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://learn.saylor.org/mod/book/view.php?id=31122 | 1,723,306,737,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640810581.60/warc/CC-MAIN-20240810155525-20240810185525-00219.warc.gz | 281,206,471 | 21,837 | ## Elasticity: A Measure of Response
Read this chapter to learn about the concept of elasticity. Be sure to read Sections 5.1-5.4 following the introduction.
### Elasticity: A Measure of Response
#### Start Up: Raise Fares? Lower Fares? What's a Public Transit Manager To Do?
Imagine that you are the manager of the public transportation system for a large metropolitan area. Operating costs for the system have soared in the last few years, and you are under pressure to boost revenues. What do you do?
An obvious choice would be to raise fares. That will make your customers angry, but at least it will generate the extra revenue you need – or will it? The law of demand says that raising fares will reduce the number of passengers riding on your system. If the number of passengers falls only a little, then the higher fares that your remaining passengers are paying might produce the higher revenues you need. But what if the number of passengers falls by so much that your higher fares actually reduce your revenues? If that happens, you will have made your customers mad and your financial problem worse!
Maybe you should recommend lower fares. After all, the law of demand also says that lower fares will increase the number of passengers. Having more people use the public transportation system could more than offset a lower fare you collect from each person. But it might not. What will you do?
Your job and the fiscal health of the public transit system are riding on your making the correct decision. To do so, you need to know just how responsive the quantity demanded is to a price change. You need a measure of responsiveness.
Economists use a measure of responsiveness called elasticity. Elasticity is the ratio of the percentage change in a dependent variable to a percentage change in an independent variable. If the dependent variable is y, and the independent variable is x, then the elasticity of y with respect to a change in x is given by:
$\mathrm{e} \mathrm{y}, \mathrm{x}=\% \text { change in } \mathrm{y} / \% \text { change in } \mathrm{x}$
A variable such as y is said to be more elastic (responsive) if the percentage change in y is large relative to the percentage change in x. It is less elastic if the reverse is true.
As manager of the public transit system, for example, you will want to know how responsive the number of passengers on your system (the dependent variable) will be to a change in fares (the independent variable). The concept of elasticity will help you solve your public transit pricing problem and a great many other issues in economics. We will examine several elasticities in this chapter – all will tell us how responsive one variable is to a change in another.
### LEARNING OBJECTIVES
1. Explain the concept of price elasticity of demand and its calculation.
2. Explain what it means for demand to be price inelastic, unit price elastic, price elastic, perfectly price inelastic, and perfectly price elastic.
3. Explain how and why the value of the price elasticity of demand changes along a linear demand curve.
4. Understand the relationship between total revenue and price elasticity of demand.
5. Discuss the determinants of price elasticity of demand.
We know from the law of demand how the quantity demanded will respond to a price change: it will change in the opposite direction. But how much will it change? It seems reasonable to expect, for example, that a 10% change in the price charged for a visit to the doctor would yield a different percentage change in quantity demanded than a 10% change in the price of a Ford Mustang. But how much is this difference?
To show how responsive quantity demanded is to a change in price, we apply the concept of elasticity. The price elasticity of demand for a good or service, eD, is the percentage change in quantity demanded of a particular good or service divided by the percentage change in the price of that good or service, all other things unchanged. Thus we can write
Equation 5.1
$\mathrm{e} \mathrm{D}=\% \text { change in quantity demanded / % change in price }$
Because the price elasticity of demand shows the responsiveness of quantity demanded to a price change, assuming that other factors that influence demand are unchanged, it reflects movements along a demand curve. With a downward-sloping demand curve, price and quantity demanded move in opposite directions, so the price elasticity of demand is always negative. A positive percentage change in price implies a negative percentage change in quantity demanded, and vice versa. Sometimes you will see the absolute value of the price elasticity measure reported. In essence, the minus sign is ignored because it is expected that there will be a negative (inverse) relationship between quantity demanded and price. In this text, however, we will retain the minus sign in reporting price elasticity of demand and will say "the absolute value of the price elasticity of demand" when that is what we are describing.
Be careful not to confuse elasticity with slope. The slope of a line is the change in the value of the variable on the vertical axis divided by the change in the value of the variable on the horizontal axis between two points. Elasticity is the ratio of the percentage changes. The slope of a demand curve, for example, is the ratio of the change in price to the change in quantity between two points on the curve. The price elasticity of demand is the ratio of the percentage change in quantity to the percentage change in price. As we will see, when computing elasticity at different points on a linear demand curve, the slope is constant – that is, it does not change – but the value for elasticity will change. | 1,187 | 5,723 | {"found_math": true, "script_math_tex": 2, "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-2024-33 | latest | en | 0.920309 |
https://unmethours.com/question/26145/plug-loads-detailed-yearly-consumption/ | 1,639,025,586,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363659.21/warc/CC-MAIN-20211209030858-20211209060858-00239.warc.gz | 620,561,911 | 14,889 | Question-and-Answer Resource for the Building Energy Modeling Community
Get s tarted with the Help page
# plug loads detailed Yearly consumption
I am looking for simple way to calculate yearly electrical consumption of specific plug load in order to calibrate my schedules and loads in OS. Any Idea how to do that? Looking for some way to get that from the output of the simulation.
edit retag close merge delete
Sort by ยป oldest newest most voted
1. You need to calculate the total peak demand of the specific plug load for a specific area type. Ex: 1W/sf of plug load density for 2,000 sf space. If you multiply the numbers, you get 2,000 W or 2Kw of peak demand for plug loads.
2. You need to calculate for how many hours your plug loads are turned on. You can calculate it easily by looking at the plug load schedules.
2.1. Calculate the number of hours for weekdays: Simply add the fractions for day (24 hour values) schedule. Ex: 0.1+0.2+0.8+0.9..........+0.4 = 15.5 hours. It means overall, the plug loads are ON for 15.6 hours (Call it A1). Do similar work for the weekends (only if the schedule is different for weekends). Lets say the value is 8 hours (Call is B1) for sat & sunday both.
2.2. Calculate total number of hours in a year when the plug loads are ON. Multiply A1 by total number of weekdays in the year, and B1 by number of weekends. Make sure you exclude the public holidays too (if). There are 260 weekdays in 2017, (15.6260) + (8105) = 4,896 hours out of 8,760.
1. Multiply 4,896 by 2Kw = 9,792 kWh.
You do exactly same calculations for lighting or any other space loads.
more
@ Harshul Singhal As much as the answer is correct it is very tedious to carry that on 20 different complicated schedules (with many day schedules). I am looking for a way to get the data as a part of the report.
( 2017-08-19 10:59:41 -0600 )edit | 488 | 1,861 | {"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} | 3.484375 | 3 | CC-MAIN-2021-49 | longest | en | 0.911853 |
https://estebantorreshighschool.com/faq-about-equations/percent-change-equation.html | 1,660,819,804,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882573193.35/warc/CC-MAIN-20220818094131-20220818124131-00372.warc.gz | 247,370,560 | 11,233 | ## How do you calculate percent change?
Next, divide the increase by the original number and multiply the answer by 100: % increase = Increase ÷ Original Number × 100. If the answer is a negative number, that means the percentage change is a decrease.
## How do you calculate percent change over time?
How do I calculate percentage increase over time?Divide the larger number by the original number.Subtract one from the result of the division.Multiply this new number by 100. Divide the percentage change by the period of time between the two numbers.You now have the percentage increase over time.
## What is the percent equation formula?
How to find what percent of X is Y. Use the percentage formula: Y/X = P% Example: What percent of 60 is 12? Important! The result will always be in decimal form, not percentage form.
## What is the percent weight change formula?
The formula to calculate your weight loss percentage is: lbs lost divided by starting weight. Then, multiply the result by 100. So, if your starting weight is 150lbs and you lost 5lbs, you’ve lost 3.33% of your body weight.
30%
## How do I work out a percentage of two numbers?
Learning how to calculate the percentage of one number vs. another number is easy. If you want to know what percent A is of B, you simple divide A by B, then take that number and move the decimal place two spaces to the right. That’s your percentage!
## How much is a 2.5 percent raise?
For example, if your union is negotiating a 2.5% increase in annual salary and you’re taking home \$2,500 per month at 30 hours per week, you can expect a \$62 raise in your monthly payments (which comes to a total of \$2,562).
## Are all percentages reversible?
And it is: Percentages are reversible. So, 16% of 25 is the same thing as 25% of 16. Now, the trick isn’t great for numbers where you can’t do either percentage in your head . . . like 17% of 39 or 39% of 17.
## How do you figure percentages on a calculator?
How to Calculate Percentages with a CalculatorIf your calculator has a “%” button. Let’s say you wanted to find 19 percent of 20. Press these buttons: 1 9 % * 2 0 = If your calculator does not have a “%” button. Step 1: Remove the percent sign and add a couple of zeros after the decimal point. 19% becomes 19.00.
You might be interested: What is a quadratic equation
40
## How do you find the tip percentage in math?
In general, the tip amount is the cost times 0. xx and your total including tip, is the cost times 1. xx where xx = the percent you want to leave. If you want to leave a 20% tip, multiply the cost by 0.20 to get the tip amount or multiply the cost by 1.20 to get the total including tip.
## How do you add 30% to a price?
How to add or subtract percentages. If your calculator does not have a percent key and you want to add a percentage to a number multiply that number by 1 plus the percentage fraction. For example 25000+9% = 25000 x 1.09 = 27250. To subtract 9 percent multiply the number by 1 minus the percentage fraction.
## How do you calculate percentage of ideal body weight?
(Percent Ideal Body Weight = (current weight/ ideal weight X 100) A loss of over 10% body weight in 6 months is considered a severe weight loss and may indicate malnutrition.
## How do you calculate ideal body weight?
Ideal body weight is computed in men as 50 + (0.91 × [height in centimeters − 152.4]) and in women as 45.5 + (0.91 × [height in centimeters − 152.4]). A simple alternative would be to compute ideal body weight as the weight corresponding to an ideal body mass index of 22 kg/m2.
### Releated
#### Depreciation equation
What are the 3 depreciation methods? There are three methods for depreciation: straight line, declining balance, sum-of-the-years’ digits, and units of production. What do you mean by depreciation? Definition: The monetary value of an asset decreases over time due to use, wear and tear or obsolescence. This decrease is measured as depreciation. How do you […]
#### Polar to cartesian equation calculator wolfram
How do you convert polar to Cartesian? Summary: to convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y) 😡 = r × cos( θ )y = r × sin( θ ) How do you find the polar Cartesian equation? Convert the polar equation r = 2sec θ to a rectangular equation, and draw its corresponding […] | 1,048 | 4,337 | {"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} | 4.34375 | 4 | CC-MAIN-2022-33 | latest | en | 0.909838 |
https://www.pcreview.co.uk/threads/histogram-count-programming-problem.992565/ | 1,721,599,942,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517796.21/warc/CC-MAIN-20240721213034-20240722003034-00582.warc.gz | 784,619,021 | 12,652 | # Histogram / Count Programming Problem
J
#### Jan Grinwis
Hi,
I have a large excel sheet (8000+ lines)
The sheet is filled with error messages etc. etc.
I want to build a chart of how many errors are there in a certain
date/time interval.
Simplified Data example:
Date Start Finish Remark
31-07-2004 23:03:00 23:30:00 Error 1
01-08-2004 00:00:00 00:15:00 Error 2
01-08-2004 00:12:00 00:25:00 Error 3
01-08-2004 01:05:00 01:31:00 Error 4
01-08-2004 01:50:00 01:58:00 Error 5
01-08-2004 01:45:00 02:02:00 Error 6
01-08-2004 01:30:00 02:00:00 Error 7
01-08-2004 01:38:00 02:10:00 Error 8
01-08-2004 03:00:00 03:15:00 Error 9
01-08-2004 04:00:00 04:12:00 Error 10
31-07-2004 06:25:00 06:45:00 Error 11
31-07-2004 06:30:00 06:45:00 Error 12
31-07-2004 06:40:00 07:00:00 Error 13
01-08-2004 04:39:00 04:46:00 Error 14
The chart should be like:
Xax is Date/time-interval
Yax is how many errors active
for instance:
Interval Errors
in the interval between 01-08-2004 01:31-01:35 2 '(error4 & 7)
01-08-2004 01:36-01:40 2 '(error7 & 8)
01-08-2004 01:41-01:45 3 '(error6 & 7 & 8)
Does anyone have a smart solution for this problem.
Jan
R
#### Rob van Gelder
I have a formula on my website: Hours affected by dates.
It's not a drop-in solution, but you might be able to get something working
from it. | 538 | 1,303 | {"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} | 2.515625 | 3 | CC-MAIN-2024-30 | latest | en | 0.669397 |
http://www.slidesearchengine.com/slide/michael-martinez-math-module-3-presentation-on-place-value-2nd-grade | 1,506,340,018,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818691476.47/warc/CC-MAIN-20170925111643-20170925131643-00687.warc.gz | 556,704,734 | 6,838 | # Michael Martinez Math Module 3 Presentation on Place Value 2nd Grade
50 %
50 %
Information about Michael Martinez Math Module 3 Presentation on Place Value 2nd Grade
Education
Published on February 16, 2014
Author: mike25
Source: slideshare.net
## Description
2nd Grade Math Module 3: Place Value by Michael Martinez
Math Module 3: Place Value 2nd By Mr. Michael Martinez Grade Meadow Hill School Michael Martinez
Problem 1: Read, Solve and Show Your Work in the Space Below. Peter had 48 baseball cards. He gave some to Mike and then he had 35 left. How many cards did Peter give to Mike? Michael Martinez
Problem 2: What number is shown below?____________________ Michael Martinez
Problem 3: Show the number 325 by drawing the base ten blocks. Michael Martinez
Problem 4: Fill in the missing numbers for each box. 5 10 15 20 Michael Martinez
Problem 5: Write 649 in expanded form. ____________________ ____________________ ____________________ ____________________ Michael Martinez
Problem 6: Which comparing symbol >, =, and < makes it correct? 854 O 842 Michael Martinez
Problem 7: Add and Solve. Show Your Work. 327 +135 Michael Martinez
Problem 8: Subtract and Solve. Show Your Work. 580 - 325 Michael Martinez
Problem 9: Fill in the missing numbers on the number line. 140--____--160--____--____--190--____--____-- Michael Martinez
Problem 10:Read and Circle what operation to use to solve the problem. Then explain why in the lines below. Maria bought 125 sunflower seeds. She gave some to Michelle to plant and then she had 100 left. How many seeds did Maria give to Michelle? Addition or Subtraction Explain:___________________________________ __________________________________________ __________________________________________ __________________________________________ __________________________________________ Michael Martinez
Place Value Games • • • • Games http://www.abcya.com/place_value_hockey.h tm http://www.ixl.com/math/grade-2 http://www.sheppardsoftware.com/mathgam es/menus/place_value.htm Video http://www.youtube.com/watch?v=omkDLmf vetk Michael Martinez
User name: Comment:
## Related presentations
September 25, 2017
#### Best Oracle course training institute ameerpet Hyd...
September 25, 2017
#### In the good English Private Teacher with Brainy Tu...
September 25, 2017
#### Cima F1 Dumps
September 25, 2017
#### Methods by Which Schools Ensure Comprehensive Deve...
September 25, 2017
#### Need Help in Math Coaching at Vienna? Contact Here
September 25, 2017
## Related pages
### Grade 3 Mathematics Module 1 | EngageNY
DDI Presentations; Video Library . ... Grade 3 Mathematics Module 1: ... Math; Operations & Algebraic Thinking; Grade(s):
### Grade 4 Mathematics Module 3 | EngageNY
Grade 4 Module 3: Multi-Digit ... In this 43-day module, students use place value understanding and visual representations to solve ... Math; Grade(s ...
### 2nd Grade Everyday Mathematics at Home
2nd Grade Everyday Mathematics at Home. Select a Unit; Unit 1. Numbers and Routines. Unit 2. Addition and Subtraction Facts. Unit 3. Place Value, Money ...
### Expanded Form Video - 1st and 2nd Grade Math - YouTube
This video teaches expanded form to kids and how each digit has a different value. This math concept takes place value into action by spreading ...
### Grade 2 maths - IXL | Maths and English Practice
Welcome to IXL's grade 2 maths page. ... Here is a list of all of the maths skills students learn in grade 2! ... L.3 Place value models ...
### Place Value Games for Children in 1st to 7th Grade To Test ...
2nd Grade. Games; Quizzes; New Worksheets; Worksheets; 3rd Grade. Games; ... 1 st to 7 th Grade. Place value math games for children in 1st grade, 2nd ...
### Common Core Navigator, Math#2 | LearnZillion
Common Core Navigator for Math, Math#2. x. Delete All. Menu. ... By end of Grade 2, ... Use place value understanding and properties of operations to add ... | 938 | 3,956 | {"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} | 4.5625 | 5 | CC-MAIN-2017-39 | longest | en | 0.744027 |
https://writerbay.net/identify-the-relationship-between-induction-of-labour-and-caesarean-section-births/ | 1,603,768,785,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107893011.54/warc/CC-MAIN-20201027023251-20201027053251-00331.warc.gz | 608,711,705 | 13,903 | identify the relationship between induction of labour and caesarean section births.
A study seeks to identify the relationship between induction of labour and caesarean section births. Data are collected about 500 births. Variables were recorded about whether induction was required (yes/no) and whether a caesarean section was required (yes/no).
What is the most appropriate statistical test to test the relationship between these two variables?
T-Test Binary logistical regression ANOVA Chi-squared
1 points
QUESTION 2
1. Researchers want to know more about the reasons people choose to purchase different levels of private health insurance. They have a data set for 1000 people. The data set includes a variable that shows how much each person spent on private health insurance in the previous year (measured in whole dollars). The data set also contains a variable that breaks people into the following income brackets:
• less than \$30,000;
• \$30,001 to \$70,000;
• \$70,001 to \$100,000;
• over \$100,000
To test whether income predicts expenditure on insurance, what is the most appropriate statistical test?
Multinomial logistic regression ANOVA Linear regression T-test
1 points
QUESTION 3
1. Janene is interested in factors that predict success in the game of rugby. Her hypothesis is that those who larger players (measured in kilograms) will score more points over the season than smaller players.What statistical test is most appropriate for her to use to test her hypothesis?
Multinomial logistical regression T-Test Chi-squared Linear regression
1 points
QUESTION 4
1. Courtnie is interested in the reading habits of children who are currently studying at home. Based o her literature review, Courtnie hypothesises that children between the ages of eight and twelve, who do not own their own technological device will spend more time reading books (measured in minutes per week) than children in the same age range who have their own device.What is the most appropriate statistical test for Courtnie to state she is using in her research proposal?
Binary logistical regression Linear regression Chi squared T-test | 438 | 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} | 3.265625 | 3 | CC-MAIN-2020-45 | latest | en | 0.944984 |
https://oeis.org/A238133 | 1,547,695,155,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583658681.7/warc/CC-MAIN-20190117020806-20190117042806-00402.warc.gz | 601,154,138 | 4,701 | This site is supported by donations to The OEIS Foundation.
Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A238133 Difference between A238131(n) and A238132(n). 2
0, 1, 1, -1, -1, -3, 0, -2, 1, 2, 1, 2, 4, 1, -1, 4, -2, -1, -3, -1, -2, -2, -6, 0, -1, 1, -4, 0, 3, 2, 2, 2, 3, 0, 4, 7, 0, 0, 2, -3, 7, -2, -1, -3, -2, -4, 0, -3, -3, -2, -1, -10, -1, 0, 1, -1, 0, -6, 2, 2, 0, 4, 3, 4, 0, 2, 4, 3, 0, 5, 8, 2, 0, 1, -1, 1, -3 (list; graph; refs; listen; history; text; internal format)
OFFSET 0,6 COMMENTS Difference between the number of parts in all partitions of n into odd number of distinct parts and the number of parts in all partitions of n into even number of distinct parts. The convolution of A000005 and A010815. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 Mircea Merca, A new look on the generating function for the number of divisors, Journal of Number Theory, Volume 149, April 2015, Pages 57-69. Mircea Merca, Combinatorial interpretations of a recent convolution for the number of divisors of a positive integer, Journal of Number Theory, Volume 160, March 2016, Pages 60-75, difference s_o(n)-s_e(n). Eric Weisstein's World of Mathematics, q-Polygamma Function, q-Pochhammer Symbol. FORMULA a(n) = Sum_{k=0..A235963(n)-1} (-1)^A110654(k) * A000005(n-A001318(k)). G.f.: Product_{k>=1} (1-x^k) * Sum_{k>=1} x^k/(1-x^k). G.f.: (x)_inf * (log(1-x) + psi_x(1))/log(x), where psi_q(z) is the q-digamma function, (q)_inf is the q-Pochhammer symbol (the Euler function). MAPLE A238133 := proc(n) add( numtheory[tau](k)*A010815(n-k), k=0..n) ; end proc: # R. J. Mathar, Jun 18 2016 # second Maple program: b:= proc(n, i) option remember; `if`(i*(i+1)/2n, 0, (p-> [p[2], p[1], p[4]+p[2], p[3]+p[1]])(b(n-i, i-1))))) end: a:= n-> (p-> p[4]-p[3])(b(n\$2)): seq(a(n), n=0..100); # Alois P. Heinz, Jun 18 2016 MATHEMATICA Table[SeriesCoefficient[QPochhammer[x] (Log[1 - x] + QPolyGamma[1, x])/Log[x], {x, 0, n}], {n, 0, 80}] (* Vladimir Reshetnikov, Nov 20 2016 *) CROSSREFS Cf. A000005, A001318, A010815, A110654, A235963, A238131, A238132. Sequence in context: A100950 A021335 A089595 * A317922 A194808 A268464 Adjacent sequences: A238130 A238131 A238132 * A238134 A238135 A238136 KEYWORD sign,look AUTHOR Mircea Merca, Feb 18 2014 STATUS approved
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.) | 1,055 | 2,788 | {"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} | 3.203125 | 3 | CC-MAIN-2019-04 | latest | en | 0.556453 |
http://www.openmiddle.com/exponent-maximum-value/ | 1,558,949,413,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232262311.80/warc/CC-MAIN-20190527085702-20190527111702-00532.warc.gz | 328,405,720 | 19,210 | Home > Grade 8 > Expressions & Equations > Exponent (Maximum Value)
# Exponent (Maximum Value)
Directions: Use the digits 1 to 9, at most one time each, to fill in the boxes to make a result that has the greatest value possible.
### Hint
How does changing the base affect the value?
How does changing the exponent affect the value?
Initially, some students may think that the answer is 8^9. This breaks the structure of the problem, as the result has to be 3-digits.
The largest possible 3-digit result is 729 from 3^6 = 729.
Source: Robert Kaplinsky
## Square Root Expression
Directions: Use the digits 1 to 9, at most one time each, to fill in … | 166 | 656 | {"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-2019-22 | latest | en | 0.867616 |
https://www.mortgagequote.com/estimated-mortgage-payment.php | 1,716,039,199,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971057422.43/warc/CC-MAIN-20240518121005-20240518151005-00179.warc.gz | 787,240,508 | 22,229 | ## Estimated Mortgage Payment
There is a lot that you need to consider when looking for a mortgage. Not only do you need to accumulate a down payment, but you need to figure out how much your mortgage payments will cost per month and whether or not this is something you can afford. Considering that, continue reading to discover everything that you need to know about estimated mortgage payments.
### Working out your estimated mortgage payments
There are a lot of different mortgage calculators available online today that can help you to work out your estimated mortgage payments. There are a number of key factors that are considered when it comes to working out how much your mortgage payments are likely to be per month. This includes the following:
• Your down payment and the percentage it amounts to
• The interest rate
• The length of your home loan
### The equation for estimating your mortgage payments
The typical equation for working out your typical mortgage payments is as follows:
M = P[r(1+r)^n/((1+r)^n)-1)]
Yes, it looks pretty complex, doesn’t it? However, if you input the figures in a calculator, we promise; it does work out. Plus, you do have those mortgage calculators that are already set up so you don’t need to worry about the equation yourself.
So, let’s take a look at what each letter represents so that you can do the equation yourself.
• M = M represents the total monthly mortgage payment, i.e. the figure that you are trying to achieve from this equation.
• P = P represents the principal loan amount.
• R = R represents your monthly interest rate. Just to make matters confusing, most lenders will provide you with a yearly interest rate. So, you will need to divide this figure by 12 in order to get your monthly interest rate.
• N = N represents the number of payments you are going to need to make over the lifetime of the loan. You need to multiply the number of years within your loan by 12 (the number of months in a year), so this will enable you to figure out the total number of payments you will need to make over the lifespan of the loan.
### Remember that a mortgage calculator will only provide an estimate
It is important to realize that a mortgage calculator is only ever going to provide you with an estimate. There are a number of different factors that can influence how much you pay. This includes insurance, property taxes, loan term, interest rate, down payment, and purchase price.
Most of the mortgage calculators will also assume a few things, for example, making assumptions about closing costs and that you are buying a property as your primary residence.
### Mortgage payments per state
While some states have relatively lower property values, homes in states like New Jersey, Hawaii, and California generally will have much higher property expenses, which means people are going to need to pay more for their mortgage every month. Plus, mortgage interest rates differ by state.
An American Community Survey carried out in 2018 revealed that homeowners paid \$1,556 per month on average. Not only did this incorporate their mortgage payment, but also HOA fees, utilities, property fees, and insurance costs where required.
Let’s take a look at some of the median monthly payments per state from the 2018 survey so that you can get a better understanding:
• Wyoming - \$1,428
• Washington - \$1,826
• Texas - \$1,549
• North Carolina - \$1,290
• New York - \$2,114
• Mississippi - \$1,134
• Hawaii - \$2,350
• Florida - \$1,466
• California - \$2,282
• Arkansas - \$1,071
### Final words on estimated mortgage payments
Hopefully, you now have a good start. You need to know about working out your estimated mortgage payments. We hope that the educational material and information we have provided above has helped you to get a better understanding of how much you are likely to pay per month for your mortgage. It is important that you have a thorough understanding of this so you can make sure you can afford your mortgage payments. Discuss further with MortgageQuote.com if you have any questions. | 855 | 4,082 | {"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} | 3.953125 | 4 | CC-MAIN-2024-22 | longest | en | 0.964277 |
http://www.9math.com/book/sum-first-n-odd-natural-numbers | 1,555,628,285,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578526904.20/warc/CC-MAIN-20190418221425-20190419003425-00375.warc.gz | 200,306,437 | 3,756 | ## The sum of the first n odd natural numbers
Is there an easy way to calculate the some of the first n natural numbers?
1+3+5+...+(2n-1) = ?
Let's look at the problem for n = 1,2,3,4,5
1=1=12
1+3=4=22
1+3+5=9=32
1+3+5+7=16=42
1+3+5+7+9=25=52
So the answer seems to be:
1+3+5+...+(2n-1) = n2
Proof 1:
We can arrange squares in this way. The big square has n2 little squares. We see that the number of little squares is also 1+3+5+...+(2n-1).
Proof 2:
We will use induction.
Step 1.
For n = 1 it's true that 1 = 2*1-1
Step 2.
We suppose that 1+3+5+...+(2n-1) = n2
and want to prove that: 1+3+5+...+(2(n+1)-1) = (n+1)2
We add (2(n+1) -1) to this:
1+3+5+...+(2n-1) = n2
and get:
1+3+5+...+(2n-1) + (2(n+1) -1) = n2 + (2(n+1) -1)
so:
1+3+5+...+(2(n+1) -1) = n2 + 2n+2 -1
but n2+2n+1 = (n+1)2
so we finally have:
1+3+5+...+(2(n+1)-1) = (n+1)2 | 412 | 853 | {"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} | 4.46875 | 4 | CC-MAIN-2019-18 | longest | en | 0.744046 |
https://www.thestudentroom.co.uk/showthread.php?t=5232884 | 1,534,358,560,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221210249.41/warc/CC-MAIN-20180815181003-20180815201003-00122.warc.gz | 1,000,422,201 | 45,578 | Turn on thread page Beta
You are Here: Home >< GCSEs
# Work out 0.17 x 6000 - confused? watch
1. So i just revised this topic and i thought you would have to do 17 x 6000 which is 102000 and then add the decimal point before the last 0 because the dp is after the first digit in the question but in the mark scheme it simply says 1020??? But that would only be if you did 17 x 60 but the question is saying 6000??
2. Instructions weren’t clear, house burned down.
Posted on the TSR App. Download from Apple or Google Play
3. (Original post by Fk90709)
Instructions weren’t clear, house burned down.
Lol I’m sorry what are you saying
4. (Original post by Jheinexx)
Lol I’m sorry what are you saying
Im as confused as you.
Posted on the TSR App. Download from Apple or Google Play
5. (Original post by Fk90709)
Im as confused as you.
Confused by how i explained it or confused by how i got my answer or by the real answer?
6. 17 x 60
1.7 x 600
0.17 x 6000
7. Well 0.17=17/100 so 0.17x6000=(17/100)x6000=(17x6000)/100.
You're out by a factor of 10 basically but I'm dying to give you the intuition of why you divide by 10 or 100 or whatever in general.
Hope this helps
8. 0.17×6000
1.7×600
17×60
Posted on the TSR App. Download from Apple or Google Play
9. (Original post by Notoriety)
17 x 60
1.7 x 600
0.17 x 6000
But why 17 x 60 when it clearly says 6000
10. (Original post by B_9710)
Well 0.17=17/100 so 0.17x6000=(17/100)x6000=(17x6000)/100.
You're out by a factor of 10 basically but I'm dying to give you the intuition of why you divide by 10 or 100 or whatever in general.
Hope this helps
No idea what you just said:/
11. (Original post by starfab)
0.17×6000
1.7×600
17×60
Buttt why would it be 17 x 60 when it says 6000
12. (Original post by Jheinexx)
No idea what you just said:/
What's your reasoning for dividing by 10 after you do 17x6000?
Maybe if you see that 0.17x6000=(0.1+0.07)x6000 then you can expand so it's just (0.1x6000)+(0.07x6000) I don't knos if this make sense to you or makes it any easier or whether you find that just as confusing.
13. Think of 0.17 exponentially : 17 x 10-2
Now multiple 17 x 10-2 by 6000 and you get an answer of 102000 x 10-2
So you move the decimal point in 102000 by 2 places to the left (because of the exponent) and your answer is 1020
14. (Original post by B_9710)
What's your reasoning for dividing by 10 after you do 17x6000?
I don’t divide by 10. I do 17 x 6000 = 102000 then add the dp before the last 0 making it 10200.0
15. (Original post by Jheinexx)
Buttt why would it be 17 x 60 when it says 6000
Because
when you move the decimal point in 0.17 you're timesing that by 10. So you need to divide by 10 on 6000.
So if you've times'ed by 10 and divided by 10 ik the same equation, it's likw you've made no changes.
so... 0.05 ×1000
is the same as 0.5 ×100
or the same as 5 × 10
Does that make sense?
Posted on the TSR App. Download from Apple or Google Play
16. (Original post by The Night King)
Think of 0.17 exponentially : 17 x 10-2
Now multiple 17 x 10-2 by 6000 and you get an answer of 102000 x 10-2
So you move the decimal point in 102000 by 2 places to the left (because of the exponent) and your answer is 1020
Please no negative numbers. I want the simplest way
17. (Original post by Jheinexx)
I don’t divide by 10. I do 17 x 6000 = 102000 then add the dp before the last 0 making it 10200.0
But it's 0.17 so theres decimal point needs to move twice. so 1020.00
if it was 01.7 then you'd move it once so then it'd be what you got, 10200.0
Posted on the TSR App. Download from Apple or Google Play
18. (Original post by Jheinexx)
I don’t divide by 10. I do 17 x 6000 = 102000 then add the dp before the last 0 making it 10200.0
Ok by putting the decimal point where you do you are in fact just dividing by 10 essentially - maybe without realising it. The key thing here though is that you have to divide by 100 so the decimal point moves two places to the left not one.
19. (Original post by Jheinexx)
Please no negative numbers. I want the simplest way
But this is the simplest way to do it without a calculator lol. Fastest too
20. (Original post by Jheinexx)
I don’t divide by 10. I do 17 x 6000 = 102000 then add the dp before the last 0 making it 10200.0
not before the last zero, before the last 2 zeros
bc there are 2 digits after the decimal place in 0.17, you move the decimal place twice when putting it back in
if it were 0.6 for example, there is only one number after the decimal place, you youd only only move the decimal by one place when putting it back in
Turn on thread page Beta
TSR Support Team
We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.
This forum is supported by:
Updated: March 5, 2018
The home of Results and Clearing
### 3,629
people online now
### 1,567,000
students helped last year
Today on TSR
### A-level grade boundaries
Hang on, have Edexcel's come out already?
### University open days
1. SAE Institute
Animation, Audio, Film, Games, Music, Business, Web Further education
Thu, 16 Aug '18
2. Bournemouth University
Clearing Open Day Undergraduate
Fri, 17 Aug '18
3. University of Bolton
Fri, 17 Aug '18
Poll
Useful resources
## Study tools
### Essay expert
Learn to write like a pro with our ultimate essay guide.
See where you can apply with our uni match tool
### Ask a question
Chat to other GCSE students and get your study questions answered.
### Make study resources
Create all the resources you need to get the grades.
### Create your own Study Plan
Organise all your homework and exams so you never miss another deadline.
### Resources by subject
From flashcards to mind maps; there's everything you need for all of your GCSE subjects.
### Find past papers
100s of GCSE past papers for all your subjects at your fingertips.
## Help out other students
Can you help? Study help unanswered threads
## Groups associated with this forum:
View associated groups
The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.
Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE | 1,840 | 6,272 | {"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} | 4.15625 | 4 | CC-MAIN-2018-34 | longest | en | 0.901888 |
https://www.tutorialspoint.com/statically-and-dynamically-induced-emf | 1,679,712,755,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945292.83/warc/CC-MAIN-20230325002113-20230325032113-00420.warc.gz | 1,155,406,515 | 11,080 | # Statically and Dynamically Induced EMF
## Induced EMF
When a magnetic flux linking a conductor or coil changes, an electromotive force (EMF) is induced in the conductor or coil, is known as induced EMF. Depending upon the way of bringing the change in magnetic flux, the induced EMF is of two types −
• Statically Induced EMF
• Dynamically Induced EMF
## Statically Induced EMF
When the conductor is stationary and the magnetic field is changing, the induced EMF in such a way is known as statically induced EMF (as in a transformer). It is so called because the EMF is induced in a conductor which is stationary. The statically induced EMF can also be classified into two categories −
• Statically Induced EMF
• Mutually Induced EMF
## Self-Induced EMF
When an EMF is induced in the coil due to the change of its own magnetic flux linked with it is known as self-induced EMF.
Explanation − When a current flows in a coil, a magnetic field produced by this current through the coil. If the current in the coil changes, then the magnetic field linking the coil also changes. Therefore, according to Faraday’s law of electromagnetic induction, an EMF being induced in the coil. The induced EMF in such a way is known as self-induced EMF.
Mathematically, self-induced EMF is given by,
$$\mathrm{e=L\frac{di}{dt}\:\:\:\:\:\:...(1)}$$
Where, L is the self-inductance of the coil.
## Mutually Induced EMF
When an EMF is induced in a coil due to changing magnetic flux of neighbouring coil is known as mutually induced EMF.
Explanation − Consider two coils coil-1 and coil-2 placed adjacent to each other (see the figure). A fraction of the magnetic flux produced by coil-1 links with the coil-2. This magnetic flux which is common to both the coils 1 and 2 is known as mutual flux $(\varphi_{m})$. Now, if the current in coil-1 changes, the mutual flux also changes and thus EMF being induced in both the coils. The EMF induced in coil-2 is known as mutually induced EMF, since it is induced due changing in flux which is produced by coil-1. Mathematically, the mutually induced EMF is given by,
$$\mathrm{e_{m}=M\frac{di_{1}}{dt}\:\:\:\:\:\:...(2)}$$
Where, M is the mutual inductance between the coils.
## Dynamically Induced EMF
When the conductor is moved in a stationary magnetic field so that the magnetic flux linking with it changes in magnitude, as the conductor is subjected to a changing magnetic, therefore an EMF will be induced in it. The EMF induced in this way is known as dynamically induced EMF (as in a DC or AC generator). It is so called because EMF is induced in a conductor which is moving (dynamic).
Explanation − Consider a conductor of length l meters moving with a velocity of v m/s at right angles to a uniform stationary magnetic field of flux density B Wb/m2.Let the conductor moves through a small distance dx in time dt seconds. Then,
$$\mathrm{Area\: swept\: by \:conductor,\mathit{a = l \times dx}\: \:m^{2}}$$
$$\mathrm{\therefore Magnetic\: flux\: cut\: by\: conductor,\mathit{dψ}= Magnetic \:Flux \:Density \:\times\: Area \:Swept}$$
$$\mathrm{\Longrightarrow \mathit{dψ=B \:l\:dx}\: \:Wb}$$
Now, according to Faraday’s law of electromagnetic induction, the induced EMF will be,
$$\mathrm{\mathit{e=N\frac{dψ}{dt}=\frac{B\:l\:dx}{dt}\: (\because N}=1)}$$
$$\mathrm{\because \mathit{\frac{dx}{dt}}=Velocity \mathit{V}}$$
$$\mathrm{\therefore \mathit{e=B\: l\:v}\: \:Volts\:\:\:\:\:\:...(3)}$$
Equation (3) gives the dynamically induced EMF when the conductor moves at right angle to the magnetic field.
If the conductor moves at an angle &theta to the magnetic field, then the EMF induced due to only the perpendicular component of the velocity to the magnetic field.
$$\mathrm{\mathit{e=B\:l\:v} \:sinθ\:\:\:\:\:\:...(4)}$$
## Numerical Example
A conductor of length of 0.8 m lies in and at right angle to a uniform magnetic field of flux density 2 $Wb/m^{2}$. The conductor moves with a velocity of 30 m/s. Calculate the EMF induced in the conductor. What will be the EMF induced if the conductor moves at an angle of 45° to the magnetic field?
## Solution
• Case 1 − When conductor moves at right angle to the magnetic field.
• $$\mathrm{\mathit{e=B\:l\:v}=2\times(0.8)\times(30)=48V}$$
• Case 2 − When the conductor moves at 45° to the magnetic field.
• $$\mathrm{\mathit{e=B\:l\:v}\:sinθ=2\times(0.8)\times(30)\times sin45=33.95V}$$ | 1,194 | 4,406 | {"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} | 3.59375 | 4 | CC-MAIN-2023-14 | latest | en | 0.979125 |
http://hupik.com/ah/three/lago/31425202fa7d751a043371f6112ca0 | 1,679,673,677,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945287.43/warc/CC-MAIN-20230324144746-20230324174746-00768.warc.gz | 21,188,753 | 10,956 | On StuDocu you will find 25 Summaries, Tutorial work, Lecture notes, Practical, Practice. Numerical computation, algebra and graphs are used; calculus is not used. By the end of the course, you will be able to perform exploratory data analysis, understand key principles of sampling, and select appropriate tests of . statistic(s)These are numeric measure(s) derived from a sample e. sample mean (x), sample2variances (s ), and sample standard deviation (s). By Posted in robert bettinardi net worth On Jun 29, 2022 . You are probably asking yourself the question, "When and where will I use statistics?" 2021/2022 None. When it comes to learning statistics, Mann delivers the information that business professionals need. Introduction to Statistics 1.1 Introduction Statistics is a collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting and drawing conclusions based on the data. One of the most useful resource available is . It is actually a form of mathematical analysis that uses different quantitative models to produce a set of experimental data or studies of real life. Any distribution's core and spread are two critical components. For many people, statistics means numbersnumerical facts, figures, or information. This Paper. Topics covered include frequency distributions; measures of location; mean, median, mode; measures of dispersion; variance; graphic presentation; elementary probability . Ideally you should select your sample ran-domly from the parent population, but in prac-tice this can be very di cult due to: { issues establishing a truly random selection scheme, { problems getting the selected users to par-ticipate.? Supplements for Intro and Business Statistics. to help make decisions about hypothesized. King has defined Statistics in a wider context, the science of Statistics is the method of judging collective, natural or social phenomena from the results obtained by the analysis or enumeration or collection of estimates. Definitions. Statistics is a branch of applied mathematics which deals with the collection, classification, analysis and interpretation of data.The word statistics is derived from the Latin word 'status' means a 'political state' or 'government'. You may find yourself using knowledge from this course in a research lab, while reading a research report, or even while watching the news! Ross S. Introductory statistics. Arial Lucida Grande Default Design Chapter 1: Introduction to Statistics Variables Population Sample Slide 5 Types of Variables Real Limits Measuring Variables 4 Types of Measurement Scales 4 Types of Measurement Scales Correlational Studies Slide 12 Experiments Experiments (cont.) This online proclamation introductory statistics notes stat help can be one of the options to accompany you like having new time. Stanford's "Introduction to Statistics" teaches you statistical thinking concepts that are essential for learning from data and communicating insights. introduction to statistics lecture notes ppt. Statistics Theory and method of analyzing. Ronald Johnston Wonnacott OC FRSC was a Canadian economist.
The new edition incorporates the most up-to-date methods and applications to present the latest information in the field. Measures of Central Tendency (Averages) As a field, Statistics provides tools for scientists, practitioners, and laypeople to better understand data. Introduction to Statistics full semester class notes with practice problems. Chi-square goodness-of-fit test. Croxton & cowden 4 RDh@ker,Lecturer,PCNMS statistics is the sciences and art of dealing with figure and facts. (0) \$20.49. Meaning of Statistics The word ' statistic' is used to refer to Numerical facts, such as the number of people living in particular area. Formula Sheet with Description. Topics discussed include displaying and describing data, the normal curve, regression, probability, statistical inference, confidence intervals, and hypothesis tests with applications in the real world. 573,149 recent views. You must log in and be a buyer of this download to submit a review. Ships from and sold by Amazon.com. Based on the studies of data obtained, people can draw conclusions, make decisions and plan wisely. 4. When to use each measure of Central Tendency. Chapter 1 Introduction To Statistics. statistics that can assist in setting up and validating statistical models are discussed in Chapter 2. They are backed with examples to more complicated questions. The study of ways of collecting, analysing and interpreting the facts. Population; The collection of all responses, measurements, or counts that are of interest. Introductory Statistics follows scope and sequence requirements of a one-semester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. BUSN 3431 Douglas College. These lecture notes are a necessary component for a student to successfully com-plete this course. 3 Important Terms.
Worksheets are Work extra examples, An introduction to basic statistics and probability, Understanding basic statistics, Introduction to statistical thinking with r without, Introduction to statistics data analysis, Math mammoth statistics work, Small student projects in an introductory statistics course, Introductory statistics notes. 2 1 The Nature of Statistics Statistics is a branch of mathematics that involves collecting, organising, interpreting, presenting, and analysing data.
Statistics is the science that turns data into information and information into knowledge. In many introductory level courses today, teachers are challenged with the task of fitting in all of the core concepts of the course in a limited period of time. Kindle Edition. The science of analyzing, organizing, and summarizing data. . A set of information used to identify asample population for statistical treatment. Representativeness is more important than ran . 1: Introduction to Statistics. | 1,142 | 6,015 | {"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} | 3.234375 | 3 | CC-MAIN-2023-14 | latest | en | 0.899128 |
https://www.penflip.com/rhgraysonii/clojure_from_zero_to_deploy/commit/f706332e5b24e38a12a50e25d17ceb06c8c64043 | 1,579,461,079,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250594705.17/warc/CC-MAIN-20200119180644-20200119204644-00016.warc.gz | 1,043,941,399 | 5,382 | ### Updated 2_On_Numbers_and_Arithmetic.txt
revision f706332e5b24e38a12a50e25d17ceb06c8c64043
2_On_Numbers_and_Arithmetic
# Chapter 2
# Numbers and Arithmetic
As demonstrated earlier, we saw there is much that will feel comfortable with Clojure and artithmetic. In a brief review we should feel comfortable with the following examples:
(+ 1 2 3 4 5)
;=>15
(- 3 (+ 1 2))
;=> 0
(/ 2 3)
;=> 2/3
(/ 2.0 3)
;=>.66666666666...
Now, let us take a deeper look.
(type 4)
;=>java.lang.Long
This simple means it is a Java type. The long. In Java, all you really need to know about a long is that it uses one bit to store the type (positive or negative) of the number and allocates the other 63 its to storing the size of the number itself. If you try to exceed its maximum number size (2^63) it will give you an error. Clojure also offers other common types from Java
(type (short 0))
;=> java.lang.Short
(type (int 11))
;=>java.lang.Integer
(type(byte 0))
;=> java.lang.Byte
(type 2.0)
;=> java.lang.Float
To express something precisely using fractions, the Ratio type comes into play.
(type(2/3))
;=> clojure.lang.Ratio
Now, lets take a look into comparison and analysis here. We have some types that your standard OO programmer may not have encountered thus far depending on the areas they have dove in.
(= 2 2.0)
;=>false
(== 2 2.0)
;=>true
Now, before we explain this. Let's try it in Ruby.
2 == 2.0
>true
And, in JS,
2 == 2.0
>true
What is this hoopla? Well, in Clojure floats are considered an approximation. This is why we are allowed to express values more precisely using the Ratio type. Now, what if we want to use a number larger than the maximum of 2^63?
(type(5N))
;=>clojure.lang.BigInt
This allows us to write arbitrary precision integers. We can examine the value of integers in order with our typical "<" ">" "<=" ">=" operators.
(< 3 2 1)
;=>true
This allows us to ensure they are in descending order. We can increment and decrement as well.
(inc 1)
;=>2
(dec 1)
;=>0
This should give you a solid fundamental understanding of the nuances of Clojures arithmetic methods and data types. For a more in depth look at these structures check out [this documentation](http://clojure.org/cheatsheet). Again, no exercises this chapter. Just play around however you see fit in a concept that may not have clicked fully, or even one that blew your face off with awesome when you realized the approach's ingenuity. | 666 | 2,440 | {"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-2020-05 | latest | en | 0.835013 |
https://calculator.academy/pond-salinity-calculator/ | 1,679,787,009,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945376.29/warc/CC-MAIN-20230325222822-20230326012822-00612.warc.gz | 189,407,963 | 44,371 | Enter the chloride concentration (mg/L) into the Pond Salinity Calculator. The calculator will evaluate the Pond Salinity.
## Pond Salinity Formula
The following two example problems outline the steps and information needed to calculate the Pond Salinity.
PS = .0018066 * CL-
Variables:
• PS is the Pond Salinity (ppt (parts per thousand))
• CL- is the chloride concentration (mg/L)
## How to Calculate Pond Salinity?
The following steps outline how to calculate the Pond Salinity.
1. First, determine the chloride concentration (mg/L).
2. Next, gather the formula from above = PS = .0018066 * CL-.
3. Finally, calculate the Pond Salinity.
4. After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
chloride concentration (mg/L) = 1.25
PS = .0018066 * CL- = ? | 206 | 910 | {"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-2023-14 | latest | en | 0.828194 |
https://respaper.com/icse/255/340/8323-pdf.html | 1,660,688,020,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572581.94/warc/CC-MAIN-20220816211628-20220817001628-00600.warc.gz | 451,587,674 | 11,702 | Trending ▼ ResFinder
# ICSE Board Exam 2006 : Physics
5 pages, 57 questions, 56 questions with responses, 158 total responses, 0 0
ICSE Indian Certificate of Secondary Education (ICSE), New Delhi
+Fave Message
Home > icse > F Also featured on: mehdi_momin
Formatting page ...
SCIENCE Paper 1 (Physics) - 2006 (One hour and a half) Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the Question Paper. The time given at the head of this paper is the time allowed for writing the answers. Section I is compulsory. Attempt any four questions from Section II. The intended marks for questions or parts of questions are given in brackets [ ]. S ECTION I (40 Marks) Attempt all questions from this Section Question 1 (a) M ention any two differences between the mass and weight of a body. [2] (b) State the amount of work done by an object when it moves in a circular path for one complete rotation. Give a reason to justify your answer. [2] (c) [2] A uniform metre scale is kept in equilibrium when supported at the 60 cm mark and a mass M is suspended from the 90 cm mark as shown in the figure. State with reasons, whether the weight of the scale is greater than, less than or equal to the weight of mass M . (d) Draw a graph showing the relationship between acceleration and mass for a constant force. (e) The speed-time graph of a moving car is as shown in the figure below:- [2]
Formatting page ...
Top Contributors
to this ResPaper
Prajwal Navada(46) Not Available(37) vishesh96(33) Ann Mary (11)
Formatting page ...
Formatting page ...
Formatting page ...
Additional Info : Solved ICSE Board exam paper study guide - ICSE 2006 : SCIENCE Paper 1 (Physics) - I.C.S.E. Free Online Question Paper
Tags : science paper 1, physics, 2006, icse physics question bank, icse physics question papers, icse, i.c.s.e., indian certificate of secondary education, council for the indian school certificate examinations, solved icse board exam papers, free sample question papers, online model answers, students, teachers, icse schools, india, icse examination results, icse physics numericals, icse free download, icse papers, pdf download 2016 2017 2018 2019 2020 2021, icse sample papers, icse books, portal for icse india, icse question bank, indian certificate of secondary education, icse question papers with answers, icse model test papers, solved past board question papers of icse last year, previous years solved question papers, free online icse solved question paper, icse syllabus, india icse board sample questions papers, last 10 years icse papers, icse question papers 2017 - 2018, icse guess sample questions papers, icse important questions, class 10 specimen / guess / mock papers, icse pre board question papers, icse 2020 - 2021 pre-board examination | 700 | 2,902 | {"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-2022-33 | latest | en | 0.878944 |
https://math.stackexchange.com/questions/3763920/solving-a-simple-differential-equation-with-dft | 1,719,227,937,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198865348.3/warc/CC-MAIN-20240624084108-20240624114108-00330.warc.gz | 333,390,019 | 38,768 | # Solving a simple differential equation with DFT
I have a simple differential equation of form $$\frac{df(x)}{dx}=u(x)$$ and u(x) is given to me in a sampled form so I need to solve this equation numerically. I decided to do this via DFT and I came up with following plan:
Since Fourier Transform of $$\frac{df(x)}{dx}$$ is given by $$2\pi i \xi F(\xi)$$ I have to:
1. Compute the DFT of my sampled derivative
2. Divide each entry of the DFT by $$2\pi i \xi$$ with corresponding frequency (except for the zero frequency component that kind of correpondes to the initial condition of my equation)
3. Compute the inverse DFT of the resulting signal and this should be the solution
I have coded this up with Python and numpy and implemented a simple unit test based on a function with known derivative (I used $$sinc(x)$$). The resulting solution differs alot from $$sinc(x)$$ and I can't figure out what am I doing wrong here. Here is the code of all this with visualization using matplotlib that illustrates the difference between target function and the result and it's not even close...
import numpy as np
from numpy.fft import fft, ifft
import matplotlib.pyplot as plt
import cmath as cm
import math
def integrate(f, fdx, a, b):
N = 1024
X = np.linspace(a, b, N)
step = (b - a) / (N - 1)
D = [step * fdx(x) for x in X]
S = [f(x) for x in X]
ft = fft(D)
w = [(2 * math.pi * 1j * i / N) for i in range(0, N)]
w[0] = 1 # dc component, ignore it
ft = ft / w
res = np.real(ifft(ft))
plt.figure()
plt.plot(X, S, 'g--', linewidth = 2.0)
plt.plot(X, res, 'r-', linewidth = 1.0)
plt.show()
f = lambda x : math.sin(x) / x if math.fabs(x) > 1e-10 else 1
fdx = lambda x : (x * math.cos(x) - math.sin(x)) / (x ** 2) if math.fabs(x) > 1e-10 else 0
integrate(f, fdx, 0, 25)
Do you have any idea on what's wrong here?
UPDATE: Here is the plot of sinc function and numeric solution obtained by this method. There are two subplots displaying the same thing with different ylimit
Fig.1: Visualization of described experiment
Another interesting thing to observe here is the amplitude of the signal spectrum before and after the division by $$2\pi i \xi$$ is applied. Here is the corresponding plot of $$log$$ amplitudes of the spectrum:
Fig.2: The spectrum amplitude before and after the procedure
It can be seen, that before the procedure spectrum is symmetic (and that's cool cause the signal that I start with is real valued), however after the procedure is applied, the spectrum turns non symmetric and the inverse DFT of the signal isn't even real anymore, it's complex. So there is clearly some flaw in the procedure but I can't see where it is. The only idea that I have in mind is that the continuous formula $$2\pi i \xi F(\xi)$$ for the FT of first order derivative doesn't hold in the discrete case, but I can't see why and what are the alternatives...
• Can you attach the figure as well? Commented Jul 21, 2020 at 8:49
• @user619894 Sure, I have attached the resulting figure to the original post. I hope this would help! Commented Jul 21, 2020 at 9:36
• shouldn't you multiply by $w$, and not divide? Commented Jul 21, 2020 at 9:55
• @user619894 Multiplying by $w$ doesn't seem to be the right thing. After I apply the Fourier Transform to both sides of the equation I get $2\pi i \xi F(\xi)= \hat u(\xi)$ so $F(\xi)=\frac{\hat u(\xi)}{2\pi i \xi}$. However I tried to do what you propose and it doesn't give the correct result as well Commented Jul 21, 2020 at 10:12
• I think that the numpy fft has the positive freqs up to $N/2$ and then negative freqs, so the $w$ vector should reflect that. Commented Jul 21, 2020 at 12:53
## 1 Answer
Ok, after some digging I think I have it figured out, at least partially:
1. There was a bug in the implementation that was kindly noted by user619894 and that is numpy FFT frequencies are not $$[0,...,N - 1]$$ but rather [0,..,N/2,-N/2,..,-1]. The most reliable way to implement division by $$2\pi i \xi$$ in numpy turns out to be using it's builtin numpy.fftfreq(N) function, this func returns an array of frequencies, corresponding to entries of FFT and with it the division procedure can be implemented in one line by:
ft = ft / np.append([1], (2 * math.pi * 1j * fftfreq(N)[1:]))
However this fix alone doesn't make the thing work for $$sinc(x)$$
1. The second but probably more shocking thing turns out to be the pereodic nature DTF based integration procedure. After staring at the result of DFT integration of my derivative I noticed that the resulting solution kind of resambles the $$sinc(x)$$ in it's shape but is bent so that it converges to the same value that it starts with. After that I have realised that DFT actually represents an endless periodic signal and the last derivative in my sampled array of derivatives actually correspondes to the difference between samples $$N - 1$$ and $$0$$ since the thing is periodic. To veryfy this I replaced the last derivative by the corresponding difference and the results became much more like the $$sinc(x)$$ after that, but with minor high frequency distortions near the begining and the end of the signal.
After that I have conducted multiple experiments with different signals weighted by various windowing fucntions that zero out the signal near the end and the beginning and the procedure works perfect for such signals and produces nice results even in presence of noise.
So it seems that it's the periodizing nature of descrete version of the transform that doesn't allow to solve for such a function like $$sinc(x)$$ in the described setup. I don't see any simple way around it. Does anybody know how to work around this or the DFT is simply not apropriate for such a non-periodic problem?
UPDATE: In the end I used the following trick to do the integration with FFT here, so it turns out to be doable dispite periodicity constraint implicitly imposed by DFT:
1. Pad the derivative with replicate border method
2. Multiply your padding with some windowing function on both sides of the signal. This makes solution to augmented equation flatten at the beginning and at the end. But the solution is still not periodic
3. Append negated and reversed copy of derivative to itself. This finally makes solution periodic
4. Solve with FFT, then extract the portion of augmented signal that correspondes to the original part of the signal
Works perfect, although the code is kinda ugly and not as cool as an initial one-liner:
half = int(N / 2) # padding size
tails = np.hanning(2 * half) * np.array(([D[0]] * half) + ([D[-1]] * half))
SP = np.hstack((tails[:half], D, tails[half:])) # flatten near boundaries
SPP = np.append(SP, -np.flip(SP)); L = SPP.shape[0] # periodize
res = np.real(ifft(fft(SPP) / np.append([1], (2 * math.pi * 1j * fftfreq(L)[1:]))))
res = res[half:half + N] # extract original signal from augmented signal
Also this quadruples the size of FFT. Maybe a smaller padding can be used, but anyway this solution at least doubles the size of FFT.
• Great catch. To solve the periodic issue, either increase the range, or multiply by a window function en.wikipedia.org/wiki/Window_function. Commented Jul 22, 2020 at 5:09
• An alternative is to detrend: decompose the signal into a linear term that is just a line between the two end points, and the original signal with this line subtracted. The subtracted signal is now periodic. You can FT the subtracted signal, divide by $w$ and iFT, then adding the integral of the linear signal as well. Commented Jul 22, 2020 at 7:25
• @user619894 Nice ideas, thanks! I padded + windowed the derivative to avoid high freq jitter and then mirrored and negated it to make the thing periodic. Works like a charm. Commented Jul 25, 2020 at 12:36 | 2,006 | 7,737 | {"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": 17, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.8125 | 4 | CC-MAIN-2024-26 | latest | en | 0.84664 |
https://www.queryhome.com/puzzle/26433/once-vicky-went-to-meet-his-friend-david-who | 1,550,867,438,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550247526282.78/warc/CC-MAIN-20190222200334-20190222222334-00151.warc.gz | 925,952,816 | 31,147 | # once vicky went to meet his friend. david who ...
–1 vote
44 views
**
### strong text
**
posted Mar 22, 2018
Looking for solution? Promote on:
Similar Puzzles
David Van Gogh (pronounced "Go") had many relatives. Can you guess by the clues who they are?
Example: His dizzy Aunt?
How many other relatives can you guess?
A fruit loving cousin?
The Grandfather from Yugoslavia?
The cousin from Illinois?
His Mexican cousin?
His Great Grandfather who drove a stage coach?
The ballroom dancing aunt?
The bird lover Uncle?
A sister who loved disco?
And his niece who travels the country in a van?
There once was a man, who usually went to the bar on Sundays, and drank. But one particular Sunday, the man was drunk when he came across a rich man staring at an old bridge. The bridge was full of dirt, sod, and bugs. The rich man then saw that the drunk man was going to cross the dirty bridge. The rich man told him, "That bridge is so dirty, nobody wants to cross it. If you can cross it, without any part of your body touching it, I will pay you \$1,000. If you do touch it with any part of your body, then you will have to pay me \$100." Being drunk, the man agreed, but then suddenly realized what he was agreeing to. But then, he thought of an idea, and then crossed the bridge according to the rich man's rules, and later returned home \$1,000 richer.
There was a man who wanted to treat his son he went to the doctor and the doctor told him that he need to get 1 orange in order to cure his son on the the same village where the man was staying there where no any single orange, so the man tried to another village when the man reached another village he saw millions of oranges in the garden when he reached the entry he realised that this garden had for 4 gates and each gate had a gatekeeper so when ever he could pass by each gate keeper they where telling him that whichever organges he bring ,they should share in between. so how many oranges did the man come out with from the garden to share with the gatekeepers and remained with 1 orange to cure his son? | 480 | 2,078 | {"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} | 3.125 | 3 | CC-MAIN-2019-09 | latest | en | 0.98229 |
https://learnzillion.com/lesson_plans/2050-9-find-missing-angles-using-angle-relationships-formed-from-transversals-fp | 1,529,700,652,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267864795.68/warc/CC-MAIN-20180622201448-20180622221448-00276.warc.gz | 632,825,592 | 39,551 | Lesson plan
# 9. Find missing angles using angle relationships formed from transversals (FP)
teaches Common Core State Standards CCSS.Math.Content.8.G.A.5 http://corestandards.org/Math/Content/8/G/A/5
teaches Common Core State Standards CCSS.Math.Practice.MP1 http://corestandards.org/Math/Practice/MP1
teaches Common Core State Standards CCSS.Math.Practice.MP3 http://corestandards.org/Math/Practice/MP3
## You have saved this lesson plan!
Here's where you can access your saved items.
Dismiss
Lesson objective: Compute missing angles using angle relationships formed from transversals.
This lesson helps to build procedural skill with angle relationships. Task Cards (with visual representations of parallel lines and transversals) are used here because they support students as they reason with angles and angle measures they can deduce from a picture. Students are then able to create equations that represent congruent and supplementary angle relationships. This work develops students' understanding that parallel lines and transversals create angle relationships that can be used to determine other angles.
Students engage in Mathematical Practice 1 as they make sense of and persevere in angle relationship problems. Students will engage in productive struggle as the determine types of angle relationships, create equations that represent them, and recognize there are multiple pathways to find missing angles.
Key vocabulary:
• alternate interior angles
• alternate exterior angles
• corresponding angles
• parallel lines
• transversal
Special materials needed:
• Amazing Race checkpoint cards | 326 | 1,615 | {"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} | 3.234375 | 3 | CC-MAIN-2018-26 | latest | en | 0.821516 |
https://mathematica.stackexchange.com/questions/108240/what-is-the-fastest-way-to-compute-digits-of-pi-using-mathematica/108248 | 1,603,256,067,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107875980.5/warc/CC-MAIN-20201021035155-20201021065155-00018.warc.gz | 419,592,873 | 38,343 | # What is the fastest way to compute digits of $\pi$ using Mathematica?
There are a lot of ways to calculate digits of $\pi$ using Mathematica. The most naïve way I can think of is
N[π, 100000000]
Of course, there are a lot of fast classic formulas (Chudnovsky, Ramanujan) to achieve this goal. I'm wondering what is the fastest way to calculate digits of $\pi$ using Mathematica. The reason that this question may be interesting is that Mathematica has a lot of unique features that can make this calculation faster (or can improve known classic ways of calculating $\pi$).
What are your ideas for calculating digits of $\pi$ using Mathematica in the fastest way possible?
• Explanation of the reason of choosing a particular formula / algorithm.
• Why this particular Method is optimal (in Mathematica at least).
• Optional: Why this Method suits best the use of Mathematica compared with other languages.
Note: As @J.M. points, Mathematica implements the Chudnovsky formula for the default calculation.
• Note that the implementation notes say that the Chudnovsky formula is used for evaluation. – J. M.'s discontentment Feb 24 '16 at 18:17
• Thanks! That's important information indeed. But I'm curious if there are other sophisticated ways of perform the calculation. – Dargor Feb 24 '16 at 18:18
• Do you want to pick out single digits or the whole expansion to a certain number of digits? Does it have to be base-10? – Kellen Myers Feb 24 '16 at 19:42
• Base 10 would be better than other base. And I want the expansion to certain number of digits. – Dargor Feb 24 '16 at 20:17
Here is an adaptation of MATLAB code from Trefethen, Ten Digit Algorithms (2005), based on Borwein & Borwein, The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions (1984) that calculates $$\pi$$ via the AGM method.
ClearAll[npi];
npi[digits_] := Block[{two, iter},
iter[{x_, y_, p_}] :=
With[{s = Sqrt@x},
{(s + 1/s)/2,
(y*s + 1/s)/(1 + y),
p*(1 + x)/(1 + y)}];
two = SetPrecision[2, 1 + digits];
With[{y = Sqrt@(Sqrt@two), eps = 10.^(-digits/2)},
NestWhile[
iter,
{(y + 1/y)/2, y, two + Sqrt@2},
Abs[Last@#1 - Last@#2] > eps &,
2]
]
];
Examples:
ClearSystemCache[] (* clears cached values of Pi *)
digits = 10^6;
N[Pi, digits]; // AbsoluteTiming
pi = Last@npi[digits]; // AbsoluteTiming
pi - Pi // Abs
(*
{0.393234, Null}
{6.24918, Null}
0.*10^-1000000
*)
ClearSystemCache["Numeric"] (* clears cached values of Pi *)
digits = 7000;
N[Pi, digits]; // AbsoluteTiming
pi = Last@npi[digits]; // AbsoluteTiming
pi - Pi // Abs
(*
{0.001243, Null}
{0.008355, Null}
0.*10^-7000
*)
The AGM algorithm is asymptotically quadratically convergent. Below are the number of digits of accuracy and the ratio with the previous step. It takes 12 iterations to reach 7000 digits and 19 to reach a million digits (in fact, about 1.43 million); in general it will take around Log2[digits] - 1 iterations.
• I upvoted partly because of your effort to translate one of the ten-digit algorithms. :) – J. M.'s discontentment Feb 25 '16 at 18:01
• @J.M. Thanks! The Borweins' paper is nice, too. As I recall, there are a couple of judiciously placed typos that help keep you on your toes. :) – Michael E2 Feb 25 '16 at 18:14
• I will accept this answer because it's the fastest so far ( 0.008355 vs 0.157986 with 7000 digits ) but both are great answers!. – Dargor Mar 1 '16 at 17:39
direct implementation of Chudnovsky formula for reference:
a[0] = 1;
a[k_] := a[k] =
a[k - 1] (-(((-1 + 2 k) (-5 + 6 k) (-1 + 6 k)
(13591409 +545140134 k))/
(10939058860032000 k^3 (-531548725 + 545140134 k))))
(pi1 = N[((426880 Sqrt[10005])/(13591409 Sum[ a[k], {k, 0, 500}])),10000])
// AbsoluteTiming // First
(pi0 = N[Pi, 10000]) // AbsoluteTiming // First
0.15705
0.00156379
Last@RealDigits[pi0 - pi1]
-7105
Note running it again (using the saved a[i] ) doesn't save that much time:
0.129899
interestingly N[Pi, 10000] gets considerably faster on repeated evals, must be caching something.
