle)ΔAOBΔBOCΔCOB (SSS congruence).Area of ΔAOB=Area of ΔBOC=Area of ΔAOC.But Area of ΔAOB+Area of ΔBOC+Area of ΔAOC=Area ofΔABC.Area of ΔBOC=13Area of ΔABC
Hence, the given statement is true.
In the given parallelogram ABCD, ΔABDΔBCD.
A. True
B. False
#### SOLUTION
Solution : B
Consider ΔABD and ΔCDB,AB=CD (Opposite sides of parallelogram)AD=CB (Opposite sides of parallelogram)ABD=CDB (Alternate angles).ΔABDΔCDB
Hence, the given statement is false as the vertices are not given in corresponding sequence in question.
In the given figure, if AD = BC and AD || BC, then
B. AB = DC
C. BC = CD
D. AC = BC
#### SOLUTION
Solution : B
CA=AC [common side]
AB=DC [CPCT]
In the given figure AD is the bisector of A and AB = AC. Then, by which criterion ACD and ABD are congruent?
A.
SSS
B.
SAS
C.
ASA
D.
None of these
Solution : B
In ACD and ABD | 1,368 | 4,061 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.71875 | 5 | CC-MAIN-2024-38 | latest | en | 0.780545 |
http://everything2.com/title/Eliminating+arbitrary+constants+by+calculus | 1,371,679,233,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368708808740/warc/CC-MAIN-20130516125328-00056-ip-10-60-113-184.ec2.internal.warc.gz | 89,899,441 | 6,603 | Overview
There is sometimes a need to elimate arbitrary constants from an equation, and the best way to do this is by use of the calculus. You'll need a basic knowledge of that discipline to make this write-up worthwhile.
Eliminating Arbitrary Constants
Consider this very simple example:
Example 1: y = x^2 + px
p is some arbitrary constant, that we would now like to eliminate. Differentiating:
dy/dx = 2x + p
p = dy/dx - 2x
Substituting this value for p into the original equation:
y = x2 + (dy/dx - 2x)x
There is no need to multiply this out, as p has evidently been removed.
Generally elimation of one constant is straight-forward, and removing multiple constants requires a little lateral thought. For example, the equation of simple harmonic motion:
Example 2: x = A*cos(pt - a)
Differentiate to give:
dx/dt = -pA*sin(pt - a)
and again...
d2x/dt2 = -p2A*cos(pt - a) = -p2x
In two steps, A and a have been eliminated. This method is easily extended to other examples. The basic technique is that, to eliminate n constants, it is necessary to differentiate n times to create n+1 equations, and then solve them just as with any set of simultaneous equations.
Practice Examples
If you need practice for consolidation, attempt to eliminate the arbitrary constant from these:
1. y = Px + P^3
2. y = A*eBx
Credit For This Write-Up
Some examples adapted, others lifted directly, from the classic Differential Equations, H.T.H. Piaggio, 1920.
Solutions
1. y = (dy/dx)x + (dy/dx)3
2. y * d2y/dx2 = (dy/dx)2
Log in or register to write something here or to contact authors. | 413 | 1,593 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.15625 | 4 | CC-MAIN-2013-20 | latest | en | 0.911257 |
https://www.jiskha.com/display.cgi?id=1260076874 | 1,516,433,802,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084889473.61/warc/CC-MAIN-20180120063253-20180120083253-00408.warc.gz | 944,515,887 | 4,213 | # statistic help pls
posted by .
a car insurance company has determined that 6% of all drivers were involved in a car accident last year,among the 12 drivers living on one particular street,3 were involved a car accident last year.if 12 drivers are randomly selected what is the probability of getting 3 or more who were involved in a car accident last year
• statistic help pls -
54825
## Similar Questions
1. ### Statistics
2.) Car insurance companies assume that the longer a person has been driving, the less likely they will be in an accident, and therefore charge new drivers higher insurance premiums than experienced drivers. To determine whether driving …
2. ### statistic
Jim has a 5-year-old car in reasonably good condition. He wants to take out a \$30,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the …
3. ### Stats
A car insurance company has determined that 7% of all drivers were involved in a car accident last year. The company randomly selects 200 drivers. Compute the mean and standard devistion of the random variable, x, the number of drivers …
4. ### statistics urgent
Consider all cars that are involved in an accident and assume that all cars are classified as either small or large. The probability that a small car is involved an accident is .2 if a small car is involved in an accident, the probabbility …
5. ### Statistics
Before i state my question I would like to note that I have to do a one tailed test but i don't know how to with the information given. I need a standard deviation, i need a mean, but do i use the mean for yrs drivin or number accidents. …
6. ### Statistics/Probability
2. Jim has a 5-year old car in reasonably good condition. He wants to take out a \$40,000 term (that is accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having and accident in … | 434 | 1,972 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2018-05 | latest | en | 0.967988 |
https://mathematica.stackexchange.com/questions/110924/how-to-recreate-the-gnuplot-color-scheme-afm-hot-in-mathematica | 1,653,603,617,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662625600.87/warc/CC-MAIN-20220526193923-20220526223923-00261.warc.gz | 436,236,172 | 69,181 | # How to recreate the gnuplot color scheme "AFM Hot" in Mathematica?
I'm trying to build an 3D AFM image from raw data with Mathematica. So how do I recreate the "AFM hot" color scheme? I've tried "SolarColors" and "RustTones", but they don't quite do the job.
"AFM hot" looks like this (I took this picture from here):
Test function:
f[x_, y_] := 0.1 + (1 - (x - 2)^2) (1 - (y - 2)^2)
So these gnuplot color maps are a little bit more complicated than can be easily achieved by Blend (although you can do some cool stuff with Blend).
If you look at this page you can see that they specify a particular mapping function for the three different RGB components as a function of the scaling parameter x.
AFMHot uses functions 33, 34, and 35, which correspond to 2 x, 2 x - 0.5, and 2x - 1.0, where x goes from 0 to 1
afmHot = RGBColor[2 #, 2 # - .5, 2 # - 1] &;
Plot3D[0.1 + (1 - (x - 2)^2) (1 - (y - 2)^2), {x, 1, 3}, {y, 1, 3},
ColorFunction -> Function[{x, y, z}, afmHot[z]] ]
DensityPlot[
0.1 + (1 - (x - 2)^2) (1 - (y - 2)^2), {x, 1, 3}, {y, 1, 3},
ColorFunction -> afmHot , PlotLegends -> Automatic]
You can do the rest of the color maps via
traditional = RGBColor[Sqrt[#], #^3, Sin[2 π #]] &;
greenRedViolet = RGBColor[#, Abs[# - .5], #^4] &;
ocean = RGBColor[3 # - 2, Abs[(3 # - 1)/2], #] &;
hot = RGBColor[3 #, 3 # - 1, 3 # - 2] &;
rainbow = RGBColor[Abs[2 # - .5], Sin[π #], Cos[π/2 #]] &;
afmHot = RGBColor[2 #, 2 # - .5, 2 # - 1] &;
LinearGradientImage[#, {300, 100}] & /@ {traditional, greenRedViolet,
ocean, hot, rainbow, afmHot} // Column
• The component functions are (piecewise) linear, so Blend[] can be used here. See my answer. Mar 24, 2016 at 13:11
• Right on - but could you do the nonlinear ones, the ones that call on Sqrt and trig functions? Also, what is meant by the notation in component 32? Mar 24, 2016 at 13:20
• Of course, you can't use Blend[] on those colors. ;) I'm not sure about those semicolons, I've looked through the manual and all I can find was that they're just separators. Mar 24, 2016 at 13:49
• Okay, it's apparently a piecewise function. Try this: f303132[x_] := RGBColor[Clip[25 x/8 - 25/32 , {0, 1}], Clip[2 x - 21/25, {0, 1}], Piecewise[{{4 x, 0 <= x < 1/4}, {1, 1/4 <= x < 21/50}, {46/25 - 2 x, 21/50 <= x < 23/25}, {(25 x - 23)/2, 23/25 <= x <= 1}}]] Mar 24, 2016 at 14:06
The gradient of interest here is actually a Gnuplot color scheme. From here we find that "AFM hot" corresponds to using components 34, 35, and 36 (with suitable clipping). Thus,
afmhot[x_] /; 0 <= x <= 1 :=
RGBColor[Min[2 x, 1], Min[Max[0, 2 x - 1/2], 1], Max[0, 2 x - 1]]
or, using Blend[],
afmhot[x_] /; 0 <= x <= 1 :=
Blend[{Black, RGBColor[1/2, 0, 0], RGBColor[1, 1/2, 0],
RGBColor[1, 1, 1/2], White}, x]
Test:
LinearGradientImage[afmhot, {300, 30}]
Plot3D[1/10 + (1 - (x - 2)^2) (1 - (y - 2)^2), {x, 1, 3}, {y, 1, 3},
ColorFunction -> (afmhot[#3] &)]
As Vitaliy pointed out, you can always define your own colour scheme.
clfun = Blend[{Black, Red, Yellow, White}, #] &; (*color scheme*)
Plot3D[0.1 + (1 - (x - 2)^2) (1 - (y - 2)^2), {x, 1, 3}, {y, 1, 3},
ColorFunction -> Function[{x, y, z}, clfun[z]]]
Before Mathematica had all the colour gradients, I used this blend:
RedTempX[x_] := RGBColor[Min[{1, 4x/3}], Max[{0, 2x-1}], Max[{0, 4x-3}]]
Don't forget you can use an exponent to modify how the colours appear. Here I used an exponent of 0.5.
Plot3D[0.1 + (1 - (x - 2)^2) (1 - (y - 2)^2), {x, 1, 3}, {y, 1, 3},
ColorFunction -> (RedTempX[#3^0.5] &), Mesh -> 20] | 1,364 | 3,529 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2022-21 | longest | en | 0.835725 |
https://www.annalsofamericus.com/how-can-i-improve-my-gre-verbal-score-in-2-days/ | 1,643,401,826,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320306335.77/warc/CC-MAIN-20220128182552-20220128212552-00136.warc.gz | 673,839,939 | 9,366 | ## How can I improve my GRE verbal score in 2 days?
When you do these questions, be sure to do the following:
1. Watch the explanation video and read the text explanation.
2. Look up the words that you don’t know or don’t know well.
3. Reread the text, question, and answer choices. Know the logic of the question well enough that you could explain it to someone else.
## How do I get a perfect GMAT score?
8 Tips to Getting a Perfect Score on the GMAT
1. #1: Study Consistently.
2. #2: Use the Best Practice Materials.
3. #3: Stay on Top of the Fundamentals.
4. #5: Focus on Timing.
6. #7: Practice in Realistic Test Conditions.
## Is GMAT negative marking?
Integrated Reasoning consists of non-MCQs. There is no negative marking in the GMAT Exam. There are 8 minute optional breaks given between the exam, the timing of whom has to be selected when selecting the order.
## How do I write a GMAT essay?
7 Essay Tips for GMAT Analytical Writing
1. Analytical writing demands objectivity.
2. Analyze the argument’s assumptions & supporting evidence.
3. Draw a conclusion from your thesis statement.
4. The AWA is about confidence—avoid hesitation.
5. Be concise, not wordy.
6. Be polished, not perfect.
7. Be yourself, use language you’re comfortable with.
## Is 320 a good GRE score?
If your programs’ averages are around 320, this will be a good score for you as it’s likely to make you a competitive applicant. But if your programs’ averages are more than 320, you’ll need to aim higher to give yourself a better chance of admission.
## How can I hack GRE?
Test Hacks for GRE Verbal
1. Guess First. For both the Sentence Equivalence and Text Completion sections, fill in the blank yourself before even looking at the answer choices.
2. Get Stylish.
3. Feel It.
4. Get Out of Line.
5. Blank Slate It.
6. Dodge the Partials.
7. Truth Means Nothing.
8. Stay in the Box.
## How do you get a 6.0 AWA GMAT?
1. General Structure. Intro – Restate argument, point out flaws or state intention to discuss them below.
2. Structural Word (should be all over the essays) Supporting examples – for example, to illustrate, for instance, because, specifically.
3. Templates. Intro:
4. Going from the templates to full-fledged essays.
5. Final tips.
## Can I crack GRE in 2 months?
So, is it possible to achieve this score in two months? Absolutely. In this post, I will try and delineate how you can score 320 in GRE in a matter of two months!
## Which GRE word list is best?
The Best GRE Word Lists
• Magoosh GRE Vocabulary Flashcards.
• Magoosh GRE Vocab Builder.
• Magoosh GRE Vocabulary eBook.
• The Economist GRE Word List.
• Other Great GRE Word Lists.
• Barron’s 3500 AND 4,759 Word Lists.
• Nova’s 4500.
• Random Internet Word Lists.
## Is a 4.5 GRE writing score good?
We’ve divided the table into different colors based on whether the GRE analytical writing scores would be considered low (0.0-3.0), average (3.5-4.0), high (4.5-5.0), or excellent (5.5-6.0). If your GRE Writing score is a 4.5 or above, you’re in good shape for most graduate programs, compared to all other GRE takers.
## Is 1 month enough for GRE?
While we know that some students have only a couple of weeks of time, and some have quite a few months on their clocks, a vast majority of them have about a month to study for the GRE. But, it is strongly recommended that you spend at least 30 days studying for the GRE. …
## Is Magoosh 1000 words enough for GRE?
This package of 1000 + 333 words can be enough in the sense that it is “likely” to cover most of the words that you would encounter in your GRE Verbal exam. But, there are chances that even after mugging up all these words you may still have to confront new words about which you might not have any clue.
## How can I improve my English GRE score?
How Can I Improve My GRE Verbal Score?
1. Text Completion. Fill in the blanks of a sentence with the right word so that the sentence makes sense.
2. Sentence Equivalence. Figure out which two words from a list of six fit a provided sentence.
## How do you master GRE words?
3. Come up with your own definitions.
1. Say words out loud.
2. Keep a GRE vocabulary list.
3. Use GRE flashcards when you’re on the go.
4. Prioritize learning words that GRE tends to test.
5. Visualizations help.
6. Understand word roots.
7. Use your new words every chance you get.
8. Don’t forget GRE math vocabulary!
## Is there an essay in GMAT?
The GMAT Essay, also called the GMAT Analytical Writing Assessment, or AWA, requires you to read a short argument and make a written analysis of the argument. This opening GMAT task has a 30 minute time limit. Well, to start out, write a good introduction, and the rest of the essay will flow very naturally.
## How should I prepare for GMAT?
10 Best Practices to Prepare for the GMAT™ Exam
1. Start your GMAT exam process at least six months before your test results are due.
2. Review and study one section of the test at a time.
3. Review basic math skills.
4. Practice pacing, because time management is critical to completing the GMAT exam.
## How many GRE words should I memorize?
Some resources list around 350, and the lists you find in test prep books can range in scope from 900 to 4,500. The best rule of thumb is to push yourself to study a lot of words but to keep it manageable. Try to keep it under 1,000 to give yourself a reasonable goal.
## Is GRE really tough?
Compared to the ACT and the SAT, the GRE is typically considered more difficult because, even though the math tested on the GRE is a lower level than the math tested on the SAT and ACT, the GRE has more challenging vocabulary and reading passages, and the math problems have trickier wording or require higher-level …
## Is a 326 GRE score good?
In addition, anything in the 90th percentile or higher can be considered an excellent score. Using this definition, we can say that all scores in this chart are great GRE scores, with most qualifying as excellent. Specifically, 162-170 on Verbal and 166-170 on Quant can be considered excellent scores.
## How long should a GMAT essay be?
Your GMAT essay should follow standard 4-5-paragraph essay structure: introduction, 2-4 body paragraphs, and conclusion. Each body paragraph should clearly address a specific (and different) aspect of the prompt.
## How do you score a 6 on the GRE essay?
A good GRE Argument essay:
1. Must limit its discussion to identifying and explaining the parts of the argument that are relevant to the essay task.
2. Must develop its ideas logically.
3. Must be organized and connect ideas smoothly.
4. Must include support for the main points of the author’s analysis.
5. Must be well-written.
## How can I learn GRE words faster?
How to Study for GRE Vocabulary
1. Go for Long Term. If you have the opportunity, spread out your vocabulary studying over a long time.
2. Use Flashcards. Flash cards may sound a little old fashioned, but they are still one of the most effective ways to learn new words.
3. Write Down Unfamiliar Words.
4. Find a Study Buddy.
6. Repeat.
7. Use the Words.
## How do you get 6 on AWA?
GMAT AWA tips – GMAT Analytical Writing Assessment Template
1. Introduction: Restate the argument and point out the flaws.
2. First paragraph: State your first critique of the argument and support your view with an example.
3. Second paragraph: State your first critique of the argument and support your view with an example. | 1,782 | 7,451 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2022-05 | latest | en | 0.865189 |
https://www.diyelectriccar.com/threads/voltage-and-amperage-differences-for-parallel-and-series-motors.51979/?u=5275 | 1,675,604,065,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500255.78/warc/CC-MAIN-20230205130241-20230205160241-00489.warc.gz | 746,677,166 | 24,179 | # voltage and amperage differences for parallel and series motors
15637 Views 5 Replies 3 Participants Last post by few2many
Does placing 2 motors in series allow for higher voltages and less amps?
Does placing 2 motors parallel allow for higher amps at less voltages?
Trying to wrap my head around the idea of series and parallel switching, as mybe 2 or 3 smaller motors could be used as an E-trans.
1 - 2 of 2 Posts
#### Anaerin
· Registered
Joined
·
290 Posts
Does placing 2 motors in series allow for higher voltages and less amps?
Does placing 2 motors parallel allow for higher amps at less voltages?
Trying to wrap my head around the idea of series and parallel switching, as mybe 2 or 3 smaller motors could be used as an E-trans.
AIUI:
Motors in series have full amperage, but half voltage.
Motors in parallel have full voltage, but half amperage.
So, if you had a 110V 500A system:
Each motor in series would see (a maximum of) 500A @ 55V.
Each motor in parallel would see (a maximum of) 250A @ 110V.
With DC motors, they create "Back EMF", essentially a voltage that has to be overcome, proportional to their RPM.
So, you start off in series, so you get maximum power (Amperage), and ramp up until the current you are putting in meets the back EMF.
Then you switch to parallel, so you can continue accelerating, albeit not quite so strongly (Higher voltage overcomes the back EMF, but the halved amperage means you don't accelerate so quickly).
You would thus end up with a torque curve something like this:
Code:
``````| | ___________|
| | ___/ |
| | ___/ |
|<- Series ->| ___/ |
| | ___/ |
| | ___/ |
R |___/ |
P __/ |
M _/ | |
| _/ | |
| _/ |<----------- Parallel ------------>|
| _/ | |
| / | |
|/ | |
+----------------------TIME------------------------``````
While the power seen by the motor (This is for one motor) looks like this:
Code:
``````|----500A----,
| |
| |
| |
| |
| |
| |
| '--------------AMPS-------------250A-
|
| ,==============VOLTS============110v=
| |
| |
|====55v====='
|
+-------------------------------------------------``````
Without switching, the graph speed/time graph would look like this (with switching shown in dotted line):
Code:
``````| ............
| .../
| .../
| .../
| .../
| .../
R ____________________________________
P __/
M _/
| _/
| _/
| _/
| /
|/
+----------------------TIME------------------------``````
#### Anaerin
· Registered
Joined
·
290 Posts
Two motors on a 220V bus, in series, would see 110V each. So yes, you could run two 110V motors that way, and both motors would see full amps.
1 - 2 of 2 Posts
This is an older thread, you may not receive a response, and could be reviving an old thread. Please consider creating a new thread. | 770 | 3,544 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2023-06 | latest | en | 0.927957 |
https://gmatclub.com/forum/v06-184915.html | 1,558,286,726,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232255071.27/warc/CC-MAIN-20190519161546-20190519183546-00445.warc.gz | 489,044,987 | 53,710 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 19 May 2019, 10:25
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# V06-09
Author Message
TAGS:
### Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 55150
### Show Tags
16 Sep 2014, 02:26
00:00
Difficulty:
15% (low)
Question Stats:
73% (01:01) correct 27% (01:17) wrong based on 91 sessions
### HideShow timer Statistics
As a result of increasingly disastrous economic fallout from mortgage foreclosures, several suburbs of Cleveland, one of the nation’s hardest-hit cities, is spending millions of dollars to maintain empty houses in an effort to contain real-estate panic and urban blight.
A. one of the nation’s hardest-hit cities, is spending millions of dollars
B. one of the hardest-hit cities in the nation, should be spending millions of dollars
C. one of the nation’s hardest-hit cities, are spending millions of dollars
D. city in the nation that has been hardest-hit, is spending millions of dollars
E. a national hard-hit city, are spending millions of dollars
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 55150
### Show Tags
16 Sep 2014, 02:27
Official Solution:
As a result of increasingly disastrous economic fallout from mortgage foreclosures, several suburbs of Cleveland, one of the nation’s hardest-hit cities, is spending millions of dollars to maintain empty houses in an effort to contain real-estate panic and urban blight.
A. one of the nation’s hardest-hit cities, is spending millions of dollars
B. one of the hardest-hit cities in the nation, should be spending millions of dollars
C. one of the nation’s hardest-hit cities, are spending millions of dollars
D. city in the nation that has been hardest-hit, is spending millions of dollars
E. a national hard-hit city, are spending millions of dollars
The subject of this sentence is several suburbs, and the verb must agree with this subject in number. It is also important that the section of the sentence in the appositive phrase (inside the commas) not be awkward.
1. The verb is does not agree in number with the subject several suburbs.
2. The imperative implied by the word should is not required by the logic of the sentence.
3. The verb are correctly agrees with the plural subject several suburbs.
4. The words in the appositive phrase are unnecessarily awkward, and is does not agree with the plural subject several suburbs.
5. The phrase a national hard-hit city is unnecessarily awkward.
_________________
Intern
Joined: 28 May 2015
Posts: 1
### Show Tags
08 Jun 2015, 23:34
why is the choice E unnecessarily awkward.
Intern
Joined: 09 Apr 2017
Posts: 25
Location: Nepal
Concentration: Finance, Entrepreneurship
WE: Information Technology (Computer Software)
### Show Tags
12 Sep 2018, 03:36
Bunuel wrote:
Official Solution:
As a result of increasingly disastrous economic fallout from mortgage foreclosures, several suburbs of Cleveland, one of the nation’s hardest-hit cities, is spending millions of dollars to maintain empty houses in an effort to contain real-estate panic and urban blight.
A. one of the nation’s hardest-hit cities, is spending millions of dollars
B. one of the hardest-hit cities in the nation, should be spending millions of dollars
C. one of the nation’s hardest-hit cities, are spending millions of dollars
D. city in the nation that has been hardest-hit, is spending millions of dollars
E. a national hard-hit city, are spending millions of dollars
The subject of this sentence is several suburbs, and the verb must agree with this subject in number. It is also important that the section of the sentence in the appositive phrase (inside the commas) not be awkward.
1. The verb is does not agree in number with the subject several suburbs.
2. The imperative implied by the word should is not required by the logic of the sentence.
3. The verb are correctly agrees with the plural subject several suburbs.
4. The words in the appositive phrase are unnecessarily awkward, and is does not agree with the plural subject several suburbs.
5. The phrase a national hard-hit city is unnecessarily awkward.
are the suburbs spending millions of dollars or the city is spending millions of dollars. Shouldnt we refer to the city, Cleveland and not the suburbs?
Manager
Status: The darker the night, the nearer the dawn!
Joined: 16 Jun 2018
Posts: 74
### Show Tags
26 Mar 2019, 21:48
pratik2018 wrote:
Bunuel wrote:
Official Solution:
As a result of increasingly disastrous economic fallout from mortgage foreclosures, several suburbs of Cleveland, one of the nation’s hardest-hit cities, is spending millions of dollars to maintain empty houses in an effort to contain real-estate panic and urban blight.
A. one of the nation’s hardest-hit cities, is spending millions of dollars
B. one of the hardest-hit cities in the nation, should be spending millions of dollars
C. one of the nation’s hardest-hit cities, are spending millions of dollars
D. city in the nation that has been hardest-hit, is spending millions of dollars
E. a national hard-hit city, are spending millions of dollars
The subject of this sentence is several suburbs, and the verb must agree with this subject in number. It is also important that the section of the sentence in the appositive phrase (inside the commas) not be awkward.
1. The verb is does not agree in number with the subject several suburbs.
2. The imperative implied by the word should is not required by the logic of the sentence.
3. The verb are correctly agrees with the plural subject several suburbs.
4. The words in the appositive phrase are unnecessarily awkward, and is does not agree with the plural subject several suburbs.
5. The phrase a national hard-hit city is unnecessarily awkward.
are the suburbs spending millions of dollars or the city is spending millions of dollars? Shouldn't we refer to the city, Cleveland and not the suburbs?
Option C:
Sentence-structure:
Subject - Verb
As a result of increasingly disastrous economic fallout from mortgage foreclosures,
Several suburbs of Cleveland, one of the nation’s hardest-hit cities, are spending millions of dollars to maintain empty houses in an effort to contain real-estate panic and urban blight.
The Subject-Verb should be in agreement.
In this case, Several suburbs of Cleveland acts as a Subject. Cleveland is the object denoting the several suburbs OF Cleveland.
Another example:
Subject - Verb
The Ninja Warriors of Southern Asia were quick with their feet and mind.
Over here, Subject: Ninja Warriors. Southern Asia is the object denoting the Warriors OF Southern Asia.
_________________
---------------------------------------------------------------------------------
“The trouble is, you think you have time.” – Buddha
Giving Kudos is the best way to encourage and appreciate people.
Re: V06-09 [#permalink] 26 Mar 2019, 21:48
Display posts from previous: Sort by
# V06-09
Moderators: chetan2u, Bunuel
Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | 1,688 | 7,635 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.59375 | 4 | CC-MAIN-2019-22 | latest | en | 0.887466 |
http://wiki.povray.org/content?title=Documentation:Tutorial_Section_3&oldid=4786 | 1,368,889,486,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368696382450/warc/CC-MAIN-20130516092622-00054-ip-10-60-113-184.ec2.internal.warc.gz | 287,938,430 | 22,836 | # Tutorial Section 3Documentation
This document is protected, so submissions, corrections and discussions should be held on this documents talk page.
## Contents
### Spline Based Shapes
After we have gained some experience with the simpler shapes available in POV-Ray it is time to go on to the more advanced, thrilling shapes.
We should be aware that the shapes described in this and the following two chapters are not trivial to understand. We need not be worried though if we do not know how to use them or how they work. We just try the examples and play with the features described in the reference chapter. There is nothing better than learning by doing.
You may wish to skip to the chapter Simple Texture Options before proceeding with these advanced shapes.
#### Lathe Object
In the real world, `lathe` refers to a process of making patterned rounded shapes by spinning the source material in place and carving pieces out as it turns. The results can be elaborate, smoothly rounded, elegant looking artefacts such as table legs, pottery, etc. In POV-Ray, a lathe object is used for creating much the same kind of items, although we are referring to the object itself rather than the means of production.
Here is some source for a really basic lathe.
``` #include "colors.inc"
background{White}
camera {
angle 10
location <1, 9, -50>
look_at <0, 2, 0>
}
light_source {
<20, 20, -20> color White
}
lathe {
linear_spline
6,
<0,0>, <1,1>, <3,2>, <2,3>, <2,4>, <0,4>
pigment { Blue }
finish {
ambient .3
phong .75
}
}
```
We render this, and what we see is a fairly simply type of lathe, which looks like a child's top. Let's take a look at how this code produced the effect. First, a set of six points is declared which the raytracer connects with lines. We note that there are only two components in the vectors which describe these points. The lines that are drawn are assumed to be in the x-y-plane, therefore it is as if all the z-components were assumed to be zero. The use of a two-dimensional vector is mandatory, attempting to use a 3D vector would trigger an error... with one exception, which we will explore later in the discussion of splines. Once the lines are determined, the ray-tracer rotates this line around the y-axis, and we can imagine a trail being left through space as it goes, with the surface of that trail being the surface of our object. The specified points are connected with straight lines because we used the `linear_spline` keyword. There are other types of splines available with the lathe, which will result in smooth curving lines, and even rounded curving points of transition, but we will get back to that in a moment. A simple lathe object.
First, we would like to digress a moment to talk about the difference between a lathe and a surface of revolution object (SOR). The SOR object, described in a separate tutorial, may seem terribly similar to the lathe at first glance. It too declares a series of points and connects them with curving lines and then rotates them around the y-axis. The lathe has certain advantages, such as different kinds of splines, linear, quadratic and cubic, and one more thing:
The simpler mathematics used by a SOR does not allow the curve to double back over the same y-coordinates, thus, if using a SOR, any sudden twist which cuts back down over the same heights that the curve previously covered will trigger an error. For example, suppose we wanted a lathe to arc up from <0,0> to <2,2>, then to dip back down to <4,0>. Rotated around the y-axis, this would produce something like a gelatin mold - a rounded semi torus, hollow in the middle. But with the SOR, as soon as the curve doubled back on itself in the y-direction, it would become an illegal declaration.
Still, the SOR has one powerful strong point: because it uses simpler order mathematics, it generally tends to render faster than an equivalent lathe. So in the end, it is a matter of: we use a SOR if its limitations will allow, but when we need a more flexible shape, we go with the lathe instead.
##### Understanding The Concept of Splines
It would be helpful, in order to understand splines, if we had a sort of Spline Workshop where we could practice manipulating types and points of splines and see what the effects were like. So let's make one! Now that we know how to create a basic lathe, it will be easy:
```#include "colors.inc"
camera {
orthographic
up <0, 5, 0>
right <5, 0, 0>
location <2.5, 2.5, -100>
look_at <2.5, 2.5, 0>
}
/* set the control points to be used */
#declare Red_Point = <1.00, 0.00>;
#declare Orange_Point = <1.75, 1.00>;
#declare Yellow_Point = <2.50, 2.00>;
#declare Green_Point = <2.00, 3.00>;
#declare Blue_Point = <1.50, 4.00>;
/* make the control points visible */
cylinder { Red_Point, Red_Point - <0,0,20>, .1
pigment { Red }
finish { ambient 1 }
}
cylinder { Orange_Point, Orange_Point - <0,0,20>, .1
pigment { Orange }
finish { ambient 1 }
}
cylinder { Yellow_Point, Yellow_Point - <0,0,20>, .1
pigment { Yellow }
finish { ambient 1 }
}
cylinder { Green_Point, Green_Point - <0,0,20>, .1
pigment { Green }
finish { ambient 1 }
}
cylinder { Blue_Point, Blue_Point- <0,0,20>, .1
pigment { Blue }
finish { ambient 1 }
}
/* something to make the curve show up */
lathe {
linear_spline
5,
Red_Point,
Orange_Point,
Yellow_Point,
Green_Point,
Blue_Point
pigment { White }
finish { ambient 1 }
}
```
Now, we take a deep breath. We know that all looks a bit weird, but with some simple explanations, we can easily see what all this does. First, we are using the orthographic camera. If we have not read up on that yet, a quick summary is: it renders the scene flat, eliminating perspective distortion so that in a side view. The objects look like they were drawn on a piece of graph paper, like in the side view of a modeler or CAD package. There are several uses for this practical type of camera, but here it is allowing us to see our lathe and cylinders edge on, so that what we see is almost like a cross section of the curve which makes the lathe, rather than the lathe itself. To further that effect, we eliminated shadowing with the `ambient 1` finish, which of course also eliminates the need for lighting. We have also positioned this particular side view so that <0,0> appears at the lower left of our scene. A simple Spline Workshop
Next, we declared a set of points. We note that we used 3D vectors for these points rather than the 2D vectors we expect in a lathe. That is the exception we mentioned earlier. When we declare a 3D point, then use it in a lathe, the lathe only uses the first two components of the vector, and whatever is in the third component is simply ignored. This is handy here, since it makes this example possible.
