Luciole-pretraining-filtered
Collection
6 items
•
Updated
url
string | fetch_time
int64 | content_mime_type
string | warc_filename
string | warc_record_offset
int32 | warc_record_length
int32 | text
string | token_count
int32 | char_count
int32 | metadata
string | score
float64 | int_score
int64 | crawl
string | snapshot_type
string | language
string | language_score
float64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
https://ex.burnettmediagroup.com/what-is-the-phraseexclamation-mark-in-x-y/
| 1,627,454,305,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-31/segments/1627046153531.10/warc/CC-MAIN-20210728060744-20210728090744-00632.warc.gz
| 265,657,037
| 7,750
|
# What is the term”exclamation mark” in mathematics?
The answer is easy. Below are some approaches to inform as soon as an equation can be really actually a multiplication equation and also how to add and subtract using”exclamation marks”. For instance,”2x + 3″ imply”multiply two integers from about a few, making a value add up to 2 and 3″.
By way of example,”2x + 3″ are multiplication by write a paper online three. In addition, we can add the values of 2 and 3 collectively. To add the worth, we’ll use”e”that I” (or”E”). With”I” means”include the worth of one to the worth of 2″.
To add the worth , we can certainly do this similar to that:”x – y” means”multiply x by y, making a worth equal to zero”. For”x”y”, we’ll use”t” (or”TE”) for the subtraction and we’ll use”x y y” to solve the equation.
You might feel that you are not supposed to utilize”e” in addition as”I” implies”subtract” however it’s perhaps not so easy. https://www.masterpapers.com For instance, to express”2 – 3″ approaches subtract from three.
So, to add the values that we utilize”t”x” (or”TE”), which might be the numbers of the worth to be included. We will use”x” to subtract the price of a person in the price of both 2 plus that will provide us precisely exactly the outcome.
To multiply the worth , we certainly can certainly do this like this:”2x + y” necessarily imply”multiply two integers by y, creating a price add up to two plus one”. You may know this is really just a multiplication equation when we use”x ray” to subtract one from 2. Or, it can be”x – y” to subtract from 2. Be aware that you can publish the equation using a decimal position and parentheses.
Now, let us take an example. Let’s say that we would like to multiply the value of”nine” by”5″ and we all have”x nine”y https://www.eurachem.org/images/stories/Guides/pdf/recovery.pdf twenty-five”. Then we’ll use”x – y” to subtract the price of one in the worth of two.
| 509
| 1,930
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.53125
| 5
|
CC-MAIN-2021-31
|
longest
|
en
| 0.901994
|
https://esingaporemath.com/program-grade-3
| 1,638,473,770,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-49/segments/1637964362287.26/warc/CC-MAIN-20211202175510-20211202205510-00559.warc.gz
| 305,205,293
| 13,865
|
Our curriculum is spiral
Please note that our virtual Singapore Math Grade 3 curriculum is spiral and it provides for the review of the important concepts that students learned in Grade 2. Our online K-5 math curriculum is aligned with all standard Singapore Math textbook series and it includes all content that these series cover, from Kindergarten grade through 5th grade.
Our Singapore Math for 3rd Grade may introduce some topics one grade level earlier or postpone coverage of some topics until grade 4. In the few instances where 3rd grade level units don’t exactly align between our curriculum and textbooks, you will still be able to easily locate the corresponding unit in our program by referring to the table of contents one grade below or above.
Correspondence to 3A and 3B
For your reference, the following topics in our curriculum correspond to Singapore Math practice Grade 3 in levels 3A and 3B:
Singapore Math 3a
Multiplication and division, multiplication tables of 2, 5, and 10, multiplication tables of 3 and 4, multiplication tables of 6, 7, 8, and 9, solving problems involving multiplication and division, and mental math computation and estimation.
Singapore Math 3b
Understanding fractions, time, volume, mass, representing and interpreting data, area and perimeter, and attributes of two-dimensional shapes.
Student prior knowledge
Prior to starting third grade Singapore Math, students should already know how to relate three-digit numbers to place value, use place-value charts to form a number and compare three-digit numbers. The initial lessons in the Singapore Math 3rd Grade are both a review and an extension of content covered in the prior grade that include mental addition of 1-digit number to a 2-digit number and counting by 2s, 5s, and 10s.
3rd Grade Singapore Math Scope and Sequence
• Multiplication And Division
This unit covers understanding of multiplication and division. In this unit students will extend their knowledge of making equal groups to formalize their understanding of multiplication and division. The focus of this unit is on understanding multiplication and division using equal groups, not on memorizing facts. Students will learn how the multiplication symbol to represent addition of quantities in groups.
• Multiplication Tables Of 2, 5, And 10
This unit covers multiplying by 2 using skip-counting, multiplying by 2 using dot paper, multiplying by 5 using skip-counting, multiplying by 5 using dot paper, multiplying by 10 using skip-counting, dividing using related multiplication facts of 2, 5, or 10. Students will learn building multiplication tables of 2, 5, and 10 to formalize their understanding of multiplication and division for facts 2, 5, and 10. Students will learn to find their division facts by thinking of corresponding multiplication facts.
• Multiplication Tables Of 3 And 4
This unit covers multiplying by 3 using skip-counting, multiplying by 3 using dot paper, multiplying by 4 using skip-counting, multiplying by 4 using dot paper, dividing using related multiplication facts of 3 or 4. Students will learn building multiplication tables of 3 and 4 to formalize their understanding of multiplication and division for facts 3 and 14. Students will learn to find their division facts by thinking of corresponding multiplication facts.
• Multiplication Tables Of 6, 7, 8, And 9
This unit covers multiplication properties, multiplying by 6, multiplying by 7, multiplying by 8, multiplying by 9, dividing using related multiplication facts of 6, 7, 8, or 9. Students will learn building multiplication tables of 6, 7, 8, and 9 to formalize their understanding of multiplication and division for facts 6, 7, 8, and 9. Students will learn to find their division facts by thinking of corresponding multiplication facts.
• Solving Problems Involving Multiplication And Division
This unit covers solving one- and two-step word problems involving multiplication and division. Students will use a part-whole and comparison models to solve word problems involving multiplication and division.
• Mental Computation And Estimation
This unit covers learning mental math strategies to solve multiplication and division problems. Students will use place value to round whole numbers.
• Understanding Fractions
This unit covers parts and wholes, fractions and number lines, comparing unit fractions, equivalence of fractions, and comparing like fractions. Students will learn fractional notation that include the terms “numerator” and “denominator.” Students will understand that a common fraction is composed of unit fractions and they will learn to compare unit fractions.
• Time
This unit covers telling time, adding time, subtracting time, and time intervals. Students will review and practice to tell time to the minute, learn telling intervals of time in hours, convert units of time between hours, minutes, seconds, days and weeks.
• Volume
This unit covers understanding of volume, comparing volume, measuring and estimating volume, and word problems involving volume.
• Mass
This unit covers measuring mass in kilograms, comparing mass in kilograms, measuring mass in grams, comparing mass in grams, and word problems involving mass.
• Representing And Interpreting Data
This unit covers scaled picture graphs and scaled bar graphs, reading and interpreting bar graphs, and line plots. Students will learn to sort data into groups and categories and use numerical data to interpret bar graphs and line plots.
• Area And Perimeter
This unit covers understanding of area, measuring area using square centimeters and square inches, measuring area using square meters and square feet, area and perimeter, solving problems involving area and perimeter. Students will learn to find and measure area of figures in square units that include square centimeters, square inches, square meters and square feet.
• Attributes Of Two-Dimensional Shapes
This unit covers categories and attributes of shapes and partitioning shapes into equal areas. Students will understand that figures with different shapes can have the same area.
| 1,234
| 6,132
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.09375
| 4
|
CC-MAIN-2021-49
|
latest
|
en
| 0.914701
|
https://www.hackmath.net/en/math-problem/8311
| 1,611,170,840,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-04/segments/1610703521987.71/warc/CC-MAIN-20210120182259-20210120212259-00634.warc.gz
| 835,761,036
| 13,306
|
# Height of the room
Given the floor area of a room as 24 feet by 48 feet and space diagonal of a room as 56 feet. Can you find the height of the room?
Correct result:
c = 16 ft
#### Solution:
We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!
Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
#### You need to know the following knowledge to solve this word math problem:
We encourage you to watch this tutorial video on this math problem:
## Next similar math problems:
• Diagonal
Determine the dimensions of the cuboid, if diagonal long 53 dm has an angle with one edge 42° and with another edge 64°.
• Cuboidal room
Length of cuboidal room is 2m breadth of cuboidal room is 3m and height is 6m find the length of the longest rod that can be fitted in the room
• Ratio of edges
The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
• Four sided prism
Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50-degree angle with the base plane.
• Cuboid diagonals
The cuboid has dimensions of 15, 20 and 40 cm. Calculate its volume and surface, the length of the body diagonal and the lengths of all three wall diagonals.
• Space diagonal angles
Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD.
• The room
The room has a cuboid shape with dimensions: length 50m and width 60dm and height 300cm. Calculate how much this room will cost paint (floor is not painted) if the window and door area is 15% of the total area and 1m2 cost 15 euro.
• Jared's room painting
Jared wants to paint his room. The dimensions of the room are 12 feet by 15 feet, and the walls are 9 feet high. There are two windows that measure 6 feet by 5 feet each. There are two doors, whose dimensions are 30 inches by 6 feet each. If a gallon of p
• Solid cuboid
A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
• Find diagonal
Find the length of the diagonal of a cuboid with length=20m width=25m height=150m
| 641
| 2,490
|
{"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}
| 4.1875
| 4
|
CC-MAIN-2021-04
|
longest
|
en
| 0.920097
|
https://leadingbittersweetchange.com/aircraft-operations/scheduling/shop-smart-for-aviation-software
| 1,675,527,797,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-06/segments/1674764500140.36/warc/CC-MAIN-20230204142302-20230204172302-00381.warc.gz
| 375,917,558
| 6,845
|
# Equation solver with square root
This Equation solver with square root supplies step-by-step instructions for solving all math troubles. Our website will give you answers to homework.
## The Best Equation solver with square root
In this blog post, we will be discussing about Equation solver with square root. As any math student knows, calculus can be a difficult subject to grasp. The concepts are often complex and require a great deal of concentration to understand. Fortunately, there are now many calculus solvers available that can help to make the subject more manageable. These tools allow you to input an equation and see the steps involved in solving it. This can be a great way to learn how to solve problems on your own. In addition, calculus solvers with steps can also help you to check your work and ensure that you are getting the correct answer. With so many helpful features, it is no wonder that these tools are becoming increasingly popular among math students of all levels.
Word phrase math is a mathematical technique that uses words instead of symbols to represent numbers and operations. This approach can be particularly helpful for students who struggle with traditional math notation. By using words, students can more easily visualize the relationships between numbers and operations. As a result, word phrase math can provide a valuable tool for understanding complex mathematical concepts. Additionally, this technique can also be used to teach basic math skills to young children. By representing numbers and operations with familiar words, children can develop a strong foundation for future mathematics learning.
A rational function is any function which can be expressed as the quotient of two polynomials. In other words, it is a fraction whose numerator and denominator are both polynomials. The simplest example of a rational function is a linear function, which has the form f(x)=mx+b. More generally, a rational function can have any degree; that is, the highest power of x in the numerator and denominator can be any number. To solve a rational function, we must first determine its roots. A root is a value of x for which the numerator equals zero. Therefore, to solve a rational function, we set the numerator equal to zero and solve for x. Once we have determined the roots of the function, we can use them to find its asymptotes. An asymptote is a line which the graph of the function approaches but never crosses. A rational function can have horizontal, vertical, or slant asymptotes, depending on its roots. To find a horizontal asymptote, we take the limit of the function as x approaches infinity; that is, we let x get very large and see what happens to the value of the function. Similarly, to find a vertical asymptote, we take the limit of the function as x approaches zero. Finally, to find a slant asymptote, we take the limit of the function as x approaches one of its roots. Once we have determined all of these features of the graph, we can sketch it on a coordinate plane.
A binomial solver is a math tool that helps solve equations with two terms. This type of equation is also known as a quadratic equation. The solver will usually ask for the coefficients of the equation, which are the numbers in front of the x terms. It will also ask for the constants, which are the numbers not attached to an x. With this information, the solver can find the roots, or solutions, to the equation. The roots tell where the line intersects the x-axis on a graph. There are two roots because there are two values of x that make the equation true. To find these roots, the solver will use one of several methods, such as factoring or completing the square. Each method has its own set of steps, but all require some algebraic manipulation. The binomial solver can help take care of these steps so that you can focus on understanding the concept behind solving quadratic equations.
Basic mathematics is the study of mathematical operations and their properties. The focus of this branch of mathematics is on addition, subtraction, multiplication, and division. These operations are the foundation for all other types of math, including algebra, geometry, and trigonometry. In addition to studying how these operations work, students also learn how to solve equations and how to use basic concepts of geometry and trigonometry. Basic mathematics is an essential part of every student's education, and it provides a strong foundation for further study in math.
## Help with math
It has helped me more than my math teacher, of course there are a few problems here and there like not scanning the exercises correctly and it never scans "±" this sign but apart from that I really love the app. Although it would be nice to not have to pay for explanations, maybe other features but explanation is an important part.
Mila Flores
Although the app doesn't solve everything it is pretty much my free math tutor. It's so easy to work with. Steps for solving are always easy to understand. I love it!!! The app is the best and it helped me with my studies at school and I now understand math better
Bethany Young
App that solves math problems with a picture Math solution calculator Free online math websites Math probability solver Geometry tutor online
| 1,041
| 5,301
|
{"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}
| 4.59375
| 5
|
CC-MAIN-2023-06
|
latest
|
en
| 0.942348
|
https://divinewsmedia.com/8312/
| 1,638,541,360,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-49/segments/1637964362879.45/warc/CC-MAIN-20211203121459-20211203151459-00576.warc.gz
| 294,291,715
| 13,221
|
# Period Of Function
by -2 views
Period of sinusoidal functions from equation. You can figure this out without looking at a graph by dividing with the frequency which in this case is 2.
Graphing Trigonometric Functions Graphing Trigonometric Functions Neon Signs
### Periodic functions are used throughout science to describe oscillations waves and other phenomena that exhibit periodicity.
Period of function. This is why this function family is also called the periodic function family. Tap for more steps. Therefore in the case of the basic cosine function f x.
When this occurs we call the horizontal shift the period of the function. If a function has a repeating pattern like sine or cosine it is called a periodic function. Amplitude a Let b be a real number.
You might immediately guess that there is a connection here to finding points on a circle. F x k f x. Horizontal stretch is measured for sinusoidal functions as their periods.
For basic sine and cosine functions the period is 2 π. Any function that is not periodic is called aperiodic. The period is defined as the length of one wave of the function.
The period is the length on the x axis in one cycle. However the amplitude does not refer to the highest point on the graph or the distance from the highest point to the x axis. Midline of sinusoidal functions from equation.
The x-value results in a unique output eg. The period of a sinusoid is the length of a complete cycle. By using this website you agree to our Cookie Policy.
Periodic Functions A periodic function occurs when a specific horizontal shift P results in the original function. More formally we say that this type of function has a positive constant k where any input x. The period is defined as the length of a functions cycle.
Period of a Function The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function. According to periodic function definition the period of a function is represented like f x f x p p is equal to the real number and this is the period of the given function f x. In other words a periodic function is a function that repeats its values after every particular interval.
Trig functions are cyclical and when you graph them youll see the ups and downs of the graph and youll see that these ups and downs. Where f x P f x for all values of x. Replace with in the formula for period.
Amplitude and Period of Sine and Cosine Functions The amplitude of y a sin x and y a cos x represents half the distance between the maximum and minimum values of the function. This is the currently selected item. Any part of the graph that shows this pattern over one period is called a cycle.
Notice that in the graph of the sine function shown that f x sin x has period. Period of sinusoidal functions from graph. The distance between and is.
Midline amplitude and period review. The absolute value is the distance between a number and zero. The period of a periodic function is the interval of x -values on which the cycle of the graph thats repeated in both directions lies.
In this case one full wave is 180 degrees or radians. So the period of or is. You are partially correct.
Khan Academy is a 501c3 nonprofit organization. The period of a periodic function is the interval of x -values on which one copy of the repeated pattern occurs. This is the currently selected item.
A periodic function repeats its values at set intervals called periods. Period can be defined as the time interval between the two occurrences of the wave. A periodic function is a function that repeats its values at regular intervals for example the trigonometric functions which repeat at intervals of 2π radians.
The period of the function can be calculated using. Our mission is to provide a free world-class education to anyone anywhere. Grade 12 trigonometry problems and questions on how to find the period of trigonometric functions given its graph or formula are presented along with detailed solutions.
So how to find the period of a function actually. Free function periodicity calculator – find periodicity of periodic functions step-by-step This website uses cookies to ensure you get the best experience. In the problems below we will use the formula for the period P of trigonometric functions of the form y a sin bx c d or y a cos bx c d and which is given by.