Edit: the above is sped up a good bit if we immediately numerically eval each a[k] ( just start with a[0]=N[1,10000] ). With that I get 0.0193068 sec for 7000 digits. Only a factor of 10 off the bulitin..not too bad.
here is a version that lets you dial in a specified number of digits:
numdigits = 7000;
(pi1 = N[((426880 Sqrt[
10005])/(13591409 (NestWhileList[
Function[{k}, {k, #[[2]] (-(((-1 + 2 k) (-5 +
6 k) (-1 + 6 k) (13591409 +
545140134 k))/
(10939058860032000 k^3 (-531548725 + 545140134 k))))}][#[[1]] + 1] &,
{0,N[1, numdigits + 1]},
(-RealDigits[#[[2]]][[2]] < numdigits) &][[All, 2]] // Total))),
numdigits + 1];) // AbsoluteTiming // First
0.259337
Last@RealDigits[pi1 - Pi]
7000
It is a good bit slower than the first form though.
• Maybe it can be compiled for better performance. – Dargor Feb 24 '16 at 20:18
• compile i think only works at machine precision, so you can't simply compile this implementation. – george2079 Feb 24 '16 at 22:58
• It would be faster to check the a[k] if they are getting sufficiently small instead of hardcoding an upper limit like 500 so that there are no needless evaluations. – J. M.'s discontentment Feb 25 '16 at 5:02
• A check would be needed if you want to specify the desired precision. I don't think you'll make it faster if the desired precision is 7105 digits though :) – george2079 Feb 25 '16 at 14:32
Here's another method, based on the fact that $$\pi$$ is a fixed point of $$x + \sin x$$ and converges quickly if $$x$$ starts moderately close to $$\pi$$. This is clear from the Taylor series or even from this picture:
I don't know that many digits of $$\pi$$ off the top of my head, but I know enough that one iteration will get me MachinePrecision. From that we can get a (more than) million digits in 11 more iterations. If you know a few more digits of $$\pi$$, e.g. 3.14159265358979324, then you need only 10 iterations and a 1/4 sec. less time.
ClearSystemCache[]
digits = 10^6;
myPi = Nest[
Function[x,
# + Sin@# &@SetPrecision[x, 1 + Min[digits, 3 Precision[x]]]
],
# + Sin@# &@3.14159654,
Ceiling@Log[3, digits/16.]
]; // AbsoluteTiming
(* {0.766425, Null} *)
myPi - Pi
(* 0.*10^-1000001 *)
Some may know this as a calculator trick: Take $$x$$ to be the calculator's $$\pi$$ and then find $$\sin x$$. Add the two numbers by hand to get $$\pi$$ to more digits than the calculator has, provided the calculator has a good sine routine. (Note: my iPhone calculators's $$\pi$$ carries extra digits or is a special symbol. The sine of the calculator $$\pi$$ is zero, and the calculator seems to have quad precision, at least for the significand. The exponent is bounded by two digits, like many calculators.)
• I don't believe I've seen this before. Thanks! – Mr.Wizard Jan 10 '19 at 11:18 | 2,028 | 6,771 | {"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": 13, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.625 | 4 | CC-MAIN-2020-45 | latest | en | 0.836137 |
http://www.tutorcircle.com/evaluation-of-definite-integral-t1JLp.html | 1,369,083,394,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368699238089/warc/CC-MAIN-20130516101358-00011-ip-10-60-113-184.ec2.internal.warc.gz | 773,171,791 | 31,571 | Â Â Â Â
     Â
# Evaluation Of Definite Integral
A Definite Integral is an integral with limits. The definite integral is of the form ∫ ab f( x ) dx where a, b, and x can be complex Numbers. The definite integral can be also be defined as- Let f( x ) be a continuous function on [ p , q ] and let F ( x ) is Antiderivative of f ( x ) then ∫pq f( x ) dx = F( x )|pq = F( p ) - F( q ).
By using fundamental theorem of Calculus we can calculate definite integrals in terms of indefinite integrals, this process is shown below-
∫ab f( x ) dx = F( b ) - F( a ),
here F is the definite indefinite integral for function f( x).
Let us take some examples understand how to evaluate definite integral-
Example 1) Calculate I( a ) = ∫0∏/2 dx / 1 + ( tan x )a.
Solution) As we know tan ( ∏ / 2 – x ) = cot x.
Let z = (tan x )a ,
So I( a ) = ∫0 ∏ / 4 dx / (1 + z) + ∫∏/4 ∏/2 dx / (1 + z),
=> ∫0∏/4 dx / ( 1 + z ) + ∫0∏/4 dx / (1 + 1 / z),
=> ∫0∏/4 ( 1 / (1 + z) + 1 / (1 + 1 / z)) dx,
=> ∫0∏/4 dx,
=> 1 / 4 ∏.
So from above example we learnt that evaluating definite integrals involves the process shown below-
First we have to find the indefinite integral, then we will find the Functions that are not continuous at any Point between the limits of Integration. Also note that the function should be continuous in the interval of integration. This is how we evaluate the definite integral.
## Evaluation of Definite Integral by substitution
Definite integral substitution provides a simple way to solve the integral problem. It is similar to the indefinite integral substitution but the difference is that we have to deal with the limits in this case.
Recall the methods of evaluating Definite Integral by first evaluating the indefinite integral and putting range on it. How...Read More
Math Topics | 516 | 1,819 | {"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} | 4.5625 | 5 | CC-MAIN-2013-20 | latest | en | 0.770612 |
http://www.citizendia.org/Electronic_filter | 1,369,010,480,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368698196686/warc/CC-MAIN-20130516095636-00006-ip-10-60-113-184.ec2.internal.warc.gz | 374,029,048 | 18,212 | Television signal splitter consisting of a high-pass filter (left) and a low-pass filter (right). The antenna is connected to the screw terminals to the left of center.
Electronic filters are electronic circuits which perform signal processing functions, specifically intended to remove unwanted signal components and/or enhance wanted ones. An electronic circuit is a closed path formed by the interconnection of Electronic components through which an Electric current can flow Signal processing is the analysis interpretation and manipulation of signals Signals of interest include sound, images, biological signals such as Electronic filters can be:
The most common types of electronic filters are linear filters, regardless of other aspects of their design. Passivity is a property of engineering systems most commonly used in electronic engineering and control systems An active filter is a type of analog Electronic filter, distinguished by the use of one or more Active components i Analogue electronics (or analog in American English) are those electronic systems with a continuously Variable signal In Electronics, Computer science and Mathematics, a digital filter is a system that performs mathematical operations on a sampling, A discrete signal or discrete-time signal is a Time series, perhaps a signal that has been sampled from a continuous-time signal. A continuous signal or a continuous-time signal is a varying quantity (a signal) that is expressed as a function of a real-valued domain usually time A linear filter applies a Linear operator to a time-varying input signal A nonlinear filter is a signal-processing device whose output is not a Linear function of its input IIR redirects here For the conference company IIR see Informa. A finite impulse response (FIR filter is a type of a Digital filter. A linear filter applies a Linear operator to a time-varying input signal See the article on linear filters for details on their design and analysis.
## History
The oldest forms of electronic filters are passive analog linear filters, constructed using only resistors and capacitors or resistors and inductors. |- align = "center"| |width = "25"| | |- align = "center"| || Potentiometer |- align = "center"| | | |- align = "center"| Resistor| | A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors An inductor is a passive electrical component designed to provide Inductance in a circuit These are known as RC and RL single pole filters respectively. In Complex analysis, a pole of a Meromorphic function is a certain type of singularity that behaves like the singularity at z = 0 More complex multipole LC filters have also existed for many years and the operation of such filters is well understood with many books having been written about them.
Hybrid filters have also been made, typically involving combinations of analog amplifiers with mechanical resonators or delay lines. Other devices such as CCD delay lines have also been used as discrete-time filters. A charge-coupled device ( CCD) is an analog Shift register, that enables the transportation of analog signals (electric charges through successive stages (capacitors With the availability of digital signal processing, active digital filters have become common.
## Classification by technology
### Passive filters
Passive implementations of linear filters are based on combinations of resistors (R), inductors (L) and capacitors (C). |- align = "center"| |width = "25"| | |- align = "center"| || Potentiometer |- align = "center"| | | |- align = "center"| Resistor| | An inductor is a passive electrical component designed to provide Inductance in a circuit A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors These types are collectively known as passive filters, because they do not depend upon an external power supply.
Inductors block high-frequency signals and conduct low-frequency signals, while capacitors do the reverse. A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors A filter in which the signal passes through an inductor, or in which a capacitor provides a path to earth, presents less attenuation to low-frequency signals than high-frequency signals and is a low-pass filter. An inductor is a passive electrical component designed to provide Inductance in a circuit A low-pass filter is a filter that passes low- Frequency signals but Attenuates (reduces the Amplitude of signals with frequencies If the signal passes through a capacitor, or has a path to ground through an inductor, then the filter presents less attenuation to high-frequency signals than low-frequency signals and is a high-pass filter. A high-pass filter is a filter that passes high frequencies well but attenuates (reduces the amplitude of frequencies lower than the Cutoff frequency Resistors on their own have no frequency-selective properties, but are added to inductors and capacitors to determine the time-constants of the circuit, and therefore the frequencies to which it responds. |- align = "center"| |width = "25"| | |- align = "center"| || Potentiometer |- align = "center"| | | |- align = "center"| Resistor| |
At very high frequencies (above about 100 Megahertz), sometimes the inductors consist of single loops or strips of sheet metal, and the capacitors consist of adjacent strips of metal. The hertz (symbol Hz) is a measure of Frequency, informally defined as the number of events occurring per Second. These inductive or capacitive pieces of metal are called stubs. Electronics "? Perhaps "In MMICs quot ? Or is that *too* specific?
The inductors and capacitors are the reactive elements of the filter. The number of elements determines the order of the filter. In this context, an LC tuned circuit being used in a band-pass or band-stop filter is considered a single element even though it consists of two components. An LC circuit is a variety of resonant circuit or tuned circuit and consists of an Inductor, represented by the letter L and a Capacitor, represented
#### Single element types
The simplest passive filters consist of a single reactive element. These are constructed of RC, RL, LC or RLC elements. A resistor–capacitor circuit (RC circuit, or RC filter or RC network, is an Electric circuit composed of resistors and capacitors driven by A resistor-inductor circuit (RL circuit, or RL filter or RL network, is one of the simplest analogue Infinite impulse response An LC circuit is a variety of resonant circuit or tuned circuit and consists of an Inductor, represented by the letter L and a Capacitor, represented An RLC circuit (also known as a Resonant circuit tuned circuit or LCR circuit is an Electrical circuit consisting of a Resistor (R an
The quality or "Q" factor is a measure that is sometimes used to describe simple band-pass or band-stop filters. For other uses of the terms Q and Q factor see Q value. In Physics and Engineering the quality A filter is said to have a high Q if it selects or rejects a range of frequencies that is narrow in comparison to the centre frequency. Q may be defined as the ratio of centre frequency divided by 3dB bandwidth. It is not commonly employed with higher order filters where other parameters are of more concern.
#### L filter
Consists of two elements, one in series and one in parallel.
#### T filter
High-pass T filter
Three element filters in a 'T' configuration can be constructed for low-pass, high-pass, band-pass or band-stop.
#### π filter
Low-pass π filter
Three element filters in a 'π' configuration can be constructed for low-pass, high-pass, band-pass or band-stop.
#### Multiple element types
Multiple element filters are usually constructed as a ladder network. These can be seen as a continuation of the L,T and π designs of filters. More elements are needed when it is desired to improve some parameter of the filter such as stop-band rejection or speed of transition from pass-band to stop-band.
### Active filters
Active filters are implemented using a combination of passive and active (amplifying) components, and require an outside power source. An active filter is a type of analog Electronic filter, distinguished by the use of one or more Active components i Operational amplifiers are frequently used in active filter designs. An operational amplifier, often called an op-amp, is a DC - coupled high- Gain electronic voltage amplifier with differential These can have high Q, and can achieve resonance without the use of inductors. Electrical resonance occurs in an electric circuit at a particular resonance frequency when the impedance between the input and output of the However, their upper frequency limit is limited by the bandwidth of the amplifiers used.
### Digital filters
A finite impulse response filter
Digital signal processing allows the inexpensive construction of a wide variety of filters. Digital signal processing ( DSP) is concerned with the representation of the signals by a sequence of numbers or symbols and the processing of these signals The signal is sampled and an analog to digital converter turns the signal into a stream of numbers. An analog-to-digital converter (abbreviated ADC, A/D or A to D) is an electronic integrated circuit which converts continuous signals to A computer program running on a CPU or a specialized DSP (or less often running on a hardware implementation of the algorithm) calculates an output number stream. A digital signal processor ( DSP or DSP micro) is a specialized Microprocessor designed specifically for Digital signal processing, generally In Mathematics, Computing, Linguistics and related subjects an algorithm is a sequence of finite instructions often used for Calculation This output can be converted to a signal by passing it through a digital to analog converter. In Electronics, a digital-to-analog converter ( DAC or D-to-A) is a device for converting a digital (usually binary code to an Analog signal There are problems with noise introduced by the conversions, but these can be controlled and limited for many useful filters. Due to the sampling involved, the input signal must be of limited frequency content or aliasing will occur. This article applies to signal processing including computer graphics See also: Digital filter. In Electronics, Computer science and Mathematics, a digital filter is a system that performs mathematical operations on a sampling,
### Other filter technologies
#### Quartz filters and piezoelectrics
In the late 1930s, engineers realized that small mechanical systems made of rigid materials such as quartz would acoustically resonate at radio frequencies, i. The 1930s were described as an abrupt shift to more radical and conservative lifestyles as countries were struggling to find a solution to the Great Depression. Quartz (from German) is the most abundant Mineral in the Earth 's Continental crust (although Feldspar is more common in e. from audible frequencies (sound) up to several hundred megahertz. Sound' is Vibration transmitted through a Solid, Liquid, or Gas; particularly sound means those vibrations composed of Frequencies Some early resonators were made of steel, but quartz quickly became favored. Steel is an Alloy consisting mostly of Iron, with a Carbon content between 0 The biggest advantage of quartz is that it is piezoelectric. Piezoelectricity is the ability of some materials (notably Crystals and certain Ceramics including bone to generate an Electric potential in response to This means that quartz resonators can directly convert their own mechanical motion into electrical signals. Quartz also has a very low coefficient of thermal expansion which means that quartz resonators can produce stable frequencies over a wide temperature range. Quartz crystal filters have much higher quality factors than LCR filters. A crystal oscillator is an Electronic circuit that uses the mechanical Resonance of a vibrating Crystal of piezoelectric material to create an When higher stabilities are required, the crystals and their driving circuits may be mounted in a "crystal oven" to control the temperature. A crystal oven is a temperature-controlled chamber used to maintain the quartz crystal in electronic Crystal oscillators at a constant temperature in order to prevent changes For very narrow band filters, sometimes several crystals are operated in series.
Engineers realized that a large number of crystals could be collapsed into a single component, by mounting comb-shaped evaporations of metal on a quartz crystal. In this scheme, a "tapped delay line" reinforces the desired frequencies as the sound waves flow across the surface of the quartz crystal. An analog delay line is a network of electrical components connected in series where each individual element creates a time difference or phase change between its input The tapped delay line has become a general scheme of making high-Q filters in many different ways.
#### SAW filters
SAW (surface acoustic wave) filters are electromechanical devices commonly used in radio frequency applications. A surface acoustic wave ( SAW) is an Acoustic wave traveling along the surface of a material having some elasticity, with an Amplitude that In Engineering, electromechanics combines the Sciences of Electromagnetism of Electrical engineering and mechanics. Radio frequency ( RF) is a Frequency or rate of Oscillation within the range of about 3 Hz to 300 GHz Electrical signals are converted to a mechanical wave in a piezoelectric crystal; this wave is delayed as it propagates across the crystal, before being converted back to an electrical signal by further electrodes. Piezoelectricity is the ability of some materials (notably Crystals and certain Ceramics including bone to generate an Electric potential in response to An electrode is an Electrical conductor used to make contact with a nonmetallic part of a circuit (e The delayed outputs are recombined to produce a direct analog implementation of a finite impulse response filter. A finite impulse response (FIR filter is a type of a Digital filter. This hybrid filtering technique is also found in an analog sampled filter. An analog sampled filter an Electronic filter that is a hybrid between an analog and a Digital filter. SAW filters are limited to frequencies up to 3GHz.
#### BAW filters
BAW (Bulk Acoustic Wave) filters are electromechanical devices. In Engineering, electromechanics combines the Sciences of Electromagnetism of Electrical engineering and mechanics. These filters are in the research state for the moment. BAW filters can implement ladder or lattice filters. BAW filters seem to be smaller than SAW filters, and can operate at frequencies up to 16 GHz.
#### Garnet filters
Another method of filtering, at microwave frequencies from 800MHz to about 5 GHz, is to use a synthetic single crystal yttrium iron garnet sphere made of a chemical combination of yttrium and iron (YIGF, or yttrium iron garnet filter). Yttrium iron garnet filter ( YIG filter) is a magnetically tunable Filter for Microwave frequencies Microwaves are electromagnetic waves with Wavelengths ranging from 1 mm to 1 m or frequencies between 0 A single crystal, also called monocrystal, is a Crystalline Solid in which the Crystal lattice of the entire sample is continuous and unbroken Yttrium iron garnet ( YIG) is a kind of synthetic Garnet, with chemical composition 32(Fe43 or Y3Fe5O12 Yttrium (ˈɪtriəm is a Chemical element with symbol Y and Atomic number 39 Iron (ˈаɪɚn is a Chemical element with the symbol Fe (ferrum and Atomic number 26 The garnet sits on a strip of metal driven by a transistor, and a small loop antenna touches the top of the sphere. In Electronics, a transistor is a Semiconductor device commonly used to amplify or switch electronic signals An antenna is a Transducer designed to transmit or Receive electromagnetic waves In other words antennas convert electromagnetic waves into An electromagnet changes the frequency that the garnet will pass. An electromagnet is a type of Magnet in which the Magnetic field is produced by the flow of an electric current. The advantage of this method is that the garnet can be tuned over a very wide frequency by varying the strength of the magnetic field. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges
#### Atomic filters
For even higher frequencies and greater precision, the vibrations of atoms must be used. Atomic clocks use caesium masers as ultra-high Q filters to stabilize their primary oscillators. An atomic clock is a type of Clock that uses an Atomic resonance Frequency standard as its timekeeping element Caesium or cesium (ˈsiːziəm is the Chemical element with the symbol Cs and Atomic number 55 A maser is a device that produces coherent Electromagnetic waves through amplification due to Stimulated emission. Another method, used at high, fixed frequencies with very weak radio signals, is to use a ruby maser tapped delay line. A Ruby is a pink to blood-red Gemstone, a variety of the Mineral Corundum ( Aluminium oxide)
## The transfer function
The transfer function $\ H(s)$ of a filter is the ratio of the output signal $\ Y(s)$ to that of the input signal $\ X(s)$ as a function of the complex frequency $\ s$:
$\ H(s)=\frac{Y(s)}{X(s)}$
with $\ s = \sigma + j \omega$. A transfer function is a mathematical representation in terms of spatial or temporal frequency of the relation between the input and output of a ( linear time-invariant)
The transfer function of all linear time-invariant filters generally share certain characteristics:
• Since the filters are constructed of discrete components, their transfer function will be the ratio of two polynomials in $\ s$, i. e. a rational function of $\ s$. In Mathematics, a rational function is any function which can be written as the Ratio of two Polynomial functions Definitions In The order of the transfer function will be the highest power of $\ s$ encountered in either the numerator or the denominator.
• The polynomials of the transfer function will all have real coefficients. Therefore, the poles and zeroes of the transfer function will either be real or occur in complex conjugate pairs.
• Since the filters are assumed to be stable, the real part of all poles (i. e. zeroes of the denominator) will be negative, i. e. they will lie in the left half-plane in complex frequency space.
The proper construction of a transfer function involves the Laplace transform, and therefore it is needed to assume null initial conditions, because
$\mathcal{L}\left\{\frac{df}{dt}\right\} = s\cdot\mathcal{L} \left\{ f(t) \right\}-f(0),$
And when f(0)=0 we can get rid of the constants and use the usual expression
$\mathcal{L}\left\{\frac{df}{dt}\right\} = s\cdot\mathcal{L} \left\{ f(t) \right\}$
An alternative to transfer functions is to give the behavior of the filter as a convolution. In Mathematics, the Laplace transform is one of the best known and most widely used Integral transforms It is commonly used to produce an easily soluble algebraic In Mathematics and in particular Functional analysis, convolution is a mathematical operation on two functions f and The convolution theorem, which holds for Laplace transforms, guarantees equivalence with transfer functions. In Mathematics, the convolution theorem states that under suitableconditions the Fourier transform of a Convolution is the Pointwise product
## Classification by transfer function
Main article: transfer function
Filters may be specified by family and passband. A transfer function is a mathematical representation in terms of spatial or temporal frequency of the relation between the input and output of a ( linear time-invariant) A filter's family is specified by certain design criteria which give general rules for specifying the transfer function of the filter. Some common filter families and their particular design criteria are:
Generally, each family of filters can be specified to a particular order. The Butterworth filter is one type of Electronic filter design Chebyshev filters are analog or Digital filters having a steeper Roll-off and more Passband ripple (type I or Chebyshev filters are analog or Digital filters having a steeper Roll-off and more Passband ripple (type I or In Electronics and Signal processing, a Bessel filter is a variety of Linear filter with a maximally flat Group delay (linear Phase response An elliptic filter (also known as a Cauer filter, named after Wilhelm Cauer) is an Electronic filter with equalized ripple ( Equiripple The Optimum "L" filter (also known as a Legendre filter) was proposed by Athanasios Papoulis in 1958 In Electronics and Signal processing, a Gaussian filter is a filter whose Filter window is the Gaussian function x The raised-cosine filter is a particular Electronic filter, frequently used for Pulse-shaping in digital Modulation due to its ability to minimise The higher the order, the more the filter will approach the "ideal" filter. The ideal filter has full transmission in the pass band, and complete attenuation in the stop band, and the transition between the two bands is abrupt (often called brick-wall).
Here is an image comparing Butterworth, Chebyshev, and elliptic filters. The filters in this illustration are all fifth-order low-pass filters. The particular implementation -- analog or digital, passive or active -- makes no difference; their output would be the same.
As is clear from the image, elliptic filters are sharper than all the others, but they show ripples on the whole bandwidth.
Each family can be used to specify a particular pass band in which frequencies are transmitted, while frequencies in the stop band (i. e. outside the pass band) are more or less attenuated.
• Low-pass filter - Low frequencies are passed, high frequencies are attenuated. A low-pass filter is a filter that passes low- Frequency signals but Attenuates (reduces the Amplitude of signals with frequencies
• High-pass filter - High frequencies are passed, Low frequencies are attenuated. A high-pass filter is a filter that passes high frequencies well but attenuates (reduces the amplitude of frequencies lower than the Cutoff frequency
• Band-pass filter - Only frequencies in a frequency band are passed. A band-pass filter is a device that passes frequencies within a certain range and rejects ( Attenuates frequencies outside that range
• Band-stop filter - Only frequencies in a frequency band are attenuated. In Signal processing, a band-stop filter or band-rejection filter is a filter that passes most frequencies unaltered but Attenuates
• All-pass filter - All frequencies are passed, but the phase of the output is modified. An all-pass filter is an Electronic filter that passes all frequencies equally but changes the phase relationship between various frequencies
The family and passband of a filter completely specify the transfer function of a filter. The transfer function completely specifies the behavior of a linear filter, but not the particular technology used to implement it. In other words, there are a number of different ways of achieving a particular transfer function when designing a circuit.
## Classification by topology
Electronic filters can be classified by the technology used to implement them. Filters using passive filter and active filter technology can be further classified by the particular electronic filter topology used to implement them. Passivity is a property of engineering systems most commonly used in electronic engineering and control systems An active filter is a type of analog Electronic filter, distinguished by the use of one or more Active components i An electronic filter topology is an electronic Analog filter circuit in which the values of the components remain undefined
Any given filter transfer function may be implemented in any electronic filter topology. An electronic filter topology is an electronic Analog filter circuit in which the values of the components remain undefined
Some common circuit topologies are:
## Classification by design methodology
Linear analog electronic filters
edit
Historically, linear analog filter design has evolved through three major approaches. Multiple feedback topology is an Electronic filter topology which is used to implement an Electronic filter by adding two poles to the Transfer function State Variable Topology refers to filters with two pole filter topology. For the digital implementation of a biquad filter check digital biquad filter The Butterworth filter is one type of Electronic filter design Chebyshev filters are analog or Digital filters having a steeper Roll-off and more Passband ripple (type I or An elliptic filter (also known as a Cauer filter, named after Wilhelm Cauer) is an Electronic filter with equalized ripple ( Equiripple In Electronics and Signal processing, a Bessel filter is a variety of Linear filter with a maximally flat Group delay (linear Phase response In Electronics and Signal processing, a Gaussian filter is a filter whose Filter window is the Gaussian function x The Optimum "L" filter (also known as a Legendre filter) was proposed by Athanasios Papoulis in 1958 A Linkwitz-Riley (L-R filter is an infinite impulse response filter used in Linkwitz-Riley Audio crossovers named after its inventors Siegfried Linkwitz Electronic filters designed from the Image impedance point of view are called image filters Constant k filters are a type of Electronic filter designed using the image method m-type filters or m-derived filters are a type of Electronic filter designed using the image method For the wave filter invented by Zobel and sometimes named after him see M-derived filters. Electronic filters designed from the Image impedance point of view are called image filters A resistor-inductor circuit (RL circuit, or RL filter or RL network, is one of the simplest analogue Infinite impulse response A resistor–capacitor circuit (RC circuit, or RC filter or RC network, is an Electric circuit composed of resistors and capacitors driven by An RLC circuit (also known as a Resonant circuit tuned circuit or LCR circuit is an Electrical circuit consisting of a Resistor (R an An LC circuit is a variety of resonant circuit or tuned circuit and consists of an Inductor, represented by the letter L and a Capacitor, represented The oldest designs are simple circuits where the main design criterion was the Q factor of the circuit. For other uses of the terms Q and Q factor see Q value. In Physics and Engineering the quality This reflected the radio receiver application of filtering as Q was a measure of the frequency selectivity of a tuning circuit. From the 1920s filters began to be designed from the image point of view, mostly being driven by the requirements of telecommunications. Image impedance is a concept used in electronic network design and analysis and most especially in filter design After WW2 the dominant methodology was network synthesis. World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including The higher mathematics used originally required extensive tables of polynomial coefficient values to be published but modern computer resources have made that unnecessary. [1]
### Direct circuit analysis
Low order filters can be designed by directly applying basic circuit laws such as Kirchoff's laws to obtain the transfer function. This kind of analysis is usually only carried out for simple filters of 1st or 2nd order.
RL filter frequency response
### Image impedance analysis
This approach analyses the filter sections from the point of view of the filter being in an infinite chain of identical sections. It has the advantages of simplicity of approach and the ability to easily extend to higher orders. It has the disadvantage that accuracy of predicted responses rely on filter terminations in the image impedance, which is usually not the case. [2]
Constant k filter response with 5 elements
Zobel network (constant R) filter, 5 sections
m-derived filter response, m=0. 5, 2 elements
m-derived filter response, m=0. 5, 5 elements
### Network synthesis
The network synthesis approach starts with a required transfer function and then expresses that as a polynomial equation of the input impedance of the filter. The actual element values of the filter are obtained by continued-fraction or partial-fraction expansions of this polynomial. Unlike the image method, there is no need for impedance matching networks at the terminations as the effects of the terminating resistors are included in the analysis from the start. [2]
1. ^ Bray, J, Innovation and the Communications Revolution, Institute of Electrical Engineers
2. ^ a b Mathaei, Young, Jones Microwave Filters, Impedance-Matching Networks, and Coupling Structures McGraw-Hill 1964
• Zverev, Anatol, I (1969). An analogue filter handles analogue signals or continuous-time signals whether Electric potential, sound waves, or mechanical In Electronics, Computer science and Mathematics, a digital filter is a system that performs mathematical operations on a sampling, Passivity is a property of engineering systems most commonly used in electronic engineering and control systems An active filter is a type of analog Electronic filter, distinguished by the use of one or more Active components i A linear filter applies a Linear operator to a time-varying input signal A nonlinear filter is a signal-processing device whose output is not a Linear function of its input Switched capacitor is a circuit design technique for discrete time Signal processing. A Voltage -controlled filter (VCF is an Electronic filter whose operating characteristics can be controlled by means of a control voltage applied to one or more inputs In Physics, resonance is the tendency of a system to Oscillate at maximum Amplitude at certain frequencies, known as the system's For other uses of the terms Q and Q factor see Q value. In Physics and Engineering the quality An audio filter is a type of filter used for processing Sound signals. Audio crossovers are a class of Electronic filters designed specifically for use in audio applications especially Hi-fi. Tone control circuits are electronic circuits used to modify an audio signal before it is fed to Speakers, Headphones or recording In Signal processing, a comb filter adds a delayed version of a signal to itself causing constructive and destructive interference. In digital signal processing, a cascaded integrator-comb (CIC is an optimized class of Finite impulse response filter combined with an interpolator or The spurline is a type of Radio-frequency and Microwave filter with Band-stop (notch characteristics most commonly used with Microstrip Handbook of Filter Synthesis. John Wiley & Sons. ISBN 0-471-98680-1. Catalog of passive filter types and component values. The Bible for practical electronic filter design.
• Williams, Arthur B & Taylor, Fred J (1995). Electronic Filter Design Handbook. McGraw-Hill. ISBN 0-07-070441-4.
• National Semiconductor AN-779 application note describing analog filter theory
• Fundamentals of Electrical Engineering and Electronics - Detailed explanation of all types of filters
• BAW filters (in French; PDF)
• Some Interesting Filter Design Configurations & Transformations
• Books and tutorials how to design RF Filters
• Analog Filters for Data Conversion
A datasheet is a Document summarizing the performance and other characteristics of a component (e
© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
network: | | | 6,342 | 31,924 | {"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": 11, "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-2013-20 | longest | en | 0.941172 |
http://mathhelpforum.com/number-theory/6412-uncomfortable-induction-hypothesis.html | 1,521,507,118,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257647244.44/warc/CC-MAIN-20180319234034-20180320014034-00414.warc.gz | 195,905,608 | 10,281 | # Thread: uncomfortable with induction hypothesis...
1. ## uncomfortable with induction hypothesis...
Hi guys, I'm totally new to number theory, so bear with me...
I'm only on page 2 of the textbook and am already stuck
To prove 1+2+3.... +n = n(n+1)/2, we are supposed to assume 1+2+3...+k = k(k+1)/2 for n<=k, and then add k+1 to both sides, etc. etc.
Okay, isn't that first assumption the very statement that we are trying to prove, except replacing n with k? Can someone enlighten me as to how this makes sense?
2. Originally Posted by yc6489
Hi guys, I'm totally new to number theory, so bear with me...
I'm only on page 2 of the textbook and am already stuck
To prove 1+2+3.... +n = n(n+1)/2, we are supposed to assume 1+2+3...+k = k(k+1)/2 for n<=k, and then add k+1 to both sides, etc. etc.
Okay, isn't that first assumption the very statement that we are trying to prove, except replacing n with k? Can someone enlighten me as to how this makes sense?
The general form of an induction proof of a statement S(N) about a natural
number N is:
1. Show S(N0) is true for some initial N=N0, this is called the base case
and N0 is often 0 or 1.
2. Show that if S(k) is true for some natural number k, then it is also
true for k+1.
3. Then as it is true for N0, it is true for N0+1, and then for N0+2, and so
on, so we conclude that for any natural number N>N0 it is true, as we can
connect it to the base case by a chain of step 2 above.
4. As we now have that S(N) is true for any natural N>=N0, we conclude
that it is true for all naturals >= N0.
Now your problem is to prove:
1+2+3.... +n = n(n+1)/2
for all natural numbers this is our statement S(n). We take as our base case
n0=1, when S(1) is the assertion:
1 = 1(2)/2 = 1,
which is true, so our base case is true.
Now we assume that S(k) is true for some k and show it true for k+1.
As we are assuming S(k) is true this is the assumption that:
1+2+3.... +k = k(k+1)/2.
Now add (k+1) to each side:
1+2+3.... +k+(k+1) = k(k+1)/2 + (k+1).
Rearrange the right hand side of this equation:
1+2+3.... +k+(k+1) = (1/2)k^2 + (3/2)k +1
..........................= (k+1)(k+2)/2
..........................= (k+1)[(k+1) + 1]/2.
But this equation is now S(k+1), which is:
1+2+3.... +(k+1) = (k+1)[(k+1)+1)/2.
So from the assumption that S(k) was true we have shown that S(k+1)
must also be true, combining this with the base case S(1) which we have
already shown to be true we may conclude by induction that S(n) is true
for all natural numbers n>=1.
RonL | 807 | 2,530 | {"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} | 4.03125 | 4 | CC-MAIN-2018-13 | latest | en | 0.951368 |
https://math.stackexchange.com/questions/1535307/r-1-r-2-r-phim-is-a-reduced-residue-system-modulo-m-iff-r-1 | 1,576,159,185,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540543850.90/warc/CC-MAIN-20191212130009-20191212154009-00446.warc.gz | 449,322,538 | 30,963 | # $\{r_1,r_2,…,r_{\phi(m)}\}$ is a reduced residue system modulo $m$ iff $\{r_1+k,r_2+k,…,r_{\phi(m)}+k\}$ be a reduced residue system modulo $m$
Let $2\lt m\in \mathbb N$ and $\{r_1,r_2,...,r_{\phi(m)}\}$ be a reduced residue system modulo $m$. I want to find a necessary and sufficient condition for $k$ such that the set $\{r_1+k,r_2+k,...,r_{\phi(m)}+k\}$ be a reduced residue system modulo $m$ to.
I now that:
Theorem: if $c_1,c_2,\ldots,c_{\varphi(m)}$ be the reduced residue set modulo $m>2$, then $$c_1+c_2+\cdots+c_{\varphi(m)} \equiv 0 \pmod{m}$$ (see here)
We want to the set $\{r_1+k,r_2+k,...,r_{\phi(m)}+k\}$ be a reduced residue system modulo $m$. So, by above theorem: $$r_1+k+r_2+k+...+r_{\phi(m)}+k\equiv 0 \pmod{m}$$ Because of the set: $\{r_1,r_2,...,r_{\phi(m)}\}$ is a reduced residue system modulo $m$, $$r_1+r_2+...+r_{\phi(m)}\equiv 0 \pmod{m}$$ So, we should have: $k\phi(m) \equiv 0 \pmod{m}$. Thus, the necessary condition is that: $k\phi(m) \equiv 0 \pmod{m}$. Is this condition sufficient? if not, what is the sufficient condition?
The condition $k\phi(m) \equiv 0 \bmod{m}$ is not sufficient.
Take $m=6$ and $k=3$.
Then $k\phi(m) = 3\cdot 2 \equiv 0 \bmod{m}$ but $\{1,5\}$ is a reduced residue system modulo $6$ and $\{1+3,5+3\} \equiv \{4,2\}$ is not a reduced residue system modulo $6$.
Some other examples are $m=10, k=5$ and $m=12, k=3$.
More generally, if $m=2^e n$, with $n$ an odd, take $k=n$. Then $k\phi(m) =n 2^{e-1}\phi(n) \equiv 0 \bmod{m}$ because $\phi(n)$ is even. But $1+n$ is even and so is not a unit mod $m$.
## The general case
Since the map $x\mapsto x+k$ is injective when considered as a map on $\mathbb Z/m$, it will induce a permutation of $U(m)$ if it sends units to units. So, the real question is:
When does $x\mapsto x+k$ preserve units mod $m$ ?
I don't have a complete proof right now, the answer seems to be this:
$x\mapsto x+k$ preserves units mod $m$ iff $k$ is a multiple of $\operatorname{rad}(m)$.
Here is a proof of one direction.
Take $k=tr$, a multiple of $r=\operatorname{rad}(m)$. Let $u$ be a unit and consider $u+k=u+tr$. If a prime divisor of $m$ divided $u+tr$, then it would divide $u$, which it doesn't. So $u+k$ is a unit whenever $u$ is unit.
I'd love to see a proof of the other direction.
As a consequence, there are no $k\ne0$ if $m$ is squarefree, because then $\operatorname{rad}(m)=m$ and $k \equiv 0 \bmod m$.
• – lhf Nov 26 '15 at 23:03 | 904 | 2,445 | {"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} | 3.46875 | 3 | CC-MAIN-2019-51 | latest | en | 0.666688 |
https://ccrma.stanford.edu/~jos/ncbs/Simulation_Results.html | 1,590,993,914,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347414057.54/warc/CC-MAIN-20200601040052-20200601070052-00251.warc.gz | 285,483,345 | 3,798 | Conclusions
Pulsed Noise
Nonlinear Commuted Synthesis of Bowed Strings Contents Global Contents
Global Index Index Search
# Simulation Results
Figure 3 displays waveforms generated by the bow-string model given a constant bow force, velocity, and position. The frictional force applied to the string by the bow can be seen to diminish as the oscillation develops. The string displacement near the bridge clearly exhibits the single main impulse once per period associated with canonical Helmholtz bowed-string motion; there are also many secondary impulses associated with the ringing of the piece of the string between the bridge and the bow. The complexity control will determine whether these secondary impulses are included or suppressed.
Figure 4 illustrates the samples of bridge displacement waveform over a longer period of time. Note that each main Helmholtz impulse plots as two adjacent samples, indicating that a single-sample impulse is traveling on the string. (The observation point is 1/2 spatial sample from the bridge, so that a single impulse at the bridge appears twice, both before and after reflection at the bridge.) Note also that late in the stroke, a strong secondary impulse has developed, making the sound tend toward an octave higher. This ``sul ponticello'' sound is associated with insufficient bow force.
Figure 5 gives a close-up of the frictional force during the initial attack transient. As can be seen, even though the applied bow force and velocity are constant, a highly complex interaction occurs between the bow and string.
Figure 6 shows an overlay of the first 40 periods of oscillation of the bowed string, with each string snapshot taken slightly later than one period after the previous, and the first snapshot being taken at time zero. The bow is at the sharp upper corner on the left. Note that the vertical scale is highly magnified relative to the horizontal scale. There is also some distortion in the string shape resulting from the lumping of the string losses at the bridge and bowing point, as is typical in waveguide string modeling.
Conclusions
Pulsed Noise
Nonlinear Commuted Synthesis of Bowed Strings Contents Global Contents
Global Index Index Search
``Nonlinear Commuted Synthesis of Bowed Strings'', by Julius O. Smith III, Proceedings of the International Computer Music Conference (ICMC-97, Thessaloniki), Computer Music Association, 1997.. | 490 | 2,428 | {"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-2020-24 | longest | en | 0.923148 |
https://documen.tv/question/your-lab-assignment-for-the-week-is-to-measure-the-amount-of-charge-on-the-6-0-cm-diameter-metal-16157766-81/ | 1,638,176,470,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358702.43/warc/CC-MAIN-20211129074202-20211129104202-00007.warc.gz | 292,943,979 | 17,433 | ## Your lab assignment for the week is to measure the amount of charge on the 6.0-cm-diameter metal sphere of a Van de Graaff generator. To do
Question
Your lab assignment for the week is to measure the amount of charge on the 6.0-cm-diameter metal sphere of a Van de Graaff generator. To do so, you’re going to use a spring with spring constant 0.65 N/m to launch a small 1.5 g bead horizontally toward the sphere. You can reliably charge the bead to 2.5 nC, and your plan is to use a video camera to measure the bead’s closest approach to the edge of the sphere as you change the compression of the spring. You’ll then add 3.0-cm, the radius of the sphere, to each to have the distance to the center of the sphere. Your data are as follows:
Compression (cm) Closest approach (cm)
1.6 5.5
1.9 2.6
2.2 1.6
2.5 0.4
Determine the sphere’s charge in nC?
in progress 0
4 months 2021-07-22T00:16:27+00:00 1 Answers 0 views 0
The charge on the sphere is = 309 nC
Explanation:
The electric potential energy is given by the equation:
where;
Permittivity constant
the distance between the two charges = r
The kinetic energy that is said to be given by the spring to the bead is converted to electric potential energy at the closest approach.
So; the kinetic energy is equal to the the elastic potential energy;
The elastic potential energy is represented by the equation:
where
k = spring constant
x = displacement from the equilibrium position
Converting the charge of the bead from nano coulombs to coulombs ; we have:
Thus, the bead is approaching the metal sphere of Van de Graff generator. Then the kinetic energy is being transferred to electric potential energy. The process ends when it reaches to the sphere with the Closest approach.
∴ The charge of the sphere can be determined by relating the electric potential energy to elastic potential energy.
Making the subject pf the formula; we have:
Thus the charge on the sphere is = 309 nC | 488 | 1,961 | {"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-2021-49 | latest | en | 0.901225 |
https://www.classace.io/learn/math/3rdgrade/writing-numbers-in-words | 1,716,543,490,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058709.9/warc/CC-MAIN-20240524091115-20240524121115-00239.warc.gz | 627,440,494 | 32,167 | Writing Numbers in Words
Start Practice
## How to Write Numbers in Words
You can write numbers with either digits or words.
1 or One
Whenever you use a number less than one hundred in a sentence, write it as a word.
For example:
I bought three tomatoes.
Kobe Bryant scored sixty goals in his last game.
### Writing Numbers up to 100
Here's how we write the multiples of Tens and Ones in words:
👉 Most two-digit numbers are a combination of these words.
How do we write 30? 🤔
30 doesn't have any Ones. So we just write:
thirty
Start by dividing it into Tens and Ones:
60 + 5
Next we turn each place value into a word, and add a hyphen (-).
sixty-five
Always add a hyphen (-) when writing numbers with both tens and ones.
Let's try one more. How do we write 91?
91 has both Tens and Ones.
90 + 1
👉 So we write each term in words with a hyphen between them.
ninety-one
### Writing 11-19
11 through 19 are special. They don't follow the pattern we just learned. 🙈
You'll have to memorize them:
11 = eleven
12 = twelve
13 = thirteen
14 = fourteen
15 = fifteen
16 = sixteen
17 = seventeen
18 = eighteen
19 = nineteen
Tip: thirteen through nineteen end in teen. That's how old teenagers are.
### Writing Numbers up to 1,000
Now that you’re in 3rd grade, you’ll learn to write numbers up to 1,000! 💪
Let’s start by adding a column to our chart:
When we have a 3-digit number, we have to write the Hundreds place out, too!
The easy part is we dont have to add a hyphen!
Let’s try it:
675
Start by writing the number out in Hundreds, Tens, and Ones.
600 + 70 + 5
Great! Now, let’s find the word for each number:
Six hundred seventy-five
We write every digit and its value, and add a hyphen only between the Tens and Ones.
Let’s try one more:
383
First, expand the number:
300 + 80 + 3
Now, write the word for each number:
Three hundred eighty-three
Great job. 🤗
Now, complete the practice. 😺 You'll really be able to write words after!
It's an important life skill. Do your best!
### Lesson Streak
0 days
T
F
S
S
M
T
W
Complete a practice every day to build your streak
Start Practice
Complete the practice to earn 1 Create Credit
1,000 Create Credits is worth \$1 in real AI compute time.
1 Create Credit is enough to get 1 question answered, or to generate 1 image from text, in the tools tab.
Teachers:
Assign to students
Duplicate
Edit Questions
Edit Article
Assign
Preview Questions
Edit
Duplicate | 648 | 2,444 | {"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} | 4.625 | 5 | CC-MAIN-2024-22 | latest | en | 0.902243 |
https://coursesity.com/free-tutorials-learn/linear-algebra?ref=detail-bread | 1,713,711,454,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817780.88/warc/CC-MAIN-20240421132819-20240421162819-00219.warc.gz | 163,058,686 | 65,349 | 10,000+ Free Udemy Courses to Start Today
View Courses
# Free Linear Algebra Courses online
Learn linear algebra with the free linear algebra tutorials and online courses.
Clear filters
Apply
## Introduction to Linear Algebra: Vectors
Learn the fundamental vector arithmetic operations.
1 reviews
1 h 31 m
## Python for linear algebra (for absolute beginners)
Dip your toes into the fascinating world of using Python code to comprehend vectors and matrices.
275 reviews
1 h 49 m
## First Steps in Linear Algebra for Machine Learning
Learn First Steps in Linear Algebra for Machine Learning from National Research University Higher School of Economics.
(*)(*)(*)(*)(*)4.3
4 reviews
14 h
## The Math of Data Science: Linear Algebra
You will discover the basic objects of linear algebra – how to compute with them, how they fit together theoretically, and how they can be used to solve real problems.
56 h
## Linear Algebra Refresher Course
Learn linear algebra by doing: you will code your own library of linear algebra functions!
64 h
## Mathematics for Machine Learning - Linear Algebra - Full Online Specialism
Welcome to the “Mathematics for Machine Learning: Linear Algebra” course, offered by Imperial College London.
4 h 23 m
## Linear Algebra Full Course for Beginners to Experts
Linear algebra is central to almost all areas of mathematics.
8 h 33 m
## Linear Algebra for Beginners
Linear algebra is the branch of mathematics concerning linear equations such as linear functions and their representations through matrices and vector spaces.
1 h 35 m
## Introduction to Abstract and Linear Algebra
Abstract and Linear Algebra are applicable to every discipline, be it engineering and technology, economics or social sciences.
32 h
## Introduction to Computation Theory
Introduction to Computation Theory is an overview of some basic principles of computation and computational complexity
### Subjects
##### Details about free Linear Algebra classes and courses
Want to learn linear algebra ? This is the list of free linear algebra courses available online. From this list, you can take any of the linear algebra course to learn linear algebra in details and become master of linear algebra.
Learn linear algebra from the free linear algebra courses and free linear algebra classes online. Select free courses for linear algebra based on your skill level either beginner or expert. These are the free linear algebra classes and courses to learn linear algebra step by step.
##### Collection of free Linear Algebra Courses
These free linear algebra courses are collected from MOOCs and online education providers such as Udemy, Coursera, Edx, Skillshare, Udacity, Bitdegree, Eduonix, QuickStart, YouTube and more. Find the free linear algebra classes, courses and get free training and practical knowledge of linear algebra.
Get started with linear algebra for free and learn fast from the scratch as a beginner. Find free linear algebra classes for beginners that may include projects, practice exercises, quizzes and tests, video lectures, examples, certificate and advanced your linear algebra level. Some courses provide free certificate on course completion.
linear algebra courses are categorized in the free, discount offers, free trials based on their availability on their original platforms like Udemy, Coursera, Edx, Udacity, skillshare, Eduonix, QuickStart, YouTube and others Moocs providers. The linear algebra courses list are updated at regular interval to maintain latest status.
After collecting courses and tutorials from different Moocs and education providers, we filter them based on its pricing, subject type, certification and categorize them in the relevant subject or programming language or framework so you do not have to waste time in finding the right course and start learning instead.
##### Suggest more Linear Algebra Courses or Tutorials ?
Do you think any linear algebra class or linear algebra course need to include on this list? Please submit new linear algebra class and share your linear algebra course with other community members now.
We have curated the high rated Linear Algebra courses to save your time.
Top Linear Algebra Courses | 806 | 4,231 | {"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-2024-18 | latest | en | 0.827066 |
http://www.presentica.com/ppt-presentation/dr-ka-fu-wong-47090 | 1,550,768,276,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550247505838.65/warc/CC-MAIN-20190221152543-20190221174543-00250.warc.gz | 420,447,444 | 14,905 | 1 / 37
# Dr. Ka-fu Wong.
68 views
Category: Medical / Health
Description
A bar diagram can be utilized to delineate any of the levels of estimation ... Pie Chart. A pie outline is valuable for showing a relative recurrence dissemination. A circle is separated ...
Transcripts
Slide 1
Dr. Ka-fu Wong ECON1003 Analysis of Economic Data
Slide 2
Chapter Two Describing Data: Frequency Distributions and Graphic Presentation GOALS Organize information into a recurrence circulation. Depict a recurrence dissemination in a histogram, recurrence polygon, and total recurrence polygon. Build up a stem-and-leaf show. Present information utilizing such realistic strategies as line graphs, bar diagrams, and pie outlines.
Slide 3
Frequency Distribution A Frequency appropriation is a gathering of information into fundamentally unrelated classifications demonstrating the quantity of perceptions in every class.
Slide 4
Construction of a Frequency Distribution Question to be tended to. Gather information (crude information). Compose information. Recurrence circulation Present information. Reach determination.
Slide 5
Terms Related to Frequency Distribution In developing a recurrence circulation, information are separated into comprehensive and fundamentally unrelated classes. Mid-point: A point that partitions a class into two a balance of. This is the normal of the upper and lower class limits. Class recurrence: The quantity of perceptions in every class. Class interim: The class interim is gotten by subtracting the lower furthest reaches of a class from the lower furthest reaches of the following class.
Slide 6
Four stages to build recurrence conveyance Decide on the quantity of classes. Decide the class interim or width. Set the individual class limits. Count the information into the classes and include the quantity of things each. For outline, it is advantageous to convey a case with us – case 1 .
Slide 7
EXAMPLE 1 Dr. Tillman is Dean of the School of Business Socastee University. He wishes to set up a report demonstrating the quantity of hours every week understudies spend concentrating on. He chooses an irregular specimen of 30 understudies and decides the quantity of hours every understudy concentrated a week ago. 15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6. Sort out the information into a recurrence dissemination.
Slide 8
Step 1: Decide on the quantity of classes. The objective is to utilize simply enough groupings or classes to uncover the state of the dissemination. " sufficiently just " Recipe –" 2 to the k principle " Select the littlest number (k) for the quantity of classes such that 2 k is more prominent than the quantity of perceptions (n).
Slide 9
Sample size (n) = 80 2 1 =2; 2 =4; 2 3 =8; 2 4 =16; 2 5 =32; 2 6 =64; 2 7 =128; … The principle propose 7 classes. Test size (n) = 1000 2 1 =2; 2 =4; 2 3 =8; 2 4 =16; 2 5 =32; 2 6 =64; 2 7 =128; 2 8 =256; 2 9 =512; 2 10 =1024 … The standard recommend 10 classes. 2 to the k guideline Select the littlest number (k) for the quantity of classes such that 2 k is more noteworthy than the quantity of perceptions (n).
Slide 10
Sample size (n)=10000 2 1 =2; 2 =4; 2 3 =8; 2 4 =16; 2 5 =32; 2 6 =64; 2 7 =128; … ,2 13 =8192; 2 14 = 16384 The standard propose 14. Test size (n)=100000 2 =4; 2 3 =8; 2 4 =16; 2 5 =32; 2 6 =64; 2 7 =128; … 2 to the k standard Select the littlest number (k) for the quantity of classes such that 2 k is more prominent than the quantity of perceptions (n).
Slide 11
2 to the k guideline Select the littlest number (k) for the quantity of classes such that 2 k is more prominent than the quantity of perceptions (n). We need to discover littlest k such that 2 k > n . Littlest k such that k log 2 > log n Smallest k such that k > (log n)/(log 2) Example: If n=10000, (log n)/(log 2) = 13.28. Subsequently the formula propose 14 classes. Note: Same result for base 10 log and normal log .
Slide 12
Step 1: Decide on the quantity of classes. 2 to the k principle Select the littlest number (k) for the quantity of classes such that 2 k is more noteworthy than the quantity of perceptions (n). Case 1 (proceeded with): Sample size (n) = 30 2 1 =2; 2 =4; 2 3 =8; 2 4 =16; 2 5 =32; 2 6 =64; 2 7 =128; … The tenet propose 5 classes . Elective, by figuring (Log 30/log 2) = 4.91, we get the same proposal of 5 classes.
Slide 13
Step 2: Determine the class interim or width. By and large the class interim or width ought to be the same for all classes . The classes all taken together should cover in any event the separation from the most minimal quality in the crude information to the most astounding worth. The classes must be totally unrelated and thorough . Class interim ≥ (Highest quality – most reduced worth)/number of classes. Generally we will picked some helpful number as class interim that fulfill the disparity.
Slide 14
Step 2: Determine the class interim or width. Class interim ≥ (Highest quality – most minimal worth)/number of classes. Case 1 (proceeded with): Highest quality = 33.8 hours Lowest esteem = 10.3 hours k=5 . Subsequently, class interim ≥ (33.8-10.3)/5 = 4.7 We pick class interim to be 5 , some helpful number.
Slide 15
Step 3: Set the individual class confines as far as possible must be set so that the classes are fundamentally unrelated and thorough . Round up so some helpful numbers.
Slide 16
Step 3: Set the individual class limits Example 1 (proceed with): Highest quality = 33.8 hours. Least esteem = 10.3 hours. Range = most noteworthy – least = 23.5. K=5 ; Interval = 5. With k=5 and interim = 5, the classes will cover a scope of 25. Let " s split the surplus in the lower and upper tail similarly. (25-23.5)/2 = 0.75. Consequently, the lower furthest reaches of the top notch ought to be around (10.3 – 0.75)=9.55 and maximum farthest point of the last class ought to be (33.8 + 0.75)=34.55. 9.55 and 34.55 look odd. Some advantageous and close numbers would be 10 and 35.
Slide 17
Step 3: Set the individual class limits Example 1 (proceed with): We have decided K=5; Interval = 5. The lower furthest reaches of the top of the line = 10 and The maximum furthest reaches of the last class = 35. "10 up to 15" implies the interim from 10 to 15 that incorporates 10 however not 15.
Slide 18
Step 4: Tally the information into the classes and include the quantity of things each 15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6. Hours studying 7 10 up to 15 12 15 up to 20 up to 25 7 25 up to 30 3 30 up to 35 1
Slide 19
EXAMPLE 1 ( proceeded with )
Slide 20
EXAMPLE 1 ( proceeded with ) A relative recurrence appropriation demonstrates the percent of perceptions in every class.
Slide 21
Stem-and-leaf Displays Stem-and-leaf show: A factual strategy for showing an arrangement of information. Each numerical quality is isolated into two sections: the main digits turn into the stem and the trailing digits the leaf. Note : preference of the stem-and-leaf show over a recurrence dissemination is we don\'t lose the personality of every perception. An impediment is that it is bad for extensive information sets.
Slide 22
EXAMPLE 2 Colin accomplished the accompanying scores on his twelve bookkeeping tests this semester: 86, 79, 92, 84, 69, 88, 91, 83, 96, 78, 82, 85. Develop a stem-and-leaf diagram.
Slide 23
EXAMPLE 2 (proceeded) 86, 79, 92, 84, 69, 88, 91, 83, 96, 78, 82, 85. Stem Leaf 6 9 8 9 7 8 6 4 8 3 2 5 9 2 6 1
Slide 24
EXAMPLE 2 (proceeded) 86, 79, 92, 84, 69, 88, 91, 83, 96, 78, 82, 85. Stem Leaf 6 9 8 7 4 2 3 8 5 6 8 9 1 6 2
Slide 25
Graphic Presentation of a Frequency Distribution The three regularly utilized realistic structures are histograms , recurrence polygons , and a total recurrence dispersion . A Histogram is a diagram in which the classes are set apart on the even pivot and the class frequencies on the vertical hub. The class frequencies are spoken to by the statures of the bars and the bars are attracted nearby each other.
Slide 26
Graphic Presentation of a Frequency Distribution A recurrence polygon comprises of line portions interfacing the focuses framed by the class midpoint and the class recurrence. An aggregate recurrence conveyance is utilized to decide what number of or what extent of the information qualities are underneath or over a specific worth.
Slide 27
Histogram for quite a long time Spent Studying Example 1 (proceeded with): A Histogram is a chart in which the classes are set apart on the level hub and the class frequencies on the vertical pivot.
Slide 28
Frequency Polygon for quite a long time Spent Studying Example 1 (proceeded with): A recurrence polygon comprises of line fragments interfacing the focuses shaped by the class midpoint and the class recurrence.
Slide 29
Cumulative Frequency Distribution For Hours Studying Example 1 (proceeded with): An aggregate recurrence circulation is utilized to decide what number of or what extent of the information qualities are underneath or over a specific worth.
Slide 30
Bar Chart A bar diagram can be utilized to delineate any of the levels of estimation (ostensible, ordinal, interim, or proportion).
Slide 31
Example 3 Construct a bar outline for the quantity of unemployed per 100,000 populace for chose urban communities amid 2001
Slide 32
Bar Chart for the Unemployment Data Example 3 (proceeded):
Slide 33
Pie Chart A pie graph is valuable for showing a relative recurrence circulation. A circle is partitioned relatively to the relative recurrence and bits of the circle are allotted for the diverse gatherings.
Slide 34
EXAMPLE 4 A specimen of 200 runners were solicited to demonstrate their most loved sort from running shoe. Draw a pie outline in light of the accompanying data.
Slide 35
EXAMPLE 4 ( proceeded with ) Compute the rate and degree every sort possess out of 360 o . Degree possessed around = rate x 360
Slide 36
Pie Chart for Running Shoes Example 4 (proceeded):
Slide 37
Chapter Two Describing Data: Frequency Distributions and Graphic Presentation - END -
Recommended
View more... | 2,864 | 10,314 | {"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} | 3.390625 | 3 | CC-MAIN-2019-09 | latest | en | 0.838368 |
https://www.lotterypost.com/thread/166560 | 1,480,807,283,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698541140.30/warc/CC-MAIN-20161202170901-00457-ip-10-31-129-80.ec2.internal.warc.gz | 964,874,466 | 18,869 | Welcome Guest
You last visited December 3, 2016, 4:44 pm
All times shown are
Eastern Time (GMT-5:00)
# Catch a falling Knife or a falling Digit Game
Topic closed. 7 replies. Last post 9 years ago by WIN D.
Page 1 of 1
Stone Mountain*Georgia
United States
Member #828
November 2, 2002
10491 Posts
Offline
Posted: November 25, 2007, 9:30 am - IP Logged
The Fun and Excitingly Dangerous ... Catch a falling Knife ... or Falling Digit Game!
There are many states that are missing a digit in all 3 positions for a long time.
Gravity will always win in the end and these digits must return to the fold ....sooner or later.
You can do it! ... You can catch the falling digit with all or part of these numbers .
*There are only 36 Single numbers that contain a certain digit....and only 18 doubles...plus a trip.
Right now in the PICK 3 World these are the top missing digits for all the Night games
VA..... missing digit 0 ..... 19 skips !
MI......missing digit 6 .......17
TX........................... 8 .... 14
IL.............................9 13
NY 7 12 skips
QC ..........9 12
TN 4 11 skips
NJ ....... 5 11 skips
WC .........4 9 skips
The only real failure .....is the failure to try.
Luck is a very rare thing....... Odds not so much.
Odds never change .....but probability does.
Win d
Stone Mountain*Georgia
United States
Member #828
November 2, 2002
10491 Posts
Offline
Posted: November 25, 2007, 9:46 am - IP Logged
You can go for just the 36 singles ...or the just doubles ....or a little of both and catch the falling digit.
.. All 10 Digit Number groups ......containing all 55 possible combinations of each Digit
Each of the 10 Digit groups will have 18 doubles 36 Single numbers and 1 Triple
Guess just one digit in the drawn number that day ........play all 55 numbers and you WIN !
Key Digits... 0 55 000 001 002 003 004 005 006 007 008 009 011 012 013 014 015 016 017 018 019 022 023 024 025 026 027 028 029 033 034 035 036 037 038 039 044 045 046 047 048 049 055 056 057 058 059 066 067 068 069 077 078 079 088 089 099 1 55 001 011 012 013 014 015 016 017 018 019 111 112 113 114 115 116 117 118 119 122 123 124 125 126 127 128 129 133 134 135 136 137 138 139 144 145 146 147 148 149 155 156 157 158 159 166 167 168 169 177 178 179 188 189 199 2 55 002 012 022 023 024 025 026 027 028 029 112 122 123 124 125 126 127 128 129 222 223 224 225 226 227 228 229 233 234 235 236 237 238 239 244 245 246 247 248 249 255 256 257 258 259 266 267 268 269 277 278 279 288 289 299 3 55 003 013 023 033 034 035 036 037 038 039 113 123 133 134 135 136 137 138 139 223 233 234 235 236 237 238 239 333 334 335 336 337 338 339 344 345 346 347 348 349 355 356 357 358 359 366 367 368 369 377 378 379 388 389 399 4 55 004 014 024 034 044 045 046 047 048 049 114 124 134 144 145 146 147 148 149 224 234 244 245 246 247 248 249 334 344 345 346 347 348 349 444 445 446 447 448 449 455 456 457 458 459 466 467 468 469 477 478 479 488 489 499 5 55 005 015 025 035 045 055 056 057 058 059 115 125 135 145 155 156 157 158 159 225 235 245 255 256 257 258 259 335 345 355 356 357 358 359 445 455 456 457 458 459 555 556 557 558 559 566 567 568 569 577 578 579 588 589 599 6 55 006 016 026 036 046 056 066 067 068 069 116 126 136 146 156 166 167 168 169 226 236 246 256 266 267 268 269 336 346 356 366 367 368 369 446 456 466 467 468 469 556 566 567 568 569 666 667 668 669 677 678 679 688 689 699 7 55 007 017 027 037 047 057 067 077 078 079 117 127 137 147 157 167 177 178 179 227 237 247 257 267 277 278 279 337 347 357 367 377 378 379 447 457 467 477 478 479 557 567 577 578 579 667 677 678 679 777 778 779 788 789 799 8 55 008 018 028 038 048 058 068 078 088 089 118 128 138 148 158 168 178 188 189 228 238 248 258 268 278 288 289 338 348 358 368 378 388 389 448 458 468 478 488 489 558 568 578 588 589 668 678 688 689 778 788 789 888 889 899 9 55 009 019 029 039 049 059 069 079 089 099 119 129 139 149 159 169 179 189 199 229 239 249 259 269 279 289 299 339 349 359 369 379 389 399 449 459 469 479 489 499 559 569 579 589 599 669 679 689 699 779 789 799 889 899 999
Win d
The only real failure .....is the failure to try.
Luck is a very rare thing....... Odds not so much.
Odds never change .....but probability does.
Win d
Carters Lake, Ga.
United States
Member #5313
June 29, 2004
1065 Posts
Offline
Posted: November 25, 2007, 9:59 am - IP Logged
Chazz,
Do you miss reading the Lewis Grizzard column in the paper?
I do and the way you write your post kinda' reminds me of him.
and...don't chase them singles...I have seen them stay out around 30 draws...
ez
........ in the long run........
Stone Mountain*Georgia
United States
Member #828
November 2, 2002
10491 Posts
Offline
Posted: November 25, 2007, 10:06 am - IP Logged
Chazz,
Do you miss reading the Lewis Grizzard column in the paper?
I do and the way you write your post kinda' reminds me of him.
and...don't chase them singles...I have seen them stay out around 30 draws...
ez
Mr G ! Got water ? LOL How about waiting and playing on the 29th skip then?
Wow... I miss that guy. Sure miss his column.... He was a frat brother of mine !
One of my favorite books that Lewis wrote was ....
"Elvis is Dead ....and I don't feel so good myself ! "
The only real failure .....is the failure to try.
Luck is a very rare thing....... Odds not so much.
Odds never change .....but probability does.
Win d
Stone Mountain*Georgia
United States
Member #828
November 2, 2002
10491 Posts
Offline
Posted: November 25, 2007, 11:20 am - IP Logged
Sorry... Big Correction on those missing digits up there.
The list is correct and the skips are correct but the ....missing digits are not correct. They are corrected below. Starting with digit 3 for VA .... skipping 19 draws
*There are only 36 Single numbers that contain a certain digit....and only 18 doubles...plus a trip.
Right now in the PICK 3 World these are the top missing digits for all the Night games
VA..... missing digit 3 ..... 19 skips !
MI......missing digit 8 .......17
TX........................... 7 .... 14
IL.............................6 13
NY 6 12 skips
QC ......... 1 12
TN 3 11 skips
NJ ....... 9 11 skips
WC .........3 9 skips
The only real failure .....is the failure to try.
Luck is a very rare thing....... Odds not so much.
Odds never change .....but probability does.
Win d
Carters Lake, Ga.
United States
Member #5313
June 29, 2004
1065 Posts
Offline
Posted: November 25, 2007, 11:36 am - IP Logged
Yeah I loved that one too..
One of my favorites..'I haven't understood anything since 1962 and other nekkid truths'
Was he really a frat brother?
What kind of a guy was he then?
ez
........ in the long run........
Stone Mountain*Georgia
United States
Member #828
November 2, 2002
10491 Posts
Offline
Posted: November 25, 2007, 12:11 pm - IP Logged
Yeah I loved that one too..
One of my favorites..'I haven't understood anything since 1962 and other nekkid truths'
Was he really a frat brother?
What kind of a guy was he then?
ez
I'll PM you. FYI .... you know his ashes were spread over the 50 yard line at Sanford Stadium. Cool !
The only real failure .....is the failure to try.
Luck is a very rare thing....... Odds not so much.
Odds never change .....but probability does.
Win d
Stone Mountain*Georgia
United States
Member #828
November 2, 2002
10491 Posts
Offline
Posted: November 30, 2007, 10:31 am - IP Logged
Ga Midday is missing the digit # 3 for ..............18 draws.
Here are all the ways in Box form to win if the digit 3 hits ....100% .