Next we do two things with the declared points. First we use them to place small diameter cylinders at the locations of the points with the circular caps facing the camera. Then we re-use those same vectors to determine the lathe.
Since trying to declare a 2D vector can have some odd results, and is not really what our cylinder declarations need anyway, we can take advantage of the lathe's tendency to ignore the third component by just setting the z-coordinate in these 3D vectors to zero.
The end result is: when we render this code, we see a white lathe against a black background showing us how the curve we have declared looks, and the circular ends of the cylinders show us where along the x-y-plane our control points are. In this case, it is very simple. The linear spline has been used so our curve is just straight lines zig-zagging between the points.
We change the declarations of `Red_Point` and `Blue_Point` to read as follows: ``` #declare Red_Point = <2.00, 0.00>; #declare Blue_Point = <0.00, 4.00>; ``` We re-render and, as we can see, all that happens is that the straight line segments just move to accommodate the new position of the red and blue points. Linear splines are so simple, we could manipulate them in our sleep, no? Moving some points of the spline.
Now let's examine the different types of splines that the lathe object supports:
First, we change the points to the following. ``` #declare Red_Point = <1.00, 0.00>; #declare Orange_Point = <2.00, 1.00>; #declare Yellow_Point = <3.50, 2.00>; #declare Green_Point = <2.00, 3.00>; #declare Blue_Point = <1.50, 4.00>; ``` We then find the lathe declaration and change `linear_spline` to `quadratic_spline`. We re-render and what do we have? Well, there is a couple of things worthy of note this time. First, we will see that instead of straight lines we have smooth arcs connecting the points. These arcs are made from quadratic curves, so our lathe looks much more interesting this time. Also, `Red_Point` is no longer connected to the curve. What happened? A quadratic spline lathe.
Well, while any two points can determine a straight line, it takes three to determine a quadratic curve. POV-Ray looks not only to the two points to be connected, but to the point immediately preceding them to determine the formula of the quadratic curve that will be used to connect them. The problem comes in at the beginning of the curve. Beyond the first point in the curve there is no previous point. So we need to declare one. Therefore, when using a quadratic spline, we must remember that the first point we specify is only there so that POV-Ray can determine what curve to connect the first two points with. It will not show up as part of the actual curve.
There is just one more thing about this lathe example. Even though our curve is now put together with smooth curving lines, the transitions between those lines is... well, kind of choppy, no? This curve looks like the lines between each individual point have been terribly mismatched. Depending on what we are trying to make, this could be acceptable, or, we might need a more smoothly curving shape. Fortunately, if the latter is true, we have another option.
The quadratic spline takes longer to render than a linear spline. The math is more complex. Taking longer still is the cubic spline, yet for a really smoothed out shape this is the only way to go. We go back into our example, and simply replace `quadratic_spline` with `cubic_spline`. We render one more time, and take a look at what we have.
While a quadratic spline takes three points to determine the curve, a cubic needs four. So, as we might expect, `Blue_Point` has now dropped out of the curve, just as `Red_Point` did, as the first and last points of our curve are now only control points for shaping the curves between the remaining points. But look at the transition from ``` Orange_Point``` to `Yellow_Point` and then back to `Green_Point`. Now, rather than looking mismatched, our curve segments look like one smoothly joined curve. A cubic spline lathe.
Finally there is another kind of quadratic spline, the `bezier_spline`. This one takes four points per section. The start point, the end points and in between, two control points. To use it, we will have to make a few changes to our work shop. Delete the Yellow point, delete the Yellow cylinder. Change the points to:
``` #declare Red_Point = <2.00, 1.00>;
#declare Orange_Point = <3.00, 1.50>;
#declare Green_Point = <3.00, 3.50>;
#declare Blue_Point = <2.00, 4.00>;
```
And change the lathe to:
``` lathe {
bezier_spline
4,
Red_Point,
Orange_Point,
Green_Point,
Blue_Point
pigment { White }
finish { ambient 1 }
}
```
The green and orange control points are not connected to the curve. Move them around a bit, for example: ```#declare Orange_Point = <1.00, 1.50>; ``` The line that can be drawn from the start point to its closest control point (red to orange) shows the tangent of the curve at the start point. Same for the end point, blue to green. A bezier spline lathe.
One spline segment is nice, two is nicer. So we will add another segment and connect it to the blue point. One segment has four points, so two segments have eight. The first point of the second segment is the same as the last point of the first segment. The blue point. So we only have to declare three more points. Also we have to move the camera a bit and add more cylinders. Here is the complete scene again:
```#include "colors.inc"
camera {
orthographic
up <0, 7, 0>
right <7, 0, 0>
location <3.5, 4, -100>
look_at <3.5, 4, 0>
}
/* set the control points to be used */
#declare Red_Point = <2.00, 1.00>;
#declare Orange_Point = <1.00, 1.50>;
#declare Green_Point = <3.00, 3.50>;
#declare Blue_Point = <2.00, 4.00>;
#declare Green_Point2 = <3.00, 4.50>;
#declare Orange_Point2= <1.00, 6.50>;
#declare Red_Point2 = <2.00, 7.00>;
/* make the control points visible */
cylinder { Red_Point, Red_Point - <0,0,20>, .1
pigment { Red } finish { ambient 1 }
}
cylinder { Orange_Point, Orange_Point - <0,0,20>, .1
pigment { Orange } finish { ambient 1 }
}
cylinder { Green_Point, Green_Point - <0,0,20>, .1
pigment { Green } finish { ambient 1 }
}
cylinder { Blue_Point, Blue_Point- <0,0,20>, .1
pigment { Blue } finish { ambient 1 }
}
cylinder { Green_Point2, Green_Point2 - <0,0,20>, .1
pigment { Green } finish { ambient 1 }
}
cylinder { Orange_Point2, Orange_Point2 - <0,0,20>, .1
pigment { Orange } finish { ambient 1 }
}
cylinder { Red_Point2, Red_Point2 - <0,0,20>, .1
pigment { Red } finish { ambient 1 }
}
/* something to make the curve show up */
lathe {
bezier_spline
8,
Red_Point, Orange_Point, Green_Point, Blue_Point
Blue_Point, Green_Point2, Orange_Point2, Red_Point2
pigment { White }
finish { ambient 1 }
}
```
A nice curve, but what if we want a smooth curve? Let us have a look at the tangents on the `Blue_Point`, draw the lines `Green_Point`, `Blue_Point` and `Green_Point2`, `Blue_Point`. Look at the angle they make, it is as sharp as the dent in the curve. What if we make the angle bigger? What if we make the angle 180°? Two bezier spline segments, not smooth.
Try a few positions for `Green_Point2` and end with:
```#declare Green_Point2 = <1.00, 4.50>;
```
It's a smooth curve. If we make sure that the two control points and the connection point are on one line, the curve is perfectly smooth. A smooth bezier spline lathe.
In general this can be achieved by:
```#declare Green_Point2 = Blue_Point + (Blue_Point - Green_Point);
```
The concept of splines is a handy and necessary one, which will be seen again in the prism and polygon objects. It's easy to see, that with a little tinkering, how quickly we can get a feel for working with splines.
#### Surface of Revolution Object
Bottles, vases and glasses make nice objects in ray-traced scenes. We want to create a golden cup using the surface of revolution object (SOR object).
We first start by thinking about the shape of the final object. It is quite difficult to come up with a set of points that describe a given curve without the help of a modeling program supporting POV-Ray's surface of revolution object. If such a program is available we should take advantage of it.
The point configuration of our cup object.
We will use the point configuration shown in the figure above. There are eight points describing the curve that will be rotated about the y-axis to get our cup. The curve was calculated using the method described in the reference section (see Surface of Revolution).
Now it is time to come up with a scene that uses the above SOR object. We create a file called `sordemo.pov` and enter the following text.
``` #include "colors.inc"
#include "golds.inc"
camera {
location <10, 15, -20>
look_at <0, 5, 0>
angle 45
}
background { color rgb<0.2, 0.4, 0.8> }
light_source { <100, 100, -100> color rgb 1 }
plane {
y, 0
pigment { checker color Red, color Green scale 10 }
}
sor {
8,
<0.0, -0.5>,
<3.0, 0.0>,
<1.0, 0.2>,
<0.5, 0.4>,
<0.5, 4.0>,
<1.0, 5.0>,
<3.0, 10.0>,
<4.0, 11.0>
open
texture { T_Gold_1B }
}
```
The scene contains our cup object resting on a checkered plane. Tracing this scene results in the image below.
A surface of revolution object.
The surface of revolution is described by starting with the number of points followed by the points. Points from second to last but one are listed with ascending heights. Each of them determines the radius of the curve for a given height. E. g. the first valid point (second listed) tells POV-Ray that at height 0.0 the radius is 3. We should take care that each point has a larger height than its predecessor. If this is not the case the program will abort with an error message. First and last point from the list are used to determine slope at beginning and end of curve and can be defined for any height.
#### Prism Object
The prism is essentially a polygon or closed curve which is swept along a linear path. We can imagine the shape so swept leaving a trail in space, and the surface of that trail is the surface of our prism. The curve or polygon making up a prism's face can be a composite of any number of sub-shapes, can use any kind of three different splines, and can either keep a constant width as it is swept, or slowly tapering off to a fine point on one end. But before this gets too confusing, let's start one step at a time with the simplest form of prism. We enter and render the following POV code (see file `prismdm1.pov`).
``` #include "colors.inc"
background{White}
camera {
angle 20
location <2, 10, -30>
look_at <0, 1, 0>
}
light_source { <20, 20, -20> color White }
prism {
linear_sweep
linear_spline
0, // sweep the following shape from here ...
1, // ... up through here
7, // the number of points making up the shape ...
<3,5>, <-3,5>, <-5,0>, <-3,-5>, <3, -5>, <5,0>, <3,5>
pigment { Green }
}
```
A hexagonal prism shape.
This produces a hexagonal polygon, which is then swept from y=0 through y=1. In other words, we now have an extruded hexagon. One point to note is that although this is a six sided figure, we have used a total of seven points. That is because the polygon is supposed to be a closed shape, which we do here by making the final point the same as the first. Technically, with linear polygons, if we did not do this, POV-Ray would automatically join the two ends with a line to force it to close, although a warning would be issued. However, this only works with linear splines, so we must not get too casual about those warning messages!
##### Teaching An Old Spline New Tricks
If we followed the section on splines covered under the lathe tutorial (see the section Understanding The Concept of Splines), we know that there are two additional kinds of splines besides linear: the quadratic and the cubic spline. Sure enough, we can use these with prisms to make a more free form, smoothly curving type of prism.
There is just one catch, and we should read this section carefully to keep from tearing our hair out over mysterious too few points in prism messages which keep our prism from rendering. We can probably guess where this is heading: how to close a non-linear spline. Unlike the linear spline, which simply draws a line between the last and first points if we forget to make the last point equal to the first, quadratic and cubic splines are a little more fussy.
First of all, we remember that quadratic splines determine the equation of the curve which connects any two points based on those two points and the previous point, so the first point in any quadratic spline is just control point and will not actually be part of the curve. What this means is: when we make our shape out of a quadratic spline, we must match the second point to the last, since the first point is not on the curve - it is just a control point needed for computational purposes.
Likewise, cubic splines need both the first and last points to be control points, therefore, to close a shape made with a cubic spline, we must match the second point to the second from last point. If we do not match the correct points on a quadratic or cubic shape, that is when we will get the too few points in prism error. POV-Ray is still waiting for us to close the shape, and when it runs out of points without seeing the closure, an error is issued.
Confused? Okay, how about an example? We replace the prism in our last bit of code with this one (see file `prismdm2.pov`).
``` prism {
cubic_spline
0, // sweep the following shape from here ...
1, // ... up through here
6, // the number of points making up the shape ...
< 3, -5>, // point#1 (control point... not on curve)
< 3, 5>, // point#2 ... THIS POINT ...
<-5, 0>, // point#3
< 3, -5>, // point#4
< 3, 5>, // point#5 ... MUST MATCH THIS POINT
<-5, 0> // point#6 (control point... not on curve)
pigment { Green }
}
```
A cubic, triangular prism shape.
This simple prism produces what looks like an extruded triangle with its corners sanded smoothly off. Points two, three and four are the corners of the triangle and point five closes the shape by returning to the location of point two. As for points one and six, they are our control points, and are not part of the shape - they are just there to help compute what curves to use between the other points.
##### Smooth Transitions
Now a handy thing to note is that we have made point one equal point four, and also point six equals point three. Yes, this is important. Although this prism would still be legally closed if the control points were not what we have made them, the curve transitions between points would not be as smooth. We change points one and six to <4,6> and <0,7> respectively and re-render to see how the back edge of the shape is altered (see file `prismdm3.pov`).
To put this more generally, if we want a smooth closure on a cubic spline, we make the first control point equal to the third from last point, and the last control point equal to the third point. On a quadratic spline, the trick is similar, but since only the first point is a control point, make that equal to the second from last point.
##### Multiple Sub-Shapes
Just as with the polygon object (see section Polygon Object) the prism is very flexible, and allows us to make one prism out of several sub-prisms. To do this, all we need to do is keep listing points after we have already closed the first shape. The second shape can be simply an add on going off in another direction from the first, but one of the more interesting features is that if any even number of sub-shapes overlap, that region where they overlap behaves as though it has been cut away from both sub-shapes. Let's look at another example. Once again, same basic code as before for camera, light and so forth, but we substitute this complex prism (see file `prismdm4.pov`).
``` prism {
linear_sweep
cubic_spline
0, // sweep the following shape from here ...
1, // ... up through here
18, // the number of points making up the shape ...
<3,-5>, <3,5>, <-5,0>, <3, -5>, <3,5>, <-5,0>,//sub-shape #1
<2,-4>, <2,4>, <-4,0>, <2,-4>, <2,4>, <-4,0>, //sub-shape #2
<1,-3>, <1,3>, <-3,0>, <1, -3>, <1,3>, <-3,0> //sub-shape #3
pigment { Green }
}
```
Using sub-shapes to create a more complex shape.
For readability purposes, we have started a new line every time we moved on to a new sub-shape, but the ray-tracer of course tells where each shape ends based on whether the shape has been closed (as described earlier). We render this new prism, and look what we have got. It is the same familiar shape, but it now looks like a smaller version of the shape has been carved out of the center, then the carved piece was sanded down even smaller and set back in the hole.
Simply, the outer rim is where only sub-shape one exists, then the carved out part is where sub-shapes one and two overlap. In the extreme center, the object reappears because sub-shapes one, two, and three overlap, returning us to an odd number of overlapping pieces. Using this technique we could make any number of extremely complex prism shapes!
##### Conic Sweeps And The Tapering Effect
In our original prism, the keyword `linear_sweep` is actually optional. This is the default sweep assumed for a prism if no type of sweep is specified. But there is another, extremely useful kind of sweep: the conic sweep. The basic idea is like the original prism, except that while we are sweeping the shape from the first height through the second height, we are constantly expanding it from a single point until, at the second height, the shape has expanded to the original points we made it from. To give a small idea of what such effects are good for, we replace our existing prism with this (see file `prismdm4.pov`):
``` prism {
conic_sweep
linear_spline
0, // height 1
1, // height 2
5, // the number of points making up the shape...
<4,4>,<-4,4>,<-4,-4>,<4,-4>,<4,4>
rotate <180, 0, 0>
translate <0, 1, 0>
scale <1, 4, 1>
pigment { gradient y scale .2 }
}
```
Creating a pyramid using conic sweeping.
The gradient pigment was selected to give some definition to our object without having to fix the lights and the camera angle right at this moment, but when we render it, what have we created? A horizontally striped pyramid! By now we can recognize the linear spline connecting the four points of a square, and the familiar final point which is there to close the spline.
Notice all the transformations in the object declaration. That is going to take a little explanation. The rotate and translate are easy. Normally, a conic sweep starts full sized at the top, and tapers to a point at y=0, but of course that would be upside down if we are making a pyramid. So we flip the shape around the x-axis to put it right side up, then since we actually orbited around the point, we translate back up to put it in the same position it was in when we started.
The scale is to put the proportions right for this example. The base is eight units by eight units, but the height (from y=1 to y=0) is only one unit, so we have stretched it out a little. At this point, we are probably thinking, why not just sweep up from y=0 to y=4 and avoid this whole scaling thing?
That is a very important gotcha! with conic sweeps. To see what is wrong with that, let's try and put it into practice (see file ``` prismdm5.pov```). We must make sure to remove the scale statement, and then replace the line which reads
``` 1, // height 2
```
with
``` 4, // height 2
```
This sets the second height at y=4, so let's re-render and see if the effect is the same.
Choosing a second height larger than one for the conic sweep.
Whoa! Our height is correct, but our pyramid's base is now huge! What went wrong here? Simple. The base, as we described it with the points we used actually occurs at y=1 no matter what we set the second height for. But if we do set the second height higher than one, once the sweep passes y=1, it keeps expanding outward along the same lines as it followed to our original base, making the actual base bigger and bigger as it goes.
To avoid losing control of a conic sweep prism, it is usually best to let the second height stay at y=1, and use a scale statement to adjust the height from its unit size. This way we can always be sure the base's corners remain where we think they are.
That leads to one more interesting thing about conic sweeps. What if we for some reason do not want them to taper all the way to a point? What if instead of a complete pyramid, we want more of a ziggurat step? Easily done. After putting the second height back to one, and replacing our scale statement, we change the line which reads
``` 0, // height 1
```
to
``` 0.251, // height 1
```
Increasing the first height for the conic sweep.
When we re-render, we see that the sweep stops short of going all the way to its point, giving us a pyramid without a cap. Exactly how much of the cap is cut off depends on how close the first height is to the second height.
#### Sphere Sweep Object
A Sphere Sweep Object is the space a sphere occupies during its movement along a spline.
So we need to specify the kind of spline we want and a list of control points to define that spline. To help POV-Ray we tell how many control points will be used. In addition, we also define the radius the moving sphere should have when passing through each of these control points.
The syntax of the sphere_sweep object is:
``` sphere_sweep {
linear_spline | b_spline | cubic_spline
NUM_OF_SPHERES,
...
[tolerance DEPTH_TOLERANCE]
[OBJECT_MODIFIERS]
}
```
An example for a linear Sphere Sweep would be:
``` sphere_sweep {
linear_spline
4,
<-5, -5, 0>, 1
<-5, 5, 0>, 1
< 5, -5, 0>, 1
< 5, 5, 0>, 1
}
```
This object is described by four spheres. You can use as many spheres as you like to describe the object, but you will need at least two spheres for a linear Sphere Sweep, and four spheres for one approximated with a cubic_spline or b_spline.
The example above would result in an object shaped like the letter "N". The sphere sweep goes through all points which are connected with straight cones.
Changing the kind of interpolation to a cubic_spline produces a quite different, slightly bent, object. It then starts at the second sphere and ends at the last but one. Since the first and last points are used to control the spline, you need two more points to get a shape that can be compared to the linear sweep. Let's add them:
``` sphere_sweep {
cubic_spline
6,
<-4, -5, 0>, 1
<-5, -5, 0>, 1
<-5, 5, 0>, 0.5
< 5, -5, 0>, 0.5
< 5, 5, 0>, 1
< 4, 5, 0>, 1
tolerance 0.1
}
```
So the cubic sweep creates a smooth sphere sweep actually going through all points (except the first and last one). In this example the radius of the second and third spheres have been changed. We also added the `tolerance` keyword, because dark spots appeared on the surface with the default value (0.000001).
When using a b_spline, the resulting object is somewhat similar to the cubic sweep, but does not actually go through the control points. It lies somewhere between them.
#### Bicubic Patch Object
Bicubic patches are useful surface representations because they allow an easy definition of surfaces using only a few control points. The control points serve to determine the shape of the patch. Instead of defining the vertices of triangles, we simply give the coordinates of the control points. A single patch has 16 control points, one at each corner, and the rest positioned to divide the patch into smaller sections. POV-Ray does not ray trace the patches directly, they are approximated using triangles as described in the Scene Description Language section.
Bicubic patches are almost always created by using a third party modeler, but for this tutorial we will manipulate them by hand. Modelers that support Bicubic patches and export to POV-Ray can be found in the links collection on our server
Let's set up a basic scene and start exploring the Bicubic patch.
```#version 3.5;
global_settings {assumed_gamma 1.0}
background {rgb <1,0.9,0.9>}
camera {location <1.6,5,-6> look_at <1.5,0,1.5> angle 40}
light_source {<500,500,-500> rgb 1 }
#declare B11=<0,0,3>; #declare B12=<1,0,3>; //
#declare B13=<2,0,3>; #declare B14=<3,0,3>; // row 1
#declare B21=<0,0,2>; #declare B22=<1,0,2>; //
#declare B23=<2,0,2>; #declare B24=<3,0,2>; // row 2
#declare B31=<0,0,1>; #declare B32=<1,0,1>; //
#declare B33=<2,0,1>; #declare B34=<3,0,1>; // row 3
#declare B41=<0,0,0>; #declare B42=<1,0,0>; //
#declare B43=<2,0,0>; #declare B44=<3,0,0>; // row 4
bicubic_patch {
type 1 flatness 0.001
u_steps 4 v_steps 4
uv_vectors
<0,0> <1,0> <1,1> <0,1>
B11, B12, B13, B14
B21, B22, B23, B24
B31, B32, B33, B34
B41, B42, B43, B44
uv_mapping
texture {
pigment {
checker
color rgbf <1,1,1,0.5>
color rgbf <0,0,1,0.7>
scale 1/3
}
finish {phong 0.6 phong_size 20}
}
}
```
The points B11, B14, B41, B44 are the corner points of the patch. All other points are control points. The names of the declared points are as follows: B for the colour of the patch, the first digit gives the row number, the second digit the column number. If you render the above scene, you will get a blue & white checkered square, not very exciting. First we will add some spheres to make the control points visible. As we do not want to type the code for 16 spheres, we will use an array and a while loop to construct the spheres.
```#declare Points=array[16]{
B11, B12, B13, B14
B21, B22, B23, B24
B31, B32, B33, B34
B41, B42, B43, B44
}
#declare I=0;
#while (I<16)
sphere {
Points[I],0.1
pigment{
#if (I=0|I=3|I=12|I=15)
color rgb <1,0,0>
#else
color rgb <0,1,1>
#end
}
}
#declare I=I+1;
#end
```
Rendering this scene will show the patch with its corner points in red and its control points in cyan. Now it is time to start exploring.
Change B41 to `<-1,0,0>` and render.
Change B41 to `<-1,1,0>` and render.
Change B41 to `< 1,2,1>` and render.
Let's do some exercise with the control points. Start with a flat patch again.
Change B42 to `<1,2,0>` and B43 to `<2,-2,0>` and render.
Change B42 and B43 back to their original positions and try B34 to `<4,2,1>` and B24 to `<2,-2,2>` and render. Move the points around some more, also try the control points in the middle.
Bicubic_patch with control points.
After all this we notice two things:
• The patch always goes through the corner points.
• In most situations the patch does not go through the control points.
Now go back to our spline work shop and have a look at the bezier_spline again. Indeed, the points B11, B12, B13, B14, make up a bezier_spline. So do the points B11, B21, B31, B41 and B41, B42, B43, B44 and B14, B24, B34, B44.
So far we have only been looking at one single patch, but one of the strengths of the Bicubic patch lays in the fact that they can be connected smoothly, to form bigger shapes. The process of connecting is relatively simple as there are actually only two rules to follow. It can be done by using a well set up set of macros or by using a modeler. To give an idea what is needed we will do a simple example by hand.
First put the patch in our scene back to its flat position.
Next change:
```#declare B14 = <3,0,3>;
#declare B24 = <3,2,2>;
#declare B34 = <3.5,1,1>;
#declare B44 = <3,-1,0>;
#declare B41 = <0,-1,0>;
```
Move the camera a bit back:
`camera { location <3.1,7,-8> look_at <3,-2,1.5> angle 40 }`
... and delete all the code for the spheres. We will now try and stitch a patch to the right side of the current one. Off course the points on the left side (column 1) of the new patch have to be in the same position as the points on the right side (column 4) of the blue one.
Render the scene, including our new patch:
```#declare R11=B14; #declare R12=<4,0,3>; //
#declare R13=<5,0,3>; #declare R14=<6,0,3>; // row 1
#declare R21=B24; #declare R22=<4,0,2>; //
#declare R23=<5,0,2>; #declare R24=<6,0,2>; // row 2
#declare R31=B34; #declare R32=<4,0,1>; //
#declare R33=<5,0,1>; #declare R34=<6,0,1>; // row 3
#declare R41=B44; #declare R42=<4,0,0>; //
#declare R43=<5,0,0>; #declare R44=<6,0,0>; // row 4
bicubic_patch {
type 1 flatness 0.001
u_steps 4 v_steps 4
uv_vectors
<0,0> <1,0> <1,1> <0,1>
R11, R12, R13, R14
R21, R22, R23, R24
R31, R32, R33, R34
R41, R42, R43, R44
uv_mapping
texture {
pigment {
checker
color rgbf <1,1,1,0.5>
color rgbf <1,0,0,0.7>
scale 1/3
}
finish {phong 0.6 phong_size 20}
}
}
```
This is a rather disappointing result. The patches are connected, but not exactly smooth. In connecting patches the same principles apply as for connecting two 2D bezier splines as we see in the spline workshop. Control point, connection point and the next control point should be on one line to give a smooth result. Also it is preferred, not required, that the distances from both control points to the connection point are the same. For the Bicubic patch we have to do the same, for all connection points involved in the joint. So, in our case, the following points should be on one line:
• B13, B14=R11, R12
• B23, B24=R21, R22
• B33, B34=R31, R32
• B43, B44=R41, R42
To achieve this we do:
```#declare R12=B14+(B14-B13);
#declare R22=B24+(B24-B23);
#declare R32=B34+(B34-B33);
#declare R42=B44+(B44-B43);
```
patches, (un)smoothly connected.
This renders a smooth surface. Adding a third patch in front is relative simple now:
```#declare G11=B41; #declare G12=B42; //
#declare G13=B43; #declare G14=B44; // row 1
#declare G21=B41+(B41-B31); #declare G22=B42+(B42-B32); //
#declare G23=B43+(B43-B33); #declare G24=B44+(B44-B34); // row 2
#declare G31=<0,0,-2>; #declare G32=<1,0,-2>; //
#declare G33=<2,0,-2>; #declare G34=<3,2,-2>; // row 3
#declare G41=<0,0,-3>; #declare G42=<1,0,-3>; //
#declare G43=<2,0,-3>; #declare G44=<3,0,-3> // row 4
bicubic_patch {
type 1 flatness 0.001
u_steps 4 v_steps 4
uv_vectors
<0,0> <1,0> <1,1> <0,1>
G11, G12, G13, G14
G21, G22, G23, G24
G31, G32, G33, G34
G41, G42, G43, G44
uv_mapping
texture {
pigment {
checker
color rgbf <1,1,1,0.5>
color rgbf <0,1,0,0.7>
scale 1/3
}
finish {phong 0.6 phong_size 20}
}
}
```
Finally, let's put a few spheres back in the scene and add some cylinders to visualize what is going on. See what happens if you move for example B44, B43, B33 or B34.
```#declare Points=array[8]{B33,B34,R32,B43,B44,R42,G23,G24}
#declare I=0;
#while (I<8)
sphere {
Points[I],0.1
pigment{
#if (I=4)
color rgb <1,0,0>
#else
color rgb <0,1,1>
#end
}
}
#declare I=I+1;
#end
union {
cylinder {B33,B34,0.04} cylinder {B34,R32,0.04}
cylinder {B43,B44,0.04} cylinder {B44,R42,0.04}
cylinder {G23,G24,0.04}
cylinder {B33,B43,0.04} cylinder {B43,G23,0.04}
cylinder {B34,B44,0.04} cylinder {B44,G24,0.04}
cylinder {R32,R42,0.04}
pigment {color rgb <1,1,0>}
}
```
The hard part in using the Bicubic patch is not in connecting several patches. The difficulty is keeping control over the shape you want to build. As patches are added, in order to keep the result smooth, control over the position of many points gets restrained.
3 patches, some control points.
#### Text Object
The `text` object is a primitive that can use TrueType fonts and TrueType Collections to create text objects. These objects can be used in CSG, transformed and textured just like any other POV primitive.
For this tutorial, we will make two uses of the text object. First, let's just make some block letters sitting on a checkered plane. Any TTF font should do, but for this tutorial, we will use the ``` timrom.ttf``` or `cyrvetic.ttf` which come bundled with POV-Ray.
We create a file called `textdemo.pov` and edit it as follows:
``` #include "colors.inc"
camera {
location <0, 1, -10>
look_at 0
angle 35
}
light_source { <500,500,-1000> White }
plane {
y,0
pigment { checker Green White }
}
```
Now let's add the text object. We will use the font ``` timrom.ttf``` and we will create the string "POV-RAY 3.0". For now, we will just make the letters red. The syntax is very simple. The first string in quotes is the font name, the second one is the string to be rendered. The two floats are the thickness and offset values. The thickness float determines how thick the block letters will be. Values of .5 to 2 are usually best for this. The offset value will add to the kerning distance of the letters. We will leave this a 0 for now.
``` text {
ttf "timrom.ttf" "POV-RAY 3.0" 1, 0
pigment { Red }
}
```
Rendering this we notice that the letters are off to the right of the screen. This is because they are placed so that the lower left front corner of the first letter is at the origin. To center the string we need to translate it -x some distance. But how far? In the docs we see that the letters are all 0.5 to 0.75 units high. If we assume that each one takes about 0.5 units of space on the x-axis, this means that the string is about 6 units long (12 characters and spaces). Let's translate the string 3 units along the negative x-axis.
``` text {
ttf "timrom.ttf" "POV-RAY 3.0" 1, 0
pigment { Red }
translate -3*x
}
```
That is better. Now let's play around with some of the parameters of the text object. First, let's raise the thickness float to something outlandish... say 25!
``` text {
ttf "timrom.ttf" "POV-RAY 3.0" 25, 0
pigment { Red }
translate -2.25*x
}
```
Actually, that is kind of cool. Now let's return the thickness value to 1 and try a different offset value. Change the offset float from 0 to 0.1 and render it again.
Wait a minute?! The letters go wandering off up at an angle! That is not what the docs describe! It almost looks as if the offset value applies in both the x- and y-axis instead of just the x axis like we intended. Could it be that a vector is called for here instead of a float? Let's try it. We replace `0.1` with ` 0.1*x` and render it again.
That works! The letters are still in a straight line along the x-axis, just a little further apart. Let's verify this and try to offset just in the y-axis. We replace ` 0.1*x` with ` 0.1*y`. Again, this works as expected with the letters going up to the right at an angle with no additional distance added along the x-axis. Now let's try the z-axis. We replace ` 0.1*y` with ` 0.1*z`. Rendering this yields a disappointment. No offset occurs! The offset value can only be applied in the x- and y-directions.