The period is the length of the smallest interval that contains exactly one copy of the repeating pattern. A function is just a type of equation where every input eg.
Amplitude Period Phase Shift Vertical Translation And Range Of Y 3 Math Videos Translation Period
The Mathematics Of Sine Cosine Functions Was First Developed By The Ancient Indian Mathematician Aryabhata H Trigonometric Functions Mathematics Theorems
Amplitude Phase Shift Vertical Shift And Period Change Of The Cosine Function Fun Learning Period Change
Transformations Of Sin Function Love Math Math Graphing
Step By Step Instructions Of How To Graph The Sine Function Graphing Trigfunction Trigonometry Sinusoidal Math Materials Math Graphic Organizers Calculus
Graphing Trigonometric Functions Graphing Trigonometric Functions Trigonometry
Geometry Trigonometry 9 Trig Graphs Amplitude And Period Trigonometry Graphing Classroom Posters
Graphs Of Trigonometric Functions Poster Zazzle Com In 2021 Trigonometric Functions Functions Math Math Poster
Applied Mathematics Period Of A Function Hard Sum Mathematics How To Apply Period
Students Will Match 10 Graphs To 10 Sine Or Cosine Equations By Finding The Amplitude And Period Of Each Function Students Will Then Graphing Sines Equations
Precal And Trig Function Posters Math Word Problems Mathematics Worksheets Word Problems
Graphing Sin Cosine W Period Change 4 Terrific Examples Graphing Precalculus Trigonometry
Translating Periodic Functions Learning Mathematics Math Methods Math Instruction
Trigonometric Graphing Math Methods Learning Math Math
Trigonometric Graphing Math Methods Learning Math Math
Pin On Math
Applied Mathematics Greatest Integer Function And Period Integers Mathematics How To Apply
Applet Allows For Students To Drag 5 Key Points Of One Period Of A Sinusoidal Wave So That The Graph Displayed Match Trigonometric Functions Graphing Equations
Functions Non Functions By Ryan Devoe Period 7 By Rmdevoe Teaching Mathematics Teaching Algebra Teaching Math
READ: Which One Of The Following Is An Example Of A Period Cost?
| 1,324
| 6,517
|
{"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}
| 4.5
| 4
|
CC-MAIN-2021-49
|
latest
|
en
| 0.922685
|
https://fiveable.me/ap-stats/unit-6/justifying-claim-based-confidence-interval-difference-population-proportions/study-guide/m6d2wvAbSyMqmNwEyt43?
| 1,632,461,363,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-39/segments/1631780057504.60/warc/CC-MAIN-20210924050055-20210924080055-00646.warc.gz
| 320,253,745
| 43,280
|
📚
All Subjects
>
📊
AP Stats
>
⚖️
Unit 6
6.9 Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions
2 min readjune 5, 2020
Josh Argo
AP Statistics📊
Bookmarked 4.3k • 246 resources
See Units
Interpretation
When interpreting a confidence interval for the difference in two population proportions, we need to show that the bounds given by the confidence interval give us an estimate of what the difference in our two population proportion are within. Our interpretation and interval is also strongly based on what our confidence level is. The standard confidence level is 95%.
When completing a confidence interval on the AP Statistics Exam, you will generally be graded on if you included the following three components:
👉 Including confidence level (given in problem)
👉 Including that our interval is making inference about the difference in population proportions, not sample proportions.
👉 Including context of the problem.
If you do these three things and get the correct answer, you will be on your way to 💯.
Testing a Claim
When we are testing a claim using a confidence interval, we want to see if 0 is included in our interval. If 0 is included in our interval, it is quite possible that there is no difference in the two population proportions we are testing. If 0 is not included in our interval, we have reason to suspect that the two population proportions are in fact different.
Image Courtesy of cbssports
Example
Recall from Unit 6.8 we constructed a confidence interval for the difference in proportions for shots made for Michael Jordan and Lebron James. We got the following output from our calculator:
A correct way to interpret this would be:
"We are 95% confident that the true difference in the population proportions for shots made between Michael Jordan and Lebron James is between (0.063, 0.133). Since 0 is not included in our interval, we have reasonable evidence that the two population proportions are actually different"
So it appears that MJ is better than Lebron. ¯\_(ツ)_/¯
However, some things to note here is that we took a sample from both of their first seasons. If we refer back to basketball-reference.com and compare the two players 10th seasons in the league, we might find a VERY different result. Another possible confounding variable is the teammates these two players have been surrounded by throughout their career.
Resources:
Was this guide helpful?
Join us on Discord
Thousands of students are studying with us for the AP Statistics exam.
join now
Studying with Hours = the ultimate focus mode
Start a free study session
🔍 Are you ready for college apps?
Take this quiz and find out!
Start Quiz
Browse Study Guides By Unit
📆Big Reviews: Finals & Exam Prep
✏️Blogs
✍️Free Response Questions (FRQs)
👆Unit 1: Exploring One-Variable Data
✌️Unit 2: Exploring Two-Variable Data
🔎Unit 3: Collecting Data
🎲Unit 4: Probability, Random Variables, and Probability Distributions
📊Unit 5: Sampling Distributions
⚖️Unit 6: Inference for Categorical Data: Proportions
😼Unit 7: Inference for Qualitative Data: Means
✳️Unit 8: Inference for Categorical Data: Chi-Square
📈Unit 9: Inference for Quantitative Data: Slopes
FREE AP stats Survival Pack + Cram Chart PDF
Sign up now for instant access to 2 amazing downloads to help you get a 5
Join us on Discord
Thousands of students are studying with us for the AP Statistics exam.
join now
💪🏽 Are you ready for the Stats exam?
Take this quiz for a progress check on what you’ve learned this year and get a personalized study plan to grab that 5!
START QUIZ
Play this on HyperTyper
Practice your typing skills while reading Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions
Start Game
Text FIVEABLE to741741to get started.
© 2021 Fiveable, Inc.
| 908
| 3,820
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.25
| 4
|
CC-MAIN-2021-39
|
latest
|
en
| 0.921178
|
http://www.studygeek.org/calculus/solving-differential-equations/
| 1,539,663,835,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-43/segments/1539583509996.54/warc/CC-MAIN-20181016030831-20181016052331-00216.warc.gz
| 549,229,649
| 26,754
|
# How to solve differential equations
Differential equations make use of mathematical operations with derivatives. Solving differential equations is a very important, but also hard concept in calculus. There exist more methods of solving this kind of exercises.
Firstly, we will have a look on how first order differential equation can be solved. Below, you will find a series of methods of solving this kind of differential equations. The first one is the separation method of variables. Practically, as the name says itself, you have to separate the variables, obtaining an equality of two functions with different variables. Then you integrate the expression and you obtain an equality of two integrals. Then you will solve the integrals and find the solution.
For the homogeneous differential equations, we use the substitution method and we reduce the equation to the variable separable. Having an exercise in which you have to solve the differential equation, you firstly have to figure out what kind of differential equation is the equation, so you know what method it's better to use.
Another method to solve differential equation is the exact form method. You know your equation is in an exact form if it has the following form: M(x,y) dx + N(x,y) dy = 0, where M and N are the functions of x and y in such a way that:
A differential equation is called linear as long as the dependent variable and its derivatives occur in the first degree and are not multiplied together.
f to fn are the functions of x.
In order to figure out how to solve differential equation, you firstly have to determine the order of the differential equation. For example, for the second order differential equation there is a more special method of finding the solution: divide the second order differential equation in 2 parts: Q(x)=0 and Q(x) is a function of x. For both members calculate the auxiliary equation and find the complementary function. Next, if Q(x) is a part of the equation, find the particular integral of the equation. In the end, sum up the complementary function with the particular integral.
## Solving differential equations video lesson
Ian Roberts Engineer San Francisco, USA "If you're at school or you just deal with mathematics, you need to use Studygeek.org. This thing is really helpful." Lisa Jordan Math Teacher New-York, USA "I will recommend Studygeek to students, who have some chalenges in mathematics. This Site has bunch of great lessons and examples. " John Maloney Student, Designer Philadelphia, USA " I'm a geek, and I love this website. It really helped me during my math classes. Check it out) " Steve Karpesky Bookkeeper Vancuver, Canada "I use Studygeek.org a lot on a daily basis, helping my son with his geometry classes. Also, it has very cool math solver, which makes study process pretty fun"
| 586
| 2,838
|
{"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}
| 4.875
| 5
|
CC-MAIN-2018-43
|
longest
|
en
| 0.953457
|
https://edurev.in/t/187535/Refraction-Reflection-of-Plane-Waves-using-Huygens
| 1,723,392,338,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-33/segments/1722641002566.67/warc/CC-MAIN-20240811141716-20240811171716-00470.warc.gz
| 179,972,470
| 66,774
|
Refraction & Reflection of Plane Waves using Huygens Principle
# Refraction & Reflection of Plane Waves using Huygens Principle | Physics Class 12 - NEET PDF Download
As we know that when light falls on an object, it bends and move through the material, this is what refraction is. Also when the light bounces off the medium it is called a reflection. Let us know study reflection and refraction of waves by Huygen’s principle.
Reflection using Huygens Principle
We can see a ray of light is incident on this surface and another ray which is parallel to this ray is also incident on this surface. Plane AB is incident at an angle ‘ i ‘ on the reflecting surface MN. As these rays are incident from the surface, so we call it incident ray. If we draw a perpendicular from point ‘A’ to this ray of light, Point A, and point B will have a line joining them and this is called as wavefront and this wavefront is incident on the surface.
These incident wavefront is carrying two points, point A and point B, so we can say that from point B to point C light is travelling a distance. If ‘ v ‘ represents the speed of the wave in the medium and if ‘ r ‘ represents the time taken by the wavefront from the point B to C then the distance
BC = vr
In order the construct the reflected wavefront we draw a sphere of radius vr from the point A. Let CE represent the tangent plane drawn from the point C to this sphere. So,
AE = BC = vr
If we now consider the triangles EAC and BAC we will find that they are congruent and therefore, the angles ‘ i ‘ and ‘r ‘ would be equal. This is the law of reflection
### Refraction using Huygen’s principle
We know that when a light travels from one transparent medium to another transparent medium its path changes. So the laws of refraction state that the angle of incidence is the angle between the incident ray and the normal and the angle of refraction is the angle between the refracted ray and the normal.
The incident ray, reflected ray and the normal, to the interface of any two given mediums all lie in the same plane. We also know that the ratio of the sine of the angle of incidence and sine of the angle of refraction is constant.
A plane wave AB is incident at an angle i on the surface PP' separating medium 1 and medium 2. The plane wave undergoes refraction and CE represents the refracted
wavefront. the figure corresponds to v2 < v1 so that the refracted waves bends towards the normal.
We can see a ray of light is incident on this surface and another ray which is parallel to this ray is also incident on this surface. As these rays are incident from the surface, so we call it incident ray.
Let PP’ represent the medium 1 and medium 2. The speed of the light in this medium is represented by v1 and v2. If we draw a perpendicular from point ‘A’ to this ray of light, Point A, and point B will have a line joining them and this is called as wavefront and this wavefront is incident on the surface.
If ‘ r ‘ represents the time taken by the wavefront from the point B to C then the distance,
BC = v1r
So to determine the shape of the refracted wavefront, we draw a sphere of radius v2r from the point A in the second medium. Let CE represent a tangent plane drawn from the point C on to the sphere. Then, AE = v2r, and CE would represent the refracted wavefront. If we now consider the triangles ABC and AEC, we readily obtain
where’ i ‘ and ‘ r ‘ are the angles of incidence and refraction, respectively. Substituting the values of v1 and v2 in terms of we get the Snell’s Law,
n1 sin i = n2 sin r
The document Refraction & Reflection of Plane Waves using Huygens Principle | Physics Class 12 - NEET is a part of the NEET Course Physics Class 12.
All you need of NEET at this link: NEET
## Physics Class 12
105 videos|425 docs|114 tests
## FAQs on Refraction & Reflection of Plane Waves using Huygens Principle - Physics Class 12 - NEET
1. What is refraction and reflection of plane waves?
Ans. Refraction is the bending of a wave as it passes from one medium to another, while reflection is the bouncing back of a wave after striking a surface. In the context of plane waves, refraction and reflection refer to the behavior of the wavefronts as they encounter different mediums or surfaces.
2. How does Huygens Principle explain refraction and reflection of plane waves?
Ans. According to Huygens Principle, every point on a wavefront acts as a source of secondary spherical wavelets. These secondary wavelets combine to form the new wavefront. In the case of refraction, the change in speed of the wavefront as it enters a new medium causes the wavefront to change direction. In reflection, the wavefront encounters a surface and the secondary wavelets bounce back, resulting in the reflection of the wave.
3. Can you explain how refraction and reflection affect the direction of plane waves?
Ans. Refraction causes a change in the direction of plane waves when they pass from one medium to another. This change occurs due to the change in speed of the wavefront in different mediums. The angle at which the wavefront enters the new medium, known as the angle of incidence, determines the angle at which it is refracted, known as the angle of refraction. Reflection, on the other hand, causes the wavefront to bounce back in the opposite direction when it encounters a surface.
4. What factors determine the extent of refraction and reflection in plane waves?
Ans. The extent of refraction depends on the change in speed and the angle of incidence of the wavefront. The greater the difference in speed between the two mediums, the greater the change in direction of the wavefront. Additionally, the angle of incidence plays a role in determining the angle of refraction. The extent of reflection depends on the nature of the surface encountered by the wavefront, as well as the angle of incidence. Smooth surfaces tend to have more reflection compared to rough surfaces.
5. How are refraction and reflection of plane waves useful in practical applications?
Ans. Refraction and reflection of plane waves have numerous practical applications. For example, in optics, lenses are designed based on the principles of refraction to focus or diverge light. In telecommunications, the reflection of radio waves off the ionosphere allows for long-distance communication. Refraction is also used in the field of medicine for techniques such as ultrasound imaging and laser eye surgery.
## Physics Class 12
105 videos|425 docs|114 tests
### Up next
Explore Courses for NEET exam
### Top Courses for NEET
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
;
| 1,521
| 6,797
|
{"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}
| 4.0625
| 4
|
CC-MAIN-2024-33
|
latest
|
en
| 0.915797
|
http://lastfiascorun.com/mexico/often-asked-what-is-a-space-figure.html
| 1,670,004,235,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-49/segments/1669446710909.66/warc/CC-MAIN-20221202150823-20221202180823-00875.warc.gz
| 27,630,672
| 20,221
|
# Often asked: What Is A Space Figure?
A space figure or three-dimensional figure is a figure that has depth in addition to width and height. Some common simple space figures include cubes, spheres, cylinders, prisms, cones, and pyramids. A space figure having all flat faces is called a polyhedron.
## What is the difference between a space figure and a solid figure?
A plane figure is two-dimensional, and a solid figure is three-dimensional. The difference between plane and solid figures is in their dimensions. The same shape takes on extra dimension by adding additional points and lines to give the shape height, width and depth.
## What are the example of spatial figures?
In mathematics, spatial figures are defined simply as three-dimensional objects. For example, a basketball or a cardboard box are spatial figures that we have likely encountered in our lives.
## How are space figures useful?
Three-dimensional geometry, or space geometry, is used to describe the buildings we live and work in, the tools we work with, and the objects we create. They made important discoveries and consequently they got to name the objects they discovered. That’s why geometric figures usually have Greek names!
## What is the space figure of volleyball?
Dimensions. The playing court is 18m long and 9m wide and is surrounded by a free zone 3m wide on all sides. The space above the playing area is known as the free playing space and is a minimum of 7m high from the playing surface.
## Is a figure in space or space figure?
Space figures are figures whose points do not all lie in the same plane. In this unit, we’ll study the polyhedron, the cylinder, the cone, and the sphere. Polyhedrons are space figures with flat surfaces, called faces, which are made of polygons. Prisms and pyramids are examples of polyhedrons.
You might be interested: What large body of water borders mexico on the east
## Can prisms have circular bases?
A triangular prism has a triangle as its base, a rectangular prism has a rectangle as its base, and a cube is a rectangular prism with all its sides of equal length. A cylinder is another type of right prism which has a circle as its base.
## What is a solid figure?
Solid figures are basically three-dimensional objects, which means that they have length, height and width. Because the solid figures have three dimensions, they have depth and take up space in our universe. Solid figures are identified according to the features that are unique to each type of solid.
## What do you call a space figure that has two circular bases and a curved surface?
A cylinder is similar to a prism, but its two bases are circles, not polygons. Also, the sides of a cylinder are curved, not flat.
## What jobs do you need geometry for?
Jobs that use geometry
• Animator.
• Mathematics teacher.
• Fashion designer.
• Plumber.
• Game developer.
• Interior designer.
• Surveyor.
## Can we live without geometry?
Without Geometry things would have been very challenging in Day to day life as well in various technological fields. Lines, Angles, Shapes, 2d & 3d designs plays a vital role in designing of home and commercial infra, mechanical and engineering design. This is feasible only because of Geometry.
