url stringlengths 6 1.61k | fetch_time int64 1,368,856,904B 1,726,893,854B | content_mime_type stringclasses 3 values | warc_filename stringlengths 108 138 | warc_record_offset int32 9.6k 1.74B | warc_record_length int32 664 793k | text stringlengths 45 1.04M | token_count int32 22 711k | char_count int32 45 1.04M | metadata stringlengths 439 443 | score float64 2.52 5.09 | int_score int64 3 5 | crawl stringclasses 93 values | snapshot_type stringclasses 2 values | language stringclasses 1 value | language_score float64 0.06 1 |
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http://mathhelpforum.com/number-theory/133947-euler-phi-function.html | 1,480,840,437,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698541220.56/warc/CC-MAIN-20161202170901-00154-ip-10-31-129-80.ec2.internal.warc.gz | 170,553,157 | 9,380 | # Thread: Euler phi-function
1. ## Euler phi-function
Let n be a positive integer having k distinct odd prime divisors. Prove that 2^k divides Euler phi-function(n).
2. Suppose $n = p_1^{\alpha_1}\cdot p_2^{\alpha_2}\cdot\cdot\cdot p_k^{\alpha_k}$ where $p_i \neq 2$.
Then $\phi(n) = \phi(p_1^{\alpha_1})\cdot\phi(p_2^{\alpha_2})\cdot \cdot\cdot\phi(p_k^{\alpha_k})$.
Note that $\phi(p_i^{\alpha_i})=p_i^{\alpha_i-1}\cdot (p_i-1)$.
So we have $2 \mid p_i-1 \; \forall i \implies 2^k \mid \phi(n)$. | 196 | 503 | {"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": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2016-50 | longest | en | 0.469228 |
https://www.prepanywhere.com/prep/textbooks/9-mathematics-nelson/chapters/chapter-5-analytic-geometry/materials/5-5-parallel-and-perpendicular-lines/videos/q17c | 1,632,064,577,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780056890.28/warc/CC-MAIN-20210919125659-20210919155659-00245.warc.gz | 966,001,575 | 7,094 | 17. Q17c
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<p>Find the equation of a line</p><p>parallel to <code class='latex inline'>y=-2x+3</code>, passing through (0,0)</p>
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<p>Determine the value of <code class='latex inline'>k</code> in each graph. </p><img src="/qimages/1374" />
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<p>A line segment has endpoints <code class='latex inline'>A(1, -5)</code> and <code class='latex inline'>B(4, 1)</code>. </p> <ul> <li>Determine the coordinate of two points, C and D, that would make ABCD a rectangle. </li> </ul>
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L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
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<p>Determine the value of <code class='latex inline'>k</code> in each graph. </p><img src="/qimages/1374" />
<p>A line segment has endpoints <code class='latex inline'>A(1, -5)</code> and <code class='latex inline'>B(4, 1)</code>. </p> <ul> <li>Determine the coordinate of two points, C and D, that would make ABCD a rectangle. </li> </ul>
<p>Determine the equation of a line perpendicular to <code class='latex inline'>2x - 5y=6</code> with the same x-intercept as the line defined by <code class='latex inline'>3x + 8y-15=0</code>.</p>
<p>A line segment has endpoints <code class='latex inline'>A(1, -5)</code> and <code class='latex inline'>B(4, 1)</code>. </p> <ul> <li>Determine the coordinate of two points, C and D, that would make ABCD a square.<br></li> </ul>
<p>Determine the equation of a line perpendicular to <code class='latex inline'>4x - 3y - 2=0</code> with the same y-intercept as the line defined by <code class='latex inline'>3x + 4y=-12</code>. </p>
<p>Use the given information to write the equation of each line. </p><p>A line perpendicular to the line defined by <code class='latex inline'>2x - 3y+18=0</code> with the same y-intercept </p>
<p>Find the equation of a line</p><p>perpendicular to <code class='latex inline'>y=-\dfrac{5}{2}x +3</code>, passing through (-2,3)</p><p>[Similar Question](FfxeGuj-hOI)</p>
<p>Use the given information to write the equation of each line. </p><p>A line perpendicular to the line defined by <code class='latex inline'>y=3x + 5</code> and passing through the point <code class='latex inline'>(3, -5)</code></p>
<p>Find the equation of a line</p><p>perpendicular to <code class='latex inline'>y=3x+4</code>, passing through (0,0)</p>
<p>Find the equation of a line. </p><p>parallel to <code class='latex inline'>y=\dfrac{1}{2}x +3</code>, passing through the origin. </p>
<p>Find the equation of a line</p><p>parallel to <code class='latex inline'>y=-2x+3</code>, passing through (0,0)</p>
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Save videos to My Cheatsheet for later, for easy studying. | 910 | 2,877 | {"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-2021-39 | latest | en | 0.624191 |
https://analystnotes.com/cfa-study-notes-the-total-probability-rule.html | 1,627,882,448,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154304.34/warc/CC-MAIN-20210802043814-20210802073814-00036.warc.gz | 108,056,682 | 9,422 | ### Seeing is believing!
Before you order, simply sign up for a free user account and in seconds you'll be experiencing the best in CFA exam preparation.
##### Subject 5. The Total Probability Rule
If we have an event or scenario S, the event not-S, called the complement of S, is written SC. Note that P(S) + P(SC) = 1, as either S or not-S must occur.
The total probability rule explains the unconditional probability of an event in terms of probabilities conditional on the scenarios.
• P(A) = P(A|S)P(S) + P(A|SC)P(SC)
• P(A) = P(A|S1)P(S1) + P(A|S2)P(S2) + ... + P(A|Sn)P(Sn)
• The first equation is just a special case of the second equation.
• The second equation states the following: the probability of any event [P(A)] can be expressed as a weighted average of the probabilities of the event, given scenarios [terms such as P(A|S1)]; the weights applied to these conditional probabilities are the respective probabilities of the scenarios [terms such as P(A1 multiplying P(A|S1)], and the scenarios must be mutually exclusive and exhaustive.
Suppose there are two events:
• Event A: IBM's revenue will increase.
• Event B: the economy is going into an expansion. P(B) = 0.6, and therefore P(Bc) = 0.4.
The probability of an increase in IBM's revenue given an economic expansion is P(A|B) = 0.8.
The probability of an increase in IBM's revenue given no economic expansion is P(A|Bc) = 0.7.
Using the total probability rule, we can compute the probability of an increase in IBM's revenue: P(A) = P(A|B) x P(B) + P(A|Bc) x P(Bc) = 0.8 x 0.6 + 0.7 x 0.4 = 0.76.
Typical exam question
An analyst constructs the following probability table for the market and Company X's stock:
1. Compute the total probability of good performance for Company X's stock.
Here we are asked to find the total probability of good performance. This means we have to find the joint probability of one stock outcome. To do this we multiply and add.
We take Σ (probability of economic state x good conditional probability): Joint probability = (0.5 x 0.4) + (0.3 x 0.5) + (0.2 x 0.5) = 45%
2. Compute the probability of simultaneously realizing a bull economy and poor stock performance for Company X.
This question asks you to determine the probability of a specific branch. If we follow the branch and multiply the probabilities, we will arrive at the correct answer as follows.
Bull economy: 0.5
Poor stock: 0.3
Probability = 0.5 x 0.3 = 0.15 = 15%
Learning Outcome Statements
h. calculate and interpret an unconditional probability using the total probability rule;
i. explain the use of conditional expectation in investment applications;
j. explain the use of a tree diagram to represent an investment problem;
CFA® 2021 Level I Curriculum, , Volume 1, Reading 8
User Comment
jackwez an easy way to remember this is the fact that A|B is like A/B multipled by B equals A.... along the same lines as teh dupont questions...
wundac thanks jack
mdejesus Man... I can't remember these formulas at all. But I CAN make a mean tree diagram. Making a tree diagram seems to be more helpful for me :)
choas69 but u cant keep making trees in an exam bro
gyee2012 Realize the change in mutliplication between independent and dependent probability and you will be set
Micheal11 The theory part is really hard to memorise, but look at the example.
Even without understanding the theory, it is so immediate. Well done AnalystNotes! | 866 | 3,424 | {"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-2021-31 | longest | en | 0.901161 |
https://iitutor.com/finding-equations-of-tangent-line/ | 1,709,410,796,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947475897.53/warc/CC-MAIN-20240302184020-20240302214020-00685.warc.gz | 303,229,182 | 31,120 | # Finding Equations of Tangent Line
Consider a curve $y=f(x)$.
A tangent to a curve is a straight line that touches the curve at a given point and represents the gradient of the curve at that point.
If $A$ is the point with $x$-coordinate $a$, then the gradient of the tangent line to the curve at this point is $f'(a)$. The equation of the tangent is;
$$y-f(a) = f'(a)(x-a)$$
## Example 1
Find the equation of the tangent line to $f(x)=x^2$ at the point where $x=3$.
\begin{align} \displaystyle \require{AMSsymbols} \require{color} f(3) &= 3^2 \\ &= 9 \\ f^{\prime}(x) &= 2x \\ f^{\prime}(3) &= 2 \times 3 \\ &= 6 \\ y-9 &= 6(x-3) &\color{red} y-f(3) = f^{\prime}(3)(x-3)\\ &= 6x-18 \\ \therefore y &= 6x-9 \\ \end{align}
## Example 2
Find the equations of tangent lines to $f(x)=2x^2-8x$ at the point where the gradient is $4$?
\begin{align} \displaystyle \require{AMSsymbols} \require{color} f^{\prime}(x) &= 4 \\ 4x-8 &= 4 \\ 4x &= 12 \\ x &= 3 \\ f(3) &= 2 \times 3^2-8 \times 3 \\ &= -6 \\ y-(-6) &= 4(x-3) &\color{red} y-f(3) = 4(x-3) \\ \therefore y &= 4x-18 \\ \end{align}
## Example 3
Find the equations of the tangents to the curve $f(x)=x^2+3x-10$ at the points where the curve cuts the $x$-axis.
\begin{align} \displaystyle \require{AMSsymbols} \require{color} f^{\prime}(x) &= 2x+3 \\ x^2+3x-10 &= 0 &\color{red} \text{the curve cuts the xaxis} \\ (x+5)(x-2) &= 0 \\ x &= -5 \text{ or } x=2 \\ f^{\prime}(-5) &= 2 \times (-5)+3 &\color{red} \text{gradient at }x=-5\\ &= -7 \\ y – 0 &= -7(x- -5) &\color{red} y-f(-5) = f^{\prime}(-5)(x–5)\\ y &= -7x-35 \\ f^{\prime}(-5) &= 2 \times 2+3 &\color{red}\text{gradient at }x=2\\ &= 7 \\ y – 0 &= 7(x-2) &\color{red} y-f(2) = f^{\prime}(2)(x-2)\\ y &= 7x-14 \\ \therefore y &= -7x-35 \text{ and } y = 7x-14 \\ \end{align}
## Example 4
Find the equations of any horizontal tangent lines to $f(x)=2x^3-3x^2-12x+1$.
$f^{\prime}(x) = 6x^2-6x-12$
Horizontal tangents have gradient $0$.
\begin{align} \displaystyle 6x^2-6x-12 &= 0 \\ x^2-x-2 &= 0 \\ (x+1)(x-2) &= 0 \\ x &= -1 \text{ or } x=2 \\ f(-1) &= 2(-1)^3-3(-1)^2-12(-1)+1 \\ &= 8 \\ f(2) &= 2(2)^3-3(2)^2-12(2)+1 \\ &= -19 \\ \end{align}
The points of contact are $(-1,8)$ and $(2,-19)$.
Therefore the horizontal tangent lines are $y=8$ and $y=-19$.
## Mastering Integration by Parts: The Ultimate Guide
Welcome to the ultimate guide on mastering integration by parts. If you’re a student of calculus, you’ve likely encountered integration problems that seem insurmountable. That’s…
## Probability Pro: Mastering Two-Way Tables with Ease
Welcome to a comprehensive guide on mastering probability through the lens of two-way tables. If you’ve ever found probability challenging, fear not. We’ll break it…
## High School Math for Life: Making Sense of Earnings
Salary Salary refers to the fixed amount of money that an employer pays an employee at regular intervals, typically on a monthly or biweekly basis,…
## Binomial Expansions
The sum $a+b$ is called a binomial as it contains two terms.Any expression of the form $(a+b)^n$ is called a power of a binomial. All…
## Factorisation Made Easy: Overcoming Harder Expressions
Factorising Cubic Expressions with Rotating Three Variables Factorising cubic expressions is a crucial skill in algebra, and it becomes even more intriguing when dealing with… | 1,171 | 3,332 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 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-2024-10 | longest | en | 0.542246 |
https://www.causeweb.org/wiki/chance/index.php?title=Chance_News_54&direction=prev&oldid=8778 | 1,652,899,266,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662522309.14/warc/CC-MAIN-20220518183254-20220518213254-00341.warc.gz | 790,243,760 | 7,878 | # Chance News 54
## Quotations
Do not put your faith in what statistics say until
you have carefully considered what they do not say.
William W. Watt
## Maynard Keynes' game and the Efficient Market Hypothesis
Jeff Norman told us about an interesting game and its relation to investment theory. The game was descried in terms of professional investment by the famous British Economist John Maynard Keynes in his book The General Theory of Employment, Interest and Money, 1936. Here he writes:
Professional investment may be likened to those newspaper competitions in which the competitors have to pick out the six prettiest faces from a hundred photographs, the price being awarded to the competitor whose choice most nearly corresponds to the average preference of the competitors as a whole; so that each competitor has to pick, not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view. It is not a case of choosing those which, to the best of one’s judgment, are really prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth and higher degrees
Keynes used this game in his argument against the Efficient-market hypothesis (EMH) theory witch is defined at Answers.com as:
An investment theory that states that it is impossible to "beat the market" because stock market efficiency causes existing share prices to always incorporate and reflect all relevant information. According to the EMH, this means that stocks always trade at their fair value on stock exchanges, and thus it is impossible for investors to either purchase undervalued stocks or sell stocks for inflated prices. Thus, the crux of the EMH is that it should be impossible to outperform the overall market through expert stock selection or market timing, and that the only way an investor can possibly obtain higher returns is by purchasing riskier investments.
That efficient market hypothesis is a controversial subject and discussed on many websites. We can see this in an article by John Mauldin who is president of Millennium Wave Advisors, LLC, a registered investment advisor. Here you will also see more about Keynes' game and its relation to the EMF.
We read here Keynes game can be easily replicated by asking people to pick a number between 0 and 100, and telling them the winner will be the person who picks the number closest to two-thirds the average number picked. The chart below shows the results from the largest incidence of the game that I have played - in fact the third largest game ever played, and the only one played purely among professional investors.
http://www.investorsinsight.com/cfs
http://www.investorsinsight.com/cfs-file.ashx/__key/CommunityServer.Blogs.Components.WeblogFiles/thoughts_5F00_from_5F00_the_5F00_frontline/jm080709image010_5F00_2F080074.jpg
The highest possible correct answer is 67. To go for 67 you have to believe that every other muppet in the known universe has just gone for 100. The fact we got a whole raft of responses above 67 is more than slightly alarming.
You can see spikes which represent various levels of thinking. The spike at fifty reflects what we (somewhat rudely) call level zero thinkers. They are the investment equivalent of Homer Simpson, 0, 100, duh 50! Not a vast amount of cognitive effort expended here!
There is a spike at 33 - of those who expect everyone else in the world to be Homer. There's a spike at 22, again those who obviously think everyone else is at 33. As you can see there is also a spike at zero. Here we find all the economists, game theorists and mathematicians of the world. They are the only people trained to solve these problems backwards. And indeed the only stable Nash equilibrium is zero (two-thirds of zero is still zero). However, it is only the 'correct' answer when everyone chooses zero.
The final noticeable spike is at one. These are economists who have (mistakenly...) been invited to one dinner party (economists only ever get invited to one dinner party). They have gone out into the world and realised the rest of the world doesn't think like them. So they try to estimate the scale of irrationality. However, they end up suffering the curse of knowledge (once you know the true answer, you tend to anchor to it). In this game, which is fairly typical, the average number picked was 26, giving a two-thirds average of 17. Just three people out of more than 1000 picked the number 17.
I play this game to try to illustrate just how hard it is to be just one step ahead of everyone else - to get in before everyone else, and get out before everyone else. Yet despite this fact, it seems to be that this is exactly what a large number of investors spend their time doing.
See also The Efficient Market Hypothesis on Trial:A Survey by Philip S. Russel and Violet M. Torbey
Submitted by Laurie Snell | 1,102 | 5,164 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2022-21 | latest | en | 0.966325 |
https://math.eretrandre.org/tetrationforum/archive/index.php?thread-936.html | 1,611,605,275,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703644033.96/warc/CC-MAIN-20210125185643-20210125215643-00107.warc.gz | 442,818,364 | 2,134 | # Tetration Forum
Full Version: [2014] Representations by 2sinh^[0.5]
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As mentioned before Im considering number theory connections to tetration.
One of those ideas is representations.
Every integer M is the sum of 3 triangular number ...
or 4 squares.
Also every integer M is the sum of at most O(ln(M)) powers of 2.
This is all classical and pretty well known.
But there are functions that have growth between polynomials and powers of 2.
So since 2sinh is close to exp and 2sinh^[0.5](0) = 0 , it is natural to ask
2S(n) := floor 2sinh^[0.5](n)
2S-1(n) := floor 2sinh^[-0.5](n)
2S numbers := numbers of type 2S(n)
2S-1 numbers := numbers of type 2S-1(n)
1) Every positive integer M is the sum of at most A(M) 2S numbers.
A(M) = ??
2) Every positive integer M is the sum of at most 2S(M) B numbers.
B numbers := B(n) = ??
Of course we want sharp bounds on A(M) and B(n).
( A(M) = 4 + 2^M works fine but is not intresting for instance )
regards
tommy1729
To estimate A(M) I use the following
Tommy's density estimate
***
Let f(n) be a strictly increasing integer function such that f(n)-f(n-1) is also a strictly increasing integer function.
Then to represent a positive density of primes between 2 and M
we need to take T_f(M) elements of f(n).
This is an upper estimate.
***
In this case to represent a positive density of primes between 2 and M we then need about
ln(M)/ln^[3/2](M) 2S numbers.
This is a brute upper estimate.
A(M) is estimated as sqrt( ln(M)/ln^[3/2](M) ).
Improvement should be possible.
regards
tommy1729 | 477 | 1,668 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5625 | 4 | CC-MAIN-2021-04 | latest | en | 0.885996 |
https://quizizz.com/en-us/three-digit-numbers-worksheets-grade-5 | 1,719,010,630,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862189.36/warc/CC-MAIN-20240621223321-20240622013321-00110.warc.gz | 434,159,968 | 26,705 | ## Recommended Topics for you
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## Explore printable Three-Digit Numbers worksheets for 5th Grade
Three-Digit Numbers worksheets for Grade 5 are an excellent resource for teachers looking to enhance their students' math skills and number sense. These worksheets provide a variety of engaging and challenging activities that will help students develop a strong foundation in understanding and working with three-digit numbers. With topics such as place value, addition, subtraction, multiplication, and division, these worksheets offer a comprehensive approach to teaching and reinforcing essential math concepts. By incorporating these worksheets into their lesson plans, teachers can ensure that their Grade 5 students are well-prepared for more advanced math topics and have a solid grasp of number sense.
In addition to Three-Digit Numbers worksheets for Grade 5, teachers can also utilize Quizizz, a popular online platform that offers a wide range of interactive quizzes and activities to supplement their math instruction. Quizizz provides a fun and engaging way for students to practice their number sense and math skills, while also offering teachers valuable insights into their students' progress and understanding. With customizable quizzes, teachers can tailor the content to align with their curriculum and address specific learning objectives. Furthermore, Quizizz offers additional resources such as flashcards, games, and collaborative learning tools, making it an invaluable resource for enhancing Grade 5 students' math skills and number sense. | 664 | 2,763 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2024-26 | latest | en | 0.915292 |
http://www.transtutors.com/questions/criterion-related-validity-108726.htm | 1,455,383,627,000,000,000 | text/html | crawl-data/CC-MAIN-2016-07/segments/1454701167113.3/warc/CC-MAIN-20160205193927-00179-ip-10-236-182-209.ec2.internal.warc.gz | 726,856,508 | 17,216 | +1.617.933.5480
# Q: Criterion Related Validity
Criterion -Related Validity is often encountered when aptitude tests are given to predict the degree of success in a course, in a job, etc. On page 80 in the text, an algebraic relationship is given between the results on an Algebra Aptitude Test and the grade(degree of success) in an Algebra class. LettingXrepresent the score on the Aptitude Test, and G represent the grade in the Algebra course, the relationship is
G = (.75)(X) + 55
(a) If a student has a score of X = 45 on the Aptitude Test, what is the predicted grade for the Algebra course?
(b) Suppose that the passing grade in the Algebra course is 70. If a student with a score of 15 on the Aptitude test asks you if you think they will pass Algebra, what would you tell them? Give your reasons.
The algebraic relationship between the results on an Algebra Aptitude Test and the grade(degree of...
Related Questions in Others | 224 | 943 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2016-07 | longest | en | 0.929695 |
https://www.physicsforums.com/threads/intuition-for-rayleigh-scattering.885072/ | 1,603,327,231,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107878662.15/warc/CC-MAIN-20201021235030-20201022025030-00059.warc.gz | 884,702,480 | 16,012 | # Intuition for Rayleigh Scattering
Is there some way to - from an intuition standpoint - justify the fact that there should be a factor of ##a^{6}##, (where ##a ## is the particle diameter) in the Rayleigh Scattering formula? I've seen a few sources hint that there should be. I can follow the derivation from e.g a Lorentz atom, but I don't see why I should immediately be thinking of the factor of ##a^{6}##? [Is it somehow related to a dipole moment?]
Rayleigh Scattering Formula:
$$I \propto I_{0} \lambda^{-4} a^{6}$$
Related Other Physics Topics News on Phys.org
Bystander
Homework Helper
Gold Member
Square of volume?
Your question got me interested to look around a bit. I found the following paper, Particle Optics in the Rayleigh Regime: http://patarnott.com/pdf/Moosmuller2009JAWMA.pdf
It's more than I wanted to read right now, and I'm not sure it meets your requirement of being intuitive, but on page 1029 they state:
Thus the r6 (for spherical particles) or more general V2 size dependence of Rayleigh particle scattering has been obtained from two simple facts: (1) the scattering cross section is proportional to the number of identical scatterers squared (i.e., n2); and (2) the number of scatterers (or molecules) in a particle is proportional to its volume, or to its radius cubed for a spherical particle.
Thanks! Sorry for the slow reply - I've been away from a connection for a while. I guess as Bystander says it does make intuitive sense that you should have a factor of volume squared for scattering of two particles. But in that case why should the photon be seen as having the same volume as the scatterer? (as much as it makes sense for a photon to have a volume...) I think the second argument is convincing. Though I've also seen another derivation now in terms of the polarization of a sphere - where the scattering intensity is proportional to the square of the amplitude reflected field, the reflected field depends on the instantaneous dipole moment, and so we get ## a^{6}## again - I can no longer find it, which is a pain, and that's all I remember - but perhaps you can get something out of that? | 505 | 2,144 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2020-45 | latest | en | 0.927636 |
https://stackabuse.com/bytes/plot-decision-trees-using-python-and-scikit-learn/ | 1,721,783,348,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518130.6/warc/CC-MAIN-20240723224601-20240724014601-00856.warc.gz | 473,669,520 | 16,336 | # Plot Decision Trees Using Python and Scikit-Learn
Decision trees are widely used in machine learning problems. We'll assume you are already familiar with the concept of decision trees and you've just trained your tree based algorithm!
Advice: If not, you can read our in-depth guide on "Decision Trees in Python with Scikit-Learn guide".
Now, it is time to try to explain how the tree has reached a decision. This means it is necessary to take a look under the hood, and see how the model has split the data internally to build the tree.
To be able to plot the resulting tree, let's create one. First, we'll load a toy wine dataset and divide it into train and test sets:
from sklearn import datasets
from sklearn.model_selection import train_test_split
SEED = 42
X = data.data
y = data.target
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=SEED)
Now that the toy data has been divided, we can fit the Decision Tree model:
dt = DecisionTreeClassifier(max_depth=4,
random_state=SEED)
dt.fit(X_train, y_train)
Great! Notice that we have defined a maximum depth of 4, this means the generated tree will have 5 levels. This will help with the interpretability when plotting, since we'll only have 5 levels to read through.
Get free courses, guided projects, and more
Now, to plot the tree and get the underlying splits made by the model, we'll use Scikit-Learn's plot_tree() method and matplotlib to define a size for the plot.
You pass the fit model into the plot_tree() method as the main argument. We will also pass the features and classes names, and customize the plot so that each tree node is displayed with rounded edges, filled with colors according to the classes, and display the proportion of each class in each node:
from sklearn.tree import plot_tree
import matplotlib.pyplot as plt
features = data.feature_names
classes = data.target_names
plt.figure(figsize=(10, 8))
plot_tree(dt,
feature_names=features,
class_names=classes,
rounded=True, # Rounded node edges
filled=True, # Adds color according to class
proportion=True); # Displays the proportions of class samples instead of the whole number of samples
That's it, this is the plotted underlying tree for this model!
Notice, that you can see that the first characteristic the tree considers to differentiate between wines is the intensity of color, followed by the amount of proline and flavonoids. Also, since we have filled the tree, class_0 nodes are orange, class_1 nodes are green, and class_2 nodes are purple.
See what else you can do with plot_tree() in the documentation!
Last Updated: April 18th, 2023 | 589 | 2,626 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2024-30 | latest | en | 0.895713 |
https://bsci-ch.org/how-many-40-lb-bags-of-topsoil-in-a-yard/ | 1,653,247,643,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662546071.13/warc/CC-MAIN-20220522190453-20220522220453-00599.warc.gz | 188,186,680 | 4,778 | What does a yard of topsoil weigh? According to Grow Your Yard, a cubic yard of topsoil can weigh 1,400 to over 2,000 pounds. The exact answer depends on the soil’s moisture and whether it contains rocks, sand, debris, or other impurities. 40 pounds of topsoil fill about 0.75 cubic feet.
You are watching: How many 40 lb bags of topsoil in a yard
How much does a yard of topsoil weigh, and how do you find how much you need? The answer to the first question depends on what’s in the soil, and the answer to the second requires a little math.
In this article, I’ll explain what topsoil is, how to measure it, what a cubic yard looks like, and how much topsoil weighs.
Contents
2 Measuring Topsoil5 FAQs
## Fill Dirt Vs Topsoil
Image credit: publicdomainpictures.net
There are two main types of dirt: fill dirt and topsoil. The former lies below topsoil and is typically composed of rockier, less organic material. It’s often used to fill holes or elevate the ground. It provides a sturdier base because it doesn’t break down as much as topsoil.
Topsoil is the darker-colored, uppermost layer of dirt. It’s typically 4 to 12 inches deep and has more organic material and nutrients than fill dirt. Most soil activity by microorganisms happens in this layer. This and that fact that it provides more oxygen to plants makes it better for gardening.
However, because it contains more organic matter, topsoil tends to break down as air pockets collapse. This makes it suitable only for the uppermost layer of a landscape. It’s also more vulnerable than fill dirt to erosion. Therefore, always place topsoil over fill dirt after the fill dirt has been set.
## Measuring Topsoil
Topsoil is typically measured in cubic yards. A cubic yard is 27 cubic feet, and a cubic foot is 12x12x12 inches.
Dirt Connections outlines two methods you can use to determine how much topsoil you need:
### Method 1
Suppose you have a flower bed that’s 6 inches deep, 12 feet long, and 12 feet wide. Follow these steps:
Convert all measurements to feet. Six inches is 0.5 feet.Find the number of cubic feet by multiplying the dimensions: 0.5x2x12 feet = 72 cubic feet.Find the number of cubic yards by dividing the number of cubic feet by 27.72 cubic feet / 27 cubic feet = 2.67 cubic yards to fill your flower bed.
### Method 2
Suppose you have a flower bed with the same dimensions as before.
This time, convert the measurements in feet and inches into yards. There are 36 inches in a yard, so six inches is 0.167 yards. There are 3 feet in a yard, so 12 feet is 4 yards.Multiply the dimensions in yards to find the number of cubic yards. 0.167 yards x 4 yards x 4 yards = 2.67 cubic yards.
## How Much Does Topsoil Weigh?
Image credit: publicdomainpictures.net
According to Dirt Connections, a cubic yard of topsoil weighs about 1,080 pounds. However, debris and moisture can make it heavier. Grow Your Yard states that topsoil can weigh between 1,400 and 2,000 or more pounds. Because topsoil contains less sediment than fill dirt, its weight tends to be more consistent.
See more: How Much Is 200Ml Of Milk In Ounces, Conversions: Us Standard To Metric
Because 1,080 is such a heavy load, Dirt Connections recommends always having a company deliver dirt to your home.
## What Does A Cubic Yard Look Like?
Greg of Adams Fairacre Farms explains that 1 cubic yard of anything will fill a 10×10-foot space, 3 inches deep: | 846 | 3,418 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2022-21 | latest | en | 0.9395 |
https://jp.mathworks.com/help/rf/ref/abcd2z.html | 1,675,116,449,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499829.29/warc/CC-MAIN-20230130201044-20230130231044-00604.warc.gz | 357,071,620 | 19,785 | # abcd2z
Convert ABCD-parameters to Z-parameters
## Syntax
``z_params = abcd2z(abcd_params)``
## Description
example
````z_params = abcd2z(abcd_params)` converts the ABCD-parameters to the impedance parameters. ```
## Examples
collapse all
Define a matrix for ABCD-parameters.
```A = 0.999884396265344 + 0.000129274757618717i; B = 0.314079483671772 + 2.51935878310427i; C = -6.56176712108866e-007 + 6.67455405306704e-006i; D = 0.999806365547959 + 0.000247230611054075i; abcd_params = [A,B; C,D];```
Convert ABCD-parameters to Z-parameters.
`z_params = abcd2z(abcd_params)`
```z_params = 2×2 complex 105 × -0.1457 - 1.4837i -0.1453 - 1.4835i -0.1459 - 1.4839i -0.1455 - 1.4836i ```
## Input Arguments
collapse all
2N-port- ABCD-Parameters, specified as a 2N-by-2N-by-M array of complex numbers, where M representing number of frequency points of 2N-port ABCD-parameters.
The function assumes that the ABCD-parameter matrices have distinct A, B, C, and D submatrices:
`$\left[\begin{array}{cc}\left[A\right]& \left[B\right]\\ \left[C\right]& \left[D\right]\end{array}\right]$`
## Output Arguments
collapse all
2N-port Z-parameters, returned as a 2N-by-2N-by-M array of complex numbers, where M represents the number of frequency points of 2N-port Z-parameters.
## Version History
Introduced before R2006a | 441 | 1,324 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2023-06 | latest | en | 0.445582 |
https://forum.poshenloh.com/topic/796/2020-amc-junior-q30/1?lang=en-US | 1,623,804,463,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487621699.22/warc/CC-MAIN-20210616001810-20210616031810-00619.warc.gz | 228,537,890 | 13,409 | # 2020 AMC Junior Q30
• I am stucked on the question below, anyone can help me?
My grandson makes wall hangings by stitching
together 16 square patches of fabric into a 4 × 4
grid. I asked him to use patches of red, blue,
green and yellow, but to ensure that no patch
touches another of the same colour, not even diagonally.
The picture shows an attempt which fails only
because two yellow patches touch diagonally.
In how many different ways can my grandson
choose to arrange the coloured patches correctly?
• Hey @gentlegorilla! Unforunately, there's no good formula to tackle this problem. I started off by trying to just make a pattern by myself and here's what I noticed:
In every 2x2 square, there can only be one of each color (this makes sense since colors can't touch each other, even diagonally). It might seem obvious, but this is really important! So, I started off by filling in the colors in the middle 2x2 square and going off from there.
Let's say I start off with
B G
Y R
in the middle 2x2. This means that the colors above B G have to be R & Y, in some order. With the same logic, the colors below Y R have to be B & G in some order. From there, you just have to pick one of each for those two and keep going.
For example, one way to continue the pattern:
R Y
B G
Y R
G B
(I just added to the top and bottom)
Now what you'll notice is that to the right of the Y & G in the top right, there has to be an R and a B. However, R can't go directly next to G because then they will touch diagonally!
R Y
B G R
Y R
G B | 398 | 1,534 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2021-25 | latest | en | 0.968462 |
http://www.radio-electronics.com/info/antennas/mimo/spatial-multiplexing.php | 1,506,184,135,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818689752.21/warc/CC-MAIN-20170923160736-20170923180736-00673.warc.gz | 534,541,381 | 10,438 | MIMO Spatial Multiplexing
- overview of MIMO - Multiple Input Multiple Output, spatial multiplexing used to provide additional data bandwidth in multipath radio scenarios.
One of the key advantages of MIMO spatial multiplexing is the fact that it is able to provide additional data capacity. MIMO spatial multiplexing achieves this by utilising the multiple paths and effectively using them as additional "channels" to carry data.
The maximum amount of data that can be carried by a radio channel is limited by the physical boundaries defined under Shannon's Law.
Shannon's Law and MIMO spatial multiplexing
As with many areas of science, there a theoretical boundaries, beyond which it is not possible to proceed. This is true for the amount of data that can be passed along a specific channel in the presence of noise. The law that governs this is called Shannon's Law, named after the man who formulated it. This is particularly important because MIMO wireless technology provides a method not of breaking the law, but increasing data rates beyond those possible on a single channel without its use.
Shannon's law defines the maximum rate at which error free data can be transmitted over a given bandwidth in the presence of noise. It is usually expressed in the form:
C = W log2(1 + S/N )
Where C is the channel capacity in bits per second, W is the bandwidth in Hertz, and S/N is the SNR (Signal to Noise Ratio).
From this it can be seen that there is an ultimate limit on the capacity of a channel with a given bandwidth. However before this point is reached, the capacity is also limited by the signal to noise ratio of the received signal.
In view of these limits many decisions need to be made about the way in which a transmission is made. The modulation scheme can play a major part in this. The channel capacity can be increased by using higher order modulation schemes, but these require a better signal to noise ratio than the lower order modulation schemes. Thus a balance exists between the data rate and the allowable error rate, signal to noise ratio and power that can be transmitted.
While some improvements can be made in terms of optimising the modulation scheme and improving the signal to noise ratio, these improvements are not always easy or cheap and they are invariably a compromise, balancing the various factors involved. It is therefore necessary to look at other ways of improving the data throughput for individual channels. MIMO is one way in which wireless communications can be improved and as a result it is receiving a considerable degree of interest.
MIMO spatial multiplexing
To take advantage of the additional throughput capability, MIMO utilises several sets of antennas. In many MIMO systems, just two are used, but there is no reason why further antennas cannot be employed and this increases the throughput. In any case for MIMO spatial multiplexing the number of receive antennas must be equal to or greater than the number of transmit antennas.
To take advantage of the additional throughput offered, MIMO wireless systems utilise a matrix mathematical approach. Data streams t1, t2, … tn can be transmitted from antennas 1, 2, …n. Then there are a variety of paths that can be used with each path having different channel properties. To enable the receiver to be able to differentiate between the different data streams it is necessary to use. These can be represented by the properties h12, travelling from transmit antenna one to receive antenna 2 and so forth. In this way for a three transmit, three receive antenna system a matrix can be set up:
r1 = h11 t1 + h21 t2 + h31 t3
r2 = h12 t1 + h22 t2 + h32 t3
r3 = h13 t1 + h23 t2 + h33 t3
Where r1 = signal received at antenna 1, r2 is the signal received at antenna 2 and so forth.
In matrix format this can be represented as:
[R] = [H] x [T]
To recover the transmitted data-stream at the receiver it is necessary to perform a considerable amount of signal processing. First the MIMO system decoder must estimate the individual channel transfer characteristic hij to determine the channel transfer matrix. Once all of this has been estimated, then the matrix [H] has been produced and the transmitted data streams can be reconstructed by multiplying the received vector with the inverse of the transfer matrix.
[T] = [H]-1 x [R]
This process can be likened to the solving of a set of N linear simultaneous equations to reveal the values of N variables.
In reality the situation is a little more difficult than this as propagation is never quite this straightforward, and in addition to this each variable consists of an ongoing data stream, this nevertheless demonstrates the basic principle behind MIMO wireless systems.
By Ian Poole
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Radio-Electronics.com is operated and owned by Adrio Communications Ltd and edited by Ian Poole. All information is © Adrio Communications Ltd and may not be copied except for individual personal use. This includes copying material in whatever form into website pages. While every effort is made to ensure the accuracy of the information on Radio-Electronics.com, no liability is accepted for any consequences of using it. This site uses cookies. By using this site, these terms including the use of cookies are accepted. More explanation can be found in our Privacy Policy | 1,236 | 6,055 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2017-39 | longest | en | 0.943191 |
https://www.esaral.com/q/prove-that-there-is-a-value-of-c-0-for-which-the-system-has-infinitely-many-solutions-find-this-value-72541 | 1,726,098,402,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651405.61/warc/CC-MAIN-20240911215612-20240912005612-00245.warc.gz | 710,824,075 | 11,919 | # Prove that there is a value of c(≠ 0) for which the system has infinitely many solutions. Find this value.
Question:
Prove that there is a value of c(≠ 0) for which the system has infinitely many solutions. Find this value.
$6 x+3 y=c-3$
$12 x+c y=c$
Solution:
GIVEN:
$6 x+3 y=c-3$
$12 x+c y=c$
To find: To determine for what value of c the system of equation has infinitely many solution
We know that the system of equations
$a_{1} x+b_{1} y=c_{1}$
$a_{2} x+b_{2} y=c_{2}$
For infinitely many solution
$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$
Here
$\frac{6}{12}=\frac{3}{c}=\frac{c-3}{c}$
Consider the following
$\frac{6}{12}=\frac{3}{c}$
$c=\frac{12 \times 3}{6}$
$c=6$
Now consider the following for c
$\frac{3}{c}=\frac{c-3}{c}$
$3 c=c(c-3)$
$3 c=c^{2}-3 c$
$6 c=c^{2}$
$6 c=c^{2}$
$c=0,6$
But it is given that $c \neq 0 .$ Hence $c=6$
Hence for $c=6$ the system of equation have infinitely many solutions. | 360 | 962 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2024-38 | latest | en | 0.799593 |
http://vellorerevolt1806.info/gohi/probability-terms-689.php | 1,552,963,068,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912201882.11/warc/CC-MAIN-20190319012213-20190319034213-00275.warc.gz | 223,710,218 | 5,059 | # Probability terms
### Probability Key Terms - Probability The probability of an
Proposal Number Sense Interactive Quiz Lesson Plans History Problem Bank Glossary Quotes Helpful Links References.Slope is defined as the vertical change between two ordered pairs divided by the horizontal change between those pairs.The ratio of the number of favorable outcomes of a probability experiment to the number of trials.It represents how many pieces the whole has been divided into.A relationship where a number either increases at the same rate that another increases or decreases at the same rate as another decreases.
Trapezoid A four-sided, closed shape with straight lines and only one pair of opposite sides equal.A quadrilateral in which both pairs of opposite sides are parallel.The difference between the first quartile and the third quartile.A single ratio comparing a part to a whole or two equivalent ratios.Percents represent part-to-whole relationships that have been converted into a ratio where the whole is equal to 100.The basis for such artifacts as wheels, wedding rings, and many types of cookies.Looks like a kitty cat when you squint and tilt your head to the left.
The length from the center of a circle to any point on its edge.For instance, instead of picking one card from a deck, you pick two cards and find the likelihood of a King of Hearts and Queen of Diamonds being selected.Compute the probability of either of two independent events occurring.These formal terms are manipulated by the rules of mathematics and logic, and any results are interpreted or translated back into the problem domain.
### Probability Terms
Rather than continue on forever, line segments are one-dimensional lengths caught between two endpoints.
Alternate interior angles are congruent if and only if the two lines crossed by the transversal are parallel.A 3D solid with two polygonal bases that are parallel and rectangular faces connecting them.Apothem The distance from the center of a regular polygon to the midpoint of one side.The pair of angles on the outside of the two lines cut by the transversal and on alternate sides of the transversal.No equal signs on these bad boys, since they represent a single value.
One collection of possible results gives an odd number on the dice.If two events A and B occur on a single performance of an experiment, this is called the intersection or joint probability of A and B, denoted as.Can be positive or negative, depending on which side of the bed it woke up on.They found something that works for them and they see no reason to change things up.We said for example. Sheesh. Any number or variable that is multiplied by something else.
Probability the likelihood of an event occurring Likelihood or chance of the occurrence of an event.This high school probability and statistics class is aligned with the Common Core State Standards.The middle value in a data set when all of the values are lined up in order.A linear plot is one that goes from one event to the next in the order they happen—no flashbacks or flashforwards, and probably not a lot of subplots.
Coplanar on the same plane Used to describe lines or points that are all on the same plane.A ball-shaped figure in which every surface point is equidistant from a center.Glossary of Statistical Terms adjusting or controlling for a variable: Assessing the e ect of one variable while. read as the probability that event Ahappens.
Lines that will never intersect, because they share the same slope.If there is no middle (like when we have an even number of data points), we just take the mean of the two numbers in the middle and, voila, a median is born.The range is the extent of land (or water) that a species occupies.Improper Fraction A fraction that tells bawdy jokes in mixed company.A triangle in which one of the angles is more than 90 degrees.Two angles that are on the inside of the parallel lines and opposite sides of the transversal.Probability theory is applied in everyday life in risk assessment and modeling.Kallenberg, O. (2005) Probabilistic Symmetries and Invariance Principles.
The first law was published in 1774 and stated that the frequency of an error could be expressed as an exponential function of the numerical magnitude of the error, disregarding sign.When a transversal crosses two parallel lines, corresponding angles are congruent Two angles that are in the same relative place compared to each of the two lines and the transversal that cuts them.A measure of the amount of 2D space it takes to cover a 3D figure without gaps or overlaps.The amount of three-dimensional space that an object takes up.Diagonal a line connecting two vertices of a polygon A segment that connects the two pairs of opposite vertices in a quadrilateral.A probability calculated from data over many trials of an experiment, and which represents the probability a given event in the sample space has of occurring.
Parallelogram A four-sided, closed shape with straight lines and two pairs of opposite sides that are parallel.A mathematical statement that says two expressions or values are equal to one another.
If two events are mutually exclusive then the probability of either occurring is.Introduction to Probability - eBook, by Charles Grinstead, Laurie Snell Source ( GNU Free Documentation License ).The insurance industry and markets use actuarial science to determine pricing and make trading decisions.By using this site, you agree to the Terms of Use and Privacy Policy.They can be as simple as 3 or as complicated as -934 a 7 b 3.
Probability terms: Rating: 94 / 100 All: 345 | 1,118 | 5,622 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.921875 | 4 | CC-MAIN-2019-13 | latest | en | 0.933115 |
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## Statistics and probability
### Course: Statistics and probability>Unit 7
Lesson 8: Multiplication rule for dependent events
# Dependent probability introduction
AP.STATS:
VAR‑4 (EU)
,
VAR‑4.D (LO)
,
VAR‑4.D.2 (EK)
Let's get you started with a great explanation of dependent probability using a scenario involving a casino game. Created by Sal Khan.
## Want to join the conversation?
• Hmm. I'm not very clear on the logic he used in determining if you would want to play the game. I said it would make sense. If you play the game 100 times for example, you win 30 times. so you get \$30. This also means you lose 70 times to you play 70 x 0.35 = \$24.5. In the end you seem to be gaining money.
• Well, you lose 0.35 EVERY time, because it costs this much to play. So when you win, you only really win 0.65, not the full \$1. (You had to pay 0.35 for the chance to get that \$1) Hence, 30 out of 100 times (to use your example), you win 0.65, and 30x0.65=19.5. The other 70 times, you lose 0.35, and 70x-0.35= -24.5, so over those 100 plays, you are losing \$5.
• What does the upside down U symbol at - mean?
• In this example, Sal is asking "what is the probability of both the first AND second being green". The upside down U symbol in this case stands for the AND.
The symbol typically stands for "intersection" and is used in set theory to refer to common numbers or letters in sets. For example, the "intersection" of {1, 3, 5, 7} and {4, 5, 6, 7} is {5, 7} because those are the numbers that you can find in both sets.
• At , why does Sal come to a conclusion that both the events need to be multiplied ? What is the explanation to multiply both the events ?
• To get the probability of both events being true. If you are asking why you multiply, it is because, for example, if there is a 1/2 probability of the 1st being green and a 1/3 probability of the 2nd being green, the probability of the 2nd being green and the 1st is green is 1/2 of the time the 2nd is green (1/3) since an of means multiplication, the probability of both being green is 1/2 x 1/3.