36 Singles
037, 136, 235, 389, 038, 137, 236, 039, 138, 237, 345, 139, 238, 346, 013, 239, 347, 356, 023, 348, 357, 123, 349, 358, 367, 034, 359, 368, 035, 134, 369, 378, 036, 135, 234, 379
18 Doubles ..1 trip
334, 335, 344, 399, 336, 003, 337, 355, 338, 113,
339, 366, 033, 133, 223, 377, 233, 333, 388
====================================================================
The numbers below are the Singles that have not hit .....in the last 6 months
037, 235, 389, 038, 137, 039, 237, 345, 238, 346, 023, 367, 368, 378, 036
Doubles un hit in 6 months
334, 344, 336, 003, 337, 355, 113, 339, 133, 223, 233, 333, 388
=====================================================================
Because the digit 5 has hit for the last 4 draws in a row...... I am gonna filter out digit 5 from all those numbers above.
Also....the last 2 hits have been mirror numbers so I will cut all those out as well.
+=====================================================================
As usual.....using .25 cent bets and looking for an over due digit to return as a double is always a good bet.
Cheap and profitable
19 x.25 = 4.75 a day ....... you can play for a doubles hit for over 2 weeks and still break even. It will never ...ever get to that. Single digits dont go missing ....37 days! LOL
18 Doubles ..1 trip ....4.75 per day
334, 335, 344, 399, 336, 003, 337, 355, 338, 113,
339, 366, 033, 133, 223, 377, 233, 333, 388
The only real failure .....is the failure to try.
Luck is a very rare thing....... Odds not so much.
Odds never change .....but probability does.
Win d
Page 1 of 1 | 3,205 | 9,547 | {"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-2016-50 | longest | en | 0.540116 |
http://www.theinfolist.com/html/ALL/l/Boolean_algebra_(logic).html | 1,701,261,146,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100081.47/warc/CC-MAIN-20231129105306-20231129135306-00550.warc.gz | 98,556,684 | 10,039 | *
picture info Boolean Algebra (logic) In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (''and'') denoted as ∧, disjunction (''or'') denoted as ∨, and the negation (''not'') denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction and division. So Boolean algebra is a formal way of describing logical operations, in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his '' An Investigation of the Laws of Thought'' (1854). According to Huntington, the term "Boolean algebra" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] picture info Mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] picture info Programming Language A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming language is usually split into the two components of syntax (form) and semantics (meaning), which are usually defined by a formal language. Some languages are defined by a specification document (for example, the C programming language is specified by an ISO Standard) while other languages (such as Perl) have a dominant implementation that is treated as a reference. Some languages have both, with the basic language defined by a standard and extensions taken from the dominant implementation being common. Programming language theory is the subfield of computer science that studies the design, implementation, analysis, characterization, and classification of programming languages. Definitions There are many considerations when defini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] Isomorphic In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them. The word isomorphism is derived from the Ancient Greek: ἴσος ''isos'' "equal", and μορφή ''morphe'' "form" or "shape". The interest in isomorphisms lies in the fact that two isomorphic objects have the same properties (excluding further information such as additional structure or names of objects). Thus isomorphic structures cannot be distinguished from the point of view of structure only, and may be identified. In mathematical jargon, one says that two objects are . An automorphism is an isomorphism from a structure to itself. An isomorphism between two structures is a canonical isomorphism (a canonical map that is an isomorphism) if there is only one isomorphism between the two structures (as it is the case for solutions of a univ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] Stone's Representation Theorem For Boolean Algebras In mathematics, Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a certain field of sets. The theorem is fundamental to the deeper understanding of Boolean algebra that emerged in the first half of the 20th century. The theorem was first proved by Marshall H. Stone. Stone was led to it by his study of the spectral theory of operators on a Hilbert space. Stone spaces Each Boolean algebra ''B'' has an associated topological space, denoted here ''S''(''B''), called its Stone space. The points in ''S''(''B'') are the ultrafilters on ''B'', or equivalently the homomorphisms from ''B'' to the two-element Boolean algebra. The topology on ''S''(''B'') is generated by a (closed) basis consisting of all sets of the form \, where ''b'' is an element of ''B''. This is the topology of pointwise convergence of nets of homomorphisms into the two-element Boolean algebra. For every Boolean algebra ''B'', ''S''(''B'') is a compact totally dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] picture info Indefinite Article An article is any member of a class of dedicated words that are used with noun phrases to mark the identifiability of the referents of the noun phrases. The category of articles constitutes a part of speech. In English, both "the" and "a(n)" are articles, which combine with nouns to form noun phrases. Articles typically specify the grammatical definiteness of the noun phrase, but in many languages, they carry additional grammatical information such as gender, number, and case. Articles are part of a broader category called determiners, which also include demonstratives, possessive determiners, and quantifiers. In linguistic interlinear glossing, articles are abbreviated as . Types Definite article A definite article is an article that marks a definite noun phrase. Definite articles such as English ''the'' are used to refer to a particular member of a group. It may be something that the speaker has already mentioned or it may be otherwise something uniquely specified. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] picture info Boolean Algebra (structure) In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets, or its elements can be viewed as generalized truth values. It is also a special case of a De Morgan algebra and a Kleene algebra (with involution). Every Boolean algebra gives rise to a Boolean ring, and vice versa, with ring multiplication corresponding to conjunction or meet ∧, and ring addition to exclusive disjunction or symmetric difference (not disjunction ∨). However, the theory of Boolean rings has an inherent asymmetry between the two operators, while the axioms and theorems of Boolean algebra express the symmetry of the theory described by the duality principle. __TOC__ History The term "Boolean algebra" honors George Boole (1815–1864), a self-educated En ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] Algebra Of Sets In mathematics, the algebra of sets, not to be confused with the mathematical structure of ''an'' algebra of sets, defines the properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations. Any set of sets closed under the set-theoretic operations forms a Boolean algebra with the join operator being ''union'', the meet operator being ''intersection'', the complement operator being ''set complement'', the bottom being \varnothing and the top being the universe set under consideration. Fundamentals The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is ref ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] Mathematical Structure In mathematics, a structure is a set endowed with some additional features on the set (e.g. an operation, relation, metric, or topology). Often, the additional features are attached or related to the set, so as to provide it with some additional meaning or significance. A partial list of possible structures are measures, algebraic structures ( groups, fields, etc.), topologies, metric structures (geometries), orders, events, equivalence relations, differential structures, and categories. Sometimes, a set is endowed with more than one feature simultaneously, which allows mathematicians to study the interaction between the different structures more richly. For example, an ordering imposes a rigid form, shape, or topology on the set, and if a set has both a topology feature and a group feature, such that these two features are related in a certain way, then the structure becomes a topological group. Mappings between sets which preserve structures (i.e., structures in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] Ernst Schröder (mathematician) Friedrich Wilhelm Karl Ernst Schröder (25 November 1841 in Mannheim, Baden, Germany – 16 June 1902 in Karlsruhe, Germany) was a German mathematician mainly known for his work on algebraic logic. He is a major figure in the history of mathematical logic, by virtue of summarizing and extending the work of George Boole, Augustus De Morgan, Hugh MacColl, and especially Charles Peirce. He is best known for his monumental ''Vorlesungen über die Algebra der Logik'' (''Lectures on the Algebra of Logic'', 1890–1905), in three volumes, which prepared the way for the emergence of mathematical logic as a separate discipline in the twentieth century by systematizing the various systems of formal logic of the day. Life Schröder learned mathematics at Heidelberg, Königsberg, and Zürich, under Otto Hesse, Gustav Kirchhoff, and Franz Neumann. After teaching school for a few years, he moved to the Technische Hochschule Darmstadt in 1874. Two years later, he took up a chair i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] picture info William Stanley Jevons William Stanley Jevons (; 1 September 183513 August 1882) was an English economist and logician. Irving Fisher described Jevons's book ''A General Mathematical Theory of Political Economy'' (1862) as the start of the mathematical method in economics. It made the case that economics, as a science concerned with quantities, is necessarily mathematical. In so doing, it expounded upon the "final" (marginal) utility theory of value. Jevons' work, along with similar discoveries made by Carl Menger in Vienna (1871) and by Léon Walras in Switzerland (1874), marked the opening of a new period in the history of economic thought. Jevons's contribution to the marginal revolution in economics in the late 19th century established his reputation as a leading political economist and logician of the time. Jevons broke off his studies of the natural sciences in London in 1854 to work as an assayer in Sydney, where he acquired an interest in political economy. Returning to the UK in 1859, he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] picture info Abstract Algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''abstract algebra'' was coined in the early 20th century to distinguish this area of study from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning. Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures. Universal algebra is a related subject that studies types of algebraic structures as single objects. For example, the structure of groups is a single object in universal algebra, which is called the ''variety of groups''. History Before the nineteenth century, algebra mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] picture info Algebra Of Concepts Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history and philology. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science. In addition, he contributed to the field of library science: while serving as overseer of the Wolfenbüttel library in Germany, he devised a cataloging system that would have served as a guide for many of Europe's largest libraries. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primarily in Latin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] | 3,037 | 14,415 | {"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} | 3.78125 | 4 | CC-MAIN-2023-50 | latest | en | 0.936406 |
http://mathhelpforum.com/advanced-statistics/158511-n-n-1-sd.html | 1,526,945,128,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794864558.8/warc/CC-MAIN-20180521220041-20180522000041-00440.warc.gz | 190,049,275 | 8,932 | Thread: n or n-1 for SD?
1. n or n-1 for SD?
Hi, I recently saw this description for how to get variance, and thereby Standard Deviation:
"...sum of the squares of the differences between each observation and the mean, and then that quantity is divided by the sample size."
Then of course SD would be the root of that result. The sample size in their example, instead of being expressed as n, was expressed as n-1. I couldn't for the life of me figure out why, and I'm not a naturally mathy person, so I just 'took their word for it' and accepted it.
I later read the following description for finding the SD from the root-mean-average:
"...
The standard deviation of a sample can be found by calculating the Rms size of the deviation from the average. To find the SD you find the average, then find the difference for each observation from the average, and finally you calculate the Rms of those deviations."
In this situation, however, they divided by the unmodified sample size, so n and not n-1. How do I know when to subtract 1 from the sample size (ie - n or n-1)? It actually never gave an explanation as to why. Thanks,
David
2. Originally Posted by dkco
How do I know when to subtract 1 from the sample size (ie - n or n-1)? It actually never gave an explanation as to why. Thanks,
When given a sample from a population the standard deviation is $\displaystyle \displaystyle s = \sqrt{\frac{\sum (x-\bar{x})^2}{n-1}}$
Fidning the standard deviation from the entire population then $\displaystyle \displaystyle \sigma = \sqrt{\frac{\sum (x-\bar{x})^2}{n}}$ | 384 | 1,574 | {"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} | 3.8125 | 4 | CC-MAIN-2018-22 | latest | en | 0.94478 |
http://danboykis.com/?p=695 | 1,526,859,568,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794863811.3/warc/CC-MAIN-20180520224904-20180521004904-00089.warc.gz | 67,113,533 | 7,374 | Exercise 1.26 of SICP
Exercise 1.26: Louis Reasoner is having great difficulty doing exercise 1.24. His fast-prime? test seems to run more slowly than his prime? test. Louis calls his friend Eva Lu Ator over to help. When they examine Louis’s code, they find that he has rewritten the expmod procedure to use an explicit multiplication, rather than calling square:
“I don’t see what difference that could make,” says Louis. “I do.” says Eva. “By writing the procedure like that, you have transformed the $\Theta(\log n)$ process into a $\Theta(n)$ process.” Explain.
Just like the recursive binary tree computational procedure for Fibonacci numbers was exponential so is this process exponential because of the double call to expmod.
This double call creates a tree of depth log2(n). The amount of nodes in a tree (the amount of computational steps to perform the algorithm), of depth log2(n) is $2^{\log_2 n} = n$. This means the algorithm is indeed $\Theta(n)$. | 224 | 966 | {"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": 4, "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-2018-22 | latest | en | 0.943341 |
https://www.get-digital-help.com/excel-template-machine-utilization-calculation/ | 1,585,621,682,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370499280.44/warc/CC-MAIN-20200331003537-20200331033537-00188.warc.gz | 872,174,603 | 80,220 | Author: Oscar Cronquist Article last updated on October 13, 2017
### Question:
I need to calculate how many hours a machine is utilized in a company with a night and day shift?
The day shift hours:
Mon: 06:15 - 15:15
Tue: 06:15 - 15:15
We: 06:15 - 15:15
Thu: 06:15 - 15:15
Fri: 06:15 - 11:15
Sat:
Sun:
The night shift hours:
Mon: 20:00 - 07:45
Tue: 20:00 - 07:45
We: 20:00 - 07:45
Thu: 21:00 - 02:45
Fri:
Sat:
Sun:
Machine utilization
Start date and time: 2007-01-02 08:00
End date and time: 2007-01-05 12:00
### Calculate weekday num and time
I have the start date in cell B4 and the end date in cell B5.
First, we have to calculate weekday numbers and times.
Formula in C4:
=WEEKDAY(B4, 2) + ENTER
Copy cell C4 and paste to cell C5.
Formula in D4:
=B4-ROUNDDOWN(B4, 0) + ENTER
Copy cell D4 and paste to cell D5.
### Setup shift hours
I converted day and night shift hours into a table in cell range A9:D18.
### Array formula in cell D21:
=SUMPRODUCT(COUNTIFS(\$C\$4, \$B\$9:\$B\$18, \$D\$4, ">="&\$C\$9:\$C\$18, \$D\$4, "<="&\$D\$9:\$D\$18)*(\$D\$9:\$D\$18))-\$D\$4 + ENTER
### Explaining array formula in cell D21
Step 1 - Find a shift time interval where the machine starts
=SUMPRODUCT(COUNTIFS(\$C\$4, \$B\$9:\$B\$18, \$D\$4, ">="&\$C\$9:\$C\$18, \$D\$4, "<="&\$D\$9:\$D\$18)*(\$D\$9:\$D\$18))-\$D\$4
COUNTIFS(\$C\$4, \$B\$9:\$B\$18, \$D\$4, ">="&\$C\$9:\$C\$18, \$D\$4, "<="&\$D\$9:\$D\$18)
becomes
COUNTIFS(2, {1; 1; 2; 2; 3; 3; 4; 4; 4; 5}, 0,333333333335759, ">="&{0,260416666666667; 0,833333333333333; 0; 0,833333333333333; 0; 0,833333333333333; 0; 0,260416666666667; 0,875; 0; 0,260416666666667}, 0,333333333335759, "<="&\${0,635416666666667; 1; 0,635416666666667; 1; 0,635416666666667; 1; 0,114583333333333; 0,635416666666667; 1; 0,114583333333333; 0,46875})
and returns this array: {0;0;1;0;0;0;0;0;0;0;0}
Step 2 - Multiply with shift time hours
SUMPRODUCT({0;0;1;0;0;0;0;0;0;0;0})*(\$D\$9:\$D\$18))
becomes
SUMPRODUCT({0;0;1;0;0;0;0;0;0;0;0})*({0,635416666666667; 1; 0,635416666666667; 1; 0,635416666666667; 1; 0,114583333333333; 0,635416666666667; 1; 0,114583333333333; 0,46875})) returns 0,635416666666667
Step 3 - Subtract shift hour with machine start time
0,635416666666667 - 0,333333333335759 equals 0,302083333333333 (07:15)
### Array formula in cell D22:
=SUMPRODUCT(COUNTIFS(\$C\$4, \$B\$9:\$B\$18, \$D\$4, "<="&\$C\$9:\$C\$18, \$D\$4, "<="&\$D\$9:\$D\$18)*(\$D\$9:\$D\$18-\$C\$9:\$C\$18)) + ENTER
### Explaining array formula in cell D22
Step 1 - Identify remaining shift hours the day machine starts
=SUMPRODUCT(COUNTIFS(\$C\$4, \$B\$9:\$B\$18, \$D\$4, "<="&\$C\$9:\$C\$18, \$D\$4, "<="&\$D\$9:\$D\$18)*(\$D\$9:\$D\$18-\$C\$9:\$C\$18))
COUNTIFS(\$C\$4, \$B\$9:\$B\$18, \$D\$4, "<="&\$C\$9:\$C\$18, \$D\$4, "<="&\$D\$9:\$D\$18)
becomes
COUNTIFS(2, {1; 1; 2; 2; 3; 3; 4; 4; 4; 5}, 0,333333333335759, ">="&{0,260416666666667; 0,833333333333333; 0; 0,833333333333333; 0; 0,833333333333333; 0; 0,260416666666667; 0,875; 0; 0,260416666666667}, 0,333333333335759, "<="&\${0,635416666666667; 1; 0,635416666666667; 1; 0,635416666666667; 1; 0,114583333333333; 0,635416666666667; 1; 0,114583333333333; 0,46875})
and returns this array: {0;0;1;0;0;0;0;0;0;0;0}
Step 2 - Multiply with shift time hours
=SUMPRODUCT(COUNTIFS(\$C\$4, \$B\$9:\$B\$18, \$D\$4, "<="&\$C\$9:\$C\$18, \$D\$4, "<="&\$D\$9:\$D\$18)*(\$D\$9:\$D\$18-\$C\$9:\$C\$18))
becomes
{0;0;1;0;0;0;0;0;0;0;0}*(\$D\$9:\$D\$18-\$C\$9:\$C\$18)
becomes
{0;0;1;0;0;0;0;0;0;0;0}*{0,375; 0,166666666666667; 0,635416666666667; 0,166666666666667; 0,635416666666667; 0,166666666666667; 0,114583333333333; 0,375;0,125; 0,114583333333333; 0,208333333333333}
and becomes
SUMPRODUCT({0;0;0;0,166666666666667;0;0;0;0;0;0;0}) and returns 0,166666666666667 (04:00)
### Array formula in cell D23:
=SUM(IF(WEEKDAY(INT(\$B\$4)+ROW(OFFSET(\$A\$1, 0, 0, INT(\$B\$5)-INT(\$B\$4)-1)), 2)=TRANSPOSE(\$B\$9:\$B\$18), TRANSPOSE(\$D\$9:\$D\$18-\$C\$9:\$C\$18))) + CTRL + SHIFT + ENTER
### Explaining array formula in cell D23
To be continued...
### Array formula in cell D24:
=SUMPRODUCT(COUNTIFS(\$C\$5, \$B\$9:\$B\$18, \$D\$5, ">="&\$C\$9:\$C\$18, \$D\$5, ">="&\$D\$9:\$D\$18)*(\$D\$9:\$D\$18-\$C\$9:\$C\$18)) + ENTER
### All above formulas in cell D27:
=SUMPRODUCT(COUNTIFS(\$C\$4, \$B\$9:\$B\$19, \$D\$4, ">="&\$C\$9:\$C\$19, \$D\$4, "<="&\$D\$9:\$D\$19)*(\$D\$9:\$D\$19))-\$D\$4+SUMPRODUCT(COUNTIFS(\$C\$4, \$B\$9:\$B\$19, \$D\$4, "<="&\$C\$9:\$C\$19, \$D\$4, "<="&\$D\$9:\$D\$19)*(\$D\$9:\$D\$19-\$C\$9:\$C\$19))+SUM(IF(WEEKDAY(INT(\$B\$4)+ROW(OFFSET(\$A\$1, 0, 0, INT(\$B\$5)-INT(\$B\$4)-1)), 2)=TRANSPOSE(\$B\$9:\$B\$19), TRANSPOSE(\$D\$9:\$D\$19-\$C\$9:\$C\$19)))+SUMPRODUCT(COUNTIFS(\$C\$5, \$B\$9:\$B\$19, \$D\$5, ">="&\$C\$9:\$C\$19, \$D\$5, ">="&\$D\$9:\$D\$19)*(\$D\$9:\$D\$19-\$C\$9:\$C\$19)) + CTRL + SHIFT + ENTER | 2,275 | 4,833 | {"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} | 4.3125 | 4 | CC-MAIN-2020-16 | longest | en | 0.165627 |
http://www.tutorsglobe.com/question/calculate-total-gah-gain-or-loss-by-d-d-x-e-in-column-f-53002776.aspx | 1,571,812,176,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570987829458.93/warc/CC-MAIN-20191023043257-20191023070757-00421.warc.gz | 315,451,812 | 8,478 | Calculate total gah gain or loss by d-(d x e) in column f
Assignment - Finance and Budgeting
1. Based on your proposed organization and structure for the GAH and the Community Clinic, we will now focus on financing and budgeting issues.
2. In order to do so, we will need to define the following requirements and assumptions:
1. Cost of facility construction, initial medical equipment, and instrumentation, will not be calculated - as they will be fully paid by the state as a grant.
2. All senior patients will be above the age of 65, and will have only the Federal Medicare health insurance. Research the major constructs of Medicare health coverage as defined by the "Medicare Prospective Payment System."
3. The hospital and clinic will be financially balanced, that is, income from Medicare payments will cover in full all operating costs.
3. "Medicare Prospective Payment System"
1. The hospital is reimbursed by the government per procedure and/or treatment by a predefined sum and not by the actual expenses performed for and on a particular patient.
2. For example - a patient requiring open heart surgery will utilize the services of physicians, nurses, OR, laboratory, pharmacy, and occupies a hospital bed on average for six days. If a certain patient is discharged after four days, the hospital will still be paid the six-day amount. Hence, the incentive to operate efficiently and effectively, enabling the hospital to "save money."
4. Based on the services you have decided to provide - at least six, complete the table (GAH Project):
1. Input services/treatments in column A.
2. Input estimated and rounded Medicare reimbursement to GAH (in thousands of dollars) for each treatment in column B (assign for each a figure between \$10,000 to \$60,000).
3. Your instructor has inputted the projected number of procedures/treatments performed annually at GAH in column C.
4. Calculate the total income for GAH by multiplying columns B*C in column D.
5. Your instructor has inputted the GAH Projected Performance percentage, relative to the Federal standard (100%) in column E.
6. Calculate the total GAH gain or loss by D-(D*E) in column F.
Format your assignment according to the following formatting requirements:
1. The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.
2. The response also includes a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.
3. Also include a reference page. The Citations and references should follow APA format. The reference page is not included in the required page length.
Attachment:- CASE-PAPER.rar
Solution Preview :
Reference No:- TGS03002776
Now Priced at \$65 (50% Discount)
Recommended (94%)
Rated (4.6/5) | 613 | 2,862 | {"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-2019-43 | longest | en | 0.930953 |
https://www.jiskha.com/display.cgi?id=1369413011 | 1,516,553,314,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084890795.64/warc/CC-MAIN-20180121155718-20180121175718-00406.warc.gz | 907,026,831 | 3,993 | # math
posted by .
There is a jar of 16 marbles. 4 red, 7 blue and 5 green. 1) What is the probability of selecting a red marble, REPLACING it, and then selecting a blue marble.
2) What is the probability of selecting a red marble, then SETTING IT ASIDEm then selecting a blue marble?
• math -
1) 4/16 * 7/16
2) 4/16 * 7/15
• Bridesmaid Dresses: Spring/Summer 2014 Styles From -
<strong>Bridesmaid Dresses: Spring/Summer 2014 Styles From Top Designers (PHOTOS)</strong></br>
Who
## Similar Questions
1. ### math
A bag contains red, blue, and orange marbles. If the probability of randomly selecting a red marble is 0.4 and the probability of selecting a red or blue marble is 0.9 what is the probability of selecting a red or orange marble?
2. ### probability
A bowl contains only red marbles, blue marbles and green marbles. The probability of selecting a red marble from the bowl is 3/13. The probability of selecting a blue marble from the bowl is 2/5. There are fewer than 100 marbles in …
3. ### Math
***PS: I can't put the diagram so I type it.*** The diagram below shows the contents of a jar from which you select marbles at random. Inside the jar there is 16 marbles. Inside the jar there is 4 red marbles. 7 blue marbles. 5 green …
4. ### statistics
a jar contains red and blue marbles. two marbles are chosen without replacement. the probability of choosing a red marble and then a blue marble is .26, and the probability of selecting a blue marble first is .43. what is the probability …
5. ### math plz help
The contents of a jar holds 4 red marbles, 7 blue marbles, and 5 green marbles from which you select marbles at random. What is the probability of selecting a red marble, replacing it, and then selecting a blue marble?
6. ### math
In a jar there are 4 red marbles 5 green marbles and 7 blue marbles. 1 what us the probability of selecting a red marble replacing it and then selecting a blue marble 2 What is the probability of selecting a red marble setting it aside … | 518 | 2,003 | {"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} | 3.78125 | 4 | CC-MAIN-2018-05 | latest | en | 0.859052 |
https://www.oreilly.com/library/view/handbook-of-graph/9781439880197/K13767_C009.xhtml | 1,642,741,260,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320302723.60/warc/CC-MAIN-20220121040956-20220121070956-00331.warc.gz | 897,103,519 | 14,349 | Chapter 9
# Graphical Measurement
## Section 9.1 Distance in Graphs
Gary Chartrand
Western Michigan University
Ping Zhang
Western Michigan University
Introduction
How far two objects (or sets of objects) are apart in a discrete structure is of interest, both theoretically and for its applications. Since discrete structures are naturally modeled by graphs, this leads us to studying distance in graphs. A book entirely devoted to this subject has been written (see [BuHa90]).
### 9.1.1 Standard Distance in Graphs
Although there is not a unique way to define the distance between two vertices in a graph, there is one definition of distance that has been used most often and is commonly accepted as the standard definition of distance.
#### Distance and Eccentricity ...
Get Handbook of Graph Theory, 2nd Edition now with O’Reilly online learning.
O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers. | 205 | 973 | {"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-2022-05 | latest | en | 0.943221 |
https://math.stackexchange.com/questions/3832052/why-does-minx-y-and-x-y-have-the-same-distribution-when-x-y-sim-u0-1/3832063 | 1,627,552,998,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153854.42/warc/CC-MAIN-20210729074313-20210729104313-00418.warc.gz | 404,530,085 | 39,883 | # Why does $\min(X,Y)$ and $|X-Y|$ have the same distribution when $X,Y\sim U(0,1)$?
Say $$X,Y \sim U(0,1)$$ be two independent uniform random variables, and $$T=|X-Y|$$. I would like to find the CDF of $$M=\max(X,Y)$$, $$L=\min(X,Y)$$, and $$T$$. I find the CDF of $$M$$ and $$L$$ as $$P(M\leq t ) = P(X\leq t)P(Y \leq t) =t^2$$ $$P(L \leq t) = 1-P(X\geq t ) P(Y\geq t) = 1-(1-t)^2$$ To find the CDF of $$T$$, I draw a rectangle with unit length and width, and compute the area within the region $$|X-Y| \leq t$$, which turns out to be $$1-(1-t)^2$$.
My question is how come the CDF of $$L$$ and $$T$$ are the same when one is the minimum of two uniform r.vs and the other is the absolute difference of two uniform r.vs? Is there something wrong with my computation? Thanks.
Your calculations are correct! Just for the sake of completeness, you have to write
$$F_M(t)=t^2\mathbb{1}_{(0;1)}(t)+\mathbb{1}_{[1;\infty)}(t)$$
...and similar notation for the other CDF's. This because the CDF is defined over all $$\mathbb{R}$$
Why the law of L and T are the same? As you did to find $$F_T$$ do the same drawing to find $$F_L$$ and you will realize that the integration area is the same
• Cool explanation. Thanks a ton. – ForumWhiner Sep 19 '20 at 10:20
Imagine a line segment $$OA$$ of unit length.
On this line segment imagine two points $$X,Y$$ each at a distance of $$x, y$$ from point $$O$$ respectively.
These two points divide $$OA$$ into three smaller segments, whose length is equal to $$min(x,y)$$; $$|x-y|$$ and $$1 - max (x,y)$$.
From symmetry it can be seen that the three values should have same Expectation values.
• $max(X;Y)$ has not the same expectation of the other rv's. This is self evident if you look at the drawing in my answer. – tommik Sep 19 '20 at 8:24
• @tommik yes, it's a typo. I'll correct it. – xax Sep 19 '20 at 8:45
• Sorry I don't get why all three segments should have same expectations. I find $E[M]=2/3$ and $E[L]=1/3$. Am I correct? – ForumWhiner Sep 19 '20 at 10:19
• Symmetry. The only rule you have is the sum of lengths of three segments should be one. And this rule is same to all three segments, which means their Expectation should be equal and be equal to one. – xax Sep 19 '20 at 19:02
• @ForumWhiner Yes, E[L] = E[T] = E[1 - M] = 1/3 – xax Sep 19 '20 at 19:03 | 754 | 2,318 | {"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": 26, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2021-31 | latest | en | 0.865279 |
https://finance.yahoo.com/news/why-yangarra-resources-ltd-tse-172031010.html | 1,568,701,891,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514573053.13/warc/CC-MAIN-20190917061226-20190917083226-00423.warc.gz | 490,499,857 | 106,285 | U.S. Markets open in 6 hrs 59 mins
# Why Yangarra Resources Ltd.’s (TSE:YGR) Return On Capital Employed Is Impressive
Want to participate in a short research study? Help shape the future of investing tools and you could win a \$250 gift card!
Today we’ll look at Yangarra Resources Ltd. (TSE:YGR) and reflect on its potential as an investment. To be precise, we’ll consider its Return On Capital Employed (ROCE), as that will inform our view of the quality of the business.
First of all, we’ll work out how to calculate ROCE. Then we’ll compare its ROCE to similar companies. Then we’ll determine how its current liabilities are affecting its ROCE.
### What is Return On Capital Employed (ROCE)?
ROCE measures the ‘return’ (pre-tax profit) a company generates from capital employed in its business. In general, businesses with a higher ROCE are usually better quality. Ultimately, it is a useful but imperfect metric. Renowned investment researcher Michael Mauboussin has suggested that a high ROCE can indicate that ‘one dollar invested in the company generates value of more than one dollar’.
### So, How Do We Calculate ROCE?
Analysts use this formula to calculate return on capital employed:
Return on Capital Employed = Earnings Before Interest and Tax (EBIT) ÷ (Total Assets – Current Liabilities)
Or for Yangarra Resources:
0.093 = CA\$30m ÷ (CA\$479m – CA\$62m) (Based on the trailing twelve months to September 2018.)
So, Yangarra Resources has an ROCE of 9.3%.
### Does Yangarra Resources Have A Good ROCE?
ROCE can be useful when making comparisons, such as between similar companies. Yangarra Resources’s ROCE appears to be substantially greater than the 5.0% average in the Oil and Gas industry. We consider this a positive sign, because it suggests it uses capital more efficiently than similar companies. Aside from the industry comparison, Yangarra Resources’s ROCE is mediocre in absolute terms, considering the risk of investing in stocks versus the safety of a bank account. Readers may find more attractive investment prospects elsewhere.
When considering this metric, keep in mind that it is backwards looking, and not necessarily predictive. Companies in cyclical industries can be difficult to understand using ROCE, as returns typically look high during boom times, and low during busts. This is because ROCE only looks at one year, instead of considering returns across a whole cycle. We note Yangarra Resources could be considered a cyclical business. Future performance is what matters, and you can see analyst predictions in our free report on analyst forecasts for the company.
### Yangarra Resources’s Current Liabilities And Their Impact On Its ROCE
Current liabilities are short term bills and invoices that need to be paid in 12 months or less. Due to the way ROCE is calculated, a high level of current liabilities makes a company look as though it has less capital employed, and thus can (sometimes unfairly) boost the ROCE. To counteract this, we check if a company has high current liabilities, relative to its total assets.
Yangarra Resources has total assets of CA\$479m and current liabilities of CA\$62m. As a result, its current liabilities are equal to approximately 13% of its total assets. This very reasonable level of current liabilities would not boost the ROCE by much.
### What We Can Learn From Yangarra Resources’s ROCE
That said, Yangarra Resources’s ROCE is mediocre, there may be more attractive investments around. Of course you might be able to find a better stock than Yangarra Resources. So you may wish to see this free collection of other companies that have grown earnings strongly.
For those who like to find winning investments this free list of growing companies with recent insider purchasing, could be just the ticket.
To help readers see past the short term volatility of the financial market, we aim to bring you a long-term focused research analysis purely driven by fundamental data. Note that our analysis does not factor in the latest price-sensitive company announcements.
The author is an independent contributor and at the time of publication had no position in the stocks mentioned. For errors that warrant correction please contact the editor at editorial-team@simplywallst.com. | 900 | 4,279 | {"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} | 2.65625 | 3 | CC-MAIN-2019-39 | latest | en | 0.924515 |
https://benbakerbooks.org/and-pdf/2179-rate-of-technical-substitution-mathematics-problems-and-answers-pdf-918-503.php | 1,643,302,488,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320305277.88/warc/CC-MAIN-20220127163150-20220127193150-00645.warc.gz | 194,431,225 | 9,258 | # Rate Of Technical Substitution Mathematics Problems And Answers Pdf
File Name: rate of technical substitution mathematics problems and answers .zip
Size: 2889Kb
Published: 16.06.2021
Actively scan device characteristics for identification. Use precise geolocation data.
## Indifference curves and marginal rate of substitution
ISBN: Get help with math homework, solve specific math problems or find information on mathematical subjects and topics. Tutorial Problems V A. Each year on the first Saturday in December, several thousand US and Canadian students spend 6 hours in two sittings trying to solve 12 problems. This collection of problems and exercises in mathematical analysis covers the maximum requirements of general courses in higher mathematics for higher technical schools.
## Marginal Rate of Technical Substitution
Photomath is FREE and works without wi-fi or data. From basic arithmetic to advanced calculus and geometry, learn with Photomath. Understand core concepts to help you advance in math and feel confident in class! Suggestions or questions? Email us at support photomath. We update the app regularly to make studying as smooth as possible.
## Marginal Rate of Technical Substitution
The marginal rate of technical substitution MRTS is the rate at which one input can be substituted for another input without changing the level of output. In other words, the marginal rate of technical substitution of Labor L for Capital K is the slope of an isoquant multiplied by In the above table, all the four factor combinations A, B, C and D produce the same level of units of output. They are all iso-product combinations. As we move from combination A to combination B, it is clear that 3 units of capital can be replaced by 5 units of labor.
#### Screenshots
Че-че-го же вы хотите? - выдавил он заикаясь. - Я ничего не знаю. Беккер зашагал по комнате. - На руке умершего было золотое кольцо. Я хочу его забрать. - У м-меня его .
Dov'ela plata. Где деньги. Беккер достал из кармана пять ассигнаций по десять тысяч песет и протянул мотоциклисту.
Найти тихо. Если он почует, что мы идем по его следу, все будет кончено. Теперь Сьюзан точно знала, зачем ее вызвал Стратмор.
Со всех сторон его окружали мужчины в пиджаках и галстуках и женщины в черных платьях и кружевных накидках на опущенных головах. Они, не замечая Халохота, шли своей дорогой, напоминая черный шуршащий ручеек. С пистолетом в руке он рвался вперед, к тупику. Но Беккера там не оказалось, и он тихо застонал от злости. Беккер, спотыкаясь и кидаясь то вправо, то влево, продирался сквозь толпу.
Venti mille pesete. La Vespa. - Cinquanta mille. Пятьдесят тысяч! - предложил Беккер.
На поиски вируса нужно время, которого нет ни у нее, ни у коммандера. Но, вглядываясь в строки программы и думая, какую ошибку она могла допустить, Сьюзан чувствовала, что тут что-то не. Она запускала Следопыта месяц назад, и никаких проблем не возникло. Могли сбой произойти внезапно, сам по. Размышляя об этом, Сьюзан вдруг вспомнила фразу, сказанную Стратмором: Я попытался запустить Следопыта самостоятельно, но информация, которую он выдал, оказалась бессмысленной.
Хейл сдавил горло Сьюзан. - Выпустите меня, или она умрет. Тревор Стратмор заключил в своей жизни достаточно сделок, когда на кону были высочайшие ставки, чтобы понимать: Хейл взвинчен и крайне опасен.
Увы, - тихо сказал Стратмор, - оказалось, что директор в Южной Америке на встрече с президентом Колумбии. Поскольку, находясь там, он ничего не смог бы предпринять, у меня оставалось два варианта: попросить его прервать визит и вернуться в Вашингтон или попытаться разрешить эту ситуацию самому. Воцарилась тишина.
- Я хочу быть абсолютно уверен, что это абсолютно стойкий шифр. Чатрукьян продолжал колотить по стеклу. - Ничего не поделаешь, - вздохнул Стратмор.
### Related Posts
4 Response
1. Juliane L.
Homework #3 Answers. 1. (a) The marginal rate of technical substitution is the ratio of the marginal (a) First, we set up the Lagrangean for the cost minimization problem. Lagr. To make the math easier, we have substituted w = 4 and r = 1.
2. Tara L.
Marginal rate of technical substitution MRTS is the rate at which a firm can substitute capital with labor.
3. Emsatalria1951
Fractions on the Number Line Standard: 3.
4. Neville S.
Power learning strategies for success in college and life 6th edition pdf the last of us art book pdf | 1,225 | 4,409 | {"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} | 3.515625 | 4 | CC-MAIN-2022-05 | latest | en | 0.625035 |
http://nrich.maths.org/public/leg.php?code=-334&cl=2&cldcmpid=2859 | 1,368,881,503,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368696382396/warc/CC-MAIN-20130516092622-00086-ip-10-60-113-184.ec2.internal.warc.gz | 192,774,108 | 9,753 | # Search by Topic
#### Resources tagged with Games similar to Odds or Sixes?:
Filter by: Content type:
Stage:
Challenge level:
### The Path of the Dice
##### Stage: 2 Challenge Level:
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
### Calculator Bingo
##### Stage: 2 Challenge Level:
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
### 100 Percent
##### Stage: 2 Challenge Level:
An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .
### Making Maths: Happy Families
##### Stage: 1 and 2 Challenge Level:
Here is a version of the game 'Happy Families' for you to make and play.
### Put Yourself in a Box
##### Stage: 2 Challenge Level:
A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.
### Tricky Track
##### Stage: 2 Challenge Level:
In this game you throw two dice and find their total, then move the appropriate counter to the right. Which counter reaches the purple box first? Is this what you would expect?
### Noughts and Crosses
##### Stage: 2 Challenge Level:
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
### Board Block Challenge
##### Stage: 2 Challenge Level:
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
### Coordinate Cunning
##### Stage: 2 Challenge Level:
A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
### Chocolate Bars
##### Stage: 2 Challenge Level:
An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.
### Fractions and Coins Game
##### Stage: 2 Challenge Level:
Work out the fractions to match the cards with the same amount of money.
### Train
##### Stage: 2 Challenge Level:
A train building game for 2 players.
### Counter Roundup
##### Stage: 2 Challenge Level:
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
### Penta Play
##### Stage: 2 Challenge Level:
A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
### Part the Piles
##### Stage: 2 Challenge Level:
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
### Building Stars
##### Stage: 2 Challenge Level:
An interactive activity for one to experiment with a tricky tessellation
### Making Maths: Birds from an Egg
##### Stage: 2 Challenge Level:
Can you make the birds from the egg tangram?
### Ratio Pairs 2
##### Stage: 2 Challenge Level:
A card pairing game involving knowledge of simple ratio.
### Endless Noughts and Crosses
##### Stage: 2 Challenge Level:
An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.
### The Twelve Pointed Star Game
##### Stage: 2 Challenge Level:
Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?
### Conway's Chequerboard Army
##### Stage: 3 Challenge Level:
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
### Tangram Pictures
##### Stage: 1, 2 and 3 Challenge Level:
Use the tangram pieces to make our pictures, or to design some of your own!
### Game of PIG - Sixes
##### Stage: 2, 3, 4 and 5 Challenge Level:
Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
### Snail Trails
##### Stage: 3 Challenge Level:
This is a game for two players. You will need some small-square grid paper, a die and two felt-tip pens or highlighters. Players take turns to roll the die, then move that number of squares in. . . .
### Counters
##### Stage: 2 Challenge Level:
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
### Football World Cup Simulation
##### Stage: 2, 3 and 4 Challenge Level:
A maths-based Football World Cup simulation for teachers and students to use.
##### Stage: 2 Challenge Level:
This is a game for 2 players. Each player has 4 counters each, and wins by blocking their opponent's counters. A good follow-on from two stones.
### Dominoes
##### Stage: 2 Challenge Level:
Everthing you have always wanted to do with dominoes! Some of these games are good for practising your mental calculation skills, and some are good for your reasoning skills.
### Stop or Dare
##### Stage: 2, 3 and 4 Challenge Level:
All you need for this game is a pack of cards. While you play the game, think about strategies that will increase your chances of winning.
### Factors and Multiples Game
##### Stage: 2 and 3 Challenge Level:
A game in which players take it in turns to choose a number. Can you block your opponent?
### Do You Measure Up?
##### Stage: 2 Challenge Level:
A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.
### Jumping Reindeer
##### Stage: 2 Challenge Level:
A game for 1 person to develop stategy and shape and space awareness. 12 counters are placed on a board. Counters are removed one at a time. The aim is to be left with only 1 counter.
### Making Maths: Snake Pits
##### Stage: 1, 2 and 3 Challenge Level:
A game to make and play based on the number line.
### Fifteen
##### Stage: 3 Challenge Level:
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
### Low Go
##### Stage: 2 Challenge Level:
A game for 2 players. Take turns to place a counter so that it occupies one of the lowest possible positions in the grid. The first player to complete a line of 4 wins.
### Games from Around the World
##### Stage: 1 and 2 Challenge Level:
Here are a collection of games from around the world to try during the holidays or the last few weeks of term.
### Domino Magic Rectangle
##### Stage: 2 Challenge Level:
An ordinary set of dominoes can be laid out as a 7 by 4 magic rectangle in which all the spots in all the columns add to 24, while those in the rows add to 42. Try it! Now try the magic square...
### SHOO
##### Stage: 2 Challenge Level:
A complicated game played on a 9 x 9 checkered grid.
### Diamond Mine
##### Stage: 3 Challenge Level:
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
### Transformation Game
##### Stage: 3 Challenge Level:
Why not challenge a friend to play this transformation game?
### Flip Flop - Matching Cards
##### Stage: 1, 2 and 3 Challenge Level:
A game for 1 person to play on screen. Practise your number bonds whilst improving your memory
### Traffic Lights
##### Stage: 2 Challenge Level:
The game uses a 3x3 square board. 2 players take turns to play, either placing a red on an empty square, or changing a red to orange, or orange to green. The player who forms 3 of 1 colour in a line. . . .
### Gotcha
##### Stage: 2 Challenge Level:
A game for 2 players. This could be played outside with people instead of counters. Try to trap or escape from your opponent.
### Multiplication Tables - Matching Cards
##### Stage: 1, 2 and 3 Challenge Level:
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
### Twinkle Twinkle
##### Stage: 2 Challenge Level:
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
### Intersection Sudoku 1
##### Stage: 3 and 4 Challenge Level:
A Sudoku with a twist.
### Estimating Angles
##### Stage: 2 and 3 Challenge Level:
How good are you at estimating angles?
### Wallpaper Sudoku
##### Stage: 3 and 4 Challenge Level:
A Sudoku that uses transformations as supporting clues.
### Sliding Game
##### Stage: 2 Challenge Level:
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board. | 2,088 | 8,862 | {"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} | 3.390625 | 3 | CC-MAIN-2013-20 | longest | en | 0.895965 |
http://www.head-fi.org/t/495631/amp-recommendations-for-audeze-lcd-2/6945 | 1,406,974,942,000,000,000 | text/html | crawl-data/CC-MAIN-2014-23/segments/1406510280868.21/warc/CC-MAIN-20140728011800-00394-ip-10-146-231-18.ec2.internal.warc.gz | 580,723,949 | 32,405 | Head-Fi.org › Forums › Equipment Forums › Headphone Amps (full-size) › Amp recommendations for Audeze LCD-2
New Posts All Forums:Forum Nav:
Amp recommendations for Audeze LCD-2 - Page 464
Signal = voltage in voltage based amps
Signal = current in current mode amps.
When voltage amps drive HP, current is generated by V=IZ where Z= impedenace.
Current is function of voltage with respect to phase.
And magnetic flux is in phase with current, not with voltage.
Because magnetic flux = H is only function of current. This means that only current generates magnetic flux, and voltage can be generated without any current for example open circuit having maximum voltage but zero current that generates no magnetic flux.
Of course voltage generates magnetic flux in relation to impedance=Z, but a phase amount delay.
Sorry for my adoption of math.
Especially impedance Z is function of frequency, when it approaches to resonance the phase will delay or advance in 90 degrees.
Because all these relations, voltage amplifier drives by voltage signal and HP responds only to current, so that there is a phase difference between signal generator ( driver) and signal producer (HP) due to impedance that depends on frequency. The higher the frequency, the larger the phase difference between driver (AMP) and driven (HP).
Edited by Joong - 12/4/13 at 4:05pm
Quote:
Originally Posted by Joong
Signal = voltage in voltage based amps
Signal = current in current mode amps.
Yes, I know.
Quote:
When voltage amps drive HP, current is generated by V=IZ where Z= impedenace.
You mean I = V/Z.
Quote:
Current is function of voltage with respect to phase.
The phase of what?
Quote:
And magnetic flux is in phase with current, not with voltage.
And why does that matter? Whether you drive the headphone from a current source or a voltage source, for a given current through the headphone, you'll have a given voltage across the headphone. I = V/Z, V = IZ.
Quote:
Because magnetic flux = H is only function of current.
Yes, just as voltage is a function of current.
Quote:
Of course voltage generates magnetic flux in relation to impedance=Z, but a phase amount delay.
But the impedance of an ortho, such as the LCD-2, which is what this thread is about, is virtually purely purely resistive. So you may just as well use R instead of Z.
Quote:
Especially impedance Z is function of frequency, when it approaches to resonance the phase will delay or advance in 90 degrees.
As I said, the LCD-2sare virtually resistive.
And even if you are talking about a resonant circuit, at resonance, phase is 0 degrees and Z is purely resistive. You only get a 90 degree lead or lag when the load is PURELY reactive, i.e. pure inductance or pure capacitance. When there is any loss, such as resistance, the lead/lag will always be less than 90 degrees.
se
The people that recommended the Lyr with the LCD2's are old new's when there weren't any V100/V200's or the Burson stuff on the market. Things have changed greatly over the past 2 years.
The voltage phase is actually signal phase in Voltage based amps.
The actual HP is a motor that responds only to current.
This means that original sounds lacks or advances with respect to actually produced sounds.
This phase difference is well related to V=IZ, so that this may not be equal to usual jitter, but there is certainly phase difference between driver and driven.
The LCD-1/2/3 or any orthors, must have inductive to produce or interact with DC field of magnet array.
There is no conductive trace that have 100% resistive only.
Of course the orthors has much less inductive than dynamic ones, so that orthos requires lots of current than those of dynamic phone, in order to compensate the lack of inductance through which magnetic flux is generated.
I generally agree that for the audio signal band there is not much appreciable inductance as you mentioned.
However, these crazy headfiers consider that any tiny amount of electric quantity might be controlled by expert like the founder of Bakgoon, for example.
He considers seriously an comfortable in several pico seconds jitter, and he tried to correct it by current mode amps. Amazing!!! He simply had been inspired by that fact that the turn table got several hundred kilograms to prevent the rotational speed variation of the turn table by gaining weight that much. That turn-table example was parallel with modern jitter concept, which pushes the DAC with superior jitter control by considerable effort.
I am also one among them crazy people.
As you mentioned, the phase difference between voltage based amps and HP will be negligible when we consider very tiny amount inductance. But when we consider signal as voltage, and sound as current of magnetic flux; there is jitter like action is always there.
That is something like the piston motion as resistive component of impedace, whereas crank acts as jittering reactive comp.
Therefore due to the length of piston rod ( resistive) much longer than the crank ( reactive) there is no way v-amp signal delaying or advancing for 90 degree, but very tiny amount that bothers headfiers here.
Edited by Joong - 12/4/13 at 4:54pm
Quote:
Originally Posted by Joong
I am also one among them crazy people.
Then I'll not waste my time trying to discuss the physics with you.
se
The audiophiles' concerns might not be measured by physics, but by the limit of human brain's sensing capability.
Therefore there is always some argue.
Nice talking was it.
Then don't bring any physics into the discussion. And don't speak of the brain's sensing capability unless you have something to back it up other than some audiophile said so.
se
Edited by Steve Eddy - 12/4/13 at 6:14pm
Steve Eddy takin' 'em to school, again.
Quote:
Originally Posted by Steve Eddy
Then don't bring any physics into the discussion.
Zing !!
Although I thought you were going to say something a little more insulting when you started with "And don't speak of the brain's sensing capability unless you have ...". Actually, almost feel a little let down now that I think about it ...
Quote:
Originally Posted by NinjaHamster
Zing !!
Although I thought you were going to say something a little more insulting when you started with "And don't speak of the brain's sensing capability unless you have ...". Actually, almost feel a little let down now that I think about it ...
Sorry to have let you down. But I'd like to think you'd feel even more let down if I got myself banned.
se
Guessing, but I'd assume that headphones uses some kind of equalizing filter at the input to tweak the signature. That filter might not behave as intended if you replace the voltage driver with a current driver. In normal filters for instance the first pole will be removed by doing this.
Quote:
Originally Posted by DrNope
Guessing, but I'd assume that headphones uses some kind of equalizing filter at the input to tweak the signature. That filter might not behave as intended if you replace the voltage driver with a current driver. In normal filters for instance the first pole will be removed by doing this.
I'm not aware of any headphones that have any response shaping equalization built into them. I'm pretty sure there's probably something out there that does, but everything I've seen has the driver driven directly.
Nor am I aware of any loudspeaker or headphone driver that's designed to be driven by a current source. Everything assumes it will be driven by a voltage source.
If you look at the impedance plot of a typical dynamic driver, whether loudspeaker or headphone, you'll see that it peaks at the driver's resonant frequency. This is where the driver is working most efficiently compared to above and below this frequency. And as was mentioned previously, it's current through the voice coil that produces the magnetic field that interacts with the driver's magnets and causes the diaphragm to move.
So now when you drive it with a voltage source, because Ohm's Law says that current is equal to voltage divided by impedance, and since impedance is highest at the resonant frequency, there will be less current flowing in the voice coil at that frequency. Which makes sense because where it's most efficient is where you need less power to get the same amount of output.
But drive that same driver from a current source, and everything gets turned upside down. Because a current source wants to drive the same amount of current through the load regardless of the impedance, when you get to the peak of the impedance curve, which again is where the driver is most efficient, there will be much more current flowing through the voice coil compared to driving it with a voltage source and as a consequence, the output of the driver will be much greater. It's the same as if you used a voltage source and used EQ to give it a peak in the response at the resonant frequency.
In other words, if you start out with a driver that has a flat response when driven from a voltage source, as you transition to a current source, the frequency response starts to look like the impedance curve with a peak at the resonant frequency (as well as at high frequencies where the voice coil inductance starts coming into play). When Nelson Pass began experimenting with current source amplifiers to drive single driver loudspeakers, he had to add networks to compensate for this and avoid peaks in the low frequency response.
This isn't an issue with orthos though due to their flat impedance. But with dynamic drivers, they're designed to be driven from a voltage source.
se
I'm looking for a new headphone amp for my LCD 2.2's, just wondering what some of the best headphone amps are in the following price ranges:
\$500-\$1000
\$1000-\$1500
\$1500-\$2000
Three of the ones I am considering in each range are the Woo Audio WA7 Fireflies, Schiit M & G combo & Burson Conductor. what do you guys think is the best bet for the LCD-2 in those price ranges?
Quote:
Originally Posted by goldendarko
I'm looking for a new headphone amp for my LCD 2.2's, just wondering what some of the best headphone amps are in the following price ranges:
\$500-\$1000
\$1000-\$1500
\$1500-\$2000
Three of the ones I am considering in each range are the Woo Audio WA7 Fireflies, Schiit M & G combo & Burson Conductor. what do you guys think is the best bet for the LCD-2 in those price ranges?
Sounded good from my burson soloist. Can probably find one for around \$700 on the FS forums. I think those are still en vogue these days.
Also sounds good from my dacmini.
Quote:
Originally Posted by goldendarko
I'm looking for a new headphone amp for my LCD 2.2's, just wondering what some of the best headphone amps are in the following price ranges:
\$500-\$1000
\$1000-\$1500
\$1500-\$2000
Three of the ones I am considering in each range are the Woo Audio WA7 Fireflies, Schiit M & G combo & Burson Conductor. what do you guys think is the best bet for the LCD-2 in those price ranges?1
1. Audio GD NFB10.33
2. Burson Soloist, Violectric V200, Schiit Mjolnir
3. I don't have an answer for #3 because I don't believe amps should cost that much.
New Posts All Forums:Forum Nav:
Return Home
Back to Forum: Headphone Amps (full-size)
• Amp recommendations for Audeze LCD-2 | 2,539 | 11,291 | {"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-2014-23 | longest | en | 0.9012 |
https://allaboutcfd-tomersblog.com/2017/10/19/direct-numerical-simulation-spectral-methods/ | 1,606,396,475,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141188146.22/warc/CC-MAIN-20201126113736-20201126143736-00037.warc.gz | 195,644,416 | 48,827 | # Direct Numerical Simulation Part I – Spectral Methods
A plea for a direct numerical description of the equations is a mixed blessing as it seems the availability of such a description is directly matched to the power of a dimensionless number reflecting on how well momentum is diffused relative to the flow velocity (in the cross-stream direction) and on the thickness of a boundary layer relative to the body – The Reynolds Number.
It is found that the computational effort in Direct Numerical Simulation (DNS) of the Navier-Stokes equations rises as Reynolds number in the power of 9/4 which renders such calculations as prohibitive for most engineering applications of practical interest and it shall remain so for the foreseeable future, its use confined to simple geometries and a limited range of Reynolds numbers in the aim of supplying significant insight into turbulence physics that can not be attained in the laboratory.
Nevertheless DNS proposes a indispensable tool for academic studies of understanding turbulent flow structure and even stepped ground in some various engineering fields for small-scale calculations.
When confronted CFD in general and especially DNS the range of scales to be accurately represented in a computation is represented by the physics of the problem at hand. the grid arrangement gives light to the scales to be represented and accuracy, which is not less of importance for a valid DNS is determined by the numerical method.
Depending on the large-scale features of the problem are determined by features such as inhomogeneous directions,mixing layer thickness, boundary layer thickness, etc…
The Kolmogorov length scale :
Is essentially the smallest scale to be modelled, although future DNS showed it may certainly be larger for some cases.
For achieving the “highest order” of numerical modeling the best route to follow is by spectral methods.
in the following a short insight about spectral methods and their features is going to be presented along with this CFD blogger favourites DNS codes.
Turbulent Boundary Layer (P. Schlatter and D. Henningson of KTH)
### SPECTRAL METHODS
As explained in the above paragraph the resolution requirements are a direct result of the numerical scheme employed. To get the best for simple large-scale geometry settings that support a lighter grid resolution most DNS imply spectral methods.
One should remember as far as discretisation error is concerned the two sources are the nonlinearity of the governing equations and the differentiation error.
To quantify the differentiation error, Fourier analysis and the concept modified wave number (which shall be explained thoroughly in future following post) is the useful procedure.
If one shall consider a single fourier mode in one dimension:
and discretisation it on a domain of 2*Pi, whilst using a uniform mesh of N points,
The mesh spacing which shall be h=2*Pi/N. It’s immediately seen by differentiation that the exact first derivative in the n node is:
The numerically computed derivatives take the form of:
k’ is dependent on k and h. It’s called the modified wave number for the first derivative operation. The difference between k and k’ demonstrates and provides the differentiation error. if we were to choose. This could be calculated and actually is a part of basic CFD courses to find the differentiation error of lower numerical schemes (see Lorena Barba CFD course lesson 9)
A must read on spectral methods for incompressible flows:
Recommended book with in-depth insight to various approaches to conduct DNS and LES: | 707 | 3,588 | {"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-2020-50 | longest | en | 0.907775 |
https://www.chi-cmg.com/365-360-amortization-schedule/ | 1,686,047,074,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224652494.25/warc/CC-MAIN-20230606082037-20230606112037-00308.warc.gz | 758,857,504 | 10,258 | # 365 360 Amortization Schedule
This calculator is for modeling purposes only – actual loan payment and amortization values may vary. Accuracy is not guaranteed. Loan payments will be projected to fall between the 1st and the 28th day of the month to simplify calculations. Interest paid on each payment is calculated based on the days in the payment period.
I had this question after viewing excel amortization formula for actual 365, actual 360. I was given an amortization schedule by the lender. Principal= \$5,150,000, Interest rate= 4.25%, Loan term= 10 years, Amortization term=25 years, and payment= \$27,899.51.
Commercial Loan Calculator. commercial loan calculator. 360 degrees of Financial Literacy is a FREE PROGRAM of the nation’s certified public accountants to help Americans understand their personal finances through every stage of life.
Further, "an amortization schedule is a table detailing each periodic payment on an amortizing loan (typically a mortgage), as generated. Loan Calculator Use this calculator to create an amortization schedule for a loan that uses a 365/365 schedule.
For a complete amortization schedule, click through the tabs at the bottom. NOTE: The model can only handle loans up to 30 years in term. Conclusion. In this article, we discussed three different loan accrual methods banks use to calculate interest on a commercial loan. The three methods are 30/360, Actual/365, and Actual/360.
So 365/365 assumes a year of 365 days and 365/360 assumes a year of 360 days. Amortization Calculator | Creates 9 Different Schedule Types – Amortization schedule shows amount paid to principal and interest. You can print or save schedules with annual and running totals.. If you set compounding to "Exact," and select a 360 day year, then that.
Download Loan Amortization Excel 365/360 that suitable with Microsoft Excel 2007, 2010, 2013 or 2016 software. Loan Amortization Excel 365/360 is Free Ms Excel Templates.
Average Interest Rate On Business Loan The average interest rate on a conventional small-business loan is around 4% to 6%. That said, interest rates will vary across lenders, with banks typically offering lower rates than alternative or online lenders.
Use this spreadsheet to estimate an amortization schedule and track. to a daily rate by dividing the annual rate by 365 (or 360 in some day count conventions). – Amortization 360 Vs 365 Days – I have a loan for 755812 at 60 for 5 years I put this. – Free Excel Help.
Always Period Calculator Buisness loan rates nab rewards business Signature Card – NAB. – Check out the current offers available on a range of our NAB credit cards. Find one that suits your needs, from earning bonus points to low interest rates.First Period Tips & Information | Always – Your first period can be confusing but exciting as well! Get all the advice that you need and answer your questions at Always. Page Header Page. Period Calculator Use our period calculator Offers.Real Dollar Calculator 5 Best Calculator Apps For Android – One of the highly acclaimed calculator apps out there, Calculator Plus comes in this free avatar for those who don’t want to spend money on an app. It has a wide range of functions like history,Mortgage On A 500K House Mortgage Payment On 250K Loan Your remaining loan balance is the amount you have left to pay on your mortgage loan. If your original mortgage loan was \$250,000 and you’ve paid \$30,000 in principal during the first five years, your remaining loan balance would be \$220,000. The loan term is the amount of time it will take to pay a debt.NEWS of the Government’s plans to help first-time buyers have received a cautious welcome from the property industry, although there have been suggestions that the move is too narrowly focused in.Fundamental Period Calculator Frequency formula period time frequency cycle. – Frequency period formula angular frequency cycle per second hertz Hz amplitude equation formulary acoustic time wavelength Hz to millisecond ms cycle duration time.
Re: Amortization 360 vs 365 Days Your banks payment is equivalent to an AER of 6.264%. Now I can get pretty close to your banks payment with ((1+6%/360)^(365/12)-1) as monthly interest rate on the outstanding balance. | 918 | 4,242 | {"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-2023-23 | latest | en | 0.909188 |
https://capitalsportsbet.com/ZuluCode5/year-round-sports-betting-scores.html | 1,568,808,632,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514573284.48/warc/CC-MAIN-20190918110932-20190918132932-00302.warc.gz | 393,739,412 | 8,003 | Absolutely. When the lines go up for the NFL, or for the first game of the NCAA men’s basketball tournament, there are several days in between the open and the game itself where movement can take place. You’ll find that the betting public tends to pile in on their favorite teams once they get home from work on Friday. You can anticipate these line movements and time your bet accordingly to take advantage.
With NFL odds the over/under can vary but usually it’s somewhere between 35 and 47 points. Let’s say in the Colts and Bengals game that the total is posted at 37.5. If Indy scores 27 and Cincy gets 13 points, the total would be at 40 and the over would win. But if the Colts rack up 35, and they shut out the Bengals, the total of 35 would be under.
Point spreads focus on a margin of victory between the two teams and again, what you’re looking for is the positive and negative signs. If there is a minus sign next to a team’s spread, that suggest that they are favored and have to win by or cover that amount. If there is a positive sign, that tells you that they are the underdog and they are getting points. For example: let’s say that the New England Patriots are playing the Buffalo Bills and the Patriots are -5.5 and the Bills are therefore +5.5. If you bet the Patriots, they have to win by six points or more to cover. If you bet the Bills, they can lose by five points or less, or they can win the game outright and you would still win your bet.
You may have heard the term “covering the spread” or the phrase “betting against the spread.” This means that if the favorite team wins an event with the point spread taken into account or that the underdog team wins with additional points, they have covered the spread. If the Packers win that game by more than 7 points, they have covered the spread.
The only real downside to betting basketball point spreads is that the sportsbook charges a vig. While this is a downside, it is to be expected and is no different from placing any other sports bet. Obviously, the sportsbook has to make money somehow because they have to pay employees, pay for their servers or equipment, and pay for their customer service to keep you happy. This really isn't a negative about point spread bets, but just something that you should be aware of.
If all the money at one sportsbook comes in on Team A and all the money comes into a second sportsbook on Team B, they’re both going to adjust their lines accordingly to what is going on in their book. This means that if you want to bet on Team A, you should go to the second sportsbook where the line will be great. If you want to be on Team B, you should go to the first sportsbook where the line will be better.
Moneyline bets can be presented in three different formats including moneyline, decimal, and fractional. While these will look very different, they will tell you the exact same information about the bet including who you are betting on, who the favorite or underdog is, and what the potential payout you would receive from a correct pick. We will cover all of this in the next few sections.
Let's look at a different option. We bet the Cowboys +3, and the final score is Chargers 21, Cowboys 19. Even though the Cowboys lost the game, we still win our bet because they lost by less than three points. How much are we going to get paid on this bet? Well, we look in the parenthesis and see we will get paid at -120. This means that for every \$100 we bet, we will get paid \$83.33 in profit.
For example: New England –2.5 (–110) or Philadelphia +2.5 (–110) means you’d wager \$110 for the chance to win an additional \$100 if you bet on the point spread. Depending on which side is receiving the most action, a sportsbook will often move the line up or down in order to incentivize betting on the less popular side. Injuries or unforeseen changes can also impact a point spread gambling line. Point spreads are often listed with a half-point (ex: 2.5) in order to prevent the final margin from landing exactly on the point spread (ex: 10-point spread, final score of 20–10). A “push” or “tie” usually goes to the house or sportsbook, unless another arrangement has been agreed upon beforehand.
```Sports betting is not just about being able to pick out the winner and loser of a game. Because of the various different bet types, there is a lot of different strategies that goes into how you approach them. Point spread bets are no different. One of the biggest tips we can offer is to make sure that you fully understand what you are betting on. A great pick is only great if you actually put your money behind it correctly. Thankfully, this guide should have you fully prepared for that.
```
"Winning Margin" (aka Result Betting) is where it is possible to bet on the final result of a game or event and select the correct ‘band’ of points between the winning team and losing team. For example, if you think the Patriots will win, but the game will be close, pick the New England Patriots 1-6 Points Winning Margin (where the Patriots winning by 1, 2, 3, 4, 5, or 6 points results in a winning selection).
But what if the basement-dweller team was spotted 24 points? That's the concept behind the point spread. When two teams meet on the football field or a basketball court, one team is typically better than the other. If all bettors had to do was to pick the winning team, everybody would simply wager on the best team and collect their money. Gambling institutions, sportsbooks, and bookies would soon go broke.
Sometimes with NFL odds you’ll see a spread posted as a whole number. Decimals or fractions are usually utilized to ensure there won’t be a tie. If in our example the spread was reset to 10 with the Colts favored and they win by 10, then the game is considered to be a tie, which in betting terms is called a push. If there is a push all bets are off and the sportsbooks return all wagers back to the bettors.
Before we had the options of wagering on future bets, parlays, teasers, alternative lines, Asian lines, prop bets and each-way, there was one betting option that reigned supreme. It was the money line bet. From a non-gambling perspective, winning a game in any sports will make a team happy. However, depending on the score, that win may not please bettors. That’s because the point spread betting option has taken over as the popular option, leaving the money line far behind. If you are the kind of person who bets on your favorite team each and every game, this is the bet for you. There is nothing worse than watching your team win the game, but lose you money by not covering the point spread.
What may look like a jumble of words, numbers, and punctuation is actually a precise and easy-to-read breakdown of the various odds and point spread details your book is offering. Here is a breakdown of each unit of information given above. Once you understand each part of the jumbled details above, you’ll be able to read a sports betting line with confidence.
In this guide, we’re going to teach you literally everything you’ve ever wanted to know about moneyline bets and then a whole lot more. Whether you are a beginner or a seasoned bettor, we’ve got something here for you. We’ll walk you through the basics of what a moneyline bet is, why you would want to make one, and how to interpret the different numbers, payouts, and presentation formats you’ll see.
#### In North American sports betting many of these wagers would be classified as over-under (or, more commonly today, total) bets rather than spread bets. However, these are for one side or another of a total only, and do not increase the amount won or lost as the actual moves away from the bookmaker's prediction. Instead, over-under or total bets are handled much like point-spread bets on a team, with the usual 10/11 (4.55%) commission applied. Many Nevada sports books allow these bets in parlays, just like team point spread bets. This makes it possible to bet, for instance, team A and the over, and be paid if both team A "covers" the point spread and the total score is higher than the book's prediction. (Such parlays usually pay off at odds of 13:5 with no commission charge, just as a standard two-team parlay would.)