## How do you explain geometry to a child?
Geometry is a kind of mathematics that deals with shapes and figures. Geometry explains how to build or draw shapes, measure them, and compare them. People use geometry in many kinds of work, from building houses and bridges to planning space travel.
You might be interested: Who is a famous person from mexico
## How far apart should volleyball posts be?
Posts should be placed 1m (3′-4”) from each side line, 36′-8” from each other. A recommended free or clearance zone of at least 10 ft is recommended. For the most versatile facility, it is recommended to install poles 36′-8” from each other to allow for both competition and recreational play.
## Who created volleyball?
Volleyball has come a long way from the dusty-old YMCA gymnasium of Holyoke, Massachusetts, USA, where the visionary William G. Morgan invented the sport back in 1895.
## Why does a volleyball court need a free zone?
The volleyball court is surrounded by a free zone. The free zone is the area outside the court that players may enter to make a play on the ball. The free zone should be at least 3 meters wide from the court. If any part of the ball crosses the net directly above or outside the antenna, the ball is out of play.
| 956
| 4,508
|
{"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}
| 4.125
| 4
|
CC-MAIN-2022-49
|
latest
|
en
| 0.96243
|
https://www.thestudentroom.co.uk/showthread.php?t=6991066
| 1,708,936,733,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-10/segments/1707947474653.81/warc/CC-MAIN-20240226062606-20240226092606-00727.warc.gz
| 1,043,375,801
| 39,149
|
# Mechanics Question
A lift of mass Mkg is being raised by a vertical cable attached to the top of the lift. A person of mass mkg stands on the floor inside the lift, as shown in Figure 1. The lift ascends vertically with constant acceleration 1.4 m s. The tension in the cable is 2800 N and the person experiences a constant normal reaction of magnitude 560 N from the floor of the lift. The cable is modelled as being light and inextensible, the person is modelled as a particle and air resistance is negligible.By writing an equation of motion for the person only, and an equation of motion for the lift only, find the value of M and the value of m.
So you need to apply Newton's second law, resultant force =mass x acceleration, on the person and lift separately.
You should get 2 equations to solve simultaneously.
Original post by GhostWalker123
A lift of mass Mkg is being raised by a vertical cable attached to the top of the lift. A person of mass mkg stands on the floor inside the lift, as shown in Figure 1. The lift ascends vertically with constant acceleration 1.4 m s. The tension in the cable is 2800 N and the person experiences a constant normal reaction of magnitude 560 N from the floor of the lift. The cable is modelled as being light and inextensible, the person is modelled as a particle and air resistance is negligible.By writing an equation of motion for the person only, and an equation of motion for the lift only, find the value of M and the value of m.
It would first be helpful to draw a diagram when attempting any mechanical problem such as this.
Motion of lift:
F=Ma
2800-Mg=M(1.4)
g=-9,8
Rearrange for M: M=250kg
Motion of person:
F=ma
560-mg=m(1.4)
g=-9,8
Rearrange for m:
Rearrange for m: m=50kg
Original post by Drogonmeister
It would first be helpful to draw a diagram when attempting any mechanical problem such as this.
Motion of lift:
F=Ma
2800-Mg=M(1.4)
g=-9,8
Rearrange for M: M=250kg
Motion of person:
F=ma
560-mg=m(1.4)
g=-9,8
Rearrange for m:
Rearrange for m: m=50kg
This is wrong for the motion of the lift u have to consider newtons 3rd law and hence there should be a downwards reaction force of 560 acting on the lift from the man. Even tho we ignore the man he still exerts a force on the floor of the lift and this force will be the same as that ofbthe lift exerting 560 to the man. The reason they dont cancel is because 1 force only acts of lift and the other force only acts on man. So ur calculations shld be 2800-560-Mg=M(1.4) and so on
Original post by Drogonmeister
It would first be helpful to draw a diagram when attempting any mechanical problem such as this.
| 680
| 2,636
|
{"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-2024-10
|
latest
|
en
| 0.918106
|
http://mathhelpforum.com/algebra/25170-havent-clue.html
| 1,481,277,357,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2016-50/segments/1480698542693.41/warc/CC-MAIN-20161202170902-00131-ip-10-31-129-80.ec2.internal.warc.gz
| 177,096,299
| 11,044
|
1. ## havent a clue!
havent a clue!
6x2+x-15=0
2. Originally Posted by jenko
havent a clue!
6x2+x-15=0
Let's try this using the method I posted in your other thread.
Mulitply 6 and -15: -90
Now list all pairs of factors of -90:
1, -90
2, -45
3, -30
6, -15
9, -10
10, -9
15, -6
30, -3
45, -2
90, -1
Now which of these pairs add to 1? The 10 and -9, of course. So 1 = 10 - 9:
$6x^2 + x - 15 = 0$
$6x^2 + (10 - 9)x - 15 = 0$
$6x^2 + 10x - 9x - 15 = 0$
$(6x^2 + 10x) + (-9x - 15) = 0$
$2x(3x + 5) - 3(3x + 5) = 0$
$(2x - 3)(3x + 5) = 0$
So set each factor equal to 0:
$2x - 3 = 0 \implies x = \frac{3}{2}$
or
$3x + 5 = 0 \implies x = -\frac{5}{3}$
-Dan
3. BTW, after a lot of practice of factorials, you will be able to look at them for a couple seconds and know what the constants will be.
I understand your plight. When I was a kid learning about factoring, my teacher didn't even show me about the additives and multiples that make up the constants right away. Needless to say, I taught it to myself.
4. i know the basics of mathematics e.g multiples etc it jus some of the terminologies that are used which i have never heared of or are unsure of ite been a while since i have done this last time i done then wen i was in high school two years ago and ever since that day i forgot it all as i thought i would never use it on it later life which i realy regret otherwise i wouldnt be here now or better still would be here with even more harder questions for you guys to help me with!
| 526
| 1,500
|
{"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": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.15625
| 4
|
CC-MAIN-2016-50
|
longest
|
en
| 0.93816
|
https://takechargeofyourmoney.blog/category/calculate-savings/
| 1,498,392,808,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-26/segments/1498128320491.13/warc/CC-MAIN-20170625115717-20170625135717-00612.warc.gz
| 816,117,911
| 19,665
|
## How to calculate the interest you can earn
Here’s a quick explanation on how to calculate the interest that you can earn on your savings (or pay on your debt).
Let’s use an example of R1,500 (don’t worry about the currency – the maths is the same) and you deposit it in your bank account that earns 3.5% interest.
First thing to note is that the interest rate is always given as the annual rate (unless very specifically detailed otherwise). If you use a calculator (or a spreadsheet such as Excel) and do the following : 1500 x 3.5% the answer you get is 52.50.
Thus R1,500 invested for 1 year at 3.5% interest will earn R52.50. That’s easy!
To calculate what the monthly interest is, simply divide 52.50 by 12 and you will get R4.38 (rounded up) interest for 1 month. You could be more accurate and divide 52.5 by 365.4 (number of days in the year) and then multiply by the exact number of days in the month (e.g. 30).
E.g. 52.5 divided 365.4 multiplied by 30 = R4.31 (a very slight difference to the first answer we received)
So, if you invest R1,500 for 1 year at an interest rate of 3.5%, the interest at the end of the year would be R52.50. However, banks and all financial institutions calculate interest on a daily basis and pay it out monthly. If you withdrew each months interest (and leave the original amount of money in the account) then you would effectively earn “simple” interest – just as we calculated above and you would have R52.50 (assuming no fees or charges)
However, if you leave the interest that you earn each month in your account, then the bank would calculate the next months interest on your original amount plus whatever extra interest is already in your account. So each month you would earn slightly more. This is what is called “compound” interest.
In this case the difference is not great, but the larger the starting amount is, and the longer time you keep reinvesting the interest, the larger the difference is! In fact, after a few years, compound interest can be really large. Remember of course that we are assuming that no fees or charges apply.
This example may seem simple, but there is no need to complicate things!
## Find Extra Money
We’d all love some extra money I’m sure, so here are some steps to literally find it.
Step 1 : Look at your bank statement
Look at your bank statement as well as your credit card statement for the past month and make a list of all automatic payments that are deducted (eg internet bill, mobile phone, insurance, Netflix, etc)
Step 2 : Analyze all payments
One-by-one look at each automatic payment and ask:
• Do I need this service / subscription or whatever it is?
• Do I need all the features I pay for? Can I downgrade at all or pay for less?
• If it is a store card, do you need the extra’s such as insurance, magazine, etc?
• If it is a debt repayment, how much interest am I paying? What must I do to pay it off?
Step 3 : Insurance
Pay special attention to your insurance payment. Look at your latest insurance policy or contact the company for it. Are the values correct? Now, get new quotes and see if you can find a cheaper option.
Look at optional features you may have on any insurance, store card or debt policies. Perhaps you have the same benefits offered by different policies; in that case you can cancel some.
Step 4 : Look for wasted money
Look at your monthly expenses and take special note of the following:
• Eating Out / Take-Aways
• Groceries
• Clothing
• Entertaining at home
• Alcohol bought
• Luxuries
• Telephone
• Electricity
• Internet
• Make-up
Can you spend less on any of the above? Try for just 1 month to spend less than the previous month and you will see that you really can survive quite easily!
Important note is that what you save today should not be spent tomorrow, don’t feel tempted to spend your savings on other things. See when saving is not really saving.
Step 5 : Be strict with yourself
Make a list of every area where you feel you can save a little and be strict with yourself over the next month to actually do this!
## When saving ins’t saving
I am constantly looking at how and where I spend my money and deciding whether what I am doing is worth it or not. There needs to be balance between enjoying live but at the same time living well within ones means and achieving ones financial goals. All it takes to be conscious about what you spend. I have come across times though when I think I am saving money when in fact I am not.
### Hosting people vs Going out
The first instance is the fallacy that entertaining at home is cheaper than going out. This can be true, but not necessarily all the time. It is great to host friends and family and one should enjoy every moment of it; life is too short not too. I am definitely not implying that one should not host people in your home, but the point of this post is about saving money. If you specifically decide to host people at your home instead of going out (in order to save) then you need to ensure that you do actually spend less money.
Think of the average restaurant bill that you would be paying if you went out, and now look at what you are about to spend in order to host your friends. Flowers, candles, snacks, wine, groceries, dessert, etc… It is easy to go overboard and spend more than you would have. (Especially if you’re married to a chef, which is the case for me.) The point is not to be stingy though. If you wish to save money then calculate the costs of going versus what you would like to spend when entertaining and chose the cheaper option.
### A picnic vs lunch out
As with the first example, if you decide to go on a picnic in order to save money (rather than an expensive restaurant), then be sure to do some calculations. It’s funny how in our minds we convince ourselves that because we’re taking the cheaper option, we can now spend more. A bottle of bubbly, expensive cheeses, some tapas, etc… It’s really easy to spend more on the picnic than in a restaurant.
###### The point of these examples is that if you choose to do something in order to save some money, keep that in mind and be sure to actually save! Don’t let yourself be tempted to buy the more expensive items to compensate for the cheaper option. You will actually end up spending more.
Now, take the money you calculated you would save and immediately transfer it into your savings account! Do it now before you find something else to spend it on!
## Calculate the Future Value of an investment
In this article we looked at the effect of extra payments into ones home loan (mortgage bond). That’s all good and well, but what if you don’t have a loan? Or perhaps you would rather invest in a Unit Trust or Interest Bearing bank account.
Microsoft Excel has a simple formula called “FV” which will help you to calculate the future value of your investment. This does not account for changing interest rates or complicated scenarios, but it will give you a simple tool to give you an idea of how your money can grow.
To start with a simple example, let’s save 600 each month for 10 years (120 months) at an interest of 6%. The answer as you see is 98,327.61.
That’s pretty easy. Let’s quickly look at the input parameters:
Rate: This is the interest rate per period. Generally speaking, financial institutions will quote an annual interest rate. In this example it is 6%. To get the monthly interest rate we simply use 6%/12. If we change the example an decide to make quarterly payments we would need to use 6%/4.
Nper: This is the number of periods (in total) for which we will make a payment. If we wish to pay monthly, this is the number of months.
Pmt: This is the amount we wish to pay each period. This figure cannot change over the lifetime of the investment. But, see further down how we can circumvent this potential problem. Excel expects the payment to be a negative figure as payments out of your account would “minus” from your account. You will see that if you use a positive figure, your answer will show negative. The figure will be the same though. (If that is confusing, try it yourself)
Pv: The present value. If you are adding money to an existing bank account, use Pv as the present value in the account. If this to calculate a new investment leave it blank or type a zero in the box.
Type: This is to specify whether the payment is being made at the beginning of each period, or at the end. This will affect the interest that you earn. By default Excel will assume you are paying at the end of each period.
So, in the example above we assumed a constant 600 payment each month for 10 years. But what if you decide to pay 10% more each year? For that we will need to spice things up a bit. See how I have calculated the Future Value for 12 months at a time. I then use the answer as my Present Value for the following year. The monthly payment is simply increased by 10% in each row.
## How much is your coffee costing you?
I love coffee! The very thought of drinking less makes me quiver with fear. But, sometimes one must take the emotion out of decisions and just look at cold, hard facts.
In a previous article on being more conscious with cash, I discussed how I buy 2 coffees each day, along with a breakfast and lunch. I’m not good at planning meals to bring to work but I have decided to spend slightly less. The savings I calculated was only R150 per week, but I’ve decided to look at how this could affect my home loan (mortgage bond) if I pay R600 extra per month.
These figures may not make sense to you if you use a different currency and your countries interest rates may be significantly different. I’ll post something soon about how you can do these calculations yourself.
The calculations can get messy so take note of the following assumptions:
Home Loan Value: R1,500,000
Interest Rate: 11% (annual)
Total Loan period: 20 years
For this example I will assume 2 years of the loan are already complete, and that up to now no additional payments have been made. Also, the R600 p.m. will remain constant (with other words I won’t save more in years to come)
This may all sound complicated, but the end result is simple to see. If I pay R600 p.m. extra into my bond until my bond is paid off I will:
• Save a total of R236,000 (rounded to nearest thousand)
• Pay the loan off 22 months earlier
That’s pretty amazing don’t you think? Considering that I am making this extra saving by cutting down on my weekly coffee/food expenses at my office. In fact, it was quite easy to find the extra R150 per week. Imagine if I actually analyze my expenses properly and relook at my insurance policies, health care, mobile phone contract, bank charges, etc. Imagine the savings I can make then!
What if you don’t have a home loan?
That’s really not a problem. If you invest this money in either a unit trust or interest bearing account for the next 15 – 20 years you will have quite a large lump sum. We’ll look at how to use the Future Value formula in Excel to calculate this.
| 2,574
| 11,078
|
{"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}
| 4.3125
| 4
|
CC-MAIN-2017-26
|
longest
|
en
| 0.956167
|
https://www.futurelearn.com/courses/through-engineers-eyes/0/steps/13718?main-nav-submenu=main-nav-categories
| 1,601,159,715,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-40/segments/1600400245109.69/warc/CC-MAIN-20200926200523-20200926230523-00523.warc.gz
| 829,163,659
| 27,102
|
## Want to keep learning?
This content is taken from the UNSW Sydney's online course, Through Engineers' Eyes: Engineering Mechanics by Experiment, Analysis and Design. Join the course to learn more.
4.7
## UNSW Sydney
Skip to 0 minutes and 9 seconds We learned earlier that a plane might crash if its centre of gravity is outside permissible limits. How can you check it? You can use the method of composite bodies.
Skip to 0 minutes and 24 seconds This table shows how to find the CG, that is the centre of gravity, of an empty aircraft by weighing the load on each wheel. The location of the CG is obtained by dividing the total moment by the total weight. More on this later. But, how do you check the CG position for each flight when the numbers of passengers and the amount of baggage and fuel might vary? There is a standard calculation and, to implement it, we can use a table like this. There are several sets of calculations here. One with just the pilot, one fully loaded, and others with various amounts of fuel. It must be OK with all of these scenarios if the aircraft is going to be safe.
Skip to 1 minute and 14 seconds The table assumes that we know the weight and CG of each component. Together, they make up our composite body. We’ve already got the weight and the CG of the bare aircraft by weight. We can now add the effect of having a pilot, a passenger, baggage, and fuel. These are the components of our composite body. We did an experiment with composite bodies. Our one was made up of squares, triangles, and circles. We can find the weight and the CG of each of these components, then combine them. But we’re going to start with a simpler example. Suppose we had two spheres connected by a weightless bar. One sphere is twice the mass, hence twice the weight of the other.
Skip to 2 minutes and 11 seconds Here are two free-body diagrams. One shows the two weights. The other shows a combined weight at the centre of gravity. Notice that the CG is not in the middle. It is nearer the larger mass. But how much nearer? We could find the position experimentally by supporting it and finding the point of balance. But that is sometimes impractical. In that case, we can calculate the position. Here’s how. These two representations must be equivalent, which means that they must generate the same force in any direction, and must generate the same moment about any axis. We can express this mathematically. It’s related to equilibrium, so you won’t be surprised to learn that you can check for equivalence by these equations.