• I'm a high school senior in India and we are studying probability at school. My question concerns conditional probability. We have defined probability to be the formula- P(A/B)= P(A int B)/P(B). However, when solving many problems we don't use the definition directly and instead use the vague notion of assuming the occurrence of the "given" event. Even though this makes some intuitive sense, it is rather vague and not at all rigorous. So I would be grateful is someone could provide me with a better explanation or working rule, and connect that to the aforementioned formula.
• Ill try explain this using an example:
Given a box of 50 marbles
20 marbles are blue and 30 marbles are white.
There are 5 smooth, and 15 rough blue marbles.
While there are 12 smooth and 18 rough white marbles.
Let event A: "Draw blue marble"
Let event B: "Draw rough marble"
What is the probability of drawing a blue marble?
1. P(A) = 20/50
What is the probability of drawing a rough marble?
2. P(B) = (15+18)/50 = 33/50
What is the probability of drawing a rough and blue marble?
3. P(A int B) = 15/50
Given as you take a marble, you feel a rough marble, what is the probability that it is a blue marble?
4. P(A | B)
= P(A int B) / P(B)
= [15/50] / [33/50]
Given that the chosen marble is blue, what is the probability that the marble is rough?
5. P(B | A) = P(B int A) / P(B)
using commutative property P(B int A) = P(A int B)
= P(A int B) / P(A)
= [15/50] / [20/50]
As you can see, the sample space has considerable changed once we have a condition. That is the main point.
I hope this simple example helps for understanding this on a small scale.
(P.S. anyone is welcome to correct me as I am only human and prone to make mistakes)
• Statistically, is removing two green marbles simultaneously identical to removing one green marble and then removing another green marble?
• It is still a 30% chance (or 3/10.) think of it this way. We have 5 different marbles: g1, g2, g3, r1, and r2, 'g' standing for green, and 'r' standing for red. There are ten different ways to pull two of these out of the bag simultaneously.
3 different pairs that are only green: g1 and g2, g1 and g3, g2 and g3. To visualize this imagine the three marbles arranged in a triangle formation. (kind like they are in the video) Then attempt to draw lines between them. You will find you can only draw three lines between them (note: in all pairings the order does not matter (e.g. g1 and g2 is the same as g2 and g1). This is because we only care about the quantity of red/green marbles (e.g. in the previous example, there are still two green marbles in each.))
Next, there are 6 different pairs that include a red marble. g1, 2, and 3 with r1 and g1, 2, and 3 with r2. Picture this as a grid with two columns (the two red marbles) and 3 rows (the three green marbles) filling all of the cells will give you six different parings.
Lastly, there is one situation where only reds are pulled out. r1 and r2.
Thus, if there are 10 possible outcomes, and 3 of those fulfill our conditions, then placing 3 over ten we get the probability is equal to 3/10, or 30%. This is because in the end, the situations are the same. If you viewed the above listed pairings of marbles drawn out simultaneously as two marbles drawn out one after the other then you would get the same probability.
• at , why did Sal write the "0.30*\$1=0.30"??
• why did he multiply "the 30% chance of winnig" with "the 1\$ prize" ?
• I and willing to play the game if I can replace the marbles and all else stays the same.
``3/5 * 3/5 = 9/259/25 * 1 = \$0.36\$0.36 - \$0.35 = \$0.01 = ¢1``
I would want to play this altered version of the game, because if I play it many times, my average gaine per game would be ¢1.
• Hi I have a question about independent probability i assume, but it is not specifically related to this video. If there is a better place to ask such a question, please do point me towards it.
Here is the question I am trying to solve:
What is the probability that, in six throws of a die, there will be exactly one each of “1” “2” “3” “4” “5” and “6”?
.00187220
.01176210
.01543210
.01432110
My thought process is that these are independent events and in each roll the probability of getting a number like 1 or 2 is 1/6. So, for six rolls, the probability should be just (1/6)^6, but that doesn't seem to be right. Can you please help explain how I can go about solving this? Thanks.
• What you have would be the correct way to find the probability of rolling the same number six times in a row. But in this problem, they are asking for the odds of rolling no repeats in six rolls, which is different.
In the first roll, there is a 100% chance you will get one a number 1 through 6, and will not repeat. On the second, , odds are 5/6 that you will not repeat....On the sixth roll, you are looking at 1/6 odds that you won't repeat. Try 1 ·5/6 ·4/6 ·3/6 ·2/6 ·1/6, and one of those choices should match.
• Since both marbles need to be green, I assume that that is the reason that Sal ignored the what would happen if the first marble wasn't green. | 2,007 | 7,412 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5625 | 5 | CC-MAIN-2023-23 | latest | en | 0.938336 |
https://community.deeplearning.ai/t/quick-question-regarding-yolo-algorithm/30205 | 1,716,928,599,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059148.63/warc/CC-MAIN-20240528185253-20240528215253-00052.warc.gz | 151,947,361 | 7,258 | # Quick question regarding YOLO algorithm
Hi everyone,
I’m trying to understand the YOLO’s label ( y= [pc, bx,by,bh,bw, c1,c2,c3] ) for ground truth data y.
In this image example used in Dr. Andrew’s course, if we look at middle square of the bottom row, pc =1 as it contains the midpoint of object car and human.
But now If we look at the left bottom corner, is pc = 0? (although it contains a large proportion of the car, it doesn’t contains the middle point of the car, so we view it as it doesn’t contain any object?) and then all other values (bx,by,…c1,c2,c3) of this left bottom box will become ‘don’t care’?
So in summary, for labels (ground truth value that we trains ), only the box includes the middle point of an object will have pc =1, and all other boxes which don’t have that mid point (even a large part of that object is present in that box, e.g., a large proportion of the car is in the bottom left box) will still have pc =0?
An additional question regards the same objects with different sizes. (e.g., big car and distant small car). It’s not mentioned in video, but does YOLO have any special processes regarding object sizes? For example, a large anchor box designed for large near cars, might be too big for distant small cars, then will the YOLO algorithm break in this situation?
Thanks!
2 Likes
As part of its approach to object localization, the YOLO network predicts the coordinates of the object center. In order to do this, like any machine learning algorithm, it must first be trained on examples. The examples tell it which locations contain an object center and which locations do not. The examples also contain the shape of the object centered there, including whether that shape is larger than one grid cell, which is how it learns about the parts of the objects in the lower left of this training image.
Anchor boxes do not have a type. They only have shape. So there is no ‘car’ anchor box or ‘person’ anchor box. Only wider-than-it-is-tall anchor box and taller-than-it-is-wide anchor box (assuming those shapes are prevalent in the training data.) There are also no ‘close’ or ‘far away’ anchor boxes…just larger or smaller. So if the training data has lots of close cars and lots of far away cars there may be large and small anchor boxes both related to objects labelled as ‘car’ in the training data.
Speaking of different anchor box shapes, having multiple anchor boxes with different shapes is what would allow a YOLO v2 network to identify both the person and the car in this image. In the training data two locations would have a 1 for object presence. Both would have the same grid cell indices and object center location coordinates, but they would have different anchor box index and predicted bounding box shape.
3 Likes
Here is a little more detail mapped specifically to the image in the OP. This grid is 3x3, with what appears to be 2 anchor boxes (one taller-than-wide, one wider-than-tall). The YOLO-independent ground truth would have 2 labels, one for the person, one for the car. When converted to YOLO input for training, there would need to be 3 * 3 * 2 == 18 locations, each holding (1 + 4 + C) == 8 values; one for p_c, 2 each for bounding box location and shape, and C class indicators (as a one hot vector). NOTE: the ground truth and the CNN output need to be the same shape in order to compare them in the loss function using a vectorized implementation. You want to just write confidence\_loss = \hat{p_c} - p_c and have Python matrix algebra work.
For this image, 16 of the 18 locations will have 0 for all 8 values. 2 locations will have non-zero values; the locations corresponding to the center grid location on the lowest row. That is, c_x = 1 and c_y = 2. Both of these locations will have p_c = 1 because there is an object present. Both of these locations will have the same values for b_x and b_y because the center of the person and the center of the car ground truth labels are colocated. One of these locations will have a C vector indicating car and the other will have a C vector indicating person. Say [0, 1, 0] and [1, 0, 0] (depends on the class index). Finally, each location will have different values for b_w and b_h to capture the different bounding box shapes of the two objects. From eyeballing the image, the location with the car record would have a b_w indicating a bounding box width of about 2.5 x grid cell width and a b_h of about 1.1 x grid cell height. The location with the person record would have a b_w of about 0.9 x grid cell width and a b_h of about 1.9 x grid cell height.
Notionally, you have something like this:
num_grid_cells_wide = 3
num_grid_cells_high = 3
num_anchor_boxes = 2
num_classes = 3
#initialize to 0
ground_truth = np.zeros(num_grid_cells_wide, num_grid_cells_high, num_anchor_boxes, (1 + 4 + num_classes))
#write values for locations that actually have data
ground_truth[1,2,0] = [1, 0.5, 0.2, 0.9, 1.9, 1, 0, 0] # person
ground_truth[1,2,1] = [1, 0.5, 0.2, 2.5, 1.1, 0, 1, 0] # car
Recap:
• 18 locations in the ground truth comes from (S*S*B) with S=3 and B=2
• 16 locations all zeros, 2 locations non-zeros
• Both non-zero locations are in the same grid cell, c_x=1, c_y=2
• Both non-zero locations have the same value for p_c (because there is a GT object present \hat{p_c} = 1. Output of the CNN will be some value 0.< p_c <= 1.)
• Both non-zero location have the same values for b_x and b_y (because in this image the labelled objects happen to have colocated centers)
• One non-zero location has the shape and class indicator for the person object
• The other non-zero location has the shape and class indicator for the car object | 1,436 | 5,682 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2024-22 | latest | en | 0.917046 |
https://or.stackexchange.com/questions/4509/scheduling-with-setup-cost | 1,624,460,382,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488539480.67/warc/CC-MAIN-20210623134306-20210623164306-00162.warc.gz | 394,663,927 | 33,744 | # Scheduling with setup cost
I have a single worker that can work on N different tasks, but his total time T is limited. Let's assume time is in steps of 10 minutes (1 step = 1 mn). The payoff from a single job is 0 for the first step (setup cost) and then $$\log_{10}(t)$$, eg payoff is 0.778 after 60 minutes (6 steps). If a worker goes back to an old job and continues it, there is another setup cost of 1, so working 2 times 60 minutes on the same job, payoff is log(12-1).
We can then show that working on each job for 30 minutes (3 steps) and then not going back to it, is better than working on fewer jobs for 60 minutes each. It maximises the total payoff. In fact working on many jobs 11 minutes (1.1 steps) is kind of the optimal thing to do.
How can I make this more realistic? Imagine the worker is a human, and the jobs are meetings. Obviously you would not switch meetings all the time.
I appreciate this is not 100% well defined. But grateful for any ideas.
• $\log_{10}(1)=0$, so working for 10 minutes on a job has no value (even without setup cost). Is this intentional? – prubin Jul 11 '20 at 22:45
• Your criterion function pays for work done but not for job completion. In most contexts, a partially done job is not all that valuable. – prubin Jul 11 '20 at 22:47
• Yes no value for first step is intentional, this is the setup cost. Yes I realise there is no benefit for getting the job done, it's just continuous – Dirk Nachbar Jul 13 '20 at 8:28
• If the first step is always setup, then shouldn't two 60 minute (six step) stints on a job be worth $\log_{10}(12-2)$ rather than $\log_{10}(12-1)$? – prubin Jul 14 '20 at 15:57
• Sounds like a work model for my teenager. Get everything set up, do a minute of work and then leave it for later....repeat on other tasks. – AirSquid Jul 24 '20 at 6:03 | 506 | 1,825 | {"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": 1, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2021-25 | latest | en | 0.923822 |
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# Randy82
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May 6, 2016
# Homework Help: math
Posted by Carol on Monday, October 25, 2010 at 12:39pm.
I'm in 5th grade pls. help.
Amanda has a collection of X, Y and Z. Every X is a Y. One half the Z's are Y's. There are 3 times as many Y's as X's. Amanda has 50 Z's and 40 X's. No Z is an X. How many Y's does Amanda have that are neither X's nor Z's? | 122 | 351 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2016-18 | longest | en | 0.99032 |
https://ch.mathworks.com/matlabcentral/cody/problems/42255-volume-of-cylinder/solutions | 1,575,682,125,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540491871.35/warc/CC-MAIN-20191207005439-20191207033439-00156.warc.gz | 319,973,710 | 14,794 | Cody
# Problem 42255. Volume of Cylinder
• What is Size?
1 – 10 of 178
#### Solution 2048283
Submitted on 5 Dec 2019 at 23:57
• Incorrect
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#### Solution 1815225
Submitted on 14 May 2019
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#### Solution 1728778
Submitted on 17 Feb 2019 by Dyuman Joshi
• Size: 20
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#### Solution 1728775
Submitted on 17 Feb 2019
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#### Solution 1728774
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#### Solution 1728757
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#### Solution 1716333
Submitted on 28 Jan 2019 by William
• Size: 26
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#### Solution 1702768
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#### Solution 1702767
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1 – 10 of 178 | 522 | 1,946 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2019-51 | latest | en | 0.855802 |
https://fr.mathworks.com/matlabcentral/cody/problems/1407-is-it-an-armstrong-number/solutions/2686220 | 1,603,371,842,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107879537.28/warc/CC-MAIN-20201022111909-20201022141909-00211.warc.gz | 331,363,153 | 17,061 | Cody
# Problem 1407. Is it an Armstrong number?
Solution 2686220
Submitted on 13 Jul 2020 by Raghunadh N
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### Test Suite
Test Status Code Input and Output
1 Pass
x = 153; y_correct = 1; assert(isequal(armno(x),y_correct))
2 Pass
x = 143; y_correct = 0; assert(isequal(armno(x),y_correct))
3 Pass
x = 370; y_correct = 1; assert(isequal(armno(x),y_correct))
4 Pass
x = 371; y_correct = 1; assert(isequal(armno(x),y_correct))
5 Pass
x = 145; y_correct = 0; assert(isequal(armno(x),y_correct))
6 Pass
x = 407; y_correct = 1; assert(isequal(armno(x),y_correct))
7 Pass
x = 136; y_correct = 0; assert(isequal(armno(x),y_correct))
### Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting! | 283 | 883 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2020-45 | latest | en | 0.595793 |
https://mail.haskell.org/pipermail/haskell-prime/2007-April/002187.html | 1,508,729,132,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187825510.59/warc/CC-MAIN-20171023020721-20171023040721-00143.warc.gz | 754,582,588 | 2,390 | # Relax the restriction on Bounded derivation
Ravi Nanavati ravi at bluespec.com
Tue Apr 17 23:05:15 EDT 2007
```On 4/17/07, Neil Mitchell <ndmitchell at gmail.com> wrote:
>
> Hi,
>
> >From Section 10 of the Haskell report, regarding automatic derivation:
>
> to derive Bounded for a type: "the type must be either an enumeration
> (all constructors must be nullary) or have only one constructor."
>
> This seems a very artificial restriction - since it allows you to be
> in any one of two camps, but no where in between. It also means that
> Either doesn't derive Bounded, while it could easily do so:
>
> instance (Bounded a, Bounded b) => Bounded (Either a b) where
> minBound = Left minBound
> maxBound = Right maxBound
>
> So I propose that this restriction be lifted, and that the obvious
> extension be given such that minBound is the lowest constructor with a
> pile of minBounds, and maxBound is the highest constructor with a pile
> of maxBound.
In general, I like the idea of of allowing more flexible derivation of
Bounded, but I'm worried your specific proposal ends up mandating the
derivation of Bounded instances for types that aren't really "bounded" (used
in a deliberately loose sense). Consider the following type:
data Foo = A Char | B Integer | C Int
On some level, there's no real problem in creating a Bounded instance as
follows (which is how I interpret your proposal):
instance Bounded Foo
minBound = A (minBound :: Char)
maxBound = C (maxBound :: Int)
On the other hand, there's a real sense in which the type isn't actually
"bounded". For instance, if it was also an instance of Enum, enumerating all
of the values from minBound to maxBound might not terminate. I'm not sure
what to do about the scenario. Should we (unnecessarily) insist that all of
the arguments of all of the constructors be Bounded to avoid this? Should
Bounded more explicitly document what properties the minBound, maxBound and
the type should satisfy? Or something else?
- Ravi
-------------- next part --------------
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https://www.igi-global.com/article/least-laxity-first-scheduling-algorithm/43899 | 1,653,068,394,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662533972.17/warc/CC-MAIN-20220520160139-20220520190139-00306.warc.gz | 953,512,218 | 34,002 | # A Least-Laxity-First Scheduling Algorithm of Variable Time Slice for Periodic Tasks
Shaohua Teng (Guangdong University of Technology, China), Wei Zhang (Guangdong University of Technology, China), Haibin Zhu (Nipissing University, Canada), Xiufen Fu (Guangdong University of Technology, China), Jiangyi Su (Guangdong University of Technology, China) and Baoliang Cui (Guangdong University of Technology, China)
DOI: 10.4018/jssci.2010040105
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## Abstract
The LLF (Least Laxity First) scheduling algorithm assigns a priority to a task according to its executing urgency. The smaller the laxity value of a task is, the sooner it needs to be executed. When two or more tasks have same or approximate laxity values, LLF scheduling algorithm leads to frequent switches among tasks, causes extra overhead in a system, and therefore, restricts its application. The least switch and laxity first scheduling algorithm is proposed in this paper by searching out an appropriate common divisor in order to improve the LLF algorithm for periodic tasks.
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## Introduction
There are many procedures and jobs with cyclical characteristics in the real world, as well as in the batch production of products. Every batch is a production cycle and there are many processes in the production cycle. For example, automobile manufacturing, production of milk, computer manufacturing, clothing making, and crops production all have cyclical characteristics. They all are composed of periodic tasks. The cycle of crops production is once or twice per year from sowing to harvesting and that of fruit production is once a year.
After analyzing the production process of these periodic tasks carefully, it is not difficult to find out the following common characteristics of them:
• There exist parallel actions among processes. For example, parallelism occurs in an assembly line. The second process of the first product making action and the first process of the second product making action are in parallel. When one product is being assembled in a process, the other might be in the next process. In general, all of the batch productions are the same, which all are parallel actions.
• The system with periodic tasks is not usually fully loaded. It might become idle in some intervals, such as the winter in agricultural production. All the batch productions have the same or similar property. Their differences are long or short in idle intervals.
• Each task is independent and has possibly different production cycles.
• There are not strict sequences among some processes.
If we extract the essential features and ignore the specific production procedure for every production task which has the periodic characteristics, we can discuss the production scheduling with the help of computer simulation. Production details of a task is not important for scheduling, but the start time of periodic task, the length of a cycle and the time of real production in a cycle are essential. In order to make full use of the production resources and make the greatest benefit, an efficient scheduling is necessary. Efficient scheduling schemes could use the least scheduling time and make a system to gain the most execution time. For instance, rural workers can take in hand more part time when his major task, i.e., crop production is idle. A production system could be used to take on other jobs in free times. This kind of scheduling is quite useful and can make an enterprise to gain more benefit. Hence, real-time task scheduling is an important topic. A computer simulation could give an exact solution for the production task scheduling in the real world.
Real-time task scheduling has been studied widely in computer science. Many scholars and experts have paid much attention to studying on the real-time task scheduling and they have achieved a lot of research results. The real-time scheduling is a fundamental problem of operating systems. When a computer is multi-programmed, it frequently has multiple processes competing for the CPU (Central Process Unit) at the same time. This situation occurs whenever two or more processes are simultaneously in the ready state. If only one CPU is available, a choice has to be made, i.e., which process runs first. The part of an operating system that makes the choice is called scheduler and the used algorithms is called scheduling algorithms. These topics form the subject matter of the process scheduling (Tanenbaum, 2002). The process is basically a program in execution. Then the real-time scheduling of tasks is very important. Scheduling is also a daily human cognitive activity, people need to think of the schedules everyday to make their work more efficient. It is a common problem in every field related with cognitive informatics (Wang, 2003, 2007; Ngolah, Wang, & Tan, 2004), such as, software development, knowledge management, natural intelligence and artificial intelligence.
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https://chess.stackexchange.com/questions/29467/can-anyone-please-explain-why-this-position-isnt-a-draw?noredirect=1 | 1,701,780,577,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100551.17/warc/CC-MAIN-20231205105136-20231205135136-00242.warc.gz | 204,915,955 | 40,984 | # Can anyone please explain why this position isn't a draw?
I was watching this game on Lichess. Both of the players have the same resource i.e., the king and only a bishop. The bishops on the board are of the opposite color. But the game was continued and one of the players flagged on time.
I ran a full computer analysis and the engine has shown the position as a draw. But, since the computer allowed the player to continue the game with that resource, my question is whether it is possible to win a game with "ONLY" a bishop, provided your opponent only has the same? If yes, then what should be the checkmate position? and will the result be different if your opponent has the same color bishop?
[FEN "8/1k1b4/8/2B5/8/K7/8/8 w - - 0 1"]
According to the FIDE Laws of Chess:
5.2.2 The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’.
The game position you show is not a draw because there are series of legal moves ending in checkmate for either side.
[FEN "8/1k1b4/8/2B5/8/K7/8/8 w - - 0 1"]
1. Kb3 Be6 2. Kc3 Kc7 3. Kd3 Kd7 4. Ke3 Ke8 5. Kf4 Kf7 6. Kg5 Kg8 7. Kh6 Kh8 8. Bd6 Bg8 9. Be5#
Of course black's moves were stupid. That doesn't matter. They were all legal moves and so were all white's moves. A similar set of moves could be constructed to allow black to checkmate white. The sensible thing to do is to agree a draw in this position, particularly if there is an increment.
If there is no increment and the player with more time wants to be spiteful then they can play on and try and flag the other player. Of course they shouldn't do this if they are playing Gata Kamsky GM FFL :-)
With same colored bishops this is not possible. The opposite colored bishop is required to block one of the king's escape squares.
• If this endgame appears on blitz, does the arbiter claim draw or he let play until one is out of time?
– user27142
Jun 18, 2021 at 6:37
• @Universal_learner There are only 3 situations in which the arbiter can intervene 1) 5-fold repetition 2) 75 moves without a pawn move or capture 3) Impossible for either side to checkmate. If there is an increment of even 1 second then neither side is ever going to lose on time. The arbiter better start counting to 75. Jun 18, 2021 at 8:49 | 636 | 2,351 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2023-50 | latest | en | 0.963787 |
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Solution_ Homework6_Inventory Management
# Solution_ Homework6_Inventory Management - 311 Operations...
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311 Operations Management Fall 2008 Solution: Homework # 6 – Inventory Management 1. (30 points; 5 points per part) A company provides free tea to their employees by sourcing their tea supplies from Trojan Tea, a new start-up run by Marshall students. Trojan Tea has promised to supply the company 50 pounds of their specialty loose leaf weekly, for 52 weeks per year. Trojan Tea, in turn, purchases their tea from a niche Indian supplier for \$10.00 per pound. The shipping cost per order is \$40. Tea storage must be done in a customized, humidity-controlled environment, and storage costs are estimated to be \$2 per pound per year. Currently, Trojan Tea places an order every 4 weeks. a. What is the current annual order cost? 52/4*40 = 520 b. What is the current storage cost? 50*4/2*2 = 200 c. What is the optimal order quantity for Trojans Tea? pounds 322 2 40 * 50 * 52 * 2 2 = = = H DS EOQ d. How many orders are placed per year? 52*50/322 = 8.06 e. Trojan Tea realizes that holding tea inventory ties up cash and its holding
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Contents
Matching algorithms are algorithms used to solve graph matching problems in graph theory. A matching problem arises when a set of edges must be drawn that do not share any vertices. Graph matching problems are very common in daily activities.
## How do you evaluate a matching algorithm?
It can be difficult to evaluate the performance of matching algorithms .For this type of algorithm, evaluating its performance is methodical and follows a clear process:Look at individual pairs of records (Pairs Analysis)Increase the granularity to matched entities (Entity Validation)Take overall metrics (Metrics)
## What is a maximum matching algorithm?
A maximum matching is a matching of maximum size (maximum number of edges). In a maximum matching, if any edge is added to it, it is no longer a matching. There can be more than one maximum matching for a given Bipartite Graph.
## How do you find the maximum match?
To solve the maximum matching problem, we need an algorithm to find these maximum matching. The main idea is to find augmenting paths in the graph which will add an extra matching to the existing current matching. augmenting paths. of two matchings M and the augmenting path P.
## Does stable matching always exist?
A stable matching always exists, and the algorithmic problem solved by the Gale–Shapley algorithm is to find one. A matching is not stable if: There is an element A of the first matched set which prefers some given element B of the second matched set over the element to which A is already matched, and.
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# Roll Crusher Angle Of Nip
Angle of nip in roll crusher definition. angle of nip of roll crusher in mining engineering. angle of nip definition of angle of nip in the free online encyclopedia. the largest angle that will just grip a lump between the jaws rolls or mantle and ring of a . get price.
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### Angle Of Nip In Roll Crusher Formulalegend Mold
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### Angle Of Nip In Roll Crusher Definition
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### Pdf Angle Of Nip In Roll Crusher
Angle of nip pdf mill grinding applied and . derive the equation for angle of nip for roll crusher. pair of rolls is to take a feed equivalent to spheres of cm in diameter and crush them to spheres having cm diameter.zone of a roll crusher and is about to be nipped for rolls that have equal radii and length, tangents drawn at the point of contact of the particle and the two rolls meet to form.
### Angle Of Nip Ball Mill
Ball mill mining nip angle felona heavy machinery. angle of nip ball mill chapter 5 gyratory and cone crusher chapter 7 tubular ball 915 the nip angle is defined as the angle that is tangent to the roll surface at the points of contact between the rolls and the is found 5 that the total energy requirement for the combined operation of hpgr and ball mill is less than the.
### Diameter Of Rolls For A Roll Crusher For The Given Feed
Diameter of roll crusher home- solved problems - mechanical operations- a pair of rolls is to take a feed equivalent to spheres of 3 cm in diameter and crush them to spheres having 1 cm diameter. if the coefficient of friction is 0.29, what would be the diameter of rolls? ... angle of nip = 2 a. we have, m = 0.29. therefore, a = tan-1 (0.29.
### Ouble Roll Crusher Nip Angle Roller Crusher
Double roll crusher nip angle double roll crusher machine design free download as pdf file the nip angle is between 20and 30but in some large roll crushers it is up to 40the nip angle for jaw cone and roll crushers is calculated according to the method value of admissible nip angle of a crusher.
### Effect A Nip Angle In A Gyratory Crusher
Effect a nip angle in a gyratory crusher. prompt : caesar is a famous mining equipment manufacturer well-known both at home and abroad, major in producing stone crushing equipment, mineral separation equipment, limestone grinding equipment, etc. maximum nip angle on gyratory crusher… model can accept. (b) nip angle:.
### What Is The Nip Angle Of A Crusher
For the double roll crusher, the nip angle is the angle of two tangent lines that derivate from the contact point between the ore block and roller. nip angle in a jaw crusher 19 apr . 4.9, if a is the angle of nip between the crusher jaws and lt and lmax are the.
### Determination Of The Nip Angle In Roller Compactors With
In roller compaction, the nip angle defines the critical transition interface between the slip and nip regions which is used to model material densification behavior and the properties of compacted ribbons. current methods to determine the nip angle require either sophisticated instrumentation on smooth rolls or input parameters that are difficult to obtain.
### Derivation Of Angle Of Nip In Roll Crusher
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### Complete Derivation Of Angle Of Nip In Roll Crusher
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### Nip Angle On Jaw Crushers
Nip angle of jaw crusher welcome to the most trusted and comprehensive jaw crushers directory on the internet. a broad range of jaw crushers resources arethe particles are drawn into the gap between the rolls by their rotating motion and a friction angle formed between the rolls and the particle, called the nip.
### Roll Crusher And Derivation Of Angle Of Nip
Roll crusher nip angle pdf roll crusher nip angle one of the main reasons for closing the circuit is the greater flexibility given to the crushing seo and sem professionals use get more info derivation for angle of nip in roll crusher learn more angle of live chat angle of nip of roll.
### Angle Of Nip In Roll Crusher Function
Roll crusher- an overview | sciencedirect topics. if is the coefficient of friction between the rolls and the particle, θ is the angle formed by the tangents to the roll surfaces at their points of contact with the particle (the angle of nip), and c is the compressive force exerted by the rolls acting from the roll centers through the particle center, then for a particle to be just gripped.
### Roll Crusher And Derivation Of Angle Of Nip
Roll crushers - 911 metallurgist. feb 23, (c) for any combination of feed size and roll diameter, heavy-duty, high-spring- pressure rolls will stand higher speeds than will lighter rolls, provided that the angle of nip is not too great for the increased.
### Dual Roll Crushers How They Function
Roll crushers have a theoretical maximum reduction ratio of 4:1. if a 2 inch particle is fed to the roll crusher the absolute smallest size one could expect from the crusher is 1/2 inch. roll crushers will only crush material down to a minimum particle size of about 10 mesh (2 mm). a roll crusher crushes using compression, with two rolls.
### Roll Crusher
Table 6.1 gives example values for 1,000 mm roll diameter where the angle of nip should be less than 20 in order for the particles to be gripped (in most practical cases the angle of nip should not exceed about 25.
### Rolls Crusher For Sale
The 24″ diameter roll crusher has an effective nip of about 14″ maximum; the 36″ machine will grip stone up to about 24″ maximum; and the 60″ crusher will handle ledges up to about 36″ thickness. these thickness are based on limestone of medium hardness; for harder materials the advisable thickness is.
### Diameter Of Rolls For A Roll Crusher For The Given Feed
The following formula relates the coefficient of friction ( m ), radius of rolls (r), radius of product (d), and radius of feed (r): cos a = (r + d) / (r + r) 1. where a is related to the coefficient of friction by the relation, m = tan a. angle of nip = 2.
### Nip Angle On Jaw Crushers
The nip angle for jaw ne and roll crusher is calculated according to the method proposed by levenson ,,,,, roll crusher,roll crusher,roll crusher supplier brief of fdm dm has engaged in pro motion and a friction angle formed between the rolls and the particle, called the nip.
### Roll Crushers
The nip angle is defined as the angle that is tangent to the roll surface at the points of contact between the rolls and the particle. it depends on the surface characteristics of the rolls. usually, the nip angle is between 20 and 30 but in some large roll crushers it is up to 40.
### Dual Roll Crushers How They Function
The particles are drawn into the gap between the rolls by their rotating motion and a friction angle formed between the rolls and the particle, called the nip angle. the two rolls force the particle between their rotating surface into the ever smaller gap area, and it fractures from the compressive forces presented by the rotating rolls. some major advantages of roll crushers are they give a very fine.
### Roll Crusher
Unless very large diameter rolls are used, the angle of nip limits the reduction ratio of the crusher, and since reduction ratios greater than 4:1 are rare, a flowsheet may require coarse crushing rolls to be followed by fine.
### Question Is ⇒ Angle Of Nip Of The Crushing Rolls Does Not
⇒ angle of nip of the crushing rolls does not depend upon the diameter of the rolls speed of the rolls product size feed size ⇒ in case of grinding in a ball mill wet grinding achieves a finer product size than dry grinding. its capacity decreases with increasing fineness of the.
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https://www.lmfdb.org/EllipticCurve/Q/7098/b/ | 1,620,842,505,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243989766.27/warc/CC-MAIN-20210512162538-20210512192538-00295.warc.gz | 923,523,211 | 5,587 | Properties
Label 7098.b Number of curves $1$ Conductor $7098$ CM no Rank $0$
Related objects
Show commands for: SageMath
sage: E = EllipticCurve("b1")
sage: E.isogeny_class()
Elliptic curves in class 7098.b
sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.b1 7098d1 $$[1, 1, 0, -16981799, -27096574539]$$ $$-112205650221491190337/745029571313664$$ $$-3596115440082935218176$$ $$[]$$ $$799680$$ $$2.9718$$ $$\Gamma_0(N)$$-optimal
Rank
sage: E.rank()
The elliptic curve 7098.b1 has rank $$0$$.
Complex multiplication
The elliptic curves in class 7098.b do not have complex multiplication.
Modular form7098.2.a.b
sage: E.q_eigenform(10)
$$q - q^{2} - q^{3} + q^{4} - 3q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + 3q^{10} - q^{11} - q^{12} - q^{14} + 3q^{15} + q^{16} + 7q^{17} - q^{18} - q^{19} + O(q^{20})$$ | 354 | 939 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2021-21 | latest | en | 0.439555 |
http://www.cplusplus.com/forum/beginner/78206/ | 1,501,108,612,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549426639.7/warc/CC-MAIN-20170726222036-20170727002036-00122.warc.gz | 396,972,080 | 4,247 | ### Putting an integer number into a vector
Hi everyone,
I have an int of several digits and i want to put that number into a vector where the all the digits are in separate elements. For example if i have
``12`` ``````int number = 567; vector myvector;``````
I would like the zeroth element of myvector to contain 5, the first element to contain 6, and the second element to contain 7.
Last edited on
You'll need an algorithm to split the number into its digits. Since integer division always rounds down, something like this will do:
``12345`` ``````for(unsigned int i = 100; i > 0; i/=10) { myvector.push_back(number/i); number -= (number/i)*i; }``````
Oh ok, i didn't think of that, but i tried your algorithm and it didn't work, but i get the idea.
thankyou
``12345678910111213141516`` ``````int main() { std::vector myvector; int number = 519; for(unsigned int i = 100; i > 0; i/=10) { myvector.push_back(number/i); number -= (number/i)*i; } for(size_t i = 0; i < myvector.size(); ++i) { std::cout<
This works for me. Just remember that if your number is longer than 3 digits i has to be initialized to something bigger.
You can determine the number of digits in your number with this piece of code:
`int digits = log10((float)number) + 1`
That way, you don't need to initialize anything as it will just work.
Topic archived. No new replies allowed. | 369 | 1,367 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2017-30 | latest | en | 0.895789 |
https://greensportsalliance.net/kalkee/linear-programming-and-its-applications.php | 1,679,568,978,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945144.17/warc/CC-MAIN-20230323100829-20230323130829-00513.warc.gz | 361,742,142 | 9,516 | Linear Programming and Its Applications SpringerLink Linear programming (LP) is useful for resource optimization, as long as the constraints and the objective function are linear or can be linearized (also, it helps if
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An ApproximationScheme for Stochastic Linear Programming and its Application to Stochastic Integer Programs David B. Shmoys Chaitanya Swamy Abstract Linear Programming and Its Applications by Eiselt, H. a. and Sandblom, C. -L available in Trade Paperback on Powells.com, also read synopsis and reviews. Based on | 3,383 | 16,506 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2023-14 | latest | en | 0.854726 |
https://www.intelligenteconomist.com/decisions-involving-uncertainty/ | 1,720,994,895,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514654.12/warc/CC-MAIN-20240714220017-20240715010017-00583.warc.gz | 745,348,934 | 17,862 | # Decisions Involving Uncertainty
Decision-making under uncertainty is a complex topic because all decisions are made with some degree of uncertainty. But there are specific scenarios in which economic experiments have shown that some people make decisions deviating from expected utility theory defined by the Von Neumann-Morgenstern theorem. While the experiments are conducted under certain restrictions, the findings can be and have been extended to many relevant real-world scenarios.
Contents
## Von Neumann-Morgenstern Expected Utility Theory and Risk Preferences
When thinking about decisions involving uncertainty, the von Neumann-Morgenstern utility function must first be discussed since it describes how rational agents should theoretically act when facing a decision. The function arises from the expected utility hypothesis and “shows that when a consumer is faced with a choice of items or outcomes subject to various levels of chance, the optimal decision will be the one that maximizes the expected value of the utility (i.e. satisfaction) derived from the choice made.” It relies on assumptions of completeness (that a decision can always be made), transitivity (consistent choices in different scenarios), independence (an irrelevant choice won’t change anything), and continuity (there are possible combinations of probabilistic choices that lead to indifference).
This theory drove the classification of agents as risk-averse, risk-neutral, and risk-loving. These classifications are referred to as risk preferences, and they inform economic analyses by categorizing agents into certain groups.
Risk-averse agents are those that dislike uncertainty – they would rather have a lower payoff with more certainty than a higher payoff with more uncertainty.
A risk-neutral agent is indifferent between choices with differing levels of uncertainty as long as the expected value is equal.
A risk-loving (or risk-seeking) agent would prefer a higher payoff with more uncertainty over a lower payoff with more certainty.
An agent’s behavior can often be predicted based on their classification as risk-averse, -neutral, or -loving. However, deviations from the expected behavior create interesting scenarios and theories and are the focus of the rest of this article.
## St. Petersburg Paradox
The St. Petersburg Paradox is one of the most interesting examples of Decisions Involving Uncertainty. The paradox was first described by Daniel Bernoulli. The St. Petersburg Paradox says that a rational investor should be willing to pay an infinite amount of money for the following game:
If a coin is flipped and it comes up heads, the investor is paid \$1. If it’s flipped again and it comes up heads again, the investor gets \$2. If it comes up heads a third time, \$4; a fourth time \$8; and so on. Once tails comes up the game is over. So, the total prize is \$2n, where n is the total number of flips.
The chart above (from an article in the Stanford Encyclopedia of Philosophy) summarizes the payoff structure for a sample of 10 flips, where P(n) indicates the probability of getting that many heads in a row. Since there is an infinite number of possible consequences and each has an expected payoff of \$1, the sum of the expected payoffs is infinity. And the rational investor should be willing to pay an infinite amount to play this game.
However, an investor would not really pay an infinite amount of money to play this game, even if that was technically possible. It’s commonly thought that people would pay about \$20-\$25 to play.
Bernoulli describes this deviation from theoretical behavior by saying that “mathematicians evaluate money in proportion to its quantity [the expected value here] while, in practice, people with common sense evaluate money in proportion to the utility they can obtain from it.” In other words, people don’t expect to get an infinite amount of money in reality, so they’ll only be willing to make a small investment to potentially earn a reasonable profit (that they could then realistically use).
Risk aversion may also play a part in describing why people won’t pay an infinite sum in practice to play the game. “Very low payments are very probable, and very high ones very rare. It’s a foolish risk to invest more than \$25 to play … many of us are risk-averse, and unwilling to gamble for a very small chance of a very large prize” (Stanford Encyclopedia). While risk aversion doesn’t explain everything, it provides a reasonable starting point for an explanation of why some people won’t play for any amount of money.
The Allais paradox is another surprising example of how people deviate from expected utility theory. The classic experiment to demonstrate this paradox is shown below. People are asked to choose between A and B in each experiment independently. Think about what you might choose before reading on.
Many people choose 1A and 2B, which are both reasonable choices if people were only asked about each experiment individually. But choosing them together violates expected utility theory (i.e. theoretically rational agents would choose 1A and 2A or 1B and 2B). The reason is that “in expected utility theory, equal outcomes added to each of the two choices should have no effect on the relative desirability of one gamble over the other; equal outcomes should ‘cancel out’.” See the choices described this way below.
Really nothing has changed here; the only thing is that the \$1 million in gamble 1A is split into an 89% chance and an 11% chance of getting \$1 million (in other words, still a 100% chance of getting \$1 million). Then the first row can be eliminated because the choices are the same between gambles for each experiment. Seeing the choices described this way shows that it would actually be rational to choose 1A and 2A or 1B and 2B (depending on one’s risk preferences) because they’re the same choices. This paradox shows that people who choose 1A and 2B together violate the independence axiom of expected utility theory because the addition of an irrelevant choice (89% chance of \$1 million or 89% chance of nothing) would change their decision.
Another paradox is the Ellsberg paradox, which was first identified by Daniel Ellsberg in 1961. Essentially, the paradox shows that people more often than not tend to prefer situations where they know the risk.
For example, if the two options are a 10% chance of winning versus and an unknown chance of winning (that is actually a 90% chance of winning), people would choose the 10% chance because there is the possibility that the unknown chance of winning is 0%. This phenomenon is often simply described as preferring the ‘devil you know’ over the one you don’t.
Ellsberg illustrates this paradox with a choice game. In the scenarios, there is one urn containing 30 red balls and one containing 60 black and yellow balls of unknown proportions (i.e. there could be 60 black balls and 0 yellow, 60 yellow and 0 black, or any combination in between).
In scenario 1, the agent must guess whether a red ball or a black ball will be pulled out of the urn. In scenario 2, the agent must choose between one of the following options: that 1) either a red or a yellow will be pulled out of the urn, or that 2) either a black or yellow will be pulled out. In both scenarios, the prize for choosing the correct ball color is \$100.
Many people choose Option I from scenario 1 and Option IV from scenario 2, but this combination of choices is inconsistent. They imply that the subject prefers to bet ‘on’ red rather than ‘on’ black by choosing I; and he or she also prefers to bet ‘against’ red rather than ‘against’ black by choosing IV.
In other words, the subject believes it is more likely for a red ball to be pulled than a black ball in scenario 1 and that it is more likely for a black ball to be pulled than a red ball in scenario 2 (because the probability of a pulling a yellow ball is the same for choices III and IV). These outcomes clearly illustrate the idea of preferring the devil you know.
In scenario 1, the subject who chooses I prefers the choice where he or she knows the chance of winning is 30%, even though the unknown proportion of black and yellow balls could be 60 black and 0 yellow, which would mean that choosing black would lead to a 60% chance of winning. In scenario 2, the subject who chooses IV prefers the choice where he or she knows the chance of winning is 60% even though the combination of red and yellow could lead to a higher than 60% chance of winning.
By choosing I and IV, subjects opt to avoid unknown risks (i.e. betting on the unknown proportion of black and yellow balls). Ambiguity aversion, as defined by Ellsberg, may help to explain some of this choice inconsistency.
## Ambiguity Aversion
Agents exhibit ambiguity aversion when they prefer known risks over unknown risks. Ellsberg discusses ambiguity aversion as a potential reason for the discrepancies observed in the urn scenarios presented above. People prefer the option for which they know the probability of winning over the one for which they don’t.
It’s important to distinguish between ambiguity and risk aversion. With risk aversion, people tend to choose the option with a smaller payoff but a higher probability of occurrence. However, in these types of scenarios, they know the probability of occurrence for all the options. On the other hand, when situations are ambiguous, the probability of occurrence is unknown. As a result, people tend to choose the option where the probability is known in order to avoid ambiguity.
## Calibration Theorem
The final theorem discussed here, the calibration theorem, has to do with risk aversion rather than ambiguity aversion. The theorem was proposed by Matthew Rabin in 2000 and “calibrates a relationship between risk attitudes over small and large stakes”, showing that “anything but virtual risk neutrality over modest stakes implies unrealistic risk aversion over large stakes”.
The typical model of risk aversion derived from the theory of diminishing marginal utility of wealth explains large-scale risk (“a dollar that helps us avoid poverty is more valuable than a dollar that helps us become very rich”), and it implies that people are risk neutral when stakes are small. However, the expected utility theory also implies that people would be approximately risk-neutral over large stakes as well (whereas economists often use this theory to incorrectly assume that people would be risk averse in the face of large stakes).
As an example, Rabin shows in the paper that someone who would turn down a 50/50 bet of losing \$100 or gaining \$110 would turn down 50/50 bets of losing \$1,000 or gaining any sum of money. Additionally, a person who would turn down 50/50 bets of losing \$1,000 and gaining \$1,050 would turn down 50/50 bets of losing \$20,000 or gaining any sum. Of course, these seem like unreasonable levels of risk aversion.
Rabin explains the theorem further with mathematical examples in the paper, but his main message is that the expected utility theory assumes a very rapid rate of money utility deterioration and that the miscalibration of expected utility theory is an explanation for why modest-scale risk aversion is observed in human behavior. | 2,320 | 11,304 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2024-30 | latest | en | 0.931225 |
http://www.chegg.com/homework-help/questions-and-answers/compute-magnetic-field-due-small-current-segment-length-1-10-m-carrying-4-amps-current-cur-q1157748 | 1,448,550,305,000,000,000 | text/html | crawl-data/CC-MAIN-2015-48/segments/1448398447729.93/warc/CC-MAIN-20151124205407-00191-ip-10-71-132-137.ec2.internal.warc.gz | 348,183,242 | 12,721 | compute the magnetic field due to small current segment of length 1/10 m and carrying 4 amps of current with the current direction and wire segment aimed toward your face. What is the current magnitude a distance of 9m to your right perpendicular to the segment?what is the direction of the magnetic field at that point(left, right, up, down, away,from your face or toward)?what would the magnitude be at the same distance but at 40 degrees away from the +x axis and toward your face? | 107 | 484 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2015-48 | latest | en | 0.946216 |
https://www.education.com/worksheets/fourth-grade/perimeter/ | 1,685,453,604,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224645810.57/warc/CC-MAIN-20230530131531-20230530161531-00750.warc.gz | 819,475,610 | 27,974 | Search Printable 4th Grade Perimeter Worksheets
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Geometry Basics: More Perimeters
Interactive Worksheet
Geometry Basics: More Perimeters
Children practice calculating the perimeter of a variety of polygons in this geometry worksheet.