Let's finish our scene by giving a fancier texture to the block letters, using that cool large thickness value, and adding a slight y-offset. For fun, we will throw in a sky sphere, dandy up our plane a bit, and use a little more interesting camera viewpoint (we render the following scene at 640x480 ` +A0.2`):
``` #include "colors.inc"
camera {
location <-5,.15,-2>
look_at <.3,.2,1>
angle 35
}
light_source { <500,500,-1000> White }
plane {
y,0
texture {
pigment { SeaGreen }
finish { reflection .35 specular 1 }
normal { ripples .35 turbulence .5 scale .25 }
}
}
text {
ttf "timrom.ttf" "POV-RAY 3.0" 25, 0.1*y
pigment { BrightGold }
finish { reflection .25 specular 1 }
translate -3*x
}
#include "skies.inc"
sky_sphere { S_Cloud5 }
```
Let's try using text in a CSG object. We will attempt to create an inlay in a stone block using a text object. We create a new file called `textcsg.pov` and edit it as follows:
``` #include "colors.inc"
#include "stones.inc"
background { color rgb 1 }
camera {
location <-3, 5, -15>
look_at 0
angle 25
}
light_source { <500,500,-1000> White }
```
Now let's create the block. We want it to be about eight units across because our text string "POV-RAY 3.0" is about six units long. We also want it about four units high and about one unit deep. But we need to avoid a potential coincident surface with the text object so we will make the first z-coordinate 0.1 instead of 0. Finally, we will give this block a nice stone texture.
``` box {
<-3.5, -1, 0.1>, <3.5, 1, 1>
texture { T_Stone10 }
}
```
Next, we want to make the text object. We can use the same object we used in the first tutorial except we will use slightly different thickness and offset values.
``` text {
ttf "timrom.ttf" "POV-RAY 3.0" 0.15, 0
pigment { BrightGold }
finish { reflection .25 specular 1 }
translate -3*x
}
```
We remember that the text object is placed by default so that its front surface lies directly on the x-y-plane. If the front of the box begins at z=0.1 and thickness is set at 0.15, the depth of the inlay will be 0.05 units. We place a difference block around the two objects.
``` difference {
box {
<-3.5, -1, 0.1>, <3.5, 1, 1>
texture { T_Stone10 }
}
text {
ttf "timrom.ttf" "POV-RAY 3.0" 0.15, 0
pigment { BrightGold }
finish { reflection .25 specular 1 }
translate -3*x
}
}
```
Text carved from stone.
When we render this at a low resolution we can see the inlay clearly and that it is indeed a bright gold color. We can render at a higher resolution and see the results more clearly but be forewarned... this trace will take a little time.
This document is protected, so submissions, corrections and discussions should be held on this documents talk page. | 11,902 | 43,861 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2013-20 | longest | en | 0.931423 |
https://www.educents.com/fractions-worksheets-4th-grade-5th-grade-multiplying-fractions-word-problems.html | 1,516,525,418,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084890394.46/warc/CC-MAIN-20180121080507-20180121100507-00206.warc.gz | 903,983,707 | 23,990 | # Multiplying Fractions Word Problems Worksheets 4th, 5th Grade
\$4.00
## Frequently Bought Together
Total Price: \$11.00
### Product Description
Learn to solve word problems using multiplying fraction by a whole number math concept. Printable fraction worksheets based on Singapore Math Bar/Block model approach.
Who is it for?
• 4th Graders (9 to 10-year-olds)
• 5th Graders (10 to 11-year-olds)
• Math learners
• Teachers, Parents looking to teach kid solve word problems by applying multiplying fraction (whole number) math concept.
• Homeschoolers
Children learn word problem solving with a step-by-step approach. Word problems are interpreted as visual fraction and equation model. Children fill in the blank for answers based on visual fraction and equation representations provided.
When children understood the concept, they are required to solve the problem by providing visual and equation representations in their working.Kids are encouraged to learn to draw Visual Fraction Bar/Block Model. Drawing Bar/Block Model helps children to :
- express, interpret and understand word problem.
- visualize and solve problem easily.
What's included?
This lesson plan worksheets (25 pages) comprise of:
• One-step story word problems- find the answer to the fractions of a whole number- find the original whole number when a fraction of the whole number is given
• Two-step story word problems
• Examples with visual fraction and equation representation instruction are provided in each section.
• Pictorial Aids such as fraction bar/block model representation to help child understand concept
* Build strong problem solving skills.
* Pictorial aids help child to visualize word problems.
* Based on Singapore Math - based on Bar/Block Model Approach
* Print as many as you like.
* Teach at any time. Print and bring it along during traveling or waiting in restaurant.
* Let your child learn at her own pace. Re-print any section if you need to reinforce any concept.
* Saves you time in preparing lesson plan. Comes with answers.
### Leave a Review!
Visualize can visualize the problems!
Mar 10, 2016
This is an excellent way to help students visualize the word problems. I like the Singapore math type resources.
Kath - Super-hero, Seller on Educents
Teach Kid Learn
(11 Reviews)
I am a Singaporean who uses one of the Best Math curriculum in the world - Singapore Mathematics (some call it Math In Focus) to coach my children at home. I advocate the importance of making math concept visible and concrete in order to help children learn abstract concept easily. Most of my math worksheets include pictorial models to make math concept visible to the learning child. Kids learn to solve problems with the aid of pictorial models before proceeding to work just on numeric terms.
Adopting the Math curriculum from Singapore and its teaching approach had proven to be effective for my kids. It has helped to build a strong math foundation for my children while they were in primary level. Both my daughter and son obtained 6/6 for their math in Cambridge Checkpoint Test for Key Stage 3. My daughter went on to obtain A* for her International General Certificate of Secondary Education Ordinary Level (IGCSE "O" level") Math. As such, I like to share these resources and urge teachers/parents to help children to lay a strong math foundation.
I like to make learning fun for kids. You can find many learning activities for kids and more information about me at my blog http://www.teachkidlearn.com
Stay in touch and Follow me on:
• http://pinterest.com/limsiewyean/
If you have any query with any of my products, please do drop me a note.
Related to this item:
˟ | 769 | 3,695 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2018-05 | latest | en | 0.912903 |
http://farmindustrynews.com/tractors/dollars-saved | 1,397,719,721,000,000,000 | text/html | crawl-data/CC-MAIN-2014-15/segments/1397609526311.33/warc/CC-MAIN-20140416005206-00226-ip-10-147-4-33.ec2.internal.warc.gz | 89,618,446 | 21,313 | Roger Hoy, professor and director of the Nebraska Tractor Test Lab, University of Nebraska-Lincoln, calculates how a difference in ratings can translate into dollars saved:
“To create a simple example, let's assume that we have two 200-hp tractors operating at rated engine speed and delivering all of their available power — one operating at 17 hp-hr./gal. and one operating at 18 hp-hr./gal. For the tractor with 17 hp-hr./gal., we divide 200 by 17 and find a result of 11.76 gal./hr. Similarly, we find the 18 hp-hr./gal. tractor to use 11.11 gal./hr., or a difference of 0.65 gal./hr. If we assume that the tractor will be used for 500 hrs. each year and ag diesel has a cost of \$4.00/gal., the annual difference in fuel costs between these two tractors is \$1,300.” | 204 | 772 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2014-15 | longest | en | 0.883543 |
https://dsp.stackexchange.com/questions/85591/how-to-achieve-3-gbps-with-210-mhz-bandwidth-in-5g | 1,701,840,392,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100583.13/warc/CC-MAIN-20231206031946-20231206061946-00508.warc.gz | 238,072,609 | 41,692 | How to achieve 3 Gbps with 210 MHz bandwidth in 5G?
I read an article from T-Mobile link where they claimed a 3Gbps speedtest with the aggregation of 3 three bands in 5G.
How it is possible to make 3 Gbps with a 210 MHz bandwidth and using 256QAM in 5G?
210e6 x 8 = 1.680e9
There must be MIMO. As Samsung S22 5G posseses 4 antenna, I would say, for example, MIMO 4x4 for the two TDD bands and MIMO 2x2 for the FDD band.
The upper bound of rate for the n41 band of 100MHz is $$(273 \times 12 \times 28) \times (8) \times (4) \approx 2800\textrm{Mbps}$$ where the factors are the number of subcarriers, the number of bit per subcarrier, and the number of spatial multiplexing layers, respectively.
Similarly, the upper bound of rate for the n41 band of 90MHz is $$(245 \times 12 \times 28) \times (8) \times (4) \approx 2512\textrm{Mbps}$$; for the n25 20MHz $$(106 \times 12 \times 14) \times (8) \times (2) \approx 271\textrm{Mbps}$$.
The theoretical rate is therefore largely greater than the 3Gbps. There must be overhead induced by signalling, retranmissions, scheduling, device capability, etc.
• I am totally new to MIMO. Do you talk about MIMO with multiple beams? Dec 2, 2022 at 11:27
• @dsp_curious Yes. Spatial Multiplexing. Dec 2, 2022 at 11:39
• another clarification, 273 x 12 x 28 = 91768 is the number of subcarriers in the 100 MHz band of n41? Dec 2, 2022 at 12:07
• @dsp_curious yes. Check 38.104 and 38.211. Dec 2, 2022 at 13:10
Likely with MIMO (Spatial Multiplexing). | 492 | 1,495 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 3, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2023-50 | longest | en | 0.822183 |
https://www.smartick.com/blog/education/psychology/dyscalculia-detected/ | 1,606,946,459,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141716970.77/warc/CC-MAIN-20201202205758-20201202235758-00179.warc.gz | 833,074,581 | 15,027 | Smartick is an advanced online program that teaches kids math and coding in only 15 min. a day
Jun20
# What is Dyscalculia? Signs and Symptoms
### Definition: Development of Dyscalculia
Dyscalculia is a specific learning disability with neurobiological origins that affects the acquisition of mathematical knowledge despite an IQ within the normal range. Dyscalculia also has an estimated prevalence of 5-7%, which is approximately the same as dyslexia (Butterworth, Varma, Laurillard, 2011; Geary, 2011). But having difficulties with mathematics does not always imply having dyscalculia! There are other causes that can explain difficulties with mathematics. For example, a low intellectual level, attention difficulties, inadequate education methods, or limited numeracy learning experiences.
### How does it manifest?
Dyscalculia is a heterogeneous disability but, generally, children with dyscalculia experience difficulties with the most basic aspects of number processing and arithmetic. Learning difficulties in mathematics manifest in different ways depending on age. The ideal age to detect a problem with dyscalculia is between 6 and 8 years old, but the first symptoms can appear as early as preschool.
These indicators can be used to look for possible signs of dyscalculia, based on age:
#### Early childhood education
• Problems learning to count. For example, they cannot remember the order of numbers correctly or when you ask them for four units they take a handful of something without counting them.
• Difficulty understanding terms related to mathematics, such as ”larger” or ”smaller.”
• Cannot understand the relationship between number and quantity. For example, they do not understand that ”4” can apply to a group of 4 cakes, 4 cars, or 4 friends.
#### Primary school
• Difficulties identifying and using +, – and other arithmetic symbols correctly.
• Difficulty learning and remembering number facts (for example 2+8, 4×7).
• Continue to use their fingers to count instead of more advanced strategies, like mental math.
• Difficulty understanding words related to mathematics, such as, ”greater than” and ”less than.”
• Problems with the visuospatial representation of numbers, such as number lines.
• Difficulty understanding the place value (units, tens, hundreds).
• Problems writing numbers or putting them in the correct column for written calculations.
#### Secondary school
• Problems applying mathematical concepts to money, including estimating the total cost or exact change.
• Difficulty understanding the information shown on graphs or on tables.
• It takes a lot of effort to learn and understand multi-step reasoning methods and calculation procedure.
• Problems trying to find different approaches to the same math problem (lack of mental flexibility).
• Difficulty measuring ingredients in a simple recipe or liquids in a bottle.
### What IS NOT dyscalculia?
However, it is important to be aware of the misconceptions and stereotypes surrounding the disorder. For example, it is important to understand that:
• Dyscalculia is not caused by a lack of motivation.
• Dyscalculia is not an intelligence problem.
• Dyscalculia is not a laziness problem.
• Dyscalculia is not rare.
### Dyscalculia in daily life
The typical learning difficulties in mathematics for children with dyscalculia do not only affect schoolwork. It can create difficulties in the daily life of children because mathematics is everywhere. We need math skills to read a clock, calculate change when shopping, or deciding how to evenly distribute a cake. In addition to the fact that the impact of mathematical achievement on the academic future, and employability, of people, is greater than the impact of literacy skills (National Center for Education Statistics, 2011). Therefore, the identification of dyscalculia in children as early as possible is crucial to early intervention in order to help reduce the problem.
References:
• Butterworth, B., Varma, S., & Laurillard, D. (2011). Dyscalculia: from brain to education. science332(6033), 1049-1053.
• Bynner, J., & Parsons, S. (2006). Does Numeracy Matter More? London: National Research and Development Centre for adult literacy and numeracy, Institute of Education, University of London.
• Geary, D. C. (2011). Consequences, characteristics, and causes of mathematical learning disabilities and persistent low achievement in mathematics. Journal of developmental and behavioral pediatrics: JDBP32(3), 250. | 946 | 4,493 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2020-50 | latest | en | 0.896415 |
http://nrich.maths.org/public/leg.php?code=-93&cl=3&cldcmpid=701 | 1,506,275,429,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818690112.3/warc/CC-MAIN-20170924171658-20170924191658-00707.warc.gz | 251,747,233 | 8,191 | # Search by Topic
#### Resources tagged with Making and proving conjectures similar to Major Trapezium:
Filter by: Content type:
Stage:
Challenge level:
### There are 35 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Making and proving conjectures
### Problem Solving, Using and Applying and Functional Mathematics
##### Stage: 1, 2, 3, 4 and 5 Challenge Level:
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
##### Stage: 4 Challenge Level:
The points P, Q, R and S are the midpoints of the edges of a convex quadrilateral. What do you notice about the quadrilateral PQRS as the convex quadrilateral changes?
##### Stage: 4 Challenge Level:
The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?
### Center Path
##### Stage: 3 and 4 Challenge Level:
Four rods of equal length are hinged at their endpoints to form a rhombus. The diagonals meet at X. One edge is fixed, the opposite edge is allowed to move in the plane. Describe the locus of. . . .
### Pericut
##### Stage: 4 and 5 Challenge Level:
Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?
##### Stage: 4 Challenge Level:
Points D, E and F are on the the sides of triangle ABC. Circumcircles are drawn to the triangles ADE, BEF and CFD respectively. What do you notice about these three circumcircles?
### Triangles Within Triangles
##### Stage: 4 Challenge Level:
Can you find a rule which connects consecutive triangular numbers?
### Dice, Routes and Pathways
##### Stage: 1, 2 and 3
This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .
### Helen's Conjecture
##### Stage: 3 Challenge Level:
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
### Triangles Within Pentagons
##### Stage: 4 Challenge Level:
Show that all pentagonal numbers are one third of a triangular number.
### Rotating Triangle
##### Stage: 3 and 4 Challenge Level:
What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?
### Polycircles
##### Stage: 4 Challenge Level:
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
### A Little Light Thinking
##### Stage: 4 Challenge Level:
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
### Close to Triangular
##### Stage: 4 Challenge Level:
Drawing a triangle is not always as easy as you might think!
### Charlie's Mapping
##### Stage: 3 Challenge Level:
Charlie has created a mapping. Can you figure out what it does? What questions does it prompt you to ask?
### Curvy Areas
##### Stage: 4 Challenge Level:
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
##### Stage: 4 Challenge Level:
Explore the relationship between quadratic functions and their graphs.
### Few and Far Between?
##### Stage: 4 and 5 Challenge Level:
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
### Always a Multiple?
##### Stage: 3 Challenge Level:
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
### On the Importance of Pedantry
##### Stage: 3, 4 and 5
A introduction to how patterns can be deceiving, and what is and is not a proof.
### Alison's Mapping
##### Stage: 4 Challenge Level:
Alison has created two mappings. Can you figure out what they do? What questions do they prompt you to ask?
### Multiplication Arithmagons
##### Stage: 4 Challenge Level:
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
### How Old Am I?
##### Stage: 4 Challenge Level:
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
### Janine's Conjecture
##### Stage: 4 Challenge Level:
Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .
### Triangles Within Squares
##### Stage: 4 Challenge Level:
Can you find a rule which relates triangular numbers to square numbers?
### Loopy
##### Stage: 4 Challenge Level:
Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture?
### Happy Numbers
##### Stage: 3 Challenge Level:
Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.
### Multiplication Square
##### Stage: 4 Challenge Level:
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
### To Prove or Not to Prove
##### Stage: 4 and 5
A serious but easily readable discussion of proof in mathematics with some amusing stories and some interesting examples.
### DOTS Division
##### Stage: 4 Challenge Level:
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
### What's Possible?
##### Stage: 4 Challenge Level:
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
### Epidemic Modelling
##### Stage: 4 and 5 Challenge Level:
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
### Consecutive Negative Numbers
##### Stage: 3 Challenge Level:
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
### Exploring Simple Mappings
##### Stage: 3 Challenge Level:
Explore the relationship between simple linear functions and their graphs. | 1,517 | 6,687 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.46875 | 4 | CC-MAIN-2017-39 | latest | en | 0.888403 |
https://www.studypug.com/trigonometry-help/trigonometric-equations/solve-first-degree-trig-equations | 1,524,159,991,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125937015.7/warc/CC-MAIN-20180419165443-20180419185443-00143.warc.gz | 876,458,217 | 36,998 | # Solving first degree trigonometric equations - Trigonometric Equations
## Trigonometric Equations:
Put simply, trigonometric equations are just equations that feature the trigonometric ratios such as sine and cosine on the variable “$x$”. Because of the presence of these trigonometric functions, solving these equations becomes a little more difficult. But, before we get into solving these trig equations, let’s make sure we understand what $1^{st}$ degree trig equations are! Below are a couple of examples of trig equations:
$\sin x = 4, \; 4\cos y + 3 = 0$
There are also other levels of trig equations, including $2^{nd}$ degree trig equations. Below are a couple examples of $2^{nd}$ degree trig equations:
$\sin^{2} x + \sin x = 4, \; \cos^{3} y - 4\cos y + 3 = 0$
Notice how the above equations feature our familiar polynomial format but with the addition of the trigonometric ratios sine and cosine. Now that we have an idea of what trig equations look like, let’s look at how to solve first degree trig equations!
## Unit Circle Table:
Oftentimes when we are dealing with first degree trig equations, we will be using the special right angles, reference angles, and the unit circle to solve for the variable $x$ (or whatever the variable is). Below is a copy of the unit circle chart, which gives the unit circle degrees and radians.
NOTE: This chart just gives the values for sine, cosine, and tangent in the first quadrant using the common reference angle. The values are based on some special triangles you should be familiar with, including the 45 45 90 triangle and the 30 60 90 triangle.
If you recall, these values will vary in their sign (+ / -) depending on which quadrant the angle is in. We can use the acronym ASTC (All Students Take Calculus) to help us to remember which trig ratio is what in each quadrant:
A – All are Positive
S – Sine is Positive
T – Tangent is Positive
C – Cosine is Positive
Lastly, it is important to recall our handy acronym SOHCAHTOA to find missing angles. Below are the formulas we get from SOHCAHTOA, as well as an image to help you visualize it:
$\sin x = \frac{opposite}{hypotenuse} \; \cos x = \frac{adjacent}{hypotenuse} \; \tan x = \frac{opposite}{adjacent}$
For a review of some of these concepts in a more detailed video, check out our clips on the reference angle, the exact values of trig functions, and All Students Take Calculus. Also, see our videos on special right triangles 45 45 90 and special right triangle 30 60 90.
As always, the best way to practice is to do some examples!
Example 1:
For the following trigonometric equation, find the exact value for $x$ for each of the following conditions:
$\sin x = \frac{\sqrt{3}}{2}$
i) For 0° $\leq x \leq$ 360°
ii) General solution in degree measure
iii) For 0° $\leq x \leq 2\pi$
iv) General solution in radian measure
Step 1: Identify if a Special Angle/Triangle is Present
The presence of such angles or triangles makes find the solution much easier, as you should have these angles memorized! Notice that $\frac{\sqrt{3}}{2}$ is a special triangle:
Therefore, since sine by definition is $\frac{opposite}{hypotenuse}$, the reference angle for $\frac{\sqrt{3}}{2}$ is 60°.
Step 2: Use ASTC to Identify Where This Angle Exists
For sine to be positive, the angles must be in first and second quadrants.
Thus, in the first quadrant, the angle is 60°. In the second quadrant, the angle is 180°- 60° = 120°
Step 3: Solve the Remainder of the Question
ii) 60° + 360°$n$, where $n$ is a whole integer; 120° + 360°$n$, where $n$ is a whole integer.
iii) $x = \frac{\pi}{3},\;x = \frac{2\pi}{3}$
iv) $\frac{\pi}{3} + 2\pi n$ where $n$ is a whole integer; $\frac{2\pi}{3} + 2\pi n$, where $n$ is a whole integer.
Example 2:
For the following trigonometric equation, find the exact value for $x$:
$\cos x = -0.4$
In this case, since we know that $-0.4$ is not a special case, we must use a calculator to find $x$. NOTE: when solving via a calculator, first remove the sign. We can identify the quadrant using ASTC later on.
$x = \cos^{-1} (0.4) = 66.42$°
Then use reference angle and quadrants to find solutions. According to ASTC, cosine is negative in the second and third quadrants. Therefore:
180° + 66.42° = 246.42°
180° - 66.42° = 113.58°
And that’s all there is to it! For an excellent tool to check you work, check out this useful calculator tool here. And, for further study, see our video on the derivative of trigonometric functions. | 1,209 | 4,498 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 41, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.71875 | 5 | CC-MAIN-2018-17 | latest | en | 0.890577 |
https://templateworksheet.com/distance-formula-worksheet-geometry/ | 1,701,969,757,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100677.45/warc/CC-MAIN-20231207153748-20231207183748-00675.warc.gz | 612,358,421 | 263,810 | # Distance Formula Worksheet Geometry
Distance Formula Worksheet Geometry. Students will evaluate the gap formula to the Pythagorean Theorem. CliffsNotes research guides are written by real lecturers and professors, so it doesn’t matter what you are learning, CliffsNotes can ease your homework headaches and help you rating excessive on exams. Students will explore the distance formula and its utility to the radius of circles. Having a worksheet template simply accessible would possibly help with furthering finding out at home.
This worksheet may be edited by Premium members utilizing the free Google Slides on-line software. Editing worksheet collections is on the market exclusively for Helping With Math Premium members. The radius is simply the gap from the center to any point on the circle. Apart from the stuff given above, when you want another stuff in math, please use our google custom search right here. The distance between from A(-2, 3) to B(2, -2) is about 6.forty models.
If you calculate the square root of this equation, you will get what is identified as the gap formula. Decide whether or not the triangle fashioned using the given vertices is a scalene, equilateral, isosceles, or proper triangle. Substitute the factors in the distance method, and discover the facet size to show. In physics, distance is expounded to the pace and hence, the space traveled by a person or a vehicle. But in math, distance refers again to the separation between two coordinate factors on a airplane.
Use the formulation to seek out the side lengths and show if the coordinates are vertices of a sq., rectangle, parallelogram, or rhombus. It is acknowledged that Anna’s house is on the center of the town. As stated, the coordinates of the boutique are B (6, -2). And, John’s house is positioned at point B with the coordinates B (-4, 7).
## Distance Formula Examples Movies, Worksheets, Solutions, Actions
Document analysis is step one in working with main sources. Teach your faculty students to suppose via main supply paperwork for contextual understanding and to extract info to make educated judgments. Below you presumably can see the 2017 Child Support Guidelines, that are applied to all youngster help orders and judgments for use by the justices of the Trial Court. These types are effective September 15, 2017 till June 14, 2018. You can add a brand new worksheet to the workbook utilizing the createSheet()method of the Spreadsheet object. In computing, spreadsheet software program presents, on a computer monitor, a client interface that resembles numerous paper accounting worksheets.
Note, you could have simply plugged the coordinates into the formulation, and arrived at the same answer. Displaying all worksheets related to – Distance And Midpoint Formulas. To remedy this downside, it’s extremely straightforward, we just apply the Midpoint Formula but this time in one other way. There is similar distance between the two endpoints of the line section, i.e.
Distance between two factors can be determined by checking the coordinates of the ordered pair plotted within the graph. This formula has been derived from the Pythagorean Theorem. Click right here to download a FREE pattern of this worksheet pack.
### Distance Method
The arrow on the larboard of a blueprint opens a card area you’ll be able to adapt the plots. Even admitting the bead bottomward for items confirmed mA and MA , every time we permitted for milliamps, it changed to mega amps. On the additional side, you can accumulation the calculators calm and look or adumbrate teams. The worksheets listed under are suitable for a similar age and grades as Distance Formula of Two Points 6th Grade Math. Interactive sources you’ll have the ability to assign in your digital classroom from TPT.
x2 – x1
### Extra Math Lesson Plans, Classes, Worksheets, And Activities
Sheets within the same workbook may be copied by making a clone of the worksheet you wish to copy, after which utilizing the addSheet() methodology to insert the clone into the workbook. Alternatively, you possibly can instantiate a mannequin new worksheet and then insert it into your workbook using theaddSheet() technique. As an example, within the United States, earnings tax is withheld from the funds made by employers to staff.
• The worksheets are simple to make use of and supply college students the flexibleness to learn at their own tempo, enabling them to develop their drawback fixing abilities.
• This distance formulation is derived from the Pythagorean theorem.
• If we do not use the Pythagorean Theorem to search out the size of the hypotenuse, we can additionally use the distance method to seek out the length of hypotenuse.
• All our worksheets are completely editable so may be tailor-made in your curriculum and audience.
• Addition affair of absorption is you can articulation the aftereffect of 1 blueprint to another.
• Distance between two points can be determined by checking the coordinates of the ordered pair plotted within the graph.
Addition affair of absorption is you’ll find a way to articulation the aftereffect of 1 blueprint to another. However, experimenting with that led to some odd outcomes. Even afterwards disconnecting the formulation there gave the impression to be article nonetheless exercise on. In identifying the distance of two factors, you should have the coordinates of the ordered pairs as plotted within the graph. The coordinates of the factors are composed of two numbers each that signifies their location within the graph.
## Can A Distance Between Two Factors Be Negative?
It’s as straightforward as deciding on a template, customizing, and sharing. Choose from lovely worksheet templates to design your personal worksheets in minutes. In each circumstances, it’s the developer’s duty to ensure that worksheet names usually aren’t duplicated. We have some pictures nearly Distance Formula Worksheet Geometry including photographs, footage, pictures, wallpapers, and more. In these web page, we after which have variety of images out there.
The line that connects your point and O is the hypotenuse of mentioned triangle and the opposite two strains are the legs. A actually nice exercise for permitting students to grasp the ideas of the Distance Formula. Members have unique facilities to obtain an individual worksheet, or an entire level. Knowing the properties of quadrilaterals is a prerequisite.
## Related posts of "Distance Formula Worksheet Geometry"
#### Alexander The Great Worksheet
Alexander The Great Worksheet. Alexander the great's legacy is as a result of of his tactical technique and his affect in spreading his grecian empire throughout north africa. Such software program is often utilized by academics to make classroom provides and checks. Questions embrace studying comprehension, vocabulary from context, and a quick math connection. Worksheet...
#### Solving Two Step Inequalities Worksheet
Solving Two Step Inequalities Worksheet. As they take a step-by-step strategy to fixing inequalities, they may also follow other essential algebra expertise like utilizing inverse operations to solve equations. Students have been utilizing inequalities for years and should have a robust understanding of the fundamental signs. Identifying the correct answer graph for each two-step inequality...
#### Geometry Worksheet Congruent Triangles
Geometry Worksheet Congruent Triangles. Match the congruence assertion to the right pair of triangles . Students use Congruence of Triangles in 20 assorted issues. The side HAS to be in between the two angles for the ASA Postulate for use. The quadrilaterals are supposed to be reduce out, measured, folded, in contrast, and even written...
#### Angular And Linear Velocity Worksheet
Angular And Linear Velocity Worksheet. However, in loads of regions, entry to the net is still an issue, so learning actions ought to depend upon offline strategies. You are allowed to maneuver at your personal tempo , but it’s intended you complete one lesson a day. The time period "Solar System" entered the English language... | 1,583 | 8,123 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2023-50 | longest | en | 0.897026 |
https://sciencing.com/add-subtract-improper-fractions-7716346.html | 1,653,631,763,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662636717.74/warc/CC-MAIN-20220527050925-20220527080925-00284.warc.gz | 600,064,290 | 89,029 | # How to Add & Subtract Improper Fractions
••• PeopleImages/E+/GettyImages
Print
The term "improper fraction" means that the numerator (the top number of the fraction) is bigger than the denominator (the bottom number of the fraction). Improper fractions are actually mixed numbers in disguise, so the last step of your math problem will usually be to convert that improper fraction into a mixed number. But if you're still performing operations like addition and subtraction, it's easiest to leave the numbers in improper fraction form for now.
The process for adding improper fractions works exactly the same as the process for adding proper fractions. (In a proper fraction, the numerator is smaller than the denominator.)
Start by making sure that both fractions you're dealing with have the same denominator. If they don't have the same denominator, you'll have to convert one or both fractions to a new denominator, so that they match.
\frac{5}{4} + \frac{13}{12}
they don't have the same denominator. But if you have sharp eyes, you might notice that 4 × 3 = 12. You can't just multiply the denominator of 5/4 by 3 to turn it into a 12, because that would change the value of the fraction. But you can multiply the fraction by 3/3, which is just another way of writing 1. This changes it to a new denominator without altering its value:
\frac{5}{4} × \frac{3}{3} = \frac{15}{12}
Now you have two fractions with the same denominator: 15/12 and 13/12.
Once you have two fractions with the same denominator, you can simply add the numerators, and then write the answer over the same denominator. To continue the example, to add the improper fractions 15/12 and 13/12, you'll first add the numerators:
15 + 13 = 28
Then write the answer over the same denominator:
\frac{28}{12}
Or to write it out another way:
\frac{15}{12} + \frac{13}{12} = \frac{28}{12}
If your answer from the previous step is already in lowest terms, you can consider the problem done. But if you can simplify the result any further, you should – and since you're dealing with at least one improper fraction, you may also be able to convert the answer to a mixed number. In this case, you can do both. Start by identifying common factors in the numerator and denominator, and then canceling them out:
\frac{28}{12} = \frac{7(4)}{3(4)} = \frac{7}{3}
(Four is a common factor in both numerator and denominator; canceling that out gives you a result of 7/3.)
Next, convert the improper fraction to a mixed number by performing the division indicated by the fraction: 7 ÷ 3. But you shouldn't divide all the way through the decimal places; instead, stop when you have a whole-number result and a remainder. In this case,
7 ÷ 3 = 2 \text{r}1
or two with a remainder of 1.
Write the whole number on its own – 2 – followed by a fraction with the remainder as the numerator and the denominator you last had – in this case, 3 – as the denominator still. To conclude the example, you have a mixed-number answer of
2 \, \frac{1}{3}
### Subtracting Improper Fractions
To subtract improper fractions, you use the same steps as adding. Consider another example:
\frac{6}{4} - \frac{5}{4}
In this case both fractions already have the same denominator, so you can go straight on to the next step.