Skip to 3 minutes and 9 seconds Firstly, sum of the forces in the y direction on diagram one equals sum of the forces in the y direction on diagram two. This gives us the total weight. Next, we can use the fact that sum of the moments about our point on diagram one must equal sum of the moments about the same point on diagram two. This locates the centre of gravity along the bar, pause the video, and uses equations to find the expressions for w, the total weight, and x, its position along the bar. You could take moments anywhere, so long as the point is the same on both diagrams. Moments about the centre of the left-hand sphere work well here.
Skip to 4 minutes and 11 seconds It’s easy to find the total weight. We get W equals W1 plus W2. It’s slightly more complicated to find the x-coordinate of the centre of gravity. Here’s what you do. Take sum of the moments about the left-hand sphere on diagram one, and put it equal to sum of the moments about the same point on diagram two. If you would like to follow the development of this, pause the video and look at each of the lines of the explanation. You can see that the final result is x equals (2/3)L, which is 2/3 of the distance between the two spheres. All this can be summed up in three equations.
Skip to 5 minutes and 1 second Capital X, capital Y, and capital Z are coordinates of the centroid of the complete body. XC, YC, and ZC are coordinates of the centroid of each component. W represents the weight of each component. For more complicated objects, like an aeroplane, you can use a table to keep track of the calculations. The summations in the equation are easily found from the table. To get the location of the centroid, you just divide one total by the other, which is what you will do next. It will be described in the design task. Now you’ve got the method sorted out. You can use it to predict where to add weight to a paper aeroplane to make it fly.
# Analysis: Centres of gravity of composite bodies
If you know the location of the centre of gravity of each component of an object you can find the overall centre of gravity of the whole thing.
You do it by taking moments.
We’ll use the method on composite objects where the components are rectangles, circles or triangles. We know the location of the centre of gravity for all of these.
If you know calculus you can apply this method to a wide range of geometric shapes. For example you can prove the standard result for a triangle. But that’s for another time.
For now we’ll stick with simple shapes and show you how to keep track of your working by using a table. A table suits a spreadsheet perfectly.
### Talking points
• What do you think are the benefits of a table when using the method of composite bodies?
• Under what the circumstances, if any, would you not use a table?
| 1,176
| 5,386
|
{"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}
| 4.375
| 4
|
CC-MAIN-2020-40
|
latest
|
en
| 0.955855
|
https://studywell.com/maths/pure-maths/algebra-functions/simultaneous-equations/
| 1,619,023,336,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-17/segments/1618039546945.85/warc/CC-MAIN-20210421161025-20210421191025-00545.warc.gz
| 639,851,267
| 18,208
|
Simultaneous equations can be thought of as being two equations in two unknowns, say x and y. Note that the word simultaneous means ‘at the same time’. It follows that for the values of x and y found both equations must be true at the same time. Sometimes it is easy to inspect the equations and guess the answers. However, when one of the equations is quadratic this becomes less likely. The answers could be surds, in which case, this is very difficult to guess.
Note that a question may ask you to solve simultaneous equations explicitly. In others, it will be implied and you must deduce that it is simultaneous equations to solve. For example, you could be asked to find out which points two curves have in common. See Example 2 below.
## Methods for solving Simultaneous Equations
There are three methods for solving simultaneous equations:
1. Elimination – this is where you multiply both equations through by different coefficient in order to eliminate one of the unknowns. This page will focus on substitution since it works for more complicated simultaneous equations. For example, when one of the equations is a quadratic. Click here to see an example using elimination.
2. Substitution – one of the equations can be quadratic, in which case, substitution is the method to use. You will need to know how to solve quadratics. By making x or y the subject of one of the equations, it can be substituted into the other. See the Worked Example and Example 1 below.
3. Graphical method – the solution of simultaneous equations can be interpreted as the intersection of their graphs. This plot shows the graphs of $y=2x-3$ in red and $4x+5y=6$ in blue. Their intersection lies on the x-axis and has coordinates (1.5,0). This is the solution when solving simultaneously. Also see Example 2 below.
## Simultaneous Equations Worked Example
Solve the simultaneous equations
$x^2+y^2=10$
and
$x+2y=5$.
This example requires solution via substitution, i.e. make either x or y the subject of one equation and insert it into the other. The obvious choice would be to make x the subject of the second equation – it is the quickest, least complicated choice. The second equation tells us that $x=5-2y$. We can insert this into the first equation: $(5-2y)^2+y^2=10$. By multiplying out the brackets and simplifying we see that this is a quadratic equation in y:
$(5-2y)^2+y^2=10$
Write out the brackets: $(5-2y)(5-2y)+y^2=10$
Expand the brackets: $25-10y-10y+4y^2+y^2=10$
Simplify: $5y^2-20y+15=0$
Divide both by sides by 5: $y^2-4y+3=0$
Factorise: $(y-3)(y-1)=0$
This tells us that y has to be either 3 or 1. If $y=3$, then $x=5-2\times 3=-1$ (from the second equation rearranged) and if $y=1$ then $x=5-2\times 1=3$.
We obtain the solutions $(x_1,y_1)=(-1,3)$ and $(x_2,y_2)=(3,1)$.
### Example 1
Solve the simultaneous equations:
$y=x-4$
$2x^2-xy=8$
### Example 2
Sketch the graphs of $x^2+y^2=10$ and $x+2y=5$ on the same plot. Determine the coordinates of the intersection points.
Click here to find Questions by Topic all scroll down to all past SIMULTANEOUS EQUATIONS questions to practice some more questions.
Are you ready to test your Pure Maths knowledge? If so, visit our Practice Papers page and take StudyWell’s own Pure Maths tests. Alternatively, try the
| 865
| 3,290
|
{"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": 27, "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}
| 4.6875
| 5
|
CC-MAIN-2021-17
|
latest
|
en
| 0.943614
|
http://schoolbag.info/mathematics/barrons_ap_calculus/50.html
| 1,493,333,131,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-17/segments/1492917122629.72/warc/CC-MAIN-20170423031202-00098-ip-10-145-167-34.ec2.internal.warc.gz
| 341,502,799
| 4,582
|
APPLICATIONS OF ANTIDERIVATIVES; DIFFERENTIAL EQUATIONS - Antidifferentiation - Calculus AB and Calculus BC
CHAPTER 5 Antidifferentiation
E. APPLICATIONS OF ANTIDERIVATIVES; DIFFERENTIAL EQUATIONS
The following examples show how we use given conditions to determine constants of integration.
EXAMPLE 48
Find f (x) if f (x) = 3x2 and f (1) = 6.
SOLUTION:
Since f (1) = 6, 13 + C must equal 6; so C must equal 6 − 1 or 5, and f (x) = x3 + 5.
EXAMPLE 49
Find a curve whose slope at each point (x, y) equals the reciprocal of the x-value if the curve contains the point (e, −3).
SOLUTION: We are given that and that y = −3 when x = e. This equation is also solved by integration. Since
Thus, y = ln x + C. We now use the given condition, by substituting the point (e, −3), to determine C. Since −3 = ln e + C, we have −3 = 1 + C, and C = −4. Then, the solution of the given equation subject to the given condition is
y = ln x − 4.
DIFFERENTIAL EQUATIONS: MOTION PROBLEMS.
An equation involving a derivative is called a differential equation. In Examples 48 and 49, we solved two simple differential equations. In each one we were given the derivative of a function and the value of the function at a particular point. The problem of finding the function is called aninitial-value problem and the given condition is called the initial condition.
In Examples 50 and 51, we use the velocity (or the acceleration) of a particle moving on a line to find the position of the particle. Note especially how the initial conditions are used to evaluate constants of integration.
EXAMPLE 50
The velocity of a particle moving along a line is given by v(t) = 4t3 − 3t2 at time t. If the particle is initially at x = 3 on the line, find its position when t = 2.
SOLUTION: Since
Since x(0) = 04 − 03 + C = 3, we see that C = 3, and that the position function is x(t) = t4 t3 + 3. When t = 2, we see that
x(2) = 24 − 23 + 3 = 16 − 8 + 3 = 11.
EXAMPLE 51
Suppose that a(t), the acceleration of a particle at time t, is given by a(t) = 4t − 3, that v(1) = 6, and that f (2) = 5, where f (t) is the position function.
(a) Find v(t) and f (t).
(b) Find the position of the particle when t = 1.
SOLUTIONS:
Using v(1) = 6, we get 6 = 2(1)2 − 3(1) + C1, and C1 = 7, from which it follows that v(t) = 2t2 − 3t + 7. Since
Using f (2) = 5, we get + 14 + C2, so Thus,
For more examples of motion along a line, see Chapter 8, Further Applications of Integration, and Chapter 9, Differential Equations.
Chapter Summary
In this chapter, we have reviewed basic skills for finding indefinite integrals. We’ve looked at the antiderivative formulas for all of the basic functions and reviewed techniques for finding antiderivatives of other functions.
We’ve also reviewed the more advanced techniques of integration by partial fractions and integration by parts, both topics only for the BC Calculus course.
| 835
| 2,910
|
{"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}
| 4.6875
| 5
|
CC-MAIN-2017-17
|
longest
|
en
| 0.905741
|
https://dearteassociazione.org/how-do-you-write-0-6-as-a-fraction/
| 1,653,022,356,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-21/segments/1652662531352.50/warc/CC-MAIN-20220520030533-20220520060533-00511.warc.gz
| 248,370,751
| 8,257
|
Three common formats for numbers room fractions, decimals, and percents.
You are watching: How do you write 0.6 as a fraction
Percents are regularly used to connect a family member amount. You have probably seen them supplied for discounts, where the percent the discount can apply to different prices. Percents are likewise used when stating taxes and also interest rates on savings and also loans.
A percent is a proportion of a number come 100. Every cent way “per 100,” or “how numerous out that 100.” You usage the price % ~ a number to show percent.
Notice the 12 that the 100 squares in the grid below have to be shaded green. This to represent 12 percent (12 per 100).
12% = 12 percent = 12 parts out the 100 =
How countless of the squares in the grid over are unshaded? due to the fact that 12 space shaded and there room a full of 100 squares, 88 space unshaded. The unshaded section of the totality grid is 88 components out of 100, or 88% of the grid. Notice that the shaded and also unshaded portions together make 100% of the network (100 out of 100 squares).
Example Problem What percent of the network is shaded? The net is separated into 100 smaller sized squares, v 10 squares in each row. 23 squares out of 100 squares room shaded. Answer 23% of the network is shaded.
Example Problem What percent of the big square is shaded? The net is divided into 10 rectangles. For percents, you need to look at 100 equal-sized parts of the whole. You can divide each of the 10 rectangles right into 10 pieces, providing 100 parts. 30 tiny squares out of 100 space shaded. Answer 30% of the huge square is shaded.
What percent that this network is shaded?
A) 3%
B) 11%
C) 38%
D) 62%
A) 3%
Incorrect. Three complete columns that 10 squares space shaded, plus an additional 8 squares indigenous the next column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the large square. The exactly answer is 38%.
B) 11%
Incorrect. Three complete columns of 10 squares room shaded, plus another 8 squares native the following column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the big square. The correct answer is 38%.
C) 38%
Correct. Three complete columns that 10 squares room shaded, plus an additional 8 squares from the next column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the large square. This means 38% that the huge square is shaded.
D) 62%
Incorrect. There room 62 tiny unshaded squares out of the 100 in the large square, therefore the percent of the large square the is unshaded is 62%. However, the inquiry asked what percent is shaded. There room 38 shaded squares that the 100 squares in the huge square, therefore the exactly answer is 38%.
Rewriting Percents, Decimals, and also Fractions
It is often helpful to readjust the layout of a number. Because that example, girlfriend may find it less complicated to add decimals 보다 to include fractions. If you have the right to write the fractions together decimals, girlfriend can add them as decimals. Then you can rewrite your decimal amount as a fraction, if necessary.
Percents can be composed as fractions and also decimals in very few steps.
Example Problem Write 25% as a simplified portion and as a decimal. Write together a fraction. 25% = Since % method “out the 100,” 25% way 25 the end of 100. You create this together a fraction, utilizing 100 together the denominator. Simplify the portion by separating the numerator and denominator through the usual factor 25. Write together a decimal. 25% = = 0.25 You can also just move the decimal suggest in the whole number 25 two locations to the left to acquire 0.25. Answer 25% = = 0.25
Notice in the diagram listed below that 25% that a network is additionally of the grid, as you found in the example.
Notice that in the vault example, rewriting a percent together a decimal takes just a shift of the decimal point. You have the right to use fractions to recognize why this is the case. Any type of percentage x can be represented as the portion , and any fraction can be created as a decimal by moving the decimal suggest in x two places to the left. For example, 81% can be composed as
, and dividing 81 by 100 results in 0.81. People often skip end the intermediary portion step and just convert a percent come a decimal by relocating the decimal suggest two places to the left.
In the same way, rewriting a decimal together a percent (or as a fraction) requires few steps.
Example Problem Write 0.6 together a percent and also as a streamlined fraction. Write as a percent. 0.6 = 0.60 = 60% Write 0.6 as 0.60, i beg your pardon is 60 hundredths. 60 hundredths is 60 percent. You can additionally move the decimal point two places to the appropriate to discover the percent equivalent. Write as a fraction. 0.6 = To compose 0.6 together a fraction, you read the decimal, 6 tenths, and write 6 tenths in fraction form. Simplify the portion by splitting the numerator and also denominator by 2, a usual factor. Answer 0.6 = 60% =
In this example, the percent is not a entirety number. You can handle this in the exact same way, yet it’s usually less complicated to convert the percent come a decimal and also then transform the decimal to a fraction.
Example Problem Write 5.6% as a decimal and also as a streamlined fraction. Write as a decimal. 5.6% = 0.056 Move the decimal point two locations to the left. In this case, insert a 0 in front of the 5 (05.6) in bespeak to be able to move the decimal come the left two places. Write as a fraction. 0.056 = Write the portion as friend would check out the decimal. The last digit is in the thousandths place, therefore the denominator is 1,000. Simplify the portion by separating the numerator and also denominator through 8, a usual factor. Answer 5.6% = = 0.056
Write 0.645 together a percent and as a simplified fraction. A) 64.5% and B) 0.645% and also C) 645% and also D) 64.5% and also Show/Hide Answer A) 64.5% and Correct. 0.645 = 64.5% = . B) 0.645% and also Incorrect. 0.645 = 64.5%, not 0.645%. Psychic that when you convert a decimal to a percent you have to move the decimal suggest two locations to the right. The correct answer is 64.5% and . C) 645% and Incorrect. 0.645 = 64.5%, not 645%. Remember that when you convert a decimal to a percent you need to move the decimal point two areas to the right. The correct answer is 64.5% and . D) 64.5% and also Incorrect. To create 0.645 as a percent, move the decimal ar two locations to the right: 64.5%. To create 0.645 together a fraction, usage 645 as the numerator. The place value that the critical digit (the 5) is thousandths, for this reason the denominator is 1,000. The fraction is . The greatest common factor the 645 and also 1,000 is 5, therefore you deserve to divide the numerator and denominator by 5 to gain . The exactly answer is 64.5% and also .
In stimulate to create a portion as a decimal or a percent, you have the right to write the fraction as an equivalent fraction with a denominator that 10 (or any kind of other strength of 10 such as 100 or 1,000), which deserve to be then converted to a decimal and then a percent.
Example Problem Write as a decimal and as a percent. Write together a decimal. Find one equivalent portion with 10, 100, 1,000, or various other power that 10 in the denominator. Due to the fact that 100 is a lot of of 4, you deserve to multiply 4 through 25 to obtain 100. Multiply both the numerator and also the denominator by 25. = 0.75 Write the fraction as a decimal through the 5 in the percentage percent place. Write as a percent. 0.75 = 75% To create the decimal together a percent, move the decimal suggest two locations to the right. Answer = 0.75 = 75%
If that is complicated to find an equivalent portion with a denominator of 10, 100, 1,000, and so on, friend can constantly divide the molecule by the denominator to discover the decimal equivalent.
Example Problem Write as a decimal and also as a percent. Write as a decimal. Divide the molecule by the denominator. 3 ÷ 8 = 0.375. Write as a percent. 0.375 = 37.5% To create the decimal together a percent, relocate the decimal allude two areas to the right. Answer = 0.375 = 37.5%
Write as a decimal and also as a percent.
A) 80.0 and 0.8%
B) 0.4 and 4%
C) 0.8 and also 80%
D) 0.8 and also 8%
A) 80.0 and also 0.8%
Incorrect. An alert that 10 is a multiple of 5, so you have the right to rewrite using 10 together the denominator. Main point the numerator and also denominator by 2 to gain . The indistinguishable decimal is 0.8. You deserve to write this together a percent by moving the decimal suggest two places to the right. Since 0.8 has only one location to the right, encompass 0 in the percentage percent place: 0.8 = 0.80 = 80%. The correct answer is 0.8 and also 80%.