Math
Interactive Worksheet
Area and Perimeter of a Rectangle
Interactive Worksheet
Area and Perimeter of a Rectangle
Math ninjas can learn the secrets of the rectangle with this practice page about the area and perimeter of a rectangle.
Math
Interactive Worksheet
Math Review Part 3: Geometry Galore!
Worksheet
Math Review Part 3: Geometry Galore!
Use this year-end assessment to check students’ grasp of key fourth grade geometry concepts.
Math
Worksheet
Find the Rectangle's Perimeter
Worksheet
Find the Rectangle's Perimeter
Use your geometry skills to find the perimeters in this worksheet. This perimeter worksheet gets your child to calculate the perimeters of rectangles.
Math
Worksheet
Polygon Perimeter Word Problems
Worksheet
Polygon Perimeter Word Problems
In this worksheet, students will follow four steps to find the perimeter of polygons in word problems.
Math
Worksheet
Perimeter: Perfect Carnival
Worksheet
Perimeter: Perfect Carnival
Your students will have a blast as they use perimeter in a real-world scenario to plan their very own carnivals in the school gym. Students will choose their activities and use their calculated dimensions to map our their carnival on the provided graph.
Math
Worksheet
Perimeter of a Rectangle
Worksheet
Perimeter of a Rectangle
Have your fourth grader stretch his math knowledge with a geometry worksheet. He'll calculate the perimeter of a rectangle, then draw two similar shapes.
Math
Worksheet
Pentagon Perimeter Practice
Worksheet
Pentagon Perimeter Practice
Help your students practice finding the perimeter as they work through problems involving pentagons.
Math
Worksheet
Fun With Perimeters
Worksheet
Fun With Perimeters
Fourth graders will calculate the perimeter of rectangles, then draw new shapes with similar perimeters. Help your child practice geometry with this worksheet.
Math
Worksheet
More Pentagon Perimeter Practice
Worksheet
More Pentagon Perimeter Practice
This is a great worksheet to practice calculating the perimeter for a pentagon.
Math
Worksheet
Perimeter Match
Worksheet
Perimeter Match
Fourth grade mathematicians will need to use their geometry skills to figure out the length of the pictured rectangles' perimeters, then make their own.
Math
Worksheet
Match the Perimeter
Worksheet
Match the Perimeter
Your fourth grader will need to use his geometry skills to calculate and create rectangle perimeters. He'll also improve addition and multiplication skills. | 549 | 2,758 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.421875 | 3 | CC-MAIN-2023-23 | latest | en | 0.815817 |
https://metanumbers.com/13063 | 1,675,269,312,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499946.80/warc/CC-MAIN-20230201144459-20230201174459-00100.warc.gz | 412,678,616 | 7,487 | # 13063 (number)
13,063 (thirteen thousand sixty-three) is an odd five-digits prime number following 13062 and preceding 13064. In scientific notation, it is written as 1.3063 × 104. The sum of its digits is 13. It has a total of 1 prime factor and 2 positive divisors. There are 13,062 positive integers (up to 13063) that are relatively prime to 13063.
## Basic properties
• Is Prime? Yes
• Number parity Odd
• Number length 5
• Sum of Digits 13
• Digital Root 4
## Name
Short name 13 thousand 63 thirteen thousand sixty-three
## Notation
Scientific notation 1.3063 × 104 13.063 × 103
## Prime Factorization of 13063
Prime Factorization 13063
Prime number
Distinct Factors Total Factors Radical ω(n) 1 Total number of distinct prime factors Ω(n) 1 Total number of prime factors rad(n) 13063 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) -1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 9.47754 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 13,063 is 13063. Since it has a total of 1 prime factor, 13,063 is a prime number.
## Divisors of 13063
2 divisors
Even divisors 0 2 1 1
Total Divisors Sum of Divisors Aliquot Sum τ(n) 2 Total number of the positive divisors of n σ(n) 13064 Sum of all the positive divisors of n s(n) 1 Sum of the proper positive divisors of n A(n) 6532 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 114.293 Returns the nth root of the product of n divisors H(n) 1.99985 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 13,063 can be divided by 2 positive divisors (out of which 0 are even, and 2 are odd). The sum of these divisors (counting 13,063) is 13,064, the average is 6,532.
## Other Arithmetic Functions (n = 13063)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 13062 Total number of positive integers not greater than n that are coprime to n λ(n) 13062 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 1556 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 13,062 positive integers (less than 13,063) that are coprime with 13,063. And there are approximately 1,556 prime numbers less than or equal to 13,063.
## Divisibility of 13063
m n mod m 2 3 4 5 6 7 8 9 1 1 3 3 1 1 7 4
13,063 is not divisible by any number less than or equal to 9.
## Classification of 13063
• Arithmetic
• Prime
• Deficient
### Expressible via specific sums
• Polite
• Non-hypotenuse
• Prime Power
• Square Free
## Base conversion (13063)
Base System Value
2 Binary 11001100000111
3 Ternary 122220211
4 Quaternary 3030013
5 Quinary 404223
6 Senary 140251
8 Octal 31407
10 Decimal 13063
12 Duodecimal 7687
20 Vigesimal 1cd3
36 Base36 a2v
## Basic calculations (n = 13063)
### Multiplication
n×y
n×2 26126 39189 52252 65315
### Division
n÷y
n÷2 6531.5 4354.33 3265.75 2612.6
### Exponentiation
ny
n2 170641969 2229096041047 29118681584196961 380377337534364901543
### Nth Root
y√n
2√n 114.293 23.5513 10.6908 6.65593
## 13063 as geometric shapes
### Circle
Diameter 26126 82077.2 5.36088e+08
### Sphere
Volume 9.33722e+12 2.14435e+09 82077.2
### Square
Length = n
Perimeter 52252 1.70642e+08 18473.9
### Cube
Length = n
Surface area 1.02385e+09 2.2291e+12 22625.8
### Equilateral Triangle
Length = n
Perimeter 39189 7.38901e+07 11312.9
### Triangular Pyramid
Length = n
Surface area 2.95561e+08 2.62701e+11 10665.9
## Cryptographic Hash Functions
md5 8f48ba716a4af57ae9b2e0308c871c00 9d199d40a050a9045bf45c64be561d35d52c457a b921c27c3053f1781f7b0ed32193c31ccfa403b2c1bf07a35ccd44d6557b3d60 9d1192234876204d062fe83fe2ff3137518b16ed51bd2b82707f4268647001b483ccef52876f8a78076fe64de4443bc2217f353f5036086efb13b7d2807cc6de dc989871645fc165b630464e1170f585addbe9fc | 1,434 | 4,110 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2023-06 | latest | en | 0.805973 |
https://pypi.org/project/fteikpy/ | 1,721,406,102,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514908.1/warc/CC-MAIN-20240719135636-20240719165636-00710.warc.gz | 417,698,608 | 13,881 | Accurate Eikonal solver for Python
## Project description
fteikpy is a Python library that computes accurate first arrival traveltimes in 2D and 3D heterogeneous isotropic velocity models. The algorithm handles properly the curvature of wavefronts close to the source which can be placed without any problem between grid points.
The code is based on FTeik implemented in Python and compiled just-in-time with numba.
## Features
Forward modeling:
• Compute traveltimes in 2D and 3D Cartesian grids with the possibility to use a different grid spacing in Z, X and Y directions,
• Compute traveltime gradients at runtime or a posteriori,
• A posteriori 2D and 3D ray-tracing.
Parallel:
• Traveltime grids are seemlessly computed in parallel for different sources,
• Raypaths from a given source to different locations are also evaluated in parallel.
## Installation
The recommended way to install fteikpy and all its dependencies is through the Python Package Index:
pip install fteikpy --user
Otherwise, clone and extract the package, then run from the package location:
pip install . --user
To test the integrity of the installed package, check out this repository and run:
pytest
## Documentation
Refer to the online documentation for detailed description of the API and examples.
Alternatively, the documentation can be built using Sphinx:
pip install -r doc/requirements.txt
sphinx-build -b html doc/source doc/build
## Usage
The following example computes the traveltime grid in a 3D homogeneous velocity model:
import numpy as np
from fteikpy import Eikonal3D
# Velocity model
velocity_model = np.ones((8, 8, 8))
dz, dx, dy = 1.0, 1.0, 1.0
# Solve Eikonal at source
eik = Eikonal3D(velocity_model, gridsize=(dz, dx, dy))
tt = eik.solve((0.0, 0.0, 0.0))
# Get traveltime at specific grid point
t1 = tt[0, 1, 2]
# Or get traveltime at any point in the grid
t2 = tt(np.random.rand(3) * 7.0)
## Contributing
Please refer to the Contributing Guidelines to see how you can help. This project is released with a Code of Conduct which you agree to abide by when contributing. | 514 | 2,102 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2024-30 | latest | en | 0.787138 |
https://www.coursehero.com/file/8722122/Thefugacityisdefinedin-suchawaythatitallowsustowritethechemicalpotentialoftherealgas-usingaverysimil/ | 1,495,764,867,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463608622.82/warc/CC-MAIN-20170526013116-20170526033116-00317.warc.gz | 841,450,569 | 23,471 | Chapter 3
# Thefugacityisdefinedin
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Unformatted text preview: s
providing
criteria
for
the
spontaneity
of
processes
occurring
either
at
constant
V
and
T
or
at
constant
P
and
T,
the
Helmholtz
and
Gibbs
Free
Energies
have
further
significant
meanings.
Let
us
consider
first
the
case
of
the
Helmholtz
free
energy.
The
second
law
states
that
dS
≥
δq
/
T.
Using
the
first
law
dU
=
δw
+
δq,
we
get:
T
dS
≥
dU
‐
δw
which
is
equivalent
to:
δw
≥
dU
‐
T
dS.
If
the
process
occurs
at
constant
temperature,
then
we
can
write:
δw
≥
dA
or
w
≥
DA
If
we
focus
on
a
process
whereby
work
is
being
done
by
the
system
(w
<
0).
We
now
recall
from
the
discussion
of
reversible
vs.
spontaneous
expansions
of
ideal
gases
that
the
maximum
work
of
expansion
is
done
by
the
system
when
the
expansion
occurs
reversibly.
This
corresponds
to
the
equality
between
w
and
ΔA.
We
therefore
conclude
that:
Δ A
is
the
maximum
work
that
can
be
done
by
a
system
at
constant
temperature.
This
is
actually
why
the
symbol
A
was
chosen
for
the
Helmholtz
Free
Energy.
In
German,
A
stands
for
“Arbeit”,
which
in
English
means
“work”.
Marand’s
Notes:
Chapter
3
‐
The
Second
Law
of
Thermodynamics
120
Let
us
consider
now
the
meaning
of
ΔG.
Using
a
similar
approach,
we
write
the
first
law
in
its
most
general
form.
dU
=
δw
+
δwe
+
δq
where
δw
is
the
volume
expansion
work
and
δwe
is
any
extra
(non‐ expansion)
work.
We
now
use
the
second
law
in
the
Clausius
formulation.
dS
≥
δq
/T
which...
View Full Document
## This note was uploaded on 01/26/2014 for the course CHEM 3615 taught by Professor Aresker during the Spring '07 term at Virginia Tech.
Ask a homework question - tutors are online | 1,012 | 1,818 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2017-22 | longest | en | 0.534474 |
http://www.sceneadvisor.com/New-York/measurements-error.html | 1,561,068,891,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627999273.79/warc/CC-MAIN-20190620210153-20190620232153-00148.warc.gz | 296,380,754 | 8,383 | # measurements error Croton Falls, New York
It may usually be determined by repeating the measurements. Notice that in order to determine the accuracy of a particular measurement, we have to know the ideal, true value. If you are measuring a football field and the absolute error is 1 cm, the error is virtually irrelevant. It is caused by inherently unpredictable fluctuations in the readings of a measurement apparatus or in the experimenter's interpretation of the instrumental reading.
Quantity Systematic errors can be either constant, or related (e.g. In educational data collection and reporting, measurement error can also become a significant issue, particularly when school-funding levels, penalties, or the perception of performance are influenced by publicly reported data, such If you measure the same object two different times, the two measurements may not be exactly the same. The measurements may be used to determine the number of lines per millimetre of the diffraction grating, which can then be used to measure the wavelength of any other spectral line.
Instead of relying on one potentially inaccurate measure, schools can get more comprehensive information by using multiple methods to assess student achievement and learning growth. Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. Finally, one of the best things you can do to deal with measurement errors, especially systematic errors, is to use multiple measures of the same construct. Apply correct techniques when using the measuring instrument and reading the value measured.
If the uncertainty ranges do not overlap, then the measurements are said to be discrepant (they do not agree). Maria also has a crude estimate of the uncertainty in her data; it is very likely that the "true" time it takes the ball to fall is somewhere between 0.29 s Martin, and Douglas G. ISBN0-935702-75-X. ^ "Systematic error".
Repeating the measurement will improve (reduce) the random error (caused by the accuracy limit of the measuring instrument) but not the systemic error (caused by incorrect calibration of the measuring instrument). Greatest Possible Error: Because no measurement is exact, measurements are always made to the "nearest something", whether it is stated or not. In any case, an outlier requires closer examination to determine the cause of the unexpected result. We want to know the error in f if we measure x, y, ...
Common sources of error in physics laboratory experiments: Incomplete definition (may be systematic or random) — One reason that it is impossible to make exact measurements is that the measurement is High rates of transfer in and out of school systems—e.g., by the children of transient workers—that make it more difficult to accurately track the enrollment status of students. Test items, questions, and problems may not address the material students were actually taught. This value is clearly below the range of values found on the first balance, and under normal circumstances, you might not care, but you want to be fair to your friend.
What if all error is not random? The Relative Error is the Absolute Error divided by the actual measurement. The Performance Test Standard PTC 19.1-2005 “Test Uncertainty”, published by the American Society of Mechanical Engineers (ASME), discusses systematic and random errors in considerable detail. Measurement errors can be divided into two components: random error and systematic error.[2] Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measures of a
It is random in that the next measured value cannot be predicted exactly from previous such values. (If a prediction were possible, allowance for the effect could be made.) In general, The important property of random error is that it adds variability to the data but does not affect average performance for the group. Examples: 223.645560.5 + 54 + 0.008 2785560.5 If a calculated number is to be used in further calculations, it is good practice to keep one extra digit to reduce rounding errors It is not to be confused with Measurement uncertainty.
G. In both of these cases, the uncertainty is greater than the smallest divisions marked on the measuring tool (likely 1 mm and 0.05 mm respectively). What is the uncertainty in this measurement? Retrieved from "https://en.wikipedia.org/w/index.php?title=Observational_error&oldid=739649118" Categories: Accuracy and precisionErrorMeasurementUncertainty of numbersHidden categories: Articles needing additional references from September 2016All articles needing additional references Navigation menu Personal tools Not logged inTalkContributionsCreate accountLog in Namespaces
Retrieved 2016-09-10. ^ "Google". Further investigation would be needed to determine the cause for the discrepancy. Systematic error is sometimes called statistical bias. But, if you are measuring a small machine part (< 3cm), an absolute error of 1 cm is very significant.
b.) The relative error in the length of the field is c.) The percentage error in the length of the field is 3. Gross personal errors, sometimes called mistakes or blunders, should be avoided and corrected if discovered. G. Another word for this variation - or uncertainty in measurement - is "error." This "error" is not the same as a "mistake." It does not mean that you got the wrong
Stochastic errors added to a regression equation account for the variation in Y that cannot be explained by the included Xs. Here are a few key points from this 100-page guide, which can be found in modified form on the NIST website. Well, we just want the size (the absolute value) of the difference. b.) the relative error in the measured length of the field.
Small sample sizes—such as in rural schools that may have small student populations and few minority students—that may distort the perception of performance for certain time periods, graduating classes, or student The accuracy of a measurement is how close the measurement is to the true value of the quantity being measured. Wrong: 1.237 s ± 0.1 s Correct: 1.2 s ± 0.1 s Comparing experimentally determined numbers Uncertainty estimates are crucial for comparing experimental numbers. of observations=155.96 cm5=31.19 cm This average is the best available estimate of the width of the piece of paper, but it is certainly not exact.
Here ... The word random indicates that they are inherently unpredictable, and have null expected value, namely, they are scattered about the true value, and tend to have null arithmetic mean when a Clearly, the pendulum timings need to be corrected according to how fast or slow the stopwatch was found to be running. It may often be reduced by very carefully standardized procedures.
Surveys The term "observational error" is also sometimes used to refer to response errors and some other types of non-sampling error.[1] In survey-type situations, these errors can be mistakes in the In the example above the Absolute Error is 0.05 m What happened to the ± ... ? Privacy, Disclaimers & Copyright COMPANY About Us Contact Us Advertise with Us Careers RESOURCES Articles Flashcards Citations All Topics FOLLOW US OUR APPS Measurement and Uncertainty Notes Reporting Measurements and | 1,459 | 7,294 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2019-26 | latest | en | 0.904311 |
https://community.fabric.microsoft.com/t5/Community-Blog/How-to-use-Tooltip-to-display-breakdown-data-for-a-specified/ba-p/3798573 | 1,723,174,528,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640751424.48/warc/CC-MAIN-20240809013306-20240809043306-00686.warc.gz | 136,445,483 | 56,126 | cancel
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## How to use Tooltip to display breakdown data for a specified ranking
Scenario:
In this post, tooltip and measure are utilized to show the breakdown of data for different classifications.
Expected Result:
Calculate the number of customers in each category, show the top five categories of customer number, merge other data into "others".
And show the data details corresponding to the top five data through tooltip.
If the data is merged into Others, the tooltip is blank.
Sample Data:
How:
1.First create a Measure to calculate the number of Customers for each product
count = CALCULATE(COUNT('Table'[Customer]), ALLEXCEPT('Table', 'Table'[Product]))
2.This step is achieved by displaying the first five products of the number of customers based on the COUNT number, merging the other data into "Other". This is a Calculated column because we need to put it into a table and not be affected by the row context.
Product1 =
VAR _rank = RANKX(ALL('Table'), [count], , DESC, Dense)
RETURN
IF(_rank <= 5, [Product], "others")
3.Here, we need to recalculate the number of Customers per Product based on the category names from the previous step.
Customercount = CALCULATE(COUNT('Table'[Customer]), ALLEXCEPT('Table', 'Table'[Product1]))
4.In this step I will explain how to create the tooltip.
I created Page2 and then changed that Page to Tooltip in Format -> Canvas Setting -> Type
Putting the breakdown data to be displayed into a table visualization. It's worth noting that you can achieve the desired effect in the Tooltip table without the Product field, but I chose to put in the Product field for readability.
Putting the breakdown data to be displayed into a table visualization. It's worth noting that you can achieve the desired effect in the Tooltip table without the Product field, but I chose to put in the Product field for readability.
Up to this point, the basic Tooltip is complete, but it is not possible to achieve the effect that Product is categorized as "others" and the Tooltip is empty.
5.Next we'll create a Measure to implement the effect of the tooltip being empty when the product is categorized as "other".
Measure =
VAR _product = CALCULATE(MAX([Product]), FILTER('Table', [Product] = [Product1]))
RETURN
IF(MAX([Product1]) = "others", 0, 1)
Put the measure into the visual-level filters, set up show items when the value is 1.
Summary:
This method can be used when you have a summary page and want to view specific details on the summary page.
Author: Xinyi X.
Reviewer: Ula and Kerry
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https://www.glassdoor.co.in/Interview/You-have-a-100-coins-laying-flat-on-a-table-each-with-a-head-side-and-a-tail-side-10-of-them-are-heads-up-90-are-tails-QTN_290837.htm | 1,611,781,473,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610704832583.88/warc/CC-MAIN-20210127183317-20210127213317-00743.warc.gz | 795,512,684 | 59,637 | Apple Interview Question: You have a 100 coins laying f... | Glassdoor.co.in
## Interview Question
Software Engineer Interview Cupertino, CA (US)
# You have a 100 coins laying flat on a table, each with a
head side and a tail side. 10 of them are heads up, 90 are tails up. You can't feel, see or in any other way find out which side is up. Split the coins into two piles such that there are the same number of heads in each pile.
Tags:
programming, coins
75
Answer #1: Place 50 coins into two piles on its edges so that both have the same amount of heads in each pile, neither facing up or down.
Answer #2: Trick question, place 50 coins in both piles and in theory they all have heads just not necessarily facing up or down.
Luis Marquez on 22-Jun-2012
17
agree with 2nd ans
Anonymous on 23-Jun-2012
162
Split into two piles, one with 90 coins and the other with 10. Flip over every coin in the pile with 10 coins.
Anonymous on 09-Jul-2012
24
Just split into two piles, each with 50 coins. The question only asks 50 heads in each one, it doesn't ask for the number of heads up!!!
JianMin on 29-Aug-2012
8
Pick 10 coins from the pile, flip it and put it in the other pile. This will ensure that the number of heads up are equal in both the piles
Anonymous on 16-Jan-2013
83
Pick 10 coins from the original 100 and put them in a separate pile. Then flip those 10 coins over. The two piles are now guaranteed to have the same number of heads. For a general solution of N heads and a total of M coins:
1.) Pick any N coins out of the original group and form a second pile.
2.) Flip the new pile of N coins over. Done.
Example (N=2, M=6):
Original group is HHTTTT (mixed randomly). Pick any two of these and flip them over. There are only three possible scenarios:
1: The two coins you picked are both tails. New groups are {HHTT} {TT} and when you flip the 2nd group you have {HHTT} and {HH}.
2.) The two coins you picked consist of one head and one tail. New groups are {HTTT} and {HT} and when you flip the 2nd group you have {HTTT} and {TH}.
3.) The two coins you picked are both heads. New groups are {TTTT} and {HH} and when you flip the 2nd group you have {TTTT} and {TT}.
ishapiro on 28-Mar-2013
6
The question says "'You' can't feel, see or in any other way find out which side is up....' Can a team member? Cooperate with a fellow engineer, or other colleague, who can see the coins to solve the problem?
JennS on 28-Jul-2013
4
Question has its answer in it...
90 coins are tail down..... so it means all 90 coins are head up....
Now, all you have to do is to split it into half. 50/50
Gagan on 29-Jul-2013
6
Let's generalise the question to where there are n heads and any number of tails on the table.
Select any n coins. This set will contain m heads, where m is between 0 and n inclusive, and n - m tails. The other n - m heads will be in the remaining coins.
We now have two piles: the selection of n coins with n-m tails and the remainder with n-m heads. All we have to do is flip the selection so that the n-m tails become n-m heads, the same number as the heads in the remainder.
This is a straightforward extension of the 'pick any 10 coins and flip' answer correctly given above by several people.
Bootlebarth on 29-Jul-2013
4
All of you are over thinking it. Read the last bloody line,
"Split the coins into two piles such that there are the same number of heads in each pile"
They're not asking for the heads to be up or down, just an equal amount & every coin has a head side so dividing the pile equally achieves that.
2
100 coins total, 10 of them are heads up, 90 are tails up. Meaning all of them are heads up AND tails down. Split it 50/50 and you are done.
Daniel on 08-Aug-2013
7
It is not as easy as to just split it. And it says heads UP tails UP.
Given 10 h, 90 t. Pick some random 10 coins call it P1. Rest is P2.
In P1, (10-x) heads, (x) tails
In P2, (x) heads, (90-x) tails
Flip the coins in P1.
In P1, (x) heads and (10-x) tails
P1 and P2 have the same number of heads.
Shafiq on 01-Nov-2013
19
trev on 20-Feb-2014
1
I agree to trev, don't think anyone read the question.
Anonymous on 02-Aug-2014
0
we already have 2 piles --> 90 coins with tails up and 10 coins with heads up, just flip over 10 of the coins from 90 coins that have tails up, we will have same number of coins with heads up in each pile.
bugaboo on 27-Feb-2015
1
get all coins in your hands, shake them, drop them.
for each coin there is a 50% probability to lay heads up, and 50% probability for tails down. now split i half
paninies on 11-Apr-2015
0
question doesn't need to look faces of which side is up after splitting it in two piles. split all coins in two part of 50 50 and they all have heads ...and thats what questioner asking..!
Kamal Bharakhda on 14-Apr-2015
0
and move them to the 10-coin pile.
Take 40 coins from 90-coin pile, flip them over on 09-May-2015
0
Take 40coins from 90-coin pile, flip them over and move to the 10-coin pile.
Anonymous on 09-May-2015
2
It's really depends on whether Apple is hiring Software Engineers who are collaborators, mathematicians or tricksters. It's clear that Apple does hire Engineers who listen to the question accurately.
Anonymous on 18-Jun-2015
2
Make two groups at random for 10 and 90 coins.
Example:-
G1(10) G2(90)
case 1:- 6H,4T 4H,86T
case2:- 3H,7T 7H,83T
Now flip all coins of smaller group G1(10). The result will always have same Heads in each pile.
G1(10) G2(90)
case 1:- 6T,4H 4H,86T
case2:- 3T,7H 7H,83T
Anonymous on 19-Jul-2015
0
We just get 5 coins head up put in each piles ==> we get the same number of head up in each pile. They just ask we "Split the coins into two piles such that there are the same number of heads in each pile" . They didn't say that we don't kow what is coin head up and they mixed together.
Tam on 16-Sep-2015
1
"The question says "'You' can't feel, see or in any other way find out which side is up....' Can a team member? Cooperate with a fellow engineer, or other colleague, who can see the coins to solve the problem?"
This is the best answer yet! Completely out of the box answer and yet so simple.
The M on 03-Oct-2015
0
Flip every other coin, 90 Tails will get split into 45 Heads and 45 Tails. Similarly 10 Heads will get converted to 5 Head and 5 Tails, so now we have 50 heads (45 + 5) and 50 tails (45 + 5). Then just split them into two equal groups.
Saurabh Pandit on 17-Nov-2015
0
Tom on 18-Nov-2015
2
Make a pile of 10 and flip them over. Then the number of heads is equal in both piles.
Patrick on 19-Nov-2015
0
question says both group should have equal heads, but doesnt specifiy, it should be up, hence, just grouping 50 each would solve the problem
Panchaxari on 19-Jan-2016
0
This is a screw you question, but yeah if you take out 10 coins you can have anywhere between 0-10 heads for every head you have you have one less head in the other pile and one less tail in your pile of 10 coins.
So if you have 100 coins 10 heads and you take lets say 10 coins
1 heads, 9 tails. The 90 coins has 9 heads (you stole one when selecting 10 coins).
2 heads, 8 tails. The 90 coins has 8 heads (same you stole 2 when selecting 10 coins ect).
This stands true for any pile that you know the amount of one category and 2 options, If you know you have 25 of one things, despite how many things there are if each thing had only two options like heads or tails, you know selecting 25 of them the same amount you know of one thing that when taking out 25 or the equal number of what you know of one thing is in there that what you unsucessfully try to filter out is the inverse of what you selected successfully to take out.
Graham on 19-Feb-2016
0
Pick 10 coins, flip them and form a separate pile. The no.of tails in both pile will be equal inspite of your choice being a tails up coins or a heads up coins. Coz when u pick a tails up coin u r reducing the no.of tails up in the first pile and since u flip it its gonna b a heads up coin the second pile, if u r picking up a heads up a coin u turn it into a tails up coin in the second pile so that it can cancel out one tails up coin in the existing first pile.
Anonymous on 13-May-2016
1
If it means heads up then separate the coins into one pile of 90 one pile of 10 then flip the ten coins it works with all scenarios Of sides you ended up choosing also like to point out that we can't feel them so we probably can't use our hands to flip them but I assume they would allow us to use something as how else would we separate them
James on 07-Oct-2016
0
The answer lies in the exact wording of the question "Split the coins into two piles such that there are the same number of heads in each pile. " It does not specify heads need to be face up, so you would simply split the piles in 50 each and you have the same number of coins with heads in each pile.
Paul Ricci on 27-Mar-2017
0
Take ten coins (consider as one pile, Pile A and other 90 coins as another pile, Pile B).
Now you have two piles. Turn all coins as in pile A, you will end up with same number of heads in both piles.
Ex: Scenario 1: Consider in Pile A, there are 2 heads and 8 tails. Hence in Pile B there will 8 heads.Now when you turn all the coins in Pile A you will end with 8 heads in Pile A.
Hence both Pile A and Pile B have same number of heads.
Scenario 2: Consider in Pile A, there are 10 heads. Hence in Pile B there will be 0 heads.Now when you turn all the coins in Pile A, you will end with 0 heads in Pile A.
Hence both Pile A and Pile B have same number of heads.
Scenario 3: Consider in Pile A, there are 0 heads. Hence in Pile B there will be 10 heads.Now when you turn all the coins in Pile A, you will end with 10 heads in Pile A.
Hence both Pile A and Pile B have same number of heads.
Vamshi Nandan on 18-May-2017
0
Take 10 coins.Split into two piles of 5 each.Flip all coins in one pile.Both piles now have equal heads and tails.Take another 10 and go through the same procedure.Follow the same process for the entire original pile.You end up with two sets of 5 piles having equal no. of heads and tails.Combine all 5 piles on each side and it's done.
Anonymous on 22-Nov-2017
0
Its very simple.
step 1
take group of 10 coins from all
now flip this pile
how?
lets see cases
100 total ( 10 H + 90T)
so you get group of 10 from them
so lets assume you will get 4 h+6T , and (6H + 84T)
then flip this smaller one
new group will be 4T+ 6H
so now we 2 groups 1 new 1 old
4t+6h and 6h+85T
both have same number of heads ....
Vinay Mahipal on 13-Mar-2019
1
LITERAL ANGLE
Split 50/50. Both piles have the same number of heads. Parameters do not require each pile to have the same number of heads facing upward.
TEAMWORK ANGLE
Ask the most efficient, skilled coin identification analyst at Apple to identify the coins so the skilled sorting robot can separate the piles equally.
PATRONIZING ANGLE
Take a picture of the table with your iPhone and sending to a laborer hired to come sort for you via a services app in the app store.
NEXT LEVEL QUANTUM ANGLE
If the coins are in no way observable, the question is impossible to answer because the coins are sitting next to Schrodinger's cat and thus are in a state of both heads and tails until observed.
Tevyn on 27-Mar-2019
One or more comments have been removed. | 3,137 | 11,369 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.828125 | 4 | CC-MAIN-2021-04 | latest | en | 0.934665 |
https://resources.wolframcloud.com/FunctionRepository/resources/SpliceAt/ | 1,701,906,436,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100626.1/warc/CC-MAIN-20231206230347-20231207020347-00283.warc.gz | 543,749,875 | 11,037 | Function Repository Resource:
# SpliceAt
Splice expressions at certain positions
Contributed by: Nikolay Murzin
ResourceFunction["SpliceAt"][expr,{e1,e2,…},pos] splices expressions ei at position pos of expr. ResourceFunction["SpliceAt"][expr,{p1→{e11,e12,…},p2→{e21,e22,…},…}] splices expressions eij at corresponding positions pi. ResourceFunction["SpliceAt"][{e1,e2,…}, pos] represents an operator form that can be applied to an expression. ResourceFunction["SpliceAt"][{p1→{e11,e12,…},p2→{e21,e22,…},…}] represents an operator form with rules.
## Examples
### Basic Examples (3)
Splice a list of expressions inside another expression:
In[1]:=
Out[1]=
Splice at multiple positions:
In[2]:=
Out[2]=
Splice with rules:
In[3]:=
Out[3]=
### Scope (3)
Use Unevaluated to prevent premature evaluation:
In[4]:=
Out[4]=
Use RuleDelayed to delay evaluation for rules:
In[5]:=
Out[5]=
Use operator forms:
In[6]:=
Out[6]=
In[7]:=
Out[7]=
### Properties and Relations (4)
In most cases, SpliceAt is just equivalent to Insert with Sequence:
In[8]:=
Out[8]=
In[9]:=
Out[9]=
But Insert will not work at deeper than first level inside held arguments:
In[10]:=
Out[10]=
While SpliceAt works as expected:
In[11]:=
Out[11]=
Also Insert does not support multiple insertions, while SpliceAt does:
In[12]:=
Out[12]=
### Possible Issues (2)
Root position is invalid:
In[13]:=
Out[13]=
In[14]:=
Out[14]=
## Version History
• 1.0.0 – 19 April 2022
## Author Notes
Main motivation was to splice inside held arguments | 461 | 1,557 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2023-50 | latest | en | 0.647931 |
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In addition to adhering to the policies and guidelines of the State Department of Education, the successful instructor will be responsible for instruction in the appropriate teaching environment and evaluates student learning.
will be responsible for instruction in the appropriate teaching environment and evaluates
will be responsible for instruction in the appropriate teaching environment and evaluate
is responsible for instruction in the appropriate teaching environment and evaluate
is being responsible for instruction in the appropriate teaching environment and for evaluating
is responsible for instructions in the appropriate teaching environment and will be evaluating
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In addition to adhering to the policies and guidelines of the State Department of Education, the successful instructor will be responsible for instruction in the appropriate teaching environment and evaluates student learning.
will be responsible for instruction in the appropriate teaching environment and evaluates
will be responsible for instruction in the appropriate teaching environment and [will] evaluate - CORRECT
is responsible for instruction in the appropriate teaching environment and evaluate
is being responsible for instruction in the appropriate teaching environment and for evaluating
is responsible for instructions in the appropriate teaching environment and will be evaluating
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13 Aug 2010, 02:10
'the successful instructor' is singular, E looks good for me.
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13 Aug 2010, 03:58
the answer is B. E is wrong because the verb tense is not consistent.
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13 Aug 2010, 07:35
But, how is "evaluate" parallel with "will be"
And. shouldn't it be evaluates since "instructor" is singular???
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13 Aug 2010, 07:41
bibha wrote:
But, how is "evaluate" parallel with "will be"
And. shouldn't it be evaluates since "instructor" is singular???
Same doubt is haunting me since i saw this question!
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14 Aug 2010, 11:36
Hey All!
There's nothing I like weighing in on more than a good parallelism question. Fun! This one is quite confusing because it's not possible to know WHERE the parallelism starts. It could start after "for" (i.e. "I'm responsible for my brother and my kids."), or it could start after "will be" ("I will be king of the world and a rock star!"). Or it could start after "will" (I will buy a car and go home). Because we don't know, we have to take each answer one by one. What we do know is that the SECOND item in the list is "evaluates/evaluate/evaluating" (because it comes after the parallel marker), so we need to match to that.
In addition to adhering to the policies and guidelines of the State Department of Education, the successful instructor will be responsible for instruction in the appropriate teaching environment and evaluates student learning.
will be responsible for instruction in the appropriate teaching environment and evaluates
PROBLEM: The parallel starts after "will" ("I will buy a car and drive home in it.") "Be responsible" and "evaluates" have matching tenses, but "evaluates" doesn't match ("the instructor will...evaluates" is wrong).
will be responsible for instruction in the appropriate teaching environment and evaluate
ANSWER: Same as above, except "evaluate" fits with the parallel.
is responsible for instruction in the appropriate teaching environment and evaluate
PROBLEM: "evaluate" doesn't go with the subject, so no parallel there. It also can't match instruction, because it's a verb.
is being responsible for instruction in the appropriate teaching environment and for evaluating
PROBLEM: the "being" is wrong and unparallel.
is responsible for instructions in the appropriate teaching environment and will be evaluating
PROBLEM: The change in tense is unjustifiable here. "is responsible" and "will be evaluating" should be in the same tense (there's no good reason to change. You ARE allowed to change tense in parallel if there's a good reason ("Yesterday I went to the store and tomorrow I will go again"), but there isn't one here). But we're describing two things the teachers have to do, so they should be in the same tense. In correct answer choice B, the "will" DISTRIBUTES to both verbs.
Oooo. It's an ugly correct answer choice, but I feel confident it's the best of the bunch. Hope that helps!
-tommy
BTW. Remember that if you're in the present tense, the singular form of the verb has an "s" on the end (He evaluates). But if you are in the future tense, the rule changes (He will evaluate).
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### Show Tags
14 Aug 2010, 13:34
TommyWallach wrote:
Hey All!
There's nothing I like weighing in on more than a good parallelism question. Fun! This one is quite confusing because it's not possible to know WHERE the parallelism starts. It could start after "for" (i.e. "I'm responsible for my brother and my kids."), or it could start after "will be" ("I will be king of the world and a rock star!"). Or it could start after "will" (I will buy a car and go home). Because we don't know, we have to take each answer one by one. What we do know is that the SECOND item in the list is "evaluates/evaluate/evaluating" (because it comes after the parallel marker), so we need to match to that.
In addition to adhering to the policies and guidelines of the State Department of Education, the successful instructor will be responsible for instruction in the appropriate teaching environment and evaluates student learning.
will be responsible for instruction in the appropriate teaching environment and evaluates
PROBLEM: The parallel starts after "will" ("I will buy a car and drive home in it.") "Be responsible" and "evaluates" have matching tenses, but "evaluates" doesn't match ("the instructor will...evaluates" is wrong).
will be responsible for instruction in the appropriate teaching environment and evaluate
ANSWER: Same as above, except "evaluate" fits with the parallel.
is responsible for instruction in the appropriate teaching environment and evaluate
PROBLEM: "evaluate" doesn't go with the subject, so no parallel there. It also can't match instruction, because it's a verb.
is being responsible for instruction in the appropriate teaching environment and for evaluating
PROBLEM: the "being" is wrong and unparallel.
is responsible for instructions in the appropriate teaching environment and will be evaluating
PROBLEM: The change in tense is unjustifiable here. "is responsible" and "will be evaluating" should be in the same tense (there's no good reason to change. You ARE allowed to change tense in parallel if there's a good reason ("Yesterday I went to the store and tomorrow I will go again"), but there isn't one here). But we're describing two things the teachers have to do, so they should be in the same tense. In correct answer choice B, the "will" DISTRIBUTES to both verbs.
Oooo. It's an ugly correct answer choice, but I feel confident it's the best of the bunch. Hope that helps!
-tommy
BTW. Remember that if you're in the present tense, the singular form of the verb has an "s" on the end (He evaluates). But if you are in the future tense, the rule changes (He will evaluate).
Excellento! I was swayed by the fact that there is the singular instructor and I should go with the singular verb - evaluates, though it did not sound right.. I guess will be takes on future so that leaves us with evaluate. What about subject-verb match though? I guess it matches in B.
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22 Sep 2010, 19:30
thanks for a great explanation, Tommy!
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23 Sep 2010, 01:26
B it is... Thanks for the explanation Tommy
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# Biomechanics
Ovid: Oncology and Basic Science
Editors: Tornetta, Paul; Einhorn, Thomas A.; Damron, Timothy A.
Title: Oncology and Basic Science, 7th Edition
16
Biomechanics
Frederick W. Werner
Some Basic Biomechanical Terms
• Force (load): A force is an action on a body. It has a direction and a magnitude.
• Oblique forces:
A force being applied at some angle to a coordinate system can be
represented as two perpendicular or orthogonal forces in that
coordinate system.
• Magnitude of the oblique force on the implant is the square root of the sum of the squares of the perpendicular forces (Fig. 16-1).
• Graphically, the force on the implant is the hypotenuse of the right triangle formed by the perpendicular forces.
Figure 16-1 Vector addition of two orthogonal forces to obtain the force, F. A force is represented by drawing either an arrow or line over the letter corresponding to that force.
• Examples: shoulder joint (Fig. 16-2) and knee joint (Fig. 16-3)
• Dynamic forces: Dynamic forces include the effect of the inertia of the person moving or an impact on an object against another.
Figure 16-2 Example of force decomposition in the shoulder joint. The deltoid force, Fd, is represented (decomposed) as a compressive force, Fc, and a shearing or tangential force, Fs. (Adapted from Buckwalter JA, Einhorn TA, Simon SR, eds. Orthopaedic Basic Sciences, 2nd ed. Chicago: American Academy of Orthopaedic Surgeons, 2000.)
P.368
Figure 16-3 Example of calculation of forces in the knee joint. The patellofemoral joint reaction force, Freaction, is the vector parallelogram sum of the quadriceps force, Fquad, and the patellar tendon force, Fpat.
• Example of normal walking gait:
During gait, the forces on the knee joint are due to the weight of the
person, the muscles causing the knee to move, the ligamentous
structures that provide stability, and the inertia of the person as the
heel strikes the floor and as he or she pushes off before toe off.
• Moment: A
moment is defined as a force being applied at some distance away from
some pivot point. Its magnitude is the force times the moment arm.
• Moment calculation:
If several moments are being applied to a bone or some object in
equilibrium, then the sum of those moments about a given point is equal
to zero.
Figure 16-4 Calculation of moments about a pivot point, 0. In a static, nonmoving situation, the sum of the vertical forces equal 0, and the sum of the moments about a pivot point equal 0. (Adapted from Buckwalter JA, Einhorn TA, Simon SR, eds. Orthopaedic Basic Sciences, 2nd ed. Chicago: American Academy of Orthopaedic Surgeons, 2000.)
Figure 16-5 After a knee patellectomy, the moment arm for the knee extension moment is decreased. Therefore, the quadriceps force required to extend the knee has to be larger than before patellectomy. (Adapted from Nordin M, Frankel VH, eds. Basic Biomechanics of the Musculoskeletal System, 2nd ed. Philadelphia, Lea & Febiger, 1989.)
• Examples: using a see-saw (Fig. 16-4), the knee joint (Fig. 16-5)
• P.369
• Torques: A
torque is typically caused by a twisting motion such as opening ajar.
There is an equal but opposite torque required to resist the torque
being applied to open the jar.
• Torque = applied force × the moment arm
• Units: Forces
are typically measured in Newtons (N). Moments and torques are measured
in Newton-meters (N-m) or Newton-millimeters (N-mm).
Kinematics
Kinematics is the study of how things move. Motions can
be viewed as displacements (translations), as rotations, or as a
combination of them. A person or object might be moving at a constant
velocity or with a changing velocity, in which case it is accelerating
or decelerating.
• Velocity: The
rate (speed) and direction of movement of an object, such as a car
moving down the road. The magnitude of the velocity is the distance or
displacement of the object per unit time.
• Acceleration and deceleration: If the speed of that object, or its direction, is changing, then the object is either accelerating or decelerating.
• Center of rotation:
For most joints in the body, one can find a center of rotation about
which the bone is rotating. For example, door hinges are the fixed
center of rotation for a rotating door. In the knee joint and many
others, the center of rotation is not fixed but changes through the
range of knee flexion.
• 3D center of rotation:
In the knee joint as well as in other joints in the body, the motion is
not necessarily planar. As the knee flexes and extends, tibial rotation
and ab/adduction cause the center of rotation to move in three
dimensions.
Mechanical Properties of Materials
• Stress: A force applied to an implant or bone will cause a stress in the material.
• Stress = applied force divided by the area over which the force is being applied (typical units are N/mm2)
• Strain: When
a force or stress is applied to some implant or bone, there will be a
small deformation. To normalize that deformation, a strain is computed.
• Strain = change in length (AL) divided by the original length (Lo); typical units are mm/mm
Plot of the resultant forces due to an applied displacement to a
structure such as a bone or ligament. It can also be a plot of the
force applied to a structure to produce a displacement.
• Structural properties
Figure 16-6 Example of a force—displacement loading curve for a linear, elastic structure.
• Stiffness: slope of the linear portion of the force—displacement curve
• Yield point: force at which the structure starts to plastically (permanently) deform
• Maximum force: maximum force the structure can support
• Energy: area under the force—displacement curve
• Stress—strain curve (Fig. 16-7): A stress—strain curve is computed from a force-displacement curve.
• Material properties
• Elastic modulus: slope of the linear portion of the curve
• Proportional limit: force at the end of the linear part of the curve
• Yield point: force at which the material starts to plastically deform
• Ultimate strength (tensile strength if in tension, compressive strength if in compression): maximum stress the material can support
Figure 16-7 Example of a stress-strain loading curve for a linear, elastic material.
• P.370
• Toughness: area under the stress—strain curve
• Ductility:
the ultimate strain (strain at rupture) for a material undergoing
inelastic deformation. Intuitively, how much a deforming material
stretches or deforms before breaking. This is typically described as a
percent elongation or reduction of area.
• Fatigue properties:
at forces and moments that are far less than the maximum force due to
the single application of a force. Most implants fail in fatigue.
• Endurance limit: the maximum stress that can be applied an infinite number of times and the material will not fail
• Nonlinear materials (Fig. 16-8):
A material that has an initial nonlinear loading curve (i.e., does not
have a straight-line relationship between force and displacement or
between stress and strain)
• Toe-in region:
Region at the beginning of a typical force—displacement or
stress—strain curve in which the flatness of the curve reflects
considerable displacement or strain with the initial application of
very little force or stress. For example, little force is required to
cause initial displacement in a ligament as the fibers straighten.