We go in depth on this in the advanced guide on understanding value that we referenced earlier, but we will give you a brief intro on it here. If you’re able to calculate the percentage chance that you have to win in order to break even, and you can figure out the percentage chance that you think you’re going to win the bet, you can figure out very quickly if there is value.
###### Betting on the point spread is completely different from betting on teams to win a game outright. Known as "betting on the moneyline", instead of using points to handicap each side of the wager, the sportsbook will use greater payouts versus the amount risked to reflect their relative perceptions; teams not expected to win (underdogs) pay more, sometimes exponentially, than when betting on the favorite to win when wagering on moneylines.
Remember with bets like this you can still be profitable by betting several options. Let's say you think Chelsea is going to win, but you also think Manchester United, Liverpool, and Everton also have a shot. If you were to place a \$100 wager on all four of these teams, you would still turn a profit! Let's pretend you did this and say that your last pick Everton pulls it off and wins the regular season according to the sportsbook. Remember, they don't have actually to win, they just need to be on top after the sportsbook makes the point spread/handicap adjustments to the final rankings.
Betting against the spread - In the sports betting industry the acronym ATS is used to label a team's record when betting against the spread. ATS records are a valuable tool in sports handicapping. A team may be playing great straight-up, winning a lot of games but at the same time they could have a dreadful ATS record because they are overvalued by the general public and the oddsmakers. And, conversely, a team could be losing a lot of games but playing in a lot of close games as underdogs and have a good ATS record going.
The two results above are the no-vig probabilities. If you're sharp, you'll notice that adding 68.57% and 31.43% up together will give you 100%. The extra 2.95% has been removed, so there's no more vig. We can now go to our odds converter and enter 68.57% into the implied probability field. This will give us moneyline odds of -218. If we enter 31.43%, we'll get moneyline odds of +218. The original moneyline market of the Celtics at -240 and the Grizzlies at +210 therefore has no-vig odds of the Celtics at -218 and the Grizzlies at +218.
Identify the type of line you are looking at. All online sports books offer you the chance to have your lines in an "American" or "Money line" version. If I were you, I would use this as my standard. An "American" line uses either a + or - before a number to indicate odds. So a -120 and a +120 are two very different odds on a team… I will explain the differences shortly. Two other less common variations exist: decimal odds and fractional odds.
Identify the type of line you are looking at. All online sports books offer you the chance to have your lines in an "American" or "Money line" version. If I were you, I would use this as my standard. An "American" line uses either a + or - before a number to indicate odds. So a -120 and a +120 are two very different odds on a team… I will explain the differences shortly. Two other less common variations exist: decimal odds and fractional odds.
When betting the point spread, there is almost always a winner and a loser. However, in some instances sportsbook decide to put out a whole number such as -3 for bettors to bet on. If the final score ends with a differential of three points - no matter who wins - the bet is considered a "push" and all money is refunded to both sides since neither team covered the spread.
Armed with the knowledge of how to remove vig, it's now possible to prevent yourself from making the same mistakes that the majority of bettors make. Most bettors understand the importance of line shopping (i.e. comparing the lines and odds at different bookmakers and betting sites). However, if they fail to also understand how moneylines and vig work, then they're probably going to make wagers where they think there's positive expected value (+EV), even though there's not.
Is there value there? Yes. Are you going to make money off that bet? Well, it depends. If you’re only able to make a bet like this once, then you’re most likely going to lose. In order to realize that value, you’ll need to be in a lot of similar opportunities. If you have a very long-term betting strategy, then you can probably get away with making this bet. But if you’re looking for some more regular profit, you might want to steer clear of this. The odds say that the team is only going to win the game a little under 3 times for every 100 times they play. There is value there, but it depends on your betting strategy if you want to make that bet.
Two possibilities existed for Seahawks backers at this point – either the team would win the game by at least three points or not. There was no possibility for a push, thanks to the use of a half-point. It’s impossible to score a half-point in football, so thanks to the magic of rounding, there’s no room for a tie outcome. Those who backed the Patriots were looking at two possible outcomes, too – either New England would pull off the upset or they would lose by just a point or two. Both would turn out in a win.
Let’s say the sportsbook has a series of bets that are all +250. You think in reality that the bets should actually be +125 and that the bet is not as big of an underdog as the sportsbook thinks. This means that you think you deserve \$125 for every \$100 bet that wins but the sportsbook is going to pay \$250. Even though you think that the bet is still supposed to lose, you should make this bet.
An over-under bet in basketball is a wager on whether the total score for the game from both teams will be above or below a certain threshold. This is a great bet to utilize when you think that a game will be defense heavy and both teams will be shooting cold, or when you think that it’s going to be a barn burner with both teams shooting lights out.
A quick word on that annoying half point in the point spread – most lines you’ll come across will use half points, but it’s not standard practice across the board. When you see a line with a full number instead of a number with a half point, your wager could end up as a push. In our example, if the line were 7 instead of 7.5 and the final difference in points was exactly 7, your wager is returned to you, and neither you nor the book makes money.
Futures betting also is offered on the major events in horse racing, such as the Kentucky Derby and Breeders' Cup. In horse racing futures, if your horse does not start the race due to injury or any other reason, you lose the bet -- there are no refunds. On the other hand, the odds on your horse racing futures bet also are "locked in," regardless of the horse's odds on race day. | 3,394 | 15,238 | {"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-2019-39 | latest | en | 0.974393 |
https://ecomodder.com/forum/229506-post1.html | 1,596,941,840,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738380.22/warc/CC-MAIN-20200809013812-20200809043812-00377.warc.gz | 291,240,998 | 5,735 | View Single Post
04-02-2011, 11:02 PM #1 (permalink) 3dplane EcoModding Apprentice Join Date: May 2008 Location: Florida Posts: 158 14 Mirage - '14 Mitsubishi Mirage DE Mitsubishi 90 day: 68.74 mpg (US) Thanks: 35 Thanked 107 Times in 38 Posts So does it take almost 4000 lb of lead to= 1 gal. of gas? I've got several automotive lead acid batteries that actually state the A/h rating on the sticker. So I started weighing them and calculate the Wh/lb. They are all pretty close to about 18 Wh/lb. According to what I can find,energy in a gallon of gasoline is 36.6 Kw/hr. 36600(W/hr) / 18(W/hr) = 2033 lb. Let's just say 2000 pounds. But that's calculating with the 20 hour discharge A/hr rating of the battery! So unless we want to drive around at 0.5 mile/hr in super granny gear for 20 hours to justify the 20 hour discharge rating of the batteries,I think it's about half of the Amp/hour rating is what is an appropriate capacity for a one hour discharge? Is that about right? In that case can we say that it takes about 4000 pounds of lead acid batteries to eaqual the energy available in a gallon of gas? Just an interesting comparison if I did it correctly. __________________ | 313 | 1,189 | {"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} | 2.953125 | 3 | CC-MAIN-2020-34 | latest | en | 0.903535 |
https://calculat.io/en/date/time/10-days--19-hours--0-minutes--ago | 1,680,000,689,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296948858.7/warc/CC-MAIN-20230328104523-20230328134523-00249.warc.gz | 189,156,323 | 24,330 | # 10 Days and 19 Hours Ago
## What is 10 Days and 19 Hours Ago?
10 Days and 19 Hours Ago Was:
10:51:29 am
Your Current Local Time:
Mar 28 2023, 10:51:29 am
(UTC)
## 10 Days and 19 Hours Ago - Timeline
March 28, 2023
1.54 Weeks
March 17, 2023
10.79 Days
10 Days and 19 Hours - It Is Also
• 0.03 Years
• or
• 0.348 Months
• or
• 1.542 Weeks
• or
• 10.792 Days
• or
• 259 Hours
• or
• 15,540 Minutes
• or
• 932,400 Seconds
• or
• 10 days and 19 hours
## About a day: March 17, 2023
• March 17, 2023 falls on a Friday (Weekday)
• This Day is on 11th (eleventh) Week of 2023
• It is the 76th (seventy-sixth) Day of the Year
• There are 289 Days left until the end of 2023
• March 17, 2023 is 20.82% of the year completed
• It is 17th (seventeenth) Day of Spring 2023
• 2023 is not a Leap Year (365 Days)
• Days count in March 2023: 31
• The Zodiac Sign of March 17, 2023 is Pisces (pisces)
• A Person Born on March 17, 2023 Will Be 0.03 Years Old
• March 17, 2023 as a Unix Timestamp: 1679068289
## About "Add or Subtract Time" Calculator
The Time Online Calculator is a useful tool that allows you to easily calculate the date and time that was or will be after a certain amount of days, hours, and minutes from now. For example, it can help you find out what is 10 Days and 19 Hours Ago? Whether you need to plan an event in the future or want to know how long ago something happened, this calculator can help you.
To use the Time Online Calculator, simply enter the number of days, hours, and minutes you want to add or subtract from the current time. For example, you might want to know What Time Was It 10 Days and 19 Hours Ago?, so you would enter '10' days, '19' hours, and '0' minutes into the appropriate fields.
Next, select the direction in which you want to count the time - either 'From Now' or 'Ago'. This will determine whether the calculator adds or subtracts the specified amount of time from the current date and time. In out case it will be 'Ago'
Once you have entered all the required information, click the 'Calculate' button to get the result. The calculator will then display the date and time in a user-friendly format, which can be easily understood and applied in your daily life.
This Time Online Calculator is a great tool for anyone who needs to plan events, schedules, or appointments in the future or past. Whether you are a student, a professional, or a business owner, this calculator will help you save time and effort by quickly determining the date and time you need to know.
March 17, 2023 | 728 | 2,534 | {"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-2023-14 | latest | en | 0.88127 |
https://psychology.stackexchange.com/questions/27055/meaning-of-a-phrase-reciprocal-of-neutral-density-value-required-arranged-o | 1,716,856,919,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059055.94/warc/CC-MAIN-20240528000211-20240528030211-00236.warc.gz | 394,369,150 | 37,894 | # Meaning of a phrase '... reciprocal of neutral density value required arranged on an inverted scale'
The article paramount for my research seems cryptic. It is for visual perception (psychology) and was written 45 years ago. There are a number of sentences hard to 'decypher'.
1. 'reciprocal of neutral density value required arranged on an inverted scale' [p. 1391]; what does it mean at all? is it about neutral density of optical filters for the stroboscope or something?
2. Figure 1 (and others) contains strange mathematical notation (a bar above floating point numbers); is it the old-fashioned way to typeset negative values? are these log relative luminance values? if yes, why isn't it explicitly stated in text and why lower negative values mean 'darker background'? if not, how can it be that higher values mean less contrast?
From earlier in the paper:
The intensity of the flash was controlled by Kodak neutral density filters in the path of the projection beam.
Neutral density filters are those that are intended to filter equally across the visible light spectrum. They're using them to control the light intensity (a lot more common back in the day when it wasn't as easy to control brightness electrically due to the light sources used, though I believe still commonly used in psychophysics experiments and certainly still used in microscopy where we still use some older types of light source). The "reciprocal of neutral density value required" is an effective luminance value, because "more neutral density (filter)" means "less light", so 1/(neutral density filter) is increasing as light is increasing. It's a unit of convenience since the experimenter knows the strength of their filters.
As far as the bars above the numbers, these are clearly to indicate negative numbers though I agree the notation is unusual, it may be a relic of an earlier day in typesetting. There is a more standard notation to indicate the first digit of a logarithm as negative with a bar (see Wikipedia; see also here where it is referred to as a "vinculum" but again only for some of the digits in a number rather than the whole thing) but that doesn't quite match the usage here.
are these log relative luminance values?
In the figure posted, these are log absolute luminance values, measured in units of log(foot-Lamberts). Negative logarithms indicate luminance values less than 1 foot-Lambert.
how can it be that higher values mean less contrast?
If the background is brighter, and the stimulus to be detected is a flash of light, then the brighter the background the less the flash will stand out: less contrast between the flash and the background. | 557 | 2,669 | {"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-2024-22 | latest | en | 0.932063 |
http://www.exampleproblems.com/wiki/index.php/Orbital_period | 1,657,199,329,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104692018.96/warc/CC-MAIN-20220707124050-20220707154050-00599.warc.gz | 69,695,265 | 9,899 | Orbital period
The orbital period is the time it takes a planet (or another object) to make one full orbit.
There are several kinds of orbital periods for objects around the Sun:
• The sidereal period is the time that it takes the object to make one full orbit around the Sun, relative to the stars. This is considered to be an object's true orbital period.
• The synodic period is the time that it takes for the object to reappear at the same spot in the sky, relative to the Sun, as observed from Earth. This is the time that elapses between two successive conjunctions with the Sun and is the object's Earth-apparent orbital period. The synodic period differs from the sidereal period since Earth itself revolves around the Sun.
• The draconitic period is the time that elapses between two passages of the object at its ascending node, the point of its orbit where it crosses the ecliptic from the southern to the northern hemisphere. It differs from the sidereal period because the object's line of nodes typically precesses or recesses slowly.
• The anomalistic period is the time that elapses between two passages of the object at its perihelion, the point of its closest approach to the Sun. It differs from the sidereal period because the object's semimajor axis typically precesses or recesses slowly.
• The tropical period, finally, is the time that elapses between two passages of the object at right ascension zero. It is slightly shorter than the sidereal period because the vernal point precesses.
Relation between sidereal and synodic period
Copernicus devised a mathematical formula to calculate a planet's sidereal period from its synodic period.
Using the abbreviations
E = the sidereal period of Earth (a sidereal year, not the same as a tropical year)
P = the sidereal period of the other planet
S = the synodic period of the other planet (wrt Earth)
During the time S, the Earth moves over an angle of (360°/E)S (assuming a circular orbit) and the planet moves (360°/P)S.
Let us consider the case of an inferior planet, i.e. a planet that will complete one orbit more than Earth before the two return to the same position relative to the Sun.
$\displaystyle \frac{S}{P} 360^\circ = \frac{S}{E} 360^\circ + 360^\circ$
and using algebra we obtain
$\displaystyle P = \frac1{\frac1E + \frac1S}$
For a superior planet one derives likewise:
$\displaystyle P = \frac1{\frac1E - \frac1S}$
The above formulæ are easily understood by considering the angular velocities of the Earth and the object: the object's apparent angular velocity is its true (sidereal) angular velocity minus the Earth's, and the synodic period is then simply a full circle divided by that apparent angular velocity.
Table of synodic periods in the Solar System, relative to Earth:
Sid. P. (a) Syn. P. (a) Syn. P. (d) Mercury 0.241 0.317 115.9 Venus 0.615 1.599 583.9 Earth 1 — — Moon 0.0748 0.0809 29.5306 Mars 1.881 2.135 780.0 1 Ceres 4.600 1.278 466.7 Jupiter 11.87 1.092 398.9 Saturn 29.45 1.035 378.1 Uranus 84.07 1.012 369.7 Neptune 164.9 1.006 367.5 Pluto 248.1 1.004 366.7
In the case of a planet's moon, the synodic period usually means the Sun-synodic period. That is to say, the time it takes the moon to run its phases, coming back to the same solar aspect angle for an observer on the planet's surface —the Earth's motion does not affect this value, because an Earth observer is not involved. For example, Deimos' synodic period is 1.2648 days, 0.18% longer than Deimos' sidereal period of 1.2624 d.
Calculation
Small body orbiting a central body
In astrodynamics the orbital period $\displaystyle T\,$ of a small body orbiting a central body in a circular or elliptical orbit is:
$\displaystyle T = 2\pi\sqrt{a^3/\mu}$
and
$\displaystyle \mu = GM \,$ (standard gravitational parameter)
where:
• $\displaystyle a\,$ is length of orbit's semi-major axis,
• $\displaystyle G \,$ is the gravitational constant,
• $\displaystyle M \,$ the mass of the central body.
Note that for all ellipses with a given semi-major axis, the orbital period is the same, regardless of eccentricity.
For the Earth (and any other spherically symmetric body with the same average density) as central body we get
$\displaystyle T = 1.4 \sqrt{(a/R)^3}$
and for a body of water
$\displaystyle T = 3.3 \sqrt{(a/R)^3}$
T in hours, with R the radius of the body.
Thus, as an alternative for using a very small number like G, the strength of universal gravity can be described using some reference material, like water: the orbital period for an orbit just above the surface of a spherical body of water is 3 hours and 18 minutes. Conversely, this can be used as a kind of "universal" unit of time.
For the Sun as central body we simply get
$\displaystyle T = \sqrt{a^3}$
T in years, with a in astronomical units.
Two bodies orbiting each other
In celestial mechanics when both orbiting bodies' masses have to be taken into account the orbital period $\displaystyle P\,$ can be calculated as follows:
$\displaystyle P = 2\pi\sqrt{\frac{a^3}{G \left(M_1 + M_2\right)}}$
where:
• $\displaystyle a\,$ is the sum of the semi-major axes of the ellipses in which the centers of the bodies move, or equivalently, the semi-major axis of the ellipse in which one body moves, in the frame of reference with the other body at the origin (which is equal to their constant separation for circular orbits),
• $\displaystyle M_1\,$ and $\displaystyle M_2\,$ are the masses of the bodies,
• $\displaystyle G\,$ is the gravitational constant.
Note that the orbital period is independent of size: for a scale model it would be the same, when densities are the same (see also Orbit#Scaling in gravity).
In a parabolic or hyperbolic trajectory the motion is not periodic, and the duration of the full trajectory is infinite. | 1,479 | 5,816 | {"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": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 18} | 3.65625 | 4 | CC-MAIN-2022-27 | latest | en | 0.929624 |
http://stackoverflow.com/questions/15072992/fermats-factorization-method-not-functioning/15073080 | 1,455,379,575,000,000,000 | text/html | crawl-data/CC-MAIN-2016-07/segments/1454701166739.77/warc/CC-MAIN-20160205193926-00058-ip-10-236-182-209.ec2.internal.warc.gz | 217,492,987 | 19,634 | # Fermats factorization method not functioning
I'm working on a program to compare different algorithms for factorization of large integers. One of the algorithms I'm including in the comparison is Fermats factorization method. The algorithm seems to work just fine for small numbers, but when I get larger numbers I get weird results.
Here's my code:
``````public void fermat(long n)
{
ArrayList<Long> factors = new ArrayList<Long>();
a = (long)Math.ceil(Math.sqrt(n));
b = a*a - n;
b_root = (long)(Math.sqrt(b)+0.5);
while(b_root*b_root != b)
{
a++;
b = a*a - n;
b_root = (long)(Math.sqrt(b)+0.5);
}
}
``````
Now, when I try to factor 42139523531366663 I get the resulting factors 6194235479 and 2984853201, which is incorrect since 6194235479 * 2984853201 = 18488883597240918279. I figured that I got this result because somewhere in the algorithm I got to a point where the numbers became too big for a long or something similar, so the algorithm got a bit messed up because of that. I added a check which calculated the product of the two factors and compared with the input value, so that I'd get an alert if the factorization was faulty:
``````long x,y;
x = factors.get(0);
y = factors.get(1);
if(x*y!=n)
System.out.println("Faulty factorization.");
``````
Interestingly enough, the check passed as true and I didn't get the alert. I tried just printing the result of the multiplication and this actually resulted in the input value. So my question is why does my program behave like this, and what can I do about it?
-
It looks like there is an overflow in a `long` somewhere, because longs have 64 bits and
``````42139523531366663 + 2^64 = 18488883597240918279
``````
For sufficiently large numbers, you may need switch to using `BigInteger`.
-
So the factors I got are correct modulo 2^64? I see. Using BigInteger instead might prove difficult though, since I haven't found any simple way to calculate the square root of a BigInteger. I'll have to look for a solution to this. Thank you! – Psyberion Feb 25 '13 at 18:16
You can use bisection: the square root of a positive integer x > 1 must be between 1 and x, so compute the midpoint, square it, and recur on the remaining half where the square root resides, stopping when the two endpoints become equal. Or use Newton's method of derivatives, or even Heron's method, which dates to the ancient Babylonians about three thousand years ago; either works perfectly well using integers. Ask a separate question if you can't figure it out yourself. – user448810 Apr 17 '13 at 14:06
Is it because there's an error in multiplying large numbers too?
That may be a valid enough reason. This is what makes the program think that it's factorization is right, but when you actually multiply the numbers without using the program, you discover the error.
-
rgettman's answer seems legit enough. – Cheeku Feb 25 '13 at 17:46 | 719 | 2,886 | {"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-2016-07 | latest | en | 0.922452 |
https://noobtomaster.com/time-series-analysis-using-python/handling-multi-variate-time-series-data/ | 1,726,060,767,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651387.63/warc/CC-MAIN-20240911120037-20240911150037-00660.warc.gz | 392,159,265 | 6,021 | # Handling Multi-Variate Time Series Data
When it comes to time series analysis, it is not uncommon to encounter data that is not just dependent on a single variable but on multiple variables. This multi-variate time series data poses unique challenges and requires special handling techniques. In this article, we will explore some methods to handle and analyze multi-variate time series data using Python.
## Understanding Multi-Variate Time Series Data
In a multi-variate time series, each observation consists of multiple variables recorded at different points in time. For example, consider a dataset where we track the daily temperature, humidity, and air pressure readings for a particular location. In this case, we have three variables (temperature, humidity, and air pressure) recorded over time.
In addition to the variation observed in each variable independently, there may also be inter-dependencies or relationships between the variables. These relationships can be analyzed to gain deeper insights into the data.
## Preprocessing Multi-Variate Time Series Data
Before diving into the analysis, it is essential to preprocess the multi-variate time series data. Here are some common preprocessing steps:
1. Handling missing values: Multi-variate time series data often has missing values. These missing values can be filled using various techniques such as interpolation, forward-fill, or backward-fill, depending on the context of the data.
2. Normalization: It is crucial to normalize the variables to a common scale. Variables with different ranges can skew the analysis, so scaling them to a similar range (e.g., using Min-Max scaling) helps in fair comparison.
3. Feature engineering: Sometimes, it is beneficial to create new features from the existing variables to capture additional information or relationships. For instance, deriving daily averages or weekly moving averages from daily temperature readings.
## Visualizing Multi-Variate Time Series Data
Visualizing multi-variate time series data can provide useful insights. Here are a few visualization techniques:
1. Line Plots: Line plots can be used to visualize each variable separately over time. This helps to observe the trends and patterns in individual variables.
2. Heatmaps or Correlation Plots: Heatmaps or correlation plots provide a visual representation of the relationships between variables. Correlation coefficients can be calculated to quantify the strength and direction of these relationships.
3. Multi-Dimensional Time Series Plots: Multi-dimensional time series plots can be used to plot multiple variables simultaneously, either in separate subplots or overlaid on the same plot. This allows us to visualize the relationships and dependencies between variables more directly.
## Analyzing Multi-Variate Time Series Data
Once the data is preprocessed and visualized, various analytical techniques can be applied to gain insights from the multi-variate time series data. Some methods include:
1. Auto-Regressive Integrated Moving Average (ARIMA): ARIMA models can be extended to handle multi-variate time series data by including lagged values of multiple variables in the model. This captures the inter-dependencies between the variables.
2. Vector Autoregression (VAR): VAR models are specifically designed for multi-variate time series data, where each variable is modeled as a linear combination of its past values and the past values of other variables. VAR models can help forecast the values of multiple variables simultaneously.
3. Granger Causality Analysis: Granger causality analysis is used to measure the causal relationships between variables in a time series. It can help determine whether one variable can be used to predict another variable, providing insights into the underlying dependencies.
## Conclusion
Handling multi-variate time series data requires special techniques to explore the relationships between variables and gain meaningful insights. Python provides various libraries and methods to preprocess, visualize, and analyze multi-variate time series data. By applying these techniques, we can uncover hidden patterns, forecast future values, and make data-driven decisions. | 771 | 4,223 | {"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} | 3.125 | 3 | CC-MAIN-2024-38 | latest | en | 0.878713 |
https://it.mathworks.com/matlabcentral/answers/164316-select-everything-not-returned-by-index?s_tid=prof_contriblnk | 1,585,764,106,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370505826.39/warc/CC-MAIN-20200401161832-20200401191832-00214.warc.gz | 534,991,787 | 25,502 | # Select everything NOT returned by index
353 views (last 30 days)
Claire on 26 Nov 2014
Edited: Mallory Nation on 25 Sep 2019
Hello,
Apologies if this is a stupid question, but I haven't found a way to properly google it.
I have an index where certain conditions are met, but I want to make everything outside of that index NaN.
e.g.
x=find(wind(:,:,1)>0&wind(:,:,2)>0);
wind(x)=NaN; % But I actually want the parts not indexed to equal NaN
I'm looking for something like
wind(~x)=NaN
but that doesn't work. I can't just change my > sign around either because of the range of values in my matrix.
I'd just like to find a way to apply wind(x)=NaN to the values NOT in x.
Thanks, Claire
Oleg Komarov on 26 Nov 2014
x > 0 & y > 2 is logically equivalent of x <= 0 | y <= 2
Claire on 26 Nov 2014
Yes, but in my case it's not quite so simple. I have values in x between -1 and 1 and values in y between -1 and 1. I'm trying to isolate the area where both x and y are positive, and make the rest NaN. Simply swapping the > sign to a < sign will only then isolate where both x and y are negative.
I could always do it in two steps, but I can easily index to find the quadrant I want in one statement, and I was hoping it was just a case of selecting everything outside of that indexed quadrant to make it NaN.
John D'Errico on 26 Nov 2014
Claire - read my comment. See that Oleg did as I did, changed the & to an or. It is time to go back to basic logical operator school. Um, maybe Venn diagrams?
Roger Stafford on 26 Nov 2014
You can always do logical indexing using the negation of whatever condition you have.
t = wind(:,:,1)>0&wind(:,:,2)>0;
wind(~t) = NaN;
Claire on 26 Nov 2014
Thank you. It seems my problem was with using "find" and when I changed it to "x=", the ~ operator worked.
Thanks! Claire
Jan on 30 Sep 2017
+1. The logical indexing is faster than the indirection over find.
John D'Errico on 26 Nov 2014
Why can't you change the inequalities?
x=find(wind(:,:,1)<=0 | wind(:,:,2) <= 0);
I'm listening, but your statement makes no sense as to why not. Basic logic tells us that:
~(A & B) == ~A | ~B
As trivially,
x=find(~(wind(:,:,1)>0 & wind(:,:,2)>0));
Finally, and equally trivially, but considerably less efficient because it is an extra and wholly unnecessary step, you might read up on what setdiff does.
doc setdiff
Show 1 older comment
John D'Errico on 26 Nov 2014
No. You did not look at what I said. Read it again. See that I changed the & to an |, thus change an and to an or. I think you need to learn about logic, or at least review what I hope you may have learned some years ago.
You have the logical expression
A & B
but in reality, you wish the expression
not(A & B)
(The find operation is not relevant here. All that matters is the logical expression.) Essentially, you wish to negate what you found in that logical expression. So one simple solution is to simply add a ~ to the command that you had.
Back in high school mathematics (maybe it was earlier, a long time ago) we learned that
not(A & B) == not(A) | not(B)
This tells us that in order to find the negation of a pair of inequalities anded together, instead, we can change the > symbols to <=, and the and(&) to an or(|).
Do people not learn the basic calculus of logical operations anymore?
I showed you two ways to find what you needed, BOTH of which are completely valid. Yes, setdiff will also provide what you need, but it is completely unnecessary, as I stated, and is thus less efficient.
Claire on 26 Nov 2014
I simple, "you misunderstood my response" would have sufficed, without the additional backhanded insults.
Roger provided the answer to the question I had asked, so the problem is now sorted. Thanks.
Oleg Komarov on 26 Nov 2014
Claire, you kept answering my comments and John's answer with your copy-paste text without even reading carefully. If there are two people telling you the same thing, and taking their time to do that in an elaborate clear way (John), it is not nice of you to paste the same sentences. I do not see much of an insult in the statement that you are missing the basics of logical truth tables (<http://en.wikipedia.org/wiki/Truth_table>) but an opportunity to go and check them out again, since much of programming is based on that.
Mallory Nation on 25 Sep 2019
Edited: Mallory Nation on 25 Sep 2019
For fun, to do what was wanted using find, you could do this:
xNot = setdiff(x,1:length(wind(:,:,1)));
wind(:,:,xNot) = nan;
But as already stated, the best way is to not use find at all. | 1,181 | 4,524 | {"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} | 3.0625 | 3 | CC-MAIN-2020-16 | latest | en | 0.949088 |
https://forums.odforce.net/search/?tags=convex&sortby=relevancy&page=1 | 1,632,793,434,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780058589.72/warc/CC-MAIN-20210928002254-20210928032254-00251.warc.gz | 308,283,417 | 18,458 | # Search the Community
Showing results for tags 'convex'.
• ### Search By Tags
Type tags separated by commas.
### Forums
• General
• Lounge/General chat
• Education
• Jobs
• Marketplace
• Houdini
• General Houdini Questions
• Effects
• Modeling
• Animation & Rigging
• Lighting & Rendering
• Compositing
• Games
• Tools (HDA's etc.)
• Coders Corner
• HDK : Houdini Development Kit
• Scripting
• Art and Challenges
• Finished Work
• Work in Progress
• VFX Challenge
• Effects Challenge Archive
• Systems and Other Applications
• Other 3d Packages
• Operating Systems
• Hardware
• Pipeline
• od|force
• Feedback, Suggestions, Bugs
• 0 Replies
• 0 Views
Found 4 results
1. ## Potato peeling
https://en.wikipedia.org/wiki/Potato_peeling https://perso.liris.cnrs.fr/dcoeurjo/publications/dcoeurjo_chassery_ismm.pdf Has anyone attempted doing something like this in Houdini? It looks like you shrink the object, convex hull, and scale it up to where the hull first touches the original surface it gets sliced (maybe using original surface normal), and then you iterate that till you have a largest possible area that lies within a given non-convex polygon. thanks, z
2. ## Smooth out concave (recessed) parts of mesh preserving convex
Hello everyone, The title says it all. But to illustrate the idea better, I've also attached an image, where red lines show concave parts, that have to be smoothed (simplified), and green mark convex parts, that have to be preserved.
3. ## Point Cloud Tools with File
Hey everyone! Here's a demo of some point cloud tools I created to calculate concave and convex curvature as well as gradient and curl direction, also sharpening. Forgot to mention in the demo that the curvature calculation is a great way to do differential growth by advection along normal * curve * noise * parm. Also, the curl calculation can be used to make grass patches and groom fur by orienting curves along the direction to add swirly variance. There's a lot of ways these tools can be handy, interested to see what you all come up with! Let me know if you have any questions, enjoy! curveGradientCurlSharpen_v002.hipnc
4. ## Bullet sim\fracture for architecture destruction
Here is my house destruction WIP. On the videos in this post you can see what I made myself, before I stuck with the problem of a concave geometry in the corners (which can not properly handled by the Bullet engine). By default, the Voronoi Fracture HDA creates concave geometry in the corners (you can see it on the screenshots below) and if there is another object located in the corner (for example bricks behind the stucco), the simulation starts to explode (because the Bullet improperly complements such geometry to convexity). I tried to search some info about how to implement a Convex Decomposition algorithm in Houdini (may be HACD*), but I haven't any result yet. All what I have for now, is my concavity-testing VEX node, that finds all the concave parts, but I have no idea how to cut them on a convex pieces. It will be cool, if somebody can help me with this problem. Below you can see my tests. *Hierarchical Approximate Convex Decomposition http://kmamou.blogsp...ate-convex.html http://www.khaledmammou.com/hacd.html http://masc.cs.gmu.edu/wiki/ACD
×
• Donations | 792 | 3,274 | {"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} | 2.609375 | 3 | CC-MAIN-2021-39 | latest | en | 0.823866 |
https://learn.careers360.com/medical/question-please-help-a-square-loop-abcd-carrying-a-current-i-is-placed-near-and-coplanar-with-a-long-straight-conductor-xy-carrying-a-current-ithe-net-force-on-the-loop-will-be/ | 1,601,287,624,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600401598891.71/warc/CC-MAIN-20200928073028-20200928103028-00727.warc.gz | 457,707,911 | 96,656 | # A square loop ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the loop will be: Option 1) Option 2) Option 3) Option 4)
Force between two parallel current carrying conductors -
$F=\frac{\mu }{4\pi } \frac{2I_{1 I_{2}}}{a} l$
$\frac{F}{l}=\frac{\mu o}{4\pi } \frac{2I_{1 I_{2}}}{a}$
- wherein
I1 and I2 current carrying two parallel wires
a-seperation between two wires
force on $F_{1}= \frac{\mu _{0}}{4\pi }\frac{2Iil}{\frac{l}{2}} = \frac{\mu _{0} Ii}{3\pi }$
force $f_{2 }= \frac{\mu _{0}}{4\pi }\frac{2IiL}{3\left ( \frac{L}{2} \right )} = \frac{\mu_{0} }{3\pi }$
Net force on the loop
$f_{1}-f_{2} = \frac{\mu _{0Ii}}{\pi }\left [ 1-\frac{1}{3} \right ]$
$= \frac{2 \mu _{0}Ii}{3\pi }$
Option 1)
This option is correct.
Option 2)
This option is incorrect.
Option 3)
This option is incorrect.
Option 4)
This option is incorrect.
### Preparation Products
##### Rank Booster NEET 2021
This course will help student to be better prepared and study in the right direction for NEET..
₹ 13999/- ₹ 9999/-
##### Knockout NEET May 2021
An exhaustive E-learning program for the complete preparation of NEET..
₹ 22999/- ₹ 14999/-
##### Knockout NEET May 2022
An exhaustive E-learning program for the complete preparation of NEET..
₹ 34999/- ₹ 24999/-
##### Test Series NEET May 2021
Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..
₹ 6999/- ₹ 4999/- | 507 | 1,511 | {"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": 6, "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-2020-40 | longest | en | 0.677987 |
https://marineprohelp.com/terms/6121/magnetic-prime-vertical | 1,560,897,952,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627998844.16/warc/CC-MAIN-20190618223541-20190619005541-00128.warc.gz | 509,202,651 | 13,218 | # MAGNETIC PRIME VERTICAL
The vertical circle through the magnetic east and west points of the horizon.
## Related Terms
### PRIME VERTICAL CIRCLE
The vertical circle perpendicular to the principal vertical circle. The intersections of the prime vertical circle with the horizon define the east and west points of the horizon. Often shortened to PRIME VERTICAL; Sometimes called TRUE PRIME VERTICAL to distinguish from magnetic, compass, or grid prime vertical, defined as the vertical circle passing through the magnetic, compass, or grid east and west points of the horizon, respectively.
### PRIME VERTICAL
A vertical circle passing through East and West points on the horizon.
### COMPASS PRIME VERTICAL
The vertical circle through the compass east and west points of the horizon
### GRID PRIME VERTICAL
The vertical circle through the grid east and west points of the horizon
### VERTICAL CIRCLE
A great circle of the celestial sphere through the zenith and nadir. Vertical circles are perpendicular to the horizon. The prime vertical circle or prime vertical passes through the east and west points of the horizon. The principal vertical circle passes through the north and south points of the horizon and coincides with the celestial meridian.
### ZENITH DISTANCE
Angular distance from the zenith; the arc of a vertical circle between the zenith and a point on the celestial sphere, measured from the zenith through 90°, for bodies above the horizon. This is the same as COALTITUDE with reference to the celestial horizon.
### HORIZONTAL INTENSITY VARIOMETER
Essentially a declination variometer with a larger, stiffer fiber than in the standard model; there is enough torsion in the fiber to cause the magnet to turn 90 out of the magnetic meridian; the magnet is aligned with the magnetic prime vertical to within 0.5 so it does not respond appreciably to changes in declination. Also known as H variometer.
### PRINCIPAL VERTICAL CIRCLE
The vertical circle passing through the north and south celestial poles. The intersection of the principal vertical circle with the horizon defines the north and south points of the horizon.
### SWINGING THE ARC
The process of rotating a sextant about the line of sight to the horizon to determine the foot of the vertical circle through a body being observed. Also called ROCKING THE SEXTANT.
### CELESTIAL MERIDIAN
A great circle of the celestial sphere, through the celestial poles and the zenith. The expression usually refers to the upper branch, that half from pole to pole which passes through the zenith; the other half being called the lower branch. The celestial meridian coincides with the hour circle through the zenith and the vertical circle through the elevated pole.
### Related questions
MarineProHelp 2018 - 2019. | 577 | 2,803 | {"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-2019-26 | longest | en | 0.849977 |
https://www.rocscience.com/help/unwedge/tutorials/tutorials-overview/advanced-joint-combinations-analysis-in-unwedge | 1,642,456,586,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320300624.10/warc/CC-MAIN-20220117212242-20220118002242-00480.warc.gz | 1,034,218,182 | 29,071 | The Rocscience International Conference 2021 Proceedings are now available. Read Now
## Search Results
This tutorial will perform a Probabilistic Analysis on a geometry with four joints. We will first look at the individual combinations. We will then proceed to compute all of the joint combinations at once.
Topics Covered in this Tutorial:
• Probabilistic Joint Combination Analysis
• Analysis of Individual Joint Combinations
• Analysis of All Joint Combinations
Finished Product:
The finished tutorial can be found in the Tutorial 11 Advanced Joint Combination.weg5 file located in the Examples > Tutorials folder in your UnWedge installation folder.
## 1.0 Model
If you have not already done so, run the UnWedge program by double-clicking on the UnWedge icon in your installation folder. Or from the Start Menu, select Programs > Rocscience > UnWedge. If the UnWedge application window is not already maximized, maximize it now so that the full screen is available for viewing the model.
For this tutorial we will start by reading in the file Tutorial 01 Quick Start.weg5, which you should find in the Examples > Tutorials folder in your UnWedge installation folder and open.
### 1.1 PROJECT SETTINGS
1. Select Project Settings from the toolbar or the Analysis menu.
2. Ensure Units = Metric, stress as MPa.
3. Change Analysis Type = Probabilistic.
4. Navigate to the Sampling tab on the left of the dialog.
5. Change the Number of Samples = 1000.
6. Ensure the Advanced Location Dependent Scaling box is checked.
7. Select OK.
### 1.2 INPUT DATA
1. Select Input Data from the toolbar or the Analysis menu.
2. Navigate to the Joint Orientations tab.
4. Change Joint 4 Dip = 60 and Dip Direction = 90.
5. Change all four joint Properties = smooth joint as shown.
6. Navigate to the Joint Properties tab.
7. Select the rough joint tab on the left of the dialog.
8. Select the Delete button to delete the rough joint.
Only the smooth joint should be displayed on the left of the dialog.
9. Change the Joint Structure Continuity from Infinite to Persistence. Keep the default Persistence = 5 m.
10. Select OK.
### 1.3 JOINT PROPERTIES
1. Select Statistics > Joint Properties to open the Joint Properties Statistics dialog.
3. Enter the following:
Property = Persistence
Distribution = Exponential
Mean = 5
Rel. Min = 4
Rel. Max = 10
4. Select OK.
## 2.0 Combination 1: Joints 1,2,3
1. Select Input Data from the toolbar or the Analysis menu.
2. Navigate to the Joint Orientations tab.
3. Note under Joint Combination that we are looking at Combination 1 of 4. Combination 1 uses Joints 1, 2, and 3.
4. Select Cancel.
We are now ready to compute.
1. Select Compute on the toolbar or the Analysis menu.
2. Switch to the Probability View .
You should see the following:
From the Sidebar, we can see that we are currently looking at the Maximum Support Pressure. Most of the roof segments have a Maximum Support Pressure of 0.032 MPa.
1. Select New Window on the toolbar or the Window menu.
The Probability View should now be vertically tiled with the 3D Wedge View.
2. Click on one of the 0.032 roof segments in the Probability View to see the resulting 3D Wedge View.
3. Close the 3D Wedge View and maximize the Probability View.
4. Right-click on one of the 0.032 roof segments (e.g., Segment 10) and select Plot Histogram .
5. Select OK.
You should see the following Histogram:
NOTE: Notice that the last column of the histogram is very high. This means there is a high frequency of wedges with a support pressure of approximately 0.031 MPa. The reason for this anomaly is due to the probabilistic range of our persistence variable. In the Joint Properties dialog we gave persistence a range between 1 m and 15 m. Whenever the persistence reaches a length such that the resulting wedge is bigger than the tunnel itself, UnWedge scales that wedge down to the maximum size for the tunnel.
Now that we have studied the results of the first joint combination, we will go on to look at the second.
Close the Histogram view.
## 3.0 Combination 2: Joints 1,2,4
1. Select Input Data from the toolbar or the Analysis menu.
2. Navigate to the Joint Orientations tab.
On the bottom of the dialog, we can see that we are looking at Combination 1 of 4 total combinations.
3. Click on the up arrow to go to Combination 2.
This combination takes joints 1, 2, and 4 into account.
4. Select OK.
5. Select Compute on the toolbar or the Analysis menu.
6. Switch to the Probability View .
The Maximum Support Pressure on the roof now varies between 0.057 MPa and 0.086 MPa.
7. Select New Window on the toolbar.
The Probability View should now be vertically tiled with the 3D Wedge View, as shown.
1. Close the 3D Wedge View and maximize the Probability View.
2. Right-click on one of the roof segments (e.g., Segment 12) and select Plot Histogram in the popup menu.
3. SelectOK in the dialog.
You should see the following Histogram:
Note that in this combination, unlike the previous one, the Support Pressure follows a generally exponential distribution without any extreme anomalies. This is because, in this combination, the maximum persistence is never met so UnWedge does not have to scale down a large number of wedges.
We will now go on to look at the third joint combination.
Close the Histogram view.
## 4.0 Combination 3: Joints 1,3,4
1. Select Input Data from the toolbar or the Analysis menu.
2. Navigate to the Joint Orientations tab.
Under Joint Combinations, we can see that we are looking at Combination 2 of 4 total combinations.
3. Click on the up arrow to go to Combination 3. This combination takes Joints 1, 3, and 4 into account.
4. Select OK.
5. Select Compute on the toolbar or the Analysis menu.
6. Switch to the Probability View .
The Maximum Support Pressure on the roof segments now varies between 0.005 MPa and 0.021 MPa.
7. Select New Window on the toolbar or Window menu.
The Probability View should now be vertically tiled with the 3D Wedge View.
8. Click on one of the 0.005 MPa segments to view the resulting wedges.
1. Close the 3D Wedge View and maximize the Probability View.
2. Right-click on one of the 0.005 MPa roof segments (e.g., Segment 15) and select Plot Histogram on the popup menu.
3. Select OK in the dialog.
You should see the following Histogram:
We will now go on to look at the fourth joint combination.
Close the Histogram view.
## 5.0 Combination 4: Joints 2,3,4
1. Select Input Data from the toolbar or the Analysis menu.
2. Navigate to the Joint Orientations tab.
Under Joint Combinations, we can see that we are looking at Combination 3 of 4 total combinations.
3. Click on the up arrow to go to Combination 4. This combination takes Joints 2, 3, and 4 into account.
4. Select OK.
5. Select Compute on the toolbar or the Analysis menu.
6. Switch to the Probability View .
The Maximum Support Pressure on the roof segments now varies between 0.011 MPa and 0.024 MPa.
7. Select New Window on the toolbar or Window menu.
The Probability View should now be vertically tiled with the 3D Wedge View.
8. Click on one of the 0.011 MPa segments (e.g., Segment 8) to view the resulting wedges.
9. Close the 3D Wedge View and maximize the Probability View.
10. Right-click on one of the 0.011 MPa roof segments (e.g., Segment 8) and select Plot Histogram on the popup menu.
11. Select OK in the dialog.
You should see the following Histogram:
Close the Histogram view.
## 6.0 All Joint Combinations
We have seen different results from each combination of joints. We will now show how we can look at all four joint combinations at once.
We should note here that the number of samples we entered in the Project Settings dialog at the beginning of the tutorial (1000) was the number of samples used for each combination. That is to say, for Joint Combination 1, 1000 wedge orientations were computed, and the Maximum Support Pressure from all these samples was studied in the Probability View. Similarly, for Joint Combination 2, 1000 samples were computed, and the Maximum Support Pressure from all these samples was studied.
In this section, we will look at all four joint combinations at once. Because there are four different combinations of joints, UnWedge will divide the number of samples by four. Therefore, for Joint Combination 1, 1000/4 = 250 samples will be computed. Similarly, 250 samples will be computed for Joint Combination 2, and so on. For the sake of consistency, and in order to have comparable results, we want 1000 samples to be computed for each joint combination as before. Therefore, we will use a sampling size of 4000.
1. Select Project Settings from the toolbar or the Analysis menu.
2. Click on the Sampling tab and change the Number of Samples = 4000.
3. Select OK.
4. Select Input Data from the toolbar or the Analysis menu.
5. Navigate to the Joint Orientations tab.
Under Joint Combinations, we can see that we are looking at Combination 4 out of the four total combinations.
6. Select the Compute All Joint Combinations (Probabilistic) checkbox.
7. Select OK.
8. Select Compute on the toolbar or the Analysis menu.
9. Switch to the Probability View .
You should see the following:
The Maximum Support Pressure on the roof segments now varies between 0.057 MPa and 0.086 MPa. Notice that the 0.086 MPa value is the Maximum Support Pressure from Joint Combination 2; it is also the maximum of the pressures we saw in the four different joint combinations, for this segment. For the right-most segment, notice that the 0.057 MPa value is the Maximum Support Pressure we saw from all the combinations for this segment. This demonstrates that we are now looking at the Maximum Support Pressure from all of the possible joint combinations.
1. Right-click on one of the 0.086 MPa roof segments (e.g., Segment 9) and select Plot Histogram .
2. Select OK.
3. Select New Window .
The Probability View should now be vertically tiled with the 3D Wedge View and the Histogram.
4. Minimize the Probability View and select Tile Vertically on the toolbar or Window menu.
You should see the following on your screen.
Recall that Joint Combination 1 gave us a maximum support pressure of 0.032 MPa for this segment.
Double-click on the Histogram where the Support Pressure is about 0.032 MPa. The resulting 3D Wedge View is almost identical to the one we saw in the Joint Combination 1 section of the tutorial. From the Sidebar we can see that the exact pressure in the figure is 0.033 MPa.
Now, double-click on the Histogram where the Support Pressure is maximum (0.086 MPa). You will notice that the resulting wedges are identical to those we saw in Joint Combination 2. Recall the maximum support pressure on this roof segment for Combination 2 was also 0.086 MPa.
It will be left as an exercise for the user to examine the wedges resulting from double-clicking on the Histogram on the same pressures seen in Joint Combination 3 and 4.
In conclusion, using the Compute All Joint Combinations (Probabilistic) checkbox, allows the user to view the results from all possible joint combinations at once.
This concludes the tutorial. You are now ready for the next tutorial, Tutorial 12 - Batch Compute in UnWedge. | 2,617 | 11,221 | {"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} | 2.671875 | 3 | CC-MAIN-2022-05 | latest | en | 0.818871 |
https://oeis.org/A091484/internal | 1,627,759,626,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154099.21/warc/CC-MAIN-20210731172305-20210731202305-00652.warc.gz | 448,850,220 | 3,324 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A091484 Recamán's Fibonacci variation : a(1)=a(2)=1 then a(n) = a(n-1)+a(n-2)-F(n) if that number is >0 and not already in the sequence; a(n) = a(n-1)+a(n-2)+F(n) otherwise where F(n) denotes the n-th Fibonacci number. 0
%I
%S 1,1,4,2,11,5,3,29,66,40,17,201,451,275,116,1378,3091,1885,795,9445,
%T 21186,12920,5449,64737,145211,88555,37348,443714,995291,606965,
%U 255987,3041261,6821826,4160200,1754561,20845113,46757491,28514435,12025940
%N Recamán's Fibonacci variation : a(1)=a(2)=1 then a(n) = a(n-1)+a(n-2)-F(n) if that number is >0 and not already in the sequence; a(n) = a(n-1)+a(n-2)+F(n) otherwise where F(n) denotes the n-th Fibonacci number.
%C Unlike Recamán's sequence, this one has "simple" behavior since the sequence of signs of a(n+1)-a(n) becomes 4-periodic sequence -1,-1,1,1,-1,-1,1,1,-1,-1,...
%F With phi=(1+sqrt(5))/2 for n>1 : a(4n)=floor(r*phi^(4n)) where r = (-675+327*sqrt(5))/90; a(4n+1)=floor(s*phi^(4n+1)) where s=(-132+66*sqrt(5))/18; a(4n+2)=floor(s*phi^(4n+2)) where t= (-15+7*sqrt(5))/2; a(4n+3)=floor(u*phi^(4n+3)) where u=(-115+52*sqrt(5))/15.
%F For n>=0, a(4n+5) = 11/3*Luc(4n+2), a(4n+6) = 5*Fib(4n+2).
%F For n>=3, the sequence satisfies the order 8 linear recurrence: a(n+8)-7*a(n+4)+a(n)=0. - _Benoit Cloitre_, Apr 30 2006
%F Empirical g.f.: x*(6*x^7-4*x^6+17*x^5-12*x^4+3*x^3-5*x^2-1) / ((x^2+x-1)*(x^4+3*x^2+1)). - _Colin Barker_, Jun 26 2013
%e a(6)+a(5)=5+11=16 and F(7)=13. Since 16-13=3 is not already in the sequence, a(7)= a(6)+a(5)-F(7)=3.
%o (PARI) m=200; a=vector(m); a[1]=1; a[2]=1; for(n=3, m, a[n]=if(n<0, 0, if(abs(sign(a[n-1]+a[n-2]-fibonacci(n))-1)+setsearch(Set(vector(n-1, i, a[i])), a[n-1]+a[n-2]-fibonacci(n)), a[n-1]+a[n-2]+fibonacci(n), a[n-1]+a[n-2]-fibonacci(n)))); a
%Y Cf. A005132, A079053 (also Fibonacci variation but starting with 1, 2).
%K nonn,easy
%O 1,3
%A _Benoit Cloitre_, Mar 03 2004
%E PARI code corrected by _Colin Barker_, Jun 26 2013
Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.
Last modified July 31 15:25 EDT 2021. Contains 346374 sequences. (Running on oeis4.) | 1,014 | 2,449 | {"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} | 3.90625 | 4 | CC-MAIN-2021-31 | latest | en | 0.524508 |
http://www.docstoc.com/docs/119958405/DFT-method | 1,441,185,253,000,000,000 | text/html | crawl-data/CC-MAIN-2015-35/segments/1440645258858.62/warc/CC-MAIN-20150827031418-00055-ip-10-171-96-226.ec2.internal.warc.gz | 410,832,578 | 40,674 | # DFT method by techtrick4u
VIEWS: 33 PAGES: 14
• pg 1
``` 1
Density Functional Theory
An Introduction
Quantum mechanical modelling method used in chemistry and physics to
g ( y g ) y
investigate the electronic structure (principally the ground state) of many
body systems, in particular atoms, molecules, and the condensed phases.
The methods we’ve bee d scuss g ca be g ouped together u de the
e e ods e e been discussing can grouped oge e under e
– They all calculate energies/properties by calculating/improving
upon the wavefunction
Density Functional Theory (DFT) instead solves for the
electron density.
2
Density Functional Theory
Generally computational cost i similar t th cost of HF
– G ll t ti l t is i il to the t f
calculations.
– Most DFT methods involve some empirical parameterization.
– Generally lacks the systematics that characterize wavefunction
methods.
– Often the best choice when dealing with very large molecules
(proteins, large organic molecules...)
(p , g g )
for theory
Nobel prize - Walter Kohn “for his development of density functional theory”
(1998)
Function: A prescription for producing a number from a set of variables.
• Wave function and
Represented in ( )
• Electron density
3
Functional: A prescription for producing a number from a Function
which in turn depends on variables.
Examples:
• An energy depending on a wave function or an electron density
• T and V are functions of density which is a function of coordinate.
Hence, T and V are called ‘density functionals’
Represented in [ ]
4
The Hohenberg-Kohn theorems:
Theorem -1:
Ground state
• Ground-state electronic energy is determined completely by the electron density
i.e. E = E [ρ ] where ρ is the ground-state density of the system.
Electron density, ρ ( r ), determines
p ()
• The external potential, V(r)
• Total number of electrons, N.
V (r ) and N Determines molecular Hamiltonian H op
N n N N N n n
ZA Z AZB
H op = −∑
2 i ∑∑ riA ∑∑ rij ∑∑ RAB
1∇2 − + 1+
i A i i< j j B< A A
5
• H op determines the energy of the system via Schrödinger’s equation,
H op Ψ = E Ψ
Ultimately, ρ ( r ), determines the energy of the system.
V (r )
ρ (r ) H op Ev [ρ (r )]
N
Theorem-2:
Density obeys the Variational principle.
i.e. It obeys variational principle for obtaining optimal ρ ( r )
which minimizes E.
6
Energy functional:
EDFT [ρ (r )] = Tni [ρ (r )] + Vne [ρ (r )] + Vee [ρ (r )] + Exc [ρ (r )]
Exc [ρ (r )] = Ex [ρ (r )] + Ec [ρ (r )] = ∫ ρ (r )εxc [ρ (r )]dr
Exc [ρ (r )] is determined as an integral of some function of the
total electron density
εxc [ρ (r )] is the energy density per electron
7
Density Functional Method
Classification
Local
Non-local
Hybrids
8
Methods in DFT
1. Local Density Approximation: (LDA functionals)
• Exchange and Correlation functional depends only on
g p y
local value of the density.
• Electron density is treated locally as a uniform electron gas or
function.
equivalently that the density is a slowly varying function
• Systems with spin polarization (open systems) LDA is called as
Local Spin Density Approximation (LSDA).
Example:
• SVWN functional: (Slater, Vosko, Wilks Nusair)
9
2. Non-local Methods (GGA functionals)
• In molecular systems, electron density is not uniform.
• Exchange and Correlation functional depends not only on
l l l f the density b t also on th extent t which
local value of th d it but l the t t to hi h
density is changing locally, i.e. gradient of the density.
constructed with the correction added to LDA functional, i.e.,
⎡ ∇ρ (r ) ⎤
ε xc [ρ (r )] = ε xc
GGA LSDA
[ρ (r )] + ∆εxc ⎢ 4 / 3 ⎥
⎢⎣ ρ (r ) ⎦⎥
Examples:
Becke GGA exchange functional: (B)
• incorporates a single empirical parameter optimized by fitting
to exactly known exchange energies of six noble gases. (He – Rn)
B86, P, PBE functionals:
• contains no empirically optimized parameter
10
3. Hybrid functionals:
B3PW91 model : Becke’s 3 parameter scheme with GGA exchange and
correlation functional of PW91
Exc3 PW 91 = (1− a ) ExLSDA + aExHF + b∆ExB 86 + EcLSDA + c∆EcPW 91
B
E
B3LYP model : LYP computes full correlation energy and not correction
to LSDA
Exc3 LYP = (1− a ) ExLSDA + aExHF + b∆ExB 86 + (1− c) EcLSDA + c∆EcLYP
B
11
Acronyms Name Type
SVWN Slater, Vosko, Wilks Nusair LDA
BLYP Becke correlation functional Gradient corrected
with Lee, Yang, Parr
PW91 Perdew and Wang 1991 Gradient corrected
B3P86 Becke exchange, Perdew Hybrid
correlation
B3PW91 exchange
Becke exchange, Perdew and Hybrid
Wang correlation
B3LYP Becke 3 term with Lee, Yang, Hybrid
Parr
12
Comparison between HF and DFT method
HF DFT
Wave function for N electron system Electron density depends only on 3
contains 3N coordinates coordinates
Accurate for very small system Upto 100 atoms
One electron operator One electron functional
Optimizes wave function Optimizes electron density
Ab-initio and semi-empirical
Ab-initio
Employ exact Hamiltonian and make Approximations in Hamiltonian
approximations in wave function operator
Gaussian basis set Numerical basis, fitting functions
Systematically extended to attain Lacks systematic way of extending a
exact energy series to approach exact energy
Transition probability, multistate
Difficult to determine
resonances determined
13
Absolute Error in
Level of theory
Basis: 6-31G(d,p) equilibrium bond
length
MO theoretical
methods
0.22
HF
0.14
MP2
0.13
CISD
0.05
CCSD(T)
LSDA Functionals
SVWN 0.17
F ti l
GGA Functionals
BLYP 0.14
BPW91 0.14
PBE 0 12
0.12
Hybrid Functionals
B1LYP 0.05
B1PW91 0.10
B3LYP 0.04
B3PW91 0.08
14
Comparative performances of molecular mechanics and electronic structure methods
Non
Semi- Local
empirical DFT
DFT
Geometry G G G G G
Transition State G G G G G
Conformation A/G G P A/G G
Thermochemistry A/G G P A/G G
g
G=good p
A=acceptable P=Poor p g
A/G=Acceptable to good
```
To top | 1,834 | 6,910 | {"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} | 2.9375 | 3 | CC-MAIN-2015-35 | longest | en | 0.834138 |
https://elemental-astrology.com/how-is-delivery-date-calculated/ | 1,679,903,685,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296948609.41/warc/CC-MAIN-20230327060940-20230327090940-00291.warc.gz | 267,918,055 | 18,599 | # How is delivery date calculated?
An estimated due date can be calculated by following steps 1 through 3: First, determine the first day of your last menstrual period. Next, count back 3 calendar months from that date. Lastly, add 1 year and 7 days to that date.
## How do you predict when you will have a baby?
You can calculate your due date if you know the first day of your last menstrual period (LMP) before you got pregnant. Your due date is 40 weeks after the day you started your last period. This method is a good way to estimate when your baby is due because many women remember the day they started their period.
## Which planet is responsible for child birth?
We have to see the position of the main planet Jupiter, the main significator for Progeny, along with that of Venus, Sun and Mars in couple’s horoscopes. Sometimes, past life flawed Karmas and Nadi Dosha also attribute to delay in child birth.
## How many babies will I have according to numerology?
To do this, add all the numbers from your date of birth. If you get a sum of two numbers, add them together to get one number. For example, you were born on June 20, 1973. 2 + 0 + 6 + 1 + 9 + 7 + 3 = 28.
## Will I have a second child astrology?
So, who is your 2nd child? He/She is younger sibling of your 1st child. House of Younger Sibling is 3rd house. So, 2nd Child will be seen by 7th house (3rd from 5th house – younger sibling of 1st child), 3rd Child will be seen by 9th house (3rd house from 7th house – younger sibling of 2nd child) and so on.
## What is the best month to have a baby?
The study found that for conceptions between January and May, gestation length declined by about a week before shooting back up to average length in June. In terms of birth weight, summer was the best time to conceive.
## Which Dasha is good for child birth?
Role of lagnesh & 7th house lord Dasha of lagnesh & 7th house lord is well placed and strong in the horoscope then also capable to give the childbirth.
## Which house in astrology is fertility?
Of all the 12 houses of the zodiac in astrology, the fifth house is most commonly associated with fertility, pregnancy, childbirth and children (it’s also linked to fun and sex).
## Which Nakshatra is good for conceive?
Nakshatras — The nakshatrasconsidered good for conception are all fixed nakshatras (Uttara-phalguni, Uttara-shada, Uttara-bhadrapada and Rohini), Mrigshira, Anuradha, Hastha, Swati, Dhanistha and shatabhisha are also considered as goodnakshatras.
## How do you calculate birth with one digit?
Basically, take your date of birth’s numerical value, add all those digits together by category (year, month, day), and keep adding each of those digits together until you finally end up with a single digit.
## How is a child born predicted in Vedic astrology?
Predict your child’s due date with the 5th and 9th house. If you’re wondering when your baby is going to be born, check the 5th and 9th house of both parents. If Jupiter and/or Saturn are in the 5th and/or 9th houses, it means that your child will be born approximately 9 months from when you check your chart.
## How many children will have palmistry?
It is considered that the number of lines indicates the number of children you are likely to have. The deep lines indicate the birth of a male child while the light ones signify the birth of a female.
## What if 5th house is empty?
If your 5th, 7th, and 11th houses are all empty houses, this means that connecting with others for you doesn’t have the same kind of baggage as it does for everyone else. This may mean subconscious, early life baggage, or baggage from past lives/karmic.
## How can I see my kids in Kundli?
If Mercury, Venus or a strong Moon is in a benefic position in the eleventh house of the horoscope and if it sees the fifth house with full vision, then there is good progeny related happiness. If Ketu is situated in the fifth house of the horoscope, then one gets blessed with a child.
## What is your 8th house?
The House of Sex, Death, and Taxes The eighth house is a mysterious sector that rules birth, death, sex, transformation, mysteries, merged energies, and bonding at the deepest level. The eighth house also rules other people’s property and money include real estate, inheritances, and investments.
## What is the luckiest birth month?
A study done in the U.K. showed that May is the luckiest month to be born, and October is the unluckiest. It could have something to do with that optimism, since positive attitudes have been associated with greater resilience.
## What is the rarest month to be born in?
February is the least common birth month, with avereage of 316,891 babies born in February annually. Tuesday is the most common day of the week for births in America.
## What is the most accurate due date calculator?
While Naegele’s rule is still the most widely used formula for a due date calculator, the Mittendorf-Williams rule is proving to be more accurate.
## Why is pregnancy calculated from last period?
If you were having regular periods before pregnancy, your doctor will calculate your due date based off of your last menstrual period. This goes back to the fact that in order to get pregnant, your body ovulated—or released an egg—roughly in the middle of your cycle and it was fertilized by sperm.
## How does ultrasound predict due date?
An ultrasound allows your doctor to measure the crown-rump length (CRL) — the length of the fetus from one end to the other. During the first trimester, this measurement provides the most accurate estimation for the age of the baby. Your doctor may change your due date based on the ultrasound measurement.
## Does rahu affect pregnancy?
In so far as Rahu’s effect on pregnancy and progeny is concerned, it may create trouble to the pregnancy in the 2nd, 3rd, 5th, 7th and 8th months, and therefore such precautions as suggested by the medical consultant must be observed strictly.
## How get pregnant tips as per Vastu?
1. You must put picture of happy babies in your bedroom.
2. Don’t sleep under the beam.
3. Chose master bedroom in southwest direction as this direction will boost romance and fertility in your life.
## Which Tithi is good for birth?
Ashwani Nakshatra is the zodiac belt’s first-ever lunar constellation. It is one of the most cherished and auspicious Nakshatras for childbirth. It signifies strength, power, and dignity. A child born during this nakshatra is filled with grand ideas and blessed with immense creativity.
## What are the signs that you are fertile?
• Positive Ovulation Test Result.
• Fertile Cervical Mucus.
• Increased Sexual Desire.
• Basal Body Temperature Increase.
• Change in Cervical Position.
• Breast Tenderness.
• Saliva Ferning Pattern.
• Ovulation Pain.
## What age will a Taurus get pregnant?
03/13Taurus Therefore, it is much likely that a Taurean will have their first kid at the age of 32, which is when they are secured in their life and can commit to parenting. | 1,653 | 7,008 | {"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-2023-14 | latest | en | 0.964625 |
https://amsp.org.uk/events/details/5463 | 1,597,104,789,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738723.55/warc/CC-MAIN-20200810235513-20200811025513-00117.warc.gz | 199,811,747 | 10,165 | # Year 12 Regular Problem Solving Classes
Peterborough
## Overview
A series of maths problem-solving sessions designed to give students the confidence to apply for university courses that require or take into consideration achievement in an admissions test.
These regular classes offer students the opportunity to develop mathematical problem-solving skills through discussion and collaboration. They are designed to help students to develop strategies and confidence when tackling unfamiliar problems in maths and will help with preparations for taking advanced papers such as the MAT, TMUA and STEP examinations.
At the same time, the problems used in the course are fun and rewarding. Attending the sessions will greatly enrich students’ mathematical experience and help them to develop a better understanding of A level Mathematics.
## Aims
• To develop initial strategies when dealing with maths problems
• To develop confidence when dealing with maths problems
• To provide some initial information about the problem solving involved in university admissions tests
• To provide a platform on which to build secure problem solving techniques
• To develop tenacity when dealing with maths problems
## Who will benefit from attending?
The course is designed for any A level Mathematics students who have an enquiring mind and wish to develop their problem solving ability for their A level studies and beyond.
It is particularly useful for those students who wish to make the first steps in preparing for university admissions tests such as the MAT, TMUA and STEP examinations.
## Content
The course covers a wide range of mathematical disciplines with problems. These can include
• Algebra: the difference between two squares and other identities
• Geometry: angles, triangle and circles
• Number: digits and divisibility
• Algebra: forming and solving equations
• Combinatorics: systematic counting
• Number: prime factorisation, fractions and irrationals
• Algebra: sequences and series
• Number: indices and logarithms
• Algebra: quadratics, cubics and other polynomials
• Geometry: trigonometry
• Combinatorics: further systematic counting and placement
• Geometry: coordinates and vectors
• Calculus: curve sketching and differentiation
• Calculus: integration
• Combinatorics: the binomial expansion
## Materials and Equipment
Students do not need any special equpiment for the course although a smartphone with the GeoGebra or the Desmos apps installed may be useful.
## Other Information
The following problems provide a taste of the sort of problem solving that will be encountered in the classes
Problem 1: How many primes greater than two can be found that are one less than a square number?
Problem 2: How many pairs of integers can you find that satisfy the equation $$x^2–y^2=45$$?