B) 0.4 and also 4%
Incorrect. To uncover a decimal indistinguishable for , an initial convert the portion to tenths. Multiply the numerator and denominator by 2 to acquire . The tantamount decimal is 0.8. So, and 0.4 space not indistinguishable quantities. The correct answer is 0.8 and 80%.
C) 0.8 and also 80%
Correct. The price is = 0.8 = 80%.
D) 0.8 and also 8%
Incorrect. It is true the = 0.8, however this does not equal 8%. To create 0.8 as a percent, relocate the decimal allude two locations to the right: 0.8 = 0.80 = 80%. The correct answer is 0.8 and also 80%.
Mixed Numbers
All the previous examples involve fractions and also decimals less than 1, so all of the percents you have actually seen so far have been much less than 100%.
Percents greater than 100% are feasible as well. Percents more than 100% are used to describe instances where there is more than one entirety (fractions and decimals higher than 1 are offered for the same reason).
In the diagram below, 115% is shaded. Every grid is taken into consideration a whole, and also you require two grids for 115%.
Expressed as a decimal, the percent 115% is 1.15; together a fraction, that is
, or
. Notice that you deserve to still convert amongst percents, fractions, and also decimals once the quantity is higher than one whole.
Numbers better than one that incorporate a fractional component can be composed as the sum of a totality number and also the fractional part. For instance, the mixed number is the amount of the entirety number 3 and the portion . = 3 + .
Example Problem Write as a decimal and as a percent. Write the mixed fraction as 2 wholes to add the spring part. Write together a decimal. Write the fractional component as a decimal by splitting the numerator by the denominator. 7 ÷ 8 = 0.875. Add 2 come the decimal. Write together a percent. 2.875 = 287.5% Now you can move the decimal allude two areas to the right to create the decimal as a percent. Answer = 2.875 = 287.5%
Note that a totality number can be created as a percent. 100% means one whole; so 2 wholes would certainly be 200%.
Example Problem Write 375% as a decimal and also as a streamlined fraction. Write together a decimal. 375% = 3.75 Move the decimal allude two areas to the left. Keep in mind that over there is a entirety number together with the decimal together the percent is more than 100%. Write as a fraction. 3.75 = 3 + 0.75 Write the decimal as a amount of the totality number and also the fractional part. 0.75 = Write the decimal part as a fraction. Simplify the portion by splitting the numerator and also denominator by a usual factor that 25. 3 + = Add the totality number component to the fraction. Answer 375% = 3.75=
Write 4.12 as a percent and also as a simplified fraction. A) 0.0412% and B) 412% and also C) 412% and also D) 4.12% and also Show/Hide Answer A) 0.0412% and Incorrect. To convert 4.12 to a percent, move the decimal suggest two locations to the right, not the left. The exactly answer is 412% and also . B) 412% and also Correct. 4.12 amounts to 412%, and also the simplified kind of is . C) 412% and Incorrect. 4.12 does equal 412%, yet it is also equivalent to , no . The correct answer is 412% and also . D) 4.12% and also Incorrect. To transform 4.12 come a percent, relocate the decimal allude two places to the right. The exactly answer is 412% and .See more: How To Build An Indoor Pitching Mound Plans: Step By Step Instructions Summary Percents space a common means to stand for fractional amounts, simply as decimals and fractions are. Any number that deserve to be composed as a decimal, fraction, or percent can also be written utilizing the various other two representations. .tags a { color: #fff; background: #909295; padding: 3px 10px; border-radius: 10px; font-size: 13px; line-height: 30px; white-space: nowrap; } .tags a:hover { background: #818182; } Home Contact - Advertising Copyright © 2022 dearteassociazione.org #footer {font-size: 14px;background: #ffffff;padding: 10px;text-align: center;} #footer a {color: #2c2b2b;margin-right: 10px;}
| 3,382
| 12,982
|
{"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}
| 4.59375
| 5
|
CC-MAIN-2022-21
|
latest
|
en
| 0.924698
|
https://byjusexamprep.com/gate-cse/difference-between-algorithm-and-pseudocode
| 1,723,651,532,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-33/segments/1722641118845.90/warc/CC-MAIN-20240814155004-20240814185004-00535.warc.gz
| 117,130,816
| 30,089
|
# Difference Between Algorithm and Pseudocode
By BYJU'S Exam Prep
Updated on: September 25th, 2023
Difference Between Algorithm and Pseudocode: In a programming language, both algorithm and pseudocode play an important role. Where an algorithm is considered the foundation of the programming language pseudocode is used to make the programming language more human-friendly. The major difference between algorithm and pseudocode is that pseudocode is a method of writing an algorithm and an algorithm is a step-by-step description of the procedure of a task.
Here, we will first read what is algorithm and pseudocode in brief then we will discuss the difference between algorithm and pseudocode on various factors.
Table of content
## Difference Between Algorithm and Pseudocode
Although there are various similarities between algorithm and pseudocode, there are a few differences between the two which are explained in the table provided below:
### Key Differences Between Algorithm and Pseudocode
Algorithm Pseudocode It is a step-by-step description of the solution. It is an easy way of writing algorithms for users to understand. It is always a real algorithm and not fake codes. These are fake codes. They are a sequence of solutions to a problem. They are representations of algorithms. It is a systematically written code. These are simpler ways of writing codes. They are an unambiguous way of writing codes. They are a method of describing codes written in an algorithm. They can be considered pseudocode. They can not be considered algorithms There are no rules to writing algorithms. Certain rules to writing pseudocode are there.
The Difference Between Algorithm, Pseudocode, and Program to know more about these topics.
## What is an Algorithm?
In the programming language, algorithms are a procedure to solve a given problem with step by step description of the solution. The steps are carried out in a finite amount of time. The problems of complex nature can be solved by a simple step-by-step description of an algorithm.
The algorithm will have a well-defined set of steps. Problems are solved with a specific solution. Natural languages, flow charts, etc can be used to represent an algorithm. Candidates can check out Prim’s Algorithm to know more about Algorithm.
## What is a Pseudocode?
Pseudocode is also known as fake codes. It is used to give a simple human-friendly description of the steps used in an algorithm. It is an informal description. It is often used to summarise the steps or flow of the algorithm but it does not specify the detail of the algorithm. It is written by the system designers so that aligned codes and requirements can be understood by the programmers.
Pseudocode is used to plan an algorithm. They are not used in complex programming languages. As we have seen the algorithm and pseudocode, let us now see the major differences between the two in the next section.
Check out some important topics related to the difference between Algorithm and Pseudocode:
POPULAR EXAMS
SSC and Bank
Other Exams
GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 help@byjusexamprep.com
| 652
| 3,197
|
{"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-2024-33
|
latest
|
en
| 0.923814
|
https://ccssmathanswers.com/into-math-grade-2-module-12-lesson-3-answer-key/
| 1,721,130,416,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-30/segments/1720763514745.49/warc/CC-MAIN-20240716111515-20240716141515-00195.warc.gz
| 140,000,363
| 57,624
|
# Into Math Grade 2 Module 12 Lesson 3 Answer Key Represent and Record Two-Digit Addition
We included HMH Into Math Grade 2 Answer Key PDF Module 12 Lesson 3 Represent and Record Two-Digit Addition to make students experts in learning maths.
## HMH Into Math Grade 2 Module 12 Lesson 3 Answer Key Represent and Record Two-Digit Addition
I Can represent and record two-digit addition with and without regrouping.
How can you represent Brianna’s cat and dog books? How many books about cats or dogs does she have?
Brianna has _________ cat or dog books.
Read the following: Brianna has 12 books about cats. She has 11 books about dogs. How many books about cats or dogs does she have?
Given that,
The total number of books about cats near Brianna is 12
The total number of books about dogs near Brianna is 11
Therefore 12 + 11 = 23
There are 23 books she has.
Build Understanding
Question 1.
Kurt has 57¢. His friend gives him 35¢. How much money does Kurt hove now?
A. How can you use tools to show the two addends for this problem? Draw to show what you did.
Given that
Kurt has money = 57 cents.
Her friend given = 35 cents.
The total money near Kurt = 57 + 35 = 92
Kurt has 92 cents.
B. Are there 10 ones to regroup?
Yes, there are 10 ones to regroup.
Adding 57 + 35 in this case you need to regroup the numbers.
when you add the ones place digits 7 + 5, you get 12 which means 1 ten and 2 ones.
Know to regroup the tens into the tens place and leave the ones. Then 57 + 35 = 92.
C. Regroup 10 ones as 1 ten. Write a 1 in the tens column to show the regrouped ten.
D. How many ones are left after regrouping? Write the number of ones left over in the ones place.
After regrouping the number of ones left over in the one place is 2.
E. How many tens are there in all? Write the number of tens ¡n the tens place.
The number of tens in the tens place is 9.
F. How much money does Kurt have now?
________ ¢
Given that
Kurt has money = 57 cents.
Her friend given = 35 cents.
The total money near Kurt = 57 + 35 = 92
Kurt has 92 cents.
Question 2.
Mateo and his friends make a list of two-digit numbers. He chooses two of the numbers to add.
A. How can you draw quick pictures to help you find the sum of 26 and 46?
B. How can you add the ones? Regroup if you need to. Show your work in the chart.
26 + 46 = 72
Adding 26 + 46 in this case you need to regroup the numbers.
when you add the ones place digits 6 + 6, you get 12 which means 1 ten and 2 ones.
Know to regroup the tens into the tens place and leave the ones. Then 26 + 46 = 72.
C. How can you odd the tens? Show your work in the chart.
D. What is the sum?
26 + 46 = 72
Adding 26 with 46 then we get 72.
Turn and Talk Are there two numbers from that Mateo could add without regrouping?
52, 11, 25 and 74
Any two numbers can add without regrouping. Because the addition of one’s place digit is less than the 10.
Step It Out
Question 1.
Add 47 and 37.
A. Find How many ones in all. Regroup if you need to. Write a I in the tens column to show the regrouped ten.
Adding 47 + 37 in this case you need to regroup the numbers.
when you add the ones place digits 7 + 7, you get 14 which means 1 ten and 4 ones.
Know to regroup the tens into the tens place and leave the ones. Then 47 + 37 = 84.
B. Write the number of ones left over in the ones place.
Number of ones left over in the ones place is 4.
C. Write the number of tens in the tens place.
Number of tens in the tens place is 8.
D. Write the sum.
47 + 37 = 84
Adding 47 with 37 then we get 84.
Check Understanding
Question 1.
There are 65 apples on a tree. There are 28 apples on another tree. How many apples are on the trees? Draw to show the addition.
________ apples
Given that,
The total number of apples on the tree = 65
The total number of apple on the another tree = 28
The total number of apples = 65 + 28 = 93.
Question 2.
Attend to Precision Mrs. Meyers plants 34 flowers. Mrs. Owens plants 42 flowers. How many flowers do they plant? Draw to show the addition.
_________ flowers
Given that,
Mrs. Meyers plants 34 flowers.
Mrs. Owens plants 42 flowers.
The total number of flowers = 34 + 42 = 76.
Question 3.
Reason Did you need to regroup 10 ones as 1 ten in Problem 2? Explain.
No need to regroup 10 ones as 1 ten. Because the addition of one’s place digits is less than 10.
So, there is no need to regroup.
Question 4.
Open Ended Rewrite Problem 2 with different numbers so that you need to regroup when you odd. Then solve.
Mrs. Meyers plants 36 flowers. Mrs. Owens plants 45 flowers. How many flowers do they plant? Draw to show the addition.
36 + 45 = 81
Adding 36 + 45 in this case you need to regroup the numbers.
when you add the ones place digits 6 + 5, you get 11 which means 1 ten and 1 ones.
Know to regroup the tens into the tens place and leave the ones.
Question 5.
Use Structure There are 25 big dogs and 19 small dogs at the dog park. How many dogs are at the park?
_________ dogs
Given that,
The total number of big dogs = 25.
The total number of small dogs = 19.
The total number of dogs = 25 + 19 = 44.
Question 6.
Add 16 and 23.
16 + 23 = 39
There is no need of regrouping.
Question 7.
Add 44 + 49
| 1,449
| 5,177
|
{"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}
| 4.9375
| 5
|
CC-MAIN-2024-30
|
latest
|
en
| 0.931496
|
https://www.physicsforums.com/threads/parabolas-math-problem.69163/
| 1,519,604,389,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2018-09/segments/1518891817523.0/warc/CC-MAIN-20180225225657-20180226005657-00012.warc.gz
| 948,129,098
| 14,586
|
# Parabolas math problem
1. Mar 29, 2005
### vitaly
I'm having difficulty with this question. All help is appreciated.
*The cross section of television antenna dish is a parabola and the receiver is located at the focus.
A. If the receiver is located 5 feet above the vertex, assume the vertex is the origin, find an equation for the cross section of the dish.
Okay, I know the vertex is 0,0. The focus is 0, 5. The equation is x^2=4ay.
I don't know where to go from there, or what equation is needed to find the cross section.
2. Mar 29, 2005
### vitaly
Actually, I figured it out. x^2 = 4ay, and a must equal 5 because the focus is (0,5).
That means teh equation is x^2 = 4(5)y or x^2 = 20y.
What I can't figure out is part B:
If the dish is 10 feet wide, how deep is it?
I have never had a question like this before. How do you know how "deep" a dish is?
3. Mar 29, 2005
### Kamataat
So the equation of the parabola is $y=x^2/20$. If it's 10 feet wide and centered at the origin, then it's cross section is between -5 and 5 on the x-axis. So, to find the depth, you need to calculate "y" for x=5... that is, if I understand the question correctly.
- Kamataat
4. Mar 29, 2005
### vitaly
Thank you for the help. I think that's right. Solving for y, it would be 1.25, which is the answer. I just didn't know how to come to it and show my work. Thanks again.
| 412
| 1,373
|
{"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}
| 4.09375
| 4
|
CC-MAIN-2018-09
|
longest
|
en
| 0.97706
|
https://www.comicsanscancer.com/how-do-you-determine-if-a-set-is-open-or-closed-examples/
| 1,721,361,051,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-30/segments/1720763514866.33/warc/CC-MAIN-20240719012903-20240719042903-00568.warc.gz
| 634,832,996
| 13,498
|
# How do you determine if a set is open or closed examples?
## How do you determine if a set is open or closed examples?
Definition 5.1.1: Open and Closed Sets A set U R is called open, if for each x U there exists an > 0 such that the interval ( x – , x + ) is contained in U. Such an interval is often called an – neighborhood of x, or simply a neighborhood of x. A set F is called closed if the complement of F, R \ F, is open.
## Which functions are not continuous?
The function value and the limit aren’t the same and so the function is not continuous at this point. This kind of discontinuity in a graph is called a jump discontinuity.
## What is a discontinuity in a graph?
Discontinuities can be classified as jump, infinite, removable, endpoint, or mixed. Removable discontinuities are characterized by the fact that the limit exists. Removable discontinuities can be “fixed” by re-defining the function. Jump Discontinuities: both one-sided limits exist, but have different values.
## How do you know a function is closed?
A domain (denoted by region R) is said to be closed if the region R contains all boundary points. If the region R does not contain any boundary points, then the Domain is said to be open. If the region R contains some but not all of the boundary points, then the Domain is said to be both open and closed.
## How do you know if a graph is discontinuous?
If the function factors and the bottom term cancels, the discontinuity at the x-value for which the denominator was zero is removable, so the graph has a hole in it. After canceling, it leaves you with x – 7. Therefore x + 3 = 0 (or x = –3) is a removable discontinuity — the graph has a hole, like you see in Figure a.
## Is a jump discontinuity removable?
Then there are two types of non-removable discontinuities: jump or infinite discontinuities. Removable discontinuities are also known as holes. Jump discontinuities occur when a function has two ends that don’t meet, even if the hole is filled in at one of the ends.
## What makes a graph discontinuous?
A discontinuous function is the opposite. It is a function that is not a continuous curve, meaning that it has points that are isolated from each other on a graph. When you put your pencil down to draw a discontinuous function, you must lift your pencil up at least one point before it is complete.
## Where is the epigraph found?
An epigraph is a quote, paragraph, or short excerpt typically found at the beginning of a book. It usually serves as a preface or introduction to your story before any character makes an appearance or the action begins.
## What are the 3 conditions of continuity?
Key Concepts. For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point.
## What is discontinuity in Earth?
Earth’s interior is made of different kinds of materials. Unique layers are there according to their characteristics inside the earth. All those layers are separated from each other through a transition zone. These transition zones are called discontinuities.
## What does a continuous graph look like?
Continuous graphs are graphs that appear as one smooth curve, with no holes or gaps. Intuitively, continuous graphs are those that can be drawn without lifting a pencil. Sometimes discrete graphs will show a pattern that seems to come from a continuous graph.
## Where is a function discontinuous on a graph?
We say the function is discontinuous when x = 0 and x = 1. There are 3 asymptotes (lines the curve gets closer to, but doesn’t touch) for this function. They are the x-axis, the y-axis and the vertical line x=1 (denoted by a dashed line in the graph above).
## What is an essential discontinuity?
Any discontinuity that is not removable. That is, a place where a graph is not connected and cannot be made connected simply by filling in a single point. Step discontinuities and vertical asymptotes are two types of essential discontinuities.