• Viscoelastic material properties: Creep and stress relaxation of materials (Fig. 16-9)
True of almost all biological tissues, especially ligaments, cartilage,
and polymeric biomaterials. Their properties change with the speed at
Figure 16-8 Example of a nonlinear material. Under initial loading, there is some initial laxity as the material starts to elongate. This region of the curve is known as the toe-in region, followed by a linear region where there is a linear elongation response to the applied force. (Adapted from Buckwalter JA, Einhorn TA, Simon SR, eds. Orthopaedic Basic Sciences, 2nd ed. Chicago: American Academy of Orthopaedic Surgeons, 2000.)
Figure 16-9 Creep and stress relaxation material behavior. (From Mow VC, Hayes WC. Basic Orthopaedic Biomechanics. New York: Raven Press, 1991;203.)
• Creep deformation: Under constant load, deformation continues with time until a plateau is reached.
• Stress relaxation:
After a sudden but then constant deformation, the stress in the
material beneath the deformation will gradually decrease until a
plateau is reached.
• Wear of materials (Fig. 16-10)
• Three-body wear: Particulate material between adjoining surfaces causes abrasion or accelerated loss of surface integrity.
• Three-body wear is encountered when bone cement or bone particles abrade the polyethylene
P.371
surface in an implanted hip prosthesis, or when ceramic particles
released from certain femoral head trunion designs accelerate wear and
loosening of the implant.
Figure 16-10 Material wear.
• Abrasive wear: One or both of the adjoining surfaces with an uneven texture cause loss of material from the surfaces during movement.
• Abrasive wear accelerates the destruction
of the natural articular surface when cartilage becomes thin or
subchondral bone is exposed, resulting in “bone on bone.” In artificial
joints, irregularities (asperities) in metal components due to
• Adhesive wear: Portion of one material is in contact with irregularities on opposing material, causing them to adhere to each other.
• Adhesive wear is an important early wear
mechanism. Ultra-high-molecular-weight polyethylene acetabular cups
have shown such wear leading to formation of a secondary socket and
distortion of mechanical function in total hip joint replacements.
• Fatigue wear:
Material is removed from articulating surfaces after repetitive
excessive stresses cause minute fracturing of the surface layer.
• Fatigue wear generally occurs as a late
failure mechanism. For example, if a polymer component in a joint
prosthesis is too thin, local stresses exerted by a metal component on
the polymer may be greater than with a thicker layer. After many cycles
the fatigue limit of the polymer can be exceeded, leading to cracking
and surface failure of the polymer.
• Hardness: The resistance to surface deformation by indentation or scratching
• Scratching hardness is commonly quantified using the Mohs original scale:
• Diamond =10, talc = 1, aluminum = 2 to 3, steels = 5 to 8
• Indentation hardness is quantified by using either a Brinell hardness or Rockwell hardness scale.
Behavior of Simple Structures
• Tension: causes material to elongate
• Compression: causes material to compress (shorten)
• Bending: causes compression on one side, tension on other side of material
• Shear: tends to cause distortion of one portion of the material relative to another portion, parallel to the direction of loading
• Torque: causes material to twist
• Three-point bending (Fig. 16-11): produced by a combination of three parallel forces applied at different points on the structure
Figure 16-11 Three-point bending. An implant or bone can be exposed to three-point bending by having an intermediate force centrally located and supported by two end supports.
• Four-point bending (Fig. 16-12): produced by a combination of four parallel forces applied at different points on the structure
• Bending stresses:
If a bone is exposed to bending, one side of the bone experiences
tensile stresses, while the other experiences compressive stresses.
• The magnitude of either stress is:
Stress magnitude = δ = Mc/I
• where M is the moment, c is the distance
from the center of the beam or bone where there are no stresses, and I
is the moment of inertia (a descriptor of the beam or bone’s
cross-sectional shape to resist bending; see below).
• Moment of inertia (Fig. 16-13):
The moment of inertia of a bone, structure, or implant is a
characteristic of its cross-sectional geometry and represents the
resistance to bending. For simple cross-sections, this property can be
easily computed. The bending moment of inertia, for example, increases
with the diameter of the bone raised to the fourth power.
• Torsional stresses:
Torques applied to a bone or beam may cause a torsional spiral
fracture. In a beam, the torsional stresses are greatest at the largest
radius from the center of the beam.
Stress magnitude = τ = Tc/J
Figure 16-12 Four-point bending. An implant or bone can be exposed to four-point bending. Here the distance between the two intermediate forces is the same as the distance to the end supports.
P.372
Figure 16-13 Cross-sectional views and the corresponding moments of inertia.
• where T is the applied torque, c is the distance from the neutral axis, and J is the polar moment of inertia (see below).
• Polar moment of inertia (Fig. 16-14):
The polar moment of inertia of a bone, structure, or implant is a
characteristic of its cross-sectional geometry. It represents the
structure’s resistance to twisting under torsional load. For simple
cross-sections, the polar moment property can be easily computed. The
polar moment of inertia of a long bone increases as the diameter raised
to the fourth power. Small changes in the size can have profound
changes in torsional strength.
Figure 16-14 Cross-sectional views and the corresponding polar moments of inertia. | 3,100 | 13,444 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2024-30 | latest | en | 0.88608 |
https://differencess.com/go-back-n-protocol-vs-selective-repeat-protocol-whats-the-difference/ | 1,675,878,069,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00170.warc.gz | 219,980,806 | 26,906 | # Go Back N Protocol Vs Selective Repeat Protocol: What’s the Difference?
Copywriting is an essential skill for any business, and with the ever-growing popularity of online marketing, it’s also becoming more important than ever for businesses to have good copy. But what’s the difference between the two copywriting protocols? And which one is better for your business? Let’s take a look.
## What is the Go Back N Protocol?
The Go Back N Protocol (GBN) is an algorithm used to determine the next node to be processed in a tree or graph. The GBN algorithm is based on a simple rule: If the current node has a parent that is not the root, then go back one more step in the tree or graph and process that parent. This process continues until the root is reached, at which point the process starts over from the beginning with a new root.
The Selective Repeat Protocol (SRP) is an algorithm used to determine the next node to be processed in a tree or graph. The SRP algorithm is based on a simple rule: If the current node has a parent that is not the root, then repeat the same process as for finding the GBN algorithm, but only consider nodes that are children of the current node. This process continues until there are no more children, at which point the SRP algorithm begins again from the root.
There are several advantages and disadvantages of each algorithm. The GBN algorithm is generally faster than the SRP algorithm because it does not have to repeat any calculations when processing nodes that are children of a previous node that was not processed by the GBN algorithm. However, if there are
## What is the Selective Repeat Protocol?
The Selective Repeat Protocol (SRP) is a retransmission protocol used in TCP known as a congestion control algorithm. The SRP is designed to help avoid unnecessary retransmissions of data that has been received but not yet acknowledged by the receiver. The SRP works by only sending data once it has been confirmed by the receiver. This helps to avoid congestion and improve overall performance.
## Background
Selective Repeat Protocol (SRP) is a reliable, adaptive and secure back-up protocol for communicating between nodes in a distributed system. SRP is based on the concept of selective repeat messages, which are sent by an initiator to a node requesting that the node send a repeat message. The node then sends back a repeat message with the same sequence number but with a different data payload.
Go Back N Protocol (GBN) is a reliable and adaptive back-up protocol for communicating between nodes in a distributed system. GBN is based on the concept of gobacks, which are sent by an initiator to a node requesting that the node send it a goback message. The node then sends back an acknowledgment message containing the sequence number of the last received goback message.
## How Do They Work?
The Go Back N protocol and the Selective Repeat protocol are two different ways that a router can send periodic updates to a destination. The Go Back N protocol sends multiple updates at a time, while the Selective Repeat protocol sends just one update at a time.
The main difference between the two protocols is how they handle situations where the data that needs to be sent is larger than the number of packets that can be sent in one batch. With the Go Back N protocol, the router sends multiple batches of data until it has sent all of the data that it needs to send. With the Selective Repeat protocol, the router only sends one batch of data at a time.
Both protocols have their own advantages and disadvantages. The Go Back N protocol is better at handling large amounts of data, while the Selective Repeat protocol is better at sending only one batch of data at a time.
## Advantages of Go Back N Protocol vs Selective Repeat Protocol
When it comes to data storage and retrieval, there are a few main protocols in use. One of these is the Go Back N protocol, which is usually used when large amounts of data need to be stored or retrieved. The selective repeat protocol is another protocol that can be used for data storage and retrieval. Here, only certain pieces of data are repeated multiple times. Which one is better? Here are the advantages of using the Go Back N protocol:
-It’s efficient: With the Go Back N protocol, only the necessary data is stored or retrieved. This means that fewer resources are used overall, which can save money on storage costs or time spent retrieving information.
-It’s reliable: The Go Back N protocol is generally reliable, which means that data retrieval will be successful most of the time. This is especially important when large amounts of data are being stored or when sensitive information is being retrieved.
-It’s versatile: The Go Back N protocol can be used with a number of different applications and devices, making it easy to find a use for it.
The advantages of using the selective repeat protocol are as follows:
-It’s efficient: With the selective repeat protocol, only the information that is needed is repeated. This means that more data can be stored or retrieved in a shorter amount of time, which can be important when resources are limited or when retrieving information is urgent.
-It’s reliable: The selective repeat protocol is generally reliable, meaning that data retrieval will be successful most of the time. This is especially important when large amounts of data are being stored or when sensitive information is being retrieved.
-It’s versatile: The selective repeat protocol can be used with a number of different applications and devices, making it easy to find a use for it.
## Disadvantages of Go Back N Protocol vs Selective Repeat Protocol
When it comes to patient care, it’s important to have a protocol in place. And, when discussing protocols, it’s important to understand the difference between Go Back N Protocol and Selective Repeat Protocol. Here are a few of the key disadvantages of each:
Go Back N Protocol:
1. It can be time-consuming.
2. It requires more communication between nurses and patients.
3. It can be disruptive to the patient’s routine.
Selective Repeat Protocol:
1. It is less time-consuming than Go Back N Protocol.
2. It does not require as much communication between nurses and patients.
3. It is less disruptive to the patient’s routine.
## What is the N protocol?
The N protocol is a selective repeat protocol. It is used when the sender wants to communicate with a receiver that is located either at the same host or on a different host but still within the same network. The N protocol assumes that the receiver will know how to handle the repeated messages.
## What is the Selective Repeat Protocol?
The selective repeat protocol is a mechanism used by some routers to allow traffic to flow back through the network if it experiences an error. This protocol works by sending periodic “query” packets out the network, and waiting for a response before forwarding the packet again. If no response is received after a certain period of time, the router assumes that the traffic has been lost and decides to discontinue forwarding it.
## The Difference between the N and Selective Repeat Protocols
There are a few key differences between the N and Selective Repeat Protocols, which you should be aware of if you’re considering using one over the other. Here’s a breakdown:
1. The N protocol sends a message every time it detects a change, while the selective repeat protocol only sends a message when there is a change that it considers significant. This can result in faster scanning, but it can also lead to missed changes.
2. The N protocol sends all changes at once, while the selective repeat protocol delays sending changes until they are deemed important. This can lead to more accurate detection, but it can also create lag time for users when changes occur.
3. The N protocol requires more overhead than the selective repeat protocol, which can impact performance.
## Why Use a Protocol?
When looking to improve the performance of a network, one of the most common solutions is to implement a protocol. A protocol is simply a set of rules that are used to communicate between two or more devices. Protocols can be used for a variety of purposes, such as improving the speed and reliability of communications. When choosing which protocol to use, it’s important to understand the differences between the two most popular options: Go Back N and Selective Repeat.
## Conclusion
If you’re new to the world of weightlifting, it can be confusing trying to figure out which type of training protocol is right for you. To make things a little bit easier, I’ve put together this article comparing the two main types of training protocols: go back N and selective repeat. Hopefully, this will help you determine which style of training is best suited for your goals and current level of fitness. Thanks for reading! | 1,775 | 8,920 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2023-06 | longest | en | 0.96177 |
https://scicomp.stackexchange.com/questions/29133/applying-neumann-boundaries-to-crank-nicolson-solution-in-python/29134 | 1,718,815,616,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861828.24/warc/CC-MAIN-20240619154358-20240619184358-00651.warc.gz | 456,811,460 | 40,363 | # Applying Neumann boundaries to Crank-Nicolson solution in python
Consider the heat equation $$u_t = \kappa u_{xx}$$ with boundary conditions of $$u(x,0)=0\\ u(0,t)=100\\ u(l,t)=0$$ Numerical analysis by pyton can be done with
import numpy as np
import matplotlib.pyplot as plt
from scipy.sparse import diags
def Crank_Nicolson(dy,ny,dt,nt,k,T,ntout):
Tout = []
T0 = T[0]
T1 = T[-1]
s = k*dt/dy**2
A = diags([-0.5*s, 1+s, -0.5*s], [-1, 0, 1], shape=(ny-2, ny-2)).toarray()
B1 = diags([0.5*s, 1-s, 0.5*s],[-1, 0, 1], shape=(ny-2, ny-2)).toarray()
for n in range(1,nt):
Tn = T
B = np.dot(Tn[1:-1],B1)
B[0] = B[0]+0.5*s*(T0+T0)
B[-1] = B[-1]+0.5*s*(T1+T1)
T[1:-1] = np.linalg.solve(A,B)
if n % int(nt/float(ntout)) == 0 or n==nt-1:
Tout.append(T.copy())
dt = 0.01
dy = 0.001
k = 10**(-4)
y_max = .1
y = np.arange(0,y_max+dy,dy)
ny = len(y)
nt = 1000
T = np.zeros((ny,))
T[0] = 100
Tout,s = Crank_Nicolson(dy,ny,dt,nt,k,T,10)
for T in Tout:
plt.plot(y,T)
plt.show()
How a Neuman boundary such as $$u_x(l,t)=0$$ can be implemented in this code?
This a case of keeping one end of a bar at temperature 100 °C while the other end is insulated.
• is there a typo in the first set of BC (missed $_x$) for the $u(l,t)$? Commented Mar 24, 2018 at 16:25
• @AntonMenshov no, it's $\partial u/\partial x = 0$ at $x=l$ Commented Mar 24, 2018 at 16:29
• You have both $u(l,t)=0$ and $u_x(l,t)=0$ at the same time? That sounds strange. Commented Mar 24, 2018 at 16:32
• @AntonMenshov the former is the boundary condition, which has been used in the code. I want to replace it with the latter condition to modify the code. Commented Mar 24, 2018 at 16:34
• Oh got it. At this moment, you have Dirichlet $u(l,t)=0$ and you want to change it to Neumann $u_x(l,t)=0$. Becuase the combination is also possible - that's Robin BC. Commented Mar 24, 2018 at 16:35
One standard technique, which will work well in your case is to introduce an additional conceptually virtual degree of freedom or "ghost" point lying at $x=l+\Delta x$, then apply the model equation at $x = l$ in the form $$\frac{du(l)}{dt}=\kappa(l)\frac{u(l+\Delta x)-2u(l)+u(l-\Delta x)}{{\Delta x}^2}$$ as well as boundary condition at $x = l$, in the form $$\frac{u(l+\Delta x,t)-u(l-\Delta x,t)}{2\Delta x} = 0.$$
Note that there is no explicit equation applied at $x=l+\Delta x$, so there are still as many equations as unknowns, so the system remains well posed. In fact, most practical implementations rearrange the boundary condition into the form $$u(l+\Delta x)=u(l-\Delta x),$$ and just substitute back into the previous equation to get $$\frac{du(l)}{dt}=\kappa(l)\frac{2u(l-\Delta x)-2u(l)}{{\Delta x}^2}.$$. | 960 | 2,673 | {"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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2024-26 | latest | en | 0.808021 |
www.spinningtrnava.com | 1,600,902,968,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400212959.12/warc/CC-MAIN-20200923211300-20200924001300-00088.warc.gz | 226,517,830 | 15,873 | ## The Equation And Basic Concepts In Accounting
Understanding the basic equation of accounting is the relationship between assets, debts, and capital owned by a company. The purpose of the basic accounting equation is the basis for recording in the accounting system which means that every time a transaction occurs must be recorded in two aspects, they are assets and liabilities. A professional Accountant surely understands this outside of his head.
The basic equation in accounting is the balance between the asset side and the liability side. If changes occur due to financial transaction events, then the balance must also be maintained. This is the basis for being able to do accounting such as keeping a journal and presenting financial statements.
To make it easier for you to learn to account, you must understand the concept of ALOE. By using the ALOE concept you will more easily learn the basic concepts of accounting. Following is the explanation from ALOE.
A = Assets
L = Liabilitias
O E = Owner’s Equity
The following basic accounting equations that apply based on the ALOE concept, earlier:
Assets = Liabilities + Capital
Assets themselves are assets were as an economic source that has a use-value for the organization or company. While the obligation consists of debt which is a liability. In addition, there is a business owner’s equity or business capital with the difference between the liability of the business owner in the future.
Before learning more, an accountant must first understand the meaning of an account. the account is an important element in the recording. The account itself serves as a form for recording similar transactions and can change the composition of assets, liabilities, and also venture capital making it easier for an accountant to prepare reports.
According to Financial Accounting Standards, accounts have two types;
– Real accounts: accounts recorded on the balance sheet include assets, liabilities, and also capital;
– Nominal account: the account that is recorded on the profit/loss statement which includes income and expenses.
Each account owns its number along with its balance. The account name is usually followed by the account number and also the normal balance. A normal balance is a balance that places an account in a debit or credit position.
## Considering Size And Look Of Apartment Furniture
A number of facilities in an apartment like Ola are likely considered into crucial aspects so that some people eventually decide to live in an apartment. Some facilities in an apartment really matter to some people that are about to live in an apartment. With a number of facilities, they expect that they can live conveniently. In addition, they do not have to spend a lot of money to cover the maintenance cost of those facilities. In fact, they can collectively cover the cost along with other people that live in the apartment. You can just imagine how much you have to spend per month if you live in a house with a number of facilities.
Meanwhile, it is not few that feel reluctant to live in an Ola apartment as they worry that they will not feel convenient due to limited space. In fact, if you want to look up some tips to live conveniently in an apartment, you probably get inspired to do the same. For instance, it is much recommended for you to consider size and looks of furniture to avoid your apartment to look narrow. You should avoid bringing some big furniture items as those possibly lead your apartment to look less spacious.
If you have a lot of spare time, you may utilize it for cleaning your Ola house. Some small parts like faucets and sinks are necessary to clean up. As every space of your house looks clean, you must be quite happy to stay at home. You can polish faucets or tiny mini-fridges to look shiny. People that use the faucets must feel convenient as you always clean and polish them regularly. There are many people that really do not care about cleaning their faucets until the faucets are in issues which require you to repair and even replace them.
## Simple Things To Socialize In A New Environment
You certainly know the expression neighbor is the closest relative. When we are experiencing difficulties in the condominium, of course, the neighbors who first approached and helped. Therefore, maintaining good relations with neighbors is certainly very important. When moving to a new place to stay, there are definitely plenty of things to do besides cleaning up the condominium to make it ready for habitation. One important thing is to build good relations in the new condominium environment. You will find amazing neighborhoods at kent ridge hill residences. There are various groups living here from full-time workers, business people, to foreign nationals who have businesses or jobs in Singapore. Here are a few simple tips that will help you blend in with the new condominium environment.
• Greet Everyone
This one is very simple. You certainly don’t know all the new neighbors in your place of residence. Feel free to greet everyone you see. If you feel difficulty greeting with a call, show a smile with polite and friendly gestures. This will dilute your interactions with new neighbors.
• Participate in Environmental Activities
In a residential environment, of course, there are various social activities. You need not hesitate to participate in activities like this. Participate in positive activities that make you more familiar with neighbors and build better relationships.
• Avoid annoying things
Sometimes trivial things in the neighborhood can lead to conflict. Playing music too loud, heating a vehicle for a long time, or making noise when working with your tools are a few examples. Living in a social environment means that you must consider the presence of other citizens in action. Always try to avoid things that might be disturbing to avoid misunderstandings with other residents.
• Invite Neighbors To Visit Your Residence
In addition to introducing you and your family, this method also aims to strengthen your relationship with local residents. By inviting all neighbors, you are showing good intentions to establish good relations with local residents. If there are neighbors who refuse, you can understand because they all have their own activities. Be part of the residents of kent ridge hill residences who are friendly and caring for neighbors.
## Scheduling Regular Repair For Your House
The inflation rate of materials to build a house is likely to be one of the strong reasons why many people even have to come to the bank to buy a house in an installment. As they think that it takes a lot of years to eventually be able to afford the costs of building a house, buying a house in the installment method must bring more advantages. You can hedge the inflation rate by buying a house through installment. Some of you may still be idealistic not to buy a house through installment, but you should ensure that you have a lot of money. Instead, you can find some second houses with affordable prices but you may still have to hire a professional team like Calgary home renovations.
You are supposed to take care of your house regularly. By this way, it is possible for you to avoid your house from some serious damages that possibly cost you a lot.
## A Broken Laptop Can Still Be Beneficial For Its Owner
Generally damaged laptops provide a dilemma for their owners. This is because actually a damaged laptop is still beneficial. Not to mention the old data in mind even though it is too expensive to fix it. However, if you want to repair it with good quality at an affordable price, we suggest you go to Computer Repair Tulsa.
But you don’t need to worry. These are some ways to use broken laptops:
Made it into a PC screen
If the broken LCD, hinges, keyboard, or other external parts, you can make it a monitor screen only. Simply capitalize on the Bluetooth keyboard and you already have a PC at home.
Turn it into an external hard drive
Even though your laptop is damaged, its hard drive can still be useful. Take the hard drive and use it as an external hard drive. You need to add a little to the cost of the case.
Sell the parts
In the worst case, you can sell your laptop parts. Whether it’s the screen, the motherboard, the memory, and so on. Don’t forget to delete the data on your hard drive.
Humane mouse trap friendly for your home. This is sheltered to use in your home on the off chance that you have a newborn child or pet. It is more secure than utilizing the mouse stick trap or the mouse snap trap where it’s conceivable that your youngster or pet will stall out in the snare or hurt themselves when the snare triggers. With the mouse trap compartment, your kid or pet won’t get hurt.
Humane mouse trap not untidy or coldhearted. This is certifiably not a muddled occupation. It is likewise not a coldhearted method to dispose of your rodent pervasion. You don’t need to tidy up the blood or dispose of a dead rodent as you would with different snares. Rodent droppings. The hindrance of utilizing this is the rodent will pee and leave rat droppings for you to tidy up. With the goal that at that point turns into an untidy activity yet it’s superior to tidying up blood and dead rodents.
## Tips for Choosing a Fine IT Company
First of all, a dependable IT support company will always respond to emerging problems. Expect the top quality when you’ve chosen such a company. It doesn’t matter when the emergency case happens. A trusted company will always make sure that your company’s IT management will always be supported, so your business can run smoothly without any technical problem. Get the best web development companies in Singapore on our website.
## These Can Be Some Causes Of Buzzing Ears
Buzzing ears occur when fine hair cells in the ear are damaged. The fine hairs function to receive sound waves and convert them into electrical signals. Furthermore, the auditory nerve in the ear will deliver these electrical signals to the brain. In the brain, the electrical signals are then translated into the sounds we hear. When fine hairs are damaged, the auditory nerve will send random electrical signals to the brain, causing ears to ring. If this happens to you, we recommend you try sonus complete supplement formula.
Conditions that affect the ear
Most of the ear buzzing is caused by the following conditions:
Meniere’s disease, which is a disorder in the ear that can cause vertigo to hear loss.
Injuries to the head and neck that affect the auditory nerve or the part of the brain that is connected to the hearing function.
Eustachian tube dysfunction or the ear canal that is connected to the throat can be due to pregnancy, obesity, or radiotherapy.
Tension in the muscles in the inner ear, for example, due to multiple sclerosis.
Earwax is too much, so it accumulates and hardens in the ear canal.
Hardening of the bones in the middle ear (otosclerosis), which is caused by abnormalities in bone growth.
Benign tumors in the nerve connecting the brain and ears, which control balance and hearing (acoustic neuroma).
Disorders of blood vessels
In rare cases, buzzing ears can be caused by disorders of blood vessels, for example:
Tumors that compress blood vessels in the head or neck.
Impaired blood flow due to narrowing of blood vessels in the neck.
Abnormal blood vessels connected to each other.
Cholesterol buildup in the blood vessels near the middle and inner ear.
High blood pressure.
Drug side effects
Some drugs can cause or worsen tinnitus, especially if taken in high doses. Sometimes, the tinnitus disappears after stopping taking this drug. A number of these drugs are:
Antibiotics, including erythromycin and neomycin.
Drugs for cancer, such as methotrexate and cisplatin.
Diuretic drugs, such as furosemide.
Antidepressants.
Aspirin.
Quinine.
## Want To Lose Weight In 7 Days? Here Is The Way
Having a slim and ideal body is everyone’s dream. But to have a slim and ideal body certainly requires process and effort. Quite often many women are willing to spend a lot of money to take classes in sports or to buy slimming drugs to lose weight. Besides using the wellness review site, you can use this method to get the ideal body for one week.
1. Breakfast
To lose weight in seven days, you need to maintain your breakfast consumption, because the diet doesn’t mean you don’t need breakfast. How to lose weight you can do by choosing a healthy breakfast such as oats, fruits, and low-fat yogurt. Also, how to lose weight can be done by eating eggs and vegetables for your breakfast, such as by making omelets, scrambled eggs, and so on.
2. Morning Snacks
Maintaining the consumption of morning snacks is also one way to lose weight in seven days which is quite effective and you can follow. The trick is to eat as much fruit as you want when you feel hungry. You can also do this way to lose weight by combining several kinds of fruits to be made into salads or smoothies.
3. Lunch
For lunch, you can add a little protein from tuna or chicken. You can also add olive oil and lemon to your food. This way to lose weight also encourages you to stay away from foods that contain bad fats like processed cheese and pasta. Instead, you can eat foods that contain good fats such as avocados or sweet potatoes.
4. Lunch snacks
If you feel hungry, then you can follow how to lose weight in these seven days. To get rid of your hunger before your dinner time, you can tuck in the afternoon snacks like by consuming fruits and seeds.
5. Dinner
For dinner, you can eat a salad of vegetables and fruits that are equipped with beets or avocados. Can with a piece of chicken breast or a can of salmon. You can also try sweet potato dishes or a little wheat pasta. Choose foods that are still fresh and new
6. Drinks
How to lose weight naturally is certainly inseparable from the consumption of drinks that enter the body. To do this diet, you need to consume lots of water. At least 2 liters of water every day. Also, this way to lose weight allows you to consume herbal tea or coffee.
## Water Damage Can Become Catasthrope But Don’t Worry Now You Can Contact Profesionals To Fix It
Water damage can do quite wreck your happy home, it also can destroy remnants of memories and possessions that are hard to exchange . You don’t want to deal with the emotions and disappointment that comes from having to live with this situation. Instead of wallowing in grief while you struggle to work out what you ought to do, so as to undertake and salvage what you’ll , contact the water damage restoration service professionals and allow them to help guide you and confirm that your home are often restored first call restoration crew.
You don’t need to be at an obstacle due to the moisture that eroded the inspiration of your home. You can still save your property and live a cheerful life once it’s restored. You can avoid having to foot the bill for all of the repairs and renovations which will got to be done. If you would like to possess a peace of mind and a few security against blemishes and catastrophes that are the results of excessive moisture, confirm you’ve got an honest water damage insurance policy. Don’t just let that policy collect dust until you would like it. It is important that you simply are well versed in what to try to to should the unexpected occur. Look over your policy and red things thoroughly. Make sure you understand everything. Don’t hesitate to contact your insurer if you meet something you do not understand. Make sure that the coverage you’ve got is enough and covers everything you would like to guard .
Contact water damage restoration service that specialize in water damage. It is an honest idea for you to screen several and obtain conversant in their staff and their services. Try to find several companies that have a superb for handling this sort of situations. Not only should they need an honest reputation within the industry, they ought to even have plenty of happy and satisfied customers who are willing to vouch for them. You want to possess a minimum of three companies on your speed dial that you simply can contact at any time if you ever need them.
While you’ll never be truly prepared for any catastrophes which will happen to your property, you’ll have safeguards in situ which will provide you with enough coverage to give you some peace of mind. Water damage restorations companies can prevent plenty of cash and stop you from losing one among your most valued possessions.
First Call Restoration Crew
Suite 402/447 Kent St Sydney NSW 2000
(02) 8311 7377
## Obesity Could Cause Brain Disorder
Obesity has become the number one killer in America so you need to be really careful when you know that you keep gaining weight and have no time in exercise. Make sure that you get the diet program because this program is proven to be the most effective way to lose weight. It contains the foods and supplements that you need to eat in order to lose weight naturally and safely. The fat flusher diet also is a perfect method for you who are looking for the quickest way to lose weight and avoid obesity.
Obesity is a condition in which the body has a lot of fat content, causing the body to be obese or overweight. Actually, everyone is required to have a certain amount of fat to store energy and others. However, if the amount is excessive, then hoard fat can harm the body’s metabolism. Clinically, a person can be said to be obese when a person’s weight is 15% heavier than their ideal weight. Grouping obesity others are also classified as follows:
– Mild obesity, overweight reached 20% to 40%.
– Obesity was, overweight reached 41% to 100%.
– Severe obesity, overweight is more than 100%.
Being overweight or obese is not just affecting a wide waist, but the effect is worse. A number of serious health problems, a danger that can occur due to obesity:
Brain Disorder
According to recent research, there are a number of cases of obesity that are harmful to the brain. As reported by My Health News Daily, that obesity can affect the brain such as the following:
– Addiction to eat, because, according to obesity research can automatically change your diet. So if this is the case, then the weight will increase because of the brain need to be satisfied by its main food is sweet and fatty.
– Change the performance of the immune system, inflammatory risk to be increased. Then this will affect the inflammation of the brain and destroyed several parts so that the mood is changing that it is difficult to break the habit of excessive eating.
## Apa Saja Keuntungan Yang Didapat Dengan Menggunakan Colocation Server?
Perusahaan yang harus mengelola data perusahaan dalam jumlah besar tentunya menggunakan jasa layanan dari colocation server. Hal ini dikarenakan colocation server akan membantu untuk mengelola data dengan jumlah besar tersebut dan menjamin akan keamanannya. Tapi, apakah kamu tahu apa itu CBTP dan apa saja keuntungannya?
Istilah dalam bidang teknologi yang semakin maju pun semakin banyak. Salah satunya adalah colocation server ini yang merupakan tempat atau rak yang mana memiliki fungsi sebagai wadah untuk server dalam sebuah data center. Tentunya dengan menggunakan rak ini akan membantu banyak dalam kelancaran suatu perusahaan bekerja. Nah, salah stu keuntungan yang sangat membantu adalah dengan cepat menerima laporan kerusakan yang terjadi sedini mungkin. Dengan begitu, perusahaan bisa bergerak lebih cepat pula untuk segera menyelesaikan kerusakan yang terjadi. Atau bahkan bisa segera menyiapkan adanya rencana cadangan untuk mencegah kerusakan lainnya yang kemungkinan akan terjadi secara tiba-tiba. Hal ini akan membuat perusahaan memiliki down time yang bisa untuk diminamilisir.
Bagaimana dengan keuntungan lainnya?
Menggunakan layanan dari penyedia jasa colocation server ini tentunya memiliki banyak keuntungan lainnya. Yang pertama adalah perusahaan akan menjadi lebih hemat biaya karena biaya yang dikeluarkan hanya untuk mendapatkan bandwith atau koneksi layanan internet yang tinggi menjadi lebih hemat. Terlebih dibandingkan dengan perusahaan yang membuat sendiri.
Kemudian keuntungan lainnya adalah teknologi dan sistem yang ditawarkan oleh penyedia jasa layanan ini maju dan terstruktur. Dalam hal ini juga berlaku pada adanya pemadaman, sehingga nantinya penyedia jasa layanan ini yang akan membayar pembangkit listrik agar server milik perusahaan tetap aman dan terjaga.
Keamanan server data miliki perusahaan yang jelas aman. Hal ini dikarenakan penyedia jasa layanan akan menyediakan sistem keamanan yang tinggi terhadap setiap data server yang dititipkan, terlebih untuk data server perusahaan dalam jumlah yang besar.
Nah, terakhir, layanan ini memberikan server selama 24 jam penuh tanpa non stop. Layanan ini bekerja untuk menghindari dari permasalahan yang terjadi atau jika pun terjadi kecelakaan maka bisa segera terselesaikan.
Melihat berbagai keuntungannya, anda sudah tidak perlu ragu lagi untuk menggunakan layanan penyedia jasa colocation ini. | 4,400 | 21,123 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2020-40 | longest | en | 0.968725 |
https://hoogle.haskell.org/?hoogle=map%20-package%3ACabal%20-package%3Abase%20-package%3Atext%20-package%3Adlist%20-package%3Aaeson%20-package%3Abytestring%20-package%3Avector%20-package%3Acase-insensitive | 1,660,921,689,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882573699.52/warc/CC-MAIN-20220819131019-20220819161019-00410.warc.gz | 287,996,695 | 35,102 | # map -package:Cabal -package:base -package:text -package:dlist -package:aeson -package:bytestring -package:vector -package:case-insensitive
Map a function over all values in the map.
```map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]
```
map f s is the set obtained by applying f to each element of s. It's worth noting that the size of the result may be smaller if, for some (x,y), x /= y && f x == f y
Map a function over all values in the map.
```map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]
```
map f s is the set obtained by applying f to each element of s. It's worth noting that the size of the result may be smaller if, for some (x,y), x /= y && f x == f y
O(n) map f xs is the ShortByteString obtained by applying f to each element of xs.
O(n) map f xs is the ShortByteString obtained by applying f to each element of xs.
Transform this map by applying a function to every value.
Transform this set by applying a function to every value. The resulting set may be smaller than the source.
```>>> HashSet.map show (HashSet.fromList [1,2,3])
HashSet.fromList ["1","2","3"]
```
Apply a transformation to all values in a stream. Subject to fusion
Apply a transformation to all values in a stream. Subject to fusion Since 0.3.0
Combinator for the <map> element. Example:
```map \$ span \$ toHtml "foo"
```
Result:
```<map><span>foo</span></map>
```
Apply a function to each element of a Stream, lazily
map f xs is the list obtained by applying f to each element of xs, i.e.,
```map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
map f [x1, x2, ...] == [f x1, f x2, ...]
```
```>>> map (+1) [1, 2, 3]
[2,3,4]
```
Generates a map using a Range to determine the length. This may fail to generate anything if the keys produced by the generator do not account for a large enough number of unique items to satify the required map size.
Apply a function to all values flowing downstream
```map id = cat
map (g . f) = map f >-> map g
```
Map a function over a NonEmpty stream.
Fold pairs into a map.
Maps a pure function over an InputStream. map f s passes all output from s through the function f. Satisfies the following laws:
```Streams.map (g . f) === Streams.map f >=> Streams.map g
Streams.map id === Streams.makeInputStream . Streams.read
```
Standard map on the elements of a stream.
```>>> S.stdoutLn \$ S.map reverse \$ each (words "alpha beta")
ahpla
ateb
``` | 694 | 2,431 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2022-33 | latest | en | 0.821113 |
https://www.esaral.com/q/solve-the-following-systems-of-equations-80716 | 1,726,743,439,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700652028.28/warc/CC-MAIN-20240919093719-20240919123719-00324.warc.gz | 688,242,263 | 11,798 | # Solve the following systems of equations:
Question:
Solve the following systems of equations:
$\frac{1}{2(x+2 y)}+\frac{5}{3(3 x-2 y)}=\frac{-3}{2}$
$\frac{5}{4(x+2 y)}-\frac{3}{5(3 x-2 y)}=\frac{61}{60}$
Solution:
The given equations are:
$\frac{1}{2(x+2 y)}+\frac{5}{3(3 x-2 y)}=-\frac{3}{2}$
$\frac{5}{4(x+2 y)}-\frac{3}{5(3 x-2 y)}=\frac{61}{60}$
Let $\frac{1}{x+2 y}=u$ and $\frac{1}{3 x-2 y}=v$ then equations are
$\frac{1}{2} u+\frac{5}{3} v=-\frac{3}{2} \ldots$$\ldots(i) \frac{5}{4} u-\frac{3}{5} v=\frac{61}{60}$$. .(i i)$
Multiply equation $(i)$ by $\frac{3}{5}$ and equation $(i i)$ by $\frac{5}{3}$ add both equations, we get
Put the value of $u$ in equation $(i)$, we get
$\frac{1}{2} \times \frac{1}{3}+\frac{5}{3} v=-\frac{3}{2}$
$\Rightarrow \frac{5}{3} v=-\frac{10}{6}$
$\Rightarrow v=-1$
ThenĀ
$\frac{1}{x+2 y}=\frac{1}{3}$
$\Rightarrow x+2 y=3$$\ldots(i i i)$
$\frac{1}{3 x-2 y}=-1$
$\Rightarrow 3 x-2 y=-1$...$(i v)$
Put the value of $x$ in equation (iii) we get
$\frac{1}{2}+2 y=3$
$\Rightarrow y=\frac{5}{2}$
$\Rightarrow y=\frac{5}{4}$
Hence the value of $x=\frac{1}{2}$ and $y=\frac{5}{4}$. | 502 | 1,142 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.625 | 5 | CC-MAIN-2024-38 | latest | en | 0.378451 |
https://math.stackexchange.com/questions/3321136/integrating-fx-frac1x-over-1-1 | 1,566,788,145,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027330962.67/warc/CC-MAIN-20190826022215-20190826044215-00011.warc.gz | 558,785,216 | 32,424 | # Integrating $f(x) = \frac{1}{x}$ over $[-1,1]$
I am reading a book where it says that improper integral $$\int_{-1}^{1}\frac{1}{x}\,dx$$ is undefined because $$\lim_{b \to 0^-}\int_{-1}^{b}\frac{1}{x}\,dx + \lim_{b \to 0^+}\int_{b}^{1}\frac{1}{x}\,dx$$ are unbounded.
I wonder, is it just a deficiency of definition of improper integral or is it universally accepted among mathematicians that $$\int_{-1}^{1}\frac{1}{x}\,dx$$ is undefined?
Function is odd, so in my opinion it is intuitively clear that this integral should be equal to $$0$$. Are there other definitions of integral that assign value of $$0$$ to this expression?
• $\infty-\infty$ is what is known as an indeterminate form. – Cheerful Parsnip Aug 12 at 15:19
• @Cheerful Parsnip See please better the question. – Michael Rozenberg Aug 12 at 15:20
• @CheerfulParsnip, I understand that, but in my opinion this integral should be equal to $0$, because it is logically appealing – Markoff Chainz Aug 12 at 15:21
• To answer your second question: Yes, see 'Cauchy Principal Value Integral' – projectilemotion Aug 12 at 15:22
• @JohnColtraneisJC: "Logically appealing" counts for a lot. It's one of the things that inform which definitions and axioms we bother to spend effort studying. – Henning Makholm Aug 12 at 15:25
In fact, behind your question, there is a very interesting mathematical "character" which is
$$PV \left( \frac{1}{x} \right).$$
We could avoid it, remaining with classical analysis tools as in this question whose interest is to introduce the concept of (Cauchy) Principal Value (abbreviated as "PV").
But the best way to attack rigorously this issue is to define it as a "distribution" in the framework of... "distribution theory", through its action on a generic "test function" $$\varphi$$ :
$$PV \left( \frac{1}{x} \right)(\varphi) := \lim_{\varepsilon\to 0} \int_{|x|>\varepsilon} \left( \frac{1}{x} \varphi(x) \right) dx$$
• the "shrinking hole" $$(-\varepsilon,\varepsilon)$$
• the fact that integral bounds are $$[-\infty,\infty)$$ (not limited to $$[-1,1]$$). See (https://en.wikipedia.org/wiki/Cauchy_principal_value).
There are different "logically appealing" ways to handle the mathematical object "$$PV \left( \frac{1}{x} \right)$$" :
• as the limit when $$\varepsilon \to 0$$ of odd functions defined by : $$f_{\varepsilon}(x):=\frac{x}{\varepsilon^2+x^2},$$
an astute way to overcome singularity $$x=0$$ !
In particular $$\int_{[-a,a]}f_{\varepsilon}(x)dx=0$$, whatever $$a>0$$...
• as the derivative of the even function $$\log|x|$$ (this one having the two "passports" : "ordinary function" and "regular distribution") (Derivative of ln|x| is the principal value of 1/x. Distribution Theory.).
• through its Fourier Transform,
$$\widehat{PV \left( \frac{1}{x} \right)} = -i\pi\,\text{sign} (\xi)$$
Remark : Distribution PV $$\left( \frac{1}{x}\right)$$ behaves, apart from properties due to singularity $$0$$, as ordinary function $$1/x$$. Thus we can await a differentiation formula generalizing $$(1/x)'=-1/x^2$$. Here it is :
$$\left(PV \left( \frac{1}{x} \right)\right)' = -FP \left( \frac{1}{x^2} \right)$$
(Derivative of principal value distribution $1/x$ is equal to finite part distribution $-1/x^2$?) where FP is for "Finite Part", a concept introduced by Hadamard in classical analysis which is different from the "Principal Value" concept. See for that (https://www.ntu.edu.sg/home/mwtang/hypersie.pdf). | 1,037 | 3,436 | {"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": 24, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2019-35 | latest | en | 0.868589 |
https://www.azom.com/article.aspx?ArticleID=3214 | 1,607,006,295,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141727782.88/warc/CC-MAIN-20201203124807-20201203154807-00013.warc.gz | 478,435,243 | 30,224 | Volume and Density Definitions and Determination Methods
There are a number of manual and automated methods for determining volume and density. This article, however, focuses on laboratory methods that are most often used in research and quality control applications.
Another large area of application is on-line monitoring in production control.
The Density Enigma
When first introduced to density, perhaps in grade school, we were taught that it simply is the mass of an object divided by its volume. We thought that was pretty much the whole story, but sooner or later we discovered that this definition was only the beginning. The difficulty in defining density is exemplified by the American Society for Testing and Materials’ book of standard definitions where one finds over forty definitions based on mass per unit volume. The British Standards Institute has narrowed it down to fourteen types of densities.
Volume Determination and Definition
Determining the mass of an object is rather straightforward; it is the determination of volume that conceals the difficulty. The ‘volume’ of a solid object, whether a single piece or a mass of finely divided powder, is one of those concepts that can’t be bundled up into a single, neat definition.
A layman’s dictionary typically defines volume in vague terms such as ‘the space occupied by an object.’ McGraw-Hill’s Dictionary of Scientific and Technical Terms expands only slightly on that definition, offering “A measure of the size of a body or definite region in three dimensional space….”
One must consult a particle technology’s lexicon to appreciate the various conditions under which volume is defined. Two sources for these definitions are the British Standards Institute (BSI) and the American Society for Testing and Materials (ASTM). Here one finds that the ‘volume’ of a material is the summation of several rigorously defined elemental volumes.
Volume and Density of A Brick
A common masonry brick will serve as a good example of an object that contains all types of elemental volumes and differs in material volume according to the measurement technique, measurement method, and conditions under which the measurements are performed.
A brick obviously is composed of solid material and it has a volume that can be calculated after measuring its length, width, and thickness.
Surface Irregularities, Small fractures, Fissures and Pores
However, it also contains surface irregularities, small fractures, fissures, and pores that both communicate with the surface and that are isolated within the structure. Voids that connect to the surface are referred to as open pores; interior voids inaccessible from the surface are called closed or blind pores.
Surface irregularities compose another type of void volume. For example, assume the bulk volume of the brick is determined from linear measurements of its length, width, and thickness. It generally is understood that the value of volume determined in this way is limited in accuracy because the surfaces are not perfect. If a perfect plane were to be laid on one of the surfaces, there would be many voids sandwiched between the two surfaces. For lack of a standard definition, this will be referred to as ‘external void volume’ and will refer to the void volume between solid surface and that of a closely fitting envelope surrounding the object.
It does not include pores that penetrate the interior of the particle. The meaning of the term is admittedly vague, but this volume can be determined or, at least, estimated under certain analytical conditions and can provide an indication of surface roughness. Figure 1 demonstrates the concept.
Figure 1. A straightedge placed along the edge of a brick demonstrates the concept of ‘external volume,’ the volume contained by virtue of surface irregularities.
When a solid material is in granular or powdered form, the bulk contains another type of void: interparticle space. The total volume of interparticle voids depends on the size and shape of the individual particles and how well the particles are packed.
Table 1 provides ‘standard’ definitions for volume in consideration of these elemental volumes. Figure 2 illustrates the bases for the differences between various volume definitions.
Table 1. Definitions of various types of volumes. BSI = British Standards Institute, ASTM = American Society for Testing and Materials.