Subtract the numerators from each other as originally directed, and then write the answer over the same numerator as both fractions you're dealing with. Keep in mind that while the order of your numbers didn't matter for addition, it does matter for subtraction – so don't swap the numbers around. In this case, you have:
6 - 5 = 1
\frac{1}{4}
In this case, your answer – 1/4 – is already in lowest terms, so you can't reduce or simplify it. And because it's no longer an improper fraction, you also can't convert it to a mixed number. So all you have to do to finish the problem is write your answer clearly:
\frac{6}{4} - \frac{5}{4} = \frac{1}{4}
### Adding Mixed Numbers With Improper Fractions
If you're asked to add mixed numbers together, or to add a mixed number to a fraction, the easiest method is almost always converting the mixed number into a fraction; this makes it easier to manipulate. For example, if you're asked to add
2 \, \frac{1}{6} + \frac{8}{6}
you'd first multiply the whole number portion of 2 1/6 by 6/6 to convert it into fraction form:
2 × \frac{6}{6} = \frac{12}{6}
Don't forget to add in the extra 1/6 from the mixed number:
\frac{12}{6} + \frac{1}{6} = \frac{13}{6}
\frac{13}{6} + \frac{8}{6}
Because both fractions have the same denominator, you can go ahead and add the numerators, and then write the answer over the existing denominator:
\frac{13}{6} + \frac{8}{6} = \frac{21}{6}
While some teachers may let you leave the answer in this form, it's always good practice to convert the answer back to a mixed number:
3 \, \frac{3}{6}
And then, using your eagle eyes, you've probably already spotted that you can cancel factors to simplify the fraction 3/6 to 1/2, which gives you a final answer of:
2 \, \frac{1}{6} + \frac{8}{6} = 3 \, \frac{1}{2}
Dont Go!
We Have More Great Sciencing Articles! | 1,316 | 5,132 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.75 | 5 | CC-MAIN-2022-21 | longest | en | 0.920034 |
https://www.transtutors.com/questions/need-the-answers-to-this-worksheet-problem-6-2a-dyna-distribution-markets-cds-of-the-4617664.htm | 1,591,212,963,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347435987.85/warc/CC-MAIN-20200603175139-20200603205139-00044.warc.gz | 916,000,626 | 15,371 | # Need the answers to this worksheet Problem 6-2A Dyna Distribution markets CDs of the performing arti
Need the answers to this worksheet
Problem
6-2A
Dyna Distribution markets
CDs of the performing artist King James. At the beginning of March, Dyna
had in beginning inventory 2,760 King James CDs with a unit
cost of $2 During March, Dyna made the following purchases of King James CDs. March 5 6,440 @$7
March
21
3,680
@
$13 March 13 7,360 @$8
March
26
3,680
@
$14 During March, 18,400 units were sold. Dyna uses a periodic inventory system. Determine the cost of goods available for sale. The cost of goods available for sale$
Text
Video
Calculate average cost per
unit. (Round answer to 4 decimal
places, e.g. $2.2520.) Average cost per unit$
Text
Video
Determine (1) the ending
inventory and (2) the cost of goods sold under each of the assumed cost
flow methods (FIFO, LIFO, and average-cost). (Round answers to 0 decimal places, e.g. $2,120.) FIFO LIFO AVERAGE-COST The ending inventory$
The
cost of goods sold
$.wileyplus.com/edugen/shared/assignment/test/qview.uni?id=quest2522578entrance1&selected_question=quest2522578&operation=take-question”>Link to Text .wileyplus.com/edugen/shared/assignment/test/qview.uni?id=quest2522578entrance1&selected_question=quest2522578&operation=take-question”>Link to Video Which cost flow method results in (1) the highest inventory amount for the balance sheet and (2) the highest cost of goods sold for the income statement? (1) produces the highest inventory amount,$.
(2)
produces
the highest cost of goods sold, \$.
Click
if you would like to Show Work for this question:
Open
Show Work
## Plagiarism Checker
Submit your documents and get free Plagiarism report
Free Plagiarism Checker | 470 | 1,765 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2020-24 | latest | en | 0.846038 |
http://gmatclub.com/forum/is-z-less-than-129362.html | 1,472,093,447,000,000,000 | text/html | crawl-data/CC-MAIN-2016-36/segments/1471982292734.19/warc/CC-MAIN-20160823195812-00284-ip-10-153-172-175.ec2.internal.warc.gz | 107,848,403 | 58,121 | Find all School-related info fast with the new School-Specific MBA Forum
It is currently 24 Aug 2016, 19:50
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# Is Z less than 0?
Author Message
TAGS:
### Hide Tags
Manager
Joined: 06 Jul 2011
Posts: 213
Location: Accra, Ghana
Followers: 1
Kudos [?]: 51 [0], given: 39
Is Z less than 0? [#permalink]
### Show Tags
20 Mar 2012, 01:03
00:00
Difficulty:
5% (low)
Question Stats:
90% (01:29) correct 10% (00:46) wrong based on 77 sessions
### HideShow timer Statistics
Is z less than 0?
(1) xy>0 and yz<0
(2) x>0
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 34420
Followers: 6251
Kudos [?]: 79415 [1] , given: 10016
Re: Is Z less than 0? [#permalink]
### Show Tags
20 Mar 2012, 01:21
1
KUDOS
Expert's post
Is z less than 0?
(1) xy>0 and yz<0 --> first inequality is useless for us since it has no z. From yz<0 we can say that y and z have opposite sings, but we don't know the sign of y to deduce something about z. Not sufficient.
(2) x>0. Not sufficient.
(1)+(2) From xy>0 we can say that x and y have the same sign, and since from (2) x>0 then y>0 too. Now, from yz<0 we have that y and z have opposite sings and as y>0 then z<0. Sufficient.
Hope it's clear.
_________________
Senior Manager
Status: May The Force Be With Me (D-DAY 15 May 2012)
Joined: 06 Jan 2012
Posts: 289
Location: India
Concentration: General Management, Entrepreneurship
Followers: 2
Kudos [?]: 213 [0], given: 16
Re: Is Z less than 0? [#permalink]
### Show Tags
20 Mar 2012, 01:28
Hi,
I hope this helps
We have to prove that Is z < 0?
Statement 1. xy>0 and yz<0
=> x & y are negative / x & y are positive
=> z is postive / z is negative
Hence Insufficient
2. x>0
Insufficient since nothing said about y or z
Combine
X is positive
= >X is positive Y is positive Thus Z is negative
Hence sufficient
_________________
Giving +1 kudos is a better way of saying 'Thank You'.
Manager
Joined: 12 Dec 2012
Posts: 230
GMAT 1: 540 Q36 V28
GMAT 2: 550 Q39 V27
GMAT 3: 620 Q42 V33
GPA: 2.82
WE: Human Resources (Health Care)
Followers: 4
Kudos [?]: 75 [0], given: 181
Re: Is Z less than 0? [#permalink]
### Show Tags
14 Mar 2013, 19:28
Bunuel wrote:
Is z less than 0?
(1) xy>0 and yz<0 --> first inequality is useless for us since it has no z. From yz<0 we can say that y and z have opposite sings, but we don't know the sign of y to deduce something about z. Not sufficient.
(2) x>0. Not sufficient.
(1)+(2) From xy>0 we can say that x and y have the same sign, and since from (2) x>0 then y>0 too. Now, from yz<0 we have that y and z have opposite sings and as y>0 then z<0. Sufficient.
Hope it's clear.
for the first statement I concluded that x and y have the same signs and since y times z is negative so z is the opposite sign . I made a chart trying +/- signs for each until I got A ... still cannot quite understand why C ?
_________________
My RC Recipe
http://gmatclub.com/forum/the-rc-recipe-149577.html
My Problem Takeaway Template
http://gmatclub.com/forum/the-simplest-problem-takeaway-template-150646.html
Math Expert
Joined: 02 Sep 2009
Posts: 34420
Followers: 6251
Kudos [?]: 79415 [0], given: 10016
Re: Is Z less than 0? [#permalink]
### Show Tags
15 Mar 2013, 01:14
TheNona wrote:
Bunuel wrote:
Is z less than 0?
(1) xy>0 and yz<0 --> first inequality is useless for us since it has no z. From yz<0 we can say that y and z have opposite sings, but we don't know the sign of y to deduce something about z. Not sufficient.
(2) x>0. Not sufficient.
(1)+(2) From xy>0 we can say that x and y have the same sign, and since from (2) x>0 then y>0 too. Now, from yz<0 we have that y and z have opposite sings and as y>0 then z<0. Sufficient.
Hope it's clear.
for the first statement I concluded that x and y have the same signs and since y times z is negative so z is the opposite sign . I made a chart trying +/- signs for each until I got A ... still cannot quite understand why C ?
Yes, xy > 0, means that x and y are either both positive or both negative. But this does not help us much.
yz < 0 means that y and z have the opposite signs. So, if y is negative then z is positive and if y is positive then z negative. Hence from the first statement z could be positive as well as negative.
Hope it's clear.
_________________
Re: Is Z less than 0? [#permalink] 15 Mar 2013, 01:14
Similar topics Replies Last post
Similar
Topics:
If x, y, and z are integers, are x and y both less than z? 6 29 Apr 2016, 02:37
If y > 0, is x less than 0? 3 13 Dec 2015, 05:36
2 Is z less than 0? 6 18 Feb 2014, 03:44
8 If x is a positive number less than 10, is z less than the 16 25 Apr 2012, 11:22
1 Is z less than 0? 7 14 Dec 2011, 09:57
Display posts from previous: Sort by | 1,655 | 5,274 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2016-36 | longest | en | 0.864512 |
https://forum.edugorilla.com/forums/topic/the-eccentricity-of-an-ellipse-with-its-centre-at-the-origin-is-1-2-if-one-of-the-directrix-is-x-2/ | 1,643,091,165,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304760.30/warc/CC-MAIN-20220125035839-20220125065839-00330.warc.gz | 313,494,239 | 16,908 | This topic contains 0 replies, has 0 voices, and was last updated by EduGorilla 2 years, 6 months ago.
• Author
Posts
EduGorilla
Keymaster
Select Question Language :
The eccentricity of an ellipse with its centre at the origin is 1/2. If one of the directrix is x = 4, then the equation of the ellipse is
Options :-
1. 4x2 + 3y2 = 1
2. 3x2 + 4y2 = 12
3. 4x2 + 3y2 = 12
4. 3x2 + 4y2 = 1
Are You looking institutes / coaching center for
• IIT-JEE, NEET, CAT
• Bank PO, SSC, Railways
Select your Training / Study category
Reply To: The eccentricity of an ellipse with its centre at the origin is 1/2. If one of the directrix is x = ….
Verify Yourself | 222 | 657 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2022-05 | latest | en | 0.884455 |
https://www.physicsforums.com/threads/how-can-bosons-made-of-fermions-occupy-the-same-quantum-state.682661/ | 1,532,011,364,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676590901.10/warc/CC-MAIN-20180719125339-20180719145339-00445.warc.gz | 946,631,807 | 16,252 | # How can bosons made of fermions occupy the same quantum state?
1. Apr 2, 2013
### andrewkirk
I've been reading about Bose-Einstein condensates, in which multiple bosons can occupy the same quantum state. I thought I understood how that could work until I learned that some atoms, such as Helium-4, are bosons.
It seemed to me that if two He-4 atoms H1 and H2 occupy the same quantum state then the four electrons must occupy the available electron quantum states, of which there are only two, so at least one of the electron quantum states must be occupied by more than one electron, which would violate the Pauli Exclusion Principle (as electrons are fermions).
Since this doesn't happen, there must be something wrong with my attempt at reasoning.
I would be grateful if someone can help me understand where I've gone wrong.
2. Apr 2, 2013
### crissyb1988
I would say its to do with the He-4 atoms being in a bound state. The spin of this bound state is a whole integer value (boson) and it doesn't matter about the constituent parts (fermions).
If you look at low temp superconductors their electrons pair up (cooper pairs) and this pairing acts as a boson. Due to this pairing superconductors act like Bose-Einstein condensates
3. Apr 2, 2013
### Charles Wilson
Edit: I'm pulling some of what I posted. Wrote something when I was very tired and made an error. Will repost tomorrow!
Find SciAm, June 1990, "The Helium3 Superfluids".
[[ZZzzz.....]]
The 2 Helium3 atoms begin orbiting each other and the behavior becomes as a Boson. Helium3 in this state behaves as a Boson and can now drop into a lowest State. It is a Superfluid as is Helium 4.
The SciAm article is absolutely first rate and goes a long way to explaining a very rich segment of low temperature physics, from Dirac Seas to Cooper Pairs.
CW
Last edited: Apr 2, 2013
4. Apr 2, 2013
### Bill_K
When you say the atoms are in the "same state", you're talking about the coordinates that describe the atom, namely the center-of-mass X, P, and total spin. The state of one of the electrons, on the other hand, also involves internal coordinates, e.g. its position x relative to its nucleus. Furthermore, the relative x in one atom is a different coordinate from the relative x in the other. So even if the atoms have the same external coordinates, and even if you assume the electrons of both are in the respective ground states, the electrons still have four states available.
5. Apr 2, 2013
6. Apr 2, 2013
### Staff: Mentor
My oath. When I saw it I thought - gee why didn't that occur to me. Brian Cox said in one of his TV shows since fermions can't occupy the same state, so if you move fermions about since it changes its state you are, in principle, affecting the state of fermions everywhere. When I heard Brian say that my hand went over my face and I thought - Brian - you know that applies only to interacting Fermions - Fermions on the other side of the universe are not affected - but he may counter - as he did - the universe can be considered to be in one big box so you have to consider the system of all Fermions - I still think is basically populist BS but its a bit harder to counter. Most certainly this question and its answer is something that really makes it hard for Brian to counter.
A really really nice question
Thanks
Bill
7. Apr 3, 2013
8. Apr 3, 2013
### Charles Wilson
I guess you get one edit per post... Let me start over sorta.
What a beautiful question!
Let me quote from the SciAm article:
"The particular ordering that takes place in liquid helium is a consequence of a fundamental division that exists in quantum mechanics between fermions...and bosons. Bosons comprise such force-carrying particles as photons and pions. Their spin is an integer multiple of the fundamental quantum of angular momentum, h-bar, Planck's constant divided by 2 pi.
"A He4 atom consists of two electrons, two protons and two neutrons, each with half integer spins. As a result, the atom is a boson." [[At 2.17 k, He4 starts to condense into its lowest energy state.]]
"Superfluidity in He3 has a different character. It's atoms contain an odd number of neutrons and so an odd number of particles in sum. Thus they are fermions and are unable to condense into a common ground state. As a result, He3 cannot become superfluid as easily as its boson sibling can. Instead, at transition temperature roughly 1000 times lower than that of He4, a weak interaction between He3 atoms begins to make itself evident. Atoms with equal and opposite momenta tend to form pairs in which the two particles orbit each other at a distance. These pairs (called Cooper pairs...) are bosons - their half integer angular momenta add up to an integer value. Therefore, they can condense to a common ground state and form a superfluid."
Better?
CW | 1,148 | 4,839 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2018-30 | latest | en | 0.943393 |
http://learn-myself.com/build-a-wind-rose-24643/ | 1,481,346,151,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698542939.6/warc/CC-MAIN-20161202170902-00426-ip-10-31-129-80.ec2.internal.warc.gz | 159,628,188 | 16,298 | Rose of winds called circular vector diagram showing the wind direction during a certain period.
Such graphics are widely used inmeteorology, climatology, as well as in the construction of runways of airfields, residential areas and industrial zones. The stylized image of the wind rose is often used in heraldry.
Today it can be seen in the symbolism of NATO or old maps.
But unlike these diagrams from the stylized image of all the rays of equal length.
You will need
• "Calendar weather" observations diary, lined paper in a cage, a ruler, a pencil, Excel spreadsheets
instructions
1
For training purposes rose winds often learn tolessons of local history and geography, as well as in building universities and colleges. Build a simple compass rose is not difficult for a certain location. This task is often performed by students grades 6-9.
2
In order to build yourself RoseWinds will need data on the daily direction of the wind for a month or more. This information can be obtained independently by the daily weather observations, and you can also take in the "Calendar of Weather" during the analyzed period.
3
the basis for the chart is then constructedordering of observation. To do this, draw a coordinate system in which the major axis will reflect the four cardinal points of the compass - north, east, south and west. Then, through the center of coordinates spend an extra two axes and mark on them the intermediate points of the compass: north-east, south-east, north-west and south-west. Each axis is uniform division, symbolizing the number of days suspended. If we consider the period of one month, the coordinate ranges can reflect one day.
4
After the preparatory work can be donego directly to the construction of the wind rose. To do this, count the number of days during which the wind was blowing in a certain direction, and put them on each of the axes. The number of days in each direction check point. Carefully connect the points obtained straightforward to obtain a closed polygon. The number of windless days (calm) mark in the circle center of the diagram. If during the studied time interval in some of the areas of light wind there was, a connecting line at this site should be interrupted.
5
As a result of the work you get a wind rose toyour region during the analyzed period. Its rays will be uneven, and the longest of them show the prevailing direction of the winds in the study area.
6
Diagrams can be and wind roseautomatic way in Excel. To do this, create a file in which are listed in a table available data on the number of days and the wind direction. You should now have two columns: the names and areas of the world with the number of windy days. Then, in the menu "Insert" - "Chart" select "Radar", and follow the advice of the master charting. The result is a graphical representation of the wind rose. | 603 | 2,868 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2016-50 | longest | en | 0.949036 |
https://www.openml.org/d/208/json | 1,568,695,130,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514573052.26/warc/CC-MAIN-20190917040727-20190917062727-00401.warc.gz | 982,048,361 | 3,574 | { "data_id": "208", "name": "detroit", "exact_name": "detroit", "version": 1, "version_label": "1", "description": "**Author**: \n**Source**: Unknown - \n**Please cite**: \n\nData from StatLib (ftp stat.cmu.edu\/datasets)\n\n This is the data set called `DETROIT' in the book `Subset selection in\n regression' by Alan J. Miller published in the Chapman & Hall series of\n monographs on Statistics & Applied Probability, no. 40. The data are\n unusual in that a subset of three predictors can be found which gives a\n very much better fit to the data than the subsets found from the Efroymson\n stepwise algorithm, or from forward selection or backward elimination.\n \n The original data were given in appendix A of `Regression analysis and its\n application: A data-oriented approach' by Gunst & Mason, Statistics\n textbooks and monographs no. 24, Marcel Dekker. It has caused problems\n because some copies of the Gunst & Mason book do not contain all of the data,\n and because Miller does not say which variables he used as predictors and\n which is the dependent variable. (HOM was the dependent variable, and the\n predictors were FTP ... WE)\n \n The data were collected by J.C. Fisher and used in his paper: \"Homicide in\n Detroit: The Role of Firearms\", Criminology, vol.14, 387-400 (1976)\n \n \n The data are on the homicide rate in Detroit for the years 1961-1973.\n FTP - Full-time police per 100,000 population\n UEMP - % unemployed in the population\n MAN - number of manufacturing workers in thousands\n LIC - Number of handgun licences per 100,000 population\n GR - Number of handgun registrations per 100,000 population\n CLEAR - % homicides cleared by arrests\n WM - Number of white males in the population\n NMAN - Number of non-manufacturing workers in thousands\n GOV - Number of government workers in thousands\n HE - Average hourly earnings\n WE - Average weekly earnings\n \n HOM - Number of homicides per 100,000 of population\n ACC - Death rate in accidents per 100,000 population\n ASR - Number of assaults per 100,000 population\n \n N.B. Each case takes two lines.", "format": "ARFF", "uploader": "Jan van Rijn", "uploader_id": 1, "visibility": "public", "creator": null, "contributor": null, "date": "2014-04-23 13:17:21", "update_comment": null, "last_update": "2014-04-23 13:17:21", "licence": "Public", "status": "active", "error_message": null, "url": "https:\/\/www.openml.org\/data\/download\/3645\/dataset_2194_detroit.arff", "default_target_attribute": "ASR", "row_id_attribute": null, "ignore_attribute": null, "runs": 2, "suggest": { "input": [ "detroit", "Data from StatLib (ftp stat.cmu.edu\/datasets) This is the data set called `DETROIT' in the book `Subset selection in regression' by Alan J. Miller published in the Chapman & Hall series of monographs on Statistics & Applied Probability, no. 40. The data are unusual in that a subset of three predictors can be found which gives a very much better fit to the data than the subsets found from the Efroymson stepwise algorithm, or from forward selection or backward elimination. The original data were g " ], "weight": 5 }, "qualities": { "NumberOfInstances": 13, "NumberOfFeatures": 14, "NumberOfClasses": 0, "NumberOfMissingValues": 0, "NumberOfInstancesWithMissingValues": 0, "NumberOfNumericFeatures": 14, "NumberOfSymbolicFeatures": 0, "Quartile2AttributeEntropy": null, "REPTreeDepth2ErrRate": null, "CfsSubsetEval_kNN1NKappa": null, "kNN1NErrRate": null, "MajorityClassPercentage": null, "MeanStdDevOfNumericAtts": 4684.078088274687, "Quartile2KurtosisOfNumericAtts": -1.0028597627887728, "REPTreeDepth2Kappa": null, "ClassEntropy": null, "kNN1NKappa": null, "MajorityClassSize": null, "MinAttributeEntropy": null, "Quartile2MeansOfNumericAtts": 245.14038461538462, "REPTreeDepth3AUC": null, "DecisionStumpAUC": null, "MaxAttributeEntropy": null, "MinKurtosisOfNumericAtts": -1.6423435643266524, "Quartile2MutualInformation": null, "REPTreeDepth3ErrRate": null, "DecisionStumpErrRate": null, "MaxKurtosisOfNumericAtts": 0.8277169417382741, "MinMeansOfNumericAtts": 3.9476923076923076, "Quartile2SkewnessOfNumericAtts": 0.27766822843268346, "REPTreeDepth3Kappa": null, "DecisionStumpKappa": null, "MaxMeansOfNumericAtts": 452507.53846153844, "MinMutualInformation": null, "PercentageOfBinaryFeatures": 0, "Quartile2StdDevOfNumericAtts": 44.66144695447802, "RandomTreeDepth1AUC": null, "Dimensionality": 1.0769230769230769, "MaxMutualInformation": null, "MinNominalAttDistinctValues": null, "PercentageOfInstancesWithMissingValues": 0, "Quartile3AttributeEntropy": null, "RandomTreeDepth1ErrRate": null, "EquivalentNumberOfAtts": null, "MaxNominalAttDistinctValues": null, "MinSkewnessOfNumericAtts": -0.8740051296230028, "PercentageOfMissingValues": 0, "Quartile3KurtosisOfNumericAtts": -0.05013295006877472, "AutoCorrelation": -29.0975, "RandomTreeDepth1Kappa": null, "J48.00001.AUC": null, "MaxSkewnessOfNumericAtts": 1.0277105820502919, "MinStdDevOfNumericAtts": 0.9665587915051506, "PercentageOfNumericFeatures": 100, "Quartile3MeansOfNumericAtts": 548.3484615384615, "CfsSubsetEval_DecisionStumpAUC": null, "RandomTreeDepth2AUC": null, "J48.00001.ErrRate": null, "MaxStdDevOfNumericAtts": 64568.12389589694, "MinorityClassPercentage": null, "PercentageOfSymbolicFeatures": 0, "Quartile3MutualInformation": null, "CfsSubsetEval_DecisionStumpErrRate": null, "RandomTreeDepth2ErrRate": null, "J48.00001.Kappa": null, "MeanAttributeEntropy": null, "MinorityClassSize": null, "Quartile1AttributeEntropy": null, "Quartile3SkewnessOfNumericAtts": 0.8309826158736997, "CfsSubsetEval_DecisionStumpKappa": null, "RandomTreeDepth2Kappa": null, "J48.0001.AUC": null, "MeanKurtosisOfNumericAtts": -0.7408342566634085, "NaiveBayesAUC": null, "Quartile1KurtosisOfNumericAtts": -1.3401945317885595, "Quartile3StdDevOfNumericAtts": 148.8337488048325, "CfsSubsetEval_NaiveBayesAUC": null, "RandomTreeDepth3AUC": null, "J48.0001.ErrRate": null, "MeanMeansOfNumericAtts": 32568.318516483512, "NaiveBayesErrRate": null, "Quartile1MeansOfNumericAtts": 41.463653846153846, "REPTreeDepth1AUC": null, "CfsSubsetEval_NaiveBayesErrRate": null, "RandomTreeDepth3ErrRate": null, "J48.0001.Kappa": null, "MeanMutualInformation": null, "NaiveBayesKappa": null, "Quartile1MutualInformation": null, "REPTreeDepth1ErrRate": null, "CfsSubsetEval_NaiveBayesKappa": null, "RandomTreeDepth3Kappa": null, "J48.001.AUC": null, "MeanNoiseToSignalRatio": null, "NumberOfBinaryFeatures": 0, "Quartile1SkewnessOfNumericAtts": -0.08862503452243534, "REPTreeDepth1Kappa": null, "CfsSubsetEval_kNN1NAUC": null, "StdvNominalAttDistinctValues": null, "J48.001.ErrRate": null, "MeanNominalAttDistinctValues": null, "Quartile1StdDevOfNumericAtts": 10.779320211599078, "REPTreeDepth2AUC": null, "CfsSubsetEval_kNN1NErrRate": null, "kNN1NAUC": null, "J48.001.Kappa": null, "MeanSkewnessOfNumericAtts": 0.27136164725935785 }, "tags": [], "features": [ { "name": "ASR", "index": "13", "type": "numeric", "distinct": "13", "missing": "0", "target": "1", "min": "218", "max": "473", "mean": "312", "stdev": "73" }, { "name": "FTP", "index": "0", "type": "numeric", "distinct": "13", "missing": "0", "min": "260", "max": "390", "mean": "305", "stdev": "47" }, { "name": "UEMP", "index": "1", "type": "numeric", "distinct": "13", "missing": "0", "min": "3", "max": "11", "mean": "6", "stdev": "2" }, { "name": "MAN", "index": "2", "type": "numeric", "distinct": "13", "missing": "0", "min": "456", "max": "614", "mean": "556", "stdev": "50" }, { "name": "LIC", "index": "3", "type": "numeric", "distinct": "13", "missing": "0", "min": "156", "max": "1131", "mean": "538", "stdev": "316" }, { "name": "GR", "index": "4", "type": "numeric", "distinct": "13", "missing": "0", "min": "180", "max": "1030", "mean": "546", "stdev": "311" }, { "name": "CLEAR", "index": "5", "type": "numeric", "distinct": "13", "missing": "0", "min": "59", "max": "94", "mean": "81", "stdev": "13" }, { "name": "WM", "index": "6", "type": "numeric", "distinct": "13", "missing": "0", "min": "359647", "max": "558724", "mean": "452508", "stdev": "64568" }, { "name": "NMAN", "index": "7", "type": "numeric", "distinct": "13", "missing": "0", "min": "538", "max": "820", "mean": "674", "stdev": "95" }, { "name": "GOV", "index": "8", "type": "numeric", "distinct": "13", "missing": "0", "min": "134", "max": "231", "mean": "186", "stdev": "37" }, { "name": "HE", "index": "9", "type": "numeric", "distinct": "13", "missing": "0", "min": "3", "max": "6", "mean": "4", "stdev": "1" }, { "name": "WE", "index": "10", "type": "numeric", "distinct": "13", "missing": "0", "min": "117", "max": "258", "mean": "170", "stdev": "43" }, { "name": "HOM", "index": "11", "type": "numeric", "distinct": "13", "missing": "0", "min": "9", "max": "52", "mean": "25", "stdev": "16" }, { "name": "ACC", "index": "12", "type": "numeric", "distinct": "13", "missing": "0", "min": "39", "max": "55", "mean": "47", "stdev": "5" } ], "nr_of_issues": 0, "nr_of_downvotes": 0, "nr_of_likes": 0, "nr_of_downloads": 0, "total_downloads": 0, "reach": 0, "reuse": 1, "impact_of_reuse": 0, "reach_of_reuse": 0, "impact": 1 } | 3,029 | 9,121 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2019-39 | latest | en | 0.865191 |
https://stackoverflow.com/questions/63491296/calculating-point-to-line-distance-in-glsl | 1,618,285,248,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038072082.26/warc/CC-MAIN-20210413031741-20210413061741-00551.warc.gz | 651,583,496 | 43,624 | # Calculating point to line distance in GLSL
I am trying to calculate a point to line distance in GSLS - precisely in turbo.js turbo.js
This is part of a more general problem in which I try to find the [closest points on GeoJSON multiline] respective to a set of GeoJSON points - the number of calculations for a 500-points set on 1000 segments line ends up being 500k point-to-distance calculations.
This is way too much to handle in the browser (even in workers) so parallelism helps a lot.
The trick is that AFAIK I can only use a vec4 as an input, which means I can only do calculations on pairs of points.
So far I've progressed to calculating distance and bearing of all pairs - but can't make the last leg to calculating point-to-line distance.
So the question is - given 3 points a, b and c, and knowing
• their position in lon and lat
• their pairwise bearing and distance
Is it possible to calculate the distance from a to the line defined by b and c using transforms that use vec2, vec3 or vec4 as input argument?
As a sub-problem - I know how to calculate the distance if the height of the triangle (a, b, c) doesn't intersect the line (a, b) because it's min(distance(a, b), distance(a, c)).
But then, how do I calculate if it intersects?
• Does this answer your question? How can I implement the distance from a point to a line segment in GLSL? – LJᛃ Aug 19 '20 at 17:16
• @LJᛃ - no, it doesn't, because the problem is how to go about it when the maximum number of input arguments for a function is 4 (the vec4 that gets pulled by `read()`x). – simone Aug 19 '20 at 23:31
• Hm okay, this isnt a `webgl` or `glsl` question then. As there's no tag for the library either I'd say your best bet is to file an issue on the github of the library. – LJᛃ Aug 20 '20 at 8:37
I'm not totally sure I understand your question.
It sounds like for 500 input points you want to know, for 1000 line segments, for each point, which segment is closest.
If that's what you're asking then put all the points in a floating point textures (another word for a texture is a 2D array). Draw a -1 to +1 quad that's the size of the number of results (500 results so 50x10 or 25x20 etc..) Pass in the resolution of the textures. Use `gl_FragCoord` to calculate an index to get the input, A, and loop over all the other lines. Read the results via readPixels by encoding the index of the closest pair as a color.
`````` precision highp float;
uniform sampler2D aValues;
uniform vec2 aDimensions; // the size of the aValues texture in pixels (texels)
uniform sampler2D bValues;
uniform vec2 bDimensions; // the size of the bValues texture in pixels (texels)
uniform sampler2D cValues;
uniform vec2 cDimensions; // the size of the cValues texture in pixels (texels)
uniform vec2 outputDimensions; // the size of the thing we're drawing to (canvas)
// this code, given a sampler2D, the size of the texture, and an index
// computes a UV coordinate to pull one RGBA value out of a texture
// as though the texture was a 1D array.
vec3 getPoint(in sampler2D tex, in vec2 dimensions, in float index) {
vec2 uv = (vec2(
floor(mod(index, dimensions.x)),
floor(index / dimensions.x)) + 0.5) / dimensions;
return texture2D(tex, uv).xyz;
}
// from https://stackoverflow.com/a/6853926/128511
float distanceFromPointToLine(in vec3 a, in vec3 b, in vec3 c) {
vec3 ba = a - b;
vec3 bc = c - b;
float d = dot(ba, bc);
float len = length(bc);
float param = 0.0;
if (len != 0.0) {
param = clamp(d / (len * len), 0.0, 1.0);
}
vec3 r = b + bc * param;
return distance(a, r);
}
void main() {
// gl_FragCoord is the coordinate of the pixel that is being set by the fragment shader.
// It is the center of the pixel so the bottom left corner pixel will be (0.5, 0.5).
// the pixel to the left of that is (1.5, 0.5), The pixel above that is (0.5, 1.5), etc...