## Study Schedule
Time: 4:15pm – 6:15pm on Weds
Dates: 13/2, (half term), 27/2, 13/3, 27/3, 3/4, (Easter), 24/4, 8/5, 22/5, (half term), 5/6, 19/6
## Key Facts
#5463
Students
Year 12
##### Curriculum focus:
University admissions tests, A level Mathematics, A level Further Mathematics
##### Mathematical focus:
Pure, Problem solving
Student course
20 hours
East of England
Ortongate, ,
Peterborough ,
PE2 5RQ
##### Date:
Wed 13th Feb 2019
##### Course times:
16:15 - 18:30
Printable Version | 729 | 3,329 | {"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} | 3.046875 | 3 | CC-MAIN-2020-34 | latest | en | 0.906939 |
https://sportsmanist.com/how-fast-is-a-bat-in-mph | 1,701,283,129,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100135.11/warc/CC-MAIN-20231129173017-20231129203017-00149.warc.gz | 591,233,867 | 16,924 | # How fast is a bat in mph?
MLB fastballs average 91 mph off of the hand and 83 mph at the plate. For example, the average exit speed in Major League Baseball is 103 mph. Bats can travel at speeds ranging from 70 to 85 miles per hour. Wood bats have a slower exit velocity than non-wood bats. Metal bats tend to produce balls that fly faster than those with wood cores.
The fastest pitch thrown in major league history was 105.6 mph by Ted Gray on May 30, 1950. The slowest pitch recorded hit ball four by a pitcher who did not give up any hits was 87.3 mph by Bud Hollowell on April 19, 1935. That's less than one out of every 20 pitches thrown in major league history!
A batter can typically reach first base if a ball is hit between the infielders' legs or behind them. A batter can usually go to second base if a ball is hit between their legs but not behind them. A ball hit into the hole between second and third base can often result in a triple play. A ball hit into the corner between third and home can result in a home run or an error if the fielder doesn't cover the base completely.
In addition to batting practice, there are several other ways players get ready for a game. In order to get ready for game time, pitchers will work on their mechanics in the bullpen before games.
## What’s the average exit speed of an MLB bat?
MLB fastballs average 91 mph off of the hand and 83 mph at the plate. For example, the average exit speed in Major League Baseball is 103 mph. Bats can travel at speeds ranging from 70 to 85 miles per hour. Wood bats have a slower exit velocity than non-wood bats.
The brain's messages can take roughly 25 milliseconds to pulse through the hitter's body and get his legs moving. The swing lasts 150 milliseconds. A fastball with backspin—up to 1800 rpm—arrives at the bat. A hitter must reverse the rotation of the ball such that it exits the bat with backspin in order to hit the ball out of the park.
When it comes to turning a hit into a home run, every 1 mph increase in swing speed adds around 8 ft to the distance. Terry Bahill of the University of Arizona discovered that the maximum bat weight before swing speed reduces is roughly 41 ounces. However, he believes that a pro player's optimal bat weight is lower, in the 31-to-32-ounce range.
## What is a good bat exit velocity?
For a point of reference, the average major league exit velocity per at bat is about 68 mph. The fastest recorded batted ball in Major League History was hit in 2012 by Ryan Zimmerman of the Washington Nationals. It traveled 95.5 miles per hour (153 km/h).
The maximum distance that a baseball can travel before it hits the ground is only about 150 feet (46 m), but most balls are hit between 90 and 100 miles per hour (145 and 160 kph). So even though the maximum distance that a ball can be hit is quite small, very few balls are hit at or above this speed.
As far as how hard a ball can be hit, there's no real limit except for your arm strength. A ball can be hit as fast as 100 miles per hour (160 kph) if you have enough power behind it. But most balls are hit below this speed because they get out of the strike zone often.
So basically, harder equals better. Or at least it should do.
There are several factors that go into determining how hard a ball is hit. Weight plays a role: the heavier the bat, the more power you can produce.
## Can you hit a 100 mph fastball?
A fastball traveling at 100 mph takes less than 400 milliseconds to reach home plate. The swing itself lasts around 150 milliseconds. Despite their popularity, 100-mph fastballs are still uncommon—rare enough that you won't see them in batting practice on a daily basis.
The fastest pitch thrown by any major league player has been 108 mph, set by Tampa Bay's J.D. Martinez on April 22, 2015. He threw the ball from a four-point stance, using only his arm and not his shoulder. The ball traveled 1 foot 11 inches into the strike zone when it reached home plate!
It is possible to hit a baseball thrown at 100 miles per hour or faster. The key is to recognize the pitch is fast and get ready for it. Hitting such a ball is difficult because there is so little time to react to the pitch.
In addition, there is no way to know how fast the ball will travel until it reaches the plate. So even if you are prepared, you can't predict where it will go. This means you have no choice but to try to hit it wherever it goes.
There have been several pitchers who have thrown 100-mph fastballs in their careers. No one has ever been struck out by one of these pitches. Instead, they tend to frighten hitters away from the plate by being too fast for them to control.
## How does bat speed relate to pitch speed?
During our Science of Baseball discussion, Dr. Nathan also emphasized that while each mph of pitch speed contributes 1 ft. to the distance, each mph of bat speed adds 1.2 mph of exit speed. Bat speed is important because exit speed is important. Each mile of bat speed increases the exit speed by around 1.2 miles. @PoBGuy on Twitter pointed out that this means that a batter's "average" speed is actually about 15 mph, which is faster than most people think.
Here are the speeds of some common pitches:
Fastball: 93-96 mph
Slider: 78-82 mph
Curveball: 72-77 mph
Changeup: 65-70 mph
Spinners: 52-58 mph
All of these numbers include velocity variation from pitch to pitch and location variation depending on how far back the pitcher releases the ball. For example, if he throws the same pitch at the same location every time, then it would go by him more quickly.
Even though all of these pitches vary in speed, it takes about the same amount of time to get from the starting point to home plate with any of them. This is because all of the pitches have so much power that they can't be caught up in the zone too long or they'll hit a batter.
##### Vincent Jarrett
Vincent Jarrett is an avid sportsman, and he loves to play basketball, tennis and golf. He also enjoys reading about sports history and learning about new techniques.
#### Disclaimer
Sportsmanist.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com. | 1,443 | 6,304 | {"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-2023-50 | latest | en | 0.964076 |
https://www.jiskha.com/search?query=Calculus+%28Answer+Check%29&page=27 | 1,537,555,649,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267157351.3/warc/CC-MAIN-20180921170920-20180921191320-00189.warc.gz | 767,019,147 | 16,202 | 89,119 results, page 27
1. ## math algebra 1
There are 4 times as many nickels as dimes in a coin bag. The coins have a total value of 600 cents (\$6.00). Find the number of nickels. Write and solve an equation to do so. (i found the answer through guess and check but i need to know the
2. ## Pre-Calculus - Reiny
Reiny you helped me with this logarithm yesterday: How did you write it out as log2 ( √A / B^3 ) Laws of logarithms combine, write as a single logarithm Need help on this question please, Im stuck, don't know where to go abouts from here: I did it on
3. ## ALGEBRA 2 help please would appreciate
x x _____ - _____ = x^2+9 ________ x+3 x-3 X^2-9 solve for x. and check answer thank you show work please
Solve w= (va)/(r^2+a^2) for a. I applied the quadratic formula a= (v/w +- sqrt (v^2/w^2 - 4*(-wr^2)) /2 and I have the answer as a= (v+/- sqrt[v^2+4w^2r^2]/w
5. ## Health law
please check my answer the right to privacy is in the first admendment True or False I said True
6. ## Math check
Factor each expression: x^2-144/x+4 times x^2-16/x+12 This is what I got: (x+12)(x-12)/x+4 times (x-8)(x+2)/x+12 How is the answer x^2-16x+48
7. ## Simplify (Another Question/problem) 3
Simplify. (27a^(-6) )^(-2/3) I got 1/(9a^4 )as my answer, but can someone again please check this. I will appreciate it. I am just unsure if it is correct or not.
8. ## medical records
please check my answer thanks you very much A medical should be completed within how many days after a pt is discharged A 30 B 35 C 60 D 15 E none of the above I picked D
9. ## dog behavior
please check my answer thanks true of false hackles up is an example of a signal I said true
Simplify 3√125a^1b^3 (By the way,in 3√, 3 is the index) 3√125a^1b^3 3√125 * 3√a^1 * 3√b^3 5 * 3√a^1 * 3√b^3 I'm stuck what to do next.
11. ## Math (factoring)
Can someone check my answer? 5x^3 - 40 =5(x^3-8) =5(x-2)(x^2+2x+4) Also, how do you factor x^6-y^6 as a difference of cubes? As a difference of squares, is it (x^3+y^3)(x^3-y^6)?
12. ## Math Help? Check my answers.
Simplify 6 x 3 divide 3 - 1. Pre-Algebra? Answers: 2 3 5 6 My answer: 5
13. ## Algebra 2 (Math)
Divide 3x^3 + 3x^2 + 2x – 2 by x + 3 using long division. Check my answer please. 3x^2 – 6x + 20 3x^2 + 12x – 16 3x^2 + 12x – 16, R 58 3x^2 – 6x + 20, R -62 (I think that it's this one)
A cylinder has a radius of 4x + 2 and a height of 5x — 4. Which polynomial in standard form best describes the total volume of the cylinder? A.80pix^3+144pix^2+84pix+16pi B.20pix^2+26pix+8pi **** C.80pix^3+144pix^2+84pix-16pi
15. ## Math
The Martin family's truck gets an average o 25 miles per gallon. Predict how many miles they can drive using 7 gallons of gas? Answer: 25 miles per gallon x 7 gallons used=175 miles driven 175/7=25 Can you please check the above answer? Thank you
1) Free energies of formation are a. always positive b. always negative c. never zero d. measured at 298K e. more than one response above is correct I think that free energies can be negative or postive so the answer cannot be e. I chose answer d, they are
17. ## Calculus 2
A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 for g and 3.14 for π. If you enter your answer in scientific notation, round the decimal value to two decimal places. Use equivalent rounding if you do not
18. ## Calculus
According to the US Census, the world population P, in billions, is approximately P=6.342e^(0.011t); where t is in years since January 1, 2004. At what rate was the world's population increasing on January 1, 2005? Give your answer in millions per year. Is
19. ## Please check my calculus
A conical tank has a height that is always 3 times its radius. If water is leaving the tank at the rate of 50 cubic feet per minute, how fast if the water level falling in feet per minute when the water is 3 feet high? Volume of a cone is V=1/3(pi)r^2h A.
20. ## math check
Simplify: sqrt(x^5 y^2)+sqrt(9xy^2) is the answer sqrtx(x^2y+3y)
Determine whether the line through (0, 4) and (2, 0) and the line through (−2, 3) and (−4, 2) are parallel, perpendicular, or neither. neither?
22. ## Math
Study the equation below. 25=2x+3 Which equation has the same solution? Answers: A. 28=2x B. 22=2x C. 50=x+3 D. 25/2=x+3 My answer is B. 22=2x. Please check if I am right. Thank you!
1. How many solutions can be found for the equation 4x + 5 = 10? A. Zero B.One**** C.Two D.Infinitely Many 2.What is the value of z in the equation 3z − 7 = 14? A.3 B.4 C.7**** D. 21
24. ## math check
what is half the difference between 187 and 49? 187-49= 138/2 answer is 69?
25. ## geometry
check my answer please!! find the image of o(-2 -1) after two reflections, first across the line y=-5, and then across the line x=1. (-2,-1) (-1,-6)# (4,-9) (1,-5)
26. ## Calculus (Global Max)
Explain the global optimization process for a continuous function over a closed interval. Be sure to identify all steps involved and clearly explain how the derivative is utilized in this process. Does this have to do with the first derivative rule or
27. ## Math
please help me I am not really sure about this please check answer thanks :) Mary has decided to purchase furniture. She has 2 choices she can pay the full amount of \$4,200.The other choice is to finance the furniture for two years with an installment
28. ## The US constitution
Please check my answer thanks :) The constitutional basis of the right to privacy is in the First admentment true or false I said True
29. ## Media (Ms.Sue or Writeteacher)
Who are the stakeholders in media? once you have helped me with this question, I will post my answer. Please check it thanks
30. ## Algebra 2
can someone show me how to do it step by step please! Use a graph and table to solve each system. check your answer {y+x=5 {3x-5y=-1
5. Acceleration is a change in position and speed. True or false I think False
3. Which of the following is a solution of x² + 14x + 112 = 0? If necessary, round to the nearest hundredth. A.) x = –0.24 B.) x = –4.24 C.) 4.24 *D.) no solution Thank you
3. Which of the following is a solution of x² + 14x + 112 = 0? If necessary, round to the nearest hundredth. A.) x = –0.24 B.) x = –4.24 C.) 4.24 *D.) no solution Thank you
34. ## math(algebra 1)
how do u answer this? please step by step *graph and check to solve the linear system y=-x+3 y=x+1 Thank you very very much!!! :)
35. ## Math
What are the odds against getting three heads in three successive flips of a coin? Odds against A = (1 – 3/6)/ (3/6)= 3/5 = 3::5 Could someone check my answer and correct me if I need it please
1 2/5 divided by 21 Which example is correct 7/5 * 1/21 = 7/105 = 1/15 or is it? 5/7 * 21/1 = 105/7 =15 You asked this question yesterday. The answer is still the same.
37. ## DanH-- I NEED ENGLISH HELP
Almost_________ work would be better than___________. anyone's hers anyone's her's anyones hers anyones' hers' Please check my previous answer.
38. ## Vectors
Two lines with the slopes m1=4/3 and m2=-7/2 intersect at (3,4). Determine the equations of the two lines and check your answer by solving them
39. ## Mathematics
1.What is 10^3 written in standard form 10 100 1,000 10,000 Please check this, my answer will be the third choice
40. ## math
Could someone check my answer to the following question? Find the other end point given the endpoint of (7,7) and midpoint of (0,0). the other endpoint would be (-7,-7)right?
41. ## Anatomy check
I just want to make sure this answer is correct: The stomach is (superior or posterior) to the diaphragm? posterior Thanks
42. ## Health
please check my answer thanks True or False Dry heat is the best method of sterilzation I said True
43. ## Geometry (Please check my work)
Find the image of O (-2,-1) after two reflections, first across the line y=-5, and then across the line x=1. I believe the answer should be (-1,-6) Can someone please confirm?
44. ## Math 8R Qs. Check!!!!!!
Why is 2/5 not an integer? my answer - Because it's a fraction and integers are whole numbers. Fractions are not whole numbers. am i correct???
45. ## Algebra II (check)
Assume that no denominator equals 0. sqrt 16x^2y^4 = sqrt (4x)y^2 = 4xy^2(answer)
46. ## Math Algebra check please
Solve w= (va)/(r^2+a^2) for a. I applied the quadratic formula a= (v/w +- sqrt (v^2/w^2 - 4*(-wr^2)) /2 and I have the answer as a= (v+/- sqrt[v^2+4w^2r^2]/w is this right?
47. ## Calculus
y = f(x) = x^2 - 3 x (a) Find the average rate of change of y with respect to x in the following intervals. from x = 2 to x = 3 Incorrect: Your answer is incorrect. from x = 2 to x = 2.5 Incorrect: Your answer is incorrect. from x = 2 to x = 2.1 Incorrect:
48. ## pre-calculus
In the following exercise, find the smallest interval for theta [from this point on i will denote theta as '*' for ease of typing] starting with * min= 0 so that your graphing utility graphs the given polar equation exactly once without retracing any
49. ## grammar
please check and let me know if this is correct. What the teacher is asking for for the sentence be changed to is to the left. Rewrite the following sentences, focusing on the grammar area specified in the left column. To enter your answer, click next to
50. ## US History
One way that opposition to the Civil War was suppressed was the denial of what right? and What is set up to make political contributions to candidates for elected office? Your answer could be states rights. Check this site for more information.
51. ## Science
I need to check my answers!! Which of these is not in the family a. sound b. light c. infrared radiation (answer) d. radio waves When an electric charge is shaken to and fro in quick succession, the vibrating charge emits a. infrasonic sound b. Ultrasonic
52. ## Science
I need to check my answers!! Which of these is not in the family a. sound b. light c. infrared radiation (answer) d. radio waves When an electric charge is shaken to and fro in quick succession, the vibrating charge emits a. infrasonic sound b. Ultrasonic
53. ## math
can someone check my answers subtract 7/9-(-13/19)=3/2 multiply (4)(-3/2)=-6f find the first and third quaritles q1 and q3 of the following set of numbers 13,4,12,16,8,14,8,3,10,8, my answer 4:12 find the first and third quaritles q1 and q3 of the
54. ## check
#19, Inclusive Language-Quoting from Biased Material - The mayors and their wives were invited on a tour of the state buildings. Answer: The maors and their wives[sic] were invited on a tour of the state buildings. #8. Puctuation-colon - Studing is
Show that the equation x^5+x+1 = 0 has exactly one real root. Name the theorems you use to prove it. I.V.T. *f(x) is continuous *Lim x-> inf x^5+x+1 = inf >0 *Lim x-> -inf x^5+x+1 = -inf <0 Rolles *f(c)=f(d)=0 *f(x) is coninuous *f(x) is
dy/dx= (y^2 -1)/x 1. Give the general equation of the curves that satisfy this equation. 2. Show that the straight lines y=1 and y=-1 are also solutions 3. Do any of the curves you found in 1) intersect y=1? My Ans: 1. The general solution i found out to
57. ## Trig.
I have answers for these problems, but I wanted to check if I had them right because I wasn't sure on some of them....Thanks. Solve the triangle: 1. a=4, b=8, alpha=30 deg. answer- beta=90 deg., gamma=60 deg., c=7 2. a=5, b=7, alpha=30 deg. answer- beta=44
58. ## Math
I posted this earlier, but got no answer. So I am re-posting. Jean deposited a check for \$625, wrote two for \$68.74 and \$29.95 and used her debit card to pay for a purchase of \$57.65. How has her account balance changed? I am a little lost, I understand
59. ## French
I am working on my French homework (direct/indirect) and would like to check my answers and make sure I am on the right track. I am having difficulty with the following: Options: Me/m’, te/t’, nous, vous, le, la, les, lui, leur, y, en A. Je vais au
60. ## calc check: average value
Find the average value of the function "f(x) = x^2 sqrt(1+x^3)" on the interval [0,2]. and this is what i did.. please check for mistakes. thanks :D f(x) = x^2 sqrt(1+x^3), [0,2] f ave = (1/(b-a))*inegral of a to b for: f(x) dx f ave = (1/(2-0))*integral
61. ## Math
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative. Remember to use ln |u| where appropriate.) (x^5+x^3+8x)/x^4
62. ## Math
What is the ratio of the measures of side BC to side RS in simplest form? (1 point) A.2:1 B.6:2 C.1:2 D.none of these @Ms.Sue My answer is A. can you please check
63. ## pre algebra check
Use the percent equation to answer the question. What percent of 130 is 156? I get 202.8??
Three fair coins are tossed. What is the probability that at least one is a head? (Enter the probability as a fraction.) I came up with 7/8 Thank you
65. ## English
Question 12 He wrote a hot check. The word hot is used poorly clearly connotatively denotatively Answer D
66. ## algebra
Check whether the ordered pair is a solution to the equation x =3/4; (1/2, 3/4). Please show me step by step how you came up with this answer because I am really confused.
In act 5 is this true? Bathasar delivers Friar's message to Romeo.
68. ## Anatomy and Physiology
Please check my answer thanks True or False An example of an organic molecule is table salt I said False
The transuranium elements A. are the elements with atomic numbers above 92. *** B. occur in nature. C. are sometimes radioactive. D. all of the above
70. ## dog behavior
please check my answer thank you for your help :) True or False Systematic desensitization can be used to reduce fear I said True
What is the simplified form of the following expression? 7m^2 + 6.5n - 4n + 2.5m^2 - n a. 9.5m^2 + 1.5n (?) b. 4.5m^2 + 1.5n c. 1.5m^2 - 4.2n d. 9.5m^2 - 1.5n Simplify the following expression. 1/3(21m + 27) a. 7m + 27 b. 7m + 9 (?) c. 63m + 9 d. 7m + 81
72. ## To @Bosnian
I posted a follow up question to your answer to my recent question about a sum of a series.Hope you can check it. Thank you!
73. ## Match Check
if carrots are selling at \$.0125 a pound, how many pound we can buy for a dollor. Answer 800 Right ?
74. ## Science 7R - Hw Qs. Check (plzzzz read!!!!)
1. Arteries branching away from the heart become Answer -larger and larger? am I correct?
75. ## dressmaking
need to check my answer, exam 042020 which type of line is considered to be softening line in design
The lack of balance can lead to disease. True or false My answer is FALSE.
77. ## Math check
multiply: sqrt-25 sqrt-100 is the answer 50?
78. ## I need someone to check this
Add and Simplify: 100x/x+10 + x^3/x+10 I have the answer as X^3+100x/X+10 is this correct?
Which of the following has a graph that is wider than the graph of y=3x^2+2? A) y=3x^2+3 B) y=0.5x^2+1 C) y=-4x^2-1 D) y=4x^2+1 Would the answer be B?
Find the slope of these two points (3,5)and (-5,-2) Is the slope 3?
81. ## Algebra
Which equation has the graph parallel to the graph 9x + 3y =-22 y=3x-22**** y=-3x + 8 y=1/3x + 12 y = -1/3x-2 Please check my answer
Find the slope of the following points(8,9) and (10,-9) -9 - 9 / 10 - 8 = -18/2 = -9 is the slope?
83. ## Pythagorean theorem
How do I check my answer when my triangle is an Acute Triangle?
84. ## calc help showed work
If the function f has a continuous derivative on [0,c], the the integral(o to c) of f'(x)dx= a)f(c)-f(0) b)absolute value (f(c)- f(0)) c) f(c) d)f'(x)=c e)f"(c)-f"(0) My work: so the the answer to the integral is f(x) and when find the answer from o t0 c,
85. ## Calculus
Let 5x^2 - 3xy + 58 = 2y^3 Use implicit differentiation to find y' for the above equation. The first thing I did was move 2y^3 over to that everything is equal to 0. With the -3xy I used the product rule and expanded that. After solving I got.... 10x(3 * y
86. ## particular tense was chosen
Why a particular tense was chosen for each of the following statements. Select the best answer. A. Jack has known Mike for about a year. 1. Use the present perfect when the exact time of a past repeated action isn't important 2. Use the past perfect to
87. ## Language Arts
Rewrite each sentence below correcting the double negative. 1. The shoppers looked for bargains at the store, but there weren't none. Answer: The shoppers looked for bargains at the store, but there were none. 2. She couldn't hardly say her own name.
88. ## Calculus
A ball is thrown up on the surface of a moon. Its height above the lunar surface (in feet) after t seconds is given by the formula h=308t−(14/6t^2) Find the time that the ball reaches its maximum height. Answer = Find the maximal height attained by
89. ## American government check my answer
5. Which of the following are examples of discriminatory laws passed by the U.S. government that impacted those depicted in the photo? Select all that apply. (2 points) Chinese Exclusion Act Civil Rights Act of 1965 Immigration Quota Act DREAM Act my
90. ## Math
Can someone please check my work for me? Write an equation of the line satisfying the given conditions. 9) Intersects the line y = 2 + 3x at infinitely many places. 9) A) y = -3x + 2 B) y = 2x + 3 C) y = -1/3x + 2 D) y = 2 + 3x Is the answer A Use the
A species of clam shows incomplete dominance in the expression of its shell color. RR is the genotype for red shell, Rr is genotype for an orange shell, and rr is the genotype for the yellow shell. Predict the outcome of a cross between an orange shelled
92. ## Calculus
Please look at my work below: Solve the initial-value problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/- Sqrt(4^2-4(1)(6)))/2(1) r=(16 +/- Sqrt(-8)) r=8 +/- Sqrt(2)*i, alpha=8, Beta=Sqrt(2) y(0)=2, e^(8*0)*(c1*cos(0)+c2*sin(0))=c2=2
93. ## Child Development
When preparing an environment for school- aged children the caregiver should ensure that the A. outdoor area allows them to continually challenge their physical ability B. Children are continually intermixed with the younger children C. Environment
94. ## Chemistry
Hi! Thanks for checking my question out! ____ 2. Which of the following takes place during a redox reaction? (1 point) a) Electrons are gained only. b) Electrons are lost only. c) Electrons are both gained and lost. d) Electrons are neither gained nor
95. ## ~MATH~
***Check Answers Plz*** 1)suppose the total momentum of two masses before a collision is 100 kg m/s.what is the total momentum of the two masses after they collide? a~0 kg m/s b~50 kg m/s c~100 kg m/s****(My answer) d~200 kg m/s 2)What is the momentum of a
Can someone check this for me? Suppose that the number of cars, C, on 1st Avenue in a city over a period of time t, in months, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of cars driven on 1st
97. ## Algebra
I'm not quite sure about these problems. I know how to do them, but it seems that I get the wrong answer. Maybe I'm supposed to get 'no solution' but I'm not sure. Could someone please help me with them? 5|6-5x|=15x-35 2|3x-7|=10x-8 1/4|4x+7|=8x+16 Ok for
98. ## Calculus
I'm having trouble trying to figure this problem out, I know the variables of the problem but I don't seem to get the right answer here is the formula that i'm using: A = P (1 + r/n)^n * t. Here is the problem: If Joe deposits \$12,000 into an account that
99. ## math
A woman buys a \$ 78 necklace at a jewelry store. She gives the jeweler a check for \$ 100. Because he does not have the \$ 22 change, he goes to another merchant next door. There he exchanges the woman's check for \$ 100 in cash. He returns and Gives the
100. ## dwrls,math
PLEASE LOOK IN THE BOTTOM OF THIS MESSAGE...... solve for x: 3x - 2y = 6 i need help in solving this: the possible answers has to be one of these: A)2y +6 divided by 3 b)3x -6 divided by 2 C) 2 + 2y D) 2/3y + 6 but how i keep trying and i don't get non of | 6,026 | 19,874 | {"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} | 3.28125 | 3 | CC-MAIN-2018-39 | latest | en | 0.896041 |
http://www3.cs.stonybrook.edu/~algorith/files/satisfiability.shtml | 1,534,311,202,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221209884.38/warc/CC-MAIN-20180815043905-20180815063905-00314.warc.gz | 614,876,179 | 5,359 | # The Stony Brook Algorithm Repository
## INPUT OUTPUT
Input Description: A set of clauses in conjunctive normal form.
Problem: Is there a truth assignment to the boolean variables such that every clause is satisfied?
Excerpt from The Algorithm Design Manual: Satisfiability arises whenever we seek a configuration or object that must be consistent with (\ie satisfy) a given set of constraints. For example, consider the problem of drawing name labels for cities on a map. For the labels to be legible, we do not want the labels to overlap, but in a densely populated region many labels need to be drawn in a small space. How can we avoid collisions?
For each of the n cities, suppose we identify two possible places to position its label, say right above or right below each city. We can represent this choice by a Boolean variable vi, which will be true if city ci's label is above ci, otherwise vi = false. Certain pairs of labels may be forbidden, such as when ci's above label would obscure cj's below label. This pairing can be forbidden by the two-element clause $(\bar{v_i} \OR v_j )$, where $\bar{v}$ means not $v$''. Finding a satisfying truth assignment for the resulting set of clauses yields a mutually legible map labeling if one exists.
Satisfiability is the original NP-complete problem. Despite its applications to constraint satisfaction, logic, and automatic theorem proving, it is perhaps most important theoretically as the root problem from which all other NP-completeness proofs originate.
## Recommended Books
Satisfiability Testing by H. Kautz and B. Selman and R. Brachman and T. Dietterich Algorithm Design by Jon Kleinberg and Éva Tardos Cliques, Coloring, and Satisfiability: Second Dimacs Implementation Challenge by David S. Johnson and Michael A. Trick, Editors Introduction to Algorithms by T. Cormen and C. Leiserson and R. Rivest and C. Stein Computers and Intractability: A Guide to the Theory of NP-Completeness by M. R. Garey and D. S. Johnson
• SAT Live! up-to-date source for papers, programs, and test sets for satisfiability and related logic optimization problems
• Reactive Search, a History-Sensitive Heuristic for Max-Sat by R. Battiti and M. Protasi
• 9th International Conference on Theory and Applications of Satisfiability Testing
• Journal on Satisfiability, Boolean Modeling and Computation
## Related Problems
Finite State Machine Minimization Traveling Salesman Problem Constrained and Unconstrained Optimization | 542 | 2,486 | {"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} | 2.5625 | 3 | CC-MAIN-2018-34 | longest | en | 0.870511 |
https://www.mdpi.com/2073-8994/11/12/1496 | 1,722,747,888,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640389685.8/warc/CC-MAIN-20240804041019-20240804071019-00764.warc.gz | 714,492,642 | 62,961 | Next Article in Journal
On the Fekete–Szegö Type Functionals for Close-to-Convex Functions
Next Article in Special Issue
Properties of Partially Degenerate Complex Appell Polynomials
Previous Article in Journal
The Influence of AlGaN/GaN Heteroepitaxial Structure Fractal Geometry on Size Effects in Microwave Characteristics of AlGaN/GaN HEMTs
Previous Article in Special Issue
Identities Involving the Fourth-Order Linear Recurrence Sequence
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article
# Some New Identities of Second Order Linear Recurrence Sequences
by
Yanyan Liu
1 and
Xingxing Lv
2,*
1
School of Education, Xizang Minzu University, Xianyang 712082, China
2
School of Mathematics, Northwest University, Xi’an 710127, China
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(12), 1496; https://doi.org/10.3390/sym11121496
Submission received: 21 November 2019 / Revised: 4 December 2019 / Accepted: 5 December 2019 / Published: 10 December 2019
## Abstract
:
The main purpose of this paper is using the combinatorial method, the properties of the power series and characteristic roots to study the computational problem of the symmetric sums of a certain second-order linear recurrence sequences, and obtain some new and interesting identities. These results not only improve on some of the existing results, but are also simpler and more beautiful. Of course, these identities profoundly reveal the regularity of the second-order linear recursive sequence, which can greatly facilitate the calculation of the symmetric sums of the sequences in practice.
MSC:
11B83
## 1. Introduction
The defined of second-order linear recurrence sequence ${ S n }$ is
where n is integers with $n ≥ 0$.
For convenience, we also extend the recursive property of $S n$ to all negative integers.
We taking $C 1 = x$, $C 2 = 1$, $S n = F n + 1 ( x )$ with $F 0 ( x ) = 0$, $F 1 ( x ) = 1$ in (1), then ${ S n }$ becomes the famous Fibonacci polynomial sequence ${ F n + 1 ( x ) }$. That is,
Especially when $x = 1$, $F n ( 1 ) = F n$ becomes known as the Fibonacci sequence.
Let $α = x + x 2 + 4 2$ and $β = x − x 2 + 4 2$ denote the two roots of the characteristic equation $λ 2 − x λ − 1 = 0$. Then we have
$F n ( x ) = α n − β n α − β , L n ( x ) = α n + β n , n = 0 , 1 , 2 , ⋯ ,$
where $L n ( x )$ denotes the Lucas polynomials, and $L n ( 1 )$ denotes the Lucas sequence.
If we take $C 1 = 2 x$, $C 2 = − 1$ in (1), then $S n = U n ( x )$ is Chebyshov polynomials of the second kind with $U 0 ( x ) = 1$ and $U 1 ( x ) = 2 x$. Chebyshov polynomials $T n ( x )$ of the first kind is defined by $T n + 2 ( x ) = 2 x T n + 1 ( x ) − T n ( x )$ for all $n ≥ 0$ with $T 0 ( x ) = 1$ and $T 1 ( x ) = x$. Let $δ = x + x 2 − 1$, $γ = x − x 2 − 1$ are two characteristic roots of the polynomial $λ 2 − 2 x λ + 1 = 0$, then (see [1])
$T n ( x ) = 1 2 δ n + γ n , U n ( x ) = δ n + 1 − γ n + 1 δ − γ , n = 0 , 1 , 2 , ⋯ .$
Many scholars have studied $S n$, and obtained a series of valuable research results. For example, Yi Yuan and Zhang Wenpeng [2] proved the following conclusion: For any positive integer n and k, one has the identity
$∑ a 1 + a 2 + ⋯ + a k = n F a 1 ( x ) · F a 2 ( x ) · F a 3 ( x ) ⋯ F a k ( x ) = ∑ m = 0 n 2 n + k − 1 − m m n + k − 1 − 2 m k − 1 · x n − 2 m ,$
where $∑ a 1 + a 2 + ⋯ + a k = n$ denotes the summation is taken over all k-dimension nonnegative integer coordinates $( a 1 , a 2 , ⋯ , a k )$ such that $a 1 + a 2 + ⋯ + a k = n$.
Ma Yuankui and Zhang Wenpeng [3] also studied this problem, and proved the following result:
$∑ a 1 + a 2 + ⋯ + a h + 1 = n F a 1 ( x ) F a 2 ( x ) ⋯ F a h + 1 ( x ) = 1 h ! · ∑ j = 1 h ( − 1 ) h − j · S ( h , j ) x 2 h − j × ∑ i = 0 n ( n − i + j ) ! ( n − i ) ! · 2 h + i − j − 1 i · ( − 1 ) i · 2 i · F n − i + j ( x ) x i ,$
where $S ( h , i )$ is defined by $S ( h , 0 ) = 0$, $S ( h , h ) = 1$, and
$S ( h + 1 , i + 1 ) = 2 · ( 2 h − 1 − i ) · S ( h , i + 1 ) + S ( h , i )$
for all positive integers $1 ≤ i ≤ h − 1$.
On the other hand, Zhang Yixue and Chen Zhuoyu [4] studied the properties of Chebyshov polynomials, and proved the following identity:
$∑ a 1 + a 2 + ⋯ + a h + 1 = n U a 1 ( x ) U a 2 ( x ) ⋯ U a h + 1 ( x ) = 1 2 h · h ! · ∑ j = 1 h C ( h , j ) x 2 h − j ∑ i = 0 n ( n − i + j ) ! ( n − i ) ! · 2 h + i − j − 1 i · U n − i + j ( x ) x i ,$
where $C ( h , i )$ is a second order non-linear recurrence sequence defined by $C ( h , 0 ) = 0$, $C ( h , h ) = 1$, $C ( h + 1 , 1 ) = 1 · 3 · 5 ⋯ ( 2 h − 1 ) = ( 2 h − 1 ) ! !$ and $C ( h + 1 , i + 1 ) = ( 2 h − 1 − i ) · C ( h , i + 1 ) + C ( h , i )$ for all $1 ≤ i ≤ h − 1$.
Many other papers related to Fibonacci numbers, Fibonacci polynomials, Chebyshov polynomials and second-order linear recurrence sequences can also be found in references [5,6,7,8,9,10,11,12,13,14,15,16,17,18], here we will no longer list them one by one.
After careful analysis of the research content in [1,2,3,4], we think it can be summarized as a sentence: That is, to study the symmetry sum problem of the generalized second-order linear recursive sequence. Of course, they are meaningful to study these problems. It not only reveals the profound properties of the generalized second-order linear recursive polynomials and sequences, but also greatly simplifies the calculation of the symmetry sums of these polynomials and sequences in practice.
Inspired by [1,2,3,4], in this paper, we will use a new method to study the computational problem of the symmetry sums of a certain second-order linear recurrence sequences, and give a simple and beautiful generalized conclusion. That is, we will use the elementary methods and the symmetry properties of the characteristic roots to prove the following results:
Theorem 1.
Let $S n = C 1 · S n − 1 + C 2 · S n − 2$ denotes any second-order linear recurrence sequence with $S 0 = 1$ and $S 1 = C 1$. Then we have the identity
$∑ a 1 + a 2 + ⋯ + a k = n S a 1 · S a 2 · S a 3 ⋯ S a k = 1 2 ∑ i = 0 n i + k − 1 k − 1 n − i + k − 1 k − 1 · ( − C 2 ) i · S n − 2 i + C 2 · S n − 2 − 2 i .$
It is clear that if we taking $C 1 = x$ and $C 2 = 1$, then from Theorem 1 we may immediately deduce the following:
Corollary 1.
For any positive integers n and k, we have the identity
$∑ a 1 + a 2 + ⋯ + a k = n F a 1 + 1 ( x ) · F a 2 + 1 ( x ) · F a 3 + 1 ( x ) ⋯ F a k + 1 ( x ) = 1 2 ∑ i = 0 n i + k − 1 k − 1 n − i + k − 1 k − 1 · ( − 1 ) i · F n + 1 − 2 i ( x ) + F n − 1 − 2 i ( x ) .$
Corollary 2.
For any positive integer m, n and k, we have the identity
$∑ a 1 + a 2 + ⋯ + a k = n U a 1 T m ( x ) · U a 2 T m ( x ) · U a 3 T m ( x ) ⋯ U a k T m ( x ) = ∑ i = 0 n i + k − 1 k − 1 n − i + k − 1 k − 1 · T m ( n − 2 i ) ( x )$
and
$∑ a 1 + a 2 + ⋯ + a k = n U a 1 x · U a 2 x · U a 3 x ⋯ U a k x = ∑ i = 0 n i + k − 1 k − 1 n − i + k − 1 k − 1 · x U n − 1 − 2 i ( x ) − U n − 2 − 2 i ( x ) .$
It is clear that our Corollary 1 and Corollary 2 are much easier than the results in [1,2,3,4]. If $S n + 2 = C 1 · S n + 1 + C 2 · S n$ with $S 0 = 1$ and $S 1 = C 1$ and $H n + 2 = D 1 · H n + 1 + D 2 · H n$ with $H 0 = 1$ and $H 1 = D 1$ are two different second-order linear recurrence sequences, such that the polynomials $x 2 − C 1 x − C 2$ and $x 2 − D 1 x − D 2$ co-prime. That is, $x 2 − C 1 x − C 2 , x 2 − D 1 x − D 2 = 1$. Then we define sequence ${ M n }$ as follows:
$M n = ∑ i = 0 n S i · H n − i n = 0 , 1 , 2 , ⋯ .$
For the sequence ${ M n }$ defined in (2), we have the following conclusion:
Theorem 2.
The sequence ${ M n }$ is a fourth-order linear recurrence sequence, and it satisfy the fourth-order linear recurrence formula
$M n + 4 = C 1 + D 1 M n + 3 + C 2 + D 2 + C 1 D 1 M n + 2 − C 1 D 2 + C 2 D 1 M n + 1 − C 2 D 2 M n , n ≥ 0 ,$
where $M 0 = 1$, $M 1 = C 1 + D 1$, $M 2 = C 1 2 + D 1 2 + C 2 + D 2 + C 1 D 1$ and
$M 3 = C 1 3 + D 1 3 + 2 C 1 C 2 + 2 D 1 D 2 + D 1 C 1 2 + C 2 + C 1 D 1 2 + D 2 .$
Taking $C 1 = x$, $C 2 = 1$, $D 1 = 2 x$ and $D 2 = − 1$, from our Theorem 2 we can deduce the following result:
Corollary 3.
For any integer $n ≥ 0$, we define the polynomials sequence
$M n ( x ) = ∑ i = 0 n F i + 1 ( x ) · U n − i ( x ) .$
Then $M n ( x )$ is a fourth-order linear recurrence polynomials, and it satisfy the recurrence formula
$M n + 4 ( x ) = 3 x M n + 3 ( x ) + 2 x 2 M n + 2 ( x ) − x M n + 1 ( x ) + M n ( x )$
for all integers $n ≥ 0$, where $M 0 ( x ) = 1$, $M 1 ( x ) = 3 x$, $M 2 ( x ) = 7 x 2$ and $M 3 ( x ) = 15 x 3 − x$, $F n ( x )$ and $U n ( x )$ denote the Fibonacci polynomials and Chebyshov polynomials of the second kind respectively.
## 2. Proof of the Theorem
In this section, we will prove our main results directly. First we prove Theorem 1.
Proof of Theorem 1.
It is clear that the characteristic equation of the sequence ${ S n }$ is $λ 2 − C 1 λ − C 2 = 0$. Let $α$ and $β$ are the two characteristic roots of the equation $λ 2 − C 1 λ − C 2 = 0$. Then we have
$S n = A α n + B β n with A + B = 1 and A α + B β = C 1 .$
That is,
$S n = A α n + B β n = α α − β · α n − β α − β · β n , n ≥ 0 .$
The generating function of the sequence ${ S n }$ is
$1 1 − C 1 x − C 2 x 2 = 1 ( 1 − α x ) ( 1 − β x ) = ∑ n = 0 ∞ S n · x n ,$
where $α · β = − C 2$ and $α + β = C 1$.
For any positive integer k, we have the identity
$1 1 − C 1 x − C 2 x 2 k = 1 ( 1 − α x ) k · ( 1 − β x ) k = ∑ n = 0 ∞ ∑ a 1 + a 2 + ⋯ + a k = n S a 1 · S a 2 · S a 3 ⋯ S a k · x n .$
On the other hand, from the properties of the power series we have
$1 ( 1 − x ) k = ∑ n = 0 ∞ n + k − 1 k − 1 · x n , | x | < 1 .$
Thus, from (5) and the properties of the power series we have
$1 ( 1 − α x ) k ( 1 − β x ) k = ∑ n = 0 ∞ n + k − 1 k − 1 α n x n ∑ n = 0 ∞ n + k − 1 k − 1 β n x n = ∑ n = 0 ∞ ∑ i = 0 n i + k − 1 k − 1 n − i + k − 1 k − 1 · α i · β n − i · x n .$
Combining (4), (6) and note that $α · β = − C 2$ and the symmetry of $α$ and $β$ we can deduce the identity
$∑ a 1 + a 2 + ⋯ + a k = n S a 1 · S a 2 · S a 3 ⋯ S a k = ∑ i = 0 n i + k − 1 k − 1 n − i + k − 1 k − 1 · α i · β n − i = ∑ i = 0 n i + k − 1 k − 1 n − i + k − 1 k − 1 · ( − C 2 ) i · β n − 2 i = ∑ i = 0 n i + k − 1 k − 1 n − i + k − 1 k − 1 · ( − C 2 ) i · α n − 2 i = ∑ i = 0 n i + k − 1 k − 1 n − i + k − 1 k − 1 · ( − C 2 ) i · 1 2 α n − 2 i + β n − 2 i .$
From the definitions A and B we have
$A · ( α − β ) = α and B · ( β − α ) = β .$
So for any integer r, from the definition of $S n$ we have
$α r + β r = α · α r − 1 + β · β r − 1 = A · ( α − β ) · α r − 1 + B · ( β − α ) · β r − 1 = A · α r + B · β r − α · β A · α r − 2 + B · β r − 2 = S r + C 2 · S r − 2 .$
Now combining (7) and (8) we may immediately deduce the identity
$∑ a 1 + a 2 + ⋯ + a k = n S a 1 · S a 2 · S a 3 ⋯ S a k = ∑ i = 0 n i + k − 1 k − 1 n − i + k − 1 k − 1 · α i · β n − i = 1 2 ∑ i = 0 n i + k − 1 k − 1 n − i + k − 1 k − 1 · ( − C 2 ) i · S 2 − 2 i + C 2 · S n − 2 − 2 i .$
This proves Theorem 1. □
Proof of Theorem 2.
Note that $x 2 − C 1 x − C 2 , x 2 − D 1 x − D 2 = 1$, so from the definitions of $α$, $β$, $δ$ and $γ$ we have
$1 − C 1 x − C 2 x 2 · 1 − D 1 x − D 2 x 2 = 1 − C 1 + D 1 x − C 2 + D 2 − C 1 D 1 x 2 + C 1 D 2 + C 2 D 1 x 3 + C 2 D 2 x 4 = ( 1 − α x ) ( 1 − β x ) ( 1 − δ x ) ( 1 − γ x ) ,$
where $α$, $β$, $δ$ and $γ$ are different each others.
It is clear that from the definitions sequences $S n$ and $H n$ we have
$1 1 − C 1 x − C 2 x 2 · 1 − D 1 x − D 2 x 2 = ∑ n = 0 ∞ ∑ i = 0 n S i · H n − i · x n .$
On the other hand, from the definition and properties of the fourth-order linear recurrence sequence we also have
$1 1 − C 1 x − C 2 x 2 · 1 − D 1 x − D 2 x 2 = 1 ( 1 − α x ) ( 1 − β x ) ( 1 − δ x ) ( 1 − γ x ) = ∑ n = 0 ∞ M n · x n ,$
where $M 0 = 1$, $M 1 = C 1 + D 1$, $M 2 = C 1 2 + D 1 2 C 2 + D 2 + C 1 D 1$,
$M 3 = C 1 3 + D 1 3 + 2 C 1 C 2 + 2 D 1 D 2 + D 1 D 1 2 + D 2 + C 1 D 1 2 + D 2$
and
$M n + 4 = C 1 + D 1 M n + 3 + C 2 + D 2 + C 1 D 1 M n + 2 − C 1 D 2 + C 2 D 1 M n + 1 − C 2 D 2 M n , n ≥ 0 .$
From (11) and (12) we know that the sequence
$M n = ∑ i = 0 n S i · H n − i$
is a fourth-order recurrence sequence, and it satisfy the recurrence Formula (12).
This completes the proof of Theorem 2. □
## Author Contributions
Writing—original draft: Y.L.; Writing—review and editing: X.L.
## Funding
This work is supported by the Xizang N. S. F. (XZ2017ZRG-65) and the N. S. F. (11771351) and (11826205) of China.
## Acknowledgments
The authors would like to thank the referees for their very helpful and detailed comments, which have significantly improved the presentation of this paper.
## Conflicts of Interest
The authors declare no conflict of interest.
## References
1. Zhang, W.P. Some identities involving the Fibonacci numbers and Lucas numbers. Fibonacci Q. 2004, 42, 149–154. [Google Scholar]
2. Yi, Y.; Zhang, W.P. Some identities involving the Fibonacci polynomials. Fibonacci Q. 2002, 40, 314–318. [Google Scholar]
3. Ma, Y.K.; Zhang, W.P. Some identities involving Fibonacci polynomials and Fibonacci numbers. Mathematics 2018, 6, 334. [Google Scholar] [CrossRef] [Green Version]
4. Zhang, Y.X.; Chen, Z.Y. A new identity involving the Chebyshev polynomials. Mathematics 2018, 6, 244. [Google Scholar] [CrossRef] [Green Version]
5. Ma, R.; Zhang, W.P. Several identities involving the Fibonacci numbers and Lucas numbers. Fibonacci Q. 2007, 45, 164–170. [Google Scholar]
6. Wang, S.Y. Some new identities of Chebyshev polynomials and their applications. Adv. Differ. Equ. 2015, 2015, 355. [Google Scholar]
7. Chen, L.; Zhang, W.P. Chebyshev polynomials and their some interesting applications. Adv. Differ. Equ. 2017, 2017, 303. [Google Scholar]
8. Li, X.X. Some identities involving Chebyshev polynomials. Math. Probl. Eng. 2015, 2015, 950695. [Google Scholar] [CrossRef]
9. Ma, Y.K.; Lv, X.X. Several identities involving the reciprocal sums of Chebyshev polynomials. Math. Probl. Eng. 2017, 2017, 4194579. [Google Scholar] [CrossRef] [Green Version]
10. Wang, T.T.; Zhang, H. Some identities involving the derivative of the first kind Chebyshev polynomials. Math. Probl. Eng. 2015, 2015, 146313. [Google Scholar] [CrossRef]
11. Zhang, W.P.; Wang, T.T. Two identities involving the integral of the first kind Chebyshev polynomials. Bull. Math. Soc. Sci. Math. Roum. 2017, 108, 91–98. [Google Scholar]
12. Chen, Z.Y.; Qi, L. Some convolution formulae related to the second-order linear recurrence sequence. Symmetry 2019, 11, 788. [Google Scholar] [CrossRef] [Green Version]
13. Kim, T.; Dolgy, D.V.; Kim, D.S. Representing sums of finite products of Chebyshev polynomials of the second kind and Fibonacci polynomials in terms of Chebyshev polynomials. Adv. Stud. Contemp. Math. 2018, 28, 321–336. [Google Scholar]
14. Kaygisiz, K.; Sahin, A. Determinantal and permanental representations of Fibonacci type numbers and polynomials. Rocky Mt. J. Math. 2016, 46, 227–242. [Google Scholar] [CrossRef]
15. Wu, Z.G.; Zhang, W.P. Several identities involving the Fibonacci polynomials and Lucas polynimials. J. Inequal. Appl. 2013, 2013, 205. [Google Scholar] [CrossRef] [Green Version]
16. Meng, Y.Y. A new identity involving balancing polynomials and balancing numbers. Symmetry 2019, 11, 1141. [Google Scholar] [CrossRef] [Green Version]
17. Kim, T.; Dolgy, D.; Kim, D.; Seo, J. Convolved Fibonacci numbers and their applications. ARS Comb. 2017, 135, 119–131. [Google Scholar]
18. Zhou, S.J.; Chen, L. Tribonacci numbers and some related interesting identities. Symmetry 2019, 11, 1195. [Google Scholar] [CrossRef] [Green Version]
## Share and Cite
MDPI and ACS Style
Liu, Y.; Lv, X. Some New Identities of Second Order Linear Recurrence Sequences. Symmetry 2019, 11, 1496. https://doi.org/10.3390/sym11121496
AMA Style
Liu Y, Lv X. Some New Identities of Second Order Linear Recurrence Sequences. Symmetry. 2019; 11(12):1496. https://doi.org/10.3390/sym11121496
Chicago/Turabian Style
Liu, Yanyan, and Xingxing Lv. 2019. "Some New Identities of Second Order Linear Recurrence Sequences" Symmetry 11, no. 12: 1496. https://doi.org/10.3390/sym11121496
Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here. | 6,243 | 16,156 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 134, "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-2024-33 | latest | en | 0.879369 |
https://www.sanfoundry.com/physics-questions-answers-gravitational-constant/ | 1,722,725,194,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640380725.7/warc/CC-MAIN-20240803214957-20240804004957-00541.warc.gz | 764,193,885 | 21,992 | # Class 11 Physics MCQ – The Gravitational Constant
This set of Class 11 Physics Chapter 8 Multiple Choice Questions & Answers (MCQs) focuses on “The Gravitational Constant”.
1. What is the value of universal gravitational constant?
a) 6.022 x 1023
b) 6.67 x 10-11 N m2/kg2
c) 1.602 x 10-19 C
d) 9.81 m/s2
Explanation: 6.022 x 1023 is the Avogadro number.
6.67 x 10-11 N m2/kg2 is the value of universal gravitational constant.
1.602 x 10-19 C is the charge of a proton.
9.81 m/s2 is the acceleration due to gravity on the surface of the earth.
2. The gravitational constant is an empirical constant.
a) True
b) False
Explanation: The gravitational constant is the value of the slope of the graph “gravitational force versus (product of masses) / (square of the distance between them). So, it is not a derived constant, but an empirical one.
3. The value of universal gravitational constant changes is which of the following medium?
a) Air
b) Water
c) Plasma
d) The gravitational constant is independent of the medium
Explanation: Since the gravitational constant is an empirical constant, it does not vary with the medium. Hence, the value of the gravitational constant is the same in any part of the known universe.
4. What are the dimensions of universal gravitational constant?
a) [M2L3T2]
b) [M-1 L3 T-2]
c) [M-1 L3 T2]
d) [M1 L3 T-2]
Explanation: N m2/kg2 are the units of universal gravitational constant.
N m2/kg2 = m3/ (kgs2)
= m3kg-1s-2
Hence, the dimensions are [M-1 L3 T-2].
5. The value of gravitational constant was first determined by _____
a) Albert Einstein
b) Isaac Newton
c) Henry Cavendish
d) Stephen Hawking
Explanation: The value of gravitational constant was first experimentally determined by Henry Cavendish in the year 1798. It is also known as the Cavendish Gravitational Constant.
6. What apparatus did Henry Cavendish use in his experiment to determine the gravitational constant?
a) 1 bar, 1 small sphere and 1 large sphere
b) 1 bar, 2 small spheres and 2 large spheres
c) 2 bar, 1 small sphere and 2 large spheres
d) 2 bar, 2 small spheres and 1 large sphere
Explanation: Henry Cavendish used 1 bar, 2 small spheres and 2 large spheres in his experiment to determine the gravitational constant. By measuring the torque and angle of deflection produced due to the proximity of large spheres to the small ones, Henry Cavendish was able to determine the universal gravitational constant.
7. What material were the spheres made up of in Henry Cavendish’s experiment?
b) Steel
c) Iron
d) Wood
Explanation: Henry Cavendish used lead spheres in his experiment because lead was easily available at the time. Iron was also abundantly available. However, Henry Cavendish chose lead because it is denser than iron and the mass of lead is about 44% higher than that of iron for the same size of the sphere – this would lead to a larger gravitational force which is easier to measure.
Sanfoundry Global Education & Learning Series – Physics – Class 11.
To practice all chapters and topics of class 11 Physics, here is complete set of 1000+ Multiple Choice Questions and Answers. | 804 | 3,113 | {"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} | 3.828125 | 4 | CC-MAIN-2024-33 | latest | en | 0.857658 |
https://www.hindawi.com/journals/aaa/2012/632628/ | 1,713,100,596,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816879.72/warc/CC-MAIN-20240414130604-20240414160604-00666.warc.gz | 753,376,188 | 131,350 | #### Abstract
The purpose of this paper is to present the fixed points and endpoints of set-valued contractions concerning with the stronger Meir-Keeler cone-type mappings in cone metric spcaes. Our results generalize the recent results of Kadelburg and Radenović, 2011; Wardowski, 2009.
#### 1. Introduction and Preliminaries
Throughout this paper, by , we denote the sets of all nonnegative real numbers and all real numbers, respectively, while is the set of all natural numbers. Let be a metric space, a subset of , and a map. We say is contractive if there exists such that, for all , The well-known Banach fixed-point theorem asserts that if , is contractive and is complete, then has a unique fixed-point in . It is well known that the Banach contraction principle [1] is a very useful and classical tool in nonlinear analysis. Also, this principle has many generalizations. For instance, Kannan [2] and Chatterjea [3] introduced two conditions that can replace (1.1) in Banach's theorem as follows:
Kannan [2]: There exists such that, for all ,
Chatterjea [3]: There exists such that for all ,
After these three conditions, many papers have been written generalizing some of the conditions (1.1), (1.2), and (1.3). In 1969, Boyd and Wong [4] showed the following fixed-point theorem.
Theorem 1.1 (see [4]). Let be a complete metric space and a map. Suppose there exists a function satisfying , for all and is right upper semicontinuous such that Then has a unique fixed-point in .
Later, Meir-Keeler [5], using a result of Chu and Diaz [6], extended Boyd-Wong's result to mappings satisfying the following more general condition: and Meir-Keeler proved the following very interesting fixed-point theorem which is a generalization of the Banach contraction principle.
Theorem 1.2 (Meir-Keeler [5]). Let be a complete metric space and let be a Meir-Keeler contraction; that is, for every , there exists such that implies for all . Then has a unique fixed-point.
Subsequently, some authors worked on this notion of Meir-Keeler contraction (e.g., [710]). In this paper, we introduce a new notion of the stronger Meir-Keeler-type mapping , , as follows.
Definition 1.3. A mapping , is called a stronger Meir-Keeler-type mapping in a metric space , if for each , there exists such that for with , there exists such that .
Example 1.4. Let be a metric space, and define , by Then is a stronger Meir-Keeler-type mapping.
The existence of fixed-points for various multi valued contractive mappings had been studied by many authors under different conditions. In 1969, Nadler [11] extended the famous Banach contraction principle from single-valued mapping to multi valued mapping and proved the following fixed-point theorem for multi valued contraction. Let denote the collection of all nonempty subsets of , the collection of all nonempty bounded subsets of , the collection of all nonempty closed subsets of , the collection of all nonempty closed and bounded subsets of , and the collection of all nonempty sequentially compact subsets of .
Theorem 1.5 (see [11]). Let be a complete metric space, and, be a mapping from into . Assume that there exists such that Then has a fixed-point in .
In 1989, Mizoguchi-Takahashi [12] proved the following fixed-point theorem.
Theorem 1.6 (see [12]). Let be a complete metric space and a map from into . Assume that for all , where satisfies for all . Then has a fixed-point in .
Remark 1.7. It is clear that if the function , satisfies then is also a stronger Meir-Keeler-type function.
In 2003, Rus [13] introduced the notion of endpoints (strict fixed-points) and proved some results on strict fixed-point theory on multi valued operator. An element is said to be a fixed-point of , if . If , then is called an endpoint of . We will denote the sets of all fixed-points and endpoints of by and , respectively. The following theorems were the main results of Rus [13].
Theorem 1.8 (see [13]). Let be a complete metric space and a multi valued operator. Suppose that (i) for all (ii)there exist a comparison function (see [14]) and a Picard sequence , such that where .
Then as and is a unique strict fixed-point of .
Recently, Wardowski [15] proved the following theorems concerning fixed-points and endpoints of set-valued contractions in complete cone metric spaces.
Definition 1.9. A function is called lower semicontinuous, if, for any sequence and ,
If is a cone metric space and , then, for , we denote
Theorem 1.10 (see [15]). Let be a complete cone metric space, let be a normal cone with normal constant , and let . Assume that a function defined by , is lower semicontinuous. If there exist , such that then .
Theorem 1.11 (see [15]). Let be a complete cone metric space, let be a normal cone with normal constant , and let . Assume that a function defined by , is lower semicontinuous. The following hold(a) If there exist , such that then .(b) If there exist , such that then .
In 1997, Zabrejko [16] introduced the -metric and -normed linear spaces and showed the existence and uniqueness of fixed-points for operators which act in -metric or -normed linear spaces. Huang and Zhang [17] introduced the concept of cone metric space by replacing the set of real numbers by an ordered Banach space, and they showed some fixed-point theorems of contractive type mappings on cone metric spaces. The category of cone metric spaces is larger than metric spaces. Subsequently, many authors like Abbas and Jungck [18] have generalized the results of Huang and Zhang [17] and studied the existence of common fixed-points of a pair of self-mappings satisfying a contractive type condition in the framework of normal cone metric spaces. However, authors like Rezapour and Hamlbarani [19] studied the existence of common fixed-points of a pair of self- and non-self-mappings satisfying a contractive type condition in the situation in which the cone does not need to be normal. Many authors studied this subject and many results on fixed-point theory are proved (see, e.g., [12, 1939]).
Definition 1.12 (see [17]). Let be a real Banach space and a nonempty subset of . , where denotes the zero element of , is called a cone if and only if: (i) is closed;(ii), , ;(iii) and .
For given a cone , we define a partial ordering with respect to by or if and only if for all . The real Banach space equipped with the partial order induced by is denoted by . We shall write to indicate that but , while or will stand for , where denotes the interior of .
Proposition 1.13 (see [40]). Suppose is a cone in a real Banach space . Then one has the following. (i)If and , then .(ii)If and , then .(iii)If and , then . (iv)If and for each , then .
Proposition 1.14 (see [41]). Suppose , and . Then there exists such that for all .
The cone is called normal if there exists a real number such that, for all ,
The least positive number , satisfying the above is called the normal constant of .
The cone is called regular if every increasing sequence which is bounded from above is convergent, that is, if is a sequence such that for some , then there is such that as . Equivalently, the cone is regular if and only if every decreasing sequence which is bounded from below is convergent. It is well known that a regular cone is a normal cone.
Definition 1.15 (see [17]). Let be a nonempty set, a real Banach space, and a cone in . Suppose that the mapping satisfies(i), for all ; (ii) if and only if ; (iii), for all ; (iv), for all . Then is called a cone metric on , and is called a cone metric space.
Definition 1.16 (see [17]). Let be a cone metric space, and let be a sequence in and . If for every with , there is such that then is said to be convergent and converges to .
Definition 1.17 (see [17]). Let be a cone metric space, and let be a sequence in . We say that is a Cauchy sequence if, for any with , there is such that
Definition 1.18 (see [17]). Let be a cone metric space. If every Cauchy sequence is convergent in , then is called a complete cone metric space.
Remark 1.19 (see [17]). If is a normal cone, then converges to if and only if as . Further, in the case is a Cauchy sequence if and only if as .
The purpose of this paper is to present the fixed-points and endpoints of set-valued contractions concerning with the stronger Meir-Keeler cone-type mappings in cone metric spcaes. Our results generalize the recent results of Kadelburg and Radenović [4244] and Wardowski [15].
#### 2. Main Results
In this section, we first introduce the following notion of stronger Meir-Keeler cone-type mapping.
Definition 2.1. Let be a cone metric space with cone , and let Then the function is called a stronger Meir-Keeler cone-type mapping, if, for each , there exists such that, for with , there exists such that .
We now are in a position to present the following fixed-point theorem.
Theorem 2.2. Let be a complete cone metric space, and let be a normal cone in and . Assume that a function defined by , is lower semicontinuous. The following holds.(*) There exists a stronger Meir-Keeler cone-type mapping such that Then .
Proof. Given , we define the sequence recursively as follows. Take any . By , there exist and such that Thus, If , then , and we are done. Assume that . Put . By the definition of the stronger Meir-Keeler cone-type mapping , corresponding to use, there exists and with such that . Taking into account (2.5), we have that
By the same process, for , there exist and such that Thus, Now, put . By the definition of the stronger Meir-Keeler cone-type mapping , corresponding to use, there exists and with such that . And we put and . Taking into account (2.9), we have that
We continue in this manner. Inductively, for , there exist and such that Thus, Put . By the definition of the stronger Meir-Keeler cone-type mapping , corresponding to use, there exist and with such that . And we put and . Taking into account (2.14), we have that
Let such that . Taking into account (2.15) and (2.16), we obtain that Let be given. Since and , we get Thus, there exists such that, for all , and we also conclude that for all . This implies that is a Cauchy sequence. Since is complete, there exists such that
By the definition of , since , there exists a sequence such that , for all . From the convergence of the sequence and from the lower semicontinuity of the function , we obtain that Thus, We claim that . To prove this, on the contrary, assume that . Then by (2.22), there exists a sequence such that , and hence . Thus, for any , Let be given. Then there exists such that for all , and , and so This implies that is a Cauchy sequence in . Since is complete, there exists such that By the closedness of the , we deduce that . Then, for any , Let be given. Since and , we can deduce that there exists such that, for all , and , and hence By Proposition 1.13, we obtain that that is, , which is a contradiction. Therefore, .
Applying Remark 1.7, it is easy to establish the following corollary.
Corollary 2.3. Let be a complete cone metric space, a normal cone in , and . Assume that a function defined by :, is lower semicontinuous. The following holds.(**) There exists a mapping such that Then .
Corollary 2.4. Let be a complete cone metric space, a normal cone in , and . Assume that a function defined by , is lower semicontinuous. The following holds.(***)There exists a stronger Meir-Keeler cone-type mapping such that Then .
Example 2.5. Let , , where , , , defined by , , , with for all and if and only if . Let be defined by , , and . Then , , . Take for all . Calculation shows that, for , that is, according to Corollary 2.4 we have that .
Theorem 2.6. Let be a complete cone metric space, a normal cone in , and . Assume that a function defined by , , is lower semicontinuous. The following hold:(A) There exists a stronger Meir-Keeler cone-type mapping such that
Then .(B) There exists a stronger Meir-Keeler cone-type mapping such that
Then .
Proof. (A) By the same proof of the part (i) of Theorem 3.2 in [15], we have that for all . The remainder proof is similar to Theorem 2.2, we can deduce that .
(B) By (A), we obtain that the existence of such that, . Taking any , we have that, for all , . Since , we get , and hence , which gives . Thus .
Example 2.7. Let , , . Let for all , and let , . Then , . Let for all . It is easy to check that all conditions of Theorem 2.6 are satisfied and that .
Corollary 2.8. Let be a complete cone metric space, a normal cone in , and . Assume that a function defined by , is lower semicontinuous. The following hold:(C) There exists a mapping such that Then .(D) There exists a mapping such that Then . | 3,093 | 12,668 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "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-2024-18 | latest | en | 0.919391 |
https://ru.scribd.com/document/24815965/UT-Dallas-Syllabus-for-math2418-001-07f-taught-by-Paul-Stanford-phs031000 | 1,597,448,318,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439740343.48/warc/CC-MAIN-20200814215931-20200815005931-00371.warc.gz | 460,497,211 | 96,546 | Вы находитесь на странице: 1из 8
Course Syllabus
Course MATH 2418-001 Linear Algebra Professor Dr. Paul Stanford Term Fall 2007 Meetings 2:30pm-3:20pm MWF in JO 3.516
Professor’s Contact Information
Phone number (972) 883-4143 Department Phone (972) 883-2161
Email paul.stanford@utdallas.edu
Office location Office hours Other information
ECSN 2.518 4:00-5:00 MW and 1:00-2:00 TR Prefers contact through WebCT
Teaching Assistant TA Office TA Office hours TA Email
Yassmin Ansari FO 2.602 TBA
yxh034100@utdallas.edu
General Course Information
Course Prerequisites Corequisites Other Restrictions
MATH 2419 (Calculus), or consent of instructor MATH 2018-301 or MATH 2018-303 Graphing calculators will not be allowed; only non-alpha display calculators are permitted.
Course Description
The main goal of the course is the presentation of some fundamental tech- niques of linear algebra. The concepts of vector spaces, matrices, determi- nants, inverses, eigenvalues and eigenvectors will be developed.
Student Learning Outcomes
Students will learn concepts and techniques of linear algebra, including vector spaces, matrices, determinant, transformations, eigenvalues and eigenvectors.