Solid Material Volume Open Pore Volume Closed Pore Volume Inter - particle Void Volume External Void Volume Absolute powder volume: (also called Absolute volume): The volume of the solid matter after exclusion of all the spaces (pores and voids) (BSI). X Apparent particle volume: The total volume of the particle, excluding open pores, but including closed pores (BSI). X X Apparent powder volume: The total volume of solid matter, open pores and closed pores and interstices (BSI). X X X X Bulk volume: The volumes of the solids in each piece, the voids within the pieces, and the voids among the pieces of the particular collection (implied by ASTM D3766). X X X X X Envelope volume: The external volume of a particle, powder, or monolith such as would be obtained by tightly shrinking a film to contain it (BSI). The sum of the volumes of the solid in each piece and the voids within each piece, that is, within close-fitting imaginary envelopes completely surrounding each piece (Implied by ASTM D3766; see Table 2). X X X X X X X X X Geometric volume: The volumes of a material calculated from measurements of its physical dimensions. X X X X X Skeletal volume: The sum of the volumes of the solid material and closed (or blind) pores within the pieces (Implied by ASTM D3766). X X True volume: Volume excluding open and closed pores (implied by BSI). X Void: Space between particles in a bed (BSI). X
Figure 2. Illustration of various volume types. At the top left is a container of individual particles illustrating the characteristics of bulk volume in which interparticle and “external” voids are included. At the top right is a single porous particle from the bulk. The particle cross-section is shown surrounded by an enveloping band. In the illustrations at the bottom, black areas shown are analogous to volume. The three illustrations at the right represent the particle. Illustration A is the volume within the envelope, B is the same volume minus the “external” volume and volume of open pores, and C is the volume within the envelope minus both open and closed pores.
Three volume definitions, those of apparent powder volume, bulk volume and envelope volume, have subtle differences. Apparent powder volume is most rigidly defined. It is the sum total of the four volumes indicated by the column headings in Table 1. Bulk and tap densities are obtained from bulk and tap volumes, which are apparent powder volumes obtained under specified conditions. Usually, this involves placing the powder into a rigid container of specific dimensions while taking specific steps to control compaction. In the case of a monolithic sample, bulk volume may be calculated from dimensional measurements or by displacement of some medium in which it is immersed.
Difference Between Envelope and Bulk Volumes
The difference between envelope and bulk volumes often is unclear. As can be seen in Table 1, ASTM’s definition of envelope volume must be inferred from their definition of envelope density in Table 2. It implies that the definition pertains only to a single particle, while BSI’s definition encompasses a particle or a monolith (singular implied), and a powder (by definition, a collection of fine particles).
Table 2. Definitions of various types of densities that follow from the volume definitions of Table 1. BSI = British Standards Institute, ASTM = American Society for Testing and Materials.
Solid Material Volume Open Pore Volume Closed Pore Volume Inter - particle Void Volume External Void Volume Absolute powder density: The mass of powder per unit of absolute volume (BSI). X Apparent particle density: The mass of a particle divided by its apparent (particle) volume (BSI). X X Apparent powder density: The mass of a powder divided by its apparent volume (BSI). X X X X Bulk density: (also called Bulk powder density): The apparent powder density under defined conditions (BSI). The mass of the particles divided by the volume they occupy that includes the space between the particles (ASTM D5004). The ratio of the mass of a collection of discrete pieces of solid material to the sum of the volumes of: the solids in each piece, the voids within the pieces, and the voids among the pieces of the particular collection (ASTM D3766). X X X X X X X X Envelope volume: The external volume of a particle, powder, or monolith such as would be obtained by tightly shrinking a film to contain it (BSI). The sum of the volumes of the solid in each piece and the voids within each piece, that is, within close-fitting imaginary envelopes completely surrounding each piece (Implied by ASTM D3766; see Table 2). X X X X X X X X Effective particle density: The mass of a particle divided by its volume including open pores and closed pores (BSI). X X X Envelope density: The ratio of the mass of a particle to the sum of the volumes of: the solid in each piece and the voids within each piece, that is, within close-fitting imaginary envelopes completely surrounding each piece (ASTM D3766). The ratio of the mass of a particle to the envelope volume of the particle (implied by BSI). X X X X X X X X X Skeletal density: The ratio of the mass of discrete pieces of solid material to the sum of the volumes of: the solid material in the pieces and closed (or blind) pores within the pieces (ASTM D3766). X X Tap density (also called Tap powder density): The apparent powder density obtained under stated conditions of tapping (BSI). X X X X Theoretical density: The ratio of the mass of a collection of discrete pieces of solid material to the sum of the volumes of said pieces, the solid material having an ideal regular arrangement at the atomic level (ASTM). X True density (also called True particle density); The mass of a particle divided by its volume, excluding open pores and closed pores (BSI). X
In regard to this document and others by Micromeritics, envelope volume and envelope density are defined following ASTM’s definition, that is, in terms of a single particle or monolith. Bulk properties pertain to collections of particles. A third definition, that of geometrical volume, is adopted and pertains to a volume calculated from the linear dimensions of the bulk or monolithic material.
Specific Gravity
Specific gravity, in general, is the ratio of the weight in air of a given volume of material at a stated temperature to the weight of the same volume of water (or other reference) at a stated temperature. It, therefore, is dimensionless and is sometimes expressed in the form, for example, 6.25 25/25 C. In this format, 6.25 is the specific gravity value and 25/25 °C indicates that the sample temperature was 25 ° and the reference water temperature was 25 °C. The type volume measurement used in calculating density determines the type specific gravity. For example, true specific gravity is calculated using true volume measurements. It is the ratio of the true density of the material (determined at a specific temperature) to the true density of water (at a specific temperature).
The reason for expressing the temperatures is that the density of pure, air-free water at 3.98 C is 1.00000 g/ml. This is the maximum density value; density decreases with both higher and lower temperatures. If one assumes a density of 1.000 for water at room temperature the error introduced is about 0.3%.
Using Manual Laboratory Devices
Although not a complete list, the following represents the most common methods by which volume and density are determined manually.
Pycnometry (Specific Gravity Bottles)
A pycnometer is a vessel with a precisely known volume. When one thinks of density determinations, one usually thinks of a pycnometer. Although a pycnometer is used to determine density or specific gravity, it measures volume ; a balance is used to determine mass . Manual pycnometers (glassware) typically are used to determine the density or specific gravity of liquids by filling the vessel, then weighing. Density is calculated by and specific gravity by the same equation and dividing both sides by the density of water with reference to temperature.
Essentially the same process can be used to determine the volume of an unknown, enclosed space. First the object containing the void is weighed empty. It is then filled with a liquid of known density and reweighed. The weight difference is the weight of the liquid and from these data, volume can be calculated by
As will be explained, this process is used to ‘calibrate’ sample cells used in mercury porosimetry.
Another pycnometer method is to place a quantity of a dry, pre-weighed solid sample in the pycnometer and fill the rest of the pycnometer with a liquid of known density (typically water), the weight of the pycnometer filled only with the liquid having previously been established. The density of the sample can be determined from the known density of the water, the weight of the pycnometer filled only with the liquid, the weight of the pycnometer containing both sample and liquid, and the weight of the sample. This is a common method used in characterizing soil samples.
Hydrostatic Weighing (Displacement Method)
By this method, the volume of a solid sample is determined by comparing the weight of the sample in air to the weight of the sample immersed in a liquid of known density. The volume of the sample is equal to the difference in the two weights divided by the density of the liquid.
Conversely, if the volume of a solid object is accurately known, the density of the liquid can be determined by the loss of weight of the immersed object. This is the basis for the hydrometer method (see next section).
If the sample is porous, one must determine if the pores are to be included or excluded from the volume. If they are to be included or the sample will react with the displacement medium, a sealing coating can be applied (see Bulk / Envelope Volume by Coating). If pore volume is to be excluded, the liquid must displace the air and completely fill the pores.
Various pretreatment methods are used including evacuation and boiling.
When determining volume by directly measuring the displaced volume, liquids, fine particles or gases can be used as the displacement medium. If the sample material is porous, fine particles will not penetrate into the smaller pores that water can enter. Mercury, being a non-wetting liquid, also will not penetrate pores under ambient pressure as will wetting liquids. Gases, Helium in particular, will penetrate readily into very fine pores.
Hydrometers
A hydrometer is a vertical float that measures the density or specific gravity of a liquid or liquid/solid suspension (slurry). The hydrometer, inscribed with a graduated scale along its length, sinks into the liquid until it has displaced a volume of liquid equal in weight to that of the float. Specific gravity or density is read directly from the inscribed scale at the liquid surface after buoyancy and gravitational forces equalize.
Float-Sink or Suspension (Buoyancy) Method
This method requires a liquid of known and adjustable density in which the sample is placed. The density of the liquid is adjusted until the sample either begins to sink or float, or is suspended at neutral density in the liquid.
The density of the object is then equated to that of the liquid. This method also is used to separate materials by their density.
A density gradient column is a column of liquid that varies in density with height. A sample is placed in the liquid and observed to determine at what vertical level in the column the sample is suspended. The density of the liquid at that level is the density of the sample, and that value is determined by standards of known density.
Tap Density and Vibratory Packing Density
These are very similar methods for determining the bulk density of a collection of particles under specific conditions of packing. In the former case, packing is achieved by tapping the container and in the latter by vibrating the container. The particles under test should not break up under test conditions.
Bulk / Envelope Volume by Coating
Coating the sample allows determination of bulk volume or apparent volume of solids while preventing absorption or reaction with suspension liquids.
Penetration of the coating into the open pores of the sample must be considered.
Following the referenced method, the mass of the sample is obtained. The sample is dipped into molten wax of known density. After withdrawal, any air bubbles in the wax coating are pressed out, and the coated sample is weighed. The difference in weight before and after coating is the weight of the wax, and dividing this number by the density of the wax provides the volume of wax composing the coating. The volume of the coated sample is determined by hydrostatic weighing. From this volume, the volume of wax (or other coating) is subtracted, yielding the bulk (or envelope) volume of the sample.
Volume and Density Determinations by Laboratory Analytical Instruments
The displacement method is the underlying principle used in all automated volume determining methods discussed below.
Skeletal Volume and Density by Gas Pycnometry
A gas pycnometer operates by detecting the pressure change resulting from displacement of gas by a solid object. Figure 3 helps explain the technique. An object of unknown volume Vx is placed into a sealed sample changer of known volume Vs. After sealing, the pressure within the sample chamber is measured Ps. Then, an isolated reference chamber of known volume Vr is charged to a pressure Pr, which is greater than that of the sample chamber. A value isolating the two chambers is opened and the pressure Psys of the system is allowed to equilibrate. The gas law, PV = nRT is applied to determine the volume of the unknown as follows:
Assume the system is maintained at a constant temperature T and there is no net loss or gain of gas, that is, the number of gas molecules n is constant throughout the experiment.
Figure 3. Essentials of the operation of a precalibrated gas pycnometer.
Logically, one deduces that when the valve is opened the pressure in the reference volume will fall and the pressure in the sample chamber will rise. The larger the volume of the unknown, the higher will be the final system pressure, the initial pressure of the reference chamber being the upper limit when 100 percent of the volume of the sample chamber is displaced by the unknown volume.
Mathematically, the initial condition is
Ps(Vs – Vx) + PrVr = nRT
where R is the gas constant.
After the valve is opened, the condition changes to
Psys(Vs + Vr – VX) = nRT
Ps(Vs – Vx) + PrVr = Psys(Vs + Vr – VX)
which can be solved in terms of the unknown
quantity Vx yielding,
VX = (PsysVs + PsysVr – PsVs – PrVr) / (Psys-Ps)
The accuracy and precision of the gas pycnometer in the determination of skeletal volume and density can be quite high, but relies greatly on the sample material and analysis gas being free of moisture. The sample also must be free of any volatile substances that can contribute their partial pressures and cause error and instability. For these reasons, the gas is a pure gas or dry air, and the sample is pretreated in a vacuum oven to remove volatiles. The contribution of the instrument to error is, for the most part, confined to leaks and temperature instability or temperature gradients.
Helium typically is the gas used because it readily diffuses into small pores. Other gases also are used and selected based on the size of the molecule or the way in which the gas reacts with the surface of the unknown sample.
Sometimes, the difference in results obtained when using different gases is indicative of some sought-after characteristic of the sample.
The gas pycnometer is used in a wide variety of applications and found in a number of configurations - manual and automated, single sample chamber and multi-chambered, and fixed chamber volume and multiple volume designs.
One variation of the design makes it especially suitable for the measurement of rigid, closed cell foams. The applications of this technique are not only for material volume and density, but also as a means for porosity determination as discussed in a later section. Citations to several diverse applications are found in the reference section, the materials under study being pitch, coatings, petroleum coke , cereal grain, tuff cores, volcanic soils, wool, compost, asteroids, chromatographic packing materials and cellulose powder.
Envelope Volume and Density by Displacement of a Dry Medium
The displacement technique applies to a solid object immersed in a bed of much smaller solid particles as well as in liquids and gases. The difference is in the way the displaced medium conforms to the surface of the immersed object.
A liquid can conform quite closely to the surface. Wetting liquids have the capability to fill voids and pores that communicate with the surface. Solid particles and non-wetting liquid displacement media do not invade pores and provide means by which envelope density can be determined in a controlled manner. The use of a non-wetting liquid (mercury, specifically) is discussed in the next section.
Micromeritics GeoPyc Model 1360
Micromeritics’ GeoPyc Model 1360 is the only known-of commercial instrument that automatically determines the volume and density of a solid object by displacement of a solid medium. The medium is a narrow distribution of small, rigid spheres that have a high degree of flowability and achieve close packing around the object under investigation.
The particles are sufficiently small that during consolidation they conform closely to the surface of the object, yet do not invade pore space.
Repeatability and reproducibility are achieved by a controlled method of compaction. The sample cell in which the dry medium is placed is a precision cylinder. A plunger compresses the powder as the cell vibrates; the force of compression is selectable and, therefore, repeatable from test to test. A preliminary compaction with only the displacement medium in the cell establishes a zero-volume baseline.
The object is then placed in the cylinder with the dry medium and the compaction process is repeated. The difference in the distance ht the piston penetrates the cylinder during the test and the distance h0 it penetrates during the baseline procedure (h = h0 – ht) is used to calculate the displacement volume of the medium using the formula for the volume of a cylinder of height h.
Figure 4 illustrates the process. This relatively new technique is finding applications where tap density and mercury displacement methods traditionally have been used.
Figure 4. Volume determination by the displacement of a dry medium.
Bulk, Envelope, and Skeletal Volumes and Densities by Mercury Porosimetry
Mercury is a non-wetting liquid that must be forced to enter a pore by application of external pressure. The surface tension of mercury and the interfacial tension between mercury and the solid surface results in mercury bridging the openings to pores, cracks, and crevices until sufficient pressure is applied to force entry.
For example, at atmospheric pressure, mercury will resist entering pores smaller than about 6 micrometers in diameter. When an object is surrounded by mercury, the mercury forms a closely fitting liquid envelope around the object. How closely the mercury conforms to the surface features of the object depends on the pressure applied. At some pressure, mercury begins to enter the pores, cracks, crevices, and voids of the sample. At a pressure of 60,000 psi (414 MPa) mercury has been forced to enter pores of diameters down to 0.003 micrometer. This fills essentially all pore volume in most materials.
There is a slight but important difference in the method of determining the volume of a solid object and that of a finely divided powder by mercury porosimetry. Therefore, the two forms of sample materials are considered separately in the subsequent discussion.
Monolithic Sample Material
First, consider a single lump of solid material of known mass. It is assumed that the exact volume of the sample cell has been established using the method described in a previous section on manual pycnometry. The sample cell (referred to as a penetrometer or dilatometer) containing the sample is evacuated and filled with mercury. Mercury surrounds the sample, but, at sub-ambient or near-ambient pressure, does not enter small cracks and crevices in the surface nor into pores in the structure of the material. Reweighing the filled sample containers and subtracting from this the weight of the empty sample cell plus sample, yields the weight of the surrounding mercury from which the volume of mercury is to be calculated. The difference in the volume of the empty sample cell and the calculated volume of mercury is equal to the envelope volume of the sample.
Skeletal Volume
The skeletal volume of the sample also can be determined by increasing pressure and causing the mercury to invade the open pore space. If, at maximum pressure, all open pores in the sample are filled, then the volume of mercury intruded is equal to total pore volume. This value subtracted from the bulk or envelope volume of the monolithic sample yields its skeletal volume.
If the sample contains no closed (blind) pores, then the volume measured is the true volume.
Finely grinding materials with closed pores (when appropriate) may allow true volume to be determined by making these pores accessible to the surface.
If the sample contains pores smaller than the minimum pore size into which mercury can intrude at maximum instrument pressure, then the accuracy of skeletal volume determination is affected. For these samples, skeletal volumes would be less than those obtained determined by gas pycnometry because gases such as helium and nitrogen can penetrate into micropores and small mesopores where mercury cannot. The difference in skeletal volume obtained by mercury porosimetry and that obtained by gas pycnometry indicates pore volume in the size range from the minimum size probed by mercury porosimetry down to approximately the size of the gas molecule.
Powdered or Granulated Sample Materials
In the second case where the sample material is a fine powder or granules, the procedure follows essentially the same preliminary steps as when the sample is a single piece. The difference is that there is an additional step in the interpretation and reduction of the experimental data.
A powdered sample is a bulk mass of grains; at low pressure mercury will not invade the interparticle voids. This is illustrated by Illustration A in Figure 5.
Figure 5. Mercury intrusion into pore space as pressure increases; black areas indicate mercury. A. Mercury envelops the mass. B. Mercury fills the interparticle voids. C. Mercury penetrates into the pores of the individual particles.
Initially, the mercury envelope forms around the bulk mass and not around the individual particles, so the bulk volume or envelope volume (according to the definition adopted) of the entire sample mass is displaced. Only when pressure is increased will mercury invade the interparticle space and envelope individual particles (Illustration B, Figure 5). At what pressure interparticle void filling begins (the breakthrough pressure) and the pressure at which it is completed depends on the size and shape of the particles and can be readily identified on a plot of volume intruded versus applied pressure. The indication of breakthrough is an abrupt increase in the slope of the intrusion curve and, when filling is completed, a notable decrease.
A further increase in pressure will force mercury into the voids within the individual particles (Illustration C, Figure 5). Only pores with access to the surface can be filled and any blind pores remain unfilled. Further increases in pressure can cause temporary or permanent structural changes in the sample material.
The critical points during the mercury intrusion process are illustrated in Figure 6.
Figure 6. The intrusion volume points on a mercury intrusion plot that are critical in the determination of volume and density. Point A is used to determine bulk or envelope volume, points A and B are used to determine interparticle void volume, and points A and C are used to determine skeletal volume.
When measuring volume (density) by mercury porosimeter, it should be recognized that the value obtained is pressure-dependent (porefilling dependent). Since the mercury porosimeter provides a continuous record of mercury volume change within the sample cell, the volume and density at any pressure can be determined. Typically, the volume of mercury displaced at minimum pressure and that displaced at maximum pressure (prior to deformation) are used to determine bulk (or envelope) density and skeletal density, respectively. For powders, an intermediate volume, the total volume of the grains only, may be determined.
A mercury porosimeter is seldom used solely for the determination of envelope, bulk, and skeletal volume determinations. These determinations more often are a by product of a data set that was obtained primarily for the determination of pore volume distribution by pore size.
Porosity Information Derived from Volume and Density Determinations
The subject of porosity was touched upon in the individual sections above as it relates to determining material volume. Material porosity is approached in this section as the primary physical characteristic of interest. However, only the analytical methods and techniques used to determine material volume are considered, so, by these analytical methods, porosity information is a byproduct of volume determinations and not the primary emphasis.
Table 3 contains various definitions of porosity. These are only a few examples and the same term may have slightly different meanings in different applications. For example, ASTM defines the term ‘porosity’ in over a dozen different ways.
Table 3. Porosity terms adapted from various sources including British Standards Institution, International Union of Pure and Applied Chemistry, American Society for Testing and Materials, and U.S. GeologicalSurvey.
Porosity Term Definition Interstice / Interstitial Void An opening in a rock or soil that is not occupied by solid matter (USGS) Void space between particles Macropore A pore of diameter greater than about 50nm Mesopore A pore of diameterfrom about 2nm to 50nm Micropore A pore of diameter less than about 2nm Pore diameter The diameter of a pore in a model in which the pores typically are assumed to be cylindrical in shape and which is calculated from data obtained by a specified procedure Pore volume, specific Pore volume per unit mass of material Pore volume The volume of open pores unless otherwise stated Pore, closed A cavity with no access to an external surface Pore, ink-bottle An open pore with a narrow neck Pore, open A cavity or channel with access to an external surface Porosity, effective The ratio, usually expressed as a percentage of the total volume of voids available for fluid transmission to the total volume of the porous medium Porosity, interparticle Void space between particles Porosity, intraparticle All porosity within the envelopes of individual particles Porosity, particle The ratio of the volume of open pore to the total volume of the particle Porosity, powder The ratio of the volume of voids plus the volume of open pores to the total volume occupied by the powder Porosity (a)The ratio of open pores and voids to the envelope volume (BSI) (b) The ratio, usually expressed as a percentage, of the total volume of voids of a given porous medium to the total volume of the porous medium (ASTM) Void The space between particles in a bed
Depending upon the measurement method, various types of volumes as defined in Table 1 can be determined. Obtaining two or more volume values by different methods allows extraction of porosity information by the application of simultaneous equations. The set of equations implied by Table 1 is:
Bulk Volume
VB = VS + VOP + VCP + VI + VExt
Apparent Particle Volume
VAPart = VS + VCP
Apparent Powder Volume
VAPow = VS + VOP + VCP + VI
Envelope Volume (BSI)
VE = VS + VOP + VCP + VI + VExt
Envelope Volume (ASTM)
VE = VS + VOP + VCP + VExt
VSk = VS + VCP
True Volume
VT = VS
In the above equations, VS is the volume of the solid material, VOP the volume of open pores, VCP the volume of closed pores, VI the volume of interparticle voids, and VExt the external void volume. Any of these equations can be rearranged and solved for pore volume. Examples follow.
Percent Porosity
From measurements of bulk volume (VB) and skeletal volume (VSk), total porosity VPt can be determined from the equation VPt = VB - VSk. This allows percent porosity to be calculated by the simple relationship
% Porosity = = (VPt/VB) x 100%.
Percent Porosity Filled
A mercury porosimeter tracks the volume of mercury intruded VI into the sample from minimum to maximum pressure. Since the total volume of mercury injected into the sample equals the total volume (VPt) of open pores, the percent of pore volume filled at any pressure can be determined by
%VP Filled = (VI / VPt) x 100%.
If the sample contains closed pores, then the above equation becomes
% VP Filled = ((VI + VPc) / VPt) x 100%.
The size of pores being invaded by mercury depends on the pressure applied. This means that, at a specific pressure (pore size), the percent porosity filled relates to pores of the current size and larger. The remaining percent of unfilled pores relates only to pores smaller than the current size.
Apparent (Skeletal) Volume, Bulk Volume and Open Porosity by Liquid Absorption
To determine the volume of open pores in a sample, first the mass of the dry sample is obtained. Then, the sample is immersed in a liquid that is capable of penetrating into the open voids. When u sing water, boiling may be required to assure pore filling. Skeletal volume is determined by hydrostatic weighing in the same liquid. The sample is weighed again after removing it from the liquid. The difference between the wet and dry mass divided by the density of the liquid is the volume of open pores in which the liquid washable to penetrate.
A variation of this method uses oil as the liquid. To assure adequate pore filling, the sample is immersed in oil and the container evacuated to a few mmHg and maintained for 1 hour. Atmospheric pressure is restored and the sample is left to equilibrate for 30 minutes.
True Volume and Closed Pore Volume by Size Reduction
Methods of determining bulk volume and open pore volume have been described. However, material may contain closed pores. If the true density of the solid material is known, then the mass of the sample divided by its density is its true volume; bulk volume minus open pore volume minus true volume is the volume of closed pores.
If the density of the solid material is not known, but its bulk volume and open pore volume have been determined, the volume of closed pores may be found by grinding the sample into a powder. Any remaining closed pores will be smaller than the particle size of the powder. The true volume of the sample (the powder) is determined by liquid or gas displacement.
Total Pore Volume
Bulk volume and true volume having been obtained for a sample by one of the methods above, the difference between the former and latter is total pore volume. Likewise, if open pore volume and closed pore volume are determined as suggested above, their sum is total pore volume.
Conclusions
Density, volume, and porosity are physical characteristics of solid materials that can be determined by a variety of experimental techniques. However, the value obtained is very likely to be dependent on the technique. This is largely because of the way the measurement technique treats volume in respect to the degree of exclusion of void spaces associated with the sample material. Various definitions of density and volume are used to differentiate these values in terms of what void volumes are included with the overall volume determination. An analyst must understand the type of volume or density sought in order to select the appropriate measurement technique.
This information has been sourced, reviewed and adapted from materials provided by Micromeritics Instrument Corporation.
Citations
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A144535 Numerators of continued fraction convergents to sqrt(3)/2. 4
%I
%S 0,1,6,13,84,181,1170,2521,16296,35113,226974,489061,3161340,6811741,
%T 44031786,94875313,613283664,1321442641,8541939510,18405321661,
%U 118973869476,256353060613,1657092233154,3570537526921,23080317394680,49731172316281,321467351292366
%N Numerators of continued fraction convergents to sqrt(3)/2.
%H Vincenzo Librandi, <a href="/A144535/b144535.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,14,0,-1).
%F a(n) = 14*a(n-2)-a(n-4). G.f.: x*(1+6*x-x^2)/((1-4*x+x^2)*(1+4*x+x^2)). - _Colin Barker_, Apr 14 2012
%F a(n) = ((-(-2-sqrt(3))^n*(-3+sqrt(3))+(2-sqrt(3))^n*(-3+sqrt(3))-(3+sqrt(3))*((-2+sqrt(3))^n-(2+sqrt(3))^n)))/(8*sqrt(3)). - _Colin Barker_, Mar 27 2016
%e 0, 1, 6/7, 13/15, 84/97, 181/209, 1170/1351, 2521/2911, 16296/18817, 35113/40545, ...
%p with(numtheory); Digits:=200: cf:=convert(evalf(sqrt(3)/2,confrac); [seq(nthconver(cf,i), i=0..100)];
%t CoefficientList[Series[x (1 + 6 x - x^2)/((1 - 4 x + x^2) (1 + 4 x + x^2)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 10 2013 *)
%t Numerator[Convergents[Sqrt[3]/2,30]] (* or *) LinearRecurrence[{0,14,0,-1},{0,1,6,13},30] (* _Harvey P. Dale_, Feb 10 2014 *)
%o (MAGMA) I:=[0, 1, 6, 13]; [n le 4 select I[n] else 14*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 10 2013
%o (PARI) Vec(x*(1+6*x-x^2)/((1-4*x+x^2)*(1+4*x+x^2)) + O(x^30)) \\ _Colin Barker_, Mar 27 2016
%Y Cf. A126664, A144536, A002531/A002530.
%Y Bisections give A001570, A011945.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_, Dec 29 2008
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Last modified August 19 20:20 EDT 2019. Contains 326133 sequences. (Running on oeis4.) | 896 | 2,154 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2019-35 | latest | en | 0.451388 |
http://mathhelpforum.com/algebra/205387-find-equation-line-perpendicular-something-passing-through-something-some-print.html | 1,503,274,489,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886106996.2/warc/CC-MAIN-20170820223702-20170821003702-00690.warc.gz | 264,851,698 | 3,871 | # Find equation of a line perpendicular to something passing through something and some
• Oct 15th 2012, 12:12 PM
Ashir
Find equation of a line perpendicular to something passing through something and some
Find equation of a line perpendicular to something passing through something and something?
Please answer without the point slope formula I prefer the substitution method. I know how to find the equation of a line perpendicular to something passing through a given co ord but not something passing through 2 given co ords. Thanks, need this for my GCSE.
• Oct 15th 2012, 01:00 PM
ebaines
Re: Find equation of a line perpendicular to something passing through something and
Sorry, but this is a bit confused. Perhaps if you define what you mean by all those "somethings" it would be clearer what you're asking. Are you asking about lines perpendicular to lines, or perpendicular to circles, or 3-dimensional surfaces, or what? By "point slope method" are you talking about how to find the equation of a line given two sets of coordinates? Finally what do you mean by finding a line perpendicular to "something ...passing through 2 given coordinates?" Perhaps if you gave an example we could be of better help.
• Oct 16th 2012, 07:31 AM
Ashir
Re: Find equation of a line perpendicular to something passing through something and
Perpendicular to a given line.
Yes, I am.
Something 1 = equation of line
Something 2&3 = set of coords
find the equation of a line perpendicular to something 1 passing through something 2 and something 3
• Oct 16th 2012, 09:52 AM
HallsofIvy
Re: Find equation of a line perpendicular to something passing through something and
It makes no sense to say that a line "passes through" a set of coordinates. Passing through the x and y axes at given points? There exist a unique line passing through given point perpendicular to a given line. Is that what you mean? PLEASE tell us exactly what the problem you are trying to solve is.
• Oct 16th 2012, 10:00 AM
Ashir
Re: Find equation of a line perpendicular to something passing through something and
Find the equation of a line perpendicular to y=4x+2 passing through (3,-5) and (4, 8)
That is an example.
• Oct 16th 2012, 10:26 AM
skeeter
Re: Find equation of a line perpendicular to something passing through something and
Quote:
Originally Posted by Ashir
Find the equation of a line perpendicular to y=4x+2 passing through (3,-5) and (4, 8)
That is an example.
that would be two lines ... both perpendicular to y = 4x+2 , one passing through (3,-5) and the other passing through (4,8)
perpendicular slope is the opposite reciprocal of the slope of the given line ... use the point-slope form of a linear equation to find each line's equation.
• Oct 16th 2012, 10:50 AM
Ashir
Re: Find equation of a line perpendicular to something passing through something and
that was just an example, switch 4,8 with 2, -4 then so it's one line
I'm not comfortable with the pointslope formula but with substituting.
• Oct 16th 2012, 11:04 AM
ebaines
Re: Find equation of a line perpendicular to something passing through something and
Quote:
Originally Posted by Ashir
Find the equation of a line perpendicular to y=4x+2 passing through (3,-5) and (4, 8)
That is an example.
This is impossible as written. You can find a line that is perpendicular to y=4x+2 that passes through (3,-5), or you can find a line that is perpendicular to y=4x+2 that passes through (4,8), but there is no single line that is perpendicular to y=4x+2 and that passes through BOTH (3,-5) and (4,8).
• Oct 16th 2012, 11:16 AM
ebaines
Re: Find equation of a line perpendicular to something passing through something and
Quote:
Originally Posted by Ashir
that was just an example, switch 4,8 with 2, -4 then so it's one line
I'm not comfortable with the pointslope formula but with substituting.
If you are given two points such as (3,-5) and (2, -4) you can find the equation of the line that includes both of these poimts using the formula:
$y=mx+b$ where m is the slope: $m=\frac {\Delta y}{\Delta x} = \frac {(y_2-y_1)}{(x_2-x_1)}$ and b (the y intercept) can be found from $y_1 = mx_1+b$. So here you have $y=\frac {-4- (-5)}{2-3} = -1$, and $-5=(-1)(3) + b$, so $b = -5+3 = -2.$ So the equation of the line passing through these two points is y=-x-2.
But this has nothing to do with a line being perpendicular to y = 4x+2, because it's not. | 1,159 | 4,401 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.59375 | 4 | CC-MAIN-2017-34 | longest | en | 0.924689 |
https://www.nsf.gov/discoveries/disc_summ.jsp?cntn_id=117540&org=MPS&preview=false | 1,516,761,213,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084892892.86/warc/CC-MAIN-20180124010853-20180124030853-00267.warc.gz | 945,026,729 | 14,129 | Discovery
## Scientists Use Math to Build Better Stents
University of Houston mathematician Sunica Canic and her colleagues build computer models to study stents; their simulations could lead to better designs and also help doctors select the right stents for specific procedures
A 3-D computer model of a stent.
August 26, 2010
Suncica "Sunny" Canic was good at math in school, so that's what she pursued as a career. But she always liked medicine, too.
When she moved to Houston, Texas, and met some cardiologists at a party, she started talking with them about what they do--and knew she could help.
"I realized we could provide them with a fluid dynamics and mechanics point of view to help them make decisions ... for example, about which stent grafts they use in their procedures," she said.
Stents are tiny mesh tubes made from metal alloys that hold blood vessels open after they've been clogged with disease-causing plaque. Even though stents are designed to be compatible with the human body, they sometimes cause unwanted reactions, such as blood clots and scar tissue formation. So, scientists have tried to coat stents with cells that make the tiny tubes even more compatible.
But these, too, aren't yet perfect, said Canic, a professor of mathematics at the University of Houston. Blood flowing over a coated stent can still clot or tear cells away. This is, as Canic put it, "not good." Supported by a joint grant from the National Science Foundation (NSF) and the National Institutes of Health's National Institute of General Medical Science (NIH/NIGMS), Cancic makes computer models to guide the search for a better stent coating.
She also uses computer models to study the strengths and weaknesses of different stent structures. Her work could help manufacturers optimize stent design and help doctors choose the right stents for their patients, ultimately improving patient outcomes.
Computer scientists usually model stents in three dimensions. Keeping track of about 200,000 points, or nodes, along the stent mesh, the models are massive.
Together with her collaborator, Josip Tambaca of the University of Zagreb in Croatia, and her doctoral student, Mate Kosor, Canic wrote a much simpler program that approximates stents as meshes of one-dimensional rods. This program let the researchers achieve the same result using just 400 nodes.
Using their simplified model, the researchers have examined the designs of several stents on the market to see which structures seem to be best for specific blood vessels or procedures. For instance, they found that stents with an "open design"--where every other horizontal rod is taken out--bend easily, which makes them good to put in curvy coronary arteries.
Canic and Tambaca have also used the model to design a stent with mechanical properties specifically tailored to an experimental heart-valve replacement procedure. She found that this specialized stent works best for the procedure when it's stiff in the middle and less stiff at the ends. In addition, she has found that combining "bendiness" with radial stiffness--where you can bend the stent into a U shape, but you can't squeeze the tube shut--produces a stent with less chance of buckling than those that are currently in use.
The most rewarding part of her work, said Canic, is that "we can use mathematics for something useful, connected to real-world problems." She reports that her collaborators are already putting the results of her simulations into practice.
Meanwhile, her greatest challenge is serving as an ambassador of mathematics to the medical and bioengineering communities.
In the beginning, she said, it was difficult to collaborate with people from different disciplines who speak different scientific languages. "But once they saw that there is a lot of information there that could be helpful, it has been much easier," she said. "Now people want to talk to us from the medical center. They come to us and ask questions, and that's good."
Today, Canic is helping a team at the Texas Heart Institute study an unusual source for stent coating: ear cartilage. The team believes this easy-to-harvest tissue will make stents more biocompatible, though they don't yet know how ear cartilage cells grow or behave in environments like human blood vessels.
Canic is using her computer programs, developed together with Tsorng-Whay Pan, Roland Glowinski and students, to simulate how blood interacts with the stent-coating cartilage cells and how the cells stick (or don't) to the stent surface. She plugs in different fluid thicknesses and shear forces of blood flowing over the stent to see what might encourage the cartilage on freshly coated stents to stabilize quickly. The models have helped her collaborators learn the best conditions to test in follow-up experiments as they search for ways to pre-treat stents before doctors implant them.
Canic wants to keep collaborating with the medical community as she moves forward with her research. She plans to look at biodegradable stents, as well as simulating the fluid dynamics of regurgitating mitral valves (where some blood flows backwards in the pumping heart) to help doctors more accurately diagnose the condition using ultrasound. "Certainly, I am going to continue working in this area," she said. "It is very rewarding."
-- Stephanie Dutchen, NIGMS/NIH, stephanie.dutchen@nih.gov
This Behind the Scenes article was provided to LiveScience in partnership with the National Science Foundation.
Investigators
Suncica Canic
Roland Glowinski
Craig Hartley
Mate Kosor
Tsorng-Whay Pan
Doreen Rosenstrauch
Josip Tambaca
Related Institutions/Organizations
Baylor College of Medicine
Texas Heart Institute
University of Houston
University of Zagreb
Locations
Texas
Croatia
Related Programs
Applied Mathematics
Mathematical Biology
Total Grants
\$1,003,000
Related Agencies
National Institute of General Medical Sciences | 1,254 | 5,939 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2018-05 | latest | en | 0.967922 |
www.suiterealestateturkey.com | 1,702,330,471,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679518883.99/warc/CC-MAIN-20231211210408-20231212000408-00051.warc.gz | 1,081,064,706 | 207,563 | top of page
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# What does the Share Share Denominator mean?
The rate of land belonging to the independent section on the land where a building is located is considered as the denominator in the part that represents the main real estate that has been allocated. Here, let's take a detailed look at what the shares mean by share and denominator, which we have examined as Emlakjet.
The numerator and denominator expressions, which are frequently encountered in title deed documents and indicate the ownership rates, show that the real estate belongs to more than one person when it comes to a real estate with shares. In a more literal expression, if we approach exactly what is the share, share and denominator, the rate of land belonging to the independent section on the land where a building is located is considered as a share, and in the part that expresses the main real estate that has been allocated, it is considered as a denominator. The share calculation process in the title deed can be done easily and in the calculation process; The current value determined by the municipality of the region where the real estate is located and the size in square meters for each independent section are taken into account. Land share calculations are made in accordance with the laws and procedures, and land share shares that are not proportional can be corrected by court.
How is Land Share Calculated?
The land share calculation process is made in the form of a ratio during the establishment of the condominium and according to the procedures of the General Directorate of Land Registry and Cadastre. The value in square meters of the total area specified in the deed is divided by the land share, and the number obtained as a result of the transaction is multiplied by the share value of the person, and the land share is formed with the obtained number.
What is the Current Value?
The current market value, which is of great importance in the land share calculation process, expresses the current market value of any property. Fair value; It ensures that the goods or immovable that will be bought, sold, tax paid or insured are prevented from being traded below their own value.
How is the Market Value Calculated?
If the square meters and prices of the three houses in the vicinity of the real estate are known, the square meter and prices can be added together and the total price divided by the total square meter, and then the current value can be found by multiplying by the square meter of the real estate to be calculated. The result of the said transaction; It represents the price of the real estate in square meters. This calculation process may differ from the actual price determined by the municipality. The reason for this situation is that factors such as earthquake resistance of the house, proximity to transportation networks, view, schools in its vicinity and development status are determinative while calculating the current value.
İnfo: Emlakjet | 569 | 2,987 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2023-50 | longest | en | 0.966424 |
https://byjus.com/question-answer/solve-the-following-quadric-equations-by-factorization-method-only-x-2-x-1-0/ | 1,695,411,130,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506421.14/warc/CC-MAIN-20230922170343-20230922200343-00034.warc.gz | 166,344,688 | 26,591 | Question
# Solve the following quadric equations by factorization method only x2+x+1=0
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Solution
## x2+x+1=0Now, completing the squares, we get(x+12)2+34=0⇒(x+12)2−(√32i)2=0⇒(x+12+√32i)(x+12−√32i)=0⇒(x+12+√32i)=0Or (x+12−√32i)=0∴x=−12+√32i,−12−√32i
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Select... | 170 | 403 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2023-40 | latest | en | 0.637222 |
https://trimdesk.com/how-long-does-it-take-for-concrete-to-be-hard-enough-to-walk-on/ | 1,685,984,314,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224652149.61/warc/CC-MAIN-20230605153700-20230605183700-00124.warc.gz | 627,605,246 | 12,483 | # How long does it take for concrete to be hard enough to walk on?
How long does it take for concrete to be hard enough to walk on? Concrete typically takes 24 to 48 hours to dry enough for you to walk or drive on it. However, concrete drying is a continuous and fluid event, and usually reaches its full effective strength after about 28 days.
How long does it take for concrete to gain sufficient strength to sustain load? Curing time of concrete is typically 24-48 hours, at which point it’s safe for normal foot traffic. After one week, concrete is typically cured enough to handle continued construction including heavy machinery. Concrete is recognized to have reached full strength 28 days after placement.
How long does it take for concrete to gain most of its strength? In standard industrial cases, full strength concrete is recognized at 28 days. At seven days, you should have concrete that is cured to 70% full strength or greater. But to answer the question of, “How long does concrete take to set?” concrete setting time is generally 24 to 48 hours.
How long does it take for concrete to reach 90% of its strength? Theoretically, if kept in a moist environment, concrete will gain strength forever, however, in practical terms, about 90% of its strength is gained in the first 28 days.
## How long does it take for concrete to be hard enough to walk on? – Additional Questions
### Can you walk on concrete after 12 hours?
How long should you wait before walking on your new concrete driveway? You should wait at least 24 hours before walking on your freshly poured concrete.
### What strength should concrete be at 7 days?
Compressive strength achieved by concrete at 7 days is about 65% and at 14 days is about 90% of the target strength.
### How long does it take for concrete to get to 100 strength?
In most cases, standard concrete (or full strength concrete) has a setting time of around one day, sometimes two days depending on the environment in which it is set. However, concrete reaches its full strength after approximately 25-28 days.
### How do you predict the 28 day strength of concrete?
Concrete mixes with st1·engths ranging from 150 to 600 kgf/cm2 (15 to 60 MPa) were tested. Test results, which were correlated by regression analyses, show that accelerated testing (hot-water curing for 31,h hours at 85 C) can be used to accurately predict 28-day concrete strengths.
### How do you find the compressive strength of concrete after 28 days?
Compressive Strength of concrete = Maximum compressive load / Cross Sectional Area, cross sectional Area = 150mm X 150mm = 22500mm2 or 225 cm2, assume the compression load is 563 KN, then Compressive Strength of M25 concrete after 28 days = (563N/22500mm2= 25N/mm2 (20MPa) or 3626 Psi.
### How is concrete strength calculated?
The compressive strength was calculated by using the equation [14] : F= P/A, where F is compressive strength of specimen in Mega Pascal, P is the maximum applied load by newton and A is the cross-sectional area estimated in mm 2 .
### Why do we test concrete at 7 days?
Because of the high capital risk in the construction industry, instead of testing the strength in 28th day, the strength can be checked in 7th and 14th day based on the concrete strength psi to predict the construction works target strength.
### What is the normal strength of concrete?
The compressive strength of normal concrete is between 20 and 40 MPa. The strength of high strength concrete is above 40 MPa. The high strength concrete has compressive strength between 40 and 140 MPa which is discussed in this article. As time goes the difference between normal and high strength concrete also changes.
### What is the highest strength of concrete?
UHPC has a compressive strength 10 times that of traditional concrete. Compressive strength is the ability of a material to resist bending under a load (or in compression). Normal concrete used in bridges has a compressive strength of 3,000 to 5,000 psi. UHPC has a compressive strength of 18,000 to 35,000 psi.
### How much weight can a 4-inch concrete slab hold?
A 4-inch thick concrete can support upto 40 pounds of weight. Weight should not exceed 40 lbs/sq ft on an undetermined 4-inch slab. 80 lb/sq ft in isolated areas is fine, but unless you know what the soil bearing and reinforcing is for that slab, you might be looking at cracking.
### How much weight can 6 inches of concrete?
A 6-inch thick concrete with a 700-pound compression strength, for example, can support 1,105-pounds of pressure. In 7-inch thickness, it could support 1,194 psi, while in 12-inch thickness, it could support 1,563 psi.
### Which is more stronger white cement or GREY cement?
White cement is stronger (harder), more cohesive, sticky, durable.
### Why is my new concrete so white?
When moisture migrates up to the concrete surface, it carries calcium salts from the concrete material. These salts react with carbon dioxide in the air and form calcium carbonate. Concrete can’t absorb the newly formed compound, causing white spots on its surface. | 1,152 | 5,091 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2023-23 | latest | en | 0.965424 |
https://socratic.org/questions/what-is-the-altitude-of-the-air-balloon-to-the-nearest-100ft-given-the-informati | 1,571,243,862,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986669057.0/warc/CC-MAIN-20191016163146-20191016190646-00071.warc.gz | 701,515,601 | 6,672 | What is the altitude of the air balloon to the nearest 100ft given the information below ?
A hot air balloon is floating above a straight stretch of highway. To estimate how high above the ground the balloon is floating, the passengers take measurement of a car below them. They assume that the car is traveling at 50mph. One minute after the car passes directly below the balloon they take a bearing on the car and find that the angle of depression of the car is 25 degrees.
Feb 24, 2018
$\approx 2000$ feet.
Explanation:
Firstly, creating a diagram with the given and needed information helps here:
Our first task is to find the distance, $d$, that the car has traveled since passing the balloon (accurately rendered in the above diagram).
We know that the car is traveling at 50 miles per hour, but we need to find the speed in hours per minute. We can do this by dividing 50 by 60:
$\frac{50 m i l \setminus e s}{1 h o u r} = \frac{50 m i l \setminus e s}{60 m i \setminus n \setminus u t e s} = .8 \overline{33}$ miles/minute
Since it's been one minute since the car passed the balloon, $d \cong .83$ miles.