// so we can compute back into a linear index
float ndx = floor(gl_FragCoord.y) * outputDimensions.x + floor(gl_FragCoord.x);
// find the closest points
float minDist = 10000000.0;
float minIndex = -1.0;
vec3 a = getPoint(aValues, aDimensions, ndx);
for (int i = 0; i < \${bPoints.length / 4}; ++i) {
vec3 b = getPoint(bValues, bDimensions, float(i));
vec3 c = getPoint(cValues, cDimensions, float(i));
float dist = distanceFromPointToLine(a, b, c);
if (dist < minDist) {
minDist = dist;
minIndex = float(i);
}
}
// convert to 8bit color. The canvas defaults to RGBA 8bits per channel
// so take our integer index (minIndex) and convert to float values that
// will end up as the same 32bit index when read via readPixels as
// 32bit values.
gl_FragColor = vec4(
mod(minIndex, 256.0),
mod(floor(minIndex / 256.0), 256.0),
mod(floor(minIndex / (256.0 * 256.0)), 256.0) ,
floor(minIndex / (256.0 * 256.0 * 256.0))) / 255.0;
}
``````
I'm only going to guess though that in general this is better solved with some spatial structure that somehow makes it so you don't have to check every line with every point but something like the code above should work and be very parallel. Each result will be computed by another GPU core.
``````const v3 = twgl.v3;
// note: I'm using twgl to make the code smaller.
// This is not lesson in WebGL. You should already know what it means
// to setup buffers and attributes and set uniforms and create textures.
// What's important is the technique, not the minutia of WebGL. If you
// don't know how to do those things you need a much bigger tutorial
// on WebGL like https://webglfundamentals.org
function main() {
const gl = document.createElement('canvas').getContext('webgl');
const ext = gl.getExtension('OES_texture_float');
if (!ext) {
return;
}
const r = max => Math.random() * max;
const hsl = (h, s, l) => `hsl(\${h * 360},\${s * 100 | 0}%,\${l * 100 | 0}%)`;
function createPoints(numPoints) {
const points = [];
for (let i = 0; i < numPoints; ++i) {
points.push(r(300), r(150), 0, 0); // RGBA
}
return points;
}
function distanceFromPointToLineSquared(a, b, c) {
const ba = v3.subtract(a, b);
const bc = v3.subtract(c, b);
const dot = v3.dot(ba, bc);
const lenSq = v3.lengthSq(bc);
let param = 0;
if (lenSq !== 0) {
param = Math.min(1, Math.max(0, dot / lenSq));
}
const r = v3.add(b, v3.mulScalar(bc, param));
return v3.distanceSq(a, r);
}
const aPoints = createPoints(6);
const bPoints = createPoints(15);
const cPoints = createPoints(15);
// do it in JS to check
{
// compute closest lines to points
const closest = [];
for (let i = 0; i < aPoints.length; i += 4) {
const a = aPoints.slice(i, i + 3);
let minDistSq = Number.MAX_VALUE;
let minIndex = -1;
for (let j = 0; j < bPoints.length; j += 4) {
const b = bPoints.slice(j, j + 3);
const c = cPoints.slice(j, j + 3);
const distSq = distanceFromPointToLineSquared(a, b, c);
if (distSq < minDistSq) {
minDistSq = distSq;
minIndex = j / 4;
}
}
closest.push(minIndex);
}
drawResults(document.querySelector('#js'), closest);
}
const vs = `
attribute vec4 position;
void main() {
gl_Position = position;
}
`;
const fs = `
precision highp float;
uniform sampler2D aValues;
uniform vec2 aDimensions; // the size of the aValues texture in pixels (texels)
uniform sampler2D bValues;
uniform vec2 bDimensions; // the size of the bValues texture in pixels (texels)
uniform sampler2D cValues;
uniform vec2 cDimensions; // the size of the cValues texture in pixels (texels)
uniform vec2 outputDimensions; // the size of the thing we're drawing to (canvas)
// this code, given a sampler2D, the size of the texture, and an index
// computes a UV coordinate to pull one RGBA value out of a texture
// as though the texture was a 1D array.
vec3 getPoint(in sampler2D tex, in vec2 dimensions, in float index) {
vec2 uv = (vec2(
floor(mod(index, dimensions.x)),
floor(index / dimensions.x)) + 0.5) / dimensions;
return texture2D(tex, uv).xyz;
}
// from https://stackoverflow.com/a/6853926/128511
float distanceFromPointToLine(in vec3 a, in vec3 b, in vec3 c) {
vec3 ba = a - b;
vec3 bc = c - b;
float d = dot(ba, bc);
float len = length(bc);
float param = 0.0;
if (len != 0.0) {
param = clamp(d / (len * len), 0.0, 1.0);
}
vec3 r = b + bc * param;
return distance(a, r);
}
void main() {
// gl_FragCoord is the coordinate of the pixel that is being set by the fragment shader.
// It is the center of the pixel so the bottom left corner pixel will be (0.5, 0.5).
// the pixel to the left of that is (1.5, 0.5), The pixel above that is (0.5, 1.5), etc...
// so we can compute back into a linear index
float ndx = floor(gl_FragCoord.y) * outputDimensions.x + floor(gl_FragCoord.x);
// find the closest points
float minDist = 10000000.0;
float minIndex = -1.0;
vec3 a = getPoint(aValues, aDimensions, ndx);
for (int i = 0; i < \${bPoints.length / 4}; ++i) {
vec3 b = getPoint(bValues, bDimensions, float(i));
vec3 c = getPoint(cValues, cDimensions, float(i));
float dist = distanceFromPointToLine(a, b, c);
if (dist < minDist) {
minDist = dist;
minIndex = float(i);
}
}
// convert to 8bit color. The canvas defaults to RGBA 8bits per channel
// so take our integer index (minIndex) and convert to float values that
// will end up as the same 32bit index when read via readPixels as
// 32bit values.
gl_FragColor = vec4(
mod(minIndex, 256.0),
mod(floor(minIndex / 256.0), 256.0),
mod(floor(minIndex / (256.0 * 256.0)), 256.0) ,
floor(minIndex / (256.0 * 256.0 * 256.0))) / 255.0;
}
`;
const programInfo = twgl.createProgramInfo(gl, [vs, fs]);
// calls gl.createBuffer, gl.bindBuffer, gl.bufferData for a -1 to +1 quad
// make an RGBA float texture for each set of points
// calls gl.createTexture, gl.bindTexture, gl.texImage2D, gl.texParameteri
const aTex = twgl.createTexture(gl, {
src: aPoints,
width: aPoints.length / 4,
type: gl.FLOAT,
minMag: gl.NEAREST,
});
const bTex = twgl.createTexture(gl, {
src: bPoints,
width: bPoints.length / 4,
type: gl.FLOAT,
minMag: gl.NEAREST,
});
const cTex = twgl.createTexture(gl, {
src: cPoints,
width: cPoints.length / 4,
type: gl.FLOAT,
minMag: gl.NEAREST,
});
const numOutputs = aPoints.length / 4;
gl.canvas.width = numOutputs;
gl.canvas.height = 1;
gl.viewport(0, 0, numOutputs, 1);
gl.useProgram(programInfo.program);
// calls gl.bindBuffer, gl.enableVertexAttribArray, gl.vertexAttribPointer
twgl.setBuffersAndAttributes(gl, programInfo, bufferInfo);
// calls gl.activeTexture, gl.bindTexture, gl.uniform
twgl.setUniforms(programInfo, {
aValues: aTex,
bValues: cTex,
bDimensions: [bPoints.length / 4, 1],
cValues: bTex,
cDimensions: [cPoints.length / 4, 1],
outputDimensions: [aPoints.length / 4, 1],
});
gl.drawElements(gl.TRIANGLES, 6, gl.UNSIGNED_SHORT, 0);
// get result
const pixels = new Uint8Array(numOutputs * 4);
const results = new Uint32Array(pixels.buffer);
gl.readPixels(0, 0, numOutputs, 1, gl.RGBA, gl.UNSIGNED_BYTE, pixels);
drawResults(document.querySelector('#glsl'), results);
function drawResults(canvas, closest) {
const ctx = canvas.getContext('2d');
// draw the lines
ctx.beginPath();
for (let j = 0; j < bPoints.length; j += 4) {
const b = bPoints.slice(j, j + 2);
const c = cPoints.slice(j, j + 2);
ctx.moveTo(...b);
ctx.lineTo(...c);
}
ctx.strokeStyle = '#888';
ctx.stroke();
// draw the points and closest lines
for (let i = 0; i < aPoints.length; i += 4) {
const a = aPoints.slice(i, i + 2);
const ndx = closest[i / 4] * 4;
const b = bPoints.slice(ndx, ndx + 2);
const c = cPoints.slice(ndx, ndx + 2);
const color = hsl(i / aPoints.length, 1, 0.4);
ctx.fillStyle = color;
ctx.strokeStyle = color;
ctx.fillRect(a[0] - 2, a[1] - 2, 5, 5);
ctx.beginPath();
ctx.moveTo(...b);
ctx.lineTo(...c);
ctx.stroke();
}
}
}
main();``````
``canvas { border: 1px solid black; margin: 5px; }``
``````<script src="https://twgljs.org/dist/4.x/twgl-full.min.js"></script>
<div>glsl</div>
<canvas id="glsl"></canvas>
<div>js</div>
<canvas id="js"></canvas>``````
If you use WebGL2 then you can use `texelFetch` so `getPoint` becomes
``````vec3 getPoint(in sampler2D tex, in int index) {
ivec2 size = textureSize(tex, 0);
ivec2 uv = ivec2(index % size.x, index / size.x);
return texelFetch(tex, uv, 0).xyz;
}
``````
and you don't need to pass in the size of the input textures, only the output size. Also you could make your output R32U and output unsigned integer indices so no need to encode the result.
note: The code assumes you are doing less then 2048 values for each a, b and c so much of the code assumes 1 dimensional textures. If you need more than 2048 you'll need to adjust the code to make rectangular textures of a size that fits your data for example if you had 9000 values then a 9x1000 texture would work. If you have 8999 values then you still need a 9x1000 texture just padded to make a rectangle since textures are 2D arrays.
Also note that calling readPixels is considered slow. For example, if you just wanted to draw the results as above, instead of rendering to the canvas and reading the values out via readPixels you could render the result to a texture, then pass the texture into another shader.
This is probably the wrong place for this but as a terse explanation of GLSL for stuff like this you can think of GLSL as a fancy version of `Array.prototype.map`. When you use `map` you don't choose what is being written to directly. It happens indirectly.
``````const a = [1, 2, 3, 4, 5];
const b = a.map((v, index) => { return v * 2 + index; });
``````
The `{ return v * 2 + index}` part is analogous to a shader. In JavaScript the function inside map returns in value. in GLSL ES 1.0 the shader sets `gl_FragColor` as the output. In the Javascript `index` is the index of the array being written to (and happens to be the index of the input array as well). In GLSL `gl_FragCoord` serves the same role.
Otherwise, the output of the vertex shader determines which pixels (which array elements of a 2D array) will get written to so that makes it a more selective version of `map`. In the code above we're drawing a -1 to +1 quad effectively saying "map over all pixels".
In fact here's a version of the above code, no GLSL, just JavaScript, but the JavaScript re-structured to look more like GLSL.
``````const v3 = twgl.v3;
function main() {
const r = max => Math.random() * max;
const hsl = (h, s, l) => `hsl(\${h * 360},\${s * 100 | 0}%,\${l * 100 | 0}%)`;
function createPoints(numPoints) {
const points = [];
for (let i = 0; i < numPoints; ++i) {
points.push(r(300), r(150), 0, 0); // RGBA
}
return points;
}
function distanceFromPointToLineSquared(a, b, c) {
const ba = v3.subtract(a, b);
const bc = v3.subtract(c, b);
const dot = v3.dot(ba, bc);
const lenSq = v3.lengthSq(bc);
let param = 0;
if (lenSq !== 0) {
param = Math.min(1, Math.max(0, dot / lenSq));
}
const r = v3.add(b, v3.mulScalar(bc, param));
return v3.distanceSq(a, r);
}
const aPoints = createPoints(6);
const bPoints = createPoints(15);
const cPoints = createPoints(15);
const gl_FragCoord = {};
let gl_FragColor;
const aValues = aPoints;
const aDimensions = {}; // N/A
const bValues = bPoints;
const bDimensions = {}; // N/A
const cValues = cPoints;
const cDimensions = {}; // N/A
const outputDimensions = {x: aPoints.length / 4, y: 1 };
function getPoint(sampler, dimension, ndx) {
return sampler.slice(ndx * 4, ndx * 4 + 3);
}
// gl_FragCoord is the coordinate of the pixel that is being set by the fragment shader.
// It is the center of the pixel so the bottom left corner pixel will be (0.5, 0.5).
// the pixel to the left of that is (1.5, 0.5), The pixel above that is (0.5, 1.5), etc...
// so we can compute back into a linear index
const ndx = Math.floor(gl_FragCoord.y) * outputDimensions.x + Math.floor(gl_FragCoord.x);
// find the closest points
let minDist = 10000000.0;
let minIndex = -1.0;
const a = getPoint(aValues, aDimensions, ndx);
for (let i = 0; i < bPoints.length / 4; ++i) {
const b = getPoint(bValues, bDimensions, i);
const c = getPoint(cValues, cDimensions, i);
const dist = distanceFromPointToLineSquared(a, b, c);
if (dist < minDist) {
minDist = dist;
minIndex = i;
}
}
// convert to 8bit color. The canvas defaults to RGBA 8bits per channel
// so take our integer index (minIndex) and convert to float values that
// will end up as the same 32bit index when read via readPixels as
// 32bit values.
gl_FragColor = [
minIndex % 256.0,
Math.floor(minIndex / 256.0) % 256.0,
Math.floor(minIndex / (256.0 * 256.0)) % 256.0,
Math.floor(minIndex / (256.0 * 256.0 * 256.0)),
].map(v => v / 255.0);
}
// do it in JS to check
{
// compute closest lines to points
const closest = [];
const width = aPoints.length / 4;
const height = 1;
// WebGL drawing each pixel
for (let y = 0; y < height; ++y) {
for (let x = 0; x < width; ++x) {
gl_FragCoord.x = x + 0.5; // because pixels represent a rectangle one unit wide in pixel space
gl_FragCoord.y = y + 0.5; // so the center of each pixel in the middle of that rectangle
const index = gl_FragColor[0] * 255 +
gl_FragColor[1] * 255 * 256 +
gl_FragColor[2] * 255 * 256 * 256 +
gl_FragColor[3] * 255 * 256 * 256 * 256;
closest.push(index);
}
}
drawResults(document.querySelector('#js'), closest);
}
function drawResults(canvas, closest) {
const ctx = canvas.getContext('2d');
// draw the lines
ctx.beginPath();
for (let j = 0; j < bPoints.length; j += 4) {
const b = bPoints.slice(j, j + 2);
const c = cPoints.slice(j, j + 2);
ctx.moveTo(...b);
ctx.lineTo(...c);
}
ctx.strokeStyle = '#888';
ctx.stroke();
// draw the points and closest lines
for (let i = 0; i < aPoints.length; i += 4) {
const a = aPoints.slice(i, i + 2);
const ndx = closest[i / 4] * 4;
const b = bPoints.slice(ndx, ndx + 2);
const c = cPoints.slice(ndx, ndx + 2);
const color = hsl(i / aPoints.length, 1, 0.4);
ctx.fillStyle = color;
ctx.strokeStyle = color;
ctx.fillRect(a[0] - 2, a[1] - 2, 5, 5);
ctx.beginPath();
ctx.moveTo(...b);
ctx.lineTo(...c);
ctx.stroke();
}
}
}
main();``````
``canvas { border: 1px solid black; margin: 5px; }``
``````<script src="https://twgljs.org/dist/4.x/twgl-full.min.js"></script>
<canvas id="js"></canvas>``````
• I suspect you understood my question correctly, I wish I could say the same about your answer which is far above and beyond my current level of understanding in GLSL. I'll study and accept it in the next days - thanks a lot! – simone Aug 20 '20 at 16:51
• What part are you having difficulty understanding? Added some comments. Also here's some WebGL tutorials – gman Aug 20 '20 at 17:10
• it's a case of it's not you, it's me. I get the general concepts and ideas, but I'm not familiar with GLSL yet, so some of the concepts remain obscure for now. Unfortunately the part I'm least clear about is reading/writing data. I'll dig through the tutorials as soon as I can. I'm already grateful for this answer and others you've given me in the past – simone Aug 20 '20 at 19:08
• Yes, I understand that you're not that familiar with GLSL. I added some more stuff just in case. I know it's not as simple as a few paragraphs of explanation but maybe it will be helpful. – gman Aug 21 '20 at 9:31 | 5,606 | 18,905 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2021-17 | latest | en | 0.921337 |
http://ilovephilosophy.com/viewtopic.php?f=4&t=190558&start=2200 | 1,590,476,393,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347390448.11/warc/CC-MAIN-20200526050333-20200526080333-00299.warc.gz | 54,775,340 | 23,633 | ## Is 1 = 0.999... ? Really?
For discussing anything related to physics, biology, chemistry, mathematics, and their practical applications.
Moderator: Flannel Jesus
## Is it true that 1 = 0.999...? And Exactly Why or Why Not?
Yes, 1 = 0.999...
12
40%
No, 1 ≠ 0.999...
15
50%
Other
3
10%
### Re: Is 1 = 0.999... ? Really?
wtf wrote:Thanks, but I'm afraid I'm getting off the roller coaster. Magnus wrote, "(Albeit, as wtf noted, the latter expression has no recognized meaning within the official language of mathematics, which means nothing with regard to this topic.)", my emphasis. If math isn't what the thread's about, I'm at a loss to contribute.
The question is:
Does $$0.999\dotso = 1$$ hold true within the standard language of mathematics?
The question is not:
Does $$0.999\dotso = 1$$ hold true within some guy's personal language of mathematics?
I have my own language, so you will often see me using standard symbols in a non-standard way (e.g. using $$\infty$$ to mean what JSS means by "infA".) With this in mind, one must approach my posts with care, lest they misunderstand me.
I did write extensively in this thread several years ago explaining why .999... = 1, but clearly to no avail. Long answer short, though, it's because .999... = 1 is a theorem that can be proved (by a computer if one likes) in standard set theory.
There's no other reason. Once you define the symbols as they are defined in standard math, the conclusion follows. If you define them differently, you can say that .999... = 47 or anything else you like. There is no moral or absolute truth to the matter, it's strictly an exercise in defining the notation and then showing that the theorem follows. Just like 1 + 1 = 2. If you give the symbols different meanings, you get a different truth value. With the standard meanings to the symbols, the statement is true.
That's correct.
The point of contention is the meaning of the symbol $$0.\dot9$$.
If $$0.\dot9$$ represents the limit of the infinite sum that is $$0.9 + 0.09 + 0.009 + \cdots$$ then it is true that $$0.\dot9 = 1$$.
However, if $$0.\dot9$$ represents the infinite sum that is $$0.9 + 0.09 + 0.009 + \cdots$$ then it is NOT true that $$0.\dot9 = 1$$.
The limit of the sum is not the sum itself. They are two different things.
The argument put forward is that the mathematical establishment defines $$0.\dot9$$ as an infinite sum and NOT as the limit of an infinite sum.
Magnus Anderson
Philosopher
Posts: 4253
Joined: Mon Mar 17, 2014 7:26 pm
### Re: Is 1 = 0.999... ? Really?
phyllo wrote:Suddenly there are two symbols for one number. And one symbol has the concept of infinity within it. That's unsettling.
$$0$$ and $$0.000\dotso$$ are two different symbols representing one and the same number with the second symbol having the concept of infinity within it.
I have no problem with this. Neither do other people who deny that $$0.\dot9 = 1$$.
wtf wrote:I don't see why this is a problem. Are you equally concerned that 4, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1 are different symbols for the same number?
How many other different ways can you think of to symbolize the number 4?
You understand that the number 4, the "actual" number 4, is an abstract idea that is "pointed to" by the representations. The representations are not the number.
It's not a problem. It's merely phyllo's best attempt to make sense of why other people disagree with him without being particularly successful at it.
By the way, $$4.000\dotso$$ is yet another way of representing $$4$$ and it has the concept of infinity within it (:
There are infinite sums that evaluate to finite numbers. The argument put forward by JSS and people on his side is that $$0.9 + 0.09 + 0.009 + \cdots$$ is not one of them.
You seem uncomfortable with the endless sequence of counting numbers 1, 2, 3, 4, 5, ..., that most people seem to be perfectly comfortable with. All infinitary reasoning in mathematics is based on this fundamental intuition of the counting numbers.
Is there something about the idea of the endless sequence of counting numbers that bothers you? If so, you would be equally troubled by decimal notation. I grant you that. But why are you bothered by it in the first place? A child knows that you can "always add 1" to any counting number.
Additionally, we live in the age of computers. Even many endless decimals, like pi, are completely characterized by finite-length descriptions as computer programs. Pi only encodes a finite amount of information. .999... only encodes a finite amount of information: "(1) Print dot; (2) Print '9'; (3) GoTo 2". That's a finite description of the symbol .999...
No no no, it's not phyllo who's uncomfortable. Phyllo is on your side. It's us. Those who deny the popular belief. We are the ones who are uncomfortable and only allegedly so.
Magnus Anderson
Philosopher
Posts: 4253
Joined: Mon Mar 17, 2014 7:26 pm
### Re: Is 1 = 0.999... ? Really?
I don't see why this is a problem. Are you equally concerned that 4, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1 are different symbols for the same number?
Not really the same issue when you put one or more operation in there. Does 0.999... look like any sort of expansion of 1. The answer seems obviously no.
You seem uncomfortable with the endless sequence of counting numbers 1, 2, 3, 4, 5, ..., that most people seem to be perfectly comfortable with.
I think that you are mistaken that most people are comfortable with it. Some of the posts in this thread deal with the difficulties of "reaching the end" of an infinite sequence. It's a big problem as far as I can tell.
A child knows that you can "always add 1" to any counting number.
Try to be a little less condescending.
Last edited by phyllo on Wed May 20, 2020 2:11 am, edited 1 time in total.
phyllo
ILP Legend
Posts: 11857
Joined: Thu Dec 16, 2010 1:41 am
### Re: Is 1 = 0.999... ? Really?
wtf wrote:But this point has been made repeatedly by myself and others in this thread to no avail. I confess to not understanding the objections, It's like asking if the knight in chess "really" moves that way. The question is a category error. Chess is a formal game and within the rules of the game, the knight moves that way. There is no real-world referent. Likewise with a notation such as .999... By the rules of the game, it evaluates to 1. It's a geometric series. If you make some other rules, you can get a different result. Efforts to imbue this with some kind of philosophical objections are likewise category errors. Rules of formal games aren't right or wrong. They're only interesting and useful, or not. The rules of math turn out to be interesting and useful so we teach them.
There is no real-world referent. I agree. That's not what's being disputed. What's being disputed is that, within the rules of the game, $$0.\dot9$$ evaluates to $$1$$.
The notation .999... is a shorthand for the infinite series 9/10 + 9/100 + 9/1000 + ... which sums to 1 as shown in freshman calculus. There truly isn't any more to it than that, though if desired one could drill this directly down to the axioms of set theory.
The infinite sum that is $$0.9 + 0.09 + 0.009 + \cdots$$ does not evaluate to $$1$$. It evaluates to a number that is less than $$1$$. This is evident in the fact that the sum NEVER attains $$1$$. In order to say that some number $$x$$ is the result of some infinite sum, there must be a point at which that number $$x$$ is attained and from there on indefinitely maintained. That's not the case here.
Rather than evaluating to $$1$$, the LIMIT of that infinite sum is $$1$$.
In short, the RESULT of the sum is less than $$1$$ whereas the LIMIT of the sum is $$1$$.
When you go to the Wikipedia article you will see that most of the proofs are trying to prove that the RESULT of the sum (and not the limit of the sum) is equal to $$1$$.
Magnus Anderson
Philosopher
Posts: 4253
Joined: Mon Mar 17, 2014 7:26 pm
### Re: Is 1 = 0.999... ? Really?
The infinite sum that is 0.9+0.09+0.009+⋯ does not evaluate to 1. It evaluates to a number that is less than 1. This is evident in the fact that the sum NEVER attains 1.
See.
What did I say?
phyllo
ILP Legend
Posts: 11857
Joined: Thu Dec 16, 2010 1:41 am
### Re: Is 1 = 0.999... ? Really?
What did you say?
Magnus Anderson
Philosopher
Posts: 4253
Joined: Mon Mar 17, 2014 7:26 pm
### Re: Is 1 = 0.999... ? Really?
More than you know.
phyllo
ILP Legend
Posts: 11857
Joined: Thu Dec 16, 2010 1:41 am
### Re: Is 1 = 0.999... ? Really?
wtf wrote:This is what brings me back to this thread. I want to understand the objection that is being made.
So you've exhausted rational proof, and you still encounter opposition.
What then do we conclude? You've correctly identified that the cause is mathematical ignorance, likely more within the context of flawed education standards than individual fault. The expected consequence of this cause is irrational opposition - as is logically consistent with the that fact that your opposition is against exhaustive rational proof.
This is why I've identified that the only valid way to approach this thread is psychological.
This is much to the frustration of the irrational opposition, but the alternative is tedious repetition. You keep repeating all the rational ways the prove your position from a point of knowledge and experience, and they keep repeating all the irrational ways that they think prove their position from a point of ignorance.
It's an interesting question to ask - why do people dig their heels in, even when they're wrestling with a topic that they know they're weak at, and dealing with people who genuinely do know what they're talking about?
Obviously the low-hanging fruit for them is to get on their high horse and protest that this is a rational debate and it should only deal with the topic directly - even though I've just rationally shown that this is not the case, and that dealing only with the topic directly is the whole problem.
From what I can tell so far, there's not much more going on than the good old Dunning-Kruger effect, along with plenty of cognitive biases and logical fallacies - notably "confirmation bias" and "moving the goalposts". There's a lot of forgetting rational arguments that already countered irrational positions, denying that they ever existed, or insisting that they're irrelevant - anything to avoid the cognitive dissonance of honest introspection.
It's a psychologically difficult process to admit you're wrong or not in the position you thought you were, that you wanted to see yourself as being in. People want to hear and remember things that support their position and make them feel validated, special and competent - especially if they don't feel that way overall in their normal life. It becomes a socially detrimental force when people begin to construct their own identity and a sense of purpose around topics in which they lack sufficient expertise, emotionally investing in them and feeling personally attacked when people challenge your cause. This is especially so when there are others around in the same fragile state of mind, looking for someone with a sense of confidence who is defying a way of thinking that they're weak at - this vicariously soothes their insecurities and only bolsters yet another movement against rationality, leaving experts such as yourself in a state of confusion about how you're supposed to deal with what's going on. It's truly toxic.
So of course they'll attack your mathematical competence as a weakness rather than admit their mathematical incompetence is their weakness.
We see it in politics all the time - e.g. "if someone sides with something you don't agree with, they've been brainwashed by them." It's taken as "the" (necessary) conclusion, when it's just "a" possible (sufficient) conclusion that might hold or might not: abductive reasoning. In some cases it's actually going to be because one person understands something that the other doesn't - yet it's so much easier and lazier to simply trust your own prejudices and assume the other person is the ignorant one. Confirmation bias so often clouds all the evidence against this, and over-emphasises all the memorable moments of victory when it's at least seemed like you were right.
It would appear as though all this "extra baggage" that you're talking about is simply, or at least largely a result of the above. Mathematically challenged people want to believe that it's maths that is at fault rather than them.
To this end they see as far as they want to see and no further.
It's easy to note "0.9 < 1", "0.99 < 1", and that since this pattern continues, it must continue indefinitely under all possible circumstances. One simply neglects the key property of infinity that changes this finite pattern, and voila - it can seem as though you were right all along.
Yet the obvious truth that you pointed out is essentially undeniably tautological - math and only math defines all the notations involved in the topic, and in like manner math completes how they equal each other.
That's as far as rationality "need" go, even though all the proofs you understand and can expertly articulate can extend this rationality far further - there's only one answer to objections to this: they're necessarily irrational. And the reason why this irrationality exists is as I've just explained.
The only issue left to resolve in this thread is how to resolve irrationality. Demonstrably the answer to this is not simply "rationality" - as the irrational response to rationality is the whole problem to begin with.
Silhouette
Philosopher
Posts: 4136
Joined: Tue May 20, 2003 1:27 am
Location: Existence
### Re: Is 1 = 0.999... ? Really?
Ecmandu wrote:My disproof for convergent series!
If you take any rational, irrational or imaginary number and divide it by half, let’s say, the number 1!
0.5 + 0.5 = 1
Then you divide that in half!
0.25 + 0.25 + 0.25 + 0.25 = 1
When you divide that in half!
You get:
0.125 + 0.125 + 0.125 + 0.125 + 0.125 + 0.125 + 0.125 + 0.125 + 0.125 = 1
Etc...
When you push this series to the convergent limit, eventually 0=1
In order for series to converge (and I reverse engineered the problem to prove this)... 1 MUST equal zero!!
Your above argument could maybe be notated as:
$$\sum_{i=1}^n\frac1{n_i}=1$$, or just $$\frac1n\times{n}=1$$
$$\therefore\lim_{n\to\infty}(\frac1n\times{n})=1$$,
$$\lim_{n\to\infty}(\frac1n)=0$$
$$0\times{n}=0$$
$$\therefore\lim_{n\to\infty}(\frac1n\times{n})=0$$
The issue is you're concluding that "1=0", instead of concluding that the only way in which you can arrive there is invalid.
What even is the infinite sum of 1 over infinity? Anything times infinity is infinite, anything times the limit of zero is zero, anything divided by itself is 1 - that's why infinity is undefined and not a number. You can get anything you want from abusing it - that's not the same as "anything you want does actually equal anything you want". Math is consistent, it's built from consistency to remain consistent, which means that when you get to inconsistencies from e.g. someone using infinity as a number, there was a problem with them using infinity as a number. In the same way, there's a problem in your reasoning get 1=0.
You even get the mathematical constant "$$e$$" from the similar sum $$\lim_{n\to\infty}(1+\frac1n)^n$$, when it might look as though the limit goes to $$(1+0)^\infty$$, which might look like 1 (actually an "indeterminate form").
All it means when you get inconsistent nonsense like "1=0" (which circularly violates the fundamentals of math that allowed you to arrive at the inconsistency in the first place) is that you need to do more work.
You don't just stop at a seeming contradiction, and stick with that as your singular definite conclusion.
You have to find valid ways to get a single answer only. This is how the sum I just mentioned can be known to equal exactly "$$e$$" and nothing else, without contradiction/inconsistency.
This is why it helps to be a mathematician, because you have the experience of being familiar with all sorts of methods to enable you to arrive at a correct answer, when non-mathematicians might be tempted to just settle for the simplest answer that they first arrive at, and conclude that "there's therefore something inconsistent in math", to justify that they never needed to gain expertise in math in the first place.
Last edited by Silhouette on Wed May 20, 2020 4:54 pm, edited 1 time in total.
Silhouette
Philosopher
Posts: 4136
Joined: Tue May 20, 2003 1:27 am
Location: Existence
### Re: Is 1 = 0.999... ? Really?
Hi wtf;
It was so much fun reading a well-informed post I hesitate to comment further.