## What is irony sentence?
Definition of Irony. a state of affairs that is contrary to what is expected and is therefore amusing. Examples of Irony in a sentence. 1. The irony of the situation is that Frank wanted to scare his little sister, but she ended up scaring him instead.
## Do discontinuous functions have limits?
3 Answers. No, a function can be discontinuous and have a limit. The limit is precisely the continuation that can make it continuous. Let f(x)=1 for x=0,f(x)=0 for x≠0.
## What are the 3 types of discontinuity?
Continuity and Discontinuity of Functions Functions that can be drawn without lifting up your pencil are called continuous functions. You will define continuous in a more mathematically rigorous way after you study limits. There are three types of discontinuities: Removable, Jump and Infinite.
## What is an epigraph in an essay?
A quote used to introduce an article, paper, or chapter is called an epigraph. It often serves as a summary or counterpoint to the passage that follows, although it may simply set the stage for it.
## How do you find a closed form expression?
A closed form is an expression that can be computed by applying a fixed number of familiar operations to the arguments. For example, the expression 2 + 4 + … + 2n is not a closed form, but the expression n(n+1) is a closed form. ” = a1 +L+an .
## How do you use an epigraph in a sentence?
Epigraph in a Sentence ?
1. One of the explorer’s quotes was used as an epigraph on the school building named after him.
2. Before the headstone is finished, it will be etched with an epigraph befitting a former president of our nation.
3. We asked one of the islanders to translate the statue’s epigraph for us.
## How do you write an epigraph in an essay?
Write your epigraph one double space beneath your title. Indent 2 inches on both sides of the epigraph, so it’s 1 inch further from the standard margin. Use single spacing for the epigraph, and center the text on the page. Put quotation marks around the text.
## How do you know if a function is continuous or discontinuous?
A function being continuous at a point means that the two-sided limit at that point exists and is equal to the function’s value. Point/removable discontinuity is when the two-sided limit exists, but isn’t equal to the function’s value….
1. f(c) is defined.
2. lim f(x) exists.
3. They are equal.
## What is a closed equation?
An equation is said to be a closed-form solution if it solves a given problem in terms of functions and mathematical operations from a given generally-accepted set. For example, an infinite sum would generally not be considered closed-form.
## What does it mean for a function to be closed?
In mathematics, a function is said to be closed if for each , the sublevel set. is a closed set. Equivalently, if the epigraph defined by is closed, then the function. is closed. This definition is valid for any function, but most used for convex functions.
## Why are epigraphs used?
Epigraphs serve to give readers some idea of the themes and subjects that will appear later in your work, while also establishing context for your story.
| 1,624
| 7,237
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.53125
| 5
|
CC-MAIN-2024-30
|
latest
|
en
| 0.963018
|
https://hamamsinistanbul.com/do-math-161
| 1,674,803,175,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-06/segments/1674764494974.98/warc/CC-MAIN-20230127065356-20230127095356-00183.warc.gz
| 307,638,017
| 3,620
|
Are you struggling with Solving quadratic equations calculator? In this post, we will show you how to do it step-by-step. So let's get started!
We will also give you a few tips on how to choose the right app for Solving quadratic equations calculator. There are a number of websites that allow users to input a math problem and receive step-by-step solutions. This can be a helpful resource for students who are struggling to understand how to solve a particular type of problem. It can also be a good way for students to check their work, as they can compare their own solutions to the ones provided online.
Factoring algebra is a process of breaking down an algebraic expression into smaller parts that can be more easily solved. Factoring is a useful tool for simplifying equations and solving systems of equations. There are a variety of methods that can be used to factor algebraic expressions, and the best method to use depends on the specific equation being considered. In general, however, the goal is to identify common factors in the equation and then to cancel or factor out those common factors. Factoring is a fundamental skill in algebra, and it can be used to solve a wide variety of problems. With practice, it can be mastered by anyone who is willing to put in the effort.
To solve for the hypotenuse of a right angled triangle, you can use the Pythagorean Theorem. This theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, in order to solve for the hypotenuse, you would need to square the other two sides and then add them together. Afterwards, you would need to take the square root of the result in order to find the value of the hypoten
Range is a psychological term that refers to the discrepancy between how much we feel like eating and when we actually eat. There are two main reasons why people may be range deprived: 1) they eat too little, or 2) they eat too much. Eating too little can lead to range deprivation because you’re not eating enough food to properly fuel your body. This can lead to cravings, overeating and weight gain. Eating too much can lead to range deprivation because you’re eating more food than your body needs, which can cause weight gain as well as health problems such as high blood pressure and heart disease. To solve range, you must first identify the source of your problem. For example, if you’re only eating 200 calories at dinner but feeling hungry, it may be because you’re not eating enough throughout the day. You can then adjust your caloric intake accordingly so that you’re eating enough for the day but not too much for the night.
## We cover all types of math problems
Amazing I have got completely correct math homework that only takes me 10 seconds to do which is convenient as I ride my pony after school and so don't have much time as the annoying Spanish teacher keeps replacing all our preps with Spanish. So, this app really helps me. Thank you so much for this wonderful app! If only I could have it in class 🤔 I would be top of the class 😂
| 646
| 3,082
|
{"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}
| 4.375
| 4
|
CC-MAIN-2023-06
|
latest
|
en
| 0.95983
|
https://mathspace.co/textbooks/syllabuses/Syllabus-866/topics/Topic-19453/subtopics/Subtopic-260240/?textbookIntroActiveTab=guide
| 1,638,669,259,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-49/segments/1637964363134.25/warc/CC-MAIN-20211205005314-20211205035314-00231.warc.gz
| 481,302,208
| 44,471
|
# 6.06 Sales tax and tip
Lesson
Two ways that percentages are commonly used in the U.S. are when calculating the amount of sales tax we will need to pay for purchasing an item and when calculating the proper tip to leave the waitstaff at a restaurant. Interestingly, we will find that in different parts of the United States the amount of tax that we will pay for the purchase of goods or services can vary. In addition, while tipping for good service is a common practice in the U.S., there are other countries that do not engage in the practice of tipping at all.
### Tips
This image below, from mint.com, displays the tipping customs of many countries around the world. You can see that tips vary from $0$0 to $20%$20%
Tipping is an amount of money left for the staff, in addition to paying the bill, as a sign that we appreciate good service. Tips are common in the service industry, but in other sectors like government receiving a tip can be considered illegal. So, it is important to know the customary amount to tip for different services and who we should not offer a tip to.
#### Worked examples
##### Question 1
David is paying for a meal with lots of friends. They received great service, so he is giving a $20%$20% tip. The meal came to $\$182.30$$182.30. How much will he leave as a tip? Think: I need to work out 20%20% of the total meal charge. 20%20% as a fraction is \frac{20}{100}20100. Do: 20%20% of \182.30$$182.30
$20%$20% of $\$182.30$$182.30 == \frac{20}{100}\times\182.3020100×182.30 20%20% is \frac{20}{100}20100 and of in mathematics means multiplication. == \frac{20\times182.30}{100}20×182.30100 == \36.46$$36.46
### Outcomes
#### 7.RP.3
Use proportional relationships to solve multi-step ratio, rate, and percent problems. Examples: simple interest, tax, price increases and discounts, gratuities and commissions, fees, percent increase and decrease, percent error.
| 517
| 1,915
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.6875
| 5
|
CC-MAIN-2021-49
|
latest
|
en
| 0.902603
|
https://trizenx.blogspot.com/2013/11/smart-word-wrap.html
| 1,721,119,345,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-30/segments/1720763514742.26/warc/CC-MAIN-20240716080920-20240716110920-00654.warc.gz
| 516,361,589
| 30,066
|
### Smart Word Wrap
Recursion? Oh, we all love it!
This post will try to illustrate how useful the recursion is and how complicated it can get sometimes.
We, programmers, use recursion frequently to create small and elegant programs which can do complicated things.
Just think about how would you split the following sequence "aaa bb cc ddddd" into individual rows with a maximum width of 6 characters per row.
Well, one solution is to go from the left side of the string and just take words, and when the width limit is reached, append a newline. This is called the 'greedy word wrap algorithm'. It is very fast, indeed, but the output is not always pretty.
Here enters another algorithm into play. We call it the 'smart word wrap algorithm'. Don't be fooled by the name. It's not smart at all! It can be, but not this one. For now it just tries in its head all the possible combinations, does some math and returns the prettiest result possible. It is much slower than the first algorithm, especially on very large strings with a great width value because it has to create and remember more combinations.
How many combinations do we have for the above sequence? Well, there are three of them:
1. ["aaa", "bb", "cc", "ddddd"]
2. ["aaa", "bb cc", "ddddd"]
3. ["aaa bb", "cc", "ddddd"]
How do we know which one is the best? We can find this by summing the squared number of remaining spaces on each line.
The combinations are represented as arrays. Each element of the array is a line. For example, the first array has four lines. Let's do the math to see what it says. Remember, the maximum width == 6;
1. "aaa" -> (6-3)**2 = 9
"bb" -> (6-2)**2 = 16
"cc" -> (6-2)**2 = 16
"ddddd" -> (6-5)**2 = 1
-------------------------
TOTAL: 42
2. "aaa" -> (6-3)**2 = 9
"bb cc" -> (6-5)**2 = 1
"ddddd" -> (6-5)**2 = 1
-------------------------
TOTAL: 11
3. "aaa bb" -> (6-6)**2 = 0
"cc" -> (6-2)**2 = 16
"ddddd" -> (6-5)**2 = 1
-------------------------
TOTAL: 17
Clearly, we can see that the first combination is the worst of all. A lower sum indicates more uniformity near the edges. The best solution is the second one, which has a sum of 11, and is the result of a smart word wrap algorithm. The third combination is achieved by a greedy word wrap algorithm.
Here are the steps of a smart word wrap algorithm with combinations:
1. Split the string into words
2. Create all the possible paths
3. Normalize the paths
4. Create all the possible combinations
5. Normalize the combinations
6. Find the best result
In phase 1, the words will look like this:
("aaa", "bb", "cc", "ddddd")
In phase 2, we will have an array with two sub-arrays, which contains other sub-arrays:
(
["aaa", ["bb", ["cc", ["ddddd"]]], ["bb", "cc", ["ddddd"]]],
["aaa", "bb", ["cc", ["ddddd"]]],
)
The phase 3 represents a small transformation of the paths from the phase 2:
(
[
{ "aaa" => [{ "bb" => [{ "cc" => "ddddd" }] }] },
{ "aaa" => [{ "bb cc" => "ddddd" }] },
],
[{ "aaa bb" => [{ "cc" => "ddddd" }] }],
)
In phase 4, we need to create the combinations using the paths from the phase 3:
(
[[[["aaa", "bb", "cc", "ddddd"]]]],
[[["aaa", "bb cc", "ddddd"]]],
[[["aaa bb", "cc", "ddddd"]]],
)
In phase 5, the combinations have to be arrays of strings, so we need to normalize them:
(
["aaa", "bb", "cc", "ddddd"],
["aaa", "bb cc", "ddddd"],
["aaa bb", "cc", "ddddd"],
)
Finally, in phase 6, after some calculations, the best result pops up:
("aaa", "bb cc", "ddddd")
As shown in the above phases (or steps), the algorithm does many useless transformations before it gets to the best result. The transformations take time, but they are beautiful. :)
Here is an example for a random text with MAX_WIDTH=20:
*** SMART WRAP
-----------------------------------------------------------------
As shown in the |
above phases |
(or steps), the |
algorithm does |
many useless |
transformations |
-----------------------------------------------------------------
*** GREEDY WRAP (Text::Wrap)
-----------------------------------------------------------------
As shown in the |
above phases (or |
steps), the |
algorithm does many |
useless |
transformations |
-----------------------------------------------------------------
An implementation of the algorithm described in this post can be found by clicking on one of the following links:
| 1,169
| 4,483
|
{"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}
| 4.28125
| 4
|
CC-MAIN-2024-30
|
latest
|
en
| 0.902383
|
http://tasks.illustrativemathematics.org/content-standards/5/NF/B/tasks/882
| 1,669,927,274,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-49/segments/1669446710869.86/warc/CC-MAIN-20221201185801-20221201215801-00360.warc.gz
| 53,922,992
| 9,511
|
# Painting a Wall
Alignments to Content Standards: 5.NF.B
Nicolas is helping to paint a wall at a park near his house as part of a community service project. He had painted half of the wall yellow when the park director walked by and said,
This wall is supposed to be painted red.
Nicolas immediately started painting over the yellow portion of the wall. By the end of the day, he had repainted $\frac56$ of the yellow portion red.
What fraction of the entire wall is painted red at the end of the day?
## IM Commentary
The purpose of this task is for students to find the answer to a question in context that can be represented by fraction multiplication. This task is appropriate for either instruction or assessment depending on how it is used and where students are in their understanding of fraction multiplication. If used in instruction, it can provide a lead-in to the meaning of fraction multiplication. If used for assessment, it can help teachers see whether students readily see that this is can be solved by multiplying $\frac56\times \frac12$ or not, which can help diagnose their comfort level with the meaning of fraction multiplication.
The teacher might need to emphasize that the task is asking for what portion of the total wall is red, it is not asking what portion of the yellow has been repainted.
## Solutions
Solution: Solution 1
In order to see what fraction of the wall is red we need to find out what $\frac56$ of $\frac12$ is. To do this we can multiply the fractions together like so:
$\frac56 \times \frac12 = \frac{5 \times 1}{6 \times 2} = \frac{5}{12}$
So we can see that $\frac{5}{12}$ of the wall is red.
Solution: Solution 2
The solution can also be represented with pictures. Here we see the wall right before the park director walks by:
And now we can break up the yellow portion into 6 equally sized parts:
Now we can show what the wall looked like at the end of the day by shading 5 out of those 6 parts red.
And finally, we can see that if we had broken up the wall into 12 equally sized pieces from the beginning, that finding the fraction of the wall that is red would be just a matter of counting the number of red pieces and comparing them to the total.
And so, since 5 pieces of the total 12 are red, we can see that $\frac{5}{12}$ of the wall is red at the end of the day.
| 534
| 2,339
|
{"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}
| 4.96875
| 5
|
CC-MAIN-2022-49
|
latest
|
en
| 0.959912
|
https://www.hackmath.net/en/math-problem/14451?tag_id=38
| 1,582,599,115,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2020-10/segments/1581875146004.9/warc/CC-MAIN-20200225014941-20200225044941-00369.warc.gz
| 751,669,500
| 8,833
|
# Plot
The land is in the shape of a square with a dimension of 22 meters. How much will we pay for the fence around the entire plot?
Result
x = 1760 Eur
#### Solution:
$a = 22 \ m \ \\ o = 4 \cdot \ a = 4 \cdot \ 22 = 88 \ m \ \\ \ \\ x = 20 \cdot \ o = 20 \cdot \ 88 = 1760 = 1760 \ \text{ Eur }$
Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!
Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):
Be the first to comment!
## Next similar math problems:
1. Annular area
The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
2. Company logo
The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo?
3. The trapezium
The trapezium is formed by cutting the top of the right-angled isosceles triangle. The base of the trapezium is 10 cm and the top is 5 cm. Find the area of trapezium.
4. Squares above sides
Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm2. The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc
5. The sides 2
The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
6. Area of a rectangle
Calculate the area of a rectangle with a diagonal of u = 12.5cm and a width of b = 3.5cm. Use the Pythagorean theorem.
7. Ratio of sides
Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
8. Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid.
9. Rectangle
In rectangle with sides, 6 and 3 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
10. Eq triangle minus arcs
In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts
11. Rectangle
There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.
12. Rectangular field
A rectangular field has a diagonal of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field.
13. Circular railway
The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?
14. 30-gon
At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
15. Trapezoid MO-5-Z8
ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm2. Determine the area of the trapezoid
16. Quarter circle
What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
| 988
| 3,652
|
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "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}
| 4.5
| 4
|
CC-MAIN-2020-10
|
latest
|
en
| 0.907034
|
https://bhavinionline.com/tag/riddle-for-kids/page/4/
| 1,657,213,976,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-27/segments/1656104495692.77/warc/CC-MAIN-20220707154329-20220707184329-00213.warc.gz
| 170,121,860
| 10,932
|
Find the Missing Number in the Given Table
Look at the table given in the riddle and find the connection between the numbers. Once you crack the logic, find the value of the missing number in the table. 432 975 543 234 579 345 123 ? 345 So were you able to solve the riddle? Leave your answers in the comment section below.