Now to find $h$, the height:
$\tan \theta = \frac{o p p o s i t e}{a \mathrm{dj} a c e n t}$
$\tan 25 = \frac{h}{.83}$
$\tan 25 \cdot .83 \cong .387 \to h \cong .387$ miles.
There are 5,280 feet in a mile, so
${h}_{i \setminus n f e e t} \cong .387 \cdot 5280 \cong 2043.55 \cong 2000$ feet.
Hope this helps. | 417 | 1,437 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 9, "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} | 4.625 | 5 | CC-MAIN-2019-43 | latest | en | 0.856055 |
https://nrich.maths.org/public/topic.php?code=-6&cl=3&cldcmpid=6650 | 1,571,760,039,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570987822458.91/warc/CC-MAIN-20191022155241-20191022182741-00530.warc.gz | 625,908,988 | 7,238 | # Search by Topic
#### Resources tagged with Modular arithmetic similar to How Much Can We Spend?:
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### There are 28 results
Broad Topics > Numbers and the Number System > Modular arithmetic
### How Much Can We Spend?
##### Age 11 to 14 Challenge Level:
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
### Where Can We Visit?
##### Age 11 to 14 Challenge Level:
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
### What Numbers Can We Make Now?
##### Age 11 to 14 Challenge Level:
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
### What Numbers Can We Make?
##### Age 11 to 14 Challenge Level:
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
### Days and Dates
##### Age 11 to 14 Challenge Level:
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
### Elevenses
##### Age 11 to 14 Challenge Level:
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
### Differences
##### Age 11 to 14 Challenge Level:
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
### A One in Seven Chance
##### Age 11 to 14 Challenge Level:
What is the remainder when 2^{164}is divided by 7?
### Take Three from Five
##### Age 14 to 16 Challenge Level:
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
### Latin Squares
##### Age 11 to 18
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
### Mod 3
##### Age 14 to 16 Challenge Level:
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
### Two Much
##### Age 11 to 14 Challenge Level:
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
### Filling the Gaps
##### Age 14 to 16 Challenge Level:
Which numbers can we write as a sum of square numbers?
### Zeller's Birthday
##### Age 14 to 16 Challenge Level:
What day of the week were you born on? Do you know? Here's a way to find out.
### Knapsack
##### Age 14 to 16 Challenge Level:
You have worked out a secret code with a friend. Every letter in the alphabet can be represented by a binary value.
### Guesswork
##### Age 14 to 16 Challenge Level:
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
### The Chinese Remainder Theorem
##### Age 14 to 18
In this article we shall consider how to solve problems such as "Find all integers that leave a remainder of 1 when divided by 2, 3, and 5."
### Transposition Fix
##### Age 14 to 16 Challenge Level:
Suppose an operator types a US Bank check code into a machine and transposes two adjacent digits will the machine pick up every error of this type? Does the same apply to ISBN numbers; will a machine. . . .
### Check Code Sensitivity
##### Age 14 to 16 Challenge Level:
You are given the method used for assigning certain check codes and you have to find out if an error in a single digit can be identified.
### Check Codes
##### Age 14 to 16 Challenge Level:
Details are given of how check codes are constructed (using modulus arithmetic for passports, bank accounts, credit cards, ISBN book numbers, and so on. A list of codes is given and you have to check. . . .
### Obviously?
##### Age 14 to 18 Challenge Level:
Find the values of n for which 1^n + 8^n - 3^n - 6^n is divisible by 6.
### More Mods
##### Age 14 to 16 Challenge Level:
What is the units digit for the number 123^(456) ?
### Odd Stones
##### Age 14 to 16 Challenge Level:
On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.
### Novemberish
##### Age 14 to 16 Challenge Level:
a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.
### Euler's Officers
##### Age 14 to 16 Challenge Level:
How many different ways can you arrange the officers in a square?
### Going Round in Circles
##### Age 11 to 14 Challenge Level:
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
### Grid Lockout
##### Age 14 to 16 Challenge Level:
What remainders do you get when square numbers are divided by 4?
### The Best Card Trick?
##### Age 11 to 16 Challenge Level:
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth? | 1,285 | 5,247 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4 | 4 | CC-MAIN-2019-43 | latest | en | 0.893003 |
http://todaylotteryresult.net/swertres-result-november-27-2019/ | 1,590,922,890,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347413097.49/warc/CC-MAIN-20200531085047-20200531115047-00090.warc.gz | 119,505,908 | 11,922 | # SWERTRES RESULT November 27 2019
SWERTRES RESULT November 27, 2019 – The Philippine Charity Sweepstakes Office or PCSO has introduced the legit Swertres consequence as of late, November 27, 2019.
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## Swertres Result November 27, 2019
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Draw Results Winners
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Source: PCSO
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In Standard or Straight Play, a participant wins P4,500.00 if he will get the three profitable numbers in precise order.
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HOW TO PLAY: You may additionally need to play the Rambolito. Select a Three-digit quantity aggregate and the gadget will robotically permutate and generate all its imaginable combos. If the chosen Three-digit aggregate has no repeating digits, e.g.123, the choice of combos generated will probably be six (6). If the chosen Three-digit aggregate has two (2) repeating digits, e.g. 122, the choice of combos generated will probably be 3 (Three).
— PCSO
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### Latest and Related Results:
Updated: November 27, 2019 — 12:23 am | 677 | 2,707 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2020-24 | latest | en | 0.812338 |
https://sites.google.com/view/iteachcoolmath/cool-math-games-article | 1,713,625,909,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817650.14/warc/CC-MAIN-20240420122043-20240420152043-00612.warc.gz | 474,180,518 | 16,117 | # Cool Math Games article
## Cool Math Games That Get Students Off Their Chairs -by Virginia Wong
In my teaching I have seen upper grade students struggle with basic number operations and how that has hindered their ability in solving complicated math problems. There are many reasons that lead to poor number sense, such as lack of practice, or practicing number operations mechanically without putting in their mind.
A few years ago I introduced two math games to my elementary and middle school students. We played the games very often in the beginning of class or when we had extra time. I have witnessed how the students have changed from “I hate math” or “I fear math” to “I have another way to do it” or “I’m staying at break time to solve it”. When we played these games, the students could never have enough and were always very excited to jump out of their chairs to show their work. These games helped create a passion for math and lay a strong mathematical foundation, allowing these students not only excel in their school math but also achieve very high rankings in many national and international math competitions. These two games are very simple to play almost anytime and anywhere. All you need are dice or a random number generating app.
Hit The Target:
In this game you first roll two 12-sided dice and multiply the numbers to get your target number. Then you roll four 6-sided dice and use the four numbers to get as close to the target number as you can, using any operation or function. All four numbers must be used exactly once. In addition, they cannot be put together to form a multi-digit number.
Because the goal is to get as close to the target, there is no loser, so to speak. But when students see other players get closer, they become motivated to refine their own method. Thus, the students’ creativity with operations and number sense grows.
24 Game:
This is a classic game. The goal is to use four numbers to yield exactly 24. For younger students, six-sided dice can be used to get those four numbers. And for more experienced students 12-sided dice are recommended. At first glance this game may seem a bit harder than Hit the Target because precision is essential. However there is a reason why 24 is chosen - it has many multiplicative factors. Students’ concepts on factors and multiples are greatly strengthened through this game.
The Sky’s The Limit
From my experience, when a student introduces a trick, the others pick up very quickly and use it in more creative ways. For example, I had a 5th grade student who used triangular numbers—a concept way beyond his school level—in his number sentence. Very quickly, the rest of class implemented triangular numbers in their creative methods; they even raced out to show their work! (See pictures posted on www.CoolMathLA.com and click on Brilliant Students)
The effect of these two games is almost instantaneous, yet they can be played over and over without becoming boring, all because the more the students play, the more new functions they learn and master. The sky’s the limit!
Upcoming Number Tournament
There will be a fun, engaging competition called Number Tournament (www.NumberTournament.org) coming up on 10/28/18 (Sun.) at Live Oak Park Community Center. The tournament is organized by a group of high school mathletes who have experience in competitions, and have played these games many times before. In the tournament participants will play the two aforementioned games, as well as compete in a team relay that highlights the joy of collaborating with other mathletes.
Virginia Wong is the director of Math is Cool, a non-profit to promote the love of math learning. She holds master degree in math education and teaching credential. Number Tournament is an initiative from Math is Cool to boost number sense through games. It is organized by Alicia Y, Merrick H, Josiah K and Mark L, most of them are from Arcadia High School. | 799 | 3,947 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4 | 4 | CC-MAIN-2024-18 | latest | en | 0.973805 |
https://superstarworksheets.com/math-worksheets/ordinal-numbers/ | 1,721,854,598,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518454.54/warc/CC-MAIN-20240724202030-20240724232030-00232.warc.gz | 469,314,237 | 63,554 | # Ordinal Numbers
Ordinal numbers for elementary students! Ordinal numbers, such as first, second, and third, play a crucial role in English grammar and are used to indicate the position or order of things. We’ve got flashcards, worksheets, and games to keep kids learning and growing in math. Continue to build your students’ math skills with our Kindergarten Interactive Math Curriculum!
## What are Ordinal Numbers?
Ordinal numbers are specific types of numbers that we use to describe the order or position of an object or element in a series. Unlike cardinal numbers, which represent quantity or count, ordinal numbers indicate rank or order. For example, while cardinal numbers tell us “there are five apples,” ordinal numbers tell us “the fifth apple in the basket.” Ordinal numbers are formed by adding a suffix (such as -st, -nd, -rd, or -th) to the cardinal numbers. They help us navigate and sequentially organize information, making them essential in various aspects of everyday life, from ranking sports teams to describing dates and addresses.
## When to Use Ordinal Numbers?
In the classroom, teachers utilize ordinal numbers to help organize and guide their students through various activities and tasks. They may use them to describe the order in which students are to line up, to establish turn-taking during group discussions or presentations, and even when distributing materials or assigning seats.
We also use ordinal numbers in day-to-day life to describe rankings, placements, or sequences. Some common instances where we use ordinal numbers include describing birth order, giving directions, expressing dates, indicating ranks in competitions or races, and discussing milestones or anniversaries. By using ordinal numbers, we provide a clear and concise way to convey the specific position or order of something in a given context.
## Ordinal Numbers vs. Cardinal Numbers
This ordinal number vs. cardinal number chart provides a visual representation to students. Cardinal numbers give an amount to number, whereas ordinal numbers describe where the number is located in a list.
## Ordinal Number Charts
Utilizing ordinal number resources in a classroom or homeschool setting is a valuable way to reinforce and practice this important mathematical concept. Start by introducing visual aids such as number charts or posters that display the sequential order of numbers. These visuals can serve as quick references for students to grasp the concept of ordinal numbers.
Engage students in hands-on activities where they can physically arrange objects or themselves in order. For example, you can have them line up in order of their birthdates or use blocks to build towers of different heights, labeling them with ordinal numbers. Incorporate worksheets or online exercises that require students to identify and write ordinal numbers in context. Consider incorporating games or interactive activities where students can compete or work collaboratively to reinforce their understanding of ordinal numbers.
## Ordinal Numbers 1-20
This free, printable ordinal numbers chart gives the correct numerical and word identification for the numbers 1-20.
• Ordinal Numbers
• Chart
• Math Concepts
• Visuals
## Ordinal Numbers in Tens
Ordinal number tens chart makes it easy to identify and recognize the numbers 1-100 in their ordinal number form.
• Math Concepts
• Ordinal Numbers
• Tens
• Visual Charts
## Ordinal Numbers Flashcards
Ordinal number flashcards makes it easy to identify and recognize the numbers 1-30 in their ordinal number form.
• Numbers
• Counting
• Sequencing
• Patterns
## Ordinal Number Worksheets
This is a FREE pack of number ordinal number worksheets! Students will get to learn about the order of numbers with these activities.
• Counting Skills
• Memorizing Facts
• Spelling
• Numbers
## How to Use Ordinal Numbers?
Incorporate hands-on activities such as organizing a classroom scavenger hunt where students have to find objects and label them with their correct ordinal positions. Another idea is to create a classroom race where students participate and earn ribbons or medals based on their ordinal placements.
If you’re looking for a fun and interactive way to continue to teach math. Check out our Interactive Math Curriculum. Specifically designed for kindergarten students!
## Kindergarten Interactive Math Curriculum
Don’t miss this low-prep, interactive, and hands-on, comprehensive math curriculum for Kindergarten! Interactive Math: Kindergarten provides a full year of hands-on and fun math activities and covers 4 days a week over 36 weeks. If you are looking for a program that excites your student(s), this program is designed to engage children while keeping the format easy and low-prep.
## Looking for More?
Want more hands on, interactive activities for your primary students? Check out the following resources: | 946 | 4,904 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5625 | 5 | CC-MAIN-2024-30 | latest | en | 0.90381 |
http://en.wikibooks.org/wiki/Calculus/Power_series | 1,433,347,214,000,000,000 | text/html | crawl-data/CC-MAIN-2015-22/segments/1433195036776.1/warc/CC-MAIN-20150601214356-00074-ip-10-180-206-219.ec2.internal.warc.gz | 67,330,751 | 10,805 | # Calculus/Power series
The study of power series is aimed at investigating series which can approximate some function over a certain interval.
## Motivations
Elementary calculus (differentiation) is used to obtain information on a line which touches a curve at one point (i.e. a tangent). This is done by calculating the gradient, or slope of the curve, at a single point. However, this does not provide us with reliable information on the curve's actual value at given points in a wider interval. This is where the concept of power series becomes useful.
### An example
Consider the curve of y = cos(x), about the point x = 0. A naïve approximation would be the line y = 1. However, for a more accurate approximation, observe that cos(x) looks like an inverted parabola around x = 0 - therefore, we might think about which parabola could approximate the shape of cos(x) near this point. This curve might well come to mind:
$y = {1 - { x^2 \over 2}}$
In fact, this is the best estimate for cos(x) which uses polynomials of degree 2 (i.e. a highest term of x2) - but how do we know this is true? This is the study of power series: finding optimal approximations to functions using polynomials.
## Definition
A power series (in one variable) is a infinite series of the form
$f(x)=a_0 (x-c)^0+a^1 (x-c)^1 +a_2 (x-c)^2...$(where $c$ is a constant)
or, equivalently,
$f(x)=\sum_{j=0}^{\infin} a_j(x-c)^j$
When using a power series as an alternative method of calculating a function's value, the equation
$f(x)=\sum_{j=0}^{\infin} a_j(x-c)^j$
can only be used to study f(x) where the power series converges - this may happen for a finite range, or for all real numbers.
The size of the interval (around its center) in which the power series converges to the function is known as the radius of convergence.
### An example
$\frac{1}{1-x}=\sum_{n=0}^\infty x^n$ (a geometric series)
this converges when | x | < 1, the range -1 < x < +1, so the radius of convergence - centered at 0 - is 1. It should also be observed that at the extremities of the radius, that is where x = 1 and x = -1, the power series does not converge.
### Another example
$e^x=\sum_{n=0}^\infty \frac{x^n}{n!}$
Using the ratio test, this series converges when the ratio of successive terms is less than one:
$\lim_{n \to \infty} \left|\frac{x^\left(n+1\right)}{\left(n+1\right)!}\frac{n!}{x^n}\right|<1$
$=\lim_{n \to \infty} \left|\frac{x^n x^1}{n! \left(n+1\right)}\frac{n!}{x^n}\right|<1$
$=\lim_{n \to \infty}\left|\frac{x}{n+1}\right|<1$
which is always true - therefore, this power series has an infinite radius of convergence. In effect, this means that the power series can always be used as a valid alternative to the original function, ex.
### Abstraction
If we use the ratio test on an arbitrary power series, we find it converges when
$\lim_{n \to \infin} \frac{|a_{n+1}x|}{|a_n|} <1$
and diverges when
$\lim_{n \to \infin} \frac{|a_{n+1}x|}{|a_n|} >1$
The radius of convergence is therefore
$r=\lim_{n \to \infin} \frac{|a_n|}{|a_{n+1}|}$
If this limit diverges to infinity, the series has an infinite radius of convergence.
## Differentiation and Integration
Within its radius of convergence, a power series can be differentiated and integrated term by term.
$\frac{d}{dx} \sum_{j=0}^\infty a_jx^j = \sum_{j=0}^\infty a_{j+1}(j+1)(x-c)^j$
$\int \sum_{j=0}^\infty a_j(x-c)^j dx = \sum_{j=1}^\infty \frac{a_{j-1}(x-c)^j}{j}+k$
Both the differential and the integral have the same radius of convergence as the original series.
This allows us to sum exactly suitable power series. For example,
$\frac{1}{1+x}=1-x+x^2-x^3+ \ldots$
This is a geometric series, which converges for | x | < 1. Integrating both sides, we get
$\ln (1+x) = x-\frac{x^2}{2}+\frac{x^3}{3} \ldots$
which will also converge for | x | < 1. When x = -1 this is the harmonic series, which diverges'; when x = 1 this is an alternating series with diminishing terms, which converges to ln 2 - this is testing the extremities.
It also lets us write series for integrals we cannot do exactly such as the error function:
$e^{-x^2}=\sum (-1)^n \frac{x^{2n}}{n!}$
The left hand side can not be integrated exactly, but the right hand side can be.
$\int_0^z e^{-x^2}dx=\sum \frac{(-1)^n z^{2n+1}}{(2n+1)n!}$
This gives us a series for the sum, which has an infinite radius of convergence, letting us approximate the integral as closely as we like.
Note that this is not a power series, as the power of z is not the index. | 1,332 | 4,503 | {"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": 19, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.4375 | 4 | CC-MAIN-2015-22 | latest | en | 0.921511 |
https://www.ctralie.com/Teaching/ImageAnalogies/ | 1,718,941,120,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862036.35/warc/CC-MAIN-20240621031127-20240621061127-00196.warc.gz | 633,053,873 | 15,144 | # Image Analogies
## Introduction / Basic Algorithm
The purpose of "Image Analogies" is to try to assess the relationship between two images, A and A', and then to synthesize a new image B' from an image B such that the relationship between B and B' is the same as the relationship between A and A'. In general, this isn't an easy problem; even for linear filters, direct "deconvolution" to determine the impulse response of a filter is usually impossible because of the zeros in the frequency domain response of the filter. And this algorithm claims to solve an even more general problem than just linear relationships between A and A'. With a few assumptions and some massaging of the problem, however, some basic results are possible (and surprisingly convincing) in a few domains. The algorithm is presented in the following paper:
Image Analogies
A. Hertzmann, C. Jacobs, N. Oliver, B. Curless, D. Salesin.
SIGGRAPH 2001 Conference Proceedings.
In this assignment, I will implement the image analogies framework by following hints given in that paper. I will break down different heuristics and results that are suggested in the paper and show examples that my program generates.
Program Usage:
`analogy A A' B B'[-mask_color r g b] [-useAColors] [-bruteForce] [-luminanceRemappling] [-noGaussianLuminance] [-steerableFilters] [-kappa float coherence] [-ANNEps float] [-levels int] [-outputPyramid string directory+prefix] [-verbose]`
Parameter Purpose A, A', B, B' A and A' are the input images with some relationship between each other. They must be the same size. The program also takes as input B, and it synthesizes an image B' that has the same size as B such that A->A' ~ B->B' -mask_color r g b For the hole filling/image inpainting feature, specifies a color (r, g, b) of the mask that's used to specify holes (i.e. pixels with this color are overwritten using texture synthesis). r, g, b are in the range [0, 1.0]. In all of my examples I use the mask (0, 0, 1) (pure blue) bruteForce Use an exhaustive search over all feature vectors instead of ANN. By default, brute force is not used luminanceRemapping Whether or not to perform luminance remapping as described in section 3.4 of the paper (NOTE: I never actually use this in my examples...it's false by default) noGaussianLuminance Specifies whether or not to scale down neighborhoods around a pixel by a gaussian (so that neighboring pixels that are closer get emphasized more in the feature vector). This is false by default since the paper recommends it (i.e. I do perform the scaling down by default), though I didn't find it made a huge difference in practice. steerableFilters Whether or not to include steerable filters at the end of each feature vector in addition to luminance neighborhoods kappa Specifies the coherence parameter (described in section 3.2 of the paper). This is zero by default ANNEps The allowed error of the Approximate Nearest Neighbors library (default 1.0) levels The number of levels in multiresolution synthesis outputPyramid directory/previx If this parameter is specified, the entire gaussian pyramid of B' will be outputted to the directory specified verbose Outputs each scanline as it is finished (useful to make sure program isn't hanging at some scanline)
NOTE: Using the program for hole filling follows a slightly different input pattern. In this case, there isn't really an analogy; just one image to be fixed. So it has the following syntax:
`analogy maskedimage fixedimage -holeFilling`
Some implementation details:
• I am using the ANN Library to calculate approximate nearest neighbors. This library uses a KD tree to accelerate the process of finding a nearest neighbor in the high dimensional space of the feature vectors, though its answer isn't neccessarily perfect (will be explored in this writeup)
• To make using ANN easy, I store the "codebook" of features as a double** array. That is, all of the features from the A->A' pair are stored in the first dimension, while the components of each one of these features is stored in the second dimension. The reason I chose to do this is because later on when constructing an ANN KD-Tree, this 2D array simply has to be casted and it's done (hardly any code is added to use ANN).
I have functions to append features together from different images, since correspondences are created between the concatenated features in A and A' and the concatenated features in B and B'. For multiresolution synthesis, the order of the different features is as follows:
[A from previous level (at a coarse resolution 3x3)] . [A' from previous level (at a coarse resolution of 3x3)] . [A from this level (at a fine resolution of 5x5] . [A' from this level (L-Shaped, at a fine resolution of 5x5)]
The same order is followed for the B and B' images, and a feature from B and B' is compared to a library of all such features from A and A'.
NOTE: When I say L-shaped, I mean that the feature only includes pixels that have been synthesized before in scan-line order.
• There is a problem at the first few scan lines because not all of the pixels in the "L shape" have been synthesized yet. So I copy the first few scanlines over without doing any nearest neighbor searching (I just find the closest pixel spatially). This screws up the bottom a little bit if you zoom way in, but it's not very noticeable and I didn't find that it affected the results very adversely. So I left this approach because it was simple
• There's a similar problem with incomplete neighborhoods for the hole filling (image inpainting) case; the neighborhood of completed pixels around a mask pixel is not guaranteed to be (and rarely is) L-Shaped. I completely abandoned ANN in this case and used brute force for everything, comparing only the pixels between each feature that are completed in both. I'll explain this more later with examples, and I'll explain a proposal I have to extend this to use ANN (which I unfortunately did not have time to implement)
## Coherence
The algorithm goes through and finds the most similar neighborhood to the neighborhood of the pixel to be synthesized, disregarding the location of that pixel. A natural extension that has been proposed by several before this (starting with this paper) is to favor pixels that are close together instead of scattering pixels from all over. This is known as "coherence." I've implemented my own version of coherence following the recommendations in the Image Analogies paper, which is called Kappa and is a positive real number. Here are some results varying the coherence parameter
Kappa A A' B B' Kappa = 0.5 `./analogy ../input/texture1.A.jpg ../input/texture1.Ap.bmp ../input/coherence.jpg ../output/coherence_0.5.bmp -kappa 0.5 -useAColors -bruteForce` Kappa = 2 `./analogy ../input/texture1.A.jpg ../input/texture1.Ap.bmp ../input/coherence.jpg ../output/coherence_2.bmp -kappa 0.5 -useAColors -bruteForce` Kappa = 4 `./analogy ../input/texture1.A.jpg ../input/texture1.Ap.bmp ../input/coherence.jpg ../output/coherence_4.bmp -kappa 4 -useAColors -bruteForce` Kappa = 8 `./analogy ../input/texture1.A.jpg ../input/texture1.Ap.bmp ../input/coherence.jpg ../output/coherence_8.bmp -kappa 8 -useAColors -bruteForce`
Discussion: First of all, I decided to do these all with brute force to avoid the inherent errors with ANN. That is, ANN will tend to choose features that have a greater error than the coherence feature, so it doesn't take as much for coherence to show.
With coherence very low (at 0.5), the output image is locally consistent at each pixel but it grows a few regions that are a factor or two bigger than the original "blobs" in A'. As coherence is increased to 2, the size of the output blobs shrinks slightly and an image is synthesized that is closer in form to the original. That is, the program strikes a better balance between synthesizing pixels that make sense locally and pulling pixels from the source image that are closer to each other. As coherence is increased more, though, the trade-off of using too much coherence is more visible. The program pulls so many pixels that are close to each other that it ends up taking large patches from the input image and putting them next to each other in the output image. But it isn't able to synthesize locally accurate pixels well enough, so there are visible seams between these patches. The problem is even more pronounced with Kappa = 8. Thus, some intermediate value of Kappa will usually need to be found that can preserve some of the features during synthesis and pull small patches, but that is also able to not rely directly on patches to the extent that they can't be blended together by pixels that aren't perfect spatial matches.
From now on in my examples I will use values of Kappa that aren't justified in this writeup; they are just values I found reasonable for the particular application I was looking at.
## Multiresolution Synthesis
One problem with using just a 5x5 neighborhood to create the feature vectors is that it's inherently difficult to capture larger features in an image pair that extend beyond that small window. A bigger window could be created, but then the time complexity would scale quadratically (which is bad). One way to "cheat the system" a little bit and encapsulate larger features is to use "multiresolution synthesis" with a Gaussian pyramid. What first happens is the images (A, A', and B) are anti-aliased and downsampled several times to form different levels in a Gaussian Pyramid. Here's an example Gaussian Pyramid generated by my program:
I implemented this using a separable Gaussian filter (for anti-aliasing) so that 2D convolution could be performed more efficiently for blur antialiasing, followed by downsampling by 2.
Once the three pyramids are constructed for A, A', and B, synthesis proceeds one level at a time with B'. The smallest B' image is constructed first, and then information from that small image is used to help construct the image at the next largest level so that the images match. And so on up the pyramid. In other words, a really low resolution image is constructed, and then an image at twice the resolution is used to "fill in the details" of that lower resolution image, and so on until B' is back up at the original resolution. Here are some results on this process in a "texture by numbers" application (explained more later):
A A' B
level 1: 119.91 sec level 2: 266.99 sec level 3: 301.54 sec level 4: 313.34 sec
Levels B' Levels = 1 `./analogy ../input/oxbow-mask.jpg ../input/oxbow.jpg ../input/oxbow-newmask.jpg ../output/multires1.jpg -levels 1 -kappa 0.0 -useAColors`Time: 119.91 Seconds Levels = 2 `./analogy ../input/oxbow-mask.jpg ../input/oxbow.jpg ../input/oxbow-newmask.jpg ../output/multires2.jpg -levels 2 -kappa 0.0 -useAColors`Time: 266.99 Seconds Levels = 3 `./analogy ../input/oxbow-mask.jpg ../input/oxbow.jpg ../input/oxbow-newmask.jpg ../output/multires3.jpg -levels 3 -kappa 0.0 -useAColors`Time: 301.54 Seconds Levels = 4 `./analogy ../input/oxbow-mask.jpg ../input/oxbow.jpg ../input/oxbow-newmask.jpg ../output/multires4.jpg -levels 4 -kappa 0.0 -useAColors -outputPyramid ../output/multires4pyramid/level`Time: 313.34 Seconds
The effect of increasing the number of levels is clearly seen in this example. Using only one level, the algorithm was unable to capture some of the larger features; it only preserved local stochastic information. So the textures are rather uniform in the output (there's greenish stuff around the forest and blue-whitish stuff in the water). As the number of levels increases, larger features with more detail are more accurately synthesized. The forest begins to come into focus with individual trees, and the water contains directional flow that couldn't be captured with a small 5x5 pixel window.
Using more levels does slow things down, though, but this is to be expected. The feature vectors have increased in size by a factor of (3x3) / (5x5) (the ratio of the neighborhood from a smaller image in the pyramid to the neighborhood of the current level) since they now include information from the level previously synthesized. Also, now L images are being synthesized instead of just 1. However the increase in time diminishes for the addition of even more levels (it more than doubles adding one level, but then hardly increases from 3 to 4 levels later on). This is because adding more levels begins adding exponentially smaller images which hardly take any time to synthesize.
Here is the image pyramid for the last example using 4 levels:
Notice how from left to right, the images are consistent but slowly come "into focus" (more detail is filled in at each multiresolution pass) n
## Approximate Nearest Neighbor Search (ANN)
As I mentioned before in the introduction, it's extremely slow to exhaustively search all features from [A, A'] to match a feature in [B, B'] associated with each new pixel. So instead all features [A, A'] can be put into an ANN data structure. This speeds up things significantly at the loss of the guarantee that the pixel from [A, A'] is the absolute closest in feature space. The pixel returned from ANN will be close, just not as close in most cases. It's unclear how badly this will impact synthesis results, because in most cases brute force takes too long to even calculate in the time that I had to do this assignment. But here are a couple of tests exploring this trade-off in a small texture synthesis example where brute force finishes in a reasonable amount of time:
Kappa A A' B B' (brute Force) B' (ANN) 0 Time: 55.11 secs Time: 0.53 secs 10.0 Time: 55.23 secs Time: 0.68 secs
First note that ANN is literally 100x faster. This makes it possible to get results for images that otherwise would have been impossible (most of the images in the rest of the writeup). Also note how for ANN, the program doesn't get stuck synthesizing large blobs as easily. Presumably this is because it's no longer choosing the best feature (which would allow it to keep growing) but something else that makes it start growing an edge sooner.
## Constrained Texture Synthesis (Hole Filling)
So far all image analogies have been synthesized by filling in new pixels in scan-line order. However, this cannot be done when filling holes since the portion of the already-synthesized neighborhood around a pixel in a hole is not necessarily L-Shaped. This makes it difficult to construct an ANN library of features as I did before because I don't know ahead of time what shapes the neighborhood will be. So I abandoned ANN completely so I could do brute force and control which pixels were compared (and no multiresolution synthesis). When finding the distance between a feature from [A, A'] and [B, B'] in brute force hole filling, I only compare the features that aren't the color of the mask pixel. This forces the program to fill in the hole using information outside of the hole.
Another problem to worry about is in what order to fill the hole. Doing it in scan line order isn't a good general solution because this will always leave one line at the bottom of the hole that can potentially be a huge seam. It's better to synthesize the hole by filling in the pixels around the border in "onion order" because they converge at a point. I set up code to do this by using the following scheme:
1. Look at the pixels in scan-line order from top to bottom until a mask pixel is found (the mask pixels indicate where the hole is). Begin synthesis at this pixel and go to step 2. Return when the end of the image is reached
2. Start by going "to the right" in clockwise order. After the current pixel is synthesized, try to move to the next pixel based on the priority presented in the following image:
In other words, the pixel in the center is the pixel that has just been synthesized, and I'm looking for a new pixel on the boundary of the hole to be synthesized. First check the pixel directly above that's labeled "1." If that pixel isn't part of the hole, see if the pixel above and right (2) is. If that's not, check the one to the right (3). And so on and so forth. If a cell with a red number is used next, then start going "to the left" to continue going counter-clockwise; that is, go to step 3. If no pixels are in the hole then go back to step 1 and pick up where the scan-line traversal left off
3. Do the same thing as step 2 except use the following successor priority square for finding the next pixel to synthesize:
And go back to step 2 if a red pixel is encountered
This scheme makes sure that all holes are synthesized by filling in pixels in clockwise boundaries, and it seems to work pretty well (please see my results in the image inpainting section).
In the interest of time, I decided to stop here and just continue to use brute force. But I believe there may be a way to speed this up with ANN using multiresolution synthesis, at the cost of results. My idea would be to continue to downsample the image until the hole shrinks down to something smaller than, say 20x20. Use brute force on this small image, and then use ANN on the larger images in the pyramid (but only taking features from the completed neighborhoods in the lower levels so that ANN can be constructed on a deterministic set of features). This way, the hole can be carefully filled in at a very coarse level that doesn't take long with brute force, and then the work that's done there can propagate up as it normally does with multires. This is a very complicated approach, though, (especially since anti-aliasing images before downsampling blurs the holes) and it would have really bloated my code so I didn't get a chance to try it to see how well it works...
## Steerable Filters (Sort Of)
I didn't have time to do steerable filters in the most rigorous sense of the term, but I wanted to try something beyond just luminance neighborhoods (even though this wasn't a required feature in this assignment). So I decided to do a watered-down version of steerable filters that just takes two directional derivatives: Fx (the gradient in x) and Fy (the gradient in y). Fx = x*exp(-(x^2+y^2)) and Fy = y*(exp(-(x^2+y^2)). The size of the filter is equal to the size of the luminance neighborhood for each filter (3x3 for coarse features from the previous level in the gaussian pyramid, and 5x5 at the finer resolution in the current level). Hence, two real numbers are appended to the feature vector for each pixel in addition to the luminance neighborhoods.
One huge motivation for me to do that was with learning motion blur, which was a huge failure case of just luminance neighborhoods that I noticed during testing. Let me now show the results of trying to learn motion blur with and without this simplified version of steerable filters:
Learning Example:
A A'
I pulled this example from my first assignment in COS 426 a couple of years ago where I blurred an image along the vector (1, 3). Here are some results:
B B' (just luminance neighborhoods) B' (with gradients Fx and Fy appended to all feature vectors) `./analogy ../input/motionblur.A.jpg ../input/motionblur.Ap.jpg ../input/blur.B.bmp ../output/motionblur1.bmp -levels 4` `./analogy ../input/motionblur.A.jpg ../input/motionblur.Ap.jpg ../input/blur.B.bmp ../output/motionblur1_steerable.bmp -levels 4 -steerableFilters` `./analogy ../input/motionblur.A.jpg ../input/motionblur.Ap.jpg ../input/blur.A.bmp ../output/motionblur2.bmp -levels 4` `./analogy ../input/motionblur.A.jpg ../input/motionblur.Ap.jpg ../input/blur.A.bmp ../output/motionblur2_steerable.bmp -levels 4 -steerableFilters` `./analogy ../input/motionblur.A.jpg ../input/motionblur.Ap.jpg ../input/photobomb3.jpg ../output/motionblur3.bmp -levels 4` `./analogy ../input/motionblur.A.jpg ../input/motionblur.Ap.jpg ../input/photobomb3.jpg ../output/motionblur3_steerable.bmp -levels 4 -steerableFilters`
As you can see, the algorithm simply doesn't have the capacity to learn a directional filter like this without gradient information. And while these results clearly aren't perfect, diagonal streaks are clearly visible in the images that use gradient information, while ones with just luminance in their feature vectors just look a little "blurry" with no clear directional component.
## Image Filters
In this section I will examine how effective image analogies are at capturing simple image filters. Specifically, I will examine the linear filters "emboss" and "blur" and the nonlinear "median filter".
### Median Filter
Levels A A' B B' Levels = 1 `./analogy ../input/salt.A.jpg ../input/salt.Ap.jpg ../input/salt.B.bmp ../output/salt.Bp_1.bmp -levels 1` Levels = 4 `./analogy ../input/salt.A.jpg ../input/salt.Ap.jpg ../input/salt.B.bmp ../output/salt.Bp_4.bmp -levels 4`
Here's one example where using more than one level isn't a good idea. I gave the program an image A corrupted by a mild level of salt-and-pepper noise, and a corrected image as A'. I then gave as B an image corrupted by worse salt-and-pepper noise to see if it could be corrected at all (a sort of stress test of the learning). If I use more than one level, the salt and pepper noise gets blended in as the image is blurred for anti-aliasing. This is bad. As you can see, the result is better for just one level, and image analogies does a surprisingly good job at learning the median filter
### Embossing
Command A A' B B' `./analogy ../input/emboss.A.bmp ../input/emboss.Ap.bmp ../input/emboss.B.bmp ../output/emboss.Bp.bmp -levels 4 -kappa 0.0 -useAColors`
This is a relatively straightforward application of image analogies that does a surprisingly good job at capturing the "emboss" feature. Note that I have to use the -useAColors parameter since I want the final output to be gray (not the colors of B)
### Uniform Blur (no motion)
Command A A' B B' `./analogy ../input/blur.A.bmp ../input/blur.Ap.bmp ../input/blur.B.bmp ../output/blur.Bp.bmp -levels 2 -kappa 0.0`
This example also works quite well
In conclusion, image analogies do well at capturing simple filters (especially linear ones). This makes sense because the algorithm is essentially using 3x3 and 5x5 luminance kernels as feature vectors. So in these cases that reduces to learning the convolution filter.
## Texture Synthesis
Image analogies can be coaxed into doing traditional texture synthesis if A is a blank image and A' is an image with the desired texture. Then B can be given as a blank image of a greater size and B' will be filled in with the texture from A'. In the examples below I synth as size textures at 2x the size and 4x the size as the input texture:
./analogy ../input/texture3.A.jpg ../input/texture3.Ap.bmp ../input/texture3.B2.jpg ../output/texture3.Bp2.bmp -levels 4 -kappa 4.0 -useAColors
Command A A' B B' `./analogy ../input/texture1.A.jpg ../input/texture1.Ap.bmp ../input/texture1.B1.jpg ../output/texture1.Bp1.bmp -levels 4 -kappa 4.0 -useAColors` `./analogy ../input/texture1.A.jpg ../input/texture1.Ap.bmp ../input/texture1.B2.jpg ../output/texture1.Bp2.bmp -levels 4 -kappa 4.0 -useAColors` ` ./analogy ../input/texture2.A.jpg ../input/texture2.Ap.bmp ../input/texture2.B1.jpg ../output/texture2.Bp.bmp -levels 7 -kappa 4.0 -useAColors` `./analogy ../input/texture3.A.jpg ../input/texture3.Ap.bmp ../input/texture3.B1.jpg ../output/texture3.Bp1.bmp -levels 4 -kappa 4.0 -useAColors` `./analogy ../input/texture3.A.jpg ../input/texture3.Ap.bmp ../input/texture3.B2.jpg ../output/texture3.Bp2.bmp -levels 4 -kappa 4.0 -useAColors`
The dirt is very stochastic so I only used one level in its synthesis. By contrast, the flower has very large features, so I used 7 levels
## Texture By Numbers
Here's where the fun really begins. The "texture by numbers" idea described in the paper in section (4.6) is as follows. Take some image A' and create an image A that is a segmented, masked version of A labeled by hand. So for example, in the human face, (which is one of the examples I use), one could draw a blue blob over the nose in A, a pink blob over the skin in A, a yellow blob over the ears, etc. Then a new mask, B, can be created, and the appropriate textures from the face can be "grown onto" B. It's easiest to see with a few examples. First I'll start with an example from the paper:
Command A A' B B' ```./analogy ../input/potomac-mask.jpg ../input/potomac.jpg ../input/potomac-newmask.jpg ../output/new-potomac.bmp -levels 4 -kappa 0.0 -useAColors ```
Now I'm going to make a mask of my face from my high school senior portrait, which will give rise to some pretty frightening results...
Command A A' B B' ```./analogy ../input/me-mask.bmp ../input/me.jpg ../input/cyclopsmask.bmp ../output/cyclops.bmp -levels 4 -kappa 15.0 -useAColors ```
```./analogy ../input/me-mask.bmp ../input/me.jpg ../input/newfacemask1.bmp ../output/newface1.bmp -levels 4 -kappa 30.0 -useAColors ```
```./analogy ../input/me-mask.bmp ../input/me.jpg ../input/newfacemask2.bmp ../output/newface2.bmp -levels 4 -kappa 30.0 -useAColors ```
Once you're finished laughing at how absurd this looks, take a careful look at the outputs. Although their not perfect, the algorithm does an amazing job at preserving local information. It has the most trouble when the new eye sockets and mouths are bigger than the original ones, since it doesn't quite know how to fill the extra space (it ends up taking a trade-off with coherence that results in a seam).
## Image Inpainting
Image inpainting is the primary application of hole-filling. The idea is to designate one color as the "mask color" in an image, and to treat every pixel that has that color as a hole in the image. The goal is to fill all holes so that their properties are consistent with the statistics of the surrounding pixels. I already explained in the hole-filling section how I do this, so let me present some results here of applying a blue mask (R, G, B) = (0, 0, 255) to four images:
Command
Original Image
Region Selected for Deletion with Mask
Fixed Hole
`./analogy ../input/hole4.bmp ../output/hole4_fixed.bmp -holeFilling -mask_color 0 0 1`
`./analogy ../input/hole1.bmp ../output/hole1_fixed.bmp -holeFilling -mask_color 0 0 1`
## N/A
(this image is just a hole; there's no original info)
`./analogy ../input/hole2.bmp ../output/hole2_fixed.bmp -holeFilling -mask_color 0 0 1`
`./analogy ../input/hole3.bmp ../output/hole3_fixed.bmp -holeFilling -mask_color 0 0 1`
I presented the images here in decreasing order of effectiveness.
1. The first image shows me removing posters from the wall behind me. It's perfect since the wall is a texture with very little variation to be filled back in.
2. The next image shows an example from an Efros and Leung paper, which also works quite well because that is a highly stochastic texture.
3. This image shows me removing a pesky ballpark employee from behind the scoreboard who's distracting from the catch being made. This works pretty well except there's a small artifact where part of the wall from the scoreboard seeped into the hole. But otherwise it's pretty good
4. This is somewhat of a failure case, although arguably still an improvement. I was trying to remove that passed out guy in the background of the image, but since only one level is used the algorithm was unable to learn some of the higher-level details such as the railings on the fence. However, the resulting image is definitely less absurd looking because now it just looks like a minor artifact, not some drunk guy passed out in the background ruining the photo
## Image Colorization
Now here comes the most challenging task of all, and an example one of the biggest shortcomings of image analogies (in spite of the somewhat contrived "success" cases given in the paper). I'm going to try to infer color in a grayscale image by presenting the program with an A that is grayscale, an A' that's a colored version of that grayscale image, and a B that's a new grayscale image. The goal is to infer colors from B by using hints from the [A, A'] pair. Here are the results:
Command A A' B B' ```./analogy ../input/blackwhite1.jpg ../input/color1.jpg ../input/blackwhite2.jpg ../output/color2.jpg -useAColors -levels 2 -kappa 1.0 ```
```./analogy ../input/blackwhite1.jpg ../input/color1.jpg ../input/blackwhite3.bmp ../output/color3.jpg -useAColors -levels 2 -kappa 1.0 ```
```./analogy ../input/blackwhite1.jpg ../input/color1.jpg ../input/blackwhite4.bmp ../output/color4.jpg -useAColors -levels 2 -kappa 1.0 ```
`./analogy ../input/blackwhite2.jpg ../input/color2.jpg ../input/blackwhite1.jpg ../output/color1_2.jpg -useAColors -levels 2 -kappa 1.0`
`./analogy ../input/blackwhite2.jpg ../input/color2.jpg ../input/blackwhite3.jpg ../output/color3_2.jpg -useAColors -levels 2 -kappa 1.0`
`./analogy ../input/blackwhite2.jpg ../input/color2.jpg ../input/blackwhite4.jpg ../output/color4_2.jpg -useAColors -levels 2 -kappa 1.0`
Overall, the results aren't so great; for the most part the grays get mapped to browns so the grayscale images essentially turn into "brownscale" images. However, I do want to point out a surprise success right at the beginning in example 1. Somehow, the analogies were able to figure out that my Einstein poster is a medium shade of orange, and they also matched the skin tone on our faces rather well. I was very surprised and impressed by that.
In general, learning the analogy on an image with a more equal histogram of colors (the globe in the classroom for the first 3 examples) also did a much better job than an image with a less equal color histogram (a picture of people in a room)
One more thing to note is how much image analogies were able to improve the salt and pepper noise image from start to finish learning the median filter and then learning colorization:
## Brief Conclusions
Overall, image analogies does a surprisingly good job at learning transformations from one image to another well enough to apply them to an unseen image. The technique works especially well on simple filters, especially ones that are linear and can be expressed as a convolution. But it also does well in some fringe applications, such as the "texture by numbers," that would be hard-pressed to find comparable methods that are as simple.
It's alive!!! | 7,218 | 30,280 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2024-26 | latest | en | 0.895288 |
https://pastebin.com/zEsihnbs | 1,624,037,801,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487640324.35/warc/CC-MAIN-20210618165643-20210618195643-00400.warc.gz | 406,399,147 | 6,282 | # Untitled
May 9th, 2021
599
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1. #include <iostream>
2. #include <cmath>
3.
4. using namespace std;
5.
6. double operation_1(double x) {
7. return 3 * pow(x, 2) - 150 * sin(x);
8. }
9.
10. double operation_2(double x) {
11. const double e = 2.7182818284;
12. return pow(e, x / 2) - pow(x, 3) + 50;
13. }
14.
15. double operation_3(double x) {
16. return pow(x, 3) - pow(x, 2) - 50;
17. }
18.
19. double operation_4(double x) {
20. return 3 * x - pow(x, 2);
21. }
22.
23. double half_division_method(double(*operations)(double), double a, double b, const double E) {
24. double x_2 = 0;
25. while (b - a > E) {
26. x_2 = (b + a) / 2;
27. if (operations(x_2) * operations(b) <= 0)
28. a = x_2;
29. else
30. b = x_2;
31. }
32. return x_2;
33. }
34.