Personally, I have been absolutely committed to a rigorous study of the foundations mathematics. You might get a Geist by looking at my post at:
viewtopic.php?f=4&t=183931&p=2422704&hilit=Mathematica+Principia#p2422704
You can skip personal reflections by scrolling down to The Foundations
For example are you personally committed to the Real Analysis definition of 1 as an equivalency class of Cauchy sequences? (If so you still have an ontological error). Perhaps you might consider {Φ, {Φ}} as the number 1, where Φ is taken to be the null set? This is taken from ZFC. On the other hand Gödel thinks that Plato’s Ideal for 1 is correct – So much for Cauchy sequences.
Since Real Analysis depends on Cauchy sequences which map the Counting numbers to the Rational numbers, Counting numbers and Rational numbers are defined prior to the Real numbers. Do you have any ontological problems with this? I.e. those numbers for ½, 1, 2, 3, … are not the same as Real numbers ½, 1, 2, 3, … .
Really, I immensely enjoyed your post.
Ed
"Albert! Stop telling God what to do." - Niels Bohr
Ed3
Thinker
Posts: 886
Joined: Sun Oct 31, 2004 2:56 pm
Location: Minneapolis, MN
### Re: Is 1 = 0.999... ? Really?
Ed3 wrote:Really, I immensely enjoyed your post.
Thank you Ed. I am so glad you read it in the right spirit, I didn't mean for it to come out as critical as it did. IMO it's misplaced energy on your part to strenuously claim that functions aren't numbers, since it's not really a very important point in the first place; and it's at least arguable and not as clear cut as you believe. IMO of course.
You ask if I'm ontologically committed to the formal set-theoretic definitions, and of course I'm not. I do take your point that functions and numbers are distinct entities in the Platonic world, even if we can define numbers as functions and probably functions as numbers in various formal symbolic ways. If that's what you're saying, we're in agreement.
So even if I fall back on saying that the real number 1 literally is the sequence .9, .99, etc. or an equivalence class containing it, I would NOT ever be confused by thinking that really "is" the number 1. The very fact that the natural number 1, the integer 1, the rational number 1, and the real number 1 are distinct set-theoretic entities is evidence that NONE of them could be the real 1, a point first made by Benacerraf.
The number 1 is some kind of thing out there in Platonic land along with Captain Ahab and the Baby Jesus. That's the problem with Platonism. If there's a non-physical realm of existence, exactly
* What is it?
* Where is it?
* What else might live there? How do we know what lives there and what doesn't?
Point being that Platonism is easily refuted. So is anti-Platonism. Ontology is hard.
Did I manage to catch the essence of your viewpoint?
tl;dr: If I acknowledge that formalisms don't imply ontology, then a function and a number definitely are two different things. I concede the antecedent and the logical conclusion; but I don't understand your insistence on the point, when (IMO) it is not an especially relevant point in this thread. I think that's what I was going on about.
wtf
Posts: 357
Joined: Sun Dec 06, 2015 5:47 am
### Re: Is 1 = 0.999... ? Really?
wtf wrote:it's misplaced energy on your part to strenuously claim that functions aren't numbers
The input of a function can be a number.
The output of a function can be a number.
Functions can have properties that can be expressed using numbers e.g. the limit of a function is a number.
However, functions themselves aren't numbers. A function is no more than a set of input-output pairs where every input is paired with exactly one output. A set of pairs of numbers is not a number (even though you can use a set of pairs of numbers to represent a number.)
So Ed is right when he says that functions aren't numbers but he's also wrong because he says that $$0.\dot9$$ is a function (which it is not.)
Magnus Anderson
Philosopher
Posts: 4253
Joined: Mon Mar 17, 2014 7:26 pm
### Re: Is 1 = 0.999... ? Really?
phyllo wrote:Not really the same issue when you put one or more operation in there. Does 0.999... look like any sort of expansion of 1. The answer seems obviously no.
Having studied math, the answer is obviously yes! It's all a matter of training and mathematical inclination. If you haven't learned basic arithmetic, you think 2 + 2 and 4 look different. After you make it through grade school, you come to recognize without a moment's hesitation that 2 + 2 and 4 refer to the same thing. Likewise one comes to recognize that .999... and 1 as two distinct expressions for the same thing, namely the Platonic or intuitive concept of the number 1.
So all you are saying here is that "My mathematical training includes 2 + 2 = 4 but not .999... = 1." That's all your remark amounts to.
phyllo wrote:I think that you are mistaken that most people are comfortable with it.
So let's leave this with you and me. I myself have a perfectly clear intuition in my mind of the endless sequence 0, 1, 2, 3, 4, ... of natural numbers; and even of the "completed" set of them which we call $$\mathbb N$$. You do not. We could still be friends. Not everyone hears the music, as I say. Some like Picasso and some like Norman Rockwell. It's all good.
I could ask you, though, to explore the nature of your own ultrafinitism. Do you believe there's a largest number that has no successor? If the process 0, 1, 2, 3, ... ends, where does it end?
phyllo wrote: Some of the posts in this thread deal with the difficulties of "reaching the end" of an infinite sequence. It's a big problem as far as I can tell.
But no, THAT IS ONE OF THE CORE CONFUSIONS of many people, pardon my shouting. I'm glad you mentioned it though.
Let's just consider the limit of a sequence, which DOES give people a lot of conceptual trouble.
Consider the sequence of rational numbers 1/2, 1/4, 1/8, 1/16, etc. We say it has a limit of 0. This causes people who have not studied Real Analysis, which to be fair is a course only math majors take, to think that the sequence "reaches" 0 in some mysterious way.
But NO! The whole point of the formalism of limits is that we DON'T TALK ABOUT REACHING. We talk instead of getting "arbitrarily close." You give me a small positive real number, no matter how tiny, and I'll show you that the sequence gets closer to 0 than that. And we DEFINE that condition as being the limit of the sequence.
The entire point of the limit formalism is that we never have to think or talk about "reaching and endpoint at infinity," which is a hopelessly muddled mess. Instead we FINESSE the whole problem by using the "arbitrarily closeness" idea. That is the brilliance of the modern approach to infinitesimals. We banish them! We don't have to talk about them.
(I mention in passing that the hyperreals of nonstandard analysis don't help you, because .999... = 1 is a theorem of nonstandard analysis as well).
So there is no mysterious endpoint, there is no reaching. These are mind-confusing illusions left over from your imprecise intuitions of infinity. And these intuitions are clarified and made logically rigorous in math. That's a fact.
phyllo wrote:
A child knows that you can "always add 1" to any counting number.
Try to be a little less condescending.
I apologize. I was not trying to be condescending. I am actually under the sincere impression that most adults, if pressed, will agree that there is no end to the sequence 0, 1, 2, 3, 4, 5, 6, ... because you can always add one. I am under the impression that most people do feel that way, if you asked them.
I believe this must be especially true in the computer age, when many people from programmers to spreadsheet users have internalized the concept of "always add 1" or "keep adding 1." We live in the age of algorithms and "given n, output n + 1" is a perfectly intuitive concept to many people.
Everyone who ever started to learn how to program came to understand (often with great difficulty) the concept of looping, or endless repetition. If you can do something once you can do it forever. That is one of the main grokitudes of programming!
If you genuinely don't agree, and genuinely reject the concept of adding one, then I'm interested to learn more about what that means. And even if it's nothing more than a convenient fiction (which is exactly what it is!) What if it's all bullshit but Newton used it to calculate the motions of the solar system. Wouldn't you at least grant that the mathematical formalisms are useful and therefore worthy of study?
Last edited by wtf on Thu May 21, 2020 1:25 am, edited 4 times in total.
wtf
Posts: 357
Joined: Sun Dec 06, 2015 5:47 am
### Re: Is 1 = 0.999... ? Really?
Magnus Anderson wrote:The input of a function can be a number.
@Magnus You're getting a little ahead of me but I will try to catch up to all your replies to me. Just working on the other ones first! You have brought up a lot of items that I need to take time to reply to.
wtf
Posts: 357
Joined: Sun Dec 06, 2015 5:47 am
### Re: Is 1 = 0.999... ? Really?
No worries, it's always better for a person to take their time (:
Magnus Anderson
Philosopher
Posts: 4253
Joined: Mon Mar 17, 2014 7:26 pm
### Re: Is 1 = 0.999... ? Really?
Magnus Anderson wrote:
The input of a function can be a number.
The output of a function can be a number.
Evidently @Ed and you both care about the topic of whether functions and numbers are essentially different. I think it's kind of a distraction but just for sake of discussion I'll play.
First, a function goes from any set to any other set. We always denote a function as $$f : X \to Y$$, meaning that $$f$$ is a function that inputs an element of a set $$X$$ and outputs an element of a set $$Y$$.
Since everything in math is a set (in the standard set-theoretic formalism), a function can input anything and output anything.
For example a function can input and output functions. A familiar example is the derivative operator in one real variable. We have a function $$D$$ that inputs a function of one real variable and outputs another. For example $$D x^2 = 2x$$. $$D sin x = cos x$$, etc.
Or a function could input a set and output a number; for example the function that counts the number of elements of a finite set, and outputs -1 if the set's not finite. That's a perfectly valid function from the proper class of all sets to the natural numbers.
So functions can be completely arbitrary in terms of what they input and output. I don't see how this sheds light.
Magnus Anderson wrote:Functions can have properties that can be expressed using numbers e.g. the limit of a function is a number.
Well numbers have properties too. Everything has properties. So that doesn't distinguish functions from numbers.
Magnus Anderson wrote:However, functions themselves aren't numbers. A function is no more than a set of input-output pairs where every input is paired with exactly one output. A set of pairs of numbers is not a number (even though you can use a set of pairs of numbers to represent a number.)
Conceptually maybe not, but formally functions are often numbers. For example in mathematical logic, we use Gödel numbering to represent a function or a formula by a specific number.
Another example would be to use the fact that there are as many continuous functions from the reals to the reals as there are reals. So in principle there's a mapping that inputs a continuous function and outputs a real number that can be used as a proxy for it. Instead of saying cosine we can just say #45.3. Every function has an associated number. So again, the distinction between numbers and functions is less clear to me than it is to you and @Ed.
Magnus Anderson wrote:So Ed is right when he says that functions aren't numbers
Well ... I question the relevance or point of the observation, since it's not clear to me that it's true, and it's definitely clear to me that it's a red herring in the .999... discussion. I don't get the bit about numbers and functions. Set theory doesn't distinguish between numbers and functions, they're both different types of sets. So I honestly don't know what point is being made here.
Magnus Anderson wrote: but he's also wrong because he says that $$0.\dot9$$ is a function (which it is not.)
Oh but of course it is. Every decimal expression is a function $$d : \mathbb N_+ \to D$$ where $$D$$ is the set of decimal digits $$D = \{0,1,2,3,4,5,6,7,8,9 \}$$. That's what a decimal expression is. You give me the number 47, I give you back the 47-th decimal digit. (Just referring to the digits to the right of the decimal point, we can patch up the idea to account for the leftward digits if needed). You give me the number 545535 and I return that digit. That is exactly what a decimal expression is, a function from the set of positive natural numbers to the set of digits.
I'm using $$\mathbb N_+$$ which is the set 1, 2, 3, ... so that the first place to the right of the decimal point is 1 and not 0 for convenience. I hope that's clear.
You see this, right? $$\pi$$ is a function, $$\sqrt 2$$ is a function. [After we deal with the pesky leftward digits].
What function represents $$\pi - 3$$?
f(1) = 1
f(2) = 4
f(3) = 1
f(4) = 5
f(5) = 9
etc.
wtf
Posts: 357
Joined: Sun Dec 06, 2015 5:47 am
### Re: Is 1 = 0.999... ? Really?
Hi Magnus,
What type of entity do you believe .999... to be?
Thanks Ed
"Albert! Stop telling God what to do." - Niels Bohr
Ed3
Thinker
Posts: 886
Joined: Sun Oct 31, 2004 2:56 pm
Location: Minneapolis, MN
### Re: Is 1 = 0.999... ? Really?
The quibble over function or number reminds me of grammar.
Function is to number as verb is to noun. The definition of the word is the same, but is the definition being used differently - as a doing or as a being? Are humans "beings" or "becomings"? Well they're still humans.
Then there's the distinction between the definite and indefinite article, or better yet - the type/token distinction. "A human" is one specific concrete specimen, whilst "human" is abstract humanity in general. Again, the definition of human: what we're dealing with and what specifically is meant, is the same.
The same goes for function and number - the meaning, and what we're dealing with is the same.
What is it that is the same in this case? Quantity.
"A quantity" is what I've been referring to as a concrete representation. "Quantity" is abstract.
You can represent "a quantity" as a function or number, arriving at it algorithmically (the journey) or the final result of doing so (the destination). "The quantity" represented is the same. "Quantity" means the same thing either way.
So yes, this objection of whether something is function or number is superficial at best, and meaningless at worst.
@wtf, what did I say about endless repetition when trying to deal rationally with irrationality?
The irrational are like flies trying to fly through a window, trying the same thing over and over in slightly different ways, and as soon as a new angle is attempted they forget their mistake in trying the old angle, and soon repeat their attempt.
The window is never escaped, sometimes even if you literally open the window for them.
I wonder if the mental block comes from how "1" is being thought of as being arrived at from one side only? In the case of "building" the representation $$0.\dot9$$ from $$0.9$$ through $$0.99$$ etc. it's approached from below only.
If it was representationally approached from the above, would it also be "1 plus some infinitessimal" as well as "1 minus some infinitessimal" simultaneously?
The algorithmic functional "doing" to get there is superficial. How the number "looks" is superficial.
A couple of people have mentioned Cauchy sequences. $$0.\dot9$$ is cauchy because there is no other quantity that it approaches than "1".
Representationally, you can get arbitrarily close to "1", but as above, whilst "the representations" can differ, "the quantity" is identical.
You can represent the quantity $$0.\dot9$$ as different to "1" with a Dedekind cut, but again this is only representation. The "quantity" is equal.
Silhouette
Philosopher
Posts: 4136
Joined: Tue May 20, 2003 1:27 am
Location: Existence
### Re: Is 1 = 0.999... ? Really?
Hi wtf,
You might be onto something here. I am thinking about Von Neumann and Godel numbering, but I need to give it some more thought.
However, with this specific example aren't you getting into some trouble representing an uncountable object with a countable object? In this specific case I think you need sequences with limits.
Ed
"Albert! Stop telling God what to do." - Niels Bohr
Ed3
Thinker
Posts: 886
Joined: Sun Oct 31, 2004 2:56 pm
Location: Minneapolis, MN
### Re: Is 1 = 0.999... ? Really?
Hi wtf,
I think I have screwed up my comments abount countable/uncountable. Though I am still not certain about your representation for Pi - 3.
Ed
"Albert! Stop telling God what to do." - Niels Bohr
Ed3
Thinker
Posts: 886
Joined: Sun Oct 31, 2004 2:56 pm
Location: Minneapolis, MN
### Re: Is 1 = 0.999... ? Really?
Perhaps some confusion can be cleared by signaling to the matter, or it's corresponding idea relating to languages in general, mathematics being a quantifier, leading to this proposition:
'formula beginning with a quantifier is called a quantified formula. A formal quantifier requires a variable, which is said to be bound by it, and a subformula specifying a property of that variable.
Formal quantifiers have been generalized beginning with the work of Mostowski and Lindström.'
As far as generalization is concerned, it appears to pair with a tendency to integrate sets that functionally demand such, to qualify within reasonable set specifications.
So the function may be set differently,
but it tends to integrate within some mixed set consisting of both: of specified and more general characteristics.
At least this is what appears to be implied here.
I may be way off with this generalization, it seems credible.
Meno_
ILP Legend
Posts: 6400
Joined: Tue Dec 08, 2015 2:39 am
Location: Mysterium Tremendum
### Re: Is 1 = 0.999... ? Really?
Ed3 wrote:Hi Magnus,
What type of entity do you believe .999... to be?
Thanks Ed
Hello.
I take $$0.999\dotso$$ to represent the same thing as every other decimal number which is a sum of the following form:
$$\cdots + d_2 \times 10^2 + d_1 \times 10^1 + d_0 \times 10^0 + d_{-1} \times 10^{-1} + d_{-2} \times 10^{-2} + \cdots$$
Every $$d_n$$ represents a decimal digit which is an integer from $$0$$ to $$9$$.
Magnus Anderson
Philosopher
Posts: 4253
Joined: Mon Mar 17, 2014 7:26 pm
### Re: Is 1 = 0.999... ? Really?
Silhouette wrote:Function is to number as verb is to noun. The definition of the word is the same, but is the definition being used differently - as a doing or as a being? Are humans "beings" or "becomings"? Well they're still humans.
Then there's the distinction between the definite and indefinite article, or better yet - the type/token distinction. "A human" is one specific concrete specimen, whilst "human" is abstract humanity in general. Again, the definition of human: what we're dealing with and what specifically is meant, is the same.
The same goes for function and number - the meaning, and what we're dealing with is the same.
What is it that is the same in this case? Quantity.
"Function" and "number" do not normally mean the same thing. You can make them mean the same thing, of course, but then, you must not equivocate.
How much money do you have? I have $$f(x) = x^2$$ money. What does that mean? Normally, it means nothing. But of course, if you have a need to, you can make it mean something.
You can use horses to represent numbers. You can say "This kind of horse represents this kind of number". For example, you can say that pegasuses represent number $$1,000$$, centaurs number $$100$$ and ponies number $$10$$. This allows you to do arithmetic with horses. You can say "A pony multiplied by a centaur equals a pegasus" without being wrong.
You can do the opposite too. You can say "This kind of number represents this kind of horse". You can say number $$1,000$$ represents pegasuses, and because pegasuses can fly, you can conclude, without making a mistake, that $$1,000$$ can fly too.
It's all fun and games until you equivocate.
For example:
1) All numbers are shapeless.
2) All horses are numbers.
3) Therefore, all horses are shapeless.
Horses qua numbers are indeed shapeless, but what is argued here is that horses qua animals are shapeless, which is not true.
In the same way, $$0.999\dotso$$ qua limit is indeed $$1$$ but what is being argued is that $$0.999\dotso$$ qua sum is $$1$$, and that is not true.
Magnus Anderson
Philosopher
Posts: 4253
Joined: Mon Mar 17, 2014 7:26 pm
### Re: Is 1 = 0.999... ? Really?
Ed3 wrote:Hi wtf,
I think I have screwed up my comments abount countable/uncountable. Though I am still not certain about your representation for Pi - 3.
Ed
You're not? What do you think a decimal expression like .1415926... means? It's a map from the positive integers to the decimal digits. 1 goes to 1. 2 goes to 4. 3 goes to 1.
The expression is then mapped to a convergent infinite series by summing 1/10 + 4/100 + ...
I cannot imagine you not knowing this. Please explain where you're coming from. You have me totally confused.
wtf
Posts: 357
Joined: Sun Dec 06, 2015 5:47 am
### Re: Is 1 = 0.999... ? Really?
Magnus Anderson wrote:
Then I'm confused. If the question is, "Is .999... = 1 true in standard math?" the answer is yes without a shred of doubt. I could point you to a hundred books on calculus and real analysis. If we're talking about standard math, how could anyone hold a different opinion?
Magnus Anderson wrote:
The question is:
Does $$0.999\dotso = 1$$ hold true within the standard language of mathematics?
The question is not:
Does $$0.999\dotso = 1$$ hold true within some guy's personal language of mathematics?
But yes! In which case .999... = 1 in standard math and there is no question or dispute, other than to clarify for people what the notation means and why it's true within standard math. It's a theorem in ZF set theory. It's a convergent geometric series in freshman calculus. It's even true in nonstandard analysis, which some people aren't aware of. There's just no question about the matter.
So you really have me puzzled, Magnus. If you agree we're talking about standard math, what is the basis of your disagreement?
Magnus Anderson wrote:
I have my own language, so you will often see me using standard symbols in a non-standard way
Ok. So you admit that you are NOT talking about standard math, but rather about your private nonstandard use of mathematical symbols. In which case you can define .999... = 47 and I would have no objection. If that's one of the rules in your game, I am fine with it; just as I learned to accept that the knight can hop over other pieces in standard chess.
Magnus Anderson wrote:
(e.g. using $$\infty$$ to mean what JSS means by "infA".) With this in mind, one must approach my posts with care, lest they misunderstand me.
You have already said that you are talking about standard math AND that you are talking about your own private nonstandard math. It's not hard to misunderstand you!
Now let me talk delicately about infA. When I came to this forum several years ago, James was already a prolific poster, an ILP Legend to beat all ILP legends. I am reluctant to criticize him since he is not here to defend himself. He has far more mindshare on this forum than I do. I respect his prolific output, if not always its content.
That said, the concept if infA is confused and wrong in the extreme. The idea seems to be some sort of mishmash of the ordinal numbers, in which we do "continue counting" after all the natural numbers are exhausted; and nonstandard analysis, in which there are true infinite and infinitesimal numbers. The infA concept borrows misunderstood elements from each of these ideas and simply makes a mess.
One really valuable thing I got from this thread a few years ago is that James caused me to go deeply into nonstandard analysis, to the point where I understand its technical aspects. For that I appreciate James. But the infA concept is just bullpucky, I don't know what else to say.
Magnus Anderson wrote:
The point of contention is the meaning of the symbol $$0.\dot9$$.
It means exactly what I've described to @Ed3. It's a particular map from the positive integers to the set of decimal digits; a constant map, in fact, in which f(n) = '9' for all inputs n. We then interpret this symbol as a real number as in the theory of geometric series, in which it's proved rigorously that .999... = 1.
Again I agree that if you choose to make up a new system in which .999... has some other meaning, you are perfect within your rights. After all there do happen to be many variants of chess; played on infinite boards, or with a new piece called the Archbishop, etc. If someone enjoys playing alternate versions of standard games it's ok by me.
Magnus Anderson wrote:
If $$0.\dot9$$ represents the limit of the infinite sum that is $$0.9 + 0.09 + 0.009 + \cdots$$ then it is true that $$0.\dot9 = 1$$.
Yes ok. Then we are done!
Magnus Anderson wrote:
However, if $$0.\dot9$$ represents the infinite sum that is $$0.9 + 0.09 + 0.009 + \cdots$$ then it is NOT true that $$0.\dot9 = 1$$.
I fail to follow that. Did you learn geometric series at one point? The definition of a limit? I can't tell where you're coming from.
Magnus Anderson wrote:
The limit of the sum is not the sum itself. They are two different things.
Actually the limit is defined as the sum. That's what a limit is. It's a clever finessing of the idea of "the point at the end" or whatever. You are adding your own faulty intuition. If you would consult a book on real analysis you would find that the limit of a geometric series is defined as the limit of the sequence of partial sums; and that the limit of a sequence is defined as a number that the sequence gets arbitrarily close to. I explained all this to @Phyllo the other day. That's the textbook definition. You're just wrong in your impression, either because you had a bad calculus class (as most students do) or none at all. It's not till Real Analysis, a class taken primarily by math majors, that one sees the formal definition and comes to understand that the sum IS defined as the limit of the sequence of partial sums. That cleverly avoids the confusion you've confused yourself with.
Magnus Anderson wrote:
The argument put forward is that the mathematical establishment defines $$0.\dot9$$ as an infinite sum and NOT as the limit of an infinite sum.
Ah, the evil cabal of mathematicians. I will fully agree with you that most math TEACHERS form an evil cabal. One doesn't get all this stuff sorted out properly till one sees the formal definitions; at which point, one learns that the limit of a sequence is defined by arbitrary closeness. The belief you have is a bad intuition that mathematical training is designed to clarify. It's sad that we don't show this to people unless they're math majors, and you can rest assured that when I am in charge of the public school math curriculum the teaching of the real numbers will be a lot better.
Till then, I apologize on behalf of the math community that you weren't taught better. But limits are very rigorously defined and your idea is just wrong.
Again I hope I'm not coming on too strong, I'm criticizing your ideas and not you. I know you are sincere. Except for the part where you say you're talking about standard math AND that you're not. That point confused me.
wtf
Posts: 357
Joined: Sun Dec 06, 2015 5:47 am
PreviousNext | 11,051 | 44,596 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2020-24 | latest | en | 0.936301 |
http://forums.wolfram.com/mathgroup/archive/1997/May/msg00266.html | 1,653,508,843,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662593428.63/warc/CC-MAIN-20220525182604-20220525212604-00085.warc.gz | 23,116,400 | 7,843 | Re: A Plot to Rotate
• To: mathgroup at smc.vnet.net
• Subject: [mg7414] Re: [mg7378] A Plot to Rotate
• From: jpk at max.mpae.gwdg.de
• Date: Sat, 31 May 1997 15:07:23 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com
```> I'm having trouble getting a Plot to work. It plots my function just fine
> but I want the whole shebang rotated 90 degrees counterclockwise.
>
> The plot is of the interior angles of the rhombic faces of polar zonohedra,
> as the polar zonohedrons "pitch" varies from 0 to 90 degrees. As it stands
> now pitch runs along the x axis. I want pitch on the y axis. Here is the
> code as it stands now, for n=11 (n<=3):
>
> n=11;
> p=Plot[Evaluate[Table[
> {{rad=N[2*(1/Degree)*ArcSin[Sin[i*Pi/n]/Sec[Degree j]]]},{circ=180-rad}},
> {i,Floor[n/2]}]], {j,0,90},
> Frame->True,
> AspectRatio->Automatic,
> PlotPoints->30,
> PlotStyle->{{AbsoluteThickness[2]},{AbsoluteThickness[1]}}]
>
> Thanks much for any help. I've tried some things but failed.
>
> Russell Towle
> Giant Gap Press: books on California history, digital topographic maps
> P.O. Box 141
> Dutch Flat, California 95714
> ------------------------------
> Voice: (916) 389-2872
> e-mail: rustybel at foothill.net
> ------------------------------
Hi Russel,
with Your p
the lines
Needs["Geometry`Rotations`"]
Show[Graphics[First[p] /.
Line[pnts_] :>
Line[Rotate2D[#,Pi/2]& /@ pnts]]];
will do what You want.
Hope that helps
Jens
```
• Prev by Date: Plot Rotation solution
• Next by Date: Re: Won't Read Entire Soundfile; Why?
• Previous by thread: Re: A Plot to Rotate
• Next by thread: Re: Get answers out of listform | 519 | 1,624 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2022-21 | latest | en | 0.76471 |
https://gtfoutside.com/thorough-understanding-of-the-millennium-prize-problems-a-comprehensive-guide-to-the-frontiers-of-mathematical-research/ | 1,701,470,383,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100308.37/warc/CC-MAIN-20231201215122-20231202005122-00649.warc.gz | 336,220,854 | 25,087 | # Thorough Understanding of the Millennium Prize Problems: A Comprehensive Guide to the Frontiers of Mathematical Research
쉬운 목차
## Introduction to the Millennium Prize Problems
In the new millennium’s dawn, the Clay Mathematics Institute (CMI) announced seven epoch-making problems that would become universally known as the Millennium Prize Problems. Proposed by the CMI, these problems are an embodiment of the toughest puzzles that continue to baffle the best minds in the field of mathematics.
## Detailed Look at Every Millennium Prize Problem
### 1. Birch and Swinnerton-Dyer Conjecture
The Birch and Swinnerton-Dyer conjecture converges on the all-encompassing arena of number theory. It concerns a specific type of equation, known as an elliptic curve, and the solutions it has. Named after mathematicians Bryan Birch and Peter Swinnerton-Dyer, this conjecture advances the claim that the behavior of rational points is reflected by the behavior of the curve near the origin.
### 2. Hodge Conjecture
The Hodge Conjecture opens the door to unravel the complicated tapestry of mathematical shapes known as algebraic cycles and their interaction with cohomology theory. The hypothesis ventures into the labyrinth of algebraic topology and touches upon the nuanced relationship between the algebraic and topological properties of a geometric shape.
### 3. Navier-Stokes Existence and Smoothness
The Navier-Stokes existence and smoothness problem primarily deals with the physics of fluid dynamics and is one of the key stumbling blocks in computational fluid dynamics (CFD). The Navier-Stokes equations, foundational pillars of CFD, are utilized to describe the movement of fluid substances, but their solutions remain elusive under certain conditions.
### 4. P vs NP Problem
The "P vs NP" problem revolves around the fascinating yet perplexing realm of computational theory. Essentially, it poses the question whether every problem for which a solution can be checked quickly (P problems) can also be solved quickly (NP problems). The implications of proving this conjecture would reach far beyond mathematics, significantly impacting fields like computer science and cryptography.
### 5. Poincaré Conjecture
Before being famously solved by Grigori Perelman in 2002, the Poincaré Conjecture was one of the most prestigious unsolved problems in topology. It proposed that any closed simply-connected three-dimensional space must be topologically equivalent to the three-dimensional sphere. Perelman’s proof of this longstanding conjecture made him the first, and to date only, mathematician to solve a Millennium Prize Problem.
### 6. Riemann Hypothesis
The Riemann Hypothesis, rooted in complex analysis and number theory, is perhaps the oldest and most famous unsolved problem in mathematics. It involves the distribution of prime numbers and zeroes of the Riemann zeta function. Proposed by Bernhard Riemann in 1859, its proof remains one of the Holy Grails of mathematics.
### 7. Yang-Mills Existence and Mass Gap
The Yang-Mills Existence and Mass Gap problem belongs to quantum field theory, the physical theory fitting quantum mechanics and special relativity together. It predicts the existence of "mass gap" in quantum fields and has huge implications for both particle physics and quantum field theory.
## Importance and Implications of the Millennium Prize Problems
The importance of the Millennium Prize Problems cannot be overstated. Solving any one of these problems would not only advance mathematics but also have profound implications on multiple disciplines, including physics, computer science, and engineering, shaping our understanding of the universe we live in.
## Present Scenario and Future Prospects
As of now, only the Poincaré Conjecture has been validated, leaving six other problems still unproven. The millennium problems continue to stimulate research and enlighten discourse in various mathematical subfields, inspiring budding mathematicians to rise to the challenge. The fortitude to solve these problems not only guarantees a million-dollar prize but also ensures your name etched in history as a contributor to the deepened understanding of mathematical truths.
## Conclusion
The Millennium Prize Problems serve as a beacon for mathematical advancement and intellectual exploration. They symbolize the ideals of persistence, intellectual rigor, and the relentless pursuit of knowledge. Whether or not the remaining problems will be solved in our lifetime remains to be seen, but the journey to explore these truths continues to open doors to revolutionary ideas, advance our understanding, and inspire generations of mathematicians to come. | 916 | 4,705 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2023-50 | latest | en | 0.909664 |
https://ask.sagemath.org/questions/56490/revisions/ | 1,719,121,526,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862430.93/warc/CC-MAIN-20240623033236-20240623063236-00698.warc.gz | 93,377,356 | 5,453 | Ask Your Question
# Revision history [back]
### How to construct a class of graphs satisfying a given matrix equation.
Here we know that $A=I_n$ satisfies the given matrix equation. But can we find other non trivial matrix ($\neq I_n$). In other words, can we construct a class of graphs satisfying the given matrix equation.
Please help regarding this.
### How to construct a class of graphs satisfying a given matrix equation.
Here we know that $A=I_n$ satisfies the given matrix equation. But can we find other non trivial matrix ($\neq I_n$). In other words, can we construct a class of graphs satisfying the given matrix equation.
Please help regarding this.
### How to construct a class of graphs matrices satisfying a given matrix equation.
Here we know that $A=I_n$ satisfies the given matrix equation. But can we find other non trivial matrix ($\neq I_n$). In other words, can we construct a class of graphs matrices satisfying the given matrix equation.