Fun With Maths Riddle: Find The Result For the Given Equations
Let’s test your skills in maths with this Riddle. Find the result for the given 2 equations. 100 + 101 x 102 – 100 ______________________ 10 4! x √42 4 √4 4 So were you able to solve the riddle? Leave your answers in the comment section below. You can check if your answer
Numerical Riddle: Find the Missing Number in the Riddle
Look at the table given in the riddle and find the connection between the numbers. Once you establish a logic connecting the number, you can easily find the missing number in the riddle. 16 100 49 ? 25 144 64 81 36 So were you able to solve the riddle? Leave your answers in the
Number Riddles: Find the Missing Number in the Last Triangle
Look at the numbers in the triangle and find how they are connected to each other. Once you get the logic behind the numbers you will be able to find the missing number in the last triangle. So were you able to solve the riddle? Leave your answers in the comment section below. You can check
Find the Value of the Missing Number in the Given Table
In this number riddle you will see a table with some numbers which are connected to each other in some way. Find the logic behind the numbers and then find the value of the missing number. Find the value of ? in the table below; 6 3 21 7 3 24 8 4 36 9
Fun Riddles: What Goes Through A Door But Never Goes In Or Comes Out?
Solve this riddle and leave your answers in the comment section below. What goes through a door but never goes in or comes out? So were you able to solve the riddle? Then you have all the bragging rights. If you get the correct answer, please share it with your friends and family on WhatsApp,
What Comes Next In The Sequence: 1, 11, 21, 1211, 111221, 312211, ?, ?
Look at the given set of numbers in the riddle and find the connection between then. Then you can find out what Comes Next In The Sequence: 1, 11, 21, 1211, 111221, 312211, ?, ? So were you able to solve the riddle? Leave your answers in the comment section below. If you get the
| 604
| 2,387
|
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}
| 4.25
| 4
|
CC-MAIN-2022-27
|
latest
|
en
| 0.910881
|
https://www.javatpoint.com/how-many-weeks-in-a-month
| 1,725,768,861,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-38/segments/1725700650958.30/warc/CC-MAIN-20240908020844-20240908050844-00312.warc.gz
| 826,242,557
| 13,160
|
# How Many Weeks in a Month
Currently, we have a seven-day week because of the Babylonians, who lived in what is now called Iraq. They chose the number seven because they were astronomers and professional observers who had studied all seven planets: the Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn. As a result, they valued this number greatly. Get a better understanding of how to complete your assignments on time by looking at how many weeks are in a month.
## How many weeks are there in a month?
Have you ever considered how the calendar operates and assists us in timing our daily activities? With the exception of leap years, which contain 366 days instead of 365, the Gregorian calendar is the one that is most often used worldwide. These days are split into 12 months, each of which has either 31 or 30 days, or 28 days (in February), allowing us to calculate the number of weeks in a month. The days are compressed into seven-day weeks. Therefore, a year typically equals 52 weeks plus one extra day.
## Weeks in a Month
Since every month on the calendar includes at least 28 days, it has 4 complete weeks every month. One week is equal to seven days. However, some months have some additional days, but they do not add up to form a new week, so such days are not included in the week.
For instance, the month of August contains 31 days (one week is equal to seven days). Therefore, 31/7 is 4 weeks plus 3 days. This displays 4 whole weeks plus 3 additional days.
## Weeks in a Month: Table Illustration
To count the number of weeks in each of the 12 months of the year, we must count the days in a month and divide that number by 7 to determine how many weeks there are in a month (one week equals seven days). Let's examine the chart that details the precise number of weeks and days in each month of the year along with the remaining additional days.
31 January 4 3
28 (29 in a leap year) February 4 0 (regular year), 1 (leap year)
31 March 4 3
30 April 4 2
31 May 4 3
30 June 4 2
31 July 4 3
31 August 4 3
30 September 4 2
31 October 4 3
30 November 4 2
31 December 4 3
## What indicators are there indicating that a year is a leap year?
We multiply the year digits (value) by 4 to determine if the year is a leap year. When a number divides evenly by four, a leap year is indicated. For example, since 2020 is exactly divisible by 4, the year 2020 is a leap year, in which February has a total of 29 days.
## Century Year is an exception!
The previously mentioned test is valid for all regular years, but to establish whether a century year is a leap year, it must be divided by 400 instead of 4. Examples of such century years are 300, 700, 1900, 2000, and many more.
2000, for instance, is a leap year since it can be completely divided by 400. A century year, for example, 1900, is divisible by four, but it is still not a leap year because it is not divisible by four hundred. We need to remember that for every centenary year to be a leap year, it must be exactly divisible by 400, not 4.
## Essential Facts to Remember
Why is there a leap year, in which there is a month of February with an extra day every four years?
• The Earth requires 365 and a quarter days to complete one orbit around the sun.
• The quarter is excluded when a regular year is calculated as 365 days alone.
• These quarter days are added every four years by adding four quarters together (1/4+1/4+1/4+1/4=1) to make a full extra day.
• For the leap year, this extra day is added. As a result, a leap year has 366 (365 + 1 =366) days.
## Summary
In short, there is no firm agreement about the number of weeks in a month. It is a popular misconception that there are four weeks in a month because this is simplistic to prove. The Gregorian calendar in common use today is composed of months that range in length from 28 to 31 days. As a result, the number of weeks in a month may change because it has extra days.
Let's go into some specifics so that we can better understand this idea. Given that there are seven days in a week and there can be at most 31 in a month, when divided by 7, the result is 4.43 weeks. If we round this figure, every month will have four full weeks. However, these are actually exceptions. Still, we stand with this theory.
| 1,054
| 4,272
|
{"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}
| 4.3125
| 4
|
CC-MAIN-2024-38
|
latest
|
en
| 0.974382
|
http://www.go4expert.com/contests/length-pole-29-sep-2009-t19620/#post58182
| 1,481,191,557,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2016-50/segments/1480698542520.47/warc/CC-MAIN-20161202170902-00027-ip-10-31-129-80.ec2.internal.warc.gz
| 489,809,854
| 11,408
|
# Length of Pole | 29 Sep 2009
Discussion in '\$1 Daily Competition' started by shabbir, Sep 29, 2009.
1. ### shabbirAdministratorStaff Member
Joined:
Jul 12, 2004
Messages:
15,293
365
Trophy Points:
83
Pole is in a lake. Half of the pole is under the ground, One-third of it is covered by water. 8 ft is out of the water.
What could be the possible length of the pole?
2. ### sameer_havakajokaNew Member
Joined:
Sep 14, 2009
Messages:
271
2
Trophy Points:
0
Occupation:
Sleeping
Location:
Hava Ke Paro Me
48
3. ### sameer_havakajokaNew Member
Joined:
Sep 14, 2009
Messages:
271
2
Trophy Points:
0
Occupation:
Sleeping
Location:
Hava Ke Paro Me
48ft is correct
Solution:
Fraction of pole in the ground = 1/2
Fraction of pole covered by water = 1/3
Fraction of pole in the ground and covered by water = 1/2 + 1/3 = (3 + 2)/6 = 5/6
Fraction of pole out of water = 1 - 5/6 = 1/6
Thus, one-sixth of the pole (out of water) is 8 ft.
So, total length of pole = 48 ft.
It may be noted that:
Length of pole in the ground = 48/2 = 24 ft.
Length of pole covered by water = 48/3 = 16 ft.
Length of pole out of water = 8 ft.
The problem may also be solved by setting up the following equation: x/2 + x/3 + 8 = x
where x denotes the total length of the pole in ft.
The equation may be solved as shown below.
5x/6 + 8 = x
8 = x - 5x/6 = x/6
x/6 = 8 or x = 48.
4. ### shabbirAdministratorStaff Member
Joined:
Jul 12, 2004
Messages:
15,293
365
Trophy Points:
83
Bingo
Joined:
Sep 14, 2009
Messages:
271
| 511
| 1,501
|
{"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-2016-50
|
latest
|
en
| 0.930352
|
http://mathandreadinghelp.org/math_games_kids_age_6.html
| 1,419,139,426,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2014-52/segments/1418802770718.139/warc/CC-MAIN-20141217075250-00058-ip-10-231-17-201.ec2.internal.warc.gz
| 182,149,929
| 8,450
|
# Fun Math Games for Kids at Age 6
## Math Concepts for 6-Year-Olds
In first grade, your 6-year-old will be learning strategies for adding and subtracting within 20. To be successful, it will also be important for her to understand place value and how to correctly group items into tens and ones. Other skills your child will develop at the first grade level are measuring the length of items and composing geometric shapes. Reinforce these concepts at home using fun review games.
### Even or Odd?
Before beginning this game, remove all the face cards from a deck of cards. Turn the cards face down on the table. Players will take turns flipping over two cards. If the sum of the two cards is even, the player will keep both cards.
If the sum of the two cards is odd, the cards will be returned to play. The player with the most cards at the end of the game wins! For more advanced players, try turning over three cards for each round of play.
### Show Me This!
For this activity, use paper clips to have your child practice grouping tens and ones. Use large paper clips to represent tens, and smaller paper clips to represent ones. For example, if you ask your child to group the number 24, he would use two large paper clips (representing the 20) and four small paper clips (representing the four). As an extension to this activity, have your child model number sentences using paper clips.
### Measure It
Before beginning this activity, ask your child to predict the length of certain areas of your house. After making predictions, have your child measure the areas using a ruler or a yardstick. For instance, have your child predict the length of her bedroom and then measure the bedroom using a ruler.
Keep in mind that your child may not understand that a ruler is one foot in length; she may only be able to tell you the number of rulers it takes to get from one side of the room to the other. It is also important that you help your child count the number of times she 'flips' the ruler when measuring.
### Piece It Together
To prepare for this activity, cut out different shapes in a variety of sizes from construction paper. Have your child explore making different shapes or symbols using the pieces of construction paper. For example, your child could make a square by piecing together two triangles. Or you could challenge your child to create an object, such as an arrow, using his choice of shapes.
Did you find this useful? If so, please let others know!
## Other Articles You May Be Interested In
• MIND Games Lead to Math Gains
Imagine a math teaching tool so effective that it need only be employed twice per week for less than an hour to result in huge proficiency gains. Impossible, you say? Not so...and MIND Research Institute has the virtual penguin to prove it.
• 5 Free and Fun Math Games for Kids
Looking for a way to get your child engaged with math? There are many free, fun math games online that explore basic concepts such as addition, subtraction, multiplication and division, as well as more advanced games that offer practice with decimals and fractions. Read on to discover five of our favorite educational - and fun!...
## We Found 7 Tutors You Might Be Interested In
### Huntington Learning
• What Huntington Learning offers:
• Online and in-center tutoring
• One on one tutoring
• Every Huntington tutor is certified and trained extensively on the most effective teaching methods
In-Center and Online
### K12
• What K12 offers:
• Online tutoring
• Has a strong and effective partnership with public and private schools
• AdvancED-accredited corporation meeting the highest standards of educational management
Online Only
### Kaplan Kids
• What Kaplan Kids offers:
• Online tutoring
• Customized learning plans
• Real-Time Progress Reports track your child's progress
Online Only
### Kumon
• What Kumon offers:
• In-center tutoring
• Individualized programs for your child
• Helps your child develop the skills and study habits needed to improve their academic performance
In-Center and Online
### Sylvan Learning
• What Sylvan Learning offers:
• Online and in-center tutoring
• Sylvan tutors are certified teachers who provide personalized instruction
• Regular assessment and progress reports
In-Home, In-Center and Online
### Tutor Doctor
• What Tutor Doctor offers:
• In-Home tutoring
• One on one attention by the tutor
• Develops personlized programs by working with your child's existing homework
In-Home Only
### TutorVista
• What TutorVista offers:
• Online tutoring
• Student works one-on-one with a professional tutor
• Using the virtual whiteboard workspace to share problems, solutions and explanations
Online Only
| 989
| 4,699
|
{"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}
| 4.1875
| 4
|
CC-MAIN-2014-52
|
longest
|
en
| 0.939056
|
https://www.enotes.com/homework-help/two-mile-pier-one-mile-pier-extend-545534
| 1,498,527,870,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2017-26/segments/1498128320887.15/warc/CC-MAIN-20170627013832-20170627033832-00547.warc.gz
| 868,986,851
| 13,255
|
# A two mile pier and a one mile pier extend perpendicularly into the ocean with four miles of shore between the two piers. A swimmer wishes to swim from the end of the longer pier to the end of the...
A two mile pier and a one mile pier extend perpendicularly into the ocean with four miles of shore between the two piers. A swimmer wishes to swim from the end of the longer pier to the end of the shorter pier with one rest stop on the beach. Assuming that the swimmer recalls that, in any right triangle, the hypotenuse2 = leg2 + leg2, find the shortest possible swim.
http://math.kendallhunt.com/documents/ALookInside/ThoughtProvokers/ThoughtProvokers_pp_44-45.pdf
embizze | High School Teacher | (Level 2) Educator Emeritus
Posted on
The swimmer begins on the end of the 2 mile pier, swims to the beach and then out to the end of the 1 mile pier, and we are asked to find the shortest possible swim.
The easiest solution is to reflect the 1 mile pier across the line formed by the beach. (See attachment.) Now draw a line from the end of the 2 mile pier to the reflected end of the 1 mile pier. Extending the 2 mile pier 1 mile "below" the beach and connecting this point to the reflection of the 1 mile pier creates a right triangle whose sides are 3 miles and 4 miles long. The hypotenuse of this triangle is 5 miles long.
If d1 is the distance from the 2 mile pier to the shore, and d2 is the distance from the shore to the 1 mile pier, and if we assume that the point on the beach is where the line from the 2 mile pier to the reflected 1 mile pier intersects the beach, then d1+d2=5 miles.
Claim: 5 miles is the shortest distance. Let A be the end of the 2 mile pier, B the end of the 1 mile pier, B' the reflected end, and X the intersection of AB' and the shore. Suppose Y is a point on the shore between the piers and Y is not X. Then the total path is AY+YB. But by construction the total path using X is AX+XB=AX+XB'. Now consider triangle AYB'. By the triangle inequality theorem, AY+YB'>AB'=AX+XB'. Thus AY+YB>AX+XB for any choice of Y not equal to X.
----------------------------------------------------------------------------------------
The shortest swimming distance is 5 miles.
----------------------------------------------------------------------------------------
You can use calculus to minimize the sum of the distance functions, or algebra to find the minimum, but the geometric argument is easier.
Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)
| 603
| 2,524
|
{"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}
| 4.3125
| 4
|
CC-MAIN-2017-26
|
longest
|
en
| 0.903555
|
https://skydivehayabusa.com/kitesurfing/best-answer-is-a-rhombus-always-a-kite.html
| 1,653,359,445,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2022-21/segments/1652662562410.53/warc/CC-MAIN-20220524014636-20220524044636-00419.warc.gz
| 578,656,673
| 18,560
|
# Best answer: Is a rhombus always a kite?
Contents
## Why is a rhombus always a kite?
With a hierarchical classification, a rhombus (a quadrilateral with four sides of the same length) is considered to be a special case of a kite, because it is possible to partition its edges into two adjacent pairs of equal length, and a square is a special case of a rhombus that has equal right angles, and thus is …
## Is a rhombus always sometimes or never a kite?
A square is a rhombus is a kite is a quadrilateral. A kite is not always a rhombus.
## What is a rhombus that is not a kite?
A kite is a convex quadrilateral with two pairs of adjacent equal sides. A rhombus has two pairs of adjacent equal sides too, but all four sides are the same length. This answer assumes a positive definition of “kite” that does not deliberately exclude such special cases as rhombuses or squares.
## What makes a kite a kite?
A Kite is a flat shape with straight sides. It has two pairs of equal-length adjacent (next to each other) sides. It often looks like. a kite! Two pairs of sides.
## How is a kite different to a rhombus?
The main difference between a kite and a rhombus is that a rhombus has all equal sides whereas a kite has two pairs of adjacent equal sides.
INTERESTING: Frequent question: What type of bird is a red kite?
## Is a kite sometimes always or never a parallelogram?
Explanation: A kite is a quadrilateral with two disjoint pairs (no side is in both pairs) of equal-length, adjacent (sharing a vertex) sides. A parallelogram also has two pairs of equal-length sides, however they must be opposite, as opposed to adjacent.
## What shape is a kite?
A kite is a four-sided shape with straight sides that has two pairs of sides. Each pair of adjacent sides are equal in length. A square is also considered a kite.
## Which is not a rhombus?
One of the two characteristics that make a rhombus unique is that its four sides are equal in length, or congruent. … If you have a quadrilateral with only one pair of parallel sides, you definitely do not have a rhombus (because two of its sides cannot be the same length). You have a trapezoid.
## How do you prove a rhombus is a kite?
Here are the two methods:
1. If two disjoint pairs of consecutive sides of a quadrilateral are congruent, then it’s a kite (reverse of the kite definition).
2. If one of the diagonals of a quadrilateral is the perpendicular bisector of the other, then it’s a kite (converse of a property).
## What forces act on a kite?
Just like rockets, jets, or birds, all kites experience a combination of forces as they fly. The main forces that determine whether or not a kite is able to fly are weight, lift, tension, and drag.
## Can a rhombus and kite be congruent?
Sometimes a kite can be a rhombus (four congruent sides), a dart, or even a square (four congruent sides and four congruent interior angles). Some kites are rhombi, darts, and squares. Not every rhombus or square is a kite.