Student Learning Objectives
1. Given a system of linear equations, students will be able to apply the Gauss-Jordon algorithm to determine all solutions, and determine whether the system is consistent and whether the solution is unique.
2. Given definitions of a set of objects with a well-defined addition and scalar multiplication, students will be able to evaluate whether this con- stitutes a Real vector Space. If valid, students will be able to demon- strate each axiom; if invalid, students will be able to present and verify an explicit counterexample to a vector space property.
3. Given a square matrix, students will be able to accurately calculate its determinant, and deduce whether the matrix is invertible or singular.
4. Given an explicit matrix, students will be able to determine its eigen- values, and for each such eigenvalue students will be able to create a basis for the corresponding eigenspace.
5. Given a matrix, students will be able to accurately determine basis vectors for its rowspace, columnspace and nullspace.
6. Students will be able to calculate the least squares approximation to an over-constrained system of linear equations.
Required Textbooks and Materials
Elementary Linear Algebra, Ninth edition, by Howard Anton
Suggested Course Materials
Solutions Manual
Classes begin Census Day Last day to drop without a “W” Labor Day WP/WF withdrawal period begins Midterm grades online WP/WF withdrawal period ends Thanksgiving holiday Last day of classes Final grades online Winter break
Thursday, August 16 Friday, August 31 Friday, August 31 Monday, September 3
Thursday, September 13 Wednesday, Oct. 3 Thursday, October 11
Thurs., Nov. 22
Monday, November 26 Friday, December 7 Monday, Dec. 24 Tues., Jan. 1
Sat., Nov. 24
First Day Friday August 17th Exam I Friday September 21st Exam II Wednesday October 24th Last day Monday November 26th Final Exam Monday December 3rd at 2:00pm-4:45pm
Each quiz is worth 25 points. The lowest two quiz scores will be dropped. The remaining quizzes are counted and converted to a percentage, giving a possible total of 100 points. Each regular examination is also worth 100 points. The comprehensive final examination is worth 200 points. This score cannot be dropped. These scores are weighted so that the final contributes 40% toward the overall grade. The remaining 60% is made up from the two exams and the quiz average (after dropping the two lowest quizzes). For these, the highest score has a weight of 30%, the next highest has a weight of 20%, and the lowest score has a weight of 10%. This means that your best scores will have the biggest impact on your course grade. Note that none of these can be completely dropped.
[90, 93) A-, [93, 97) A, [97, 100] A+, [80, 83) B-, [83, 87) B, [87, 90) B+, [70, 73) C-, [73, 77) C, [77, 80) C+, [60, 63) D-, [63, 67) D, [67, 70) D+, [0, 60) F
Midterm grades will be computed and submitted to the records office when requested. This grade will be computed in the following manner: Av- erage of all quizzes up to this time (no drops) 50%. Average of all exams up to this time (no drops) 50%.
Course & Instructor Policies
Make-up exams There will be no makeups except in extraordinary cir- cumstances. Missed exams are a zero.
Extra credit n/a
Late work All students are expected to take the examinations at the an- nounced time.
Special assignments Problems will be assigned on a regular basis. An- swers to most of these problems are given at the back of the textbook. Complete solutions to many of these problems may be found in the Solutions Manual.
Class attendance Classroom attendance and problem session attendance is required.
Classroom citizenship Professional behavior is expected at all times. Class- room discussions are not permitted between students. Cellphones must be turned off.
Technical Support
If you experience any problems with your UTD account you may send an email to: as- sist@utdallas.edu or call the UTD Helpdesk at 972 883-2911.
Field Trip Policies
Off-Campus Instruction and Course Activities Off-campus, out-of-state, and foreign instruction and activities are subject to state law and University policies and procedures regarding travel and risk-related activities. Information regarding these rules and regulations may be found at the website address
able from the office of the school dean. Below is a description of any travel and/or risk- related activity associated with this course.
Student Conduct & Discipline
The University of Texas System and The University of Texas at Dallas have rules and regulations for the orderly and efficient conduct of their business. It is the responsibility of each student and each student organization to be knowledgeable about the rules and regulations which govern student conduct and activities. General information on student conduct and discipline is contained in the UTD printed publication, A to Z Guide, which is provided to all registered students each academic year. The University of Texas at Dal- las administers student discipline within the procedures of recognized and established due process. Procedures are defined and described in the Rules and Regulations, Series 50000, Board of Regents, The University of Texas System, and in Title V, Rules on Student Ser- vices and Activities of the universitys Handbook of Operating Procedures. Copies of these rules and regulations are available to students in the Office of the Dean of Students, where staff members are available to assist students in interpreting the rules and regulations (SU
1.602, 972/883-6391) and online at http://www.utdallas.edu/judicialaffairs/UTDJudicialAffairs-
HOPV.html A student at the university neither loses the rights nor escapes the responsi- bilities of citizenship. He or she is expected to obey federal, state, and local laws as well as the Regents Rules, university regulations, and administrative rules. Students are subject to discipline for violating the standards of conduct whether such conduct takes place on or off campus, or whether civil or criminal penalties are also imposed for such conduct.
The faculty expects from its students a high level of responsibility and academic honesty. Because the value of an academic degree depends upon the absolute integrity of the work done by the student for that degree, it is imperative that a student demonstrate a high standard of individual honor in his or her scholastic work. Scholastic Dishonesty, any student who commits an act of scholastic dishonesty is sub- ject to discipline. Scholastic dishonesty includes but is not limited to cheating, plagiarism, collusion, the submission for credit of any work or materials that are attributable in whole
or in part to another person, taking an examination for another person, any act designed to give unfair advantage to a student or the attempt to commit such acts. Plagiarism, especially from the web, from portions of papers for other classes, and from any other source is unacceptable and will be dealt with under the universitys pol- icy on plagiarism (see general catalog for details). This course will use the resources of turnitin.com, which searches the web for possible plagiarism and is over 90% effective.
The copyright law of the United States (Title 17, United States Code) governs the making of photocopies or other reproductions of copyrighted materials, including music and soft- ware. Copying, displaying, reproducing, or distributing copyrighted works may infringe the copyright owners rights and such infringement is subject to appropriate disciplinary action as well as criminal penalties provided by federal law. Usage of such material is only appropriate when that usage constitutes fair use under the Copyright Act. As a UT Dallas student, you are required to follow the institutions copyright policy (Pol- icy Memorandum 84-I.3-46). For more information about the fair use exemption, see
http://www.utsystem.edu/ogc/intellectualproperty/copypol2.htm
Email Use
The University of Texas at Dallas recognizes the value and efficiency of communication between faculty/staff and students through electronic mail. At the same time, email raises some issues concerning security and the identity of each individual in an email exchange. The university encourages all official student email correspondence be sent only to a stu- dents U.T. Dallas email address and that faculty and staff consider email from students official only if it originates from a UTD student account. This allows the university to maintain a high degree of confidence in the identity of all individual corresponding and the security of the transmitted information. UTD furnishes each student with a free email ac- count that is to be used in all communication with university personnel. The Department of Information Resources at U.T. Dallas provides a method for students to have their U.T. Dallas mail forwarded to other accounts. Withdrawal from Class The administration of this institution has set deadlines for withdrawal of any college- level courses. These dates and times are published in that semester’s course catalog. Administration procedures must be followed. It is the student’s responsibility to handle withdrawal requirements from any class. In other words, I cannot drop or withdraw any student. You must do the proper paperwork to ensure that you will not receive a final grade of ”F” in a course if you choose not to attend the class once you are enrolled.
Student Grievance Procedures
Procedures for student grievances are found in Title V, Rules on Student Services and Activities, of the universitys Handbook of Operating Procedures. In attempting to resolve any student grievance regarding grades, evaluations, or other fulfillments of academic responsibility, it is the obligation of the student first to make a
serious effort to resolve the matter with the instructor, supervisor, administrator, or com- mittee with whom the grievance originates (hereafter called the respondent). Individual faculty members retain primary responsibility for assigning grades and evaluations. If the matter cannot be resolved at that level, the grievance must be submitted in writing to the respondent with a copy of the respondents School Dean. If the matter is not resolved by the written response provided by the respondent, the student may submit a written appeal to the School Dean. If the grievance is not resolved by the School Deans decision, the student may make a written appeal to the Dean of Graduate or Undergraduate Edu- cation, and the deal will appoint and convene an Academic Appeals Panel. The decision of the Academic Appeals Panel is final. The results of the academic appeals process will be distributed to all involved parties. Copies of these rules and regulations are available to students in the Office of the Dean of Students, where staff members are available to assist students in interpreting the rules and regulations.
As per university policy, incomplete grades will be granted only for work unavoidably missed at the semesters end and only if 70% of the course work has been completed. An incomplete grade must be resolved within eight (8) weeks from the first day of the subsequent long semester. If the required work to complete the course and to remove the incomplete grade is not submitted by the specified deadline, the incomplete grade is changed automatically to a grade of F.
Disability Services
The goal of Disability Services is to provide students with disabilities educational oppor- tunities equal to those of their non-disabled peers. Disability Services is located in room 1.610 in the Student Union. Office hours are Monday and Thursday, 8:30 a.m. to 6:30 p.m.; Tuesday and Wednesday, 8:30 a.m. to 7:30 p.m.; and Friday, 8:30 a.m. to 5:30 p.m. The contact information for the Office of Disability Services is:
The University of Texas at Dallas, SU 22 PO Box 830688 Richardson, Texas 75083-0688 (972) 883-2098 (voice or TTY) disabilityservice@utdallas.edu
If you anticipate issues related to the format or requirements of this course, please meet with the Coordinator of Disability Services. The Coordinator is available to dis- cuss ways to ensure your full participation in the course. If you determine that formal, disability-related accommodations are necessary, it is very important that you be registered with Disability Services to notify them of your eligibility for reasonable accommodations. Disability Services can then plan how best to coordinate your accommodations. It is the students responsibility to notify his or her professors of the need for such an accommodation. Disability Services provides students with letters to present to faculty
members to verify that the student has a disability and needs accommodations. Individuals requiring special accommodation should contact the professor after class or during office hours.
Religious Holy Days
The University of Texas at Dallas will excuse a student from class or other required activities for the travel to and observance of a religious holy day for a religion whose places of worship are exempt from property tax under Section 11.20, Tax Code, Texas Code Annotated. The student is encouraged to notify the instructor or activity sponsor as soon as possible regarding the absence, preferably in advance of the assignment. The student, so excused, will be allowed to take the exam or complete the assignment within
a reasonable time after the absence: a period equal to the length of the absence, up
to a maximum of one week. A student who notifies the instructor and completes any missed exam or assignment may not be penalized for the absence. A student who fails to complete the exam or assignment within the prescribed period may receive a failing grade for that exam or assignment. If a student or an instructor disagrees about the nature of
the absence [i.e., for the purpose of observing a religious holy day] or if there is similar disagreement about whether the student has been given a reasonable time to complete any missed assignments or examinations, either the student or the instructor may request
a ruling from the chief executive officer of the institution, or his or her designee. The
chief executive officer or designee must take into account the legislative intent of TEC 51.911(b), and the student and instructor will abide by the decision of the chief executive officer or designee.
These descriptions and timelines are subject to change at the discretion of the Professor. | 3,420 | 15,706 | {"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-2020-34 | latest | en | 0.722295 |
http://www.youdao.com/w/eng/confusion_matrix/ | 1,606,704,020,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141204453.65/warc/CC-MAIN-20201130004748-20201130034748-00331.warc.gz | 166,920,743 | 8,740 | go top
## confusion matrix [kənˈfjuːʒn ˈmeɪtrɪks]
• [计] 混淆矩阵
### 网络释义专业释义英英释义
[计] 混淆矩阵
混合矩阵
混淆矩阵
...c回归为例(1): 混淆矩阵 分类模型的性能评估——以SAS Logistic回归为例(2): ROC和AUC 一些准备 说，混淆矩阵(Confusion Matrix)是我们永远值得信赖的朋友： 预测 1 0 实 1 d, True Positive c, False Negative c+d, Actual Positive 际 0 b, False Positive ...
confusion-matrix 混淆矩阵
chinese confusion matrix 汉字混淆矩阵
odorant confusion matrix 气味混乱基质
更多收起网络短语
• 混淆矩阵 - 引用次数：8
参考来源 - 基于FSVM的高光谱遥感影像分类算法研究
混合矩阵
·2,447,543篇论文数据，部分数据来源于NoteExpress
#### Confusion matrix
• In the field of machine learning, a confusion matrix is a specific table layout that allows visualization of the performance of an algorithm, typically a supervised learning one (in unsupervised learning it is usually called a matching matrix). Each column of the matrix represents the instances in a predicted class, while each row represents the instances in an actual class.
### 双语例句权威例句
• The output from such a test in Mahout is a data structure called a confusion matrix.
这种测试 Mahout 中输出数据结构混合矩阵
• Then a measurement of this relationship has been proposed by utilizing the confusion matrix.
进而提出了基于混淆矩阵度量模式间混淆关系的方法。
• A new block cipher is designed where the diffusion of matrix multiplication is combined with the confusion of specially designed matrix operation to encrypt information.
设计新的分组密码算法，该算法利用矩阵乘法扩散作用专门设计矩阵运算混乱作用实现信息加密
• Despite the potential confusion that this duality creates, matrix management was enormously popular in the 1970s and 1980s.
ECONOMIST: Idea
\$firstVoiceSent
- 来自原声例句 | 542 | 1,524 | {"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-2020-50 | latest | en | 0.580831 |
https://www.eduzip.com/ask/question/solve-int-dfract4-3-t2-2t2-1-t2-dt-580864 | 1,623,705,956,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487613453.9/warc/CC-MAIN-20210614201339-20210614231339-00181.warc.gz | 684,837,749 | 8,576 | Mathematics
# Solve : $\int \dfrac{t^4 - 3 t^2 + 2}{t^2 (1 + t^2)} , dt$
##### SOLUTION
$I=\displaystyle \int \dfrac {t^4 -3t^2 +2}{t^2 (1+t^2)}dt$
$=\displaystyle \int \dfrac {t^4 +t^2 4t^2+2}{t^2 (1+t^2)}dt$
$\Rightarrow \ \displaystyle \int dt-\displaystyle \int \dfrac {4t^2}{t^2 (1+t^2)}dt +\displaystyle \int \dfrac {2}{t^2 (1+t^2)}dt$
$I\Rightarrow \ t-\displaystyle \int \dfrac {4}{(1+t^2)}dt+\displaystyle \int 2 \left[\dfrac {1}{t^2}-\dfrac {1}{1+t^2}\right] dt$
$I\Rightarrow \ t-4\tan^{-1} (t)+2 \displaystyle \int \dfrac {1}{t^2}dt+\displaystyle \int \dfrac {2}{(1+t^2)}dt$
$I=t-4\tan^{-1}t+2\left(\dfrac {t^{-2+1}}{-2+1}\right)-2\tan^{-1} (t)+C$
$\boxed {I\Rightarrow \ t-\dfrac {2}{t}-6\tan^{-1} (t)+C}$
$\therefore \ \boxed {\displaystyle \int \dfrac {t^4-3t^2+2}{t^2 (1+t^2)}dt=t-\dfrac {2}{t}-6\tan^{-1} (t)+C}$
Its FREE, you're just one step away
Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84
#### Realted Questions
Q1 Subjective Hard
Evaluate: $\int_{0}^{\pi}\dfrac {4x \sin x}{1 + \cos^{2}x} dx.$
1 Verified Answer | Published on 17th 09, 2020
Q2 One Word Medium
Evaluate:$\displaystyle \int \frac{dx}{\sqrt{x^{2}+6x+5}}$
1 Verified Answer | Published on 17th 09, 2020
Q3 Single Correct Medium
$\displaystyle \int\frac{e^{x}}{(e^{x}+2)(e^{x}-1)}dx=$
• A. $\displaystyle \frac{1}{3}\log|\displaystyle \frac{e^{x}+1}{e^{x}-1}|+c$
• B. $\displaystyle \frac{1}{3}\log|\displaystyle \frac{e^{x}+1}{e^{x}+2}|+c$
• C. $\displaystyle -\frac{1}{3}\log|\displaystyle \frac{e^{x}+1}{e^{x}+2}|+c$
• D. $\displaystyle \frac{1}{3}\log|\frac{e^{x}-1}{e^{x}+2}|+c$
1 Verified Answer | Published on 17th 09, 2020
Q4 Single Correct Medium
$\displaystyle \int _{-3\pi}^{3\pi} \sin^{2}{\theta}\sin^{2}{2\theta}\ dx$ is equal to :
• A. $\dfrac{3\pi}{2}$
• B. $\dfrac{5\pi}{2}$
• C. $6\pi$
• D. $\pi$
Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$ | 921 | 2,090 | {"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} | 4.25 | 4 | CC-MAIN-2021-25 | latest | en | 0.41495 |
https://www.convertunits.com/from/reed/to/meter | 1,653,440,875,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662577757.82/warc/CC-MAIN-20220524233716-20220525023716-00358.warc.gz | 767,857,160 | 17,233 | ## ››Convert reed [Israel] to metre
reed meter
How many reed in 1 meter? The answer is 0.3732736095558.
We assume you are converting between reed [Israel] and metre.
You can view more details on each measurement unit:
reed or meter
The SI base unit for length is the metre.
1 metre is equal to 0.3732736095558 reed, or 1 meter.
Note that rounding errors may occur, so always check the results.
Use this page to learn how to convert between reed [Israel] and metres.
Type in your own numbers in the form to convert the units!
## ››Quick conversion chart of reed to meter
1 reed to meter = 2.679 meter
5 reed to meter = 13.395 meter
10 reed to meter = 26.79 meter
15 reed to meter = 40.185 meter
20 reed to meter = 53.58 meter
25 reed to meter = 66.975 meter
30 reed to meter = 80.37 meter
40 reed to meter = 107.16 meter
50 reed to meter = 133.95 meter
## ››Want other units?
You can do the reverse unit conversion from meter to reed, or enter any two units below:
## Enter two units to convert
From: To:
## ››Definition: Meter
The metre, symbol: m, is the basic unit of distance (or of "length", in the parlance of the physical sciences) in the International System of Units. The internationally-accepted spelling of the unit in English is "metre", although the American English spelling meter is a common variant. However, both American and non-American forms of English agree that the spelling "meter" should be used as a suffix in the names of measuring devices such as chronometers and micrometers.
## ››Metric conversions and more
ConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 100 kg, US fluid ounce, 6'3", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more! | 519 | 2,007 | {"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-2022-21 | latest | en | 0.844688 |
http://www.gamedev.net/topic/619948-how-to-blockcostcells-based-on-the-terrain-ready-for-a-path-finding/ | 1,481,345,697,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698542939.6/warc/CC-MAIN-20161202170902-00214-ip-10-31-129-80.ec2.internal.warc.gz | 463,420,626 | 28,149 | • Create Account
## How To Block(Cost)Cells Based on the Terrain ready for A* path finding.
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.
6 replies to this topic
### #1ankhd Members
2284
Like
0Likes
Like
Posted 07 February 2012 - 11:40 PM
Hello All.
I would like to know how to work out the cost(or blocking) of each cell based on the terrain under the cell.
What I have is a grid of cells that overlay's the terrain. This I will use the A* algorithm on, but I need my cells set up based on the terrain.
I have a image that has the terrain and the grid overlyed onto the terrain with black dots to show what I mean.
Like I want the unit to walk up the ramp but not the cliff wall and on the ridge. But the ridge cell covers to whole of the top(See Image).
How to handle that sort of thing
### #2Postie Members
1459
Like
2Likes
Like
Posted 08 February 2012 - 01:21 AM
Calculate the slope between adjacent cells and then construct a formula to convert that slope into a movement cost. If the slope exceeds a certain value, the terrain is too steep and you can simply treat that cell as inaccessible.
In my current project I actually use the height difference, since the slope is deltaHeight/deltaX and deltaX is always 1 in my case. If it exceeds 1m, which corresponds to a 45 degree angle, I consider the cell to be inaccessible. Otherwise I multiply the current movement cost (calculated from factors such as the terrain underfoot) by 1 + deltaHeight. So at maximum it increases the movement cost of that tile by about 2x. That might not be realistic, but in testing its behaviour looks ok to me at the moment.
I should mention this is for creatures walking around. Slope affects vehicles much more severely I believe.
Currently working on an open world survival RPG - For info check out my Development blog:
### #3ankhd Members
2284
Like
0Likes
Like
Posted 14 February 2012 - 05:48 PM
Only one reply thanks.
You know the articles don't talk about setting up the cost and things.
### #4TehOwn Members
134
Like
1Likes
Like
Posted 14 February 2012 - 06:57 PM
I'm sorry but I've seen way too many people acting as if this community owes them their time. This is FREE advice you're getting here, try to respect it a bit better. One reply is better than none.
His advice is sound. There is nothing wrong with it. Perhaps if you provided a little more information about your A* implementation then people would be able to tailor their answers better to your... ability... to comprehend.
I sounds to me like you're using an A* algorithm that was coded by someone else and you don't really understand how it works.
There is a great section on pathfinding here:
http://theory.stanfo...ameProgramming/
Specifically to costs:
http://theory.stanford.edu/~amitp/GameProgramming/MovementCosts.html
This is all I needed to write any pathfinders I've ever wanted.
### #5ankhd Members
2284
Like
0Likes
Like
Posted 16 February 2012 - 12:58 AM
firstly I would like to thank you for your time and link. As I don't have that a* link in my collection of links on a*.
And I am part of this community as well and I hope I have helped others.
and No I have not stolen some ones A* algo. This will in fact be my second A* algo, My first one only used blocking or not blocking and it was on a smaller scale then the one
I need now as my cells are larger.
And a point for you in future is not to assume things, It will just make you and me look like an ass.
### #6ankhd Members
2284
Like
0Likes
Like
Posted 16 February 2012 - 01:02 AM
now back to the problem at hand.
See the cliff at the left top the cell covers the top and the wall of the cliff how should I handle that sort of thing besides making smaller cells.
I want the units to go up there if they need to. thanks.
### #7TehOwn Members
134
Like
1Likes
Like
Posted 16 February 2012 - 09:44 AM
now back to the problem at hand.
See the cliff at the left top the cell covers the top and the wall of the cliff how should I handle that sort of thing besides making smaller cells.
I want the units to go up there if they need to. thanks.
If you want to deal with variable size pathfinding nodes then perhaps it's worth looking into using Quadtree nodes for pathfinding.
This isn't a completed algorithm (and it's not my video either) but this demonstrates the idea well: | 1,106 | 4,478 | {"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} | 3.03125 | 3 | CC-MAIN-2016-50 | latest | en | 0.921028 |
https://www.dailymail.co.uk/health/article-11829941/Exactly-steps-takes-burn-Britains-best-loved-foods.html | 1,719,026,910,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862249.29/warc/CC-MAIN-20240622014659-20240622044659-00827.warc.gz | 648,243,061 | 162,290 | # How many steps will it take to burn off YOUR favourite foods and drinks? Our handy guide reveals all... and you may want to get walking now if you've got a pizza lined up tonight
• Walking 10,000 steps is not enough to burn off the calories in a Big Mac
• To burn off a Greggs sausage roll you will need to walk more than 8,000 steps
• Just one chocolate digestive takes over 2,000 steps to walk off
Many of us have the goal of walking 10,000 steps a day in our quest to stay fit and healthy.
Yet, this isn't even enough to burn off a Greggs steak bake.
But, as MailOnline's fascinating guide reveals, it is just about enough to banish all of the calories lurking within a luxurious High Street cookie.
Or, if you've not got a sweet tooth, it would stave off five chicken wings at Nando's, or a ham and cheese toastie from Starbucks.
All three of those options contain fewer than 400 calories, which can, in theory, be blasted away by just 10,000 steps.
Here is a breakdown of some Britain's best-loved food and how many steps it could take to burn off based on an average height and weight. Eating a Big Mac could cost you 12,325 steps to burn it all off. In comparison, a Greggs sausage roll, which is 329 calories, takes the average person 8,225 steps to burn the calories. Even a cappuccino from Costa is more than 6,600 steps to walk off
This calculation is based on someone being between 5'6 and 5'11 and weighing around 73kg (160lb).
In other words, average height and weight.
A person of this size will burn about about 40 calories every 1,000 steps they take, if they are walking at three miles an hour.
That is according to an online steps to calories calculator based on research by the American College of Sports Medicine.
The 2011 study looked at how many calories are burned in one step. It produced the calorie numbers by taking the average calories burned at walking speeds from 2 to 4 miles per hour.
### READ MORE: Exact number of steps needed to burn off your favourite alcoholic drink revealed - and it's bad news for cider fans
The energy you burn while walking depends on your height, weight, pace and the number of steps you take.
The faster you walk, the faster your heart beats and the more calories you burn.
And the heavier you are the fewer steps you will need to take to burn off the extra calories.
The recommended calories intake a day for women is 2,000 calories and 2,500 for men, according to the NHS.
MailOnline trawled through the nutritional breakdown of 100 of the UK's best-loved foods and drinks, ranging from the menu of McDonalds to the aisles of Tesco.
Of the randomly-selected products, the most calorific was Pizza Hut's margherita individual stuffed crust 11-inch (1,380 calories).
This, according to the calculations, and if you chose to hog it to yourself, would require a mammoth 34,500 steps. That in itself would take, on average, around 5 hours and 15 minutes.
A Big Mac (493 cals) would cost you roughly 12,325 steps, if you wanted to burn it all off.
### HOW TO STAY HEALTHY THROUGH EXERCISE
Adults are encouraged to do some type of physical activity every day. Exercise just once or twice a week can reduce the risk of heart disease or stroke.
Over-18s should aim to:
• Do strengthening activities that work all the major muscle groups (legs, hips, back, abdomen, chest, shoulders and arms) on at least two days a week. This includes carrying heavy shopping bags, yoga, pilates and lifting weights.
• Do at least 150 minutes of moderate intensity activity a week or 75 minutes of vigorous intensity activity a week. Moderate activity includes brisk walking, riding a bike, dancing and doubles tennis. Vigorous activity includes running, swimming and riding a bike fast or on hills.
• Spread exercise evenly over four to five days a week, or every day
• Reduce time spent sitting or lying down and break up long periods of not moving with some activity
Adults can also achieve weekly activity target with:
• Several short sessions of very vigorous intensity activity. This includes lifting heavy weights, circuit training and sprinting up hills.
• A mix of moderate, vigorous and very vigorous intensity activity
Source; NHS
For comparison, a Greggs sausage roll (329 cals) would require 8,225 steps to fully banish.
A cinnamon bun from Gail's amounts to 15,050 steps (602 cals) and a double berry muffin from Pret (441 cals) is close to 11,025 steps.
Drinks are not much better, either.
Unsurprisingly, one of the most calorific is a hot chocolate. A large one from Costa (524 cals) requires about 13,100 steps if you want to march it off.
Around 5,300 steps are needed to burn a large Coca Cola at McDonald's (212 cals).
A similar number — 5,250 — are needed to power through a pint of Guinness (210 cals).
But a 175ml glass of Sauvignon Blanc is 133 calories and 3,325 steps to burn off.
Small snacks from biscuits to crisps also rack up your daily calorie intake and need a surprising amount of steps to walk off.
Eating just one milk chocolate digestive (83 cals) would need 2,000 steps which is about 18 minutes of walking.
A Jammie Dodger (74 cals) requires 1,850 steps and a KitKat (104 cals) would need to walk 2,600 steps to expel the extra energy.
It's not just the sweet treat, you would need to walk 5,850 steps to burn off a packet of Walkers ready salted crisps (234 cals).
Personal trainer Matt Roberts, who has helped the likes of Adele, Naomi Campbell and Ellie Goulding, suggests taking the stairs instead of the lift and walking to work as ways of fitting in extra steps.
Mr Roberts said: 'It’s the quickest way to burn extra calories throughout the day, without setting out a specific training slot in your schedule.
'With just these small changes, you will be amazed by how many more you can add to your daily count, allowing you to hit even more of the extra 500 plus calories you can burn by reaching or exceeding that 10,000-step goal.'
Registered dietitian Dr Duane Mellor, at Birmingham's Aston University, warns that we should not feel guilty about the foods we eat and 'absolve ourselves by doing exercise'.
Instead, he urges people to stick to a healthy and balanced diet and stay active.
He said: 'Although some may find it beneficial to see the number of steps might be equivalent to certain foods, the key is to look at our overall dietary pattern and seek to enjoy foods that are high in fat, salt and sugar only occasionally, so that we can mostly eat a varied and healthy diet and maintain health through being active as part of our daily lives, not trying to match activity to eating.'
How many steps it takes to burn off Britain's best-loved food and drink
Product Calories Steps
One Oreo Vanilla 52kcal 1,300
Mini Babybel 59kcal 1,475
One Jammie Dodger 74kcal 1,850
One Mcvitie's Milk Chocolate Digestive Biscuit 83kcal 2,075
Haribo Starmix Mini Bag 85.5kcal 2,137
Nestle Aero chocolate mouse 89kcal 2,225
Tesco green olives with herbs 92kcal 2,300
McDonalds large Fanta 95kcal 2,375
Freddo 95kcal 2,375
5 Tesco pork cocktail sausages 104kcal 2,600
Activia strawberry yoghurt 104kcal 2,600
KitKat 104kcal 2,600
Tesco crumpet 105kcal 2,625
Tesco organic houmous 1/4 pot 107kcal 2,675
Kellogg's Frosties per 30g 113kcal 2,825
Jacobs Mini Cheddars 117kcal 2,925
Innocent mangoes passion fruit smoothie 127kcal 3,175
One slice of Hovis Original 7 Seeds Bread 131kcal 3,275
Wetherspoon villa Maria Sauvignon Blanc 175ml 133kcal 3,325
Weetabix 2 biscuits 136kcal 3,400
Greggs hash brown 2 pack 151kcal 3,775
Sainsbury's garlic baguette 1/4 166kcal 4,150
Grande Starbucks latte 175kcal 4,375
KFC 2 hot wings 180kcal 4,500
Cornetto Classic 181kcal 4,525
Cadbury Crunchie 186kcal 4,650
Sainsbury's fruity hot cross buns 189kcal 4,725
Nature Valley crunchy oats & honey cereal bars 196kcal 4,900
Sainsbury's 4 falafels 199kcal 4,975
Heinz Cream of Tomato Soup 400g can 204kcal 5,100
Lovett's Family Favourite Profiterole Dessert 208kcal 5,200
Guinness pint 210kcal 5,250
Cadbury Dairy Milk Buttons Chocolate Dessert 211kcal 5,275
McDonalds large Coca-Cola 212kcal 5,300
Tesco beer battered onion rings 3 213kcal 5,325
John West tuna Italian light lunch 216kcal 5,400
Tesco extra large vegetable samosa 218kcal 5,450
Taco Bell crunchy taco supreme beef 220kcal 5,500
McCain home chips straight cut 110g 222kcal 5,550
Stella Artois pint 227 kcal 5,675
Mars bar 228kcal 5,700
Walkers ready salted crisps 234kcal 5,850
2 Tesco egg waffles 238kcal 5,950
Doritos Tangy Cheese 240kcal 6,000
Sainsbury's sultana scones 241kcal 6,025
Higgidy spinach feta red pepper quiche 246kcal 6,150
Burger King 6 chicken nuggets 249.4kcal 6,235
1/4 Tesco quiche lorraine 256kcal 6,400
Sainsbury's On the Go fish sushi selection 260kcal 6,500
Costa large cappuccino 265kcal 6,625
Tesco scotch egg 265kcal 6,625
Starbucks tall caramel frappuccino 275kcal 6,875
Wendy's regular vanilla frosty 296kcal 7,400
Costa almond croissant 319kcal 7,975
Pret smashed avo open sandwich 322kcal 8,050
Greggs yum yum 323kcal 8,075
Greggs bacon breakfast roll 329kcal 8,225
Greggs sausage roll 329kcal 8,225
Heinz Baked Beans 415g can 336kcal 8,400
Costa BLT sandwich 393kcal 9,825
Nando's 5 chicken wings 393kcal 9,825
Starbucks oak smoked ham & cheese toastie 394kcal 9,850
Ben's Cookie milk chocolate chunk 398kcal 9,950
Tesco smoked ham & cheddar sandwich 405kcal 10,125
Greggs steak bake 409kcal 10,225
Tesco spicy bean wrap 412kcal 10,300
McDonalds Sausage & Egg McMuffin 423kcal 10,575
Tesco tuna & sweetcorn pasta 434kcal 10,850
Bachelors Super Noodles Chicken 90g 438kcal 10,950
Sainsbury's chicken salad sandwich 438kcal 10,950
Pret double berry muffin 441kcal 11,025
McDonalds large fries 444kcal 11,100
Itsu spicy salmon dragon rolls 448kcal 11,200
Taco Bell 7-layer Burrito 467kcal 11,675
Subway footlong The Notorious B.M.T 476kcal 11,900
Wendy's chili cheese fries 481kcal 12,025
Pukka steak and kidney pie 481kcal 12,025
Big Mac 493kcal 12,325
KFC Kentucky Mayo Twister 520kcal 13,000
Costa large hot chocolate 524kcal 13,100
Subway footlong The Baller 530kcal 13,250
Pukka veggie leek & potato pie 553kcal 13,825
Leon grilled halloumi wrap 561kcal 14,025
Nando's grilled chicken wrap 566kcal 14,150
Wasabi spicy tom yum soup 568kcal 14,200
Ginsters large Cornish pasty 569kcal 14,225
Leon Love Burger 574kcal 14,350
The Real Greek pork skewer souvlaki wrap 585kcal 14,625
Gail's cinnamon bun 602kcal 15,050
Burger King Whopper 609.2kcal 15,227
Dominoes New Yorker classic crust three slices 644kcal 16,100
Sainsbury's pepperoni pizza 736kcal 18,400
West Cornwall Pasty Co cheese & onion pasty 781kcal 19,525
Wetherspoon traditional breakfast 812kcal 20,300
West Cornwall Pasty Co traditional pasty 847kcal 21,175
Wagamama chicken katsu curry 998kcal 24,950
Five Guys bacon cheeseburger 1,060kcal 26,500
Wendy's Dave's Triple Burger 1204kcal 30,100
Wetherspoon freshly battered cod and chips 1303kcal 32,575
Pizza Hut margherita individual stuffed crust 11" 1380kcal 34,500
### WHAT SHOULD A BALANCED DIET LOOK LIKE?
Meals should be based on potatoes, bread, rice, pasta or other starchy carbohydrates, ideally wholegrain, according to the NHS
• Eat at least 5 portions of a variety of fruit and vegetables every day. All fresh, frozen, dried and canned fruit and vegetables count
• Base meals on potatoes, bread, rice, pasta or other starchy carbohydrates, ideally wholegrain
• 30 grams of fibre a day: This is the same as eating all of the following: 5 portions of fruit and vegetables, 2 whole-wheat cereal biscuits, 2 thick slices of wholemeal bread and large baked potato with the skin on
• Have some dairy or dairy alternatives (such as soya drinks) choosing lower fat and lower sugar options
• Eat some beans, pulses, fish, eggs, meat and other proteins (including 2 portions of fish every week, one of which should be oily)
• Choose unsaturated oils and spreads and consuming in small amounts
• Drink 6-8 cups/glasses of water a day
• Adults should have less than 6g of salt and 20g of saturated fat for women or 30g for men a day
Source: NHS Eatwell Guide
## Most watched News videos
The comments below have not been moderated.
The views expressed in the contents above are those of our users and do not necessarily reflect the views of MailOnline. | 3,468 | 12,280 | {"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} | 2.625 | 3 | CC-MAIN-2024-26 | latest | en | 0.951405 |
https://sites.google.com/site/numeropedia/numbers13k | 1,397,846,997,000,000,000 | text/html | crawl-data/CC-MAIN-2014-15/segments/1397609535095.7/warc/CC-MAIN-20140416005215-00362-ip-10-147-4-33.ec2.internal.warc.gz | 786,463,729 | 19,396 | Numbers 13,000s
A page of the Numeropedia - the Special Encyclopedia of Numbers
- 11K - 12K - 13K - 14K - 15K - 16K - 17K - 18K - 19K
& [100K]...
1 - 10 - 100 - 1000 - 10,000 - 100,000 - 1M - 10M - 100M1B10B - 100B - 1T - 10T - 100T - 1Q - ...
13,000
[EECS] 13K(W) is one of standard numerical values for resistors (of tolerance class 5%).
[Gov.] The U.S. National Exit Poll was designed to survey at least 13,000 respondents.
13,107
[Math.] A regular polygon with this odd number (product of Fermat prime numbers) of sides is constructible by using only straightedge and compass. 13107 = 3×17×257.
13,147
[Math.] A prime number. 131472 = 172,843,609, a square using all 9 digits 0-9 once, except digit 5.
13,268
[Math.] 132682 = 176,039,824, a square using all 9 digits 0-9 once, except digit 5.
13,278
[Math.] 132782 = 176,305,284, one of 22 squares using all 9 digits 0-8 once.
13,334
[Math.] 133,346,667 = 13,3342–66672 = (13334+6667)×6667, where 13334 = 6667×2.
13,343
[Math.] 133432 = 178,035,649, a square using all 9 digits 0-9 once, except digit 2.
13,434
[Math.] 134342 = 180,472,356, one of 22 squares using all 9 digits 0-8 once.
13,458
[Math.] The ratio 13458/6729 = 2, using each of 9 digits 1-9 once, shows how to arrange a 9-book set on 2 shelves to mark the book #2.
13,467
[Math.] 13,467 = 1342–672 = (134+67)×67, where 134 = 67×2.
13,485
[Math.] The ratio 13485/2697 = 5, using each of 9 digits 1-9 once, shows how to arrange a 9-book set on 2 shelves to mark the book #5.
13,509
[Geology] The “Traveling Salesman Problem” for 13,509 cities (of population at least 500) in the U.S. solved in 1998.
13,530
[Math.] The denominator of the 40th Bernoulli number.
13,545
[Math.] 135452 = 183,467,025, one of 22 squares using all 9 digits 0-8 once.
13,584
[Math.] The ratio 13584/6792 = 2 using each of 9 digits 1-9 once, shows how to arrange a 9-book set on 2 shelves to mark the book #2.
13,597
Math.] The smallest prime number of all 5 different odd digits.
13,698
[Math.] 136982 = 187,635,204, one of 22 squares using all 9 digits 0-8 once.
13,698
[Math.] Two multiples of number 6849, 6849×2 = 13,698 and 6849×3 = 20,547, use each of 10 digits 0-9 once.
13,759
[Math.] A prime number of all 5 different odd digits.
13,790
[Math.] Two multiples of number 6895, 6895×2 = 13,790 and 6895×7 = 48,265, use each of 10 digits 0-9 once.
13,832
[Math.] A number that is the sum of 2 cube numbers in 2 ways: 13,832 = 243+23 = 203+183.
13,845
[Math.] The ratio 13845/2769 = 5, using each of 9 digits 1-9 once, shows how to arrange a 9-book set on 2 shelves to mark the book #5.
13,854
[Math.] Each ratio 13854/6927 = 2, using each of 9 digits 1-9 once, shows how to arrange a 9-book set on 2 shelves to mark the book #2.
13,955
[Literature] A famously long sentence in English literature is of 13955-word, in Jonathan Coe’s “The Rotters’ Club”.
13nnn
[Zip] U.S. Postal Zip Codes of New York: 10nnn-14nnn and 005nn. | 1,129 | 3,022 | {"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} | 4.09375 | 4 | CC-MAIN-2014-15 | longest | en | 0.568129 |
http://mathhelpforum.com/differential-geometry/181409-weaker-condition-continuity.html | 1,502,904,743,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886102309.55/warc/CC-MAIN-20170816170516-20170816190516-00649.warc.gz | 256,053,005 | 10,977 | # Thread: weaker condition for continuity.
1. ## weaker condition for continuity.
Let $f:\mathbb{R} \rightarrow \mathbb{R}, \, a\in S \subset \mathbb{R}$.Suppose $f$ has the property that:
$x_n \in S, \, x_n \rightarrow a \Rightarrow (f(x_n))$ is convergent. Prove that $f$ is continuous at $a$.
my approach:
Let $(x_n)$ and $(y_n)$ be two sequences in $S$ with $x_n \rightarrow a, \, y_n \rightarrow a$. let $f(x_n) \rightarrow L_1$ and $f(y_n) \rightarrow L_2$. I need to prove that $L_1=L_2$. how do i go about it?
2. Originally Posted by abhishekkgp
Let $f:\mathbb{R} \rightarrow \mathbb{R}, \, a\in S \subset \mathbb{R}$.Suppose $f$ has the property that:
$x_n \in S, \, x_n \rightarrow a \Rightarrow (f(x_n))$ is convergent. Prove that $f$ is continuous at $a$.
my approach:
Let $(x_n)$ and $(y_n)$ be two sequences in $S$ with $x_n \rightarrow a, \, y_n \rightarrow a$. let $f(x_n) \rightarrow L_1$ and $f(y_n) \rightarrow L_2$. I need to prove that $L_1=L_2$. how do i go about it?
I think this is false. Take for example $\displaystyle{f(x):=\left\{\begin{array}{cc}\frac{ \sin x}{x}&\mbox{ , if } x\neq 0\\{}\\ 8&\mbox { , if } x=0\end{array}\right.}$ , and let
$a\in S:=(-1,1)\subset \mathbb{R}$ .
Tonio
3. Originally Posted by abhishekkgp
Let $f:\mathbb{R} \rightarrow \mathbb{R}, \, a\in S \subset \mathbb{R}$.Suppose $f$ has the property that:
$x_n \in S, \, x_n \rightarrow a \Rightarrow (f(x_n))$ is convergent. Prove that $f$ is continuous at $a$.
my approach:
Let $(x_n)$ and $(y_n)$ be two sequences in $S$ with $x_n \rightarrow a, \, y_n \rightarrow a$. let $f(x_n) \rightarrow L_1$ and $f(y_n) \rightarrow L_2$. I need to prove that $L_1=L_2$. how do i go about it?
You can do this by considering the sequence $x_1,y_1,x_2,y_2,x_3,y_3,\ldots$.
Notice that it is not sufficient just to show that $L_1=L_2$. You need to show that this limit is equal to $f(a)$. You can do that by taking one of your sequences to be the constant sequence $x_n=a$ for all n.
4. Originally Posted by tonio
I think this is false. Take for example $\displaystyle{f(x):=\left\{\begin{array}{cc}\frac{ \sin x}{x}&\mbox{ , if } x\neq 0\\{}\\ 8&\mbox { , if } x=0\end{array}\right.}$ , and let
$a\in S:=(-1,1)\subset \mathbb{R}$ .
Tonio
a typo error in my question.... i had written $f:\mathbb{R} \rightarrow \mathbb{R}$ while it should be $f:S \rightarrow \mathbb{R}$. | 850 | 2,376 | {"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": 46, "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} | 3.75 | 4 | CC-MAIN-2017-34 | longest | en | 0.736577 |
https://onlinetest.ibpsexamguru.in/questions/PO-Quantitative-Aptitude/Q-Test-No-213 | 1,534,537,784,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221212910.25/warc/CC-MAIN-20180817202237-20180817222237-00137.warc.gz | 746,376,160 | 9,233 | # Bank PO :: PO Quantitative Aptitude Q Test No 213
## Home Bank PO / PO Quantitative Aptitude Q Test No 213 Questions and Answers
1 .
In a party every person shakes hands with every other person. If there were a total of 120 handshakes in the party then what is the number of persons present in the party ?
15
16
17
18
2 .
An unbiased coin is tossed 5 times. Find the chance that head will appear exactly 3 times.
18/32
10/16
5/16
5/32
3 .
There are three persons A, B and C when the age of A is added to half of the age of B, the result is equal to C's age. One-third of the age of 'B' is equal to one-fourth of the age of 'C'. If one-fifth of A's age is added to half of B's age, the result is equal to half of C's age. Then what is the age of 'B' ?
16 yrs
20 yrs
24 yrs
30 yrs
4 .
A train crosses a 120-metre and a 70-metre long plat form in 17 seconds and 12 seconds respectively. What is the speed of the train ?
10 ms-1
16 ms-1
20 ms-1
24 ms-1
5 .
Ram can complete a work in 45 days and Mohan can do the same work in 27 days. If Ram leaves the work after 5 days, then in how many days will Mohan do the remaining work ?
18 days
20 days
24 days
21 days
6 .
Direction (Q. 6 - 10) : In an examination total students passed from five different cities A, B, C, D and E is 6000. The given pie-chart shows the percentage distribution of these passed students among these five cities. Line graph shows the percentage of girls passed from each cities. Answer the following question based on these graphs.
What is the number of students passed from City A, B and C together ?
3600
3700
3800
3900
7 .
Wha... he total number of female students passed from these five cities together ?
2816
2919
3140
3210
8 .
What is the ratio of the total number of boys passed from city 'E' to the total number of girls passed from city 'B' ?
1:2
2:3
2:1
3:2
9 .
The number of girls passed from city 'E' is what percentage of the total number of students passed from city 'B' ?
24%
30%
36%
40%
10 .
The number of students passed from city 'D' is what percentage more the number of boys passed from City 'A' ?
24%
30%
32 1/2%
None of these | 621 | 2,141 | {"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} | 3.734375 | 4 | CC-MAIN-2018-34 | latest | en | 0.848451 |
https://stupidsid.com/previous-question-papers/download/integrated-circuits-16464 | 1,719,141,738,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862466.81/warc/CC-MAIN-20240623100101-20240623130101-00551.warc.gz | 457,525,777 | 21,211 | MORE IN Integrated Circuits
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary
Answer any one question from Q1 and Q2
1 (a) Draw the block diagram of op-amp and explain the function of each block in detail
6 M
1 (b) Compare different types of op-amp technologies.
3 M
1 (c) Explain the effect of temperature on:
(i) Input Bias Current
(ii) Input Offset Voltage
(iii) Input Resistance
3 M
2 (a) Find the Q-point VC and IB for dual input balanced output differential amplifier when, RE=RC=65 KΩ. Assume IE=IC, β=100 for both transistors Q1 and Q2; VS=± 12 V.
6 M
2 (b) What is the need of frequency compensation? Explain any one method of frequency compensation.
6 M
Answer any one question from Q3 and Q4
3 (a) Design a lossy integrator with square wave input of 2 Vp-p and 5 Khz frequency. Draw input and output waveforms.
6 M
3 (b) Explain with a neat circuit diagram working of symmetric Schmitt trigger using op-amp. Also derive the equation for the trigger points.
6 M
4 (a) Design an adder using op-amp to get output expression as:
V0= - (2V1 + 3V2+5V3) Where V1, V2 and V3 are inputs.
6 M
Answer any one question from Q5 and Q6
5 (a) With a neat circuit diagram, explain voltage to frequency Converter.
5 M
5 (b) Write a short note on Binary weighted Digital to Analog Converter (DAC).
5 M
5 (c) What output voltage would be produced by a D/A converter whose output range is 0 to 10 V and input binary number is:
(i) 10 (for a 2-bit DAC converter)
(ii) 0110 (for a 4-bit DAC)
(iii) 10111100 (for a 8-bit DAC).
3 M
6 (a) Write a short note on Flash type Analog to Digital Converter.
5 M
6 (b) What are the different types of V to I converter. Explain any one.
5 M
6 (c) List various specification of ADC.
3 M
Answer any one question from Q7 and Q8
7 (a) With the help of neat block diagram explain operation of PLL.
5 M
7 (b) What is the need of current boosting circuit ? Explain with the help of any one circuit.
5 M
7 (c) Draw block diagram of frequency multiplier. Draw input-output waveforms.
3 M
8 (a) For PLL circuit shown in Fig. 1, calculate the following:
(i) Free running frequency
(ii) Lock range
(iii) Capture range
6 M
8 (b) Write a short note on practical voltage regulator using LM317.
5 M
8 (c) Explain the following terms: | 668 | 2,391 | {"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} | 2.78125 | 3 | CC-MAIN-2024-26 | latest | en | 0.821465 |
https://www.rdocumentation.org/packages/base/versions/3.4.3/topics/is.finite | 1,718,941,586,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862036.35/warc/CC-MAIN-20240621031127-20240621061127-00519.warc.gz | 832,070,996 | 9,155 | base (version 3.4.3)
# is.finite: Finite, Infinite and NaN Numbers
## Description
`is.finite` and `is.infinite` return a vector of the same length as `x`, indicating which elements are finite (not infinite and not missing) or infinite.
`Inf` and `-Inf` are positive and negative infinity whereas `NaN` means ‘Not a Number’. (These apply to numeric values and real and imaginary parts of complex values but not to values of integer vectors.) `Inf` and `NaN` are reserved words in the R language.
## Usage
```is.finite(x)
is.infinite(x)
is.nan(x)Inf
NaN```
## Arguments
x
R object to be tested: the default methods handle atomic vectors.
## Value
A logical vector of the same length as `x`: `dim`, `dimnames` and `names` attributes are preserved.
## Details
`is.finite` returns a vector of the same length as `x` the jth element of which is `TRUE` if `x[j]` is finite (i.e., it is not one of the values `NA`, `NaN`, `Inf` or `-Inf`) and `FALSE` otherwise. Complex numbers are finite if both the real and imaginary parts are.
`is.infinite` returns a vector of the same length as `x` the jth element of which is `TRUE` if `x[j]` is infinite (i.e., equal to one of `Inf` or `-Inf`) and `FALSE` otherwise. This will be false unless `x` is numeric or complex. Complex numbers are infinite if either the real or the imaginary part is.
`is.nan` tests if a numeric value is `NaN`. Do not test equality to `NaN`, or even use `identical`, since systems typically have many different NaN values. One of these is used for the numeric missing value `NA`, and `is.nan` is false for that value. A complex number is regarded as `NaN` if either the real or imaginary part is `NaN` but not `NA`. All elements of logical, integer and raw vectors are considered not to be NaN.
All three functions accept `NULL` as input and return a length zero result. The default methods accept character and raw vectors, and return `FALSE` for all entries. Prior to R version 2.14.0 they accepted all input, returning `FALSE` for most non-numeric values; cases which are not atomic vectors are now signalled as errors.
All three functions are generic: you can write methods to handle specific classes of objects, see InternalMethods.
## References
The IEC 60559 standard, also known as the ANSI/IEEE 754 Floating-Point Standard.
D. Goldberg (1991) What Every Computer Scientist Should Know about Floating-Point Arithmetic ACM Computing Surveys, 23(1). Postscript version available at http://www.validlab.com/goldberg/paper.ps Extended PDF version at http://www.validlab.com/goldberg/paper.pdf
The C99 function `isfinite` is used for `is.finite`.
`NA`, ‘Not Available’ which is not a number as well, however usually used for missing values and applies to many modes, not just numeric and complex.
`Arithmetic`, `double`.
## Examples
Run this code
``````# NOT RUN {
pi / 0 ## = Inf a non-zero number divided by zero creates infinity
0 / 0 ## = NaN
1/0 + 1/0 # Inf
1/0 - 1/0 # NaN
stopifnot(
1/0 == Inf,
1/Inf == 0
)
sin(Inf)
cos(Inf)
tan(Inf)
# }
``````
Run the code above in your browser using DataLab | 802 | 3,094 | {"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-2024-26 | latest | en | 0.792174 |
http://slideplayer.com/slide/4034500/ | 1,527,111,531,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794865809.59/warc/CC-MAIN-20180523200115-20180523220115-00368.warc.gz | 273,915,359 | 18,022 | # 9/22/2013PHY 711 Fall 2013 -- Lecture 121 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 12: Continue reading.
## Presentation on theme: "9/22/2013PHY 711 Fall 2013 -- Lecture 121 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 12: Continue reading."— Presentation transcript:
9/22/2013PHY 711 Fall 2013 -- Lecture 121 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 12: Continue reading Chapter 3 & 6 1.Hamiltonian formalism 2.Phase space 3.Liouville’s theorem
9/22/2013PHY 711 Fall 2013 -- Lecture 122
9/22/2013PHY 711 Fall 2013 -- Lecture 123 Hamiltonian formalism
9/22/2013PHY 711 Fall 2013 -- Lecture 124 Hamiltonian formalism and time evolution:
9/22/2013PHY 711 Fall 2013 -- Lecture 125 Poisson brackets: Hamiltonian formalism and time evolution:
9/22/2013PHY 711 Fall 2013 -- Lecture 126 Poisson brackets -- continued: Liouville theorem
9/22/2013PHY 711 Fall 2013 -- Lecture 127 Phase space
9/22/2013PHY 711 Fall 2013 -- Lecture 128 x p Phase space diagram for one-dimensional motion due to constant force
9/22/2013PHY 711 Fall 2013 -- Lecture 129 Phase space diagram for one-dimensional motion due to spring force
9/22/2013PHY 711 Fall 2013 -- Lecture 1210 Liouville’s Theorem (1838) The density of representative points in phase space corresponding to the motion of a system of particles remains constant during the motion.
9/22/2013PHY 711 Fall 2013 -- Lecture 1211 Liouville’s theorem x p (x,p) (x+ x,p) (x+ x,p+ p) (x,p+ p)
9/22/2013PHY 711 Fall 2013 -- Lecture 1212 Liouville’s theorem -- continued x p (x,p) (x+ x,p) (x+ x,p+ p) (x,p+ p)
9/22/2013PHY 711 Fall 2013 -- Lecture 1213 Liouville’s theorem -- continued x p (x,p) (x+ x,p) (x+ x,p+ p) (x,p+ p)
9/22/2013PHY 711 Fall 2013 -- Lecture 1214 Importance of Liouville’s theorem to statistical mechanical analysis: In statistical mechanics, we need to evaluate the probability of various configurations of particles. The fact that the density of particles in phase space is constant in time, implies that each point in phase space is equally probable and that the time average of the evolution of a system can be determined by an average of the system over phase space volume.
9/22/2013PHY 711 Fall 2013 -- Lecture 1215 Virial theorem (Clausius ~ 1860)
Download ppt "9/22/2013PHY 711 Fall 2013 -- Lecture 121 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 12: Continue reading."
Similar presentations | 798 | 2,601 | {"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} | 2.84375 | 3 | CC-MAIN-2018-22 | latest | en | 0.506966 |
https://www.rdocumentation.org/packages/spatialEco/versions/1.3-2/topics/poly.regression | 1,611,186,372,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703522133.33/warc/CC-MAIN-20210120213234-20210121003234-00502.warc.gz | 949,994,815 | 6,095 | # poly.regression
0th
Percentile
##### Local Polynomial Regression
Calculates a Local Polynomial Regression for smoothing or imputation of missing data.
This is a wrapper function for loess that simplifies data smoothing and imputation of missing values. The function allows for smoothing a vector, based on an index (derived automatically) or covariates. If the impute option is TRUE NA values are imputed, otherwise the returned vector will still have NA's present. If impute and na.only are both TRUE the vector is returned, without being smoothed but with imputed NA values filled in. The loess weight function is defined using the tri-cube weight function w(x) = (1-|x|^3)^3 where; x is the distance of a data point from the point the curve being fitted.
##### Usage
poly.regression(
y,
x = NULL,
s = 0.75,
impute = FALSE,
na.only = FALSE,
ci = FALSE,
...
)
##### Arguments
y
Vector to smooth or impute NA values
x
Optional x covariate data (must match dimensions of y)
s
Smoothing parameter (larger equates to more smoothing)
impute
(FALSE/TRUE) Should NA values be inputed
na.only
(FALSE/TRUE) Should only NA values be change in y
ci
(FALSE/TRUE) Should confidence intervals be returned
...
Additional arguments passed to loess
##### Value
If ci = FALSE, a vector of smoothed values, otherwise a list object with:
• loess - A vector, same length of y, representing the smoothed or inputed data
• lower.ci - Lower confidence interval
• upper.ci - Upper confidence interval
loess for loess ... model options
##### Aliases
• poly.regression
##### Examples
# NOT RUN {
x <- seq(-20, 20, 0.1)
y <- sin(x)/x + rnorm(length(x), sd=0.03)
p <- which(y == "NaN")
y <- y[-p]
r <- poly.regression(y, ci=TRUE, s=0.30)
plot(y,type="l", lwd=0.5, main="s = 0.10")
y.polygon <- c((r$lower.ci)[1:length(y)], (r$upper.ci)[rev(1:length(y))])
x.polygon <- c(1:length(y), rev(1:length(y)))
polygon(x.polygon, y.polygon, col="#00009933", border=NA)
lines(r\$loess, lwd=1.5, col="red")
# Impute NA values, replacing only NA's
y.na <- y
y.na[c(100,200,300)] <- NA
p.y <- poly.regression(y.na, s=0.10, impute = TRUE, na.only = TRUE)
y - p.y
plot(p.y,type="l", lwd=1.5, col="blue", main="s = 0.10")
lines(y, lwd=1.5, col="red")
# }
Documentation reproduced from package spatialEco, version 1.3-2, License: GPL-3
### Community examples
Looks like there are no examples yet. | 680 | 2,385 | {"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} | 3.015625 | 3 | CC-MAIN-2021-04 | latest | en | 0.598282 |
http://multiwingspan.co.uk/cipher.php?page=atbash | 1,539,958,811,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583512400.59/warc/CC-MAIN-20181019124748-20181019150248-00115.warc.gz | 276,361,185 | 3,127 | # Atbash Cipher
## Introduction
The Atbash cipher is a substitution cipher originally applied to the Hebrew alphabet. Its name derives from the Hebrew names of some letters. Its cipher alphabet is as follows,
Plain 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 Cipher Z Y X W V U T S R Q P O N M L K J I H G F E D C B A
In simple terms, the cipher alphabet is the reverse of the plain alphabet.
## Programming Atbash
If you were writing an algorithm to implement Atbash as your first cipher, you would probably look at the mathematical relationship between the positions of letters in the plain and cipher alphabets. If you number the letter positions of the plain alphabet from 0 to 25, then the letter you substitute is always 25 minus the position of the current letter. A is position 0 and is replaced with Z at position 25 (25 - 0 = 25). B is position 1 and is replaced with Y at position 24 (25 - 1 = 24).
We can also use the arbitrary letter substitution pseudocode if we replace the cipher alphabet with the Atbash cipher alphabet,
``` cipherAlphabet ← "ZYXWVUTSRQPONMLKJIHGFEDCBA" plain ← "The secret is out." upper ← UPPERCASE(plain) cipherText ← "" FOR letter ← 0 TO upper.LENGTH - 1 tmpASC ← ASCII CODE OF upper[letter] IF tmpASC > = 65 AND tmpASC <= 90 THEN cipherText ← cipherText + cipherAlphabet[tmpASC-65] ELSE cipherText ← cipherText + upper[letter] END IF END FOR OUTPUT cipherText```
## Challenges
One obvious challenge is to implement both algorithms for Atbash.
As with ROT-13, Atbash throws up a few quirky situations where encrypted words make other words. This approach is claimed to be used in a few places in ancient religious texts. You can use word lists and dictionaries to uncover some of these for yourself. Here are a few,
ALL ZOO ARK ZIP ART ZIG GILT TROG GIRL TRIO GLOW TOLD GROG TILT HOB SLY HOLD SLOW HOLY SLOB HORN SLIM ILL ROO IRK RIP OLD LOW | 507 | 1,925 | {"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-2018-43 | longest | en | 0.855656 |
https://www.answers.com/Q/How_the_apparent_change_of_position_of_constellations_over_time_provides_evidence_of_earths_revolution_around_the_sun | 1,708,693,202,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474412.46/warc/CC-MAIN-20240223121413-20240223151413-00891.warc.gz | 654,285,686 | 47,554 | 0
# How the apparent change of position of constellations over time provides evidence of earths revolution around the sun?
Updated: 12/2/2022
Wiki User
8y ago
Be notified when an answer is posted
Earn +20 pts
Q: How the apparent change of position of constellations over time provides evidence of earths revolution around the sun?
Submit
Still have questions?
Related questions
### How does the change in the apparent position of the constellations provide evidence for earth's rotation and revolution?
A guess was made as to the layout and behavior of the players, then this model extrapolated to see if it matched the real thing.
### The fact that the position of the constellations seems to change throughout the year is evidence that?
the earth is revolving
### Where does the earth have to be in order to see constellations?
The earth's position has no affect on constellations' visibility. The position of the viewer on the surface of the earth will affect what constellations are visible.
### A constellations changing position in the sky at the same time of the evening over a period of several weeks is evidence that what?
Earth's rotation around the Sun.
### One lines of evidence of earth's revolution around the sun is?
It is the varying position of a constellation over a period of weeks.
### Why do you name meteor showers after constellations?
Periodic showers which, due to their position and trajectory, appear to originate from specific constellations are named for that constellation.
### Does the constellation Eridanus change from hour to hour and if so what direction does it move in?
No, the constellations appear to be moving but it is the earth that is rotating around the constellations. The constellations rise and set but they dont change position.
Motion
duhhh
### The fact that the position of the constellations seems to change throughout the year is?
Earth is revolving....
### What is constellations changing position in the night sky due to?
That is due to the rotation of Earth.
### What are the evidences that earth revolves around the sun?
Several pieces of evidence. For example, the parallax: the apparent position of a nearby star changes slightly, because of the change in Earth's position. That is, its position now will not be exactly the same as its position 6 months later, when Earth is on the other side of its orbit. This is used to calculate the distance of nearby stars. | 514 | 2,448 | {"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-2024-10 | latest | en | 0.925013 |
http://excel.bigresource.com/Index-function-data-identified-based-on-a-list-of-account-numbers-and-return-this-data-to-a-new-sheet-MO9MR1bO.html | 1,550,483,543,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550247484928.52/warc/CC-MAIN-20190218094308-20190218120308-00194.warc.gz | 89,682,766 | 14,772 | # Index Function - Data Identified Based On A List Of Account Numbers And Return This Data To A New Sheet
May 8, 2007
I have a multiple column spreadsheet (Call it- "Money") whereby I need the data identified based on a list of account numbers and return this data to a new sheet.
In "Money" I have:
IE; columns B, C respectively have cust #A100 & 20.00
columns E, F respectively have cust #B100 & 40.00
columns G,H respectively have cust #C100 & 60.00
Etc.
(above for illustration-there are 100 lines of data in these columns with varied account numbers and respective dollars)
So what I have now is a new sheet I have named "Control". I have listed all my account numbers like A100,B100 etc. in column A. These are the account numbers for ident purposes.
I need the data entered in "Money" identified by those columns B,E,G with respective amounts from C,F,H and based on the list I have in "Control" whereby in "Control" if A100 is listed in column A then the figure to be returned in column B is all the data bits found in all columns C,F,H from the entire sheet "Money". Tough to explain but ie below....
## Index Function To Return List Of Values
Apr 3, 2012
I am looking for a formula which will return the names of in Column A where Column B is equal to 0.
ColumnA
David ColumnB
0 Joe 0 Susan 1 Steve 2 Janet 0 Bonnie 8 Emma 8
## Offset / Index / Match - Using 3 Functions To Search For And Return Values From Data Sheet
Jan 19, 2014
Trying to grasp the concept of using these 3 functions to search for and return values from a data sheet.
The attached spread sheet has performance data for a group of employees.
What I need to do is find a particular employee then return a value for one of the category's.
For instance, I need to find "10TE03 ANGIE HOLLIS" Parts Usage on color or cell C10 in the attached sample.
Sometimes new category's are added to column A adding to the number of rows so a simple offset is not reliable.
Once I get that working, I then need to use a named range to total and average different data points for groups of employees by teams.
Maybe Offset-Index-Match is not even the way to go here?
## Index - Match Function To Output Data Based On User Input
Apr 30, 2009
I have a list of data that I'm using the index - match function to output data based on user input.
For example, I have:
1 10
2 15
3 20
So when '1' is selected another cell outputs '10'.
However what I want is for example if 1.25 is input, I want it to interpolate to spit out the correct number between 10 and 15.
## Mapping Account . How To Add Additional Data In To Account#
Aug 21, 2009
I have two sheets. First contains Department # 0002549, and the other one contains 5 more digits(#02001 0002549). I will need to find the exact match for the first sheet to contain all 12 digits. THey are all in different order, so I probably have to match them first then add whatever the first 5 digits number. How should I tackle this issue? I was thinking to use vlookup but how could you use vlook up if only last 7 digit matches and add addtional digits to exisiting number?
## Calculate Profit And Loss Data Based Off Lots Of Account Criteria?
Jun 15, 2014
I'm trying to design a Profit and Loss template that calculates off an accounting software data dump. I will attempt to explain the problem here but I have included a summary in the linked workbook which would be easier.
I have two problems:
The Formula: Basically, I need to calculate every cell in the Profit and Loss statement based on the below criteria: The Profit and Loss item accounts, e.g. Gross Income has 6 accounts. There is a reference table for these - so incorporate index match/vlookup? User selected data from 4 combo boxes.
I am thinking a SUMIFS formula (using the combo box values) and somehow combining a vlookup to pull the items accounts. I'm starting to think that VBA is the best method?
Tweaking: The attached workbook is a small example. The full data dump contains 60,000 rows.
## Return Data To Another Sheet Based On Criteria
Jul 28, 2006
Sheet 1
Column A = Dates
Row 1 = Filenames
I enter a Y in the intersecting cells of the Filenames & Dates to show which files were downloaded.
I need is a formula that will rearrange this layout onto Sheet 2 so that each ‘Y’ (downloaded) filename is inserted in a cell corresponding to the Date.
(see attached sample)
## Sum Accounts Based On Middle 2 Numbers In Account Code
Jul 17, 2012
I have a large workbook that contains hundreds of account codes and values. For example, cell A2 contains the account code "55021357122 Global Business Sales", cell A3 contains code "55021753221 Global Business Purchases" and so on through the column. Column B contains the values.