Please help regarding this. | 217 | 1,001 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2024-26 | latest | en | 0.849515 |
https://www.wordaz.com/Homotopy.html | 1,571,030,632,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986649232.14/warc/CC-MAIN-20191014052140-20191014075140-00010.warc.gz | 1,238,555,323 | 4,536 | Definition of Homotopy. Meaning of Homotopy. Synonyms of Homotopy
# Definition of Homotopy. Meaning of Homotopy. Synonyms of Homotopy
Here you will find one or more explanations in English for the word Homotopy. Also in the bottom left of the page several parts of wikipedia pages related to the word Homotopy and, of course, Homotopy synonyms and on the right images related to the word Homotopy.
## Definition of Homotopy
No result for Homotopy. Showing similar results...
## Meaning of Homotopy from wikipedia
- a deformation being called a homotopy between the two functions. A notable use of homotopy is the definition of homotopy groups and cohomotopy groups...
- In mathematics, homotopy groups are used in algebraic topology to cl****ify topological spaces. The first and simplest homotopy group is the fundamental...
- In mathematical logic and computer science, homotopy type theory (HoTT /hɒt/) refers to various lines of development of intuitionistic type theory, based...
- The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological...
- In mathematics, in particular in homotopy theory within algebraic topology, the homotopy lifting property (also known as an instance of the right lifting...
- In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other....
- In mathematics, the homotopy category is a category built from the category of topological spaces which in a sense identifies two spaces that have the...
- in homotopy theory and (higher) category theory, coherency is the standard that equalities or diagrams must satisfy when they hold "up to homotopy" or...
- topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory. This cl**** of spaces is broader and has some better categorical...
- The homotopy analysis method (HAM) is a semi-analytical technique to solve nonlinear ordinary/partial differential equations. The homotopy analysis method... | 467 | 2,097 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2019-43 | latest | en | 0.910858 |
http://www.nhn.ou.edu/~bumm/ELAB/Lect_Notes/Op_Amps_v1_2_2.html | 1,516,122,364,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084886476.31/warc/CC-MAIN-20180116164812-20180116184812-00653.warc.gz | 517,867,837 | 7,318 | Notes on Operational Amplifiers (Op Amps).
Comments. The name Op Amp comes from “operational amplifier.”
Op Amp Golden Rules (memorize these rules)
1) The op amp has infinite open-loop gain.
2) The input impedance of the +/− inputs is infinite. (The inputs are ideal voltmeters). The output impedance is zero. (The output is an ideal voltage source.)
3) No current flows into the +/− inputs of the op amp. This is really a restatement of golden rule 2.
4) In a circuit with negative feedback, the output of the op amp will try to adjust its output so that the voltage difference between the + and − inputs is zero (V+ = V).
Ideal Op Amp Behavoir.
The relationship between the input and the output of an ideal op amp (assumptions: infinite open loop gain, unlimited voltage).
Op Amp Schematic Symbol (The upper input is usually the inverting input. Occasionally it is drawn with the non-inverting input on top when it makes the schematic easier to read. The position of the inputs may vary within the same schematic, so always look closely at the schematic! )
Negative Feedback. Most of the basic op amp building blocks rely on negative feedback. You can easily identify the type of feedback used by the op amp circuit. For negative feedback, the output is connected to the inverting input (− input). For positive feedback, the output is connected to the non-inverting input (+ input).
The Input Impedance of the Circuit is defined as the rate of change of Vin with respect to a change of Iin. This is simply the derivative. The input impedance of the circuit is not in general the same as the impedance of the op amp’s inputs.
The Output Impedance of the Circuit, for the examples shown here, is the output impedance of the op amp. Output impedance is defined as the rate of change of Vout with respect to a change of Iout. This is simply the derivative. For the ideal op amp, the output impedance is zero.
Basic Op Amp Building Blocks
Inverting Amplifier
Analysis of the inverting amplifier starts with our op amp golden rules. From rule #4 we know that and that V = 0 because V+ is connected to ground. From rule #3 we know that because no current flows into the inverting input.
Then we can find the relationship between Vin and Vout using Ohm’s law (OL) and Kirchhoff’s voltage law (KVL).
The voltage gain AV is the derivative of Vout with respect to Vin. When the amplifier has only one input and Vout = 0 when Vin = 0, we will make the assumption that AV = Vout/Vin.
Alternatively we could have started our analysis from the voltage divider formed by Rf and Rin. The voltage divider will relate the voltage at V with Vout and Vin. In this case the total voltage across the divider is VoutVin. Because the bottom end of the divider is not connected to ground, we must add the extra Vin term to offset V. We arrive at the same result.
The input impedance of the inverting amplifier is determined by Rin. Note that V is held at the same voltage as V+ by the op amp feedback. Because V+ is connected to ground, the input impedance is just Rin.
Non-inverting Amplifier
Analysis of the non-inverting amplifier starts with our op amp golden rules. From rule #4 we know that and that V = Vin because V+ is connected to Vin. From rule #3 we know that because no current flows into the inverting input.
Then we can find the relationship between Vin and Vout using Ohm’s law (OL) and Kirchhoff’s voltage law (KVL).
The voltage gain AV is the derivative of Vout with respect to Vin. When the amplifier has only one input and Vout = 0 when Vin = 0, we will make the assumption that AV = Vout/Vin.
Alternatively we could have started our analysis from the voltage divider formed by Rf and Rin. The voltage divider will relate the voltage at V with Vout and Vin. In this case The total voltage across the divider is Vout and the we know that V = Vin. We arrive at the same result.
The input impedance of the non-inverting amplifier is the input impedance of the op amps input. For an ideal op amp the input impedance is infinite.
Voltage Follower
This is a special case of the non-inverting amplifier with Rin → ∞ and Rf = 0. The follower has a very high input impedance. Voltage follower has application when the source voltage can not supply very much current, a pH meter for example.
Current-to-Voltage Converter (AKA, I-V Converter, Transimpedance Amplifier). This circuit takes an input current and converts it to an output voltage. The input impedance of the ideal current to voltage converter is zero (the ideal current meter).
Analysis of the current-to-voltage converter starts with our op amp golden rules. From rule #4 we know that and that V = 0 because V+ is connected to ground. From rule #3 we know that because no current flows into the inverting input.
Then we can find the relationship between Vin and Vout using Ohm’s law (OL) and Kirchhoff’s voltage law (KVL).
The current-to-voltage converter has transimpedance gain. Transimpedance gain is not unitless, it has units of impedance (Ohms). The units can also be expressed as V/A (volts/ampere), which is often a more useful way to think of the gain—the output voltage per input ampere. The transimpedance gain AZ is the derivative of Vout with respect to Iin. When the amplifier has only one input and Vout = 0 when Iin = 0, we will make the assumption that AV = Vout/Iin.
Voltage-to-Current Converter (AKA, V-I Converter, Transadmittance Amplifier). This circuit takes an input voltage and converts it to an output current. The input impedance of the voltage-to-current converter is the input impedance of the op amps input. For an ideal op amp the input impedance is infinite. The schematic looks strange at first because there is no output terminal! However the output is the current flowing through the load.
Analysis of the voltage-to-current converter starts with our op amp golden rules. From rule #4 we know that and that V+ = Vin and V = I1R1 (OL). From rule #3 we know that because no current flows into the inverting input.
Then we can find the relationship between Vin and Iout.
The current-to-voltage converter has transadmittance gain. Transadmittance gain is not unitless, it has units of admittance (Siemens, AKA Ohm–1). The units can also be expressed as A/V (amperes/volt), which is often a more useful way to think of the gain—the output current per input volt. The transadmittance gain AY is the derivative of Iout with respect to Vin. When the amplifier has only one input and Iout = 0 when Vin = 0, we will make the assumption that AY = Iout/Vin.
Summing Amplifier. This circuit will add (and subtract) the input voltages. Subtraction is accomplished by inverting the voltages before adding them. Note that summing can only occur for inputs to the inverting side of the op amp. This is because of the V node is a current summing junction where the input currents sum to the feedback current.
This is another look at the summing amplifier that emphases the summing junction.
Analysis of the summing amplifier starts with our op amp golden rules. From rule #4 we know that and that V = 0 because V+ is connected to ground. From rule #3 we know that because no current flows into the inverting input. (Iinn is the current of the nth input.)
Then we can find the relationship between Vin and Vout using Ohm’s law (OL) and Kirchhoff’s voltage law (KVL).
The voltage gain AV is the derivative of Vout with respect to Vin.
Differential Amplifier. The term differential is used in the sense of difference. Do not confuse the differential amplifier with the differentiator. One important application of the differential amplifier overcomes the problem of grounding that you encountered in lab when using the oscilloscope to make measurements. The typical oscilloscope always performs voltage measurements with respect to is own ground. A differential amplifier used before the scope input could measure the V+in with respect to V−in. The ground of the differential amplifier would be connected to the ground of the scope for this application, so the Vout will be measured correctly.
Analysis of the differential amplifier starts with our op amp golden rules. From rule #4 we know that . From rule #3 we know that and that because no current flows into the inputs.
Then we can find the relationship between V+in, Vin, and Vout using the voltage divider equations. We recognize that and that V+ will be the output of the voltage divider formed by the two resistors connected to the non-inverting input. The voltage at V is the output of the voltage divider formed by the two resistors connected to the inverting input.
The voltage gain AV is the derivative of Vout with respect to each input Vin.
The inverting amplifier with generalized impedances. The results derived above can be extended to general impedances. Note that Zf and Zin can be the impedance of any network. The following are examples of the inverting amplifier, but ANY of the previous examples can be generalized in this way.
Integrator. A capacitor as the feedback impedance.
Analysis of the integrator in the frequency domain is a simple extension of our generalized result for the inverting amplifier.
Time Domain Analysis of the Integrator starts with our op amp golden rules. From rule #4 we know that and that V = 0 because V+ is connected to ground. From rule #3 we know that because no current flows into the inverting input.
Then we can find the relationship between Vin and Vout using Ohm’s law (OL) and Kirchhoff’s voltage law (KVL).
Differentiator. A capacitor as the input impedance.
Analysis of the differentiator in the frequency domain is a simple extension of our generalized result for the inverting amplifier.
Time Domain Analysis of the Differentiator starts with our op amp golden rules. From rule #4 we know that and that V = 0 because V+ is connected to ground. From rule #3 we know that because no current flows into the inverting input.
Then we can find the relationship between Vin and Vout using Ohm’s law (OL) and Kirchhoff’s voltage law (KVL).
The General Op Amp Circuit
Example: an op amp circuit with 3 inverting and 3 non-inverting inputs
What can we say about such a complicated looking amplifier? Don’t panic, we can use what we have learned from the above analyses to painlessly arrive at the solution. Without doing any analysis, what can we say? First, we know that
Second, we know that the voltage gains for V1, V2, and V3 will be inverting (negative) and that the voltage gains for V4, V5, and V6 will be non-inverting (positive). We could simply blaze away at the problem by applying the op amp golden rules just like we did for the derivations for the basic op amp building blocks, but there is a better way.
The Strategy.
We will make use of the results for the basic op amp building blocks and the principle of superposition (e.g. the inverting amplifier and the non-inverting amplifier). To apply the principle of super position, we analyze the gain for one input at a time and turn off all the other inputs (set them to zero). We treat each input as an ideal voltage source, so that an input that is turned off is equivalent to a connecting the input terminal directly to ground. The inverting inputs and the non-inverting inputs will behave differently.
Analysis of the Inverting Inputs by Superposition
Let’s first use analyze the voltage gain AV1 of the input V1. We proceed by connecting all the other inputs to ground. (Analysis of the voltage gain for the other inverting inputs (Av2 and Av3) is analogous.)
This simplifies to:
Notice that the non-inverting input, V+ is connected to ground though a resistor. Because no current flows into the op amp’s inputs, V+ = 0, equivalent to it being connected directly to ground (see below).
This looks like a summing amplifier with V2 = V3 = 0. The result for the summing amplifier is . We can do the same analysis for each inverting input. (Why don’t the two resistors R2 and R3 enter this analysis for AV1? Hint: Consider the voltage across these two resistors.)
Analysis of the Non-Inverting Inputs by Superposition
Now let’s analyze the voltage gain AV4 of the non-inverting input V4. We proceed by connecting all the other inputs to ground. (Analysis of the voltage gain for the other non-inverting inputs (Av5 and Av6) is analogous.)
This simplifies to:
This is a non-inverting amplifier. The resistors on the non-inverting side, R4, R5, R6, and R8, form a voltage divider that reduces the voltage seen by V+. It is the voltage at V+ that is seen by the op amp. The voltage gain of V+ is determined by the resistors on the inverting side, R1, R2, R3, and R7. Hence the voltage gain AV4 of the V4 input has a term from the voltage divider, relating V4 to V+, and a term for the voltage gain of V+, relating V+ to Vout. The voltage gain AV4 is the product of the two term and relates V4 to Vout.
The voltage gains for the other non-inverting inputs can be found in this way.
An important observation is that multiple inputs into the non-inverting side of the op amp do not sum in the simple way that they do for inverting inputs. Thus the summing amplifier that we listed as a basic building block does not have a non-inverting analog! (If we need a non-inverted sum, we just follow the summing amplifier with a unity gain inverting amplifier.) | 3,063 | 13,391 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2018-05 | latest | en | 0.82203 |
https://proofwiki.org/wiki/Tower_of_Hanoi/Variant | 1,638,955,449,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363465.47/warc/CC-MAIN-20211208083545-20211208113545-00093.warc.gz | 506,856,369 | 11,547 | Tower of Hanoi/Variant
Problem
There is a tower of $n$ disks, stacked in decreasing size on one of $3$ pegs.
The object of the exercise is to move the disks onto a different peg, obeying the rules:
$(1): \quad$ Only one disk can be moved at a time
$(2): \quad$ No disk may be placed on a peg with a smaller disk beneath it
$(3): \quad$ The disks must all be moved from the peg $1$ to peg $3$
$(4): \quad$ A move consists of transferring a disk from the peg $1$ to peg $2$, or back, or from peg $2$ to peg $3$, or back
$(5): \quad$ No disk can cross over peg $2$ if it contains a smaller disk.
Solution
For a tower of $n$ disks, it takes $3^n - 1$ moves.
Proof
To move a tower of $n$ disks from the peg $1$ to peg $3$, the following must happen:
$(1): \quad$ The tower of $n - 1$ disks above the $n$th disk is transferred from peg $1$ to peg $3$.
$(2): \quad$ The $n$th disk is transferred from peg $1$ to peg $2$.
$(3): \quad$ The tower of $n - 1$ disks above the $n$th disk is transferred from the peg $3$ to peg $1$.
$(4): \quad$ The $n$th disk is transferred from the peg $2$ to peg $3$.
$(5): \quad$ The tower of $n - 1$ disks above the $n$th disk is transferred from the peg $1$ to peg $3$.
Let ${T_n}'$ be the number of moves needed to transfer the $n$-disk tower from peg $1$ to peg $3$.
Then we see that:
${T_n}' = 3 {T_{n - 1}}' + 2$
A simple proof by induction shows that:
${T_n}' = 3^n - 1$
$\blacksquare$
Historical Note
The Tower of Hanoi was invented by François Édouard Anatole Lucas in $1893$, under the name M. Claus.
He backed this up by inventing the romantic story about the Tower of Brahma, as follows:
In the great temple of Benares, beneath the dome which marks the centre of the world, rests a brass plate in which there are fixed three diamond needles, each a cubit high and as thick as the body of a bee. On one of these needles, at the creation, God placed $64$ discs of pure gold, the largest disc resting on the brass plate, and the others getting smaller and smaller up to the top one. This is the Tower of Bramah. Day and night unceasingly the priests transfer the discs from one diamond needle to another according to the fixed and immutable laws of Bramah, which require that the priest on duty must not move more than one disc at a time and that he must place this disc on a needle so that there is no smaller disc below it. When the $64$ discs have been thus transferred from the needle on which at the creation God placed them to one of the other needles, tower, temple, and Brahmins alike will crumble into dust, and with a thunderclap the world will vanish.
It is seen from the solution of the problem that the Brahmin priests would need $2^{64} - 1$ moves:
$18 \, 446 \, 744 \, 073 \, 709 \, 551 \, 615$
At $1$ move per second, that is nearly $600 \, 000 \, 000 \, 000$ years. | 817 | 2,837 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.34375 | 4 | CC-MAIN-2021-49 | latest | en | 0.893773 |
https://www.shaalaa.com/question-bank-solutions/express-the-following-as-a-roman-numeral-475-roman-numbers-system-and-its-application_135380 | 1,618,189,098,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038065903.7/warc/CC-MAIN-20210411233715-20210412023715-00236.warc.gz | 1,127,587,017 | 8,799 | # Express the Following as a Roman Numeral: 475 - Mathematics
Sum
Express the following as a Roman numeral: 475
#### Solution
475 = (500 - 100) + 50 + 10 + 10 + 5 = CDLXXV
Is there an error in this question or solution?
#### APPEARS IN
RS Aggarwal Class 6 Mathematics
Chapter 1 Number System
Exercise 1G | Q 2.5 | Page 19 | 103 | 328 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.375 | 3 | CC-MAIN-2021-17 | latest | en | 0.751879 |
dim.kln.ac.lk | 1,566,422,873,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027316194.18/warc/CC-MAIN-20190821194752-20190821220752-00238.warc.gz | 54,245,962 | 5,778 | BACHELOR OF SCIENCE IN SOFTWARE ENGINEERING
PMAT 12102 DISCRETE MATHEMATICS FOR COMPUTING I Status : Core Pre-requisite : G.C.E. (A/L) Co-requisite : None
On completion of this course, the student should be able to:
• Explain logic, sets, relations and functions
• Apply Boolean algebra in simplifying combinatorial circuits.
Propositional Logic: Propositions, Truth values, Logical connectives, Truth table, Tautology and Contradiction, Logical equivalence, Algebra of propositions, Validity of an argument.
Predicate Logic: Quantifiers, Nested quantifiers, Negation of quantified statements, Validity of an argument with quantifiers.
Methods of Proof: Informal idea of a theorem and a proof, Converse, inverse and the contrapositive of a statement, Direct proof, Proof by contradiction, contrapositive, exhaustion and cases, Disproving by counter-examples, Principle of mathematical induction (weak and strong form).
Sets: Set notations, Sets of numbers, Subsets of the real numbers and interval notation, Operations on sets, Algebra of sets, Set identities, Power set, Cartesian product of sets.
Relations: Equivalence relations and equivalence classes, Properties of equivalence classes, Partitioning of sets.
Functions: Function notations, Image and pre-image, One-to-one and onto functions, Composition of functions, Inverse Function, Image and inverse image of subsets under functions.
Boolean algebra: Axioms of Boolean algebra and its properties, Correspondence between Boolean algebra and combinatorial logic circuits, Simplifications of combinatorial logic circuits using Boolean algebra.
Lectures, interactive classroom sessions, and case discussions.
End of course unit examination, group assignments, mid-term examination,class attendance.
1. Johnsonbaugh, R (2009). Discrete Mathematics. MacMillan
2. Lipschutz, S (2009). Discrete Mathematics. McGraw-Hill, New York. | 409 | 1,895 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2019-35 | latest | en | 0.793818 |
https://numberoneproperty.com/debt-to-income-ratio/ | 1,720,953,808,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514564.41/warc/CC-MAIN-20240714094004-20240714124004-00134.warc.gz | 367,401,469 | 31,205 | # Understanding Your Financial Health: How to Calculate Your Debt-to-Income Ratio for a Mortgage | Calculate your DTI
by | Oct 4, 2023
## What is a Debt-to-Income Ratio?
A debt-to-income ratio (DTI) is a financial measure that compares an individual’s monthly debt payments to their monthly income.
It is a crucial factor that lenders use to assess a borrower’s creditworthiness and their ability to repay loans.
### What is a DTI?
Calculating your DTI involves summing up all your monthly debt payments and dividing it by your total monthly income.
The result is expressed as a percentage, which represents the proportion of your income that is used to pay off debts.
Lenders consider this percentage when evaluating your creditworthiness.
A credit score, credit report, and credit history are key factors that lenders rely on.
In addition to this, lenders look at your credit limits and credit utilization rate, which is the percentage of credit that you are utilizing.
All this information is used to assess your overall financial health.
### How is DTI calculated?
Monthly debt includes expenses such as rent or mortgage payments, car loans, credit card payments, and other monthly obligations.
Monthly income refers to your monthly earnings before taxes.
To calculate your DTI, divide your monthly debt by your monthly income and then multiply the result by 100 to get the percentage.
For example, if your monthly debt is \$1,500 and your monthly income is \$5,000, your DTI would be 30% (1500/5000 * 100).
### Why is DTI important?
The DTI ratio is important for both lenders and borrowers.
For lenders, it helps them gauge the risk associated with lending to a particular borrower.
A higher DTI indicates that a borrower has a higher debt burden compared to their income, making them a riskier borrower.
For potential borrowers, understanding their DTI can provide insight into their financial health and help them assess their creditworthiness.
It allows them to determine if they are within acceptable levels and if they can comfortably handle additional debt.
It is generally recommended to maintain a DTI below 36%, although specific lenders may have different requirements.
A lower DTI indicates a better ability to manage and repay debts, increasing your chances of getting approved for credit or loans.
In conclusion, understanding and managing your debt-to-income ratio is essential for your financial well-being.
By keeping your DTI within acceptable levels, you can demonstrate your creditworthiness to lenders and maintain a healthy financial profile.
## Key Takeaways
1. What is DTI? DTI measures the percentage of monthly income used for debt payments, crucial for assessing creditworthiness.
2. Calculating DTI: Calculate DTI by dividing total monthly debt by monthly income, expressed as a percentage.
3. Importance of DTI: Lenders use DTI to gauge borrower risk, while borrowers can assess creditworthiness. Maintain DTI below 36% for optimal financial health.
4. DTI in Singapore: In Singapore, DTI helps lenders assess creditworthiness for loans and credit cards.
5. Calculate Singapore DTI: Gather financial info, calculate total debt and income, and use the DTI formula: (Total Monthly Debt / Monthly Gross Income) x 100.
6. Good DTI in Singapore: A good DTI is typically below 40% in Singapore, but lenders may have specific requirements.
7. DTI’s Impact on Credit: DTI affects your credit score; a lower DTI indicates lower risk to lenders.
8. DTI and Loan Approval: Your DTI directly influences loan approval; lower DTI increases chances of approval.
9. Improve DTI: Pay down debt, increase income, and negotiate lower interest rates to improve your DTI.
10. Tips for Mortgage Rates: Compare rates, explore terms, and get pre-approved to secure the best mortgage rate in Singapore.
## How to Calculate Your DTI in Singapore
Debt-to-income ratio (DTI) is a crucial financial tool that helps individuals assess their ability to manage their debt.
It measures the proportion of a person’s monthly debt payments to their gross monthly income.
In Singapore, understanding your DTI ratio is important when applying for loans or credit cards, as it helps lenders determine your creditworthiness.
To calculate your DTI in Singapore, start by gathering your financial information.
This includes identifying your current debt obligations, such as credit card balances, mortgages, car loans, student loans, and any other outstanding debts.
Make a list of these debts and note down the monthly payments for each.
Next, determine your gross monthly income.
This includes your salary, bonuses, commissions, and any other sources of income.
It’s essential to consider your tax income after deducting CPF contributions and additional income from rental properties or other income streams.
### Calculate your total debt and total monthly income
Once you have gathered your financial information, calculate your total debt and total monthly income.
Add up all your monthly debt payments, including credit card minimum payments, mortgage payments, and other loan payments.
This will give you a clear picture of your financial situation.
Multiply the result by 100 to get your DTI ratio as a percentage.
### Use the DTI formula to calculate your DTI
The DTI ratio is calculated using the formula: DTI = (Total Monthly Debt Payments / Monthly Gross Income) x 100.
For example, if your total monthly debt payments amount to SGD 2,000 and your monthly gross income is SGD 6,000, your DTI ratio would be (2,000 / 6,000) x 100 = 33.33%.
This means that 33.33% of your gross monthly income goes towards debt payments.
Different lenders in Singapore have varying maximum DTI ratios they consider acceptable for loan approvals.
It’s important to note that a lower DTI ratio generally indicates a lower risk to lenders and may increase your chances of securing a loan or credit card.
By understanding and calculating your DTI, you can better manage your debt and make informed financial decisions.
It’s important to review your DTI regularly, especially when considering new financial commitments or evaluating your overall financial health.
## What is a Good Debt-to-Income Ratio in Singapore?
### What is considered a good DTI?
When it comes to managing your finances and applying for loans, understanding your debt-to-income ratio (DTI) is crucial.
DTI is the percentage of your monthly income that goes towards paying debts.
In Singapore, a good DTI is generally considered to be less than 40%.
This means that your total monthly debt payments should be at most 40% of your monthly income.
Having a good DTI is essential as it shows lenders that you have a manageable level of debt and are more likely to be able to repay the loan.
If your DTI is too high, it may be easier for you to qualify for certain loans, especially those with stricter requirements.
It’s worth noting that different lenders may have different acceptable levels of DTI.
For example, if you’re applying for a mortgage or credit card debt, lenders might require a lower DTI, around 30%.
In such cases, having a higher DTI could result in the need for private mortgage insurance or even disqualification from securing the loan.
A credit score is a number that represents your creditworthiness and is used by lenders to assess your credit eligibility.
A good credit score is essential as it can help you secure favorable loan terms and interest rates.
A high DTI can negatively impact your credit score.
This is because credit scoring formulas take into account your DTI when calculating your credit score.
If your DTI is too high, it may indicate to lenders that you have a high level of debt and may need help to make payments on time.
As a result, your credit score may be lower than desired.
On the other hand, maintaining a low DTI can contribute to a good credit score and overall credit health.
By keeping your debts in check and ensuring that your DTI is within acceptable limits, you can improve your credit eligibility and increase your chances of securing loans and favorable interest rates.
### How does your DTI affect your ability to qualify for a loan?
Your DTI has a direct impact on your ability to qualify for a loan.
Lenders use your DTI as one of the factors in determining whether you are a suitable candidate for a loan.
A lower DTI indicates that you have a more manageable level of debt and are more likely to be able to repay the loan.
When you apply for a mortgage or any other type of loan, lenders will assess your DTI along with other factors such as credit history, credit limits, and credit utilization rate.
If your DTI is too high, lenders may view you as a higher-risk borrower and may be hesitant to approve your loan application.
On the other hand, if your DTI is at an acceptable level, lenders will be more confident in your ability to repay the loan.
This can make the loan approval process smoother and increase your chances of getting favorable terms and interest rates.
In conclusion, understanding and maintaining an excellent debt-to-income ratio in Singapore is essential for managing your finances and securing loans.
By keeping your DTI within acceptable limits, you can improve your credit score, increase your chances of loan approval, and achieve better financial stability.
## How to Improve Your Debt-to-Income Ratio in Singapore
### Pay down debt
One of the most effective ways to improve your debt-to-income ratio is to pay down your debt.
The debt-to-income ratio is the percentage of your monthly income that goes towards paying off debts.
By reducing your debt payments, you can lower this ratio and improve your overall financial health.
To start, take a look at your monthly expenses and identify areas where you can cut back.
This could mean reducing discretionary spending or finding ways to save on essential costs.
Use the money you save to pay down your debts more aggressively.
If you have multiple debts, consider prioritizing the ones with the highest interest rates.
Paying off these high-interest debts first can save you money in the long run and help you pay down your debt more quickly.
Another way to improve your debt-to-income ratio is to increase your income.
Look for opportunities to earn additional income, such as taking on a side gig or freelance work.
You could also explore other sources of income, such as rental income from a property or dividends from investments.
Increasing your income not only helps you pay down your debt faster but also improves your overall financial situation.
### Get a lower interest rate on your debt
If you’re carrying high-interest debt, getting a lower interest rate can significantly improve your debt-to-income ratio.
High-interest debt can make it difficult to pay down your debts and can increase the amount of money you’re spending on debt payments each month.
Consider talking to your creditors or lenders to negotiate a lower interest rate.
You can also explore refinancing options that offer lower interest rates.
By reducing the interest rate on your debt, you can lower your monthly debt payments and improve your debt-to-income ratio.
Improving your debt-to-income ratio is an essential step towards financial stability.
It not only makes it easier to manage your debts but also opens up more opportunities for you in the long run.
By paying down debt, increasing your income, and getting a lower interest rate, you can take control of your financial future and improve your overall economic well-being.
Note: The debt-to-income ratio is a calculation used by lenders to assess your ability to repay debts.
It compares your monthly debt payments to your monthly income before taxes.
A lower debt-to-income ratio indicates a lower level of debt compared to your income, which is generally considered more favorable.
Different lenders may have different acceptable levels of debt-to-income ratios, so it’s essential to check with them to understand their specific requirements.
## Tips for Getting the Best Mortgage Rate in Singapore
### Compare mortgage rates from different lenders
When looking to get the best mortgage rate in Singapore, it’s crucial to compare rates from different lenders.
Each lender has its criteria for determining mortgage rates, so it’s essential to find one that fits your financial situation.
By comparing rates, you can ensure that you’re getting the best possible deal.
Make sure to provide all relevant details to each lender to have a confident comparison.
### Shop around for the best mortgage terms
In addition to comparing rates, it’s essential to shop around for the best mortgage terms.
This includes considering the type of loan, closing costs, and private mortgage insurance.
Different lenders may have additional terms, so it’s crucial to explore multiple options.
Some popular mortgage lenders in Singapore include IDFC FIRST Bank, Ally Bank, and Bank of America.
Taking the time to research and compare the terms offered by each lender can help you secure the best mortgage rate.
### Get pre-approved for a mortgage before you start shopping for a home
Before you start shopping for a home, it’s wise to get pre-approved for a mortgage.
This involves applying for a mortgage with lenders and providing all necessary financial information.
By contacting pre-approved, you’ll know exactly how much you can afford to borrow, which will help you narrow down your home search.
It also gives you an edge when negotiating with sellers, as they know you’re a serious potential buyer.
By addressing these issues beforehand, you can improve your chances of securing a favorable mortgage rate.
By comparing rates from different lenders, shopping around for the best terms, and getting pre-approved for a mortgage, you can set yourself up for success in finding an affordable and suitable home loan.
Remember to thoroughly research each lender, their terms, and the mortgage process to ensure you make informed decisions.
## Conclusion
### Debt-to-income ratio Singapore Conclusion
Calculating your debt-to-income ratio is an essential step in understanding your financial health and determining your ability to take on more debt.
By understanding how much of your income is going towards recurring monthly debt, such as credit card bills or loan payments, you can make more informed decisions about your finances.
In Singapore, the debt-to-income ratio is a crucial factor for lenders when considering loan applications.
Most lenders prefer a ratio of 36 percent or lower, although some may accept a higher percentage for certain types of loans.
It’s essential to calculate your debt-to-income ratio to have a better understanding of where you stand financially and whether you qualify for a loan.
A high debt-to-income ratio can impact your ability to secure a loan or be eligible for specific financial assistance programs.
If your balance exceeds 36 percent, consider options for lowering your debt, such as debt consolidation or seeking debt relief.
By calculating your debt-to-income ratio, you can also identify areas of improvement in your financial situation.
If a significant portion of your income is going towards debt payments, you may need to evaluate your spending habits and find ways to lower your debt or increase your revenue.
Remember that the debt-to-income ratio varies depending on the lender and the type of debt.
For example, the front-end DTI, which includes only your monthly mortgage or rent payment, should ideally be lower than 30 percent.
On the other hand, the total debt-to-income ratio, which consists of all recurring monthly debt, should ideally be lower than 36 percent.