## Can you fly a kite without wind?
Before you can fly your kite, you need wind. … Others are especially made to fly in light wind. But most kites are made to fly in average winds of between four and ten miles per hour. If you can feel the wind on your face, there is probably enough to fly.
| 784
| 3,282
|
{"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-2022-21
|
latest
|
en
| 0.938773
|
grace.bluegrass.kctcs.edu
| 1,685,607,346,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-23/segments/1685224647639.37/warc/CC-MAIN-20230601074606-20230601104606-00454.warc.gz
| 325,899,401
| 4,278
|
Boolean Algebra and Reduction Techniques
# Boolean Algebra Laws and Rules
There are three laws of Boolean Algebra that are the same as ordinary algebra.
1. The Commutative Law
addition A + B = B + A (In terms of the result, the order in which variables are ORed makes no difference.)
multiplication AB = BA (In terms of the result, the order in which variables are ANDed makes no difference.)
2. The Associative Law
addition A + (B + C) = (A + B) + C (When ORing more than two variables, the result is the same regardless of the grouping of the variables.)
multiplication A(BC) = (AB)C (When ANDing more than two variables, the result is the same regardless of the grouping of the variables.)
3. The Distributive Law - The distributive law is the factoring law. A common variable can be factored from an expression just as in ordinary algebra.
A(B + C) = AB + AC
(A + B)(C + D) = AC + AD + BC + BD Remeber FOIL(First, Outer, Inner, Last)?
# Ten Basic Rules of Boolean Algebra
1. Anything ANDed with a 0 is equal to 0. A * 0 = 0
2. Anything ANDed with a 1 is equal to itself. A * 1 = A
3. Anything ORed with a 0 is equal to itself. A + 0 = A
4. Anything ORed with a 1 is equal to 1. A + 1 = 1
5. Anything ANDed with itself is equal to itself. A * A = A
6. Anything ORed with itself is equal to itself. A + A = A
7. Anything ANDed with its own complement equals 0.
8. Anything ORed with its own complement equals 1.
9. Anything complemented twice is equal to the original.
10. The two variable rule.
# Simplification of Combinational Logic Circuits Using Boolean Algebra
• Complex combinational logic circuits must be reduced without changing the function of the circuit.
• Reduction of a logic circuit means the same logic function with fewer gates and/or inputs.
• The first step to reducing a logic circuit is to write the Boolean Equation for the logic function.
• The next step is to apply as many rules and laws as possible in order to decrease the number of terms and variables in the expression.
• To apply the rules of Boolean Algebra it is often helpful to first remove any parentheses or brackets.
• After removal of the parentheses, common terms or factors may be removed leaving terms that can be reduced by the rules of Boolean Algebra.
• The final step is to draw the logic diagram for the reduced Boolean Expression.
# Some Examples of Simplification
Perform FOIL (Firt - Outer - Inner - Last)
AA = A (Anything ANDed with itself is itself)
Find a like term (A) and pull it out. (There is an A in A, AC, and AB). Make sure you leave the BC alone at the end.
Anything ORed with a 1 is a 1 (1+C+B=1).
Anthing ANDed with a 1 is itself (A1=A)
# Some Examples of Simplification (cont.)
Find like term (B) and pull it out.
Anything ORed with its own complement equals 1.
Anything ANDed with 1 is itself.
# Some Examples of Simplification (cont.)
Find like term and pull them out. Make sure you leave the one.
Anything ORed with a 1 is 1.
Anything ANDed with a 1 is itself
# Some Examples of Simplification (cont.)
Find like terms and pull them out.
Anything ORed with its own complement equals 1.
Anything ANDed with 1 equals itself.
NOTE: I will workout many examples in the video.
# DeMorgan's Theorem
• De Morgan's theorem allows large bars in a Boolean Expression to be broken up into smaller bars over individual variables.
• De Morgan's theorem says that a large bar over several variables can be broken between the variables if the sign between the variables is changed.
• De Morgan's theorem can be used to prove that a NAND gate is equal to an OR gate with inverted inputs.
• De Morgan's theorem can be used to prove that a NOR gate is equal to an AND gate with inverted inputs.
• In order to reduce expressions with large bars, the bars must first be broken up. This means that in some cases, the first step in reducing an expression is to use De Morgan's theorem.
• It is highly recommended to place parentheses around terms where lines have been broken.
For example:
# DeMorgan (cont.)
Applying DeMorgan's theorem and the distribution law:
# Bubble Pushing
• Bubble pushing is a technique to apply De Morgan's theorem directly to the logic diagram.
1. Change the logic gate (AND to OR and OR to AND).
2. Add bubbles to the inputs and outputs where there were none, and remove the original bubbles.
• Logic gates can be De Morganized so that bubbles appear on inputs or outputs in order to satisfy signal conditions rather than specific logic functions. An active-low signal should be connected to a bubble on the input of a logic gate.
# The Universal Capability of NAND and NOR Gates
• NAND and NOR gates are universal logic gates.
• The AND, Or, Nor and Inverter functions can all be performed using only NAND gates.
• The AND, OR, NAND and Inverter functions can all be performed using only NOR gates.
• An inverter can be made from a NAND or a NOR by connecting all inputs of the gate together.
• If the output of a NAND gate is inverted, it becomes an AND function.
• If the output of a NOR gate is inverted, it becomes an OR function.
• If the inputs to a NAND gate are inverted, the gate becomes an OR function.
• If the inputs to a NOR gate are inverted, the gate becomes an AND function.
• When NAND gates are used to make the OR function and the output is inverted, the function becomes NOR.
• When NOR gates are used to jake the AND function and the output is inverted, the function becomes NAND.
# AND-OR-Invert Gates for Implementing Sum-of-Products Expressions
• Most Boolean reductions result in a Product-of-Sums (POS) expression or a Sum-of-Products (SOP) expression.
• The Sum-of-Products means the variables are ANDed to form a term and the terms are ORed. X = AB + CD.
• The Product-of-Sums means the variables are ORed to form a term and the terms are ANDed. X = (A + B)(C + D)
• AND-OR-Inverter gate combinations (AOI) are available in standard ICs and can be used to implement SOP expressions.
• The 74LS54 is a commonly used AOI.
• Programmable Logic Devices (PLDs) are available for larger and more complex functions than can be accomplished with an AOI.
# Karnaugh Mapping
• Karnaugh mapping is a graphic technique for reducing a Sum-of-Products (SOP) expression to its minimum form.
• Two, three and four variable k-maps will have 4, 8 and 16 cells respectively.
• Each cell of the k-map corresponds to a particular combination of the input variable and between adjacent cells only one variable is allowed to change.
• Use the following steps to reduce an expression using a k-map.
1. Use the rules of Boolean Algebra to change the expression to a SOP expression.
2. Mark each term of the SOP expression in the correct cell of the k-map. (kind of like the game Battleship)
3. Circle adjacent cells in groups of 2, 4 or 8 making the circles as large as possible. (NO DIAGONALS!)
4. Write a term for each circle in a final SOP expression. The variables in a term are the ones that remain constant across a circle.
• The cells of a k-map are continuous left-to-right and top-to-bottom. The wraparound feature can be used to draw the circles as large as possible.
• When a variable does not appear in the original equation, the equation must be plotted so that all combinations of the missing variable(s) are covered.
This is a very visual problem so watch the video for examples on how to complete and solve Karnaugh Maps!
| 1,757
| 7,406
|
{"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-2023-23
|
latest
|
en
| 0.912511
|
https://nrich.maths.org/public/topic.php?code=5030&cl=2&cldcmpid=2646
| 1,611,026,911,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2021-04/segments/1610703517559.41/warc/CC-MAIN-20210119011203-20210119041203-00285.warc.gz
| 485,026,071
| 5,505
|
Resources tagged with: Digit cards
Filter by: Content type:
Age range:
Challenge level:
There are 12 results
Broad Topics > Physical and Digital Manipulatives > Digit cards
The Thousands Game
Age 7 to 11 Challenge Level:
Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?
Song Book
Age 7 to 11 Challenge Level:
A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit cards. What is the minimum number of small cards that is needed?
Magic Circles
Age 7 to 11 Challenge Level:
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
Twenty Divided Into Six
Age 7 to 11 Challenge Level:
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
All the Digits
Age 7 to 11 Challenge Level:
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Reach 100
Age 7 to 14 Challenge Level:
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Magic Vs
Age 7 to 11 Challenge Level:
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Sealed Solution
Age 7 to 11 Challenge Level:
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Finding Fifteen
Age 7 to 11 Challenge Level:
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Four-digit Targets
Age 7 to 11 Challenge Level:
You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?
Penta Primes
Age 7 to 11 Challenge Level:
Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?
Fifteen Cards
Age 7 to 11 Challenge Level:
Can you use the information to find out which cards I have used?
| 595
| 2,416
|
{"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-2021-04
|
latest
|
en
| 0.932535
|
https://library.fiveable.me/ap-physics-2/unit-3/forces-potential-energy/study-guide/O5RUx6QUCquPp7vmlyTT
| 1,685,899,273,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2023-23/segments/1685224650201.19/warc/CC-MAIN-20230604161111-20230604191111-00645.warc.gz
| 392,423,299
| 39,566
|
# 3.2 Forces and Potential Energy
Riya Patel
Riya Patel
61 resources
See Units
## Hooke's Law
Robert Hooke came up with an equation to describe an ideal "linear" spring acting in a system.
The equation for Hooke's Law is as follows:
Where Fs is the spring force, k is the spring constant, and Δ x is the displacement of the spring from its equilibrium position. Keep in mind spring force is a restoring force!
⚠️Hang on...what's a spring constant?
A spring constant is a number used to describe the properties of a spring, primarily its stiffness. Essentially, the easier a spring is to stretch, the smaller the spring constant is (start thinking about how this relates back to Newton's Third Law).
Many times, students will be asked to graph this relationship in order to find the spring constant k. Here's an example of a graph from a lab:
As you may be able to tell, the spring constant of the spring used in the lab should be the slope of the graph. (You can also see why this law describes "linear" springs)
Now let's connect this back to energy! The elastic potential energy of a spring can be defined as:
## Conservative Forces
A conservative force is a force where the total work done on an object is solely dependent on the final and initial positions of the object. Dissipative forces are the opposite of conservative forces, and the ones typically seen are friction or external applied forces.
Fast facts of conservative forces:
• Independent of the path taken
• Total work on a closed path is zero
Examples of conservative forces:
• Gravitational force
• Spring force
Work done by conservative forces is also equal to the negative change in potential energy (U).
It can also be written as:
Where F is a conservative force and a and b are typically the the initial and final radius.
The differential version of this equation is:
We can do some fun things with this version of the equation, especially with graphs. The most important thing to note is that force is the negative slope of a potential energy versus position graph. AP loves to make students analyze energy graphs. Let's take a look at some examples!
Taken from LibreTexts
From your expert calculus knowledge, you should be able to see that equilibrium is wherever the slope is zero, meaning there is no net force. When analyzing these graphs, you should attempt to determine the total mechanical energy and draw a horizontal line for it. Occasionally you will find graphs that contain a section known as Potential Energy Wells which are typically caused by oscillations. You can spot a potential energy well at a local minimum!
## Gravitational Potential Energy
The gravitational potential energy of a system with an object very near/on the Earth in a uniform gravitational field is:
Where delta U is the change in potential energy, m is mass, g is acceleration due to gravity, and delta h is the change in height.
Here's the derivation for the equation for Gravitational Potential Energy (for large masses at a distance:
Where W is work, F(r) is a function for the force and r is the radius/distance.
Plug in the formula for Newton's Law of Universal Gravitation as a function of F(r). Where m1 and m2 are the masses in the system and G is the gravitational constant.
Take the integral evaluated from the initial radius to the final radius.
Gravity is a conservative force, so:
To make equations work nicely, we usually state that Ro(initial r) is set at infinity and that the initial potential energy is 0. So it simplifies the above to be:
Which should be the formula you see on your formula chart!
Practice Questions
1. A 5.00 × 10^5-kg subway train is brought to a stop from a speed of 0.500 m/s in 0.400 m by a large spring bumper at the end of its track. What is the force constant k of the spring? (Taken from Lumen Learning)
Energy is not conserved because there is acceleration from a force, therefore we can tackle this problem with work!
So we know that W = Fd, and we know our d, so let's try to find the force.
F=ma
We don't know acceleration! But we know our displacement, our initial velocity, and our final velocity...so we can recall an equation from unit 1.
Then we know that W = F*d so:
Another relationship we know about work is:
Spring energy is elastic potential energy so we can plug that formula into the equation.
2. Suppose a 350-g kookaburra (a large kingfisher bird) picks up a 75-g snake and raises it 2.5 m from the ground to a branch. (a) How much work did the bird do on the snake?
(b) How much work did it do to raise its own center of mass to the branch? (Taken from Lumen Learning)
(a)
(b)
3.
Taken from CollegeBoard
Make sure to use the variables they want you to use and place bounds if they exist in the problem.
4.
Browse Study Guides By Unit
💧Unit 1 – Fluids
🔥Unit 2 – Thermodynamics
💡Unit 4 – Electric Circuits
🧲Unit 5 – Magnetism & Electromagnetic Induction
🔍Unit 6 – Geometric & Physical Optics
⚛️Unit 7 – Quantum, Atomic, & Nuclear Physics
📆Big Reviews: Finals & Exam Prep
| 1,149
| 5,009
|
{"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}
| 4.375
| 4
|
CC-MAIN-2023-23
|
latest
|
en
| 0.925706
|
https://15worksheets.com/worksheet-category/11-times-tables/
| 1,723,238,930,000,000,000
|
text/html
|
crawl-data/CC-MAIN-2024-33/segments/1722640782236.55/warc/CC-MAIN-20240809204446-20240809234446-00545.warc.gz
| 53,625,182
| 35,171
|
# 11 Times Tables Worksheets
• ###### Wheel of 11s
The multiplication table of 11 has some unique characteristics that make it fascinating and slightly different from other times tables. For instance, when multiplying 11 by any single-digit number, the result is that number repeated twice. So, 11 x 3 is 33, 11 x 5 is 55, and so forth.
However, when you multiply 11 by a two-digit number, the trick is slightly different. That’s where the 11 Times Tables Worksheets come in handy. They allow you to repeatedly practice these problems, understand the pattern, and improve your speed and accuracy.
When you look at the worksheet, you will see multiple multiplication problems. These problems are usually arranged in a structured way. For example, the first few problems might involve multiplying 11 by single-digit numbers. As you move further down the sheet, you might find problems where you have to multiply 11 by two-digit numbers.
You may be wondering how this worksheet will help you, given that calculators are so readily available and easy to use. However, understanding the multiplication table and being able to do it mentally gives you a strong foundation in mathematics. It helps you quickly solve problems and gain confidence in math. For instance, when you have to solve complex equations later in algebra or geometry, this fundamental knowledge will help you simplify and solve problems quickly.
Using these worksheets is pretty straightforward. You usually start by solving the problems from the top of the worksheet, then gradually make your way down. If you get stuck, don’t worry. Remember, practice makes perfect. The more you work with these problems, the better you will understand the patterns and the quicker you will be able to solve them.
What’s more, these worksheets all have an answer key at the end. This means you can check your work once you’re done. This immediate feedback can help you understand your mistakes and learn from them. If you get a problem wrong, don’t get discouraged. Instead, try to figure out what went wrong and how to avoid making the same mistake in the future.
### What Is the 11 Times Table Trick?
There is a neat trick you can use to quickly find products when a multiplier of 11 is involved. Please note that is only works under certain conditions. here’s a trick for multiplying a two-digit number by 11:
Step 1) Separate the Digits (Multiplicand) – If you’re multiplying 11 by a two-digit number, say 35, you would first separate the two digits (3 and 5).
Step 2) Add the Two Digits Together – Next, you would add those two numbers together. In this case, 3 + 5 equals 8.
Step 3) Insert the Sum – Insert this sum between the two digits you started with. So you now have 385.
Therefore, 35 times 11 equals 385.
But remember, there’s a catch when the sum of two digits is more than 9. In that case, you should carry over the value to the next digit.
For example, let’s calculate 11 times 78:
1) Separate the digits, 7 and 8.
2) Add those two numbers together. 7 + 8 equals 15.
3) Here, since 15 is a two-digit number, we only place the unit digit (5) in the middle and carry over the tens digit (1) to the 7, which then becomes 8.
So, the final result is 858.
Therefore, 78 times 11 equals 858.
| 738
| 3,271
|
{"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}
| 4.1875
| 4
|
CC-MAIN-2024-33
|
latest
|
en
| 0.936217
|
End of preview. Expand
in Data Studio
YAML Metadata
Warning:
empty or missing yaml metadata in repo card
(https://huggingface.co/docs/hub/datasets-cards)
Finemath-4plus filtered using this code:
def my_filter(example):
lscore = example["language_score"] > 0.9
score = example["score"] > 4
lengh = example["token_count"] < 5000
return lscore and score and lengh
This remove 86% of the dataset in average.
- Downloads last month
- -
Size of downloaded dataset files:
1.79 GB
Size of the auto-converted Parquet files:
1.79 GB
Number of rows:
974,568