I need a formula that will sum all the values in column B if the middle 2 number are "21" (positions 4 & 5 in the number). My current range for column A is A6:A366. I've tried SumIFs but that fails on the array because it fails on the MID function.
## Formula To Add Up Values Based On Range Of Account Numbers
Apr 2, 2013
I would like a formula to add up values in Col E based on a range of account numbers in Col C
For eg adding up Sales values in Col E based on Account number being series 3000-3015 in Col C (this particular series must exclude numbers ending in an alpha). I also have account numbers ending in an Alpha where I need to add up the values pertaining to these for eg 3000D-3015D, 3000K-3015K etc.
## Getting Function That Will Return Numerical Value Based On Dropdown List
Aug 3, 2014
What I am trying to do is have a drop down list in one cell and have the next cell bring in the correct price for the item in the first cell. Sounds fairly easy? Well both lists are 200 items.
I have been trying to do this with just three items so far. On sheet two, I have created two lists. The first list in column A contains dogs, cats, mice. The second list in column B contains 1, 2, 3. On sheet one, I have created the drop down list for the animals in the A12 cell. I would like for B12 to auto populate the corresponding number to the animal without having to create an if formula for each animal and number.
## Show List Of Data Based On Value In A Column On Another Sheet
Jun 26, 2014
formula to use in my report
Let's say I have a summary table on Sheet 1 6000 rows of data on sheet 2.
In Sheet 2 I have 3 columns, Name, Month and Score. Name Column (A) has names of students Month Column (B) has months January, February and so on. Score Column (C) has data from Green, Yellow and Red. Red is if they failed.
In the summary table on Sheet 1, I need to show all the names that got a "Red" Score. And their corresponding months.
It should look like this.
Month l Name l Score
-----------------------------------------
January l Mike J l Red
-----------------------------------------
March l Joe M l Red
## Index Function For Filtered Data
Jun 10, 2006
I have a table A3:C118 and I am filtering the data and finding the subtotal for the maximum value in column C. How do I find the corresponding data point for column A? I have tried several formulas and they are not giving me exactly what I need.
## Conditional PRODUCT Function Formula (return The Product Of A List Of Numbers In A Column)
Sep 30, 2009
I am trying to use a PRODUCT formula to return the product of a list of numbers in a column, between 2 specified dates. The spreadsheet is arranged as follows:
Column BA list of dates
Column C & DNumerical data not used in any calculations
Column EThe numbers to multiply together
Cell A1Start date to be used in the PRODUCTformula
Cell A2End date to be used in the PRODUCT formula
The formula I have to multiply the data in column E, subject to the start and end dates in Column A is:
{=PRODUCT(IF(B15:B1000>A1,IF(B15:B1000<=A2,INDEX(B15:E1000,0,4))))}
This returns zero though works appropriately if I replace “PRODUCT” with a “SUM”.
## Index Formula (find The Relevant Data And Return In To Sheet2)
Oct 26, 2009
I have a spreadsheet with multiple columns. (Sheet1) The heading row is my customer name. (Sheet1) My column are the dates. On another spreadsheet, I would like to find the customer in Sheet2 in Sheet1, then do an index to find the relevant data I need, returned in Sheet2.
Sheet2: find customer "ABC" in Sheet1, if found, then find the date that also matches Sheet1 and Sheet2, and return data "apple" .
sheet1
DATE ABC DEF
2007-04-01 £55.60 £61.13
2007-04-02 £56.33 £60.27
2007-04-03 £52.14 £62.58
2007-04-04 £51.69 £61.28
sheet2
CUSTOMER DATE RATE
DEF 2007-04-04 This should be £61.28
ABC 2007-04-02 This should be £56.33
## Index Match Vs D Function To Summarize Data
Oct 24, 2008
I have a project that has several worksheets of "summarized" data all pulled from one worksheet. The data worksheet is run through an external program and pasted into the workbook to update the information.
To this point I have used tons of index match array formula's to pull the information but I've found this to be extremely inefficient because there are hundreds if not thousands of formulas, and it takes several minutes to update. The file is also around 3MB which is way too big.
I was thinking about using VBA to simplify the worksheets, but then I came across an article about D_Functions and I'm thinking they may be the solution to my problems.
However there is one catch...I'm not sure how I would build these formulas to work in my worksheets. I understand the principle behind the D_Functions, but I can't seem to grasp the concept of integration and making it work in my scenario.
I've attached an example of this workbook, it has most of the forumla's deleted out to reduce the file size, but it should give you an idea of what I'm doing. Once you open it you'll have to unhide some columns to get to the nitty gritty of the sheet.
Feel free to take a gander...I'm open to any suggestions you may have at this point (except to trash the whole project hehehehe ). If you find a solution please explain the concept behind it. I really want to learn how to make this work rather than plugging in someone elses formulas.
## Copy Data Of Index Match Function According Date?
Jun 24, 2014
I have the first sheet named "DPF" where I have a column "Date", "FIT", "Group" On my second Sheet named "Tracker" what I do want to do:
I select a date for example 18-07-2014 (Cell E3), if cell E4 I Have "Fit" and F4 "Group" In C6 I have E3-15, to get the date minus 15 days (03-07-2014) In C7 I have E3-12 (06-07-2014) and so on
What I want is, if the date of today is C6 or C7 or whatever, use the index match function to get the number corresponding to the date chosen (18-07-2014) for the FIT. But, once I get the figure, I want to keep it, because with the if function, once we are the 4th of July, the figure for C6 disappears...
Fri
18-Jul
FITGroup
Start
D-1503-Jul
D-1206-Jul
D-909-Jul
D-612-Jul
D-615-Jul
D-216-Jul
D-117-Jul
D18-Jul
So either a macro to copy the specific data into another sheet or a another way to keep it. Because the idea as the end is to do different scenario based on the result got per period..
## How To Handle Duplicate Data Using Index And Match Function
Feb 4, 2014
How to deal with duplicate data in excel using index and match function. Is it possible to use the following function without having a unique value?
## Return Cell On Separate Sheet Based On Selection From Drop Down List?
Mar 18, 2014
I am trying to create individualized worksheets based off a master worksheet. I have different committee names that I want to appear on the individualized sheets, based on whether the person is apart of that committee or not. On my master sheet, I choose the persons name under the committee and I want that committee name to show on the individualized sheet. For example, I want A1 on Master to show on Name 1, B3 and A10 on Master to show on Name 1, C3. Can I write a formula to achieve this or or am I asking too much? In my actual file, I will have about 10 names and 5 committees with one person being on up to all 5 of the committees.
## Index Function - Return Only First Record
Feb 13, 2014
I have attached a sheet with what I am trying to accomplish...
I have several records that I am doing a lookup through. Most records have the same "work order number". As you can see on the attached sheet, my lookup function returns all the work order numbers that match my criteria.
What I need is to only return the first instance of the work order number then return the next unique work order number that meets my criteria.
Attachment 297239!
## Use INDEX Function To Return Blanks?
Jan 30, 2003
Is there a way to use the INDEX function to return Blanks or NAs instead of zeros when the corresponding row & column match is a blank/null cell?
e.g. =INDEX(F10:H13,1,1) returns 0 even if cell F10 is blank?
## Formula / Function To Collect Data From Multiple Sheets And Store Data In One Sheet?
Dec 17, 2013
- I have total of 13 sheets in a workbook - 12 sheets represent 12 months with data; 13th sheet is single sheet in which i would like to get complete overview of 12 months
- each of 12 sheets has actually sales results for multiple products with following data: internal code, manufacturer part number, name, and qty sold in that month
- situation is that some products have been phased out during the year and some were introduced so each sheet is slightly different in terms of in which row certain product is located
What i would like to achive is to make 13th sheet (whole year overview) do the following:
- there is a list of all the products in it, each product has unique internal code - this code (from each line) should be used to find that code in each monthly sheet, then find its monthly sales value (copy it) and paste it in sheet 13 in cell that represents this product and particular month.
In other words i would like to see for each product what was monthly sales throughout this year, but avoid manually filling in qty for each product per month.
## Double Click Row To Return Data To Userform For Edit Then Return Back To Sheet
Jan 30, 2014
I am trying to create a data entry sheet to enter quotes on. When a quote is received, I click on my "Add quote" button and a userform appears. Data is entered into the userform (frmEntryForm) and returned back to the next available row.
I also need to be able to:
Edit a row by double-clicking it. When a row is double-clicked, data from that row is passed back to the userform, edited and returned back to the same row (to prevent duplicates).Validate that all fields are complete within the userform where relevant (i.e. if the work is not complete or in progress then the "Invoice Number" and "Actual Cost" fields are disabled and blanked to prevent entry (I think this is almost sorted judging by my tests)
I have attached my sheet : 2014 Gatwick Quote Log (Macro Enabled).xlsm‎
## Index Function With Multiple Ifs Won't Return More Than First Result
Aug 11, 2014
I am attempting to get an INDEX function with multiple "IF" statements to return more than one result. Building multiple IF statements. That portion of the below formula works. However, I can only get the INDEX formula to return the first, single result.
Formula:
=IFERROR(INDEX(Func_Area,SMALL(IF(Const_Start<=DATE(YEAR(\$B\$2),MONTH(\$B\$2),DAY(\$B\$2)), IF(Cost_End>=DATE(YEAR(\$C\$2),MONTH(\$C\$2),DAY(\$C\$2)),ROW(Func_Area)-MIN(ROW(Func_Area))+1,"")),ROWS(\$A\$4:A4)))," ")
Func_Area,Const_Start,Cost_End are all Named Ranges on Sheet "Proposed". My intention is to return a list of projects on Sheet Test1 for all projects starting construction after a certain date and completing construction before a certain date. I suspect something in my ROWS fuction or ROW-MIN+1 is wrong.
This formula returns the first result in the first row, but every subsequent row is blank...see attached spreadsheet.
## Create Index Of Sheet Data
Jan 7, 2010
Is it possible to create an index of cell data (in my case personal names)? And if so can it be done so that each entry is a button to click to go to the cell?
Would save a lot of manual labour....
## Formula Needed To Copy Same Set Of Data From Cells And INDEX Into A List
Nov 27, 2012
I have a list of data in columns Q R S and i need to in between each line insert the data from columns D E F underneath and then underneath that the data from G H I
so bascially i have a list at the moment like this
Q
R
S
[Code]....
There is 2 sheets in total , 1 i need to inc 1-1 draw as above and the other sheet to be exc the 1-1 draw . I have attached an example of what i am trying to achieve . can offer as i have had this on excelforum.com with over 150 views and no solution
## Using If Function To Pull Data From One Cell Based On Data From Merged Cells
Jul 24, 2014
Looking for a formula to accomplish the following:
I'm trying to populate cell A31 on a worksheet titled "VolumeTotals" with the data in Cell E23 from a worksheet titled "CurrentCustomers" if the merged cells F3-F22 on worksheet "CurrentCustomers" are equal to the word "Contract".
## VBA Code To Pull Data From A Sheet Based On Date And Add That Data To Another Sheet?
Aug 8, 2014
I use my workbook to track sales data from one store to the next. I use my workbooks to compare data from year to year. Each year's data is displayed on a separate worksheet. '2013' has 2013's data, '2014' has 2014's. On the 2014 sheet, I have a Prior Year's Sales that pulls data from the previous year's spreadsheet using a formula which I just drag down each day I enter sales. I would like to automate this process and have the VBA code check for today's date and automatically pull the previous year's sales data from the '2013' sheet and put it in the appropriate cell on the '2014' worksheet. I hope I have explained this well enough to understand. I've included a link to my workbook for reference.
I had to use dropbox since I can't post a file over 1 MB. The file size is around 1.25 MB.
## Formula To Return Array To Use In Index / Match Function?
May 8, 2013
I need to find a way to find an array in a tab to use for an index/match function I have.
this is what i would normally use: =index(tab_array,match(\$a2, tab!\$a\$1:\$a\$1000,0),match(\$B\$1,tab!\$a\$1:\$zz\$1,0))
This formula would usually work fine when I know that within the tab, the array in which the row match is searching doesn't change. However, that array may change in the future, to say column H, without my knowing as it is a database that gets automatically populated from an upstream system.
Is there a way to search for an array within an index/match?
## Activate Sheet Identified By Cell Next To Button
Aug 15, 2008
I have an index page with hundreds of worksheets (poor spreadsheet design i know) I am looking for a button to go next to the sheet name on the index sheet, read the cell in the button's macro code and when pushed go to that sheet's location. I can easily make a button to go to one sheet but with hundreds of sheets this becomes a monotonous task. Example
Index Sheet
Sheet 2 (Button) <-- Button reads the text, takes you to the "Sheet 2" location
Sheet 3 (Button)
Sheet 4 (Button
Sheet 5 (Button)
## Data From Sheet A To Appear In Sheet B Based On Data Posted In A Column In Sheet A?
Jan 1, 2014
I have a workbook where Sheet A is a Master Order Form. Employees will input the quantities they need in Column C. The sheet will be otherwise protected. Sheet B is a "printable" order form that only contains the rows from Sheet A where the Quantity on Sheet A is not blank and is >=1. This will allow me to print sheet B with no blank rows for the items I don't need.
I found the following formula which claims to be able to do what I want:
=IF(ROWS(\$1:1)>MAX(C:C),"",INDEX(A:A,MATCH(ROWS(\$1:1),C:C,0)))
I can't get it to work correctly across two sheets.
I've attached Sample of spreadsheet for review : HDForm_Test01.xlsx | 4,947 | 19,980 | {"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-2019-09 | latest | en | 0.862728 |
https://philip.greenspun.com/blog/2014/03/15/stealing-and-stashing-a-boeing-777/ | 1,575,763,421,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540503656.42/warc/CC-MAIN-20191207233943-20191208021943-00496.warc.gz | 489,160,963 | 13,070 | Stealing and stashing a Boeing 777?
Friends have been asking me, usually prefaced with “I’m not typically prone to conspiracy theory,” about the difficulty of stealing and hiding a Boeing 777. I’m hoping this is because of my experience as an airline pilot and not because they think that I am an expert on stealing and hiding things…
Anyway, one question that they seem to have is how big an airport one needs for such an airplane. If you want to land in bad weather, with lots of safety margin, and have a nice terminal for passengers, the number of places where a B777 could be landed is pretty small. FAR 121.195 requires that a turbojet be able to land in 60 percent of the available runway. You need to assume that the thrust reversers have failed and the plane can be stopped only with brakes (plus spoilers that pop out of the wings, typically, to destroy lift and make the brakes more effective). Pilots don’t even try to land on the first 1000′, since a wind variation or pilot error might result in landing a bit short. Thus if one is going to land and roll 5000′ one needs a 10,000′ runway to be legal. (See this posting about my LaGuardia landing for why this FAA rule is prudent.) For departure you need to be able to accelerate to about 180 mph, lose an engine, think for one second, hit the brakes, and stop without running off the runway (or a special overrun area beyond). Alternatively you must be able to accelerate to about 180 mph, lose an engine (i.e., half of your power), and continue the takeoff with that one engine, clearing whatever obstacles are beyond the runway.
What if you are willing to assume that you’ll make a reasonably competent landing and that the thrust reversers will function normally? Certainly a B777 could be landed in 5000′ of runway (less than one mile). See this article on how a Boeing 747 was landed at a ridiculously small airport in South Africa. The calculated landing roll, without reverse thrust, was 3000′ (the article says “landing distance” so this might actually be 1000′ of flying and then 2000′ of rolling). An Air Canada crew managed land a Boeing 767 at an abandoned airport that originally had a 6800′ runway (Wikipedia) despite a lack of engine power that limited their use of flight controls and therefore necessitated a higher-than-normal approach speed.
Could you take off again from a short runway? Sure. In this test flight, a journalist reports lifting off in a 777 about 3300′ down the runway. A Southwest Airlines B737 joined the Cessna crowd at an airport with a 3700′ runway and took off again without incident (story).
I don’t have any special knowledge about Malaysia 370, but it would definitely be possible to land such a plane at an out-of-the-way or decommissioned airport, refuel it, and take off again.
What could a person do with a stolen Boeing 777? The parts don’t have as much commercial value as one might think, due to the fact that operators in most countries need to comply with a lot of regulations regarding the serial numbers and provenance of all of the parts that are placed onto a certified aircraft, particularly one of “transport class.” Countries that the U.S. government doesn’t like, such as Iran, have trouble operating Boeing airplanes because we make it tough for them to get spare parts (see Wikipedia story on Iran Air).
Those are the answers that I’ve given to friends. I’m about as confused by the situation as anyone else, however. Certainly my personal hope is that the plane is parked under a tarp somewhere and the passengers will eventually return home.
6 thoughts on “Stealing and stashing a Boeing 777?”
1. louie wear says:
i belive the 777 lost cabin pressure for some reason and the piolet didn’t get a chance to compleat his turn and the plane when on Auto till it ran out of fuel …was something like this happin to the Burino famility years aago
2. Steven says:
Over at my table we’re discussing why the plane rose to 45000 feet. Easier to kill the passengers by releasing cabin pressure, some say. Then the living pilots or hijackers could have traveled north by misidentifying itself to ATC as another plane. Bound for Uzbekistan/Iran or whereever the hijackers wanted the plane and the cargo.
http://www.telegraph.co.uk/news/worldnews/asia/malaysia/10700790/Malaysian-Airlines-MH370-how-much-do-we-really-know.html
If we suspect foul play, and we do, who’d be behind the foul play to obtain what?
3. Steve says:
What could a person do with a stolen Boeing 777? We could ask the vicious human beings that flew a pair of 767’s into a well known pair of buildings in New York one fine September morning not all that long ago, but fortunately, they were the first to meet their maker that day.
I sure hope that the NSA, the CIA, the FBI or whomever has got a bead on this, and that any great big freakin’ unknown blips heading into US territorial airspace are intercepted with all due diligence. To quote Han Solo (and a score of others) ….”I’ve got a bad feeling about this.”
4. frank says:
I am wondering if the on board computers,were tampered with.If was flown some were else I would look at secondary air fields,or abandon air fields in a 6 hour radius. another possibility. what has happen as in trans Canada air,flight that dispersed over Vancouver in the late 1940’s was not found until 50 years later this not unusal.IT happens all over the world.I believe what has most people concern is how something that big can just vanish.
5. swen says:
How difficult would it be to land a 777 on a grass, dirt, or unpaved landing strip? You know, making a short-field soft-field landing? I realize that this is a heavy and fully loaded plane. I looked on google map, and there are many small islands in that area. If this was a preplanned incident that’s where I would be looking.
6. Agreed – except I believe it was taken to reuse. On my blog at http://www.misterwriter.info I have a scenario for one possible use that I believe is feasible and somewhat easy if the plane was taken. See what you think. | 1,364 | 6,044 | {"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-2019-51 | latest | en | 0.951147 |
https://www.physicsforums.com/threads/vector-calculus-region-density-mass.953362/ | 1,618,156,478,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038064520.8/warc/CC-MAIN-20210411144457-20210411174457-00370.warc.gz | 1,061,606,825 | 19,767 | Vector calculus- region-density-mass
Homework Statement
View attachment 229290
The Attempt at a Solution
I am not sure what equation to use for the volume[/B]
Attachments
17.5 KB · Views: 623
3.4 KB · Views: 489
• 39245723_483901692074113_9059923629021593600_n.jpg
12.5 KB · Views: 435
Chandra Prayaga
The attempt that you posted is too small and I cannot click on it to get a better view. But from what I can see, I suggest the following.
1. Understand, from the ranges of x, y and z given by you, the shape of the region you are interested in. In other words, answer the first question and sketch the region. In your graph, you only showed a few isolated points. You did not sketch the region in space.
2. The relevant equation posted by you is not adequate. Density = mass / volume is good only if the density is constant. In your case, the density depends on position (your equation: ρ = 1 + z). Then you must use the differential form:
dm = ρ dV,
and integrate this to get the total mass. It will be a triple integral.
Jozefina Gramatikova
The attempt that you posted is too small and I cannot click on it to get a better view. But from what I can see, I suggest the following.
1. Understand, from the ranges of x, y and z given by you, the shape of the region you are interested in. In other words, answer the first question and sketch the region. In your graph, you only showed a few isolated points. You did not sketch the region in space.
2. The relevant equation posted by you is not adequate. Density = mass / volume is good only if the density is constant. In your case, the density depends on position (your equation: ρ = 1 + z). Then you must use the differential form:
dm = ρ dV,
and integrate this to get the total mass. It will be a triple integral.
I hope you can see the picture better now. I was wondering if I need the whole rectangle as a region or just the purple triangle that I sketched there?
Attachments
• 39391323_441607066351057_5453612862436016128_n.jpg
10.2 KB · Views: 195
• 39229078_246147629366978_5680765097081831424_n.jpg
21.3 KB · Views: 178
• 39177607_1094553904033685_3707489651934625792_n.jpg
23.1 KB · Views: 108
Last edited:
I guess it is just the triangle, because we have
Is my final equation ok?
Attachments
2.4 KB · Views: 115
• 39177658_527569687683464_3169768074417012736_n.jpg
16.6 KB · Views: 194
• 39177658_527569687683464_3169768074417012736_n.jpg
9.1 KB · Views: 129
Last edited:
haruspex | 684 | 2,459 | {"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 | 4 | CC-MAIN-2021-17 | longest | en | 0.912462 |
http://wikien4.appspot.com/wiki/Muhammad_ibn_Musa_al-Khwarizmi | 1,596,713,791,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439736902.24/warc/CC-MAIN-20200806091418-20200806121418-00372.warc.gz | 123,493,699 | 71,756 | Statue of aw-Khwārizmī carrying Astrowabe in Amir Kabir University, Tehran, Iran
Bornc. 780
Diedc. 850
EraMedievaw era (Iswamic Gowden Age)
Notabwe worksThe Compendious Book on Cawcuwation by Compwetion and Bawancing, Book of de Description of de Earf, Astronomicaw tabwes of Siddhanta
Notabwe ideasTreatises on awgebra and Indian numeraws
InfwuencedAbu Kamiw[1]
Muḥammad ibn Mūsā aw-Khwārizmī[note 1] (Persian: Muḥammad Khwārizmī محمد بن موسی خوارزمی; c. 780 – c. 850), Arabized as aw-Khwarizmi and formerwy Latinized as Awgoridmi, was a Persian[2][3][4] powymaf who produced vastwy infwuentiaw works in madematics, astronomy, and geography. Around 820 CE he was appointed as de astronomer and head of de wibrary of de House of Wisdom in Baghdad.[5]:14
Aw-Khwarizmi's popuwarizing treatise on awgebra (The Compendious Book on Cawcuwation by Compwetion and Bawancing, c. 813–833 CE[6]:171) presented de first systematic sowution of winear and qwadratic eqwations. One of his principaw achievements in awgebra was his demonstration of how to sowve qwadratic eqwations by compweting de sqware, for which he provided geometric justifications.[5]:14 Because he was de first to treat awgebra as an independent discipwine and introduced de medods of "reduction" and "bawancing" (de transposition of subtracted terms to de oder side of an eqwation, dat is, de cancewwation of wike terms on opposite sides of de eqwation),[7] he has been described as de fader[2][8][9] or founder[10][11] of awgebra. The term awgebra itsewf comes from de titwe of his book (de word aw-jabr meaning "compwetion" or "rejoining").[12] His name gave rise to de terms awgorism and awgoridm,.[13] as weww as Spanish guarismo[14] and Portuguese awgarismo meaning "digit".
In de 12f century, Latin transwations of his textbook on aridmetic (Awgoridmo de Numero Indorum) which codified de various Indian numeraws, introduced de decimaw positionaw number system to de Western worwd.[15] The Compendious Book on Cawcuwation by Compwetion and Bawancing, transwated into Latin by Robert of Chester in 1145, was used untiw de sixteenf century as de principaw madematicaw text-book of European universities.[16][17][18][19]
In addition to his best-known works, he revised Ptowemy's Geography, wisting de wongitudes and watitudes of various cities and wocawities.[20]:9 He furder produced a set of astronomicaw tabwes and wrote about cawendaric works, as weww as de astrowabe and de sundiaw.[21]:669 He awso made important contributions to trigonometry, producing accurate sine and cosine tabwes, and de first tabwe of tangents.
## Life
Few detaiws of aw-Khwārizmī's wife are known wif certainty. He was born into a Persian famiwy[4] and Ibn aw-Nadim gives his birdpwace as Khwarezm[22] in Greater Khorasan (modern Khiva, Xorazm Region, Uzbekistan).
Muhammad ibn Jarir aw-Tabari gives his name as Muḥammad ibn Musá aw-Khwārizmiyy aw-Majūsiyy aw-Quṭrubbawiyy (محمد بن موسى الخوارزميّ المجوسـيّ القطربّـليّ). The epidet aw-Qutrubbuwwi couwd indicate he might instead have come from Qutrubbuw (Qatrabbuw),[23] a viticuwture district near Baghdad. However, Rashed denies dis:[24]
There is no need to be an expert on de period or a phiwowogist to see dat aw-Tabari's second citation shouwd read "Muhammad ibn Mūsa aw-Khwārizmī and aw-Majūsi aw-Qutrubbuwwi," and dat dere are two peopwe (aw-Khwārizmī and aw-Majūsi aw-Qutrubbuwwi) between whom de wetter wa [Arabic 'و' for de conjunction 'and'] has been omitted in an earwy copy. This wouwd not be worf mentioning if a series of errors concerning de personawity of aw-Khwārizmī, occasionawwy even de origins of his knowwedge, had not been made. Recentwy, G.J. Toomer ... wif naive confidence constructed an entire fantasy on de error which cannot be denied de merit of amusing de reader.
Regarding aw-Khwārizmī's rewigion, Toomer writes:[25]
Anoder epidet given to him by aw-Ṭabarī, "aw-Majūsī," wouwd seem to indicate dat he was an adherent of de owd Zoroastrian rewigion. This wouwd stiww have been possibwe at dat time for a man of Iranian origin, but de pious preface to aw-Khwārizmī's Awgebra shows dat he was an ordodox Muswim, so aw-Ṭabarī's epidet couwd mean no more dan dat his forebears, and perhaps he in his youf, had been Zoroastrians.
Ibn aw-Nadīm's Kitāb aw-Fihrist incwudes a short biography on aw-Khwārizmī togeder wif a wist his books. Aw-Khwārizmī accompwished most of his work between 813 and 833. After de Muswim conqwest of Persia, Baghdad had become de centre of scientific studies and trade, and many merchants and scientists from as far as China and India travewed dere, as did aw-Khwārizmī[citation needed]. He worked in de House of Wisdom estabwished by de Abbasid Cawiph aw-Ma’mūn, where he studied de sciences and madematics, incwuding de transwation of Greek and Sanskrit scientific manuscripts.
Dougwas Morton Dunwop suggests dat Muḥammad ibn Mūsā aw-Khwārizmī might have been de same person as Muḥammad ibn Mūsā ibn Shākir, de ewdest of de dree Banū Mūsā.[26]
## Contributions
A page from aw-Khwārizmī's Awgebra
Aw-Khwārizmī's contributions to madematics, geography, astronomy, and cartography estabwished de basis for innovation in awgebra and trigonometry. His systematic approach to sowving winear and qwadratic eqwations wed to awgebra, a word derived from de titwe of his book on de subject, "The Compendious Book on Cawcuwation by Compwetion and Bawancing".[27]
On de Cawcuwation wif Hindu Numeraws written about 820, was principawwy responsibwe for spreading de Hindu–Arabic numeraw system droughout de Middwe East and Europe. It was transwated into Latin as Awgoritmi de numero Indorum. Aw-Khwārizmī, rendered as (Latin) Awgoritmi, wed to de term "awgoridm".
Some of his work was based on Persian and Babywonian astronomy, Indian numbers, and Greek madematics.
Aw-Khwārizmī systematized and corrected Ptowemy's data for Africa and de Middwe East. Anoder major book was Kitab surat aw-ard ("The Image of de Earf"; transwated as Geography), presenting de coordinates of pwaces based on dose in de Geography of Ptowemy but wif improved vawues for de Mediterranean Sea, Asia, and Africa.[citation needed]
He awso wrote on mechanicaw devices wike de astrowabe and sundiaw.
He assisted a project to determine de circumference of de Earf and in making a worwd map for aw-Ma'mun, de cawiph, overseeing 70 geographers.[28]
When, in de 12f century, his works spread to Europe drough Latin transwations, it had a profound impact on de advance of madematics in Europe.[citation needed]
### Awgebra
Left: The originaw Arabic print manuscript of de Book of Awgebra by Aw-Khwārizmī. Right: A page from The Awgebra of Aw-Khwarizmi by Fredrick Rosen, in Engwish.
The Compendious Book on Cawcuwation by Compwetion and Bawancing (Arabic: الكتاب المختصر في حساب الجبر والمقابلةaw-Kitāb aw-mukhtaṣar fī ḥisāb aw-jabr waw-muqābawa) is a madematicaw book written approximatewy 820 CE. The book was written wif de encouragement of Cawiph aw-Ma'mun as a popuwar work on cawcuwation and is repwete wif exampwes and appwications to a wide range of probwems in trade, surveying and wegaw inheritance.[29] The term "awgebra" is derived from de name of one of de basic operations wif eqwations (aw-jabr, meaning "restoration", referring to adding a number to bof sides of de eqwation to consowidate or cancew terms) described in dis book. The book was transwated in Latin as Liber awgebrae et awmucabawa by Robert of Chester (Segovia, 1145) hence "awgebra", and awso by Gerard of Cremona. A uniqwe Arabic copy is kept at Oxford and was transwated in 1831 by F. Rosen, uh-hah-hah-hah. A Latin transwation is kept in Cambridge.[30]
It provided an exhaustive account of sowving powynomiaw eqwations up to de second degree,[31] and discussed de fundamentaw medods of "reduction" and "bawancing", referring to de transposition of terms to de oder side of an eqwation, dat is, de cancewwation of wike terms on opposite sides of de eqwation, uh-hah-hah-hah.[32]
Aw-Khwārizmī's medod of sowving winear and qwadratic eqwations worked by first reducing de eqwation to one of six standard forms (where b and c are positive integers)
• sqwares eqwaw roots (ax2 = bx)
• sqwares eqwaw number (ax2 = c)
• roots eqwaw number (bx = c)
• sqwares and roots eqwaw number (ax2 + bx = c)
• sqwares and number eqwaw roots (ax2 + c = bx)
• roots and number eqwaw sqwares (bx + c = ax2)
by dividing out de coefficient of de sqware and using de two operations aw-jabr (Arabic: الجبر "restoring" or "compwetion") and aw-muqābawa ("bawancing"). Aw-jabr is de process of removing negative units, roots and sqwares from de eqwation by adding de same qwantity to each side. For exampwe, x2 = 40x − 4x2 is reduced to 5x2 = 40x. Aw-muqābawa is de process of bringing qwantities of de same type to de same side of de eqwation, uh-hah-hah-hah. For exampwe, x2 + 14 = x + 5 is reduced to x2 + 9 = x.
The above discussion uses modern madematicaw notation for de types of probwems dat de book discusses. However, in aw-Khwārizmī's day, most of dis notation had not yet been invented, so he had to use ordinary text to present probwems and deir sowutions. For exampwe, for one probwem he writes, (from an 1831 transwation)
If some one says: "You divide ten into two parts: muwtipwy de one by itsewf; it wiww be eqwaw to de oder taken eighty-one times." Computation: You say, ten wess a ding, muwtipwied by itsewf, is a hundred pwus a sqware wess twenty dings, and dis is eqwaw to eighty-one dings. Separate de twenty dings from a hundred and a sqware, and add dem to eighty-one. It wiww den be a hundred pwus a sqware, which is eqwaw to a hundred and one roots. Hawve de roots; de moiety is fifty and a hawf. Muwtipwy dis by itsewf, it is two dousand five hundred and fifty and a qwarter. Subtract from dis one hundred; de remainder is two dousand four hundred and fifty and a qwarter. Extract de root from dis; it is forty-nine and a hawf. Subtract dis from de moiety of de roots, which is fifty and a hawf. There remains one, and dis is one of de two parts.[29]
In modern notation dis process, wif x de "ding" (شيءshayʾ) or "root", is given by de steps,
${\dispwaystywe (10-x)^{2}=81x}$
${\dispwaystywe 100+x^{2}-20x=81x}$
${\dispwaystywe x^{2}+100=101x}$
Let de roots of de eqwation be x = p and x = q. Then ${\dispwaystywe {\tfrac {p+q}{2}}=50{\tfrac {1}{2}}}$, ${\dispwaystywe pq=100}$ and
${\dispwaystywe {\frac {p-q}{2}}={\sqrt {\weft({\frac {p+q}{2}}\right)^{2}-pq}}={\sqrt {2550{\tfrac {1}{4}}-100}}=49{\tfrac {1}{2}}}$
So a root is given by
${\dispwaystywe x=50{\tfrac {1}{2}}-49{\tfrac {1}{2}}=1}$
Severaw audors have awso pubwished texts under de name of Kitāb aw-jabr waw-muqābawa, incwuding Abū Ḥanīfa Dīnawarī, Abū Kāmiw Shujāʿ ibn Aswam, Abū Muḥammad aw-‘Adwī, Abū Yūsuf aw-Miṣṣīṣī, 'Abd aw-Hamīd ibn Turk, Sind ibn ‘Awī, Sahw ibn Bišr, and Sharaf aw-Dīn aw-Ṭūsī.
J.J. O'Conner and E.F. Robertson wrote in de MacTutor History of Madematics archive:
Perhaps one of de most significant advances made by Arabic madematics began at dis time wif de work of aw-Khwarizmi, namewy de beginnings of awgebra. It is important to understand just how significant dis new idea was. It was a revowutionary move away from de Greek concept of madematics which was essentiawwy geometry. Awgebra was a unifying deory which awwowed rationaw numbers, irrationaw numbers, geometricaw magnitudes, etc., to aww be treated as "awgebraic objects". It gave madematics a whowe new devewopment paf so much broader in concept to dat which had existed before, and provided a vehicwe for future devewopment of de subject. Anoder important aspect of de introduction of awgebraic ideas was dat it awwowed madematics to be appwied to itsewf in a way which had not happened before.[33]
R. Rashed and Angewa Armstrong write:
Aw-Khwarizmi's text can be seen to be distinct not onwy from de Babywonian tabwets, but awso from Diophantus' Aridmetica. It no wonger concerns a series of probwems to be sowved, but an exposition which starts wif primitive terms in which de combinations must give aww possibwe prototypes for eqwations, which henceforward expwicitwy constitute de true object of study. On de oder hand, de idea of an eqwation for its own sake appears from de beginning and, one couwd say, in a generic manner, insofar as it does not simpwy emerge in de course of sowving a probwem, but is specificawwy cawwed on to define an infinite cwass of probwems.[34]
According to Swiss-American historian of madematics, Fworian Cajori, Aw-Khwarizmi's awgebra was different from de work of Indian madematicians, for Indians had no ruwes wike de ''restoration'' and ''reduction''.[35] Regarding de dissimiwarity and significance of Aw-Khwarizmi's awgebraic work from dat of Indian Madematician Brahmagupta, Carw Benjamin Boyer wrote:
It is true dat in two respects de work of aw-Khowarizmi represented a retrogression from dat of Diophantus. First, it is on a far more ewementary wevew dan dat found in de Diophantine probwems and, second, de awgebra of aw-Khowarizmi is doroughwy rhetoricaw, wif none of de syncopation found in de Greek Aridmetica or in Brahmagupta's work. Even numbers were written out in words rader dan symbows! It is qwite unwikewy dat aw-Khwarizmi knew of de work of Diophantus, but he must have been famiwiar wif at weast de astronomicaw and computationaw portions of Brahmagupta; yet neider aw-Khwarizmi nor oder Arabic schowars made use of syncopation or of negative numbers. Neverdewess, de Aw-jabr comes cwoser to de ewementary awgebra of today dan de works of eider Diophantus or Brahmagupta, because de book is not concerned wif difficuwt probwems in indeterminant anawysis but wif a straight forward and ewementary exposition of de sowution of eqwations, especiawwy dat of second degree. The Arabs in generaw woved a good cwear argument from premise to concwusion, as weww as systematic organization – respects in which neider Diophantus nor de Hindus excewwed.[36]
Page from a Latin transwation, beginning wif "Dixit awgorizmi"
### Aridmetic
Awgorists vs. abacists, depicted in a sketch from 1508 CE
Aw-Khwārizmī's second most infwuentiaw work was on de subject of aridmetic, which survived in Latin transwations but wost in de originaw Arabic. His writings incwude de text kitāb aw-ḥisāb aw-hindī ('Book of Indian computation'[note 2]), and perhaps a more ewementary text, kitab aw-jam' wa'w-tafriq aw-ḥisāb aw-hindī ('Addition and subtraction in Indian aridmetic').[38][39] These texts described awgoridms on decimaw numbers (Hindu–Arabic numeraws) dat couwd be carried out on a dust board. Cawwed takht in Arabic (Latin: tabuwa), a board covered wif a din wayer of dust or sand was empwoyed for cawcuwations, on which figures couwd be written wif a stywus and easiwy erased and repwaced when necessary. Aw-Khwarizmi's awgoridms were used for awmost dree centuries, untiw repwaced by Aw-Uqwidisi's awgoridms dat couwd be carried out wif pen and paper.[40]
As part of 12f century wave of Arabic science fwowing into Europe via transwations, dese texts proved to be revowutionary in Europe.[41] Aw-Khwarizmi's Latinized name, Awgorismus, turned into de name of medod used for computations, and survives in de modern term "awgoridm". It graduawwy repwaced de previous abacus-based medods used in Europe.[42]
Four Latin texts providing adaptions of Aw-Khwarizmi's medods have survived, even dough none of dem is bewieved to be a witeraw transwation:[38]
• Dixit Awgorizmi (pubwished in 1857 under de titwe Awgoritmi de Numero Indorum[43])[44]
• Liber Awchoarismi de Practica Arismetice
• Liber Ysagogarum Awchorismi
• Liber Puwveris
Dixit Awgorizmi ('Thus spake Aw-Khwarizmi') is de starting phrase of a manuscript in de University of Cambridge wibrary, which is generawwy referred to by its 1857 titwe Awgoritmi de Numero Indorum. It is attributed to de Adeward of Baf, who had awso transwated de astronomicaw tabwes in 1126. It is perhaps de cwosest to Aw-Khwarizmi's own writings.[44]
Aw-Khwarizmi's work on aridmetic was responsibwe for introducing de Arabic numeraws, based on de Hindu–Arabic numeraw system devewoped in Indian madematics, to de Western worwd. The term "awgoridm" is derived from de awgorism, de techniqwe of performing aridmetic wif Hindu-Arabic numeraws devewoped by aw-Khwārizmī. Bof "awgoridm" and "awgorism" are derived from de Latinized forms of aw-Khwārizmī's name, Awgoritmi and Awgorismi, respectivewy.
### Astronomy
Page from Corpus Christi Cowwege MS 283. A Latin transwation of aw-Khwārizmī's Zīj.
Aw-Khwārizmī's Zīj aw-Sindhind[45] (Arabic: زيج السند هند, "astronomicaw tabwes of Siddhanta"[46]) is a work consisting of approximatewy 37 chapters on cawendricaw and astronomicaw cawcuwations and 116 tabwes wif cawendricaw, astronomicaw and astrowogicaw data, as weww as a tabwe of sine vawues. This is de first of many Arabic Zijes based on de Indian astronomicaw medods known as de sindhind.[47] The work contains tabwes for de movements of de sun, de moon and de five pwanets known at de time. This work marked de turning point in Iswamic astronomy. Hiderto, Muswim astronomers had adopted a primariwy research approach to de fiewd, transwating works of oders and wearning awready discovered knowwedge.
The originaw Arabic version (written c. 820) is wost, but a version by de Spanish astronomer Maswamah Ibn Ahmad aw-Majriti (c. 1000) has survived in a Latin transwation, presumabwy by Adeward of Baf (January 26, 1126).[48] The four surviving manuscripts of de Latin transwation are kept at de Bibwiofèqwe pubwiqwe (Chartres), de Bibwiofèqwe Mazarine (Paris), de Bibwioteca Nacionaw (Madrid) and de Bodweian Library (Oxford).
### Trigonometry
Aw-Khwārizmī's Zīj aw-Sindhind awso contained tabwes for de trigonometric functions of sines and cosine.[47] A rewated treatise on sphericaw trigonometry is awso attributed to him.[33]
Aw-Khwārizmī produced accurate sine and cosine tabwes, and de first tabwe of tangents.[49][50]
### Geography
Daunicht's reconstruction of de section of aw-Khwārizmī's worwd map concerning de Indian Ocean.
A 15f-century version of Ptowemy's Geography for comparison, uh-hah-hah-hah.
A stamp issued September 6, 1983 in de Soviet Union, commemorating aw-Khwārizmī's (approximate) 1200f birdday.
Statue of Aw-Khwārizmī in his birf town Khiva, Uzbekistan.
Aw-Khwārizmī's dird major work is his Kitāb Ṣūrat aw-Arḍ (Arabic: كتاب صورة الأرض, "Book of de Description of de Earf"),[51] awso known as his Geography, which was finished in 833. It is a major reworking of Ptowemy's 2nd-century Geography, consisting of a wist of 2402 coordinates of cities and oder geographicaw features fowwowing a generaw introduction, uh-hah-hah-hah.[52]
There is onwy one surviving copy of Kitāb Ṣūrat aw-Arḍ, which is kept at de Strasbourg University Library. A Latin transwation is kept at de Bibwioteca Nacionaw de España in Madrid.[citation needed] The book opens wif de wist of watitudes and wongitudes, in order of "weader zones", dat is to say in bwocks of watitudes and, in each weader zone, by order of wongitude. As Pauw Gawwez[dubious ] points out, dis excewwent system awwows de deduction of many watitudes and wongitudes where de onwy extant document is in such a bad condition as to make it practicawwy iwwegibwe. Neider de Arabic copy nor de Latin transwation incwude de map of de worwd itsewf; however, Hubert Daunicht was abwe to reconstruct de missing map from de wist of coordinates. Daunicht read de watitudes and wongitudes of de coastaw points in de manuscript, or deduces dem from de context where dey were not wegibwe. He transferred de points onto graph paper and connected dem wif straight wines, obtaining an approximation of de coastwine as it was on de originaw map. He den does de same for de rivers and towns.[53]
Aw-Khwārizmī corrected Ptowemy's gross overestimate for de wengf of de Mediterranean Sea[54] from de Canary Iswands to de eastern shores of de Mediterranean; Ptowemy overestimated it at 63 degrees of wongitude, whiwe aw-Khwārizmī awmost correctwy estimated it at nearwy 50 degrees of wongitude. He "awso depicted de Atwantic and Indian Oceans as open bodies of water, not wand-wocked seas as Ptowemy had done."[55] Aw-Khwārizmī's Prime Meridian at de Fortunate Iswes was dus around 10° east of de wine used by Marinus and Ptowemy. Most medievaw Muswim gazetteers continued to use aw-Khwārizmī's prime meridian, uh-hah-hah-hah.[54]
### Jewish cawendar
Aw-Khwārizmī wrote severaw oder works incwuding a treatise on de Hebrew cawendar, titwed Risāwa fi istikhrāj ta’rīkh aw-yahūd (Arabic: رسالة في إستخراج تأريخ اليهود, "Extraction of de Jewish Era"). It describes de Metonic cycwe, a 19-year intercawation cycwe; de ruwes for determining on what day of de week de first day of de monf Tishrei shaww faww; cawcuwates de intervaw between de Anno Mundi or Jewish year and de Seweucid era; and gives ruwes for determining de mean wongitude of de sun and de moon using de Hebrew cawendar. Simiwar materiaw is found in de works of Abū Rayḥān aw-Bīrūnī and Maimonides.[45]
### Oder works
Ibn aw-Nadim's Kitāb aw-Fihrist, an index of Arabic books, mentions aw-Khwārizmī's Kitāb aw-Taʾrīkh (Arabic: كتاب التأريخ), a book of annaws. No direct manuscript survives; however, a copy had reached Nusaybin by de 11f century, where its metropowitan bishop, Mar Ewyas bar Shinaya, found it. Ewias's chronicwe qwotes it from "de deaf of de Prophet" drough to 169 AH, at which point Ewias's text itsewf hits a wacuna.[56]
Severaw Arabic manuscripts in Berwin, Istanbuw, Tashkent, Cairo and Paris contain furder materiaw dat surewy or wif some probabiwity comes from aw-Khwārizmī. The Istanbuw manuscript contains a paper on sundiaws; de Fihrist credits aw-Khwārizmī wif Kitāb ar-Rukhāma(t) (Arabic: كتاب الرخامة). Oder papers, such as one on de determination of de direction of Mecca, are on de sphericaw astronomy.
Two texts deserve speciaw interest on de morning widf (Ma‘rifat sa‘at aw-mashriq fī kuww bawad) and de determination of de azimuf from a height (Ma‘rifat aw-samt min qibaw aw-irtifā‘).
He awso wrote two books on using and constructing astrowabes.
## Notes
1. ^ There is some confusion in de witerature on wheder aw-Khwārizmī's fuww name is ابو عبد الله محمد بن موسى الخوارزميAbū ʿAbdawwāh Muḥammad ibn Mūsā aw-Khwārizmī or ابو جعفر محمد بن موسی الخوارزمیAbū Ja‘far Muḥammad ibn Mūsā aw-Khwārizmī. Ibn Khawdun notes in his encycwopedic work: "The first who wrote upon dis branch [awgebra] was Abu ‘Abdawwah aw-Khowarizmi, after whom came Abu Kamiw Shoja‘ ibn Aswam." (MacGuckin de Swane)[citation needed]. In de introduction to his criticaw commentary on Robert of Chester's Latin transwation of aw-Khwārizmī's Awgebra, L.C. Karpinski notes dat Abū Ja‘far Muḥammad ibn Mūsā refers to de ewdest of de Banū Mūsā broders. Karpinski notes in his review on (Ruska 1917) dat in (Ruska 1918): "Ruska here inadvertentwy speaks of de audor as Abū Ga‘far M. b. M., instead of Abū Abdawwah M. b. M."
2. ^ Some schowars transwate de titwe aw-ḥisāb aw-hindī as "computation wif Hindu numeraws", but Arabic Hindī means 'Indian' rader dan 'Hindu'. A. S. Saidan states dat it shouwd be understood as aridmetic done "in de Indian way", wif Hindu-Arabic numeraws, rader dan as simpwy "Indian aridmetic". The Arab madematicians incorporated deir own innovations in deir texts.[37]
## References
1. ^ O'Connor, John J.; Robertson, Edmund F., "Abū Kāmiw Shujā‘ ibn Aswam", MacTutor History of Madematics archive, University of St Andrews.
2. ^ a b Corbin, Henry (1998). The Voyage and de Messenger: Iran and Phiwosophy. Norf Atwantic Books. p. 44. ISBN 978-1-55643-269-9.
3. ^ Cwifford A. Pickover (2009). The Maf Book: From Pydagoras to de 57f Dimension, 250 Miwestones in de History of Madematics. Sterwing Pubwishing Company, Inc. p. 84. ISBN 978-1-4027-5796-9.
4. ^ a b Sawiba, George (September 1998). "Science and medicine". Iranian Studies. 31 (3–4): 681–690. doi:10.1080/00210869808701940. Take, for exampwe, someone wike Muhammad b. Musa aw-Khwarizmi (fw. 850) who may present a probwem for de EIr, for awdough he was obviouswy of Persian descent, he wived and worked in Baghdad and was not known to have produced a singwe scientific work in Persian, uh-hah-hah-hah.
5. ^ a b Maher, P. (1998). From Aw-Jabr to Awgebra. Madematics in Schoow, 27(4), 14–15.
6. ^ Oaks, J. (2009). Powynomiaws and eqwations in Arabic awgebra. Archive for History of Exact Sciences, 63(2), 169–203.
7. ^ (Boyer 1991, "The Arabic Hegemony" p. 229) "It is not certain just what de terms aw-jabr and muqabawah mean, but de usuaw interpretation is simiwar to dat impwied in de transwation above. The word aw-jabr presumabwy meant someding wike "restoration" or "compwetion" and seems to refer to de transposition of subtracted terms to de oder side of an eqwation; de word muqabawah is said to refer to "reduction" or "bawancing" – dat is, de cancewwation of wike terms on opposite sides of de eqwation, uh-hah-hah-hah."
8. ^ Boyer, Carw B., 1985. A History of Madematics, p. 252. Princeton University Press. "Diophantus sometimes is cawwed de fader of awgebra, but dis titwe more appropriatewy bewongs to aw-Khowarizmi..." , "...de Aw-jabr comes cwoser to de ewementary awgebra of today dan de works of eider Diophantus or Brahmagupta..."
9. ^ S Gandz, The sources of aw-Khwarizmi's awgebra, Osiris, i (1936), 263–277,"Aw-Khwarizmi's awgebra is regarded as de foundation and cornerstone of de sciences. In a sense, aw-Khwarizmi is more entitwed to be cawwed "de fader of awgebra" dan Diophantus because aw-Khwarizmi is de first to teach awgebra in an ewementary form and for its own sake, Diophantus is primariwy concerned wif de deory of numbers."
10. ^ Katz, Victor J. "STAGES IN THE HISTORY OF ALGEBRA WITH IMPLICATIONSFOR TEACHING" (PDF). VICTOR J.KATZ, University of de District of Cowumbia Washington DC, USA: 190. Archived from de originaw (PDF) on 2019-03-27. Retrieved 2017-10-07 – via University of de District of Cowumbia Washington DC, USA. The first true awgebra text which is stiww extant is de work on aw-jabr and aw-muqabawa by Mohammad ibn Musa aw-Khwarizmi, written in Baghdad around 825.
11. ^ Esposito, John L. (2000-04-06). The Oxford History of Iswam. Oxford University Press. p. 188. ISBN 978-0-19-988041-6. Aw-Khwarizmi is often considered de founder of awgebra, and his name gave rise to de term awgoridm.
12. ^ Brentjes, Sonja (2007-06-01). "Awgebra". Encycwopaedia of Iswam, THREE.
13. ^ Daffa 1977
14. ^ Knuf, Donawd (1979). Awgoridms in Modern Madematics and Computer Science (PDF). Springer-Verwag. ISBN 978-0-387-11157-5. Archived from de originaw (PDF) on 2006-11-07.
15. ^ Struik 1987, p. 93
16. ^ Phiwip Khuri Hitti (2002). History of de Arabs. p. 379. ISBN 978-1-137-03982-8.
17. ^ Fred James Hiww, Nichowas Awde (2003). A History of de Iswamic Worwd. Hippocrene Books. p. 55. ISBN 978-0-7818-1015-9. "The Compendious Book on Cawcuwation by Compwetion and Bawancing" (Hisab aw-Jabr wa H-Muqabawa) on de devewopment of de subject cannot be underestimated. Transwated into Latin during de twewff century, it remained de principaw madematics textbook in European universities untiw de sixteenf century
18. ^ Shawn Overbay, Jimmy Schorer, and Header Conger, University of Kentucky. "Aw-Khwarizmi". Archived from de originaw on 2013-12-12.CS1 maint: muwtipwe names: audors wist (wink)
19. ^ "Iswam Spain and de history of technowogy". www.sjsu.edu. Retrieved 2018-01-24.
20. ^ L., V.D. (1985). A history of awgebra: from aw – Khwarizmi to emmy noeder. Berwin: Springer-Verwag.
21. ^ Cite error: The named reference Arndt was invoked but never defined (see de hewp page).
22. ^ Cristopher Moore and Stephan Mertens, The Nature of Computation, (Oxford University Press, 2011), 36.
23. ^ "Iraq After de Muswim Conqwest", by Michaew G. Morony, ISBN 1-59333-315-3 (a 2005 facsimiwe from de originaw 1984 book), p. 145
24. ^ Rashed, Roshdi (1988). "aw-Khwārizmī's Concept of Awgebra". In Zurayq, Qusṭanṭīn; Atiyeh, George Nichowas; Oweiss, Ibrahim M. (eds.). Arab Civiwization: Chawwenges and Responses : Studies in Honor of Constantine K. Zurayk. SUNY Press. p. 108. ISBN 978-0-88706-698-6.CS1 maint: ref=harv (wink)
25. ^ Toomer 1990
26. ^ Dunwop 1943
27. ^ "Madematics Education in Iran From Ancient to Modern" (PDF). Shima Sawehi ( Stanford University ), Yahya Tabesh ( Sharif University of Technowogy ).CS1 maint: oders (wink)
28. ^ "aw-Khwarizmi". Encycwopædia Britannica. Retrieved 2008-05-30.
29. ^ a b Rosen, Frederic. "The Compendious Book on Cawcuwation by Compwetion and Bawancing, aw-Khwārizmī". 1831 Engwish Transwation. Retrieved 2009-09-14.
30. ^ Karpinski, L.C. (1912). "History of Madematics in de Recent Edition of de Encycwopædia Britannica". Science. 35 (888): 29–31. Bibcode:1912Sci....35...29K. doi:10.1126/science.35.888.29. PMID 17752897.CS1 maint: ref=harv (wink)
31. ^ Boyer, Carw B. (1991). "The Arabic Hegemony". A History of Madematics (Second ed.). John Wiwey & Sons, Inc. p. 228. ISBN 978-0-471-54397-8.
"The Arabs in generaw woved a good cwear argument from premise to concwusion, as weww as systematic organization — respects in which neider Diophantus nor de Hindus excewwed."
32. ^ (Boyer 1991, "The Arabic Hegemony" p. 229) "It is not certain just what de terms aw-jabr and muqabawah mean, but de usuaw interpretation is simiwar to dat impwied in de transwation above. The word aw-jabr presumabwy meant someding wike "restoration" or "compwetion" and seems to refer to de transposition of subtracted terms to de oder side of an eqwation; de word muqabawah is said to refer to "reduction" or "bawancing" — dat is, de cancewwation of wike terms on opposite sides of de eqwation, uh-hah-hah-hah."
33. ^ a b
34. ^ Rashed, R.; Armstrong, Angewa (1994). The Devewopment of Arabic Madematics. Springer. pp. 11–12. ISBN 978-0-7923-2565-9. OCLC 29181926.CS1 maint: ref=harv (wink)
35. ^ Fworian Cajori (1919). A History of Madematics. Macmiwwan, uh-hah-hah-hah. p. 103. That it came from Indian source is impossibwe, for Hindus had no ruwes wike "restoration" and "reduction". They were never in de habit of making aww terms in an eqwation positive, as is done in de process of "restoration, uh-hah-hah-hah.
36. ^ Carw Benjamin Boyer (1968). A History of Madematics. p. 252.
37. ^ Saidan, A. S. (Winter 1966), "The Earwiest Extant Arabic Aridmetic: Kitab aw-Fusuw fi aw Hisab aw-Hindi of Abu aw-Hasan, Ahmad ibn Ibrahim aw-Uqwidisi", Isis, The University of Chicago Press, 57 (4): 475–490, doi:10.1086/350163, JSTOR 228518
38. ^ a b Burnett 2017, p. 39.
39. ^ Avari, Burjor (2013), Iswamic Civiwization in Souf Asia: A history of Muswim power and presence in de Indian subcontinent, Routwedge, pp. 31–32, ISBN 978-0-415-58061-8
40. ^ Van Brummewen, Gwen (2017), "Aridmetic", in Thomas F. Gwick (ed.), Routwedge Revivaws: Medievaw Science, Technowogy and Medicine (2006): An Encycwopedia, Taywor & Francis, p. 46, ISBN 978-1-351-67617-5
41. ^ Thomas F. Gwick, ed. (2017), "Aw-Khwarizmi", Routwedge Revivaws: Medievaw Science, Technowogy and Medicine (2006): An Encycwopedia, Taywor & Francis, ISBN 978-1-351-67617-5
42. ^ Van Brummewen, Gwen (2017), "Aridmetic", in Thomas F. Gwick (ed.), Routwedge Revivaws: Medievaw Science, Technowogy and Medicine (2006): An Encycwopedia, Taywor & Francis, pp. 46–47, ISBN 978-1-351-67617-5
43. ^ "Awgoritmi de numero Indorum", Trattati D'Aritmetica, Rome: Tipografia dewwe Scienze Fisiche e Matematiche, 1857, pp. 1–
44. ^ a b Crosswey, John N.; Henry, Awan S. (1990), "Thus Spake aw-Khwārizmī: A Transwation of de Text of Cambridge University Library Ms. Ii.vi.5", Historia Madematica, 17 (2): 103–131, doi:10.1016/0315-0860(90)90048-I
45. ^ a b Cite error: The named reference toomer was invoked but never defined (see de hewp page).
46. ^ Thurston, Hugh (1996), Earwy Astronomy, Springer Science & Business Media, pp. 204–, ISBN 978-0-387-94822-5
47. ^ a b Kennedy 1956, pp. 26–29
48. ^ Kennedy 1956, p. 128
49. ^ Jacqwes Sesiano, "Iswamic madematics", p. 157, in Sewin, Hewaine; D'Ambrosio, Ubiratan, eds. (2000). Madematics Across Cuwtures: The History of Non-western Madematics. Springer Science+Business Media. ISBN 978-1-4020-0260-1.
50. ^ "trigonometry". Encycwopædia Britannica. Retrieved 2008-07-21.
51. ^ The fuww titwe is "The Book of de Description of de Earf, wif its Cities, Mountains, Seas, Aww de Iswands and de Rivers, written by Abu Ja'far Muhammad ibn Musa aw-Khwārizmī, according to de Geographicaw Treatise written by Ptowemy de Cwaudian", awdough due to ambiguity in de word surah it couwd awso be understood as meaning "The Book of de Image of de Earf" or even "The Book of de Map of de Worwd".
52. ^ "The history of cartography". GAP computer awgebra system. Archived from de originaw on 2008-05-24. Retrieved 2008-05-30.
53. ^ Daunicht.
54. ^ a b Edward S. Kennedy, Madematicaw Geography, p. 188, in (Rashed & Morewon 1996, pp. 185–201)
55. ^ Covington, Richard (2007). "The Third Dimension". Saudi Aramco Worwd, May–June 2007: 17–21. Archived from de originaw on 2008-05-12. Retrieved 2008-07-06.CS1 maint: ref=harv (wink)
56. ^ LJ Dewaporte (1910). Chronographie de Mar Ewie bar Sinaya. Paris. p. xiii.
### Specific references
Biographicaw
Awgebra
Aridmetic
Astronomy
• Gowdstein, B.R. (1968). Commentary on de Astronomicaw Tabwes of Aw-Khwarizmi: By Ibn Aw-Mudanna. Yawe University Press. ISBN 978-0-300-00498-4.
• Hogendijk, Jan P. (1991). "Aw-Khwārizmī's Tabwe of de "Sine of de Hours" and de Underwying Sine Tabwe". Historia Scientiarum. 42: 1–12.CS1 maint: ref=harv (wink)
• King, David A. (1983). Aw-Khwārizmī and New Trends in Madematicaw Astronomy in de Ninf Century. New York University: Hagop Kevorkian Center for Near Eastern Studies: Occasionaw Papers on de Near East 2. Bibcode:1983antm.book.....K. LCCN 85150177.
• Neugebauer, Otto (1962). The Astronomicaw Tabwes of aw-Khwarizmi.
• Rosenfewd, Boris A. (1993). Menso Fowkerts; J.P. Hogendijk (eds.). "Geometric trigonometry" in treatises of aw-Khwārizmī, aw-Māhānī and Ibn aw-Haydam. Vestiga Madematica: Studies in Medievaw and Earwy Modern Madematics in Honour of H.L.L. Busard. Amsterdam: Rodopi. ISBN 978-90-5183-536-6.CS1 maint: ref=harv (wink)
• Suter, Heinrich. [Ed.]: Die astronomischen Tafewn des Muhammed ibn Mûsâ aw-Khwârizmî in der Bearbeitung des Maswama ibn Ahmed aw-Madjrîtî und der watein, uh-hah-hah-hah. Übersetzung des Adewhard von Baf auf Grund der Vorarbeiten von A. Bjørnbo und R. Besdorn in Kopenhagen, uh-hah-hah-hah. Hrsg. und komm. Kopenhagen 1914. 288 pp. Repr. 1997 (Iswamic Madematics and Astronomy. 7). ISBN 3-8298-4008-X.
• Van Dawen, B. Aw-Khwarizmi's Astronomicaw Tabwes Revisited: Anawysis of de Eqwation of Time.
Sphericaw trigonometry
• B.A. Rozenfewd. "Aw-Khwarizmi's sphericaw trigonometry" (Russian), Istor.-Mat. Isswed. 32–33 (1990), 325–339.
Jewish cawendar
Geography
• Daunicht, Hubert (1968–1970). Der Osten nach der Erdkarte aw-Ḫuwārizmīs : Beiträge zur historischen Geographie und Geschichte Asiens (in German). Bonner orientawistische Studien, uh-hah-hah-hah. N.S.; Bd. 19. LCCN 71468286.
• Mžik, Hans von (1915). "Ptowemaeus und die Karten der arabischen Geographen". Mitteiw. D. K. K. Geogr. Ges. In Wien. 58: 152.CS1 maint: ref=harv (wink)
• Mžik, Hans von (1916). "Afrika nach der arabischen Bearbeitung der γεωγραφικὴ ὑφήγησις des Cw. Ptowomeaus von Muh. ibn Mūsa aw-Hwarizmi". Denkschriften D. Akad. D. Wissen, uh-hah-hah-hah. In Wien, Phiw.-hist. Kw. 59.CS1 maint: ref=harv (wink)
• Mžik, Hans von (1926). Das Kitāb Ṣūrat aw-Arḍ des Abū Ǧa'far Muḥammad ibn Mūsā aw-Ḫuwārizmī. Leipzig.
• Nawwino, C.A. (1896), "Aw-Ḫuwārizmī e iw suo rifacimento dewwa Geografia di Towemo", Atti dewwa R. Accad. Dei Lincei, Arno 291, Serie V, Memorie, Cwasse di Sc. Mor., Vow. II, Rome
• Ruska, Juwius (1918). "Neue Bausteine zur Geschichte der arabischen Geographie". Geographische Zeitschrift. 24: 77–81.CS1 maint: ref=harv (wink)
• Spitta, W. (1879). "Ḫuwārizmī's Auszug aus der Geographie des Ptowomaeus". Zeitschrift Deutschen Morgenw. Geseww. 33.CS1 maint: ref=harv (wink) | 11,617 | 36,105 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 7, "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-2020-34 | latest | en | 0.877403 |
https://community.smartsheet.com/discussion/14386/counting-number-of-tasks-by-top-level-then-by-rag-status | 1,716,835,695,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059045.25/warc/CC-MAIN-20240527175049-20240527205049-00828.warc.gz | 149,280,192 | 106,202 | #### Welcome to the Smartsheet Forum Archives
The posts in this forum are no longer monitored for accuracy and their content may no longer be current. If there's a discussion here that interests you and you'd like to find (or create) a more current version, please Visit the Current Forums.
# Counting number of tasks, by top level then by RAG status
Options
edited 12/09/19
Hi everyone
i.e.
- Red (3)
- Amber (27)
- Green (70)
- Red (2)
- Amber (8)
- Green (140)
etc
The card view is good for counting RAG, but only by one or all levels.
I thought the Ancestors function might be able to do this for each top level item, but I can't get that to work; neither does reporting seem to get any sort of counting going.
Would appreciate someone pointing me in the right direction.
Regards
Ward
• ✭✭✭✭✭✭
Options
Hi
What I suggest you do is using Hierarchy to Hide/ expand it, create a dashboard at the top of the project sheet that uses Formulaic calculations to populate the KPIs you indicate are important in the sheet below.
You could even then create a Master statistics sheet showing ALL your Projects and their KPIs by using Cell Linking.
Good design of the workflow is needed but we do offer a free initial consultation if you want to see this working?
Hope that helps?
RichardR
• edited 10/05/17
Options
Not sure if this would help. I've used the RYG counting at a top level with the following:
="R(" + COUNTIF(CHILDREN(), "Red") + "), Y(" + COUNTIF(CHILDREN(), "Yellow") + "), G(" + COUNTIF(CHILDREN(), "Green") + ")"
and it will return something like:
R(2), Y(7), G(4) but as you've said, it will do that for the current children.
RE: Ancestor, I've used it with conditional formatting to change row colors based on where they have been placed in a hierarchy.
=IFERROR(COUNT(CHILDREN([Primary Column]40)) + " - " + COUNT(ANCESTORS([Primary Column]40)) + " - " + PARENT([Primary Column]40) + " Phase:" + INDEX(ANCESTORS([Primary Column]40), 1), "- Header Row -")
That returns "- Header Row -" for any root level rows and the following basd on how deeply the row is nested.
2 - 1 - be used to organize - Building Phase Phase:be used to organize - Building Phase
0 - 2 - a complex sheet Phase:be used to organize - Building Phase
Thinking though your issue you may want to see if you can address it in two steps, maybe a column added that does an index count and then a formula that checks color at that index.
Not a solution to your problem but maybe something in there helps.
Cheers.
Oh, here's my formula 'scratch pad'.
https://app.smartsheet.com/b/publish?EQBCT=a0123120a0b747aebd8162322e85f01d
• Options
I'll give this a shot. You let me know if this works out.
This formula will go in each parent Top Level Task row, in the "Status" column. It will count each color and show in the parent row.