In conclusion, understanding and calculating your debt-to-income ratio is crucial for managing your finances and making informed decisions.
By being aware of how much debt you have relative to your income, you can take steps to lower your DTI and improve your financial health.
Whether you’re considering taking on more debt or looking for ways to reduce your existing debt, monitoring and managing your debt-to-income ratio is an essential part of achieving financial stability.
#### What is a debt-to-income ratio?
A debt-to-income ratio is a financial term that is used to measure the percentage of a person’s monthly income that goes toward paying off debt.
#### How is the debt-to-income ratio calculated?
The debt-to-income ratio is calculated by dividing your total monthly debt payments by your gross monthly income and multiplying the result by 100.
#### Why is the debt-to-income ratio important?
The debt-to-income ratio is important because lenders use it to determine your creditworthiness.
It helps them assess your ability to take on additional debt and make timely payments.
#### How can I lower your debt-to-income ratio?
There are several ways to lower your debt-to-income ratio, such as paying off debt, increasing your income, or reducing your monthly expenses.
#### What is considered a good debt-to-income ratio?
A good debt-to-income ratio is typically below 36%.
Lenders prefer borrowers with lower ratios as it indicates that they have a more remarkable ability to manage their existing debt.
#### Can I use a debt-to-income ratio calculator?
Yes, you can use a debt-to-income ratio calculator to determine your ratio.
#### How does the DTI ratio impact my ability to get a mortgage?
Mortgage lenders use the debt-to-income ratio to assess your ability to repay a loan.
If your balance is too high, it may be easier for you to qualify for a mortgage.
#### What is the difference between the front-end ratio and back-end ratio?
The front-end ratio is a measure of the percentage of your income that goes toward your housing expenses, such as your monthly mortgage payment.
The back-end ratio, on the other hand, includes all of your monthly debt obligations, such as credit card payments, personal loans, and auto loans.
#### How much debt is too much for the debt-to-income ratio?
There is no specific threshold for how much debt is too much for the debt-to-income ratio.
However, a higher percentage means that a more significant portion of your income is going towards debt payments, which may indicate financial stress and make it harder to obtain new loans.
#### Can my debt-to-income ratio impact my credit score?
While your debt-to-income ratio is not directly factored into your credit score calculation, it can indirectly impact your credit score.
For example, if you have a high debt-to-income percentage, it may increase your credit utilization ratio, which can negatively affect your credit score. | 3,677 | 18,741 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2024-30 | latest | en | 0.952989 |
https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/189/2/c/c/ | 1,721,932,940,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763861452.88/warc/CC-MAIN-20240725175545-20240725205545-00391.warc.gz | 729,083,605 | 57,312 | Properties
Label 189.2.c.c Level $189$ Weight $2$ Character orbit 189.c Analytic conductor $1.509$ Analytic rank $0$ Dimension $4$ Inner twists $4$
Related objects
Show commands: Magma / PariGP / SageMath
Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,2,Mod(188,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.188");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: $$N$$ $$=$$ $$189 = 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 189.c (of order $$2$$, degree $$1$$, minimal)
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: no Analytic conductor: $$1.50917259820$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\sqrt{-2}, \sqrt{3})$$ comment: defining polynomial gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} + 4x^{2} + 1$$ x^4 + 4*x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficients of the $$q$$-expansion are expressed in terms of a basis $$1,\beta_1,\beta_2,\beta_3$$ for the coefficient ring described below. We also show the integral $$q$$-expansion of the trace form.
$$f(q)$$ $$=$$ $$q - \beta_1 q^{2} - \beta_{2} q^{5} + ( - \beta_{3} + 1) q^{7} - 2 \beta_1 q^{8}+O(q^{10})$$ q - b1 * q^2 - b2 * q^5 + (-b3 + 1) * q^7 - 2*b1 * q^8 $$q - \beta_1 q^{2} - \beta_{2} q^{5} + ( - \beta_{3} + 1) q^{7} - 2 \beta_1 q^{8} + \beta_{3} q^{10} - \beta_1 q^{11} - \beta_{3} q^{13} + ( - 2 \beta_{2} - \beta_1) q^{14} - 4 q^{16} + 3 \beta_{2} q^{17} + 3 \beta_{3} q^{19} - 2 q^{22} + 2 \beta_1 q^{23} - 2 q^{25} - 2 \beta_{2} q^{26} + 5 \beta_1 q^{29} - \beta_{3} q^{31} - 3 \beta_{3} q^{34} + ( - \beta_{2} + 3 \beta_1) q^{35} + 5 q^{37} + 6 \beta_{2} q^{38} + 2 \beta_{3} q^{40} + 5 \beta_{2} q^{41} + 5 q^{43} + 4 q^{46} - 5 \beta_{2} q^{47} + ( - 2 \beta_{3} - 5) q^{49} + 2 \beta_1 q^{50} + 8 \beta_1 q^{53} + \beta_{3} q^{55} + ( - 4 \beta_{2} - 2 \beta_1) q^{56} + 10 q^{58} + 5 \beta_{2} q^{59} + \beta_{3} q^{61} - 2 \beta_{2} q^{62} - 8 q^{64} + 3 \beta_1 q^{65} + 2 q^{67} + (\beta_{3} + 6) q^{70} - 10 \beta_1 q^{71} - 5 \beta_1 q^{74} + ( - 2 \beta_{2} - \beta_1) q^{77} - 13 q^{79} + 4 \beta_{2} q^{80} - 5 \beta_{3} q^{82} + \beta_{2} q^{83} - 9 q^{85} - 5 \beta_1 q^{86} - 4 q^{88} - 6 \beta_{2} q^{89} + ( - \beta_{3} - 6) q^{91} + 5 \beta_{3} q^{94} - 9 \beta_1 q^{95} + 7 \beta_{3} q^{97} + ( - 4 \beta_{2} + 5 \beta_1) q^{98}+O(q^{100})$$ q - b1 * q^2 - b2 * q^5 + (-b3 + 1) * q^7 - 2*b1 * q^8 + b3 * q^10 - b1 * q^11 - b3 * q^13 + (-2*b2 - b1) * q^14 - 4 * q^16 + 3*b2 * q^17 + 3*b3 * q^19 - 2 * q^22 + 2*b1 * q^23 - 2 * q^25 - 2*b2 * q^26 + 5*b1 * q^29 - b3 * q^31 - 3*b3 * q^34 + (-b2 + 3*b1) * q^35 + 5 * q^37 + 6*b2 * q^38 + 2*b3 * q^40 + 5*b2 * q^41 + 5 * q^43 + 4 * q^46 - 5*b2 * q^47 + (-2*b3 - 5) * q^49 + 2*b1 * q^50 + 8*b1 * q^53 + b3 * q^55 + (-4*b2 - 2*b1) * q^56 + 10 * q^58 + 5*b2 * q^59 + b3 * q^61 - 2*b2 * q^62 - 8 * q^64 + 3*b1 * q^65 + 2 * q^67 + (b3 + 6) * q^70 - 10*b1 * q^71 - 5*b1 * q^74 + (-2*b2 - b1) * q^77 - 13 * q^79 + 4*b2 * q^80 - 5*b3 * q^82 + b2 * q^83 - 9 * q^85 - 5*b1 * q^86 - 4 * q^88 - 6*b2 * q^89 + (-b3 - 6) * q^91 + 5*b3 * q^94 - 9*b1 * q^95 + 7*b3 * q^97 + (-4*b2 + 5*b1) * q^98 $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 4 q^{7}+O(q^{10})$$ 4 * q + 4 * q^7 $$4 q + 4 q^{7} - 16 q^{16} - 8 q^{22} - 8 q^{25} + 20 q^{37} + 20 q^{43} + 16 q^{46} - 20 q^{49} + 40 q^{58} - 32 q^{64} + 8 q^{67} + 24 q^{70} - 52 q^{79} - 36 q^{85} - 16 q^{88} - 24 q^{91}+O(q^{100})$$ 4 * q + 4 * q^7 - 16 * q^16 - 8 * q^22 - 8 * q^25 + 20 * q^37 + 20 * q^43 + 16 * q^46 - 20 * q^49 + 40 * q^58 - 32 * q^64 + 8 * q^67 + 24 * q^70 - 52 * q^79 - 36 * q^85 - 16 * q^88 - 24 * q^91
Basis of coefficient ring in terms of a root $$\nu$$ of $$x^{4} + 4x^{2} + 1$$ :
$$\beta_{1}$$ $$=$$ $$\nu^{3} + 3\nu$$ v^3 + 3*v $$\beta_{2}$$ $$=$$ $$\nu^{2} + 2$$ v^2 + 2 $$\beta_{3}$$ $$=$$ $$\nu^{3} + 5\nu$$ v^3 + 5*v
$$\nu$$ $$=$$ $$( \beta_{3} - \beta_1 ) / 2$$ (b3 - b1) / 2 $$\nu^{2}$$ $$=$$ $$\beta_{2} - 2$$ b2 - 2 $$\nu^{3}$$ $$=$$ $$( -3\beta_{3} + 5\beta_1 ) / 2$$ (-3*b3 + 5*b1) / 2
Character values
We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$$.
$$n$$ $$29$$ $$136$$ $$\chi(n)$$ $$-1$$ $$-1$$
Embeddings
For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.
For more information on an embedded modular form you can click on its label.
comment: embeddings in the coefficient field
gp: mfembed(f)
Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
188.1
0.517638i − 1.93185i − 0.517638i 1.93185i
1.41421i 0 0 −1.73205 0 1.00000 2.44949i 2.82843i 0 2.44949i
188.2 1.41421i 0 0 1.73205 0 1.00000 + 2.44949i 2.82843i 0 2.44949i
188.3 1.41421i 0 0 −1.73205 0 1.00000 + 2.44949i 2.82843i 0 2.44949i
188.4 1.41421i 0 0 1.73205 0 1.00000 2.44949i 2.82843i 0 2.44949i
$$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles
Inner twists
Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
7.b odd 2 1 inner
21.c even 2 1 inner
Twists
By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 189.2.c.c 4
3.b odd 2 1 inner 189.2.c.c 4
4.b odd 2 1 3024.2.k.g 4
7.b odd 2 1 inner 189.2.c.c 4
9.c even 3 2 567.2.o.e 8
9.d odd 6 2 567.2.o.e 8
12.b even 2 1 3024.2.k.g 4
21.c even 2 1 inner 189.2.c.c 4
28.d even 2 1 3024.2.k.g 4
63.l odd 6 2 567.2.o.e 8
63.o even 6 2 567.2.o.e 8
84.h odd 2 1 3024.2.k.g 4
By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
189.2.c.c 4 1.a even 1 1 trivial
189.2.c.c 4 3.b odd 2 1 inner
189.2.c.c 4 7.b odd 2 1 inner
189.2.c.c 4 21.c even 2 1 inner
567.2.o.e 8 9.c even 3 2
567.2.o.e 8 9.d odd 6 2
567.2.o.e 8 63.l odd 6 2
567.2.o.e 8 63.o even 6 2
3024.2.k.g 4 4.b odd 2 1
3024.2.k.g 4 12.b even 2 1
3024.2.k.g 4 28.d even 2 1
3024.2.k.g 4 84.h odd 2 1
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator $$T_{2}^{2} + 2$$ acting on $$S_{2}^{\mathrm{new}}(189, [\chi])$$.
Hecke characteristic polynomials
$p$ $F_p(T)$
$2$ $$(T^{2} + 2)^{2}$$
$3$ $$T^{4}$$
$5$ $$(T^{2} - 3)^{2}$$
$7$ $$(T^{2} - 2 T + 7)^{2}$$
$11$ $$(T^{2} + 2)^{2}$$
$13$ $$(T^{2} + 6)^{2}$$
$17$ $$(T^{2} - 27)^{2}$$
$19$ $$(T^{2} + 54)^{2}$$
$23$ $$(T^{2} + 8)^{2}$$
$29$ $$(T^{2} + 50)^{2}$$
$31$ $$(T^{2} + 6)^{2}$$
$37$ $$(T - 5)^{4}$$
$41$ $$(T^{2} - 75)^{2}$$
$43$ $$(T - 5)^{4}$$
$47$ $$(T^{2} - 75)^{2}$$
$53$ $$(T^{2} + 128)^{2}$$
$59$ $$(T^{2} - 75)^{2}$$
$61$ $$(T^{2} + 6)^{2}$$
$67$ $$(T - 2)^{4}$$
$71$ $$(T^{2} + 200)^{2}$$
$73$ $$T^{4}$$
$79$ $$(T + 13)^{4}$$
$83$ $$(T^{2} - 3)^{2}$$
$89$ $$(T^{2} - 108)^{2}$$
$97$ $$(T^{2} + 294)^{2}$$ | 3,732 | 7,439 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2024-30 | latest | en | 0.545285 |
https://oeis.org/A161980 | 1,708,686,873,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474377.60/warc/CC-MAIN-20240223085439-20240223115439-00577.warc.gz | 454,976,507 | 3,975 | The OEIS is supported by the many generous donors to the OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A161980 a(n) = the smallest positive multiple of n containing {the string made by reversing the order of the binary digits of n, and removing leading 0's} as a substring when a(n) is written in binary. 2
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 55, 12, 91, 14, 15, 16, 17, 18, 57, 20, 21, 110, 253, 24, 275, 182, 27, 28, 87, 30, 31, 32, 33, 34, 455, 36, 333, 114, 741, 40, 1189, 42, 215, 220, 45, 506, 893, 48, 931, 550, 51, 364, 689, 54, 495, 56, 627, 174, 885, 60, 1403, 62, 63, 64 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,2 LINKS Table of n, a(n) for n=1..64. EXAMPLE 13 in binary is 1101, which reversed is 1011. a(13) = the positive multiple of 13 that contains the string 1011 as a substring in its binary representation. a(13) therefore equals 91 = 7*13, which is 1011011 in binary. (Binary 91 actually contains the substring 1011 twice.) CROSSREFS Cf. A030101, A161979. Sequence in context: A062683 A363765 A137857 * A183533 A132576 A161948 Adjacent sequences: A161977 A161978 A161979 * A161981 A161982 A161983 KEYWORD base,nonn AUTHOR Leroy Quet, Jun 23 2009 EXTENSIONS Extended by Ray Chandler, Mar 12 2010 STATUS approved
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified February 23 06:06 EST 2024. Contains 370267 sequences. (Running on oeis4.) | 574 | 1,634 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2024-10 | latest | en | 0.791484 |
https://web2.0calc.com/questions/pre-algebra_1 | 1,563,924,090,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195529737.79/warc/CC-MAIN-20190723215340-20190724001340-00503.warc.gz | 588,426,942 | 5,691 | +0
# pre-algebra
+8
516
1
what is the greatest common factor of 16/36. then simplify it.
Feb 3, 2012
#1
+5
the greatest common factor is 4. 4*4=16 and 9*4=36 so it would be simplified to 4/9
Mar 11, 2015 | 87 | 209 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.640625 | 4 | CC-MAIN-2019-30 | latest | en | 0.91767 |
https://www.java-forums.org/new-java/93893-creating-reverse-list-integer-using-recursion-help.html | 1,586,432,961,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585371833063.93/warc/CC-MAIN-20200409091317-20200409121817-00227.warc.gz | 973,686,346 | 13,504 | # Thread: Creating a reverse List<Integer> using recursion - HELP!
1. Member
Join Date
Apr 2014
Posts
6
Rep Power
0
## Creating a reverse List<Integer> using recursion - HELP!
Can someone help me?
I created this code, seems like it should be working properly and the code is right, but the output is not what it should be.
The action gets a List<Integer> and should make it reversed.
As example: 1 2 3 4 5 ---> 5 4 3 2 1
The Nodes in the new list (lst2) should be in a reversed position.
The code does compile with no errors.
Note: I do have Node<T> and List<T> classes
Java Code:
```public class NodeReverse
{
public static void reverse (List<Integer> lst, Node<Integer> node, int counter, List<Integer> lst2, Node<Integer> pos) // Should make lst = lst2 while lst2 is the opposite to lst
{
node = node.getNext();
counter++;
if(node.getNext()!=null)
reverse(lst, node, counter, lst2, pos);
pos = lst2.insert(pos,node.getInfo());
if(counter==0)
lst = lst2;
}
public static final int Nfor=5, Nnode=10;
public static void main(String[] args)
{
Node<Integer> node = new Node<Integer>(Nnode);
Node<Integer> temp = node;
for(int i=0 ; i<Nfor ; i++) // Setting a new Node<Integer> chain
{
Node<Integer> next = new Node<Integer>((Nnode+i+1));
temp.setNext(next);
temp=temp.getNext();
}
List<Integer> list = new List<Integer>();
Node<Integer> pos = list.getFirst();
for(int i=0 ; i<=Nfor ; i++) // Inserts the Node<Integer> chain into the List<Integer> 'list' and presents it
{'
int info = node.getInfo();
pos = list.insert(pos,info);
System.out.print(info+" "); // Prints: "10 11 12 13 14 15"
node = node.getNext();
}
System.out.println();
List<Integer> list2 = new List<Integer>(); // Creates an empty List<Integer>
Node<Integer> rNode = list.getFirst();
int counter=0;
reverse(list, rNode, counter, list2, null); // Should make the List<Integer> 'list' equals to List<Integer> 'list2'
pos = list.getFirst();
for(int i=0 ; i<=Nfor ; i++) // Presents the new-old List<Integer> 'list'
{
int info = pos.getInfo();
System.out.print(info+" "); // Prints the same: "10 11 12 13 14 15"
pos = pos.getNext();
}
}
}```
The output:
10 11 12 13 14 15
10 11 12 13 14 15
The output I need:
10 11 12 13 14 15
15 14 13 12 11 10
I think the problem is the part where I typed: lst = lst2;
HELP!
Last edited by Ben Bublil; 01-02-2015 at 01:56 PM.
2. ## Re: Creating a reverse List<Integer> using recursion - HELP!
The posted code doesn't compile without errors.
Please fix the errors and make sure all class definitions are provided.
Also add some comments describing what the statements in the code are trying to do.
3. Senior Member
Join Date
Jan 2013
Location
Northern Virginia, United States
Posts
6,226
Rep Power
14
## Re: Creating a reverse List<Integer> using recursion - HELP!
There must be more to this than just what you stated in the title. Why do you have a class Node? And since you can't instantiate an interface that code could not possibly be correct.
Regards,
Jim
#### Posting Permissions
• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
• | 871 | 3,137 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2020-16 | longest | en | 0.425316 |
http://www.slideserve.com/tocho/lesson-4-2-triangle-congruence-sss-sas-asa-aas | 1,508,590,835,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187824775.99/warc/CC-MAIN-20171021114851-20171021134851-00799.warc.gz | 571,063,849 | 13,142 | Lesson 4-2: Triangle Congruence – SSS, SAS, ASA, & AAS
1 / 11
# Lesson 4-2: Triangle Congruence – SSS, SAS, ASA, & AAS - PowerPoint PPT Presentation
Lesson 4-2: Triangle Congruence – SSS, SAS, ASA, & AAS. Vocab SSS (side-side-side) congruence Included angle SAS (side-angle-side) congruence. Draw the following figures using a ruler. Draw a triangle, measure its lengths
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
## PowerPoint Slideshow about ' Lesson 4-2: Triangle Congruence – SSS, SAS, ASA, & AAS' - tocho
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Lesson 4-2: Triangle Congruence – SSS, SAS, ASA, & AAS
Vocab
SSS (side-side-side) congruence
Included angle
SAS (side-angle-side) congruence
Draw the following figures using a ruler
• Draw a triangle, measure its lengths
• Draw another triangle in a different “manner” using the same length sides.
• Are the 2 triangles different? Are they the same shape, same size?
They’re
Congruent!
SSS congruence
• If 3 sides are congruent to other 3 sides
→ ∆’s congruent bySSS (side-side-side)
Rule
Draw the following figures using a ruler
• A triangle with a 900 angle. Measure only the 2 sides that touch the 900
• Draw another triangle in a different “manner” using the 2 measured lengths and 900 angle between them
• Are the 2 triangles different? Are they the same shape, same size?
They’re
Congruent!
SAS congruence
• If 2 sides and the included angle between them are congruent to other 2 sides and the included angle
→ ∆’s congruent by SAS (side-angle
side) Rule
→ Look for SAS – list S or A in order
8
8
750
750
12
12
Examples
• In ∆VGB, which sides include B?
2. In ∆STN, which angle is included between
and ?
3. Which triangles can you prove congruent? Tell whether you would use the SSS or SAS Postulate.
Y
A
P
X
B
D
4. What other information do you need to prove ∆DWO∆DWG?
5. Can you prove ∆SED ∆BUT from the information given? Explain.
O
G
W
U
T
D
E
S
B
Proving Congruence in ∆’s
• Go in a circle around triangle naming markings or measures in order (S or A)
• ∆’s congruent if :
• SSS : all 3 sides
• SAS : an angle between (included) 2 sides
• ASA : a side between 2 angles
• AAS : a side after 2 angles
NEW ONES!
Hints
• Use facts/rules to find any missing angle or side measures first
• Is a side congruent to itself?
• Can you use any angle facts to find missing angle measures?
• Look for parallel lines
Which side is included between R and F in∆FTR?
• 2. Which angles in ∆ STU include ?
• Tell whether you can prove the triangles congruent by ASA or
• AAS. If you can, state a triangle congruence and the postulate
• or theorem you used. If not, write not possible.
• 3.
• 4.
• 5.
Q
H
G
P
I
R
P
L
Quiz
Tomorrow!
4-1, 4-2
4-3
Y
A
A
B
C
X | 971 | 3,278 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.21875 | 4 | CC-MAIN-2017-43 | latest | en | 0.863869 |
http://mathhelpforum.com/trigonometry/168288-trigonometry-print.html | 1,511,096,466,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934805578.23/warc/CC-MAIN-20171119115102-20171119135102-00775.warc.gz | 196,349,397 | 2,753 | # Trigonometry
• Jan 13th 2011, 09:10 PM
Harolld
Trigonometry
Angle measurements r taken from two points on directly opposite sides of a tree. How high is the tree??
tree is in the middle. the angle above the tree is 115
and the two side angles are 35 and 30.
the tree is 20.6m tall but how do u find that answer???
• Jan 14th 2011, 12:12 AM
earboth
Quote:
Originally Posted by Harolld
Angle measurements r taken from two points on directly opposite sides of a tree. How high is the tree??
tree is in the middle. the angle above the tree is 115
and the two side angles are 35 and 30.
the tree is 20.6m tall but how do u find that answer???
Is this the complete text of the question?
With the given values the tree can have any height from bonsai to sequoia. In my opinion there is missing a length (Thinking) | 227 | 814 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2017-47 | longest | en | 0.921329 |
http://www.gmathacks.com/officialguide12ed/data-sufficiency-040-explanation.html | 1,500,936,618,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549424931.1/warc/CC-MAIN-20170724222306-20170725002306-00332.warc.gz | 450,922,858 | 5,550 | ### Bookshelf
Total GMAT Math Jeff's complete Quant guide, on sale now!
Total GMAT Verbal Everything you need to ace GMAT Verbal!
New: GMAT 111 Improve every aspect of your GMAT prep!
1,800 Practice Math Questions
GMAT Official Guide
OG Math | OG Verbal
Guides To the Official Guide
Free: OG12 explanations!
GMAT Question of the Day
Beginner's Guide to the GMAT
GMAT Hacks Affiliate Program
### Resources
MBA.com
GMAC Official Site
Free GMATPrep Practice Tests
Stacy Blackman Consulting
Book | Essay Guides
GRE HQ
Total GRE Math
Ultimate SAT Verbal
## Official Guide Explanation:Data Sufficiency #40
Background
This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.
These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.
Question: 40
Page: 276
Difficulty: 5 (Moderate)
Category 1: Word Problems > Data Interpretation >
Explanation: To find the value of x, you'll need to find the distance between R and T. Note that no other distances--for instance the distance between R and S combined with the distance between S and T--would be sufficient to answer the question, since we don't know if that would be the most direct route between R and T.
Statement (1) compares the lengths of the routes betwen S and T and S and R, which would allow you to solve for y, but does nothing to help you solve for x. Statement (2), however, is sufficient: the distance between T and U is 69, so if 69 is 1.5 times the distance beween R and T, you can find that distance. Choice (B) is correct.
You should follow me on Twitter. While you're at it, take a moment to subscribe to GMAT Hacks via RSS or Email.
Total GMAT Math The comprehensive guide to the GMAT Quant section. It's "far and away the best study material available," including over 300 realistic practice questions and more than 500 exercises! Click to read more. | 523 | 2,248 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.890625 | 4 | CC-MAIN-2017-30 | longest | en | 0.917162 |
http://mathhelpforum.com/calculus/48600-area-surfaces-revolution.html | 1,481,395,670,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698543434.57/warc/CC-MAIN-20161202170903-00158-ip-10-31-129-80.ec2.internal.warc.gz | 171,139,682 | 11,699 | # Thread: Area of surfaces of revolution
1. ## Area of surfaces of revolution
HELP! I'm in Calc BC, i need step by step help
Problem: Set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the x-axis.
41. y=((x^3)/6)+((1)/(2x)), [1,2]
Set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the y-axis
43. y=(x^1/3)+2
x values [2,8]
y values [3,4]
2. Ok start with the formula for the SA of a solid of revolution around the x-axis. $S.A. = \int_{a}^{b} 2\pi f(x)\sqrt{1+f'[x]^2}dx$ Can you setup the integrals and try them?
3. i know the eqn and all that...i just need help with the step by step...
4. I'm on this to!
I did it like this (i'd get a second opinion since i'm new to this topic):
5. Originally Posted by Jameson
Ok start with the formula for the SA of a solid of revolution around the x-axis. $S.A. = \int_{a}^{b} 2\pi{\color{red}f[x]}\sqrt{1+f'[x]^2}dx$ Can you setup the integrals and try them?
You forgot that vital term!
--Chris
6. Originally Posted by vstexas09
HELP! I'm in Calc BC, i need step by step help
Problem: Set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the x-axis.
41. y=((x^3)/6)+((1)/(2x)), [1,2]
Let $y=f(x)=\tfrac{1}{6}x^3+\frac{1}{2x}$
Thus, $f'(x)=\tfrac{1}{2}x^2-\frac{1}{2x^2}$
Therefore, $[f'(x)]^2=\left(\tfrac{1}{2}x^2-\tfrac{1}{2}x^{-2}\right)^2=\tfrac{1}{4}x^4-\tfrac{1}{2}+\tfrac{1}{4}x^{-4}$
Plugging this into the surface area equation, we get:
\begin{aligned}S.A.&=2\pi\int_1^2 f(x)\sqrt{1+\left(\tfrac{1}{4}x^4-\tfrac{1}{2}+\tfrac{1}{4}x^{-4}\right)}\,dx\\
&=2\pi\int_1^2 f(x)\sqrt{\tfrac{1}{4}x^4+\tfrac{1}{2}+\tfrac{1}{4 }x^{-4}}\,dx\end{aligned}
Note that $\tfrac{1}{4}x^4+\tfrac{1}{2}+\tfrac{1}{4}x^{-4}$ is a perfect square: $\tfrac{1}{4}x^4+\tfrac{1}{2}+\tfrac{1}{4}x^{-4}=\left(\tfrac{1}{2}x^2+\tfrac{1}{2}x^{-2}\right)^2$
Thus, the integral becomes:
\begin{aligned}S.A.&=2\pi\int_1^2 f(x)\sqrt{\left(\tfrac{1}{2}x^2+\tfrac{1}{2}x^{-2}\right)^2}\,dx\\
&=2\pi\int_1^2 f(x) \left(\tfrac{1}{2}x^2+\tfrac{1}{2}x^{-2}\right)\,dx\end{aligned}
Since, $f(x)=\tfrac{1}{6}x^3+\frac{1}{2x}$, we see that the integral transforms into
\begin{aligned}S.A.&=2\pi\int_1^2\left(\tfrac{1}{1 2}x^5+\tfrac{1}{3}x^3+\tfrac{1}{4}x^{-3}\right)\,dx\\
&=\frac{\pi}{6}\int_1^2 \left(x^5+4x^2+3x^{-3}\right)\,dx\end{aligned}
Take it from here. You should be able to do this!
I hope this helps!
--Chris
7. Originally Posted by Chris L T521
You forgot that vital term!
--Chris
You are right! That was a very bad typo. Thank you. Fixed now.
8. darn it! That means i've just found the length of it!
I worked it out again and got 115pi/36.
I would post my working except I did it on a whiteboard. | 1,088 | 2,823 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.15625 | 4 | CC-MAIN-2016-50 | longest | en | 0.735915 |
http://forums.wolfram.com/mathgroup/archive/2007/Feb/msg00354.html | 1,590,499,336,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347390758.21/warc/CC-MAIN-20200526112939-20200526142939-00570.warc.gz | 49,565,207 | 8,110 | Re: Coaxing N[] to work
• To: mathgroup at smc.vnet.net
• Subject: [mg73410] Re: Coaxing N[] to work
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Thu, 15 Feb 2007 05:10:23 -0500 (EST)
• References: <equo6r\$in0\$1@smc.vnet.net>
```N is often the subject of queries in this forum especially for
persons
not so experienced in Mathematica.
In your example N works in the desirable way.
Note that you have used inexact numbers like 2.0 and 1.0 of
MachinePrecision
In[82]:=
Precision[1.0]
Out[82]=
MachinePrecision
and in the end you want you want your output with almost 30 digits of
precision!
3=2E0 (also 3.) IS different from 3
In[83]:=
Out[83]=
{Real, Real, Integer}
Also
In[84]:=
Precision /@ {3.2, 3.23456789023, 44/3, Sqrt[3.], 3., 3, Sqrt[3]}
Out[84]=
{MachinePrecision, MachinePrecision, Infinity, MachinePrecision,
MachinePrecision, Infinity,Infinity}
So the correct code here is
In[85]:=
x = {2, 3, 5};
A = {{6, 2, 1}, {2, 3, 1}, {1, 1, 1}};
For[k = 0, k < 15, ++k, lambda = x . A . x/x . x; y = LinearSolve[A,
x]; x = y/Norm[y, Infinity]; ]
N[lambda, 30]
Out[88]=
0=2E578933385691052787623495851171798813974781362303`30.
In[89]:=
Precision[%]
Out[89]=
30.
Execute the following command for more details (or search within the
archives of this forum)
FrontEndExecute[{HelpBrowserLookup["MainBook", "3.1"]}]
Also
http://library.wolfram.com/infocenter/Demos/91/
Best Regards
Dimitris
first learn Mathematica and after criticize it!
This attitude will make better and better in its using!
=CF/=C7 p at dirac.org =DD=E3=F1=E1=F8=E5:
> Sometimes N[,] doesn't appear to work. Like here:
>
>
> x = {2.0, 3.0, 5.0};
> A = { {6.0, 2.0, 1.0}, {2.0, 3.0, 1.0}, {1.0, 1.0, 1.0} };
> For[ k=0, k<15, ++k,
> lambda = x.A.x/(x.x);
> y = LinearSolve[A,x];
> x = y / Norm[y,Infinity];
> ]
> N[lambda, 30]
>
>
> The output is:
>
> Out[5]= 0.578933
>
> I was expecting 30 digits. Why did N[] ignore my request for 30 digits?
```
• Prev by Date: Re: MathPlayerSetup installation
• Next by Date: Re: Comments in the front end
• Previous by thread: Re: Coaxing N[] to work
• Next by thread: Re: Coaxing N[] to work | 784 | 2,146 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2020-24 | longest | en | 0.71938 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.