35. double(*operations[4])(double) = { operation_1,operation_2,operation_3,operation_4 };
36. enum { first_operation, second_operation, third_operation, fourth_operation };
37.
38. int main() {
39. setlocale(LC_ALL, "Russian");
40. double a, b, x;
41. int number;
42. const double E = 0.0001;
43. cout << "Введите интервал: " << endl;
44. cout << "Левая граница: ";
45. cin >> a;
46. cout << "Правая граница: ";
47. cin >> b;
48.
49. cout << "На интервале [" << a << ";" << b << "] :" << endl;
50. for (;;) {
51. cout << endl << "Введите номер требуемой вам функции: " << endl;
52. cout << "1. Уравнение 3*x2-150*sin(x)=0." << endl;
53. cout << "2. Уравнение e^x/2-x3+50=0. " << endl;
54. cout << "3. Уравнение x3-x2-50=0. " << endl;
55. cout << "4. Уравнение 3x-x2=0. " << endl;
56. cout << "0-конец расчета. " << endl;
57. cout << "Ваш выбор: ";
58. cin >> number;
59. if (number < 5 && number != 0) {
60. double x = half_division_method(operations[number - 1], a, b, E);
61. cout << x;
62. }
63. if (number >= 5) {
64. cout << "Ошибка ввода.";
65. }
66. if (number == 0) {
67. cout << "Расчет окончен.";
68. break;
69. }
70. }
71.
72. return 0;
73. }
74.
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www.nallssherbakoff.com | 1,726,481,369,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651682.69/warc/CC-MAIN-20240916080220-20240916110220-00468.warc.gz | 822,765,365 | 41,743 | }
Mon-Thur, 9am-5pm; Fri, 9am-1pm
(865) 691-0898
“The greatest shortcoming of the human race is the inability to understand the exponential function.” – Dr. Albert Bartlett
Do you understand the theory of exponential growth and its relationship to investing? Could you teach the concepts to a middle school class? Well, if not, you are in a large majority of investors. People tend to think linearly, so many of us have trouble grasping the effect of compounding, or exponential growth. For example, if you saved a penny on February 1 and then doubled that the next day to save 2 pennies on February 2, and doubled again to 4 pennies on the 3rd, then 8 on the 4th until the last day of February, the 28th, how much money do you think you would have? (Here’s a hint, at the end of the first week you would have \$1.27.) Make your best guess now, and we’ll reveal the correct answer later in this letter, after we explain the concept of exponential growth.
In 2016, the price value of the S&P 500 grew by 9.54%. It closed 2015 at 2,043.93 and closed out 2016 at 2,238.83. Since 1950, a portfolio made up of 50% equities and 50% bonds (50/50 portfolio) has had an average annual return of 8.9%. In other words, the annual rate of change from 1950 to the end of 2016 has been 8.9% per year. However, the amount of change over that time for even a modest portfolio would be quite substantial. The amount of change each year is dependent on the previous period’s value, and the amount of change will be a little bit larger each period, on average.
In investing, exponential growth has phenomenal power over the long term. Say you started investing at age 25 and for the next 40 years you put \$2,000 per year into a 50/50 portfolio averaging 8.9%, until you turned 65. The power is in the fact that you are receiving growth upon growth. Although each year you are receiving the same percentage change, 8.9%, the amount of change is growing larger at a faster rate.
To illustrate how the amount of growth of a \$2,000 annual contribution accelerates each year, let’s look at some key milestones along the way.
Unlike the rate of change, 8.9%, the amount of change is not constant in exponential growth. As shown above, \$100,000 milestones are met in much shorter time frames. In exponential growth, you can either think of the speeding up as (1) the accounts accelerate in size over each fixed time period or (2) you can think about how the amount of time shortens between each fixed amount added.
Exponential growth and the compounding of interest can be difficult for investors to understand and not understanding can have severe consequences. In a recent study using data from RAND American Life Panel and Understanding America Study data, researchers found that only 25% of respondents correctly perceived account balances to grow exponentially over time. There exists a significant “exponential growth bias” that limits investors’ expected return of saving and, thus, investors do not adequately fund their retirement accounts. Further, when an exponential growth bias of lower returns is coupled with a “present bias” to defer investing to sometime in the future, that unfortunate combination leads to smaller retirement account balances later in life.
In today’s world, with the decline of traditional pension plans and the possibility of smaller than expected Social Security benefits, future retirement income is the responsibility of the worker/investor primarily through company-sponsored 401(k) and IRAs. As a result, the individual skills, knowledge, abilities, habits and attitudes toward saving are incredibly consequential for their retirement security. Individuals who use commitment strategies such as auto-enrollment and auto-escalation in 401(k) accounts to counteract present bias, or who use tools and expert advice to address exponential growth bias, have a higher likelihood of experiencing a fully funded retirement.
If you know of someone who struggles with saving today for retirement income in the future due to an exponential growth bias or present bias, we would be happy to sit down with them. Please give us a call.
By the way, here’s the answer to the exponential growth problem in the opening paragraph: after 28 doublings starting with just one penny on day one, you would have \$2,684,354.55. And, if you began to double every day in March, which has 31 days, those extra three days’ worth of daily doublings would bring your total to a massive \$21,474,836.47.
We hope you’ve found this review to be educational and helpful. As we like to emphasize, it is our job to assist you. Thank you very much for the trust and confidence you’ve placed in our firm. We treasure our relationships with our clients, and seek to serve a few more people like you. If you know of someone who would benefit from our advice and services, we would welcome an introduction.
DISCLOSURES: The information provided in this letter is for general informational purposes only and should not be considered an individualized recommendation of any particular security, strategy or investment product, and should not be construed as investment, legal, or tax advice. The Nalls Sherbakoff Group, LLC makes no warranties with regard to the information or results obtained by third parties and its use and disclaim any liability arising out of, or reliance on the information. These indexes reflect investments for a limited period of time and do not reflect performance in different economic or market cycles and are not intended to reflect the actual outcomes of any client of The Nalls Sherbakoff Group, LLC. Past performance does not guarantee future results. | 1,235 | 5,675 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2024-38 | latest | en | 0.954078 |
https://issbprguide.com/coding-and-decoding-test-verbal-intelligence-test/ | 1,696,258,757,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233511000.99/warc/CC-MAIN-20231002132844-20231002162844-00115.warc.gz | 359,229,080 | 25,876 | Mon. Oct 2nd, 2023
# Coding and Decoding Verbal Intelligence Test
## General Instructions
Candidates appearing for any test that consists Verabl Intelligence Tests can learn how to solve it, by preparing the following different types of Verbal Intelligence Tests.
## Different Types of Verbal Intelligence Tests
Following are the 20 Types of Verbal Intelligence Tests which are used to test the inborn mental efficiency or the capacity to react favourably or find solutions to problems of an unfamiliar and novel nature.
## 6th: Coding Decoding Tests
In this test Coding & Decoding is done using some of the undermentioned techniques
Letter Coding/Decoding: The letters/alphabets of a word are replaced by other particular letters/aplhabets using a common rule. Candidates are required to know the
Rules
Next letter of alphabet is code.
Fourth letter of the alphabet is code.
Each preceding letter of the alphabet is code.
The second preceding letter of the alphabet is code.
Moreover, the rules can be judged by finding the pattern of given questions.
Example:
(1) If PAK is coded as QBL then WAR is coded as :
Choices:
(a) XBS
(b) XDS
(c) VBS
(d) XBQ
Solution:
(1) In order to code PAK the succeeding letter is use such as, Q successes L, B successes A & K successes L.
Similarly, for WAR. X successes W, B successes A & S successes R.
The vise versa is used in order to decode.
Number Coding/Decoding: The letters/alphabets are assigned with corresponding alphabetic position or the numerical code value is assigned to a word.
Example:
(1) If DOG is coded as 4157 then FOG is coded as : (According to the corresponding alphabetic position)
Choices:
(a) 6157
(b) 6715
(c) 1576
(d) 7156
(2) If LAHORE us coded as 592648 & CAT is coded as 193 then CLEAR will be coded as : (According to the numerical code value)
Choices:
(a) 49851
(b) 15894
(c) 89451
(d) 15893
Solution:
(1) The corresponding alphabetic position of D is 4, O is 15 and G is 7. Therefore, the corresponding alphabetic position of F is 6, O is 15 and G is 7.
(2) The numerical code value of L is 5, A is 9, H is 2, O is 6, R is 4, E is 8, C is 1 and T is 3.
Therefore, the numerical code value of CLEAR will be 15894.
Substitution of Words: This test comprises code names of particular words, names, places etc. Candidates are required to answer the question in coded language.
Example:
(1) If orange is called butter, butter is called soap, soap is called ink, ink is called honey and honey is called orange, which of the following is used for filling a pen?
Choices:
(a) Soap
(b) Ink
(c) Butter
(d) Honey
Solution:
(1) As Ink is called as Honey. So, the Honey would be used to fill the pen. | 769 | 2,828 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2023-40 | latest | en | 0.765782 |
https://numberworld.info/10012011 | 1,725,774,739,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700650960.90/warc/CC-MAIN-20240908052321-20240908082321-00430.warc.gz | 413,359,650 | 3,906 | # Number 10012011
### Properties of number 10012011
Cross Sum:
Factorization:
3 * 67 * 49811
Divisors:
Count of divisors:
Sum of divisors:
Prime number?
No
Fibonacci number?
No
Bell Number?
No
Catalan Number?
No
Base 2 (Binary):
Base 3 (Ternary):
Base 4 (Quaternary):
Base 5 (Quintal):
Base 8 (Octal):
98c56b
Base 32:
9hhbb
sin(10012011)
0.25440877017301
cos(10012011)
0.96709677781443
tan(10012011)
0.26306443781971
ln(10012011)
16.119296030215
lg(10012011)
7.0005213180873
sqrt(10012011)
3164.1761961054
Square(10012011)
### Number Look Up
Look Up
10012011 (ten million twelve thousand eleven) is a very amazing figure. The cross sum of 10012011 is 6. If you factorisate the number 10012011 you will get these result 3 * 67 * 49811. The figure 10012011 has 8 divisors ( 1, 3, 67, 201, 49811, 149433, 3337337, 10012011 ) whith a sum of 13548864. 10012011 is not a prime number. 10012011 is not a fibonacci number. 10012011 is not a Bell Number. 10012011 is not a Catalan Number. The convertion of 10012011 to base 2 (Binary) is 100110001100010101101011. The convertion of 10012011 to base 3 (Ternary) is 200211122220020. The convertion of 10012011 to base 4 (Quaternary) is 212030111223. The convertion of 10012011 to base 5 (Quintal) is 10030341021. The convertion of 10012011 to base 8 (Octal) is 46142553. The convertion of 10012011 to base 16 (Hexadecimal) is 98c56b. The convertion of 10012011 to base 32 is 9hhbb. The sine of 10012011 is 0.25440877017301. The cosine of the figure 10012011 is 0.96709677781443. The tangent of the number 10012011 is 0.26306443781971. The root of 10012011 is 3164.1761961054.
If you square 10012011 you will get the following result 100240364264121. The natural logarithm of 10012011 is 16.119296030215 and the decimal logarithm is 7.0005213180873. You should now know that 10012011 is very impressive number! | 662 | 1,853 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2024-38 | latest | en | 0.668518 |
https://physics.stackexchange.com/questions/671123/gravitational-potential-energy-lab-confusion | 1,701,860,886,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100593.71/warc/CC-MAIN-20231206095331-20231206125331-00423.warc.gz | 526,219,761 | 42,039 | # Gravitational Potential Energy Lab Confusion
I had a lab that tested the dependence of gravitational potential energy on its position and the goal out of each exercise was to see if kinetic energy equaled potential energy. A cart was on a flat frictionless track, with a string attached to it and a hanging 20-g mass on the opposite end of the string hanging down by a pulley. We saw that the kinetic energy was inversely proportional to the PE in this exercise and that in this case there were multiple kinetic energy forms and a single potential energy term.
My confusion lied in the exercise that followed, where the track was now raised at an angle, the front of the cart pointing down the ramp. The difference aside from the elevated track was now we had multiple potential and kinetic energy forms. Our lab instructor mentioned that the carts height will change as it moves along the ramp but NOT by the same amount as the hanging mass. I don't understand that statement because when I plotted the potential and kinetic energy vs time graphs for both exercises they were basically identical, showing that both KE and PE were inversely proportional. Am I not understanding the question correctly when I relate it to the the kinetic energy and potential energy graphs?
Disclaimer: I know the colors suck and are distracting but the software I use in class to collect data doesn't have an easy way of making the graphs appealing to the eye.
For both exercises I used the equation to plot the graphs where kinetic energy was:
$$KE=\frac{1}{2}mv_f^2-\frac{1}{2}mv_i^2$$
and potential energy was:
$$PE = mgh_i+mgh_f$$
Flat Surface Exercise
Surface Raised At Angle Exercise
• Are you sure they said direction and not say distance or height? This is straightforward to prove that the inclined carts change in height is not the same as the falling mass just using trigonometry. Oct 11, 2021 at 19:58
• Oof I'm dumb I'll edit that, I just went back and it did say height not direction. That's the part I'm stuck on is how I'd use the trig components to solve this. Oct 11, 2021 at 20:05
• Your best bet is to start with a drawing of the set-up Oct 11, 2021 at 20:08
## 1 Answer
Where the cart is on a flat surface, when you release the weight it drops and both it and the cart gain speed, which means that they gain kinetic energy. Since they are connected by a string, they both move at the same speed. Assuming they are stationary at the start of the experiment, the kinetic energy they gain is half of their combined mass times the square of their velocity at the point you measure it. You can equate that to mgh, where m is the mass of the weight and h is the vertical distance through which it has dropped. The cart is moving horizontally, so its potential energy does not change.
Then the cart is on a slope, it is no longer moving horizontally, but gradually moving downwards. It does not move downwards as quickly as the weight, since the weight is falling vertically. The gain in kinetic energy can be calculated in the same way as before, namely as half the combined mass of the cart plus the weight times the square of their common speed. The PE lost by the weight is again mgh, where m is the mass of the weight and h is the height through which it has fallen. What you now have to calculate is the loss of PE of the cart. You know that the distance it has travelled along the slope is equal to h, since the cart and the weight are connected by a string. So now you need only resolve that into two components, namely the horizontal component and the vertical. You should find that the vertical component is h times the sine of the angle the slope makes with the horizontal.
• So what I ended up getting was GPE = mg(0.93-x)sin(2). Where 0.93 was the distance the cart travelled from it's initial point to it's final point. Oct 11, 2021 at 23:04
• Also the 2 is the degree the ramp was raised Oct 11, 2021 at 23:59 | 886 | 3,937 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2023-50 | longest | en | 0.96844 |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=16&t=34785&view=print | 1,610,770,435,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703499999.6/warc/CC-MAIN-20210116014637-20210116044637-00034.warc.gz | 429,729,439 | 1,826 | Page 1 of 1
### Example 1.5 Part C in 6th Edition
Posted: Wed Oct 24, 2018 11:08 pm
In the textbook there is an example of analyzing the photoelectric effect. The first two parts I understand but I don't understand part C conceptually. The questions asks us: "To find the longest wavelength of radiation that is able to eject an electron." They go on to set Ek = 0 which I do not understand. Why would they set Ek = 0?
### Re: Example 1.5 Part C in 6th Edition
Posted: Wed Oct 24, 2018 11:51 pm
Since wavelength and frequency are inversely related, the longest wavelength possible corresponds to the lowest frequency possible to eject an electron, and since the equation for photoelectric effect is Ek=hv - work function, the lowest frequency that ejects an electron is when hv-work function=0 since Ephoton (hv) must be at least equal to work function to eject an electron, so Ek must be 0. | 226 | 895 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2021-04 | latest | en | 0.926651 |
http://mathhelpforum.com/discrete-math/36754-finding-equivalence-classes.html | 1,480,748,660,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698540909.75/warc/CC-MAIN-20161202170900-00186-ip-10-31-129-80.ec2.internal.warc.gz | 176,154,048 | 10,322 | 1. ## finding equivalence classes
S is the set of all real #'s
relation R on S is:
R= ((a,b) : a,b are elements of S and a-b is an integer)
R is reflexive, transitive and symmetric, making it an equivalence relation.
how do i find the equivalence classes? i know there are infinitely many.
thanks.
2. Originally Posted by CSkyle
S is the set of all real #'s
relation R on S is:
R= ((a,b) : a,b are elements of S and a-b is an integer)
R is reflexive, transitive and symmetric, making it an equivalence relation.
how do i find the equivalence classes? i know there are infinitely many.
thanks.
Hint: we want a - b = k for some integer k. that means, a = k + b. what do you think forms the equivalence class of the element a?
3. so, the equivalence classes for R consist of all sets (a,b) with a,b being elements of S, that have the form ((k+b),(a-k)) for some integer K ?
4. Originally Posted by CSkyle
so, the equivalence classes for R consist of all sets (a,b) with a,b being elements of S, that have the form ((k+b),(a-k)) for some integer K ?
If $a \in \mathbb{R}, [a] = a + \mathbb{Z}$
For example:
$[\pi] = \{\pi,\pi \pm 1,\pi \pm 2,......\}$ | 331 | 1,162 | {"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": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.515625 | 4 | CC-MAIN-2016-50 | longest | en | 0.883359 |
https://forum.altair.com/tags/shape/ | 1,601,125,103,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400241093.64/warc/CC-MAIN-20200926102645-20200926132645-00134.warc.gz | 382,358,456 | 21,076 | # Search the Community
Showing results for tags 'shape'.
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Found 10 results
1. ## Shape Optimization, Frequency Response Modal Analysis: Minimize dynamic Stiffness
Hello, i want to reduce the dynamic stiffness of a rubber bearing by changing the geometry. I have an approximate idea of the "optimized" geometry of this rubber bearing therefore I created morphvolumes and changed the specified area (solid elements) by translating the handles. I saved these changes as shapes which are my design variables. I know that the optimum is between the initial model and the changed model. I want to do an optimization with optistruct to find the optimum. To reduce the dynamic Stiffness i need 3 responses and an equation (dont know another way so far). The calculation of the dynamic Stiffness is simple: Cdyn = Force/Displacement. First i defined an equation with the dequation-panel: F(x,y)=x/y --> where x is the "frf force (ELFORCE)" and y the displacement (frf displacement) which are two of the three responses. The Last response is "function" which includes the dequation and the other two responses defined before. I would like to minimize the response "function" (which is the dynamic stiffness). But it's not possible to create an objective which minimizes my response "function", i get following error: *** ERROR # 1812 *** Multiple responses are assigned to the DESOBJ objective function. A MINMAX/MAXMIN objective function definition with DOBJREF should be used instead. Number of responses = 1000 1) Do you know what the maximum number of responses is? (It's an frequency response analyis from 0 Hz to 3000 Hz with an increment of 3, thats why its 1000 responses (i guess)) . I created an obj reference "dobjref" which includes the response "function", then i created MINMAX objective.This works, and i can start the optimization but here i have some questions: 2) When i define the obj reference i can choose neg and pos reference. What can i do with these references? 3) I don't really know what this minmax function does. Does it minimize the maximum value of the equation? It is not my goal to minimize only the maximum value of the equation, it's rather minimizing the area of the function. 4) Is it normal that optistruct finds a solution after 2 iterations? I have two different shapes and i would expect that it takes a lot of time and iterations to find the optimum. I guess i did something wrong or forgot sth. Sry for asking so many questions and sry for my bad english. I thank you so much in advance. Regards, Fatih Uysal
2. ## OptiStruct Composite optimization number of ply shapes
In a free size optimization, i always get from a ply, 4 different ply shapes, How can i change this number?
3. ## Shapefile Template for OSSmooth
Hello, I would like to generate my own shapefiles to be used with OSSmooth to create new topologies. Is there any information on how the file is constructed? I understand that the beginning of the file has element ids with their associated relative densities but there are many other fields whose contents are unknown to me. Thank you in advance, -Eric
4. ## Shape (?) Optimization for 1D Elements
Hey guys, I was wondering if it is possible to setup the following optimization problem. Lets say I have a set of nodes and bar elements. This framework has some loads and boundary conditions. I am not sure if the node position of each node is optimal regarding compliance. I would like to define "shapes" for the nodes where I can set some pertubations e.g. Node x can move in a sphere of radius y. I have not seen this kind of optimization although I think it must be possible from an algorithmic point of view. Any suggestions? Thanks!
5. ## Shape optimisation error
I am doing the shape optimisation and I am getting the responce error. H:/New folder (2)/Opti/sh2.fem "DSYSID 1 Shapeopt" *** ERROR # 1000 *** in the input data: Incorrect data in field # 4. I have given the responce from... responses>response name> response type = static stress> Prop(select components,inlet,outlet,wall)> create. But its not working.
6. ## Change Soft convergence criterion
Hello, when i start an optimization with optistruct the calculation is finished after 1 Iteration. In the Output-file i found following Information: Soft convergence criterion satisfied; the design did not change during the last Iteration. What does this mean? I already did a lot of successful shape-optimizations but in this case i don't really know why the shape didn't change. I changed the default OBJTOL value from the opti control card but the problem still occurs. The most interesting thing is: When i change the inital value in the shape panel to 0.5 I don't have any problems and the optimization finds the best shape. When I start with an inital value of 0.0 then i get the problem with the soft convergence criterion. Thank you Greets, Fatih Uysal
7. ## OptiStruct Composite optimization
Hello, I've built a composite I beam and optimatized the thickness plys only, but, I would like to get the best height for the beam web. At the moment i'm doing this manually, comparing the results of the composite optimization for differents heights, but for each height, at this moment, i have to build all the laminate again, from zero. How can i automatized this process? or at least do it in a smart way. It's possible to do a shape optimization for composites to get the best web height without it buckling or failure? more info about the simulation: In the optimization process, for the free size stage: obj :min compliance constrains: vfrac 0.3 for the size stage: obj: min mass constrains: -buckling modes 1, 2 and 3 λ >1 -max displacement of the node on the center of the beam < 12mm -Tsai Hill failure criteria < 1 The files are attached Thanks: Lucas Pereira cat_A_optimization_freesize.hm cat_A_optimization_size.hm
8. ## ERROR # 7315 No DSHAPE grids are on the boundary
Hello, I am new to Optistruct and having a repeating error for my 1D linear static free shape optimization of truss. When I try to run it w/Optistruct, the error that I get is: *** ERROR # 7315 *** No DSHAPE grids are on the boundary. Any ideas about a possible reason for this error? I checked card of DSHAPE and everything looks ok. Thanks, kosa26
9. ## Hypermorph radius and rotate
Hi, I give the radius value in the corners, and the component direction separately as shapes. I will use these shapes as DOE in Hyperstudy. But when I change the two shapes at the same time, a useless shape like the one in figure 'radiusandrotatecombined' appears. How can I design a proper shape by correcting this situation? Thank you, rotateandradius.hm
10. ## After the analysis shape change
Hı everyone, My structure has very less weight and size. I want to lattice optimization and I do. But shape of my structure is changing. shape is very thin. I think this can be due to the weight. Can you help me? Thank you. First picture my structure, Secondly figure at the end of the analysis.
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• Create New... | 1,946 | 7,908 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2020-40 | latest | en | 0.496862 |
https://www.nagwa.com/en/videos/876176075184/ | 1,718,733,338,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861773.80/warc/CC-MAIN-20240618171806-20240618201806-00349.warc.gz | 801,239,030 | 36,088 | Question Video: Identifying One-to-One Functions | Nagwa Question Video: Identifying One-to-One Functions | Nagwa
# Question Video: Identifying One-to-One Functions Mathematics • Second Year of Secondary School
## Join Nagwa Classes
Which of the following is a one-to-one function? [A] π(π₯) = π₯β΄ + π₯Β² [B] π(π₯) = π₯Β² [C] π(π₯) = cos π₯ [D] π(π₯) = π₯Β³
02:21
### Video Transcript
Which of the following is a one-to-one function? Is it a) π of π₯ equals π₯ to the fourth power plus π₯ squared, b) π of π₯ equals π₯ squared, c) π of π₯ equals cos of π₯, or d) π of π₯ equals π₯ cubed?
We begin by recalling what it actually means for a function to be one-to-one. A function is one-to-one if each element of the range of the function corresponds to exactly one element of the domain and vice versa. One way of testing for a one-to-one function is to consider the shape of the graph. If it passes the vertical line test, that is a vertical line anywhere on the graph intersects the graph exactly once, and the horizontal line test, that is a horizontal line intersects the curve exactly once. Then, we can say a function is one-to-one. And so, the easiest way to check whether our functions are one-to-one is to sketch their curves.
Letβs start with a graph of π₯ to the fourth power plus π₯ squared. This is sometimes called a quartic graph. It has a positive leading coefficient of π₯. And if weβre to factor the expression, we see that it only has one root, and thatβs at π₯ equals zero. And so, the graph of π¦ equals π₯ to the fourth power plus π₯ squared looks a little something like this. It does indeed pass the vertical line test, a vertical line intersects the curve exactly once. However, if we add a horizontal line here, we see that it intersects the curve twice. And this means our function is not one-to-one. In this case, an element of the range can correspond to more than one element of its domain.
Now, in fact, our graph of π of π₯ equals π₯ squared looks very similar. And so, by the same reasoning, it cannot be one-to-one. Weβll now move on to the graph of π of π₯ equals cos of π₯. We know one full period of the graph of π¦ equals cos of π₯ looks a little something like this. Once again, this craft does indeed pass the vertical line test. But it absolutely doesnβt pass the horizontal line test. And since the graph of π¦ equals cos of π₯ is periodic, we can see that a horizontal line will intercept the curve of π¦ equals cos of π₯ an infinite number of times. And so, π of π₯ equals cos of π₯ cannot be a one-to-one function.
Weβll now test π of π₯ equals π₯ cubed. The graph of π¦ equals π₯ cubed looks like this. And we can see it quite clearly passes the vertical line test. This time it also passes the horizontal line test. A horizontal line added to the graph intersects that curve exactly once. So, we can say that the correct answer is d. The one-to-one function is π of π₯ equals π₯ cubed.
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• Realistic Exam Questions | 956 | 3,283 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.71875 | 5 | CC-MAIN-2024-26 | latest | en | 0.901429 |
https://www.unitconverters.net/density/kilogram-cubic-meter-to-gram-liter.htm | 1,519,558,854,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891816370.72/warc/CC-MAIN-20180225110552-20180225130552-00704.warc.gz | 947,431,050 | 3,506 | Home / Density Conversion / Convert Kilogram/cubic Meter to Gram/liter
# Convert Kilogram/cubic Meter to Gram/liter
Please provide values below to convert kilogram/cubic meter to gram/liter [g/L], or vice versa.
From: kilogram/cubic meter To: gram/liter
### Kilogram/cubic Meter to Gram/liter Conversion Table
Kilogram/cubic MeterGram/liter [g/L]
0.01 kilogram/cubic meter0.01 g/L
0.1 kilogram/cubic meter0.1 g/L
1 kilogram/cubic meter1 g/L
2 kilogram/cubic meter2 g/L
3 kilogram/cubic meter3 g/L
5 kilogram/cubic meter5 g/L
10 kilogram/cubic meter10 g/L
20 kilogram/cubic meter20 g/L
50 kilogram/cubic meter50 g/L
100 kilogram/cubic meter100 g/L
1000 kilogram/cubic meter1000 g/L
### How to Convert Kilogram/cubic Meter to Gram/liter
1 kilogram/cubic meter = 1 g/L
1 g/L = 1 kilogram/cubic meter
Example: convert 15 kilogram/cubic meter to g/L:
15 kilogram/cubic meter = 15 × 1 g/L = 15 g/L | 282 | 900 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2018-09 | longest | en | 0.317371 |
http://cg.huminf.aau.dk/Module_II/1203.html | 1,550,952,572,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550249530087.75/warc/CC-MAIN-20190223183059-20190223205059-00222.warc.gz | 49,911,920 | 2,796 | # 18 Another example of usage (Ad)
## Introduction
In logic, there is a logical connective which is usually written as a long, single-lined arrow. It is used to connect two statements, e.g., p and q, like this:
p --> q
It means "If p is true, then q is true". According to the definition of this logical connective, this statement is true unless p is true but q is false. This also means that if p is false, then the whole statement is true regardless of whether q is true or false.
The statement can defined in terms of the boolean operators "and" and "not" as follows:
p --> q is equivalent to not(p and not(q))
This definition allows us to use Peirce's rules to form such a statement. It can be formulated as follows:
```
<!--
var agt=navigator.userAgent.toLowerCase();
var is_win = ( (agt.indexOf("win")!=-1) || (agt.indexOf("16bit")!=-1) );
var is_gecko = (agt.indexOf('gecko') != -1);
if (is_win && !is_gecko) {
document.write("<FONT FACE=\"Symbol\">Ø</FONT>");
} else {
document.write("¬");
}
-->
[Proposition:
P
<!--
var agt=navigator.userAgent.toLowerCase();
var is_win = ( (agt.indexOf("win")!=-1) || (agt.indexOf("16bit")!=-1) );
var is_gecko = (agt.indexOf('gecko') != -1);
if (is_win && !is_gecko) {
document.write("<FONT FACE=\"Symbol\">Ø</FONT>");
} else {
document.write("¬");
}
-->
[Proposition:
Q
]
]
```
where P and Q stand for any conceptual graphs. Verify for yourself that this closely matches the definition.
Thus we have a way to say "if p is true, then q is true".
## Application to Peirce's rules
Consider the statement, "If I were rich, I would be happy". This is not generally true, of course, but this is just an example. What we are now going to do is to prove that, given that I am happy, then one reason for this could be that I am rich.
Thus we are going to start with the statement "I am happy" and apply Peirce's rules to say "If I am rich, then I am happy."
## Step 1
```[Person: #I]<-(Expr)<-[State: Happy]
"I am the experiencer of a State which is Happy."
```
We will assume that this is true.
## Step 2
Then we apply the "Double negation" rule:
Double negation:
A double negation may be drawn around or removed from any graph or set of graphs in any context.
```
<!--
var agt=navigator.userAgent.toLowerCase();
var is_win = ( (agt.indexOf("win")!=-1) || (agt.indexOf("16bit")!=-1) );
var is_gecko = (agt.indexOf('gecko') != -1);
if (is_win && !is_gecko) {
document.write("<FONT FACE=\"Symbol\">Ø</FONT>");
} else {
document.write("¬");
}
-->
[Proposition:
<!--
var agt=navigator.userAgent.toLowerCase();
var is_win = ( (agt.indexOf("win")!=-1) || (agt.indexOf("16bit")!=-1) );
var is_gecko = (agt.indexOf('gecko') != -1);
if (is_win && !is_gecko) {
document.write("<FONT FACE=\"Symbol\">Ø</FONT>");
} else {
document.write("¬");
}
-->
[Proposition:
[Person: #I]<-(Expr)<-[State: Happy]
]
]
```
The statement is still true:
"It is not the case that it is not the case that I am happy," which is equivalent to "I am happy."
## Step 3
Then we apply the "Insertion" rule:
Insertion:
Any graph may be inserted in any oddly enclosed context.
```
<!--
var agt=navigator.userAgent.toLowerCase();
var is_win = ( (agt.indexOf("win")!=-1) || (agt.indexOf("16bit")!=-1) );
var is_gecko = (agt.indexOf('gecko') != -1);
if (is_win && !is_gecko) {
document.write("<FONT FACE=\"Symbol\">Ø</FONT>");
} else {
document.write("¬");
}
-->
[Proposition:
[Person: #I]<-(Expr)<-[State: Rich]
<!--
var agt=navigator.userAgent.toLowerCase();
var is_win = ( (agt.indexOf("win")!=-1) || (agt.indexOf("16bit")!=-1) );
var is_gecko = (agt.indexOf('gecko') != -1);
if (is_win && !is_gecko) {
document.write("<FONT FACE=\"Symbol\">Ø</FONT>");
} else {
document.write("¬");
}
-->
[Proposition:
[Person: #I]<-(Expr)<-[State: Happy]
]
]
"It is not the case that: (I am rich AND it is not the case that: (I
am happy))"
```
This perfectly fits our schema for the "if...then" statement. So what we have said, in effect, is "If I am rich, I am happy."
## Summary
We started by assuming that I was happy. Therefore, there is nothing magical in this derivation. The statement is bound to be true, and we have just proved the statement "If I am rich, I am happy" from the true statement "I am happy". An implication can only be false if the premise is true and the conclusion is false. Since the conclusion is true, i.e., since it is true that I am happy, there is no way the implication can be false.
## Next
Next, we have a summary.
Prev: 17 Example of usage (Ad)
Up: Part IV: Peirce's rules (Ad) | 1,251 | 4,583 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2019-09 | latest | en | 0.845356 |
https://im.kendallhunt.com/k5/teachers/grade-4/center--estimate-and-measure-1-4/center.html | 1,725,932,365,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651164.37/warc/CC-MAIN-20240909233606-20240910023606-00700.warc.gz | 283,476,447 | 28,740 | # Center
Estimate and Measure (1–4)
## Stage 1: Choose Your Unit
### Narrative
Students choose an object and a familiar unit to measure it with. They estimate the length of the object and then measure to see the actual length to the nearest whole unit.
Variation:
Students may use base-ten cubes and add the length of two objects to practice adding within 100.
Gather or identify objects of various lengths that are less than 20 units (pencils, markers, books, glue, scissors, shoe, tape dispenser, side of desk).
## Stage 2: Centimeters and Inches
### Narrative
Students choose an object and a unit (inches, feet, centimeters) to measure it with. They estimate the length of the object and then measure to see the actual length to the nearest whole unit.
Gather or identify objects of various lengths (pencils, markers, books, glue, scissors, shoes, tape dispensers, sides of desk, length of bulletin board).
## Stage 3: Quarter Inches
### Narrative
Students choose and estimate the length of the object and then measure to see the actual length to the nearest $$\frac{1}{4}$$ inch.
Students choose and estimate the length of the object and then measure to see the actual length to the nearest $$\frac{1}{8}$$ Inch. | 284 | 1,231 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2024-38 | latest | en | 0.824245 |
https://wiki2.org/en/Utility | 1,656,760,343,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104054564.59/warc/CC-MAIN-20220702101738-20220702131738-00429.warc.gz | 664,716,820 | 52,113 | To install click the Add extension button. That's it.
The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.
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Congratulations on this excellent venture… what a great idea!
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Utility
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosophers such as Jeremy Bentham and John Stuart Mill. The term has been adapted and reapplied within neoclassical economics, which dominates modern economic theory, as a utility function that represents a single consumer's preference ordering over a choice set but is not comparable across consumers. This concept of utility is personal and based on choice rather than on pleasure received, and so is specified more rigorously than the original concept but makes it less useful (and controversial) for ethical decisions.
Utility function
Consider a set of alternatives among which a person can make a preference ordering. The utility obtained from these alternatives is an unknown function of the utilities obtained from each alternative, not the sum of each alternative.[1] A utility function is able to represent that ordering if it is possible to assign a real number to each alternative in such a manner that alternative a is assigned a number greater than alternative b if and only if the individual prefers alternative a to alternative b. In this situation someone who selects the most preferred alternative is necessarily also selecting the alternative that maximizes the associated utility function.
Suppose James has utility function ${\displaystyle U={\sqrt {xy}}}$ such that x is the number of apples and y is the number of chocolates. Alternative A has ${\displaystyle x=9}$ apples and ${\displaystyle y=16}$ chocolates; alternative B has ${\displaystyle x=13}$ apples and ${\displaystyle y=13}$ chocolates. Putting the values x, y into the utility function yields ${\displaystyle {\sqrt {9\times 16}}=12}$ for alternative A and ${\displaystyle {\sqrt {13\times 13}}=13}$ for B, so James prefers alternative B.
In general economic terms, a utility function measures preferences concerning a set of goods and services. Utility is often correlated with concepts such as happiness, satisfaction, and welfare which are difficult to measure. Thus, economists utilize consumption baskets of preferences in order to measure these abstract, nonquantifiable ideas.
Gérard Debreu precisely defined the conditions required for a preference ordering to be representable by a utility function.[2] For a finite set of alternatives these require only that the preference ordering is complete (so the individual is able to determine which of any two alternatives is preferred or that they are equal), and that the preference order is transitive.
Very often the set of alternatives is not finite, because even if the number of goods is finite, the quantity chosen can be any real number on an interval. A commonly specified Choice Set in Consumer Choice is ${\displaystyle R_{+}^{n}}$, where ${\displaystyle n}$ is the number of goods. In this case, there exists a continuous utility function to represent a consumer's preferences if and only if the consumer's preferences are complete, transitive and continuous.[3]
Applications
Utility is usually applied by economists to such constructs as the indifference curve, which plot the combination of commodities that an individual would accept to maintain a given level of satisfaction. Utility and indifference curves are used by economists to understand the causes of demand curves as part of supply and demand analysis, which is used to analyze the workings of goods markets.
A diagram of a general indifference curve is shown below (Figure 1). The vertical axes and the horizontal axes represent an individual's consumption of commodity Y and X respectively. All the combinations of commodity X and Y along the same indifference curve are regarded indifferently by individuals, which means all the combinations along an indifference curve result in the same value of utility.
Figure 1
Individual utility and social utility can be construed as the value of a utility function and a social welfare function respectively. When coupled with production or commodity constraints, by some assumptions these functions can be used to analyze Pareto efficiency, such as illustrated by Edgeworth boxes in contract curves. Such efficiency is a major concept in welfare economics.
In finance, utility is applied to generate an individual's price for an asset known as the indifference price. Utility functions are also related to risk measures, with the most common example being the entropic risk measure. For artificial intelligence, utility functions are used to convey the value of various outcomes to intelligent agents. This allows the agents to plan actions with the goal of maximizing the utility (or "value") of available choices.
Preference
Preference, as human's specific likes and dislikes, is used primarily when individuals make choices or decisions among different alternatives. Individual preferences are influenced by various factors such as geographical location, gender, cultures and education. The ranking of utility indicates individuals’ preferences.
Although preferences are the conventional foundation of microeconomics, it is often convenient to represent preferences with a utility function and analyze human behavior indirectly with utility functions. Let X be the consumption set, the set of all mutually-exclusive baskets the consumer could conceivably consume. The consumer's utility function ${\displaystyle u\colon X\to \mathbb {R} }$ ranks each package in the consumption set. If the consumer strictly prefers x to y or is indifferent between them, then ${\displaystyle u(x)\geq u(y)}$.
For example, suppose a consumer's consumption set is X = {nothing, 1 apple,1 orange, 1 apple and 1 orange, 2 apples, 2 oranges}, and his utility function is u(nothing) = 0, u(1 apple) = 1, u(1 orange) = 2, u(1 apple and 1 orange) = 5, u(2 apples) = 2 and u(2 oranges) = 4. Then this consumer prefers 1 orange to 1 apple, but prefers one of each to 2 oranges.
In micro-economic models, there are usually a finite set of L commodities, and a consumer may consume an arbitrary amount of each commodity. This gives a consumption set of ${\displaystyle \mathbb {R} _{+}^{L}}$, and each package ${\displaystyle x\in \mathbb {R} _{+}^{L}}$ is a vector containing the amounts of each commodity. For the example, there are two commodities: apples and oranges. If we say apples is the first commodity, and oranges the second, then the consumption set is ${\displaystyle X=\mathbb {R} _{+}^{2}}$ and u(0, 0) = 0, u(1, 0) = 1, u(0, 1) = 2, u(1, 1) = 5, u(2, 0) = 2, u(0, 2) = 4 as before. Note that for u to be a utility function on X, however, it must be defined for every package in X, so now the function needs to be defined for fractional apples and oranges too. One function that would fit these numbers is ${\displaystyle u(x_{apples},x_{oranges})=x_{apples}+2x_{oranges}+2x_{apples}x_{oranges}.}$
Preferences have three main properties:
• Completeness
Assume an individual has two choices, A and B. By ranking the two choices, one and only one of the following relationships is true: an individual strictly prefers A (A>B); an individual strictly prefers B (B>A); an individual is indifferent between A and B (A=B). Either a ≥ b OR b ≥ a (OR both) for all (a,b)
• Transitivity
Individuals’ preferences are consistent over bundles. If an individual prefers bundle A to bundle B, and prefers bundle B to bundle C, then it can be assumed that the individual prefers bundle A to bundle C. (If a ≥ b and b ≥ c, then a ≥ c for all (a,b,c)).
• Non-Satiation (Monotone Preferences)
All else being constant, individuals always prefer more of positive goods rather than negative goods, vice versa. In terms of the indifferent curves, individuals will always prefer bundles that are on a higher indifference curve. In other words, all else being the same, more is better than less of the commodity.
• When a commodity is good, more of it is preferred to less.
• When a commodity is bad, less of it is preferred more, like pollution.
Revealed preference
It was recognized that utility could not be measured or observed directly, so instead economists devised a way to infer relative utilities from observed choice. These 'revealed preferences', as termed by Paul Samuelson, were revealed e.g. in people's willingness to pay:
Utility is assumed to be correlative to Desire or Want. It has been argued already that desires cannot be measured directly, but only indirectly, by the outward phenomena which they cause: and that in those cases with which economics is mainly concerned the measure is found by the price which a person is willing to pay for the fulfillment or satisfaction of his desire.[4]: 78
Revealed preference in finance
For financial applications, e.g. portfolio optimization, an investor chooses a financial portfolio which maximizes his/her own utility function, or, equivalently, minimizes his/her risk measure. For example, modern portfolio theory selects variance as a measure of risk; other popular theories are expected utility theory,[5] and prospect theory.[6] To determine a specific utility function for any given investor, one could design a questionnaire procedure with questions in the form: How much would you pay for x% chance of getting y? Revealed preference theory suggests a more direct method: observe a portfolio X* which an investor currently has, and then find a utility function/risk measure such that X* becomes an optimal portfolio.[7]
.mw-parser-output .vanchor>:target~.vanchor-text{background-color:#b1d2ff}Functions
There has been some controversy concerning whether the utility of a commodity can be measured or not. At one time, it was assumed that the consumer was able to say exactly how much utility he got from the commodity. The economists who made this assumption belonged to the 'cardinalist school' of economics. Presently utility functions, expressing utility as a function of the amounts of the various goods consumed, are treated as either cardinal or ordinal, depending on whether they are or are not interpreted as providing more information than simply the rank ordering of preferences among bundles of goods, such as information concerning the strength of preferences.
Cardinal
Cardinal utility states that the utilities obtained from consumption can be measured and ranked objectively and are representable by numbers.[8] There are fundamental assumptions of cardinal utility. Economic agents should be able to rank different bundles of goods based on their own preferences or utilities, and also sort different transitions of two bundles of goods.[9]
A cardinal utility function can be transformed to another utility function by a positive linear transformation (multiplying by a positive number, and adding some other number); however, both utility functions represent the same preferences.[10]
When cardinal utility is assumed, the magnitude of utility differences is treated as an ethically or behaviorally significant quantity. For example, suppose a cup of orange juice has utility of 120 "utils", a cup of tea has a utility of 80 utils, and a cup of water has a utility of 40 utils. With cardinal utility, it can be concluded that the cup of orange juice is better than the cup of tea by exactly the same amount by which the cup of tea is better than the cup of water. Formally, this means that if a person has a cup of tea, he or she would be willing to take any bet with a probability, p, greater than .5 of getting a cup of juice, with a risk of getting a cup of water equal to 1-p. One cannot conclude, however, that the cup of tea is two thirds of the goodness of the cup of juice, because this conclusion would depend not only on magnitudes of utility differences, but also on the "zero" of utility. For example, if the "zero" of utility was located at -40, then a cup of orange juice would be 160 utils more than zero, a cup of tea 120 utils more than zero. Cardinal utility can be considered as the assumption that utility can be measured by quantifiable characteristics, such as height, weight, temperature, etc.
Neoclassical economics has largely retreated from using cardinal utility functions as the basis of economic behavior. A notable exception is in the context of analyzing choice with conditions of risk (see below).
Sometimes cardinal utility is used to aggregate utilities across persons, to create a social welfare function.
Ordinal
Instead of giving actual numbers over different bundles, ordinal utilities are only the rankings of utilities received from different bundles of goods or services.[8] For example, ordinal utility could tell that having two ice creams provide a greater utility to individuals in comparison to one ice cream but could not tell exactly how much extra utility received by the individual. Ordinal utility, it does not require individuals to specify how much extra utility he or she received from the preferred bundle of goods or services in comparison to other bundles. They are only required to tell which bundles they prefer.
When ordinal utilities are used, differences in utils (values assumed by the utility function) are treated as ethically or behaviorally meaningless: the utility index encodes a full behavioral ordering between members of a choice set, but tells nothing about the related strength of preferences. For the above example, it would only be possible to say that juice is preferred to tea to water. Thus, ordinal utility utilizes comparisons, such as "preferred to", "no more", "less than", etc.