="Red-" + COUNTIF(CHILDREN(), ="RED") + ", Yellow-" + COUNTIF(CHILDREN(), ="YELLOW") + ", Green-" + COUNTIF(CHILDREN(), ="GREEN")
This formula will go in a Top Top Summary parent row to count all statuses for all tasks. I used the Column name of "Status". Please update for your column name.
="Red-" + COUNTIF(Status:Status, ="RED") + ", Yellow-" + COUNTIF(Status:Status, ="YELLOW") + ", Green-" + COUNTIF(Status:Status, ="GREEN")
Go for it
Shawn
• Options
Richard, Jason and SmSulli ... thanks for your great suggestions. I'll take them for a gallop over the weekend.
Your suggestions are looking a lot more elegant than my effort last evening ... using the joinancestors function to create a string of task titles in each row:
Then a nested if statement ...
Then creating a filter for each stream, viewing in card view. Gotta love workarounds, but not as much as doing it the right way so tks again for pointing me in right direction
Ward
This discussion has been closed. | 980 | 3,832 | {"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-2024-22 | latest | en | 0.901543 |
https://ccm.net/faq/26890-excel-specifications-and-limitations-of-sheets | 1,632,170,046,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057091.31/warc/CC-MAIN-20210920191528-20210920221528-00183.warc.gz | 209,589,638 | 23,899 | 0
Thanks
A few words of thanks would be greatly appreciated.
# Excel - Specifications and limitations of Sheets
This tips aims to provide some information on the rationale of values ??(specifications and limits) apparently arbitrary under Excel:
• Why is there a limitation of 256 displayable characters in a cell and not 250 or 300?
• Why 16,384 columns in Excel 2007, and not 16,000 or 17,000?
## Situation
"I'm faced with a limitation of 65,536 rows under Excel, but I do not understand the reasons for this limitation.. Could someone explain the logic behind?
## Explanations
A byte consists of 8 bits (binary digit: 0 or 1) and can be represented as 2 ^ 8 = 256 different values. Hence the restriction
• 256 ASCII codes
• 256 displayable characters in an Excel cell,
• 256 columns in Excel 2003, etc..
Other limitations:
• With 2 bytes, or 16 bits, you can define 2 ^ 16 = 65536 values, number of rows in Excel 2003.
• With 14 bits, you can define 2 ^ 14 = 16384 values. This is the number of columns in Excel 2007.
• With 20 bits, you can define 2 ^ 20 = 1048576 values. This is the number of rows in Excel 2007.
In the Excel 2007 Help Topics go to the "Specifications and limits for spreadsheets and workbooks" chapter:
You shall notice that that most of these limitations are based on power of 2:
• 2 ^ 4 = 16 layers and line styles
• 2 ^ 5 = 32 styles, fields in a form
• 2 ^ 9 = 512 fonts for workbook
• 2 ^ 10 = 1024 page breaks
• 2 ^ 15 = 32767 characters stored in a cell.
It should be noted that Excel 2010 specifications are the same as the ones used for Excel 2007.
0
Thanks
A few words of thanks would be greatly appreciated. | 455 | 1,658 | {"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} | 3.4375 | 3 | CC-MAIN-2021-39 | longest | en | 0.85641 |
https://etestbank.net/test-bank-for-foundations-of-astronomy-enhanced-13th-edition-by-michael-a-seeds/ | 1,669,626,484,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710488.2/warc/CC-MAIN-20221128070816-20221128100816-00355.warc.gz | 295,767,461 | 40,662 | Test Bank For Foundations of Astronomy Enhanced 13th Edition by Michael A. Seeds
# Test Bank For Foundations of Astronomy Enhanced 13th Edition by Michael A. Seeds
\$25.00
Edition:Â 13th Edition
Resource Type:Â Test bank
# Test Bank For Foundations of Astronomy Enhanced 13th Edition by Michael A. Seeds
True / False
1. ​The most widely accepted system of measurement is the metric system.
a. True b. False
ANSWER:Â Â True REFERENCES:Â Â Where Are You? QUESTIONÂ TYPE:Â Â True / False LEARNINGÂ OBJECTIVES:Â Â ASTR.SEED.16.1-1 – Where is Earth in the Universe? OTHER:Â Â Bloom’s: Remember
2. ​Earth is approximately 13,000 km in diameter.
a. True b. False
ANSWER:Â Â True REFERENCES:Â Â Where Are You? QUESTIONÂ TYPE:Â Â True / False LEARNINGÂ OBJECTIVES:Â Â ASTR.SEED.16.1-1 – Where is Earth in the Universe? OTHER:Â Â Bloom’s: Remember
3. ​A convenient method to write very large numbers is to use scientific notation.
a. True b. False
ANSWER:Â Â True REFERENCES:Â Â Where Are You? QUESTIONÂ TYPE:Â Â True / False LEARNINGÂ OBJECTIVES:Â Â ASTR.SEED.16.1-1 – Where is Earth in the Universe? OTHER:Â Â Bloom’s: Remember
4. ​The Universe consists of the Sun, its family of planets, and some smaller bodies such as moons, asteroids, and comets.
a. True b. False
ANSWER:Â Â False REFERENCES:Â Â Where Are You? QUESTIONÂ TYPE:Â Â True / False LEARNINGÂ OBJECTIVES:Â Â ASTR.SEED.16.1-1 – Where is Earth in the Universe? OTHER:Â Â Bloom’s: Remember
5. ​Jupiter, Saturn, Uranus and Neptune are only located at a distance of 1 AU or less from the Sun.
a. True b. False
ANSWER:Â Â False REFERENCES:Â Â Where Are You? QUESTIONÂ TYPE:Â Â True / False LEARNINGÂ OBJECTIVES:Â Â ASTR.SEED.16.1-1 – Where is Earth in the Universe? OTHER:Â Â Bloom’s: Remember
0
TOP | 570 | 1,797 | {"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-2022-49 | longest | en | 0.782335 |
https://kr.mathworks.com/matlabcentral/profile/authors/5314347?s_tid=cody_local_to_profile | 1,611,151,819,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703520883.15/warc/CC-MAIN-20210120120242-20210120150242-00678.warc.gz | 417,508,016 | 21,709 | Community Profile
# Michael
### MathWorks
81 2014 이후 총 참여 횟수
#### Michael's 배지
세부 정보 보기...
참여 게시물
보기 기준
해결됨
Is this triangle right-angled?
Given any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return f...
1년 이상 전
해결됨
Project Euler: Problem 2, Sum of even Fibonacci
Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 te...
약 2년 전
해결됨
Simple equation: Annual salary
Given an hourly wage, compute an annual salary by multiplying the wage times 40 and times 50, because salary = wage x 40 hours/w...
4년 이하 전
해결됨
Distance walked 1D
Suppose you go from position 7 to 10 to 6 to 4. Then you have walked 9 units of distance, since 7 to 10 is 3 units, 10 to 6 is 4...
4년 이상 전
해결됨
Add a block to a model
Produce the following signal: <<http://blogs.mathworks.com/images/seth/cody/add-block-eqn.png>> In this case, the slope of...
4년 이상 전
해결됨
Produce a cosine wave
Produce the following signal: <<http://blogs.mathworks.com/images/seth/cody/cosine-eqn.png>>
4년 이상 전
해결됨
Connect blocks in a model
Connect the blocks in the model to produce the following signal: <<http://blogs.mathworks.com/images/seth/cody/connect-blocks...
4년 이상 전
문제
Find longest run
Write a function longest_run that takes as input an array of 0's and 1's and outputs the length and index of the longest consecu...
4년 이상 전 | 2 | 솔버 수: 49
해결됨
Swap the input arguments
Write a two-input, two-output function that swaps its two input arguments. For example: [q,r] = swap(5,10) returns q = ...
6년 이하 전
해결됨
Create a row array using double colon operator
Create a row array from 9 to 1, using the double colon operator.
6년 이하 전
해결됨
Circle area using pi
Given a circle's radius, compute the circle's area. Use the built-in mathematical constant pi.
6년 이하 전
해결됨
Clean the List of Names
Given a list of names in a cell array, remove any duplications that result from different capitalizations of the same string. So...
6년 이하 전
해결됨
Test for balanced parentheses
Given the input inStr, give the boolean output out indicating whether all the parentheses are balanced. Examples: * If ...
6년 이하 전
해결됨
Scrabble Scores
Given a word, determine its score in <http://en.wikipedia.org/wiki/Scrabble Scrabble>. The input string will always be provi...
6년 이하 전
해결됨
Indexed Probability Table
This question was inspired by a Stack Overflow question forwarded to me by Matt Simoneau. Given a vector x, make an indexed pro...
6년 이하 전
해결됨
Alphabetize by last name
Given a list of names in a cell array, sort the list by the last name. So if list = {'Barney Google','Snuffy Smith','Dagwood ...
6년 이하 전
해결됨
The Hitchhiker's Guide to MATLAB
Output logical "true" if the input is the answer to life, the universe and everything. Otherwise, output logical "false".
6년 이하 전
해결됨
Function Iterator
Given a handle fh to a function which takes a scalar input and returns a scalar output and an integer n >= 1, return a handle f...
6년 이하 전
해결됨
Remove all the words that end with "ain"
Given the string s1, return the string s2 with the target characters removed. For example, given s1 = 'the main event' your ...
6년 이하 전
해결됨
Sums with Excluded Digits
Add all the integers from 1 to n in which the digit m does not appear. m will always be a single digit integer from 0 to 9. no...
6년 이하 전
해결됨
<http://en.wikipedia.org/wiki/Benford%27s_law Benford's Law> states that the distribution of leading digits is not random. This...
6년 이하 전
해결됨
QWERTY coordinates
Given a lowercase letter or a digit as input, return the row where that letter appears on a <http://en.wikipedia.org/wiki/Keyboa...
6년 이하 전
해결됨
Summing Digits within Text
Given a string with text and digits, add all the numbers together. Examples: Input str = '4 and 20 blackbirds baked in a...
6년 이하 전
해결됨
Make a Palindrome Number
Some numbers like 323 are palindromes. Other numbers like 124 are not. But look what happens when we add that number to a revers...
6년 이하 전
해결됨
Pattern matching
Given a matrix, m-by-n, find all the rows that have the same "increase, decrease, or stay same" pattern going across the columns...
6년 이하 전
해결됨
Trimming Spaces
Given a string, remove all leading and trailing spaces (where space is defined as ASCII 32). Input a = ' singular value deco...
6년 이하 전
해결됨
Return a list sorted by number of occurrences
Given a vector x, return a vector y of the unique values in x sorted by the number of occurrences in x. Ties are resolved by a ...
6년 이하 전
해결됨
Which doors are open?
There are n doors in an alley. Initially they are all shut. You have been tasked to go down the alley n times, and open/shut the...
6년 이하 전
해결됨
Reverse Run-Length Encoder
Given a "counting sequence" vector x, construct the original sequence y. A counting sequence is formed by "counting" the entrie...
6년 이하 전
해결됨
Making change
Given an amount of currency, return a vector of this form: [100 50 20 10 5 2 1 0.5 0.25 0.1 0.05 0.01] Example: Input a = ...
6년 이하 전 | 1,445 | 5,078 | {"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} | 3.171875 | 3 | CC-MAIN-2021-04 | latest | en | 0.455316 |
http://stackoverflow.com/questions/24541914/complexity-of-two-cumulative-sum-cumsum-functions-in-haskell | 1,441,286,212,000,000,000 | text/html | crawl-data/CC-MAIN-2015-35/segments/1440645315227.83/warc/CC-MAIN-20150827031515-00130-ip-10-171-96-226.ec2.internal.warc.gz | 219,650,795 | 18,616 | # Complexity of two cumulative sum (cumsum) functions in Haskell
Consider the following two cumulative sum (cumsum) functions:
``````cumsum :: Num a => [a] -> [a]
cumsum [] = []
cumsum [x] = [x]
cumsum (x:y:ys) = x : (cumsum \$ (x+y) : ys)
``````
and
``````cumsum' :: Num a => [a] -> [a]
cumsum' x = [sum \$ take k x | k <- [1..length x]]
``````
Of course, I prefer the definition of `cumsum` to that of `cumsum'` and I understand that the former has linear complexity.
But just why does `cumsum'` also have linear complexity? `take` itself has linear complexity in the length of its argument and `k` runs from `1` to `length x`. Therefore I'd have expected quadratic complexity for `cumsum'`.
Moreover, the constant of `cumsum'` is lower than that of `cumsum`. Is that due to the recursive list appending of the latter?
NOTE: welcoming any smart definition of a cumulative sum.
EDIT: I'm measuring execution times using (after enabling `:set +s` in GHCi):
``````last \$ cumsum [1..n]
``````
-
I suspect that you are mistaken in your measurements - I can't see how `cumsum'` could have linear complexity. – Ganesh Sittampalam Jul 2 '14 at 22:18
FWIW, `scanl (+) 0` – luqui Jul 2 '14 at 22:18
I just measured it myself and it's definitely quadratic. Did you do something a bit too lazy to avoid getting the output printed out? – Ganesh Sittampalam Jul 2 '14 at 22:19
That is indeed a bit too lazy. It won't compute the intermediate sums. I used `max` rather than `last`. – Ganesh Sittampalam Jul 2 '14 at 22:21
`\x -> [take k x | k <- [1..length x]]` is `tail . inits`, except the latter doesn't compute the length, and doesn't start over to produce each sublist. Your function is `map sum . tail . inits` – user2407038 Jul 2 '14 at 22:22
This is a measurement error caused by laziness.
Every value in Haskell is lazy: it isn't evaluated until necessary. This includes sub-structure of values - so for example when we see a pattern (`x:xs`) this only forces evaluation of the list far enough to identify that the list is non-empty, but it doesn't force the head `x` or the tail `xs`.
The definition of `last` is something like:
``````last [x] = x
last (x:xs) = last xs
``````
So when `last` is applied to the result of `cumsum'`, it inspects the list comprehension recursively, but only enough to track down the last entry. It doesn't force any of the entries, but it does return the last one.
When this last entry is printed in ghci or whatever, then it is forced which takes linear time as expected. But the other entries are never calculated so we don't see the "expected" quadratic behaviour.
Using `maximum` instead of `last` does demonstrate that `cumnorm'` is quadratic whereas `cumnorm` is linear.
[Note: this explanation is somewhat hand-wavy: really evaluation is entirely driven by what's needed for the final result, so even `last` is only evaluted at all because its result is needed. Search for things like "Haskell evaluation order" and "Weak Head Normal Form" to get a more precise explanation.]
- | 822 | 3,036 | {"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} | 3.25 | 3 | CC-MAIN-2015-35 | latest | en | 0.903663 |
https://www.billmongan.com/Ursinus-CS377-Fall2021/Modules/Python/Warmup/Exercise | 1,638,683,560,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363135.71/warc/CC-MAIN-20211205035505-20211205065505-00079.warc.gz | 730,462,397 | 5,504 | # CS377: Database Design - Quadratic Formula in Python (3 Points)
Developed by Professor Tralie and Professor Mongan.
# Exercise Goals
The goals of this exercise are:
1. To write mathematical expressions in Python
2. To write a function that computes an expression and returns its result
Write a function that computes one of the roots of a quadratic equation. In addition to multiplying b by itself, you can compute b*b using the b** with the ** operator. The math.sqrt() method takes a single parameter, which is the number whose root should be computed, and returns the result. Now complete the code to compute one of the roots of the quadratic formula
Enter your Ursinus netid before clicking run. This is not your ID number or your email. For example, my netid is wmongan (non Ursinus students can simply enter their name to get this to run, but they won't get an e-mail record or any form of credit).
Netid
Clicking Run below will check your work and, if it passes, will submit your work automatically. You must be connected to the VPN for submission to be successful! You will receive a copy of your code via e-mail, so you'll know that it was submitted if you receive that e-mail! VPN access requires Multi-Factor Authentication, which sends you a code when you log into the network. Instructions on configuring these for your account can be found here.
import math def get_quadratic_roots(a, b, c): """ Compute the right root of of the quadratic equation f(x) = ax^2 + bx + c """ return 0 # This is a default value
### main.py
# Run some tests on the method print(get_quadratic_roots(1, -1, -6), end=',') print(get_quadratic_roots(1, 0, -1))
### Output
For reference, the quadratic formula is:
$\frac{-b \pm \sqrt{(b^{2} - 4ac)}}{2a}$
given an equation:
$ax^{2} + bx + c = 0$
In this exercise, you can simply compute one of the roots, as follows:
$\frac{-b + \sqrt{(b^{2} - 4ac)}}{2a}$ | 472 | 1,910 | {"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} | 3.765625 | 4 | CC-MAIN-2021-49 | latest | en | 0.856014 |
https://wcipeg.com/problem/wc96p2 | 1,619,026,869,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618039546945.85/warc/CC-MAIN-20210421161025-20210421191025-00146.warc.gz | 700,140,430 | 4,473 | ## Problem 2: Row and Column Compressions
To represent an m by n table of capital letters such as
A B B B B A A A A C B A A C C B B C C C
in a text file we could either type out all (m*n) characters or figure out some way to compress the data to a smaller size. Two ways we could do this are:
Column Compression
We could go down each column, left to right, and for consecutive repeated characters within a column replace them by a single occurence of that character preceded by a number indicating how many of that character there are. For this example we have, in the first column, AABB which becomes 2A2B. In the 2nd column we get B2AB and so on... Note that we have dropped the 1s from 1B2A1B and assumed there is only one occurence if there is no number preceding the letter. Thus compression by this method gives 2A2BB2ABB2ACBA2CB3C.
Row Compression
Likewise, we could compress each row going from left to right in the same fashion to get A4B4ACB2A2C2B3C in the above example.
Your task is to convert a column compression into a row compression given the size of the table: m, the number of rows and n, the number of columns.
### Input
In the data file there are 5 data sets. The first line of each data set contains m and n, the height and width of the table. Both m and n will be integers from 1 to 10. The second line of each data set will contain a column-compressed representation of the table.
### Output
For each data set output the row-compressed representation of the table.
### Sample Input
```4 5
2A2BB2ABB2ACBA2CB3C
3 3
3W3W3W
```
(and 3 more data sets)
### Sample Output
```A4B4ACB2A2C2B3C
3W3W3W
```
Point Value: 7
Time Limit: 2.00s
Memory Limit: 16M | 468 | 1,686 | {"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} | 3.703125 | 4 | CC-MAIN-2021-17 | longest | en | 0.870708 |
http://mathematica.stackexchange.com/questions/4961/unexpected-differences-with-various-uses-of-normfunction | 1,469,815,029,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257831770.41/warc/CC-MAIN-20160723071031-00134-ip-10-185-27-174.ec2.internal.warc.gz | 161,796,461 | 18,306 | Unexpected differences with various uses of NormFunction
I would expect all of the following to give the same answer (2.12467) but only half of them give this answer. The others seem to be using the default NormFunction:>(Norm[#,2]&). Can anyone explain this?
α = 3;
n /. FindFit[{1, 3, 9, 20}, x^n, n, x, NormFunction :> ((Null; Norm[#, α]) &)]
n /. FindFit[{1, 3, 9, 20}, x^n, n, x, NormFunction :> ((Norm[#, α]) &)]
n /. FindFit[{1, 3, 9, 20}, x^n, n, x, NormFunction :> (Norm[#, 3] &)]
Block[{α = 3}, n /. FindFit[{1, 3, 9, 20}, x^n, n, x, NormFunction :> (Norm[#, α] &)]]
With[{α = 3}, n /. FindFit[{1, 3, 9, 20}, x^n, n, x, NormFunction :> (Norm[#, α] &)]]
Module[{α = 3}, n /. FindFit[{1, 3, 9, 20}, x^n, n, x, NormFunction :> (Norm[#, α] &)]]
(* Outputs: 2.12467, 2.13284, 2.12467, 2.13284, 2.12467, 2.13284 *)
-
Actually, the last three cases can be reduced to the second and third: Block just has the effect of temporarily setting a to 3 therefore the expression is exactly equivalent to the second case (indeed, if executed in that order, the Block is even redundant because a already has the value 3). The With replaces the a by the literal 3, therefore it's exactly equivalent to the third case. And Module replaces a by a temporary variable which is set to 3, but of course the name (and life time) of the variable doesn't matter, therefore it's again equivalent to case 2. – celtschk May 1 '12 at 19:20
This must have to do with the symbolic preprocessing, happening in FindFit. In all cases when you get 2.13284, this was a result of symbolic preprocessing, which was possible because the norm function could be evaluated on symbolic arguments. The subsequent result is likely explained by the mechanism described by @Searke.
But if you define your own norm as
ClearAll[norm];
norm[vec_?(VectorQ[#, NumericQ] &), alpha_] := Norm[vec, alpha];
and replace Norm with norm in all your examples, you always get 2.12467. You can gain more insight into this by using Trace with TraceInternal -> True.
-
In fact it seems to be enough to write norm=Norm, so the symbolic preprocessing must be doing something very fragile. – Lev Bishop May 1 '12 at 19:36
@LevBishop Good point. Alas, I don't have enough time right now to dig deeper into it. – Leonid Shifrin May 1 '12 at 20:08
FindFit[{1, 3, 9, 20}, x^n, n, x, NormFunction :> ((Norm[#, thisisnotavariable]) &)]
When the NormFunction fails and is not well designed, FindFit just quietly chooses the 2-norm.
What, in this case, makes Norm[#, α]& not well designed? – rcollyer May 1 '12 at 19:10
It's not so simple: FindFit[{1, 3, 9, 20}, x^n, n, x, NormFunction :> (notavariable &)] gives a straightforward error message ("not a real number"). And why does adding a redundant compoundexpression (Null;) change my NormFunction from "not well designed" to "well designed"? – Lev Bishop May 1 '12 at 19:11 | 884 | 2,873 | {"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} | 3.359375 | 3 | CC-MAIN-2016-30 | latest | en | 0.901568 |
https://exercism.io/tracks/elixir/exercises/beer-song/solutions/383df792094843cb98f6bd11bfc7b277 | 1,606,871,271,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141685797.79/warc/CC-MAIN-20201201231155-20201202021155-00078.warc.gz | 246,165,393 | 8,974 | 🎉 Exercism Research is now launched. Help Exercism, help science and have some fun at research.exercism.io 🎉
# bryansoto's solution
## to Beer Song in the Elixir Track
Published at Oct 27 2020 · 0 comments
Instructions
Test suite
Solution
Recite the lyrics to that beloved classic, that field-trip favorite: 99 Bottles of Beer on the Wall.
Note that not all verses are identical.
``````99 bottles of beer on the wall, 99 bottles of beer.
Take one down and pass it around, 98 bottles of beer on the wall.
98 bottles of beer on the wall, 98 bottles of beer.
Take one down and pass it around, 97 bottles of beer on the wall.
97 bottles of beer on the wall, 97 bottles of beer.
Take one down and pass it around, 96 bottles of beer on the wall.
96 bottles of beer on the wall, 96 bottles of beer.
Take one down and pass it around, 95 bottles of beer on the wall.
95 bottles of beer on the wall, 95 bottles of beer.
Take one down and pass it around, 94 bottles of beer on the wall.
94 bottles of beer on the wall, 94 bottles of beer.
Take one down and pass it around, 93 bottles of beer on the wall.
93 bottles of beer on the wall, 93 bottles of beer.
Take one down and pass it around, 92 bottles of beer on the wall.
92 bottles of beer on the wall, 92 bottles of beer.
Take one down and pass it around, 91 bottles of beer on the wall.
91 bottles of beer on the wall, 91 bottles of beer.
Take one down and pass it around, 90 bottles of beer on the wall.
90 bottles of beer on the wall, 90 bottles of beer.
Take one down and pass it around, 89 bottles of beer on the wall.
89 bottles of beer on the wall, 89 bottles of beer.
Take one down and pass it around, 88 bottles of beer on the wall.
88 bottles of beer on the wall, 88 bottles of beer.
Take one down and pass it around, 87 bottles of beer on the wall.
87 bottles of beer on the wall, 87 bottles of beer.
Take one down and pass it around, 86 bottles of beer on the wall.
86 bottles of beer on the wall, 86 bottles of beer.
Take one down and pass it around, 85 bottles of beer on the wall.
85 bottles of beer on the wall, 85 bottles of beer.
Take one down and pass it around, 84 bottles of beer on the wall.
84 bottles of beer on the wall, 84 bottles of beer.
Take one down and pass it around, 83 bottles of beer on the wall.
83 bottles of beer on the wall, 83 bottles of beer.
Take one down and pass it around, 82 bottles of beer on the wall.
82 bottles of beer on the wall, 82 bottles of beer.
Take one down and pass it around, 81 bottles of beer on the wall.
81 bottles of beer on the wall, 81 bottles of beer.
Take one down and pass it around, 80 bottles of beer on the wall.
80 bottles of beer on the wall, 80 bottles of beer.
Take one down and pass it around, 79 bottles of beer on the wall.
79 bottles of beer on the wall, 79 bottles of beer.
Take one down and pass it around, 78 bottles of beer on the wall.
78 bottles of beer on the wall, 78 bottles of beer.
Take one down and pass it around, 77 bottles of beer on the wall.
77 bottles of beer on the wall, 77 bottles of beer.
Take one down and pass it around, 76 bottles of beer on the wall.
76 bottles of beer on the wall, 76 bottles of beer.
Take one down and pass it around, 75 bottles of beer on the wall.
75 bottles of beer on the wall, 75 bottles of beer.
Take one down and pass it around, 74 bottles of beer on the wall.
74 bottles of beer on the wall, 74 bottles of beer.
Take one down and pass it around, 73 bottles of beer on the wall.
73 bottles of beer on the wall, 73 bottles of beer.
Take one down and pass it around, 72 bottles of beer on the wall.
72 bottles of beer on the wall, 72 bottles of beer.
Take one down and pass it around, 71 bottles of beer on the wall.
71 bottles of beer on the wall, 71 bottles of beer.
Take one down and pass it around, 70 bottles of beer on the wall.
70 bottles of beer on the wall, 70 bottles of beer.
Take one down and pass it around, 69 bottles of beer on the wall.
69 bottles of beer on the wall, 69 bottles of beer.
Take one down and pass it around, 68 bottles of beer on the wall.
68 bottles of beer on the wall, 68 bottles of beer.
Take one down and pass it around, 67 bottles of beer on the wall.
67 bottles of beer on the wall, 67 bottles of beer.
Take one down and pass it around, 66 bottles of beer on the wall.
66 bottles of beer on the wall, 66 bottles of beer.
Take one down and pass it around, 65 bottles of beer on the wall.
65 bottles of beer on the wall, 65 bottles of beer.
Take one down and pass it around, 64 bottles of beer on the wall.
64 bottles of beer on the wall, 64 bottles of beer.
Take one down and pass it around, 63 bottles of beer on the wall.
63 bottles of beer on the wall, 63 bottles of beer.
Take one down and pass it around, 62 bottles of beer on the wall.
62 bottles of beer on the wall, 62 bottles of beer.
Take one down and pass it around, 61 bottles of beer on the wall.
61 bottles of beer on the wall, 61 bottles of beer.
Take one down and pass it around, 60 bottles of beer on the wall.
60 bottles of beer on the wall, 60 bottles of beer.
Take one down and pass it around, 59 bottles of beer on the wall.
59 bottles of beer on the wall, 59 bottles of beer.
Take one down and pass it around, 58 bottles of beer on the wall.
58 bottles of beer on the wall, 58 bottles of beer.
Take one down and pass it around, 57 bottles of beer on the wall.
57 bottles of beer on the wall, 57 bottles of beer.
Take one down and pass it around, 56 bottles of beer on the wall.
56 bottles of beer on the wall, 56 bottles of beer.
Take one down and pass it around, 55 bottles of beer on the wall.
55 bottles of beer on the wall, 55 bottles of beer.
Take one down and pass it around, 54 bottles of beer on the wall.
54 bottles of beer on the wall, 54 bottles of beer.
Take one down and pass it around, 53 bottles of beer on the wall.
53 bottles of beer on the wall, 53 bottles of beer.
Take one down and pass it around, 52 bottles of beer on the wall.
52 bottles of beer on the wall, 52 bottles of beer.
Take one down and pass it around, 51 bottles of beer on the wall.
51 bottles of beer on the wall, 51 bottles of beer.
Take one down and pass it around, 50 bottles of beer on the wall.
50 bottles of beer on the wall, 50 bottles of beer.
Take one down and pass it around, 49 bottles of beer on the wall.
49 bottles of beer on the wall, 49 bottles of beer.
Take one down and pass it around, 48 bottles of beer on the wall.
48 bottles of beer on the wall, 48 bottles of beer.
Take one down and pass it around, 47 bottles of beer on the wall.
47 bottles of beer on the wall, 47 bottles of beer.
Take one down and pass it around, 46 bottles of beer on the wall.
46 bottles of beer on the wall, 46 bottles of beer.
Take one down and pass it around, 45 bottles of beer on the wall.
45 bottles of beer on the wall, 45 bottles of beer.
Take one down and pass it around, 44 bottles of beer on the wall.
44 bottles of beer on the wall, 44 bottles of beer.
Take one down and pass it around, 43 bottles of beer on the wall.
43 bottles of beer on the wall, 43 bottles of beer.
Take one down and pass it around, 42 bottles of beer on the wall.
42 bottles of beer on the wall, 42 bottles of beer.
Take one down and pass it around, 41 bottles of beer on the wall.
41 bottles of beer on the wall, 41 bottles of beer.
Take one down and pass it around, 40 bottles of beer on the wall.
40 bottles of beer on the wall, 40 bottles of beer.
Take one down and pass it around, 39 bottles of beer on the wall.
39 bottles of beer on the wall, 39 bottles of beer.
Take one down and pass it around, 38 bottles of beer on the wall.
38 bottles of beer on the wall, 38 bottles of beer.
Take one down and pass it around, 37 bottles of beer on the wall.
37 bottles of beer on the wall, 37 bottles of beer.
Take one down and pass it around, 36 bottles of beer on the wall.
36 bottles of beer on the wall, 36 bottles of beer.
Take one down and pass it around, 35 bottles of beer on the wall.
35 bottles of beer on the wall, 35 bottles of beer.
Take one down and pass it around, 34 bottles of beer on the wall.
34 bottles of beer on the wall, 34 bottles of beer.
Take one down and pass it around, 33 bottles of beer on the wall.
33 bottles of beer on the wall, 33 bottles of beer.
Take one down and pass it around, 32 bottles of beer on the wall.
32 bottles of beer on the wall, 32 bottles of beer.
Take one down and pass it around, 31 bottles of beer on the wall.
31 bottles of beer on the wall, 31 bottles of beer.
Take one down and pass it around, 30 bottles of beer on the wall.
30 bottles of beer on the wall, 30 bottles of beer.
Take one down and pass it around, 29 bottles of beer on the wall.
29 bottles of beer on the wall, 29 bottles of beer.
Take one down and pass it around, 28 bottles of beer on the wall.
28 bottles of beer on the wall, 28 bottles of beer.
Take one down and pass it around, 27 bottles of beer on the wall.
27 bottles of beer on the wall, 27 bottles of beer.
Take one down and pass it around, 26 bottles of beer on the wall.
26 bottles of beer on the wall, 26 bottles of beer.
Take one down and pass it around, 25 bottles of beer on the wall.
25 bottles of beer on the wall, 25 bottles of beer.
Take one down and pass it around, 24 bottles of beer on the wall.
24 bottles of beer on the wall, 24 bottles of beer.
Take one down and pass it around, 23 bottles of beer on the wall.
23 bottles of beer on the wall, 23 bottles of beer.
Take one down and pass it around, 22 bottles of beer on the wall.
22 bottles of beer on the wall, 22 bottles of beer.
Take one down and pass it around, 21 bottles of beer on the wall.
21 bottles of beer on the wall, 21 bottles of beer.
Take one down and pass it around, 20 bottles of beer on the wall.
20 bottles of beer on the wall, 20 bottles of beer.
Take one down and pass it around, 19 bottles of beer on the wall.
19 bottles of beer on the wall, 19 bottles of beer.
Take one down and pass it around, 18 bottles of beer on the wall.
18 bottles of beer on the wall, 18 bottles of beer.
Take one down and pass it around, 17 bottles of beer on the wall.
17 bottles of beer on the wall, 17 bottles of beer.
Take one down and pass it around, 16 bottles of beer on the wall.
16 bottles of beer on the wall, 16 bottles of beer.
Take one down and pass it around, 15 bottles of beer on the wall.
15 bottles of beer on the wall, 15 bottles of beer.
Take one down and pass it around, 14 bottles of beer on the wall.
14 bottles of beer on the wall, 14 bottles of beer.
Take one down and pass it around, 13 bottles of beer on the wall.
13 bottles of beer on the wall, 13 bottles of beer.
Take one down and pass it around, 12 bottles of beer on the wall.
12 bottles of beer on the wall, 12 bottles of beer.
Take one down and pass it around, 11 bottles of beer on the wall.
11 bottles of beer on the wall, 11 bottles of beer.
Take one down and pass it around, 10 bottles of beer on the wall.
10 bottles of beer on the wall, 10 bottles of beer.
Take one down and pass it around, 9 bottles of beer on the wall.
9 bottles of beer on the wall, 9 bottles of beer.
Take one down and pass it around, 8 bottles of beer on the wall.
8 bottles of beer on the wall, 8 bottles of beer.
Take one down and pass it around, 7 bottles of beer on the wall.
7 bottles of beer on the wall, 7 bottles of beer.
Take one down and pass it around, 6 bottles of beer on the wall.
6 bottles of beer on the wall, 6 bottles of beer.
Take one down and pass it around, 5 bottles of beer on the wall.
5 bottles of beer on the wall, 5 bottles of beer.
Take one down and pass it around, 4 bottles of beer on the wall.
4 bottles of beer on the wall, 4 bottles of beer.
Take one down and pass it around, 3 bottles of beer on the wall.
3 bottles of beer on the wall, 3 bottles of beer.
Take one down and pass it around, 2 bottles of beer on the wall.
2 bottles of beer on the wall, 2 bottles of beer.
Take one down and pass it around, 1 bottle of beer on the wall.
1 bottle of beer on the wall, 1 bottle of beer.
Take it down and pass it around, no more bottles of beer on the wall.
No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
``````
## For bonus points
Did you get the tests passing and the code clean? If you want to, these are some additional things you could try:
• Remove as much duplication as you possibly can.
• Optimize for readability, even if it means introducing duplication.
• If you've removed all the duplication, do you have a lot of conditionals? Try replacing the conditionals with polymorphism, if it applies in this language. How readable is it?
Then please share your thoughts in a comment on the submission. Did this experiment make the code better? Worse? Did you learn anything from it?
## Running tests
Execute the tests with:
``````\$ mix test
``````
### Pending tests
In the test suites, all but the first test have been skipped.
Once you get a test passing, you can unskip the next one by commenting out the relevant `@tag :pending` with a `#` symbol.
For example:
``````# @tag :pending
test "shouting" do
assert Bob.hey("WATCH OUT!") == "Whoa, chill out!"
end
``````
Or, you can enable all the tests by commenting out the `ExUnit.configure` line in the test suite.
``````# ExUnit.configure exclude: :pending, trace: true
``````
If you're stuck on something, it may help to look at some of the available resources out there where answers might be found.
## Source
Learn to Program by Chris Pine http://pine.fm/LearnToProgram/?Chapter=06
## Submitting Incomplete Solutions
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
### beer_song_test.exs
``````defmodule BeerSongTest do
use ExUnit.Case
describe "verse" do
# @tag :pending
test "first generic verse" do
assert BeerSong.verse(99) == """
99 bottles of beer on the wall, 99 bottles of beer.
Take one down and pass it around, 98 bottles of beer on the wall.
"""
end
@tag :pending
test "last generic verse" do
assert BeerSong.verse(3) == """
3 bottles of beer on the wall, 3 bottles of beer.
Take one down and pass it around, 2 bottles of beer on the wall.
"""
end
@tag :pending
test "verse with 2 bottles" do
assert BeerSong.verse(2) == """
2 bottles of beer on the wall, 2 bottles of beer.
Take one down and pass it around, 1 bottle of beer on the wall.
"""
end
@tag :pending
test "verse with 1 bottle" do
assert BeerSong.verse(1) == """
1 bottle of beer on the wall, 1 bottle of beer.
Take it down and pass it around, no more bottles of beer on the wall.
"""
end
@tag :pending
test "verse with 0 bottles" do
assert BeerSong.verse(0) == """
No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
"""
end
end
describe "lyrics" do
@tag :pending
test "first two verses" do
assert BeerSong.lyrics(99..98) == """
99 bottles of beer on the wall, 99 bottles of beer.
Take one down and pass it around, 98 bottles of beer on the wall.
98 bottles of beer on the wall, 98 bottles of beer.
Take one down and pass it around, 97 bottles of beer on the wall.
"""
end
@tag :pending
test "last three verses" do
assert BeerSong.lyrics(2..0) == """
2 bottles of beer on the wall, 2 bottles of beer.
Take one down and pass it around, 1 bottle of beer on the wall.
1 bottle of beer on the wall, 1 bottle of beer.
Take it down and pass it around, no more bottles of beer on the wall.
No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
"""
end
@tag :pending
test "all verses" do
assert BeerSong.lyrics() == """
99 bottles of beer on the wall, 99 bottles of beer.
Take one down and pass it around, 98 bottles of beer on the wall.
98 bottles of beer on the wall, 98 bottles of beer.
Take one down and pass it around, 97 bottles of beer on the wall.
97 bottles of beer on the wall, 97 bottles of beer.
Take one down and pass it around, 96 bottles of beer on the wall.
96 bottles of beer on the wall, 96 bottles of beer.
Take one down and pass it around, 95 bottles of beer on the wall.
95 bottles of beer on the wall, 95 bottles of beer.
Take one down and pass it around, 94 bottles of beer on the wall.
94 bottles of beer on the wall, 94 bottles of beer.
Take one down and pass it around, 93 bottles of beer on the wall.
93 bottles of beer on the wall, 93 bottles of beer.
Take one down and pass it around, 92 bottles of beer on the wall.
92 bottles of beer on the wall, 92 bottles of beer.
Take one down and pass it around, 91 bottles of beer on the wall.
91 bottles of beer on the wall, 91 bottles of beer.
Take one down and pass it around, 90 bottles of beer on the wall.
90 bottles of beer on the wall, 90 bottles of beer.
Take one down and pass it around, 89 bottles of beer on the wall.
89 bottles of beer on the wall, 89 bottles of beer.
Take one down and pass it around, 88 bottles of beer on the wall.
88 bottles of beer on the wall, 88 bottles of beer.
Take one down and pass it around, 87 bottles of beer on the wall.
87 bottles of beer on the wall, 87 bottles of beer.
Take one down and pass it around, 86 bottles of beer on the wall.
86 bottles of beer on the wall, 86 bottles of beer.
Take one down and pass it around, 85 bottles of beer on the wall.
85 bottles of beer on the wall, 85 bottles of beer.
Take one down and pass it around, 84 bottles of beer on the wall.
84 bottles of beer on the wall, 84 bottles of beer.
Take one down and pass it around, 83 bottles of beer on the wall.
83 bottles of beer on the wall, 83 bottles of beer.
Take one down and pass it around, 82 bottles of beer on the wall.
82 bottles of beer on the wall, 82 bottles of beer.
Take one down and pass it around, 81 bottles of beer on the wall.
81 bottles of beer on the wall, 81 bottles of beer.
Take one down and pass it around, 80 bottles of beer on the wall.
80 bottles of beer on the wall, 80 bottles of beer.
Take one down and pass it around, 79 bottles of beer on the wall.
79 bottles of beer on the wall, 79 bottles of beer.
Take one down and pass it around, 78 bottles of beer on the wall.
78 bottles of beer on the wall, 78 bottles of beer.
Take one down and pass it around, 77 bottles of beer on the wall.
77 bottles of beer on the wall, 77 bottles of beer.
Take one down and pass it around, 76 bottles of beer on the wall.
76 bottles of beer on the wall, 76 bottles of beer.
Take one down and pass it around, 75 bottles of beer on the wall.
75 bottles of beer on the wall, 75 bottles of beer.
Take one down and pass it around, 74 bottles of beer on the wall.
74 bottles of beer on the wall, 74 bottles of beer.
Take one down and pass it around, 73 bottles of beer on the wall.
73 bottles of beer on the wall, 73 bottles of beer.
Take one down and pass it around, 72 bottles of beer on the wall.
72 bottles of beer on the wall, 72 bottles of beer.
Take one down and pass it around, 71 bottles of beer on the wall.
71 bottles of beer on the wall, 71 bottles of beer.
Take one down and pass it around, 70 bottles of beer on the wall.
70 bottles of beer on the wall, 70 bottles of beer.
Take one down and pass it around, 69 bottles of beer on the wall.
69 bottles of beer on the wall, 69 bottles of beer.
Take one down and pass it around, 68 bottles of beer on the wall.
68 bottles of beer on the wall, 68 bottles of beer.
Take one down and pass it around, 67 bottles of beer on the wall.
67 bottles of beer on the wall, 67 bottles of beer.
Take one down and pass it around, 66 bottles of beer on the wall.
66 bottles of beer on the wall, 66 bottles of beer.
Take one down and pass it around, 65 bottles of beer on the wall.
65 bottles of beer on the wall, 65 bottles of beer.
Take one down and pass it around, 64 bottles of beer on the wall.
64 bottles of beer on the wall, 64 bottles of beer.
Take one down and pass it around, 63 bottles of beer on the wall.
63 bottles of beer on the wall, 63 bottles of beer.
Take one down and pass it around, 62 bottles of beer on the wall.
62 bottles of beer on the wall, 62 bottles of beer.
Take one down and pass it around, 61 bottles of beer on the wall.
61 bottles of beer on the wall, 61 bottles of beer.
Take one down and pass it around, 60 bottles of beer on the wall.
60 bottles of beer on the wall, 60 bottles of beer.
Take one down and pass it around, 59 bottles of beer on the wall.
59 bottles of beer on the wall, 59 bottles of beer.
Take one down and pass it around, 58 bottles of beer on the wall.
58 bottles of beer on the wall, 58 bottles of beer.
Take one down and pass it around, 57 bottles of beer on the wall.
57 bottles of beer on the wall, 57 bottles of beer.
Take one down and pass it around, 56 bottles of beer on the wall.
56 bottles of beer on the wall, 56 bottles of beer.
Take one down and pass it around, 55 bottles of beer on the wall.
55 bottles of beer on the wall, 55 bottles of beer.
Take one down and pass it around, 54 bottles of beer on the wall.
54 bottles of beer on the wall, 54 bottles of beer.
Take one down and pass it around, 53 bottles of beer on the wall.
53 bottles of beer on the wall, 53 bottles of beer.
Take one down and pass it around, 52 bottles of beer on the wall.
52 bottles of beer on the wall, 52 bottles of beer.
Take one down and pass it around, 51 bottles of beer on the wall.
51 bottles of beer on the wall, 51 bottles of beer.
Take one down and pass it around, 50 bottles of beer on the wall.
50 bottles of beer on the wall, 50 bottles of beer.
Take one down and pass it around, 49 bottles of beer on the wall.
49 bottles of beer on the wall, 49 bottles of beer.
Take one down and pass it around, 48 bottles of beer on the wall.
48 bottles of beer on the wall, 48 bottles of beer.
Take one down and pass it around, 47 bottles of beer on the wall.
47 bottles of beer on the wall, 47 bottles of beer.
Take one down and pass it around, 46 bottles of beer on the wall.
46 bottles of beer on the wall, 46 bottles of beer.
Take one down and pass it around, 45 bottles of beer on the wall.
45 bottles of beer on the wall, 45 bottles of beer.
Take one down and pass it around, 44 bottles of beer on the wall.
44 bottles of beer on the wall, 44 bottles of beer.
Take one down and pass it around, 43 bottles of beer on the wall.
43 bottles of beer on the wall, 43 bottles of beer.
Take one down and pass it around, 42 bottles of beer on the wall.
42 bottles of beer on the wall, 42 bottles of beer.
Take one down and pass it around, 41 bottles of beer on the wall.
41 bottles of beer on the wall, 41 bottles of beer.
Take one down and pass it around, 40 bottles of beer on the wall.
40 bottles of beer on the wall, 40 bottles of beer.
Take one down and pass it around, 39 bottles of beer on the wall.
39 bottles of beer on the wall, 39 bottles of beer.
Take one down and pass it around, 38 bottles of beer on the wall.
38 bottles of beer on the wall, 38 bottles of beer.
Take one down and pass it around, 37 bottles of beer on the wall.
37 bottles of beer on the wall, 37 bottles of beer.
Take one down and pass it around, 36 bottles of beer on the wall.
36 bottles of beer on the wall, 36 bottles of beer.
Take one down and pass it around, 35 bottles of beer on the wall.
35 bottles of beer on the wall, 35 bottles of beer.
Take one down and pass it around, 34 bottles of beer on the wall.
34 bottles of beer on the wall, 34 bottles of beer.
Take one down and pass it around, 33 bottles of beer on the wall.
33 bottles of beer on the wall, 33 bottles of beer.
Take one down and pass it around, 32 bottles of beer on the wall.
32 bottles of beer on the wall, 32 bottles of beer.
Take one down and pass it around, 31 bottles of beer on the wall.
31 bottles of beer on the wall, 31 bottles of beer.
Take one down and pass it around, 30 bottles of beer on the wall.
30 bottles of beer on the wall, 30 bottles of beer.
Take one down and pass it around, 29 bottles of beer on the wall.
29 bottles of beer on the wall, 29 bottles of beer.
Take one down and pass it around, 28 bottles of beer on the wall.
28 bottles of beer on the wall, 28 bottles of beer.
Take one down and pass it around, 27 bottles of beer on the wall.
27 bottles of beer on the wall, 27 bottles of beer.
Take one down and pass it around, 26 bottles of beer on the wall.
26 bottles of beer on the wall, 26 bottles of beer.
Take one down and pass it around, 25 bottles of beer on the wall.
25 bottles of beer on the wall, 25 bottles of beer.
Take one down and pass it around, 24 bottles of beer on the wall.
24 bottles of beer on the wall, 24 bottles of beer.
Take one down and pass it around, 23 bottles of beer on the wall.
23 bottles of beer on the wall, 23 bottles of beer.
Take one down and pass it around, 22 bottles of beer on the wall.
22 bottles of beer on the wall, 22 bottles of beer.
Take one down and pass it around, 21 bottles of beer on the wall.
21 bottles of beer on the wall, 21 bottles of beer.
Take one down and pass it around, 20 bottles of beer on the wall.
20 bottles of beer on the wall, 20 bottles of beer.
Take one down and pass it around, 19 bottles of beer on the wall.
19 bottles of beer on the wall, 19 bottles of beer.
Take one down and pass it around, 18 bottles of beer on the wall.
18 bottles of beer on the wall, 18 bottles of beer.
Take one down and pass it around, 17 bottles of beer on the wall.
17 bottles of beer on the wall, 17 bottles of beer.
Take one down and pass it around, 16 bottles of beer on the wall.
16 bottles of beer on the wall, 16 bottles of beer.
Take one down and pass it around, 15 bottles of beer on the wall.
15 bottles of beer on the wall, 15 bottles of beer.
Take one down and pass it around, 14 bottles of beer on the wall.
14 bottles of beer on the wall, 14 bottles of beer.
Take one down and pass it around, 13 bottles of beer on the wall.
13 bottles of beer on the wall, 13 bottles of beer.
Take one down and pass it around, 12 bottles of beer on the wall.
12 bottles of beer on the wall, 12 bottles of beer.
Take one down and pass it around, 11 bottles of beer on the wall.
11 bottles of beer on the wall, 11 bottles of beer.
Take one down and pass it around, 10 bottles of beer on the wall.
10 bottles of beer on the wall, 10 bottles of beer.
Take one down and pass it around, 9 bottles of beer on the wall.
9 bottles of beer on the wall, 9 bottles of beer.
Take one down and pass it around, 8 bottles of beer on the wall.
8 bottles of beer on the wall, 8 bottles of beer.
Take one down and pass it around, 7 bottles of beer on the wall.
7 bottles of beer on the wall, 7 bottles of beer.
Take one down and pass it around, 6 bottles of beer on the wall.
6 bottles of beer on the wall, 6 bottles of beer.
Take one down and pass it around, 5 bottles of beer on the wall.
5 bottles of beer on the wall, 5 bottles of beer.
Take one down and pass it around, 4 bottles of beer on the wall.
4 bottles of beer on the wall, 4 bottles of beer.
Take one down and pass it around, 3 bottles of beer on the wall.
3 bottles of beer on the wall, 3 bottles of beer.
Take one down and pass it around, 2 bottles of beer on the wall.
2 bottles of beer on the wall, 2 bottles of beer.
Take one down and pass it around, 1 bottle of beer on the wall.
1 bottle of beer on the wall, 1 bottle of beer.
Take it down and pass it around, no more bottles of beer on the wall.
No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
"""
end
end
end``````
### test_helper.exs
``````ExUnit.start()
ExUnit.configure(exclude: :pending, trace: true)``````
``````defmodule BeerSong do
@doc """
Get a single verse of the beer song
"""
@spec verse(integer) :: String.t()
def verse(2) do
"""
2 bottles of beer on the wall, 2 bottles of beer.
Take one down and pass it around, 1 bottle of beer on the wall.
"""
end
def verse(1) do
"""
1 bottle of beer on the wall, 1 bottle of beer.
Take it down and pass it around, no more bottles of beer on the wall.
"""
end
def verse(0) do
"""
No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
"""
end
def verse(number) do
"""
#{number} bottles of beer on the wall, #{number} bottles of beer.
Take one down and pass it around, #{number - 1} bottles of beer on the wall.
"""
end
@doc """
Get the entire beer song.
"""
@spec lyrics() :: String.t()
def lyrics(), do: lyrics(99..0)
@doc """
Get the entire beer song for a given range of numbers of bottles.
"""
@spec lyrics(Range.t()) :: String.t()
def lyrics(range) do
range
|> Enum.map(&verse/1)
|> Enum.join("\n")
end
end`````` | 7,566 | 28,800 | {"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-2020-50 | latest | en | 0.906434 |
http://openstudy.com/updates/508804e1e4b058e80cf667f6 | 1,448,761,682,000,000,000 | text/html | crawl-data/CC-MAIN-2015-48/segments/1448398455135.96/warc/CC-MAIN-20151124205415-00172-ip-10-71-132-137.ec2.internal.warc.gz | 168,424,905 | 10,286 | ## rebecca1233 3 years ago When you write the given number in scientific notation, what is the exponent in the power of 10? (Type only the value of the exponent.) 31,800,000=3.18 * 10^?
1. SheldonEinstein
just like : 100 = 1 * 10^2
2. rebecca1233
so its 2?
3. SheldonEinstein
31800000 = 318 * 100000 = 318 * 10^5 318/100 * 10^7 = 3.18 * 10^7
4. rebecca1233
ok so ^7
5. SheldonEinstein
No , it is 7 @rebecca1233 Check it again!
6. SheldonEinstein
Yeah it is 7
7. rebecca1233 | 182 | 486 | {"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} | 3.25 | 3 | CC-MAIN-2015-48 | longest | en | 0.681659 |
https://roman-numerals.info/CCXCI | 1,726,069,283,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651390.33/warc/CC-MAIN-20240911152031-20240911182031-00870.warc.gz | 462,065,939 | 3,947 | Roman Numerals
Roman Numerals: CCXCI = 291
Convert Roman Numerals
Arabic numerals:
Roman numerals:
Arabicnumerals 0 1 M C X I 2 MM CC XX II 3 MMM CCC XXX III 4 CD XL IV 5 D L V 6 DC LX VI 7 DCC LXX VII 8 DCCC LXXX VIII 9 CM XC IX
The converter lets you go from arabic to roman numerals and vice versa. Simply type in the number you would like to convert in the field you would like to convert from, and the number in the other format will appear in the other field. Due to the limitations of the roman number system you can only convert numbers from 1 to 3999.
To easily convert between roman and arabic numerals you can use the table above. The key is to handle one arabic digit at a time, and translate it to the right roman number, where zeroes become empty. Go ahead and use the converter and observe how the table shows the solution in realtime!
Current date and time in Roman Numerals
2024-09-11 17:41:23 MMXXIV-IX-XI XVII:XLI:XXIII
Here is the current date and time written in roman numerals. Since the roman number system doesn't have a zero, the hour, minute, and second component of the timestamps sometimes become empty.
The year 291
Here you can read more about what happened in the year 291.
The number 291
The number 291 is divisble by 3 and 97 and can be prime factorized into 3×97.
291 as a binary number: 100100011
291 as an octal number: 443
291 as a hexadecimal number: 123
Numbers close to CCXCI
Below are the numbers CCLXXXVIII through CCXCIV, which are close to CCXCI. The right column shows how each roman numeral adds up to the total.
288 = CCLXXXVIII = 100 + 100 + 50 + 10 + 10 + 10 + 5 + 1 + 1 + 1 289 = CCLXXXIX = 100 + 100 + 50 + 10 + 10 + 10 + 10 − 1 290 = CCXC = 100 + 100 + 100 − 10 291 = CCXCI = 100 + 100 + 100 − 10 + 1 292 = CCXCII = 100 + 100 + 100 − 10 + 1 + 1 293 = CCXCIII = 100 + 100 + 100 − 10 + 1 + 1 + 1 294 = CCXCIV = 100 + 100 + 100 − 10 + 5 − 1 | 601 | 1,908 | {"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-2024-38 | latest | en | 0.759998 |
http://nrich.maths.org/public/leg.php?code=-600&cl=3&cldcmpid=7338 | 1,503,271,076,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886106996.2/warc/CC-MAIN-20170820223702-20170821003702-00264.warc.gz | 304,429,355 | 5,878 | # Search by Topic
#### Resources tagged with STEM - Data Handling similar to Counting Dolphins:
Filter by: Content type:
Stage:
Challenge level:
### There are 13 results
Broad Topics > STEM mapping > STEM - Data Handling
### Counting Dolphins
##### Stage: 4 Challenge Level:
How would you go about estimating populations of dolphins?
### How Do You React?
##### Stage: 4 Challenge Level:
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
### Investigating Epidemics
##### Stage: 3 and 4 Challenge Level:
Simple models which help us to investigate how epidemics grow and die out.
### Reaction Timer
##### Stage: 3 Challenge Level:
This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.
### Avalanche!
##### Stage: 2 and 3 Challenge Level:
Investigate how avalanches occur and how they can be controlled
### Bird Watch
##### Stage: 2 and 3 Challenge Level:
Do you know which birds are regular visitors where you live?
### Terrariums
##### Stage: 3 Challenge Level:
Build a mini eco-system, and collect and interpret data on how well the plants grow under different conditions.
### Observing the Sun and the Moon
##### Stage: 2 and 3 Challenge Level:
How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.
### Troublesome Triangles
##### Stage: 2 and 3 Challenge Level:
Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .
### Using the Haemocytometer
##### Stage: 4 Challenge Level:
Practise your skills of proportional reasoning with this interactive haemocytometer.
### Flip Your Mat!
##### Stage: 2 and 3 Challenge Level:
What shape and size of drinks mat is best for flipping and catching?
### Helicopters
##### Stage: 2, 3 and 4 Challenge Level:
Design and test a paper helicopter. What is the best design?
### Solving the Genome Puzzle
##### Stage: 4 and 5
The human genome is represented by a string of around 3 billion letters. To deal with such large numbers, genome sequencing relies on clever algorithms. This article investigates. | 524 | 2,399 | {"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} | 3.390625 | 3 | CC-MAIN-2017-34 | latest | en | 0.839863 |
http://lifeyoga.ro/what-you-do-not-know-about-physics-problem/ | 1,582,716,225,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875146341.16/warc/CC-MAIN-20200226084902-20200226114902-00386.warc.gz | 83,957,426 | 74,995 | • 0
• 0
• Share
## What You Need to Know About Physics Problem
For these reasons, it has occupied an essential role in the historical evolution of the three-body issue. It’s possible to chat with our specialists to find out more about their abilities. The significance of planning increase if you’re working with a team.
Like other regions of learning and life, a few of these habits could possibly be beneficial and some can actually hinder your progress in figuring out how to solve physics issues. That which we’ve shown is that the spectral gap is among these undecidable difficulties. Click on these links to assess the approach to solving those types of issues.
## The Appeal of Physics Problem
The best dissertation writing majority of the moment, your results are going to teach you something specific concerning the Universe. There isn’t any reason why it ought to be. In this manner, if you create a mistake, it is simpler to find it.
## Top Choices of Physics Problem
There’s a really straightforward remedy to this. The value appears reasonable enough. Again, a fair price.
## What’s Really Going on with Physics Problem
Boat wakes can actually have a totally different angle under certain conditions, and can even be off-centered with regard to the direction of the boat. At the peak of the loop, the force of the automobile’s acceleration pushes the passenger off the seat toward the middle of the loop, whilst inertia pushes the passenger back in the seat. At the peak of the hill, the cars possess a huge quantity of likely energy.
## The Rise of Physics Problem
By having the test, all you will need to do is write the expected outcome of a particular input for the function. https://www.palissy.fr/ Understand the Results Remember that you just have induction in the event the magnetic flux by means of a loop changes. Quite simply, you need to find how much force is needed to convert the roller-coaster’s kinetic energy into heat and sound in a particular distance.
## Physics Problem Secrets That No One Else Knows About
Later, exactly the same rebelliousness would be crucial in revolutionizing physics. To run operations, atoms want to get moved around so they can speak to one another. Single atoms are not simple to trap and even harder to move.
Science isn’t a procedure for accepting a theory. The study of energy is referred to as physics. There are several ways to fix a physics issue.
A next step is to use what is known to discover the proper equation to obtain what’s unknown. Since theories can contradict one another, but there aren’t any contradictions in reality, every problem signals our knowledge has to be flawed or inadequate. https://www.grademiners.com/ Determine which physical principles will be able to help you solve the issue.
You may see with this 3 variable problem that you could only chose the ideal scenario for a single variable or have a mix of less than optimal values. This is the very first time you truly start to find quantitative relationships among the variables. If you’re given the elements of a vector and asked for the direction, you will want to un-do one of the previous few equations.
## Physics Problem Help!
Dont slacken off toward the close of the semester. Physics assignments might appear tricky, particularly for freshmen. Most students face a true battle when they’re handling math problems homework.
You’re able to control the entire process via our live chat. It’s also a great notion to return to the picture to make certain that you correctly assigned signs to every component. EXECUTE the PLAN Now you’re prepared to execute the strategy.
As Einstein advised, it’s in nature that you will see the answers to your questions. The fact of the statement needs to be based on something outside science. In this instance, the question becomes why our universe has properties that appear to be so finely tuned to permit for the presence of life.
According to my observation, it’s because of the lack or limitation of Visualisation that may be generated in your thoughts by just reading the mere words and seeing diagrams. After all, it is a whole lot simpler to find the proper answer if you ask the proper question. What’s cool, however, is you may just give the entire world view access and this script will nonetheless get the job done.
When you compose the test for this function, the test is going to do the testing for the validation and the database query at the same time. EVALUATE the SOLUTION Finally, you’re prepared to assess your answer. Microfluidics provides a possible remedy to such issues.
## The Argument About Physics Problem
After the test fails, you don’t have any idea which part breaks. A suitable body suit is just one of the most crucial parts of diving equipment, because the comfort of your trip is dependent on a superior style and fit. Huge parks want various rider experiences and launch coasters are an excellent way to modify the feel, states Rhoads. | 1,002 | 4,981 | {"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-2020-10 | latest | en | 0.92254 |
https://gmatclub.com/forum/state-spokesperson-many-business-people-who-have-not-been-46051.html?kudos=1 | 1,490,292,512,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218187193.40/warc/CC-MAIN-20170322212947-00069-ip-10-233-31-227.ec2.internal.warc.gz | 806,872,660 | 61,409 | Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
GMAT Club
It is currently 23 Mar 2017, 11:08
# R2 Decisions:
Berkeley Haas; Decision Tracker (Join Chat Room 5) | Yale SOM; Decision Tracker (Join Chat Room 4
### 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
# State Spokesperson: Many business people who have not been
Author Message
TAGS:
### Hide Tags
CEO
Joined: 29 Mar 2007
Posts: 2575
Followers: 20
Kudos [?]: 435 [0], given: 0
### Show Tags
23 May 2007, 19:56
00:00
Difficulty:
(N/A)
Question Stats:
78% (01:59) correct 22% (01:40) wrong based on 4 sessions
### HideShow timer Statistics
State Spokesperson:
Many business people who have not been to our state believe that we have an inadequate road system. Those people are mistaken, as is obvious from the fact that in each of the past six years, our state has spent more money per mile on road improvements than any other state.
Which of the following, if true, most seriously undermines the reasoning in the spokesperson's argument?
A. In the spokesperson's state, spending on road improvements has been increasing more slowly over the past six years than it has in other states.
B. Adequacy of a state's road system is generally less important to a businessperson considering doing business there than is the availability of qualified employees.
C. Over the past six years, numerous businesses have left the spokesperson's state, but about as many businesses have moved into the state.
D. In general, the number of miles of road in a state's road system depends on both the area and the population of the state.
E. Only states with seriously inadequate road systems need to spend large amounts of money on road improvements.
OA Later.
If you have any questions
New!
Director
Joined: 24 Aug 2006
Posts: 749
Location: Dallas, Texas
Followers: 6
Kudos [?]: 153 [0], given: 0
### Show Tags
23 May 2007, 23:16
No brainer (E)
_________________
"Education is what remains when one has forgotten everything he learned in school."
Senior Manager
Joined: 28 Feb 2007
Posts: 304
Followers: 1
Kudos [?]: 40 [0], given: 0
### Show Tags
24 May 2007, 01:24
Another vote for: E
24 May 2007, 01:24
Similar topics Replies Last post
Similar
Topics:
3 Approximately 5 ,000 people who have been convicted of nonvi 14 29 Mar 2014, 06:38
3 Milville business spokesperson: Snowmobiles brings many 4 21 Jul 2012, 17:18
11 State spokesperson: Many businesspeople who have not been to 19 12 May 2011, 08:31
2 Recent surveys show that many people who have left medical 9 20 Apr 2008, 05:47
9 People who live unusually long tend to have been lean young 8 01 Feb 2008, 13:37
Display posts from previous: Sort by | 841 | 3,246 | {"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-2017-13 | longest | en | 0.931481 |
https://www.cliffsnotes.com/tutors-problems/Statistics-and-Probability/55738854--Circumference-vs-Diameter-for-circular-objects-Diameter-Can-1/ | 1,708,973,391,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474661.10/warc/CC-MAIN-20240226162136-20240226192136-00067.warc.gz | 715,786,360 | 101,938 | Circumference vs. Diameter for circular objects Diameter Can 1...
Question
# Circumference vs. Diameter for circular objects Diameter Can 1...
Circumference vs. Diameter for circular objects
Y1 = 18.2 cm Y2 = 32.7 cm
X1 = 5.2 cm X2 = 9.9 cm
Calculate Slope of Trendline:
(y₂ - y₁)/(x₂ - x₁) = (32.7-18.2) / (9.9-5.2) = 14.5 / 4.7 = 3.085 cm
Answer the questions below. You will need to following equation to answer part b.
Circumference = ( π )(Diameter)
A. What was the calculated value for the slope of your trendline? The calculated value for the slope of my trendline is 3.1 cm OR 3.085 cm
B. What is the expected value for the slope of your trendline?
C. Calculate the % error.
% error = (measured value - true value) x 100%
True value
D. Based upon your % error, how good were your measurements? What are other sources of error? Identify 2 points of the trendline
Solved by verified expert
sectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellentesque dapibus efficitur laoreet. Nam risus ante, dapibus a molestie consequat, ultrices ac magna. Fusce dui lectus, congue vel laoreet ac, dictum vitae odio. Donec aliquet
sectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellent
10,000 step-by-step explanations
<p>sectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellentesque dapibus efficitur laoreet. Nam risus ante, dapibus a molestie consequat, ultrices ac magna. Fusce dui lectus, congue vel laoreet ac, dictum vitae odio. Donec aliquet</p>sectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellent
## Step-by-step explanation
sectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis.
sectetur adipiscing elit. Nam lacinia pulvinar tortor nec
sectetur
sectetur adipiscing elit. Nam lacinia pul
sectetur adipiscing elit. Nam lacinia pulv
sectetur adipiscing elit. Nam lacinia pulvin
sectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis
sectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellentesque dapibus efficitur laoreet. Nam risus ante, dapibus a molestie c
sectetur adipiscing elit. Nam lacinia pulvinar tortor n
sectetur
sectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellentesque dapibus efficitur laoreet. Nam risus
sectetur
sectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellentesque dapibus efficitur laoreet. Nam risus ante, dapibus a molestie consequat, ultrices ac magna. Fus
sectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellentesque dapibus efficitur
sectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellentesque dapibus efficitur laoreet. Nam risus ante, dapibus a molestie consequat, ultrices ac magna. Fusce dui lectus, congue vel laoreet ac
sectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellentesque dapibus efficitur laoreet. Nam risus ante, dapibus a molestie consequat, ultrices ac magna. Fusce dui lectus, congue vel laoreet ac, dictum vitae odio. Donec aliqu
sectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellentesque dapibus efficitur laoreet. Nam risus ante, dapibus a molestie consequat, ultrices ac magna. Fusce dui lectus, congue vel laoreet ac, dictum vitae odio. Donec aliquet. Lorem ipsum dolor sit amet, consectetur adipiscing elit. | 974 | 3,441 | {"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-2024-10 | latest | en | 0.41971 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.