If a function ${\displaystyle u(x)}$ is ordinal, it is equivalent to the function ${\displaystyle u(x)^{3}}$, because taking the 3rd power is an increasing monotone (or monotonic) transformation. This means that the ordinal preference induced by these functions is the same (although they are two different functions). In contrast, if ${\displaystyle u(x)}$ is cardinal, it is not equivalent to ${\displaystyle u(x)^{3}}$.
Constructing utility functions
For many decision models, utility functions are determined by the problem formulation. For some situations, the decision maker's preference must be elicited and represented by a utility (or objective) scalar-valued function. The methods existing for constructing such functions are collected in the proceedings of two dedicated conferences.[11][12] The mathematical foundations for the most common types of utility functions — quadratic and additive — were laid down by Gerard Debreu,[13][14] and the methods for their construction from both ordinal and cardinal data, in particular from interviewing a decision maker, were developed by Andranik Tangian.[15][16]
Examples
In order to simplify calculations, various alternative assumptions have been made concerning details of human preferences, and these imply various alternative utility functions such as:
Most utility functions used for modeling or theory are well-behaved. They are usually monotonic and quasi-concave. However, it is possible for preferences not to be representable by a utility function. An example is lexicographic preferences which are not continuous and cannot be represented by a continuous utility function.[17]
Marginal utility
Economists distinguish between total utility and marginal utility. Total utility is the utility of an alternative, an entire consumption bundle or situation in life. The rate of change of utility from changing the quantity of one good consumed is termed the marginal utility of that good. Marginal utility therefore measures the slope of the utility function with respect to the changes of one good.[18] Marginal utility usually decreases with consumption of the good, the idea of "diminishing marginal utility". In calculus notation, the marginal utility of good X is ${\displaystyle MU_{x}={\frac {\partial U}{\partial X}}}$. When a good's marginal utility is positive, additional consumption of it increases utility; if zero, the consumer is satiated and indifferent about consuming more; if negative, the consumer would pay to reduce his consumption.[19]
Law of diminishing marginal utility
Rational individuals only consume additional units of goods if it increases the marginal utility. However, the law of diminishing marginal utility means an additional unit consumed brings a less marginal utility than that brought by the previous unit consumed. For example, drinking one bottle of water makes a thirsty person satisfied; as the consumption of water increases, he may feel begin to feel bad which causes the marginal utility to decrease to zero or even become negative. Furthermore, this is also used to analyze progressive taxes as the greater taxes can result in the loss of utility.
Marginal rate of substitution (MRS)
Marginal rate of substitution is the slope of the indifference curve, which measures how much an individual is willing to switch from one good to another. Using a mathematic equation, ${\displaystyle MRS=-\operatorname {d} \!x_{2}/\operatorname {d} \!x_{1}}$keeping U (x1,x2) constant. Thus, MRS is how much an individual is willing to pay for consuming a greater amount of x1.
MRS is related to marginal utility. The relationship between marginal utility and MRS is: ${\displaystyle MRS={\frac {MU_{1}}{MU_{2}}}}$[18]
Expected utility
Expected utility theory deals with the analysis of choices among risky projects with multiple (possibly multidimensional) outcomes.
The St. Petersburg paradox was first proposed by Nicholas Bernoulli in 1713 and solved by Daniel Bernoulli in 1738. D. Bernoulli argued that the paradox could be resolved if decision-makers displayed risk aversion and argued for a logarithmic cardinal utility function. (Analysis of international survey data during the 21st century has shown that insofar as utility represents happiness, as for utilitarianism, it is indeed proportional to log of income.)
The first important use of the expected utility theory was that of John von Neumann and Oskar Morgenstern, who used the assumption of expected utility maximization in their formulation of game theory.
In finding the probability-weighted average of the utility from each possible outcome:
EU=[Pr(z)×u(value(z))]+[Pr(y)×u(value(y))]
von Neumann–Morgenstern
Von Neumann and Morgenstern addressed situations in which the outcomes of choices are not known with certainty, but have probabilities associated with them.
A notation for a lottery is as follows: if options A and B have probability p and 1 − p in the lottery, we write it as a linear combination:
${\displaystyle L=pA+(1-p)B}$
More generally, for a lottery with many possible options:
${\displaystyle L=\sum _{i}p_{i}A_{i},}$
where ${\displaystyle \sum _{i}p_{i}=1}$.
By making some reasonable assumptions about the way choices behave, von Neumann and Morgenstern showed that if an agent can choose between the lotteries, then this agent has a utility function such that the desirability of an arbitrary lottery can be computed as a linear combination of the utilities of its parts, with the weights being their probabilities of occurring.
This is termed the expected utility theorem. The required assumptions are four axioms about the properties of the agent's preference relation over 'simple lotteries', which are lotteries with just two options. Writing ${\displaystyle B\preceq A}$ to mean 'A is weakly preferred to B' ('A is preferred at least as much as B'), the axioms are:
1. completeness: For any two simple lotteries ${\displaystyle L}$ and ${\displaystyle M}$, either ${\displaystyle L\preceq M}$ or ${\displaystyle M\preceq L}$ (or both, in which case they are viewed as equally desirable).
2. transitivity: for any three lotteries ${\displaystyle L,M,N}$, if ${\displaystyle L\preceq M}$ and ${\displaystyle M\preceq N}$, then ${\displaystyle L\preceq N}$.
3. convexity/continuity (Archimedean property): If ${\displaystyle L\preceq M\preceq N}$, then there is a ${\displaystyle p}$ between 0 and 1 such that the lottery ${\displaystyle pL+(1-p)N}$ is equally desirable as ${\displaystyle M}$.
4. independence: for any three lotteries ${\displaystyle L,M,N}$ and any probability p, ${\displaystyle L\preceq M}$ if and only if ${\displaystyle pL+(1-p)N\preceq pM+(1-p)N}$. Intuitively, if the lottery formed by the probabilistic combination of ${\displaystyle L}$ and ${\displaystyle N}$ is no more preferable than the lottery formed by the same probabilistic combination of ${\displaystyle M}$ and ${\displaystyle N,}$ then and only then ${\displaystyle L\preceq M}$.
Axioms 3 and 4 enable us to decide about the relative utilities of two assets or lotteries.
In more formal language: A von Neumann–Morgenstern utility function is a function from choices to the real numbers:
${\displaystyle u\colon X\to \mathbb {R} }$
which assigns a real number to every outcome in a way that represents the agent's preferences over simple lotteries. Using the four assumptions mentioned above, the agent will prefer a lottery ${\displaystyle L_{2}}$ to a lottery ${\displaystyle L_{1}}$ if and only if, for the utility function characterizing that agent, the expected utility of ${\displaystyle L_{2}}$ is greater than the expected utility of ${\displaystyle L_{1}}$:
${\displaystyle L_{1}\preceq L_{2}{\text{ iff }}u(L_{1})\leq u(L_{2})}$.
Of all the axioms, independence is the most often discarded. A variety of generalized expected utility theories have arisen, most of which omit or relax the independence axiom.
As probability of success
Castagnoli and LiCalzi (1996) and Bordley and LiCalzi (2000) provided another interpretation for Von Neumann and Morgenstern's theory. Specifically for any utility function, there exists a hypothetical reference lottery with the expected utility of an arbitrary lottery being its probability of performing no worse than the reference lottery. Suppose success is defined as getting an outcome no worse than the outcome of the reference lottery. Then this mathematical equivalence means that maximizing expected utility is equivalent to maximizing the probability of success. In many contexts, this makes the concept of utility easier to justify and to apply. For example, a firm's utility might be the probability of meeting uncertain future customer expectations.[20][21][22][23]
Indirect utility
An indirect utility function gives the optimal attainable value of a given utility function, which depends on the prices of the goods and the income or wealth level that the individual possesses.
Money
One use of the indirect utility concept is the notion of the utility of money. The (indirect) utility function for money is a nonlinear function that is bounded and asymmetric about the origin. The utility function is concave in the positive region, representing the phenomenon of diminishing marginal utility. The boundedness represents the fact that beyond a certain amount money ceases being useful at all, as the size of any economy at that time is itself bounded. The asymmetry about the origin represents the fact that gaining and losing money can have radically different implications both for individuals and businesses. The non-linearity of the utility function for money has profound implications in decision-making processes: in situations where outcomes of choices influence utility by gains or losses of money, which are the norm for most business settings, the optimal choice for a given decision depends on the possible outcomes of all other decisions in the same time-period.[24]
Budget constraints
Individuals' consumptions are constrained by their budget allowance. The graph of budget line is a linear, downward-sloping line between X and Y axes. All the bundles of consumption under the budget line allow individuals to consume without using the whole budget as the total budget is greater than the total cost of bundles (Figure 2). If only considers prices and quantities of two goods in one bundle, a budget constraint could be formulated as ${\displaystyle p_{1}X_{1}+p_{2}X_{2}=Y}$, where p1 and p2 are prices of the two goods, X1 and X2 are quantities of the two goods.
Figure 2
Slope = -P(x)/P(y)
Constrained utility optimisation
Rational consumers wish to maximise their utility. However, as they have budget constraints, a change of price would affect the quantity of demand. There are two factors could explain this situation:
• Purchasing Power. Individuals obtain greater purchasing power when the price of a good decreases. The reduction of the price allows individuals to increase their savings so they could afford to buy other products.
• Substitution Effect. If the price of good A decreases, then the good becomes relatively cheaper with respect to its substitutes. Thus, individuals would consume more of good A as the utility would increase by doing so.
Discussion and criticism
Cambridge economist Joan Robinson famously criticized utility for being a circular concept: "Utility is the quality in commodities that makes individuals want to buy them, and the fact that individuals want to buy commodities shows that they have utility".[25]: 48 Robinson also stated that because the theory assumes that preferences are fixed this means that utility is not a testable assumption. This is so because if we observe changes of peoples' behavior in relation to a change in prices or a change in budget constraint we can never be sure to what extent the change in behavior was due to the change of price or budget constraint and how much was due to a change of preference.[26] This criticism is similar to that of the philosopher Hans Albert who argued that the ceteris paribus (all else equal) conditions on which the marginalist theory of demand rested rendered the theory itself a meaningless tautology, incapable of being tested experimentally.[27] In essence, a curve of demand and supply (a theoretical line of quantity of a product which would have been offered or requested for given price) is purely ontological and could never have been demonstrated empirically.
Another criticism derives from the assertion that neither cardinal nor ordinal utility are observable empirically in the real world. For the case of cardinal utility it is impossible to measure the degree of satisfaction "quantitatively" when someone consumes or purchases an apple. For ordinal utility, it is impossible to determine what choices were made when someone purchases, for example, an orange. Any act would involve preference over a vast set of choices (such as apple, orange juice, other vegetable, vitamin C tablets, exercise, not purchasing, etc.).[28][29]
Other questions of what arguments ought to be included in a utility function are difficult to answer, yet seem necessary to understanding utility. Whether people gain utility from coherence of wants, beliefs or a sense of duty is important to understanding their behavior in the utility organon.[30] Likewise, choosing between alternatives is itself a process of determining what to consider as alternatives, a question of choice within uncertainty.[31]
An evolutionary psychology theory is that utility may be better considered as due to preferences that maximized evolutionary fitness in the ancestral environment but not necessarily in the current one.[32]
References
1. ^ Edgeworth, F. Y. (1987). "Numerical Determination of the Laws of Utility". The New Palgrave Dictionary of Economics. pp. 1–2. doi:10.1057/978-1-349-95121-5_1822-1. ISBN 978-1-349-95121-5.
2. ^ Debreu, Gérard (1954), "Representation of a preference ordering by a numerical function", in Thrall, Robert M.; Coombs, Clyde H.; Raiffa, Howard (eds.), Decision processes, New York: Wiley, pp. 159–167, OCLC 639321.
3. ^ Jehle, Geoffrey; Reny, Philipp (2011), Advanced Microeconomic Theory, Prentice Hall, Financial Times, pp. 13–16, ISBN 978-0-273-73191-7.
4. ^ Marshall, Alfred (1920). Principles of Economics. An introductory volume (8th ed.). London: Macmillan.
5. ^ Von Neumann, J.; Morgenstern, O. (1953). Theory of Games and Economic Behavior (3rd ed.). Princeton University Press.
6. ^ Kahneman, D.; Tversky, A. (1979). "Prospect Theory: An Analysis of Decision Under Risk" (PDF). Econometrica. 47 (2): 263–292. doi:10.2307/1914185. JSTOR 1914185.
7. ^ Grechuk, B.; Zabarankin, M. (2016). "Inverse Portfolio Problem with Coherent Risk Measures". European Journal of Operational Research. 249 (2): 740–750. doi:10.1016/j.ejor.2015.09.050. hdl:2381/36136.
8. ^ a b Dominick, Salvatore (2008). Principles Of Microeconomics. New Delhi: Oxford Higher Education/Oxford University Press. p. 60. ISBN 9780198062301.
9. ^ Lin, Chung-Cheng; Peng, Shi-Shu (2019). "The role of diminishing marginal utility in the ordinal and cardinal utility theories". Australian Economic Papers. 58 (3): 233–246. doi:10.1111/1467-8454.12151. S2CID 159308055 – via Wiley Online Library.
10. ^ Moscati, Ivan (2013). "How Cardinal Utility Entered Economic Analysis, 1909-1944". SSRN Electronic Journal. doi:10.2139/ssrn.2296881. hdl:10419/149700. ISSN 1556-5068. S2CID 55651414.
11. ^ Tangian, Andranik; Gruber, Josef (Eds) (1997). Constructing Scalar-Valued Objective Functions. Proceedings of the Third International Conference on Econometric Decision Models: Constructing Scalar-Valued Objective Functions, University of Hagen, held in Katholische Akademie Schwerte September 5–8, 1995. Lecture Notes in Economics and Mathematical Systems. Vol. 453. Berlin: Springer.
12. ^ Tangian, Andranik; Gruber, Josef (Eds) (2002). Constructing and Applying Objective Functions. Proceedings of the Fourth International Conference on Econometric Decision Models Constructing and Applying Objective Functions, University of Hagen, held in Haus Nordhelle, August, 28 — 31, 2000. Lecture Notes in Economics and Mathematical Systems. Vol. 510. Berlin: Springer.
13. ^ Debreu, Gérard (1952). "Definite and semidefinite quadratic forms". Econometrica. 20 (2): 295–300. doi:10.2307/1907852. JSTOR 1907852.
14. ^ Debreu, Gérard (1960). "Topological methods in cardinal utility theory". In Arrow, Kenneth (ed.). Mathematical Methods in the Social Sciences,1959. Stanford: Stanford University Press. pp. 16–26.
15. ^ Tangian, Andranik (2002). "Constructing a quasi-concave quadratic objective function from interviewing a decision maker". European Journal of Operational Research. 141 (3): 608–640. doi:10.1016/S0377-2217(01)00185-0.
16. ^ Tangian, Andranik (2004). "A model for ordinally constructing additive objective functions". European Journal of Operational Research. 159 (2): 476–512. doi:10.1016/S0377-2217(03)00413-2.
17. ^ Ingersoll, Jonathan E. Jr. (1987). Theory of Financial Decision Making. Totowa: Rowman and Littlefield. p. 21. ISBN 0-8476-7359-6.
18. ^ a b Castro, Luiz Carvalho; Araujo, Antônio Souza (2019). "Marginal Utility & its Diminishing Methods" (PDF). International Journal of Tax Economics and Management: 36–47. eISSN 2618-1118.
19. ^ Bloomenthal, Andrew. "Marginal Utility". Investopedia. Retrieved 25 April 2021.
20. ^ Castagnoli, E.; LiCalzi, M. (1996). "Expected Utility Without Utility" (PDF). Theory and Decision. 41 (3): 281–301. doi:10.1007/BF00136129. hdl:10278/4143. S2CID 154464803.
21. ^ Bordley, R.; LiCalzi, M. (2000). "Decision Analysis Using Targets Instead of Utility Functions". Decisions in Economics and Finance. 23 (1): 53–74. doi:10.1007/s102030050005. hdl:10278/3610. S2CID 11162758.
22. ^ Bordley, R.; Kirkwood, C. (2004). "Multiattribute preference analysis with Performance Targets". Operations Research. 52 (6): 823–835. doi:10.1287/opre.1030.0093.
23. ^ Bordley, R.; Pollock, S. (2009). "A Decision-Analytic Approach to Reliability-Based Design Optimization". Operations Research. 57 (5): 1262–1270. doi:10.1287/opre.1080.0661. S2CID 18605492.
24. ^ Berger, J. O. (1985). "Utility and Loss". Statistical Decision Theory and Bayesian Analysis (2nd ed.). Berlin: Springer-Verlag. ISBN 3-540-96098-8.
25. ^ Robinson, Joan (1962). Economic Philosophy. Harmondsworth, Middle-sex, UK: Penguin Books.
26. ^ Pilkington, Philip (17 February 2014). "Joan Robinson's Critique of Marginal Utility Theory". Fixing the Economists. Archived from the original on 13 July 2015.
27. ^ Pilkington, Philip (27 February 2014). "utility Hans Albert Expands Robinson's Critique of Marginal Utility Theory to the Law of Demand". Fixing the Economists. Archived from the original on 19 July 2015.
28. ^ "Revealed Preference Theory". Archived from the original on 16 July 2011. Retrieved 11 December 2009.
29. ^ "Archived copy" (PDF). Archived from the original (PDF) on 15 October 2008. Retrieved 9 August 2008.{{cite web}}: CS1 maint: archived copy as title (link)
30. ^ Klein, Daniel (May 2014). "Professor" (PDF). Econ Journal Watch. 11 (2): 97–105. Archived (PDF) from the original on 5 October 2014. Retrieved 15 November 2014.
31. ^ Burke, Kenneth (1932). Towards a Better Life. Berkeley, Calif: University of California Press.
32. ^ Capra, C. Monica; Rubin, Paul H. (2011). "The Evolutionary Psychology of Economics". Applied Evolutionary Psychology. Oxford University Press. doi:10.1093/acprof:oso/9780199586073.003.0002. ISBN 9780191731358. | 7,944 | 33,852 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 53, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2022-27 | latest | en | 0.93195 |
https://www.assignguru.com/multiple-choice/l/civil-engineering/dock-and-harbour-engineering/dock-and-harbour-engineering-set-2/ | 1,674,888,152,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499524.28/warc/CC-MAIN-20230128054815-20230128084815-00197.warc.gz | 635,375,060 | 10,973 | ### Dock And Harbour Engineering Set 2
This set of Dock and Harbour Engineering Multiple Choice Questions & Answers (MCQs) focuses on Dock And Harbour Engineering Set 2
Q1 | At a given port, the fetch is 400 nautical miles, the maximum height of storm wave will be
• 2.073 m
• 8.169 m
• 9.144 m
• 6.8 m
Q2 | Pick up the correct statement from the following:
• Spring tides are caused at new and full moon
• Neap tides are caused when the moon is in her quarters
• Spring tides are roughly twice the height of neap tides
• All of the above
Q3 | Which of the following is a fixed type mooring accessory?
• Bollard
• Buoys
• Cables
• Anchors
Q4 | According to the recommendations of International Navigational Congress in 1912, the ratio of length to width at the entrance for cargo vessels is
• 5.5 and 6.0 to 1
• 6.2 and 6.8 to 1
• 7.4 and 7.8 to 1
• 8.2 and 8.5 to 1
Q5 | Consider the following statements.(i) Fender is the cushion provided on the face of the jetty for ships to come in contact,(ii) Slip is the space of water area between two adjacent piers where ships are berthed,(iii) Pier head is a structure constructed near the tip of break water near the harbour entrance. Of the statements
• (i) and (ii) are correct
• (ii) and (iii) are correct
• (i) and (iii) are correct
• (i), (ii) and (iii) are correct
Q6 | Pick up the correct statement from the following:
• For nautical purposes, low water level is generally referred to by the navigators
• The depth of the bed of the sea from the surface of water is called sounding
• The contour lines on the bed of a water body are called fathoms
• All the above
Q7 | The maximum harbour depth below lowest low water is generally equal to(i) Loaded draft +1.2 m when bottom is rock(ii) Loaded draft +1.8 m when bottom is soft(iii) Loaded draft +1.2 m when bottom is soft(iv) Loaded draft +1.8 m when bottom is rockOf these statements
• (i) and (ii) are correct
• (i) and (iii) are correct
• (ii) and (iv) are correct
• (iii) and (iv) are correct
Q8 | Which one of the following statements is correct?
• The soundings are made with respect to the mean low water
• The soundings which are below the datum are written in black on the map
• The spot heights of the features above datum are written in red on the map
• All the above
Q9 | Which of the following are repair docks?
• Marine railways, dry docks, floating docks, wet docks
• Dry docks, wet docks, floating docks, lift docks
• Wet docks, floating docks, lift docks, marine railways
• Wet docks, lift docks, marine railways, dry docks
Q10 | The smoothened surface of the front face of the guay walls, is known as fending which is made of
• Granite stone
• Timber
• Steel
• All the above
Q11 | Assertion A: Depth and width required at the entrance to a harbour are more than those required in the channel.Reason R: The entrance to a harbour is usually more exposed to waves as compared to the harbour itself.Select your answer based on the coding system given below:
• Both A and R is true and R is the correct explanation of A
• Both A and R is true but R is not the correct explanation of A
• A is true but R is false
• A is false but R is true
Q12 | Pick up the incorrect statement from the following: In a dry dock block made of hard wood,
• Spacing of the blocks is 1.35 m
• The lowest block is 1.8 m long 40 cm × 40 cm in cross-section
• The middle block is 1.6 m long 40 cm × 40 cm in cross-section
• None of these
Q13 | Which one of the following lines is used for tying a ship with a dock?
• Bow line
• Stern line
• Spring line
• All of these
Q14 | In a wet dock system,
• Minimum required depth of water for the vessels is maintained
• Entrance locks are provided with massive gates
• The cost of construction is quite heavy
• All the above
Q15 | Assertion A: Marine structures are made specially bulky and strong.Reason R: Sea insects result in undermining of the hardest and the soundest building materialSelect your answer based on the coding system given below:
• Both A and R is true and R is the correct explanation of A
• Both A and R is true but R is not the correct explanation of A
• A is true but R is false
• A is false but R is true
Q16 | A dock:
• Is provided with a dock gate
• Is provided with an arrangement to pump out water when required
• All the above
Q17 | Which of the following type of sea walls results in greatest protection of shore structures?
• Vertical sea wall
• Sea wall with batter
• Stepped sea wall
• Sea wall with concave face
Q18 | Pick up the correct statement from the following:
• An artificial barrier which makes the enclosed area safe for anchorage of ships, is known as break water
• The length of the quay wall is governed by the length of the largest vessel likely to be berthed
• All the above
Q19 | If the maximum spring rise is 2 m and height of the waves expected is 4 m , then thebreakwater height above the datum will be
• 2.5 m
• 4 m
• 5 m
• 7 m
Q20 | Pick up the correct statement function following:
• The coarse material which has a smaller angle of repose, causes a steeper beach slope
• The coarse material which has a greater angle of repose, causes a steeper beach slope
• The flattening out of the beach is caused due to the movement of small and uniform particles leeward
• Both (b) and (c)
Q21 | Consider the following statements in regard to Beaufort scale for wind speeds,(i) The Beaufort number ranges from 1 to 12.(ii) Higher Beaufort number indicates higher speed of wind,(iii) Beaufort number for calm is smallest and for hurricane ishighest Of these statements
• (i) and (ii) are correct
• (ii) and (iii) are correct
• (i) and (iii) are correct
• (i), (ii) and (iii) are correct
Q22 | The shore line survey includes:
• Depicting the shore line
• Depicting the prominent details on shore line
• Depicting the high water line
• All the above
Q23 | A harbour is a place where
• Ships get shelter and protection against destructive forces due to sea waves
• Facilities are provided for receiving cargo and passengers
• Port buildings are constructed for commercial purposes
• All of the above
Q24 | Assertion A: Large size stones are required in stone revetment in shore protection.Reason R: Resistance of stone to wave force is proportional to its volume and wave force is proportional to the exposed area of the stone. Select your answer based on the coding system given below.
• Both A and R is true and R is the correct explanation of A
• Both A and R is true but R is not a correct explanation of A
• A is true but R is false
• A is false but R is true | 1,701 | 6,543 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2023-06 | latest | en | 0.892774 |
https://quant.stackexchange.com/questions/60333/calibrate-geometric-brownian-motion-of-trading-volume-time-series | 1,702,043,680,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100745.32/warc/CC-MAIN-20231208112926-20231208142926-00290.warc.gz | 538,475,651 | 40,992 | # Calibrate Geometric Brownian Motion of trading volume time series
Let's say I'm modeling the trading volume of a stock price (e.g. Apple Inc.) to follow a Geometric Brownian Motion and I want to estimate the parameters (i.e. drift and volatility) using historical data. I am assuming that a GBM matches the time series pretty well. If I was modeling a stock price itself, I would calculate the drift and volatility by looking at the returns. However, applying this to the trading volume does not seem right to me since the trading volume, unlike a stock price, does not have any returns and if I am not looking at the returns the time series is non-stationary.
Q: How would I calculate the drift and volatility of such a historical time series to calibrate my GBM?
• If the dynamics of the trading volume do not match a GBM, why do not try a different process? Given the time-series of the trading volume, you could select an econometric model that fits the properties of you process. Jan 5, 2021 at 16:38
• @alexbougias I didn't say that the time series does not match a GBM, in fact I assume that it matches a GBM pretty well. My question is only about the calculation of the drift and volatility based on historical data. To me it doesn't seem right to calculate the drift and volatility based on the returns since trading volume, unlike to a stock price, has no returns (you can't really invest in it and make a profit/loss). So again, I assume a GBM matches the time series, I just don't know how to calibrate it considering it is not a stock. Jan 6, 2021 at 8:40
• If that is the case, then taking the returns would be ok. There is no economic rationale behind this, but a technical reason. You have to make your time series stationary first and then estimate the parameters. In econometrics, this is analogous to taking differences in the log-process to make the process I(1). Jan 6, 2021 at 8:51
• @alexbougias That explanation makes sense. Just a follow up question since you mentioned the possibility that trading volume may not match a GBM, do you have a stochastic process in mind that I should look at? Note that it should be a stochastic process, an econometric model would go beyond the scope since the modeling of the trading volume is just a small piece of a rather complex model, so I don't want to develop a sub-model. Jan 6, 2021 at 9:12
• I do not have a specific process, but my thoughts are that you should model the dependence between trading volume and stock returns simultaneously. There should be a work in the microstructure literature that explicitly models both variables. Jan 6, 2021 at 12:18 | 605 | 2,628 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2023-50 | latest | en | 0.933385 |
https://www.gradesaver.com/textbooks/math/applied-mathematics/elementary-technical-mathematics/chapter-6-section-6-2-equations-with-variables-in-both-members-exercises-page-240/19 | 1,686,433,651,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224646350.59/warc/CC-MAIN-20230610200654-20230610230654-00186.warc.gz | 888,146,309 | 12,410 | ## Elementary Technical Mathematics
Published by Brooks Cole
# Chapter 6 - Section 6.2 - Equations with Variables in Both Members - Exercises - Page 240: 19
x=-9
#### Work Step by Step
Simplifying 27 + 5x = 9 + 3x Solving 27 + 5x = 9 + 3x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3x' to each side of the equation. 27 + 5x + -3x = 9 + 3x + -3x Combine like terms: 5x + -3x = 2x 27 + 2x = 9 + 3x + -3x Combine like terms: 3x + -3x = 0 27 + 2x = 9 + 0 27 + 2x = 9 Add '-27' to each side of the equation. 27 + -27 + 2x = 9 + -27 Combine like terms: 27 + -27 = 0 0 + 2x = 9 + -27 2x = 9 + -27 Combine like terms: 9 + -27 = -18 2x = -18 Divide each side by '2'. x = -9 Simplifying x = -9
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 331 | 909 | {"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-2023-23 | latest | en | 0.830691 |
http://devmaster.net/forums/user/14122-tottel/page__tab__topics | 1,369,253,797,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368702444272/warc/CC-MAIN-20130516110724-00053-ip-10-60-113-184.ec2.internal.warc.gz | 68,671,027 | 8,284 | # Tottel
Member Since 18 Sep 2010
Offline Last Active Mar 31 2013 09:41 AM
### Run geometry shader over newly-created geometry?
08 June 2012 - 11:02 AM
I'm trying to subdivide a quad (2 triangles) multiple times.
I send it to the geometry as triangleadj and ouput 8 triangles from that.
However, I want to subdivide multiple times and someone told me I can send the geometry output back to the vertex shader and run the geometry shader again on that new geometry. He couldn't tell me how though.
Thanks.
### HLSL Geometry shader normals problem
07 June 2012 - 09:21 AM
Hello,
I'm making a geometry shader that generates waves on a mesh (preferably a flat plane), using a heightMap.
Everything is working fine, except the normals don't really work out.
http://i.imgur.com/2WGoT.png
I set the normal for each vertex using the crossproduct, which is correct for each triangle individually.
However, the geometry shader goes over every vertex multiple times, so it will assign a different normal for every triangle (right?).
Which means it cannot interpolate correctly.
I tried to be creative and check for every vertex if its normal is default (0,1,0), like so:
if ((vertices[0].Normal.y >= 1.01f && vertices[0].Normal.y <= 0.99f)) normal0 = vertices[0].Normal;
else normal0 = normalize(cross(top0 - top1, top0 - top2));
So that it will reuse the normal if it's already assigned to that vertex. However, it's still giving me the same problem. Any ideas how to solve this? | 369 | 1,482 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2013-20 | latest | en | 0.907181 |
https://www.gradesaver.com/textbooks/math/algebra/college-algebra-10th-edition/chapter-3-section-3-2-the-graph-of-a-function-3-2-assess-your-understanding-page-218/5 | 1,537,964,544,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267164925.98/warc/CC-MAIN-20180926121205-20180926141605-00352.warc.gz | 751,796,339 | 12,314 | College Algebra (10th Edition)
$a=-2$
We need to find $a$ so that (-1,2) is on the graph of: $f(x)=ax^{2}+4$ We plug in the point: $f(-1)=a(-1)^{2}+4$ $f(-1)=a+4$ $2=a+4$ $a=2-4$ $a=-2$ | 91 | 186 | {"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 | 4 | CC-MAIN-2018-39 | latest | en | 0.730898 |
https://www.stat.math.ethz.ch/pipermail/r-help/2014-December/423875.html | 1,653,307,052,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662558015.52/warc/CC-MAIN-20220523101705-20220523131705-00075.warc.gz | 1,153,822,312 | 3,754 | # [R] if else for cumulative sum error
David L Carlson dcarlson at tamu.edu
Tue Dec 2 23:22:46 CET 2014
```Let's try a different approach. You don't need a loop for this. First we need a reproducible example:
> set.seed(42)
> dadosmax <- data.frame(above=runif(150) + .5)
Now compute your sums using cumsum() and diff() and then compute enchday using ifelse(). See the manual pages for each of these functions to understand how they work:
> sums <- diff(c(0, cumsum(dadosmax\$above)), 45)
> dadosmax\$enchday <- c(ifelse(sums >= 45, 1, 0), rep(NA, 44))
[1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[26] 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[51] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[76] 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[101] 1 1 1 1 1 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
[126] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
See the NA's? Those are what David Winsemius is talking about. For the 106th value, 106+44 is 150, but for the 107th value 107+144 is 151 which does not exist. Fortunately diff() understands that and stops at 106, but we have to add 44 NA's because that is the number of rows in your data frame.
You might find this plot informative as well:
> plot(sums, typ="l")
> abline(h=45)
Another way to get there is to use sapply() which will add the NA's for us:
> sums <- sapply(1:150, function(x) sum(dadosmax\$above[x:(x+44)]))
> dadosmax\$enchday <- ifelse(sums >= 45, 1, 0)
But it won't be as fast if you have a large data set.
-------------------------------------
David L Carlson
Department of Anthropology
Texas A&M University
College Station, TX 77840-4352
-----Original Message-----
From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of David Winsemius
Sent: Tuesday, December 2, 2014 2:50 PM
To: Jefferson Ferreira-Ferreira
Cc: r-help at r-project.org
Subject: Re: [R] if else for cumulative sum error
On Dec 2, 2014, at 12:26 PM, Jefferson Ferreira-Ferreira wrote:
> Thank you for replies.
>
> David,
>
> I tried your modified form
>
No. it is either 1: .... or seq_along(...). in this case perhaps 1:(nrow(dadosmax)-44 would be safer
You do not seem to have understood that you cannot use an index of i+44 when i is going to be the entire set of rows of the dataframe. There is "no there there" to quote Gertrude Stein's slur against Oakland. In fact there is not there there at i+1 when you get to the end. You either need to only go to row
> 0
> }
>
> However, I'm receiving this warning:
> Warning message:
> numerical expression has 2720 elements: only the first used
>
> I can't figure out why only the first row was calculated...
You should of course read these, but the error is not from your if-statement but rahter you for-loop-indexing.
?'if'
?ifelse
> Any ideas?
>
>
>
> Em Tue Dec 02 2014 at 15:22:25, John McKown <john.archie.mckown at gmail.com>
> escreveu:
>
>> On Tue, Dec 2, 2014 at 12:08 PM, Jefferson Ferreira-Ferreira <
>> jecogeo at gmail.com> wrote:
>>
>>> Hello everybody;
>>>
>>> I'm writing a code where part of it is as follows:
>>>
>>> }
>>>
>>
>> Without some test data for any validation, I would try the following
>> formula
>>
>>
>>
>>
>>>
>>> That is for each row of my data frame, sum an specific column (0 or 1) of
>>> that row plus 44 rows. If It is >=45 than enchday is 1 else 0.
>>>
>>> The following error is returned:
>>>
>>> Error in if (sum(dadosmax\$above[i:(i + 44)]) >= 45) 1 else 0 :
>>> missing value where TRUE/FALSE needed
>>>
>>> I've tested the ifelse statement assigning different values to i and it
>>> works. So I'm wondering if this error is due the fact that at the final of
>>> my data frame there aren't 45 rows to sum anymore. I tried to use "try"
>>> but
>>> It's simply hide the error.
>>>
>>> How can I deal with this? Any ideas?
>>> Thank you very much.
>>>
>>> [[alternative HTML version deleted]]
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>
>>
>>
>> --
>> The temperature of the aqueous content of an unremittingly ogled
>> culinary vessel will not achieve 100 degrees on the Celsius scale.
>>
>> Maranatha! <><
>> John McKown
>>
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> and provide commented, minimal, self-contained, reproducible code.
David Winsemius
Alameda, CA, USA
______________________________________________
R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help | 1,639 | 5,012 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.59375 | 4 | CC-MAIN-2022-21 | latest | en | 0.751231 |
stmichaelssoccer.com | 1,723,539,395,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641075627.80/warc/CC-MAIN-20240813075138-20240813105138-00761.warc.gz | 427,547,846 | 28,355 | # Court Conversion: How Many Basketball Courts Can Fit in a Soccer Field?
Discover the fascinating world of court conversion! Explore just how many basketball courts can be accommodated on a soccer field.
## 1. The Potential of Court Conversion: Exploring the Feasibility of Transforming Soccer Fields into Basketball Courts
Soccer fields and basketball courts are two popular sporting venues that cater to different athletes. However, what if we told you that soccer fields have the potential to be transformed into multiple basketball courts? In this post, we will explore the feasibility of court conversion and uncover just how many basketball courts can fit within the dimensions of a standard soccer field.
Soccer fields typically have larger dimensions than basketball courts, providing an opportunity for maximizing space utilization. The rectangular shape of soccer fields allows for an efficient conversion process. With proper planning and design, a single soccer field can accommodate multiple basketball courts side by side. By dividing the soccer field into evenly spaced lanes, each lane can be transformed into a separate basketball court. This innovative approach allows for multiple games to be played simultaneously, providing the opportunity to cater to a larger number of basketball enthusiasts within the same space.
• Utilizing the existing infrastructure of soccer fields offers a cost-effective solution for creating additional basketball courts.
• The conversion process involves installing goal posts on the sidelines, transforming them into boundary markers for each basketball court.
• With this conversion, the length of a soccer field can accommodate multiple shorter basketball courts arranged end-to-end.
• By using markings on the turf or floor, each basketball court can maintain its standardized dimensions.
The potential of court conversion is an exciting prospect that can make a significant impact on the availability of basketball facilities. Stay tuned for further exploration of the logistics, benefits, and potential challenges that come with transforming soccer fields into basketball courts in future posts.
## 2. Analyzing Space Requirements: Calculating the Maximum Number of Basketball Courts that Can Fit on a Standard Soccer Field
For sports enthusiasts and facility managers, the concept of converting a soccer field into a multi-purpose space might seem daunting. However, by analyzing the space requirements and calculating the maximum number of basketball courts that can fit, you can transform your soccer field into a hub for various sports activities. Here, we will explore the key factors involved in this process.
Firstly, let’s consider the dimensions of a basketball court. The standard dimensions of a basketball court are 94 feet in length and 50 feet in width. Keeping this in mind, we can evaluate the dimensions of a soccer field, which typically measures around 120-150 yards in length and 70-80 yards in width. This means that a well-maintained soccer field can easily accommodate multiple basketball courts. With simple calculations, you can determine the maximum number of courts that can fit, allowing you to make the most efficient use of your space.
However, it’s important to consider a few additional factors that can impact the court conversion. These include safety aspects such as maintaining adequate space between the courts to prevent collisions, ensuring proper height clearance for basketball goals, and providing ample space for spectator seating. By incorporating these elements into your planning process, you can optimize your court layout and maximize the potential for a seamless transition from a soccer field to a multi-court sports facility. So, get ready to unleash the untapped potential of your soccer field and create a space that caters to the diverse needs of athletes and sports enthusiasts alike!
## 3. Key Factors for Successful Court Conversion: Considerations for Adapting Soccer Fields for Basketball Use
One of the key factors to consider when converting a soccer field into a basketball court is the size and dimensions of the field itself. Soccer fields come in different sizes, ranging from small to regulation size, so it’s important to measure and assess the field you have to work with. A regulation basketball court measures 94 feet in length and 50 feet in width. Depending on the size of the soccer field, you can fit multiple basketball courts within it. For example, if you have a regulation-sized soccer field, you can fit two basketball courts side by side, with enough space for spectators and other amenities. However, if you have a smaller soccer field, you may only be able to fit one basketball court comfortably.
Another factor to take into consideration is the surfacing of the field. Soccer fields usually have natural grass or artificial turf, which may not be suitable for basketball. Basketball courts typically have hardwood or rubberized surfaces for better traction and ball control. To convert a soccer field into a basketball court, you may need to remove the existing turf or grass and install a suitable surfacing material such as sports tiles or acrylic paint. This will ensure a safe and optimal playing surface for basketball.
In conclusion, successful court conversion from a soccer field to a basketball court requires careful consideration of the size and dimensions of the field, as well as the type of surfacing needed. With the right planning and implementation, it’s possible to adapt a soccer field to accommodate multiple basketball courts and provide an enjoyable playing experience for athletes and spectators alike.
## 4. Designing Multi-Purpose Spaces: Innovative Strategies for Integrating Both Soccer and Basketball Facilities in a Single Field
In the realm of sports facility design, the challenge of incorporating both soccer and basketball facilities within a single field has sparked a wave of innovation. These multi-purpose spaces provide opportunities for athletes of different disciplines to utilize the same space efficiently, maximizing its potential. But just how many basketball courts can fit within a soccer field? Let’s delve into this fascinating concept and explore the strategies employed in transforming these fields into versatile arenas.
One popular approach is the concept of court conversion, where a soccer field is designed with the ability to transform into multiple basketball courts. With the help of advanced retractable seating systems, the field can be seamlessly converted into several smaller courts, utilizing the same space and infrastructure. This innovative design not only maximizes the utilization of the area but also offers flexibility in accommodating different sporting events, training sessions, or tournaments simultaneously. The possibilities are endless – from hosting soccer matches in the morning to converting the field into multiple basketball courts for afternoon training sessions or regional tournaments.
To achieve this feat, designing a multi-purpose space requires careful planning and attention to detail. Here are some innovative strategies used to integrate both soccer and basketball facilities seamlessly:
1. Retractable Seating: Installing retractable seating systems allows for quick and easy conversion of the soccer field into multiple basketball courts. These seating systems can effortlessly slide in and out, accommodating spectators during soccer matches while creating space for the basketball courts when retracted.
2. Modular Court Flooring: Utilizing modular court flooring that can be easily assembled and disassembled is a game-changer. This technology enables the transformation of the soccer field into a perfectly leveled and marked basketball court, providing a safe and professional playing surface for basketball athletes. The modular flooring is designed to be durable, slip-resistant, and capable of adjusting to different configurations, making it suitable for a range of basketball activities.
By embracing these innovative strategies and designing multi-purpose spaces that seamlessly integrate both soccer and basketball facilities, sports enthusiasts are now able to enjoy the best of both worlds. These versatile arenas not only promote inclusivity but also allow for increased usage, making them a valuable asset for sports communities and organizations. So, the next time you set foot on a soccer field, remember that it may just hold the potential to transform into a multiplex of basketball courts with a touch of ingenuity.
## 5. Ensuring Safety and Accessibility: Guidelines for Modifying Soccer Fields into Regulation Basketball Courts
So, you have a soccer field, and you’re wondering how many basketball courts you can fit into it? Look no further! Converting a soccer field into regulation basketball courts requires careful planning and adherence to safety and accessibility guidelines. Here, we’ll outline some essential considerations and steps to take for this exciting transformation.
1. Evaluating the Field: Before proceeding with any modifications, assess the existing soccer field to determine its suitability for basketball court conversion. Take into account the overall dimensions, slope, drainage, and any vegetation or obstacles that may hinder the process. Address any maintenance issues and ensure that the base is stable and flat to lay the basketball court foundation.
2. Boundaries and Markings: Creating clear boundaries and markings is crucial for a seamless transition. Install basketball court lines that conform to standard regulations, including the mid-court line, three-point line, and key area markings. Proper spacing and accurate measurements are essential to guarantee an authentic basketball experience. Remember to refer to official governing bodies’ guidelines for precise court dimensions and markings.
## 6. Economic Viability: Exploring the Cost-Effectiveness and Financial Considerations of Court Conversion Projects
When considering court conversion projects, one of the most crucial aspects to explore is their economic viability. Is it cost-effective and financially feasible to convert a soccer field into multiple basketball courts? This post delves into the various considerations related to the cost-effectiveness and financial aspects of court conversion projects.
Understanding the Potential Costs:
Before embarking on a court conversion project, it is important to have a comprehensive understanding of the potential costs involved. Factors such as material procurement, labor expenses, equipment installation, and maintenance should be carefully assessed. Additionally, any necessary modifications to facilities or infrastructure must be taken into account. By having a clear idea of these cost components, project managers can develop an accurate budget and ensure the project remains economically viable.
Maximizing Utilization:
A key consideration in court conversion projects is maximizing utilization once the conversion is completed. By converting a soccer field into multiple basketball courts, the facility can accommodate a larger number of users simultaneously. This can lead to increased revenue generation through court rentals, organized tournaments, or sport events. Additionally, by diversifying the sporting activities offered, the facility can attract a wider range of users, further contributing to its economic viability.
## 7. Case Studies: Successful Examples of Soccer Field Conversions for Basketball Use from Around the World
When it comes to converting soccer fields into basketball courts, there have been numerous successful examples from around the world. These case studies highlight the innovative solutions that have allowed multiple basketball courts to fit within a single soccer field, optimizing the use of space and creating opportunities for more sporting activities. Here are a few notable examples:
1. Wukesong Arena, Beijing, China: In preparation for the 2008 Olympic Games, the Wukesong Arena underwent a remarkable transformation. The original soccer field was converted into a state-of-the-art basketball arena that could accommodate two full-size courts simultaneously. By utilizing retractable seats that could be moved closer to the court, the arena provided an optimal viewing experience for spectators. This conversion not only allowed for basketball games to be hosted during the Olympics but also created a lasting legacy as the arena became the home of various basketball events afterward.
2. Stadio Olimpico, Rome, Italy: In a city where soccer is a way of life, the Stadio Olimpico found a unique way to incorporate basketball. By installing a modular flooring system over the soccer field, the stadium is now able to host multiple basketball courts. This flexible solution not only ensures the preservation of the playing surface but also allows for quick and easy conversion between sporting events. The Stadio Olimpico has successfully hosted several important basketball matches, proving that the conversion of a soccer field can bring new sporting opportunities to historic venues.
## 8. Community Engagement and Practical Recommendations: Involving Stakeholders in Decision-Making and Planning Court Conversion Projects
When it comes to court conversion projects, a crucial element is engaging with the community and involving stakeholders in decision-making and planning processes. As an integral part of the project, community engagement ensures that the converted court caters to the needs and preferences of the local residents.
Practical recommendations for involving stakeholders in court conversion projects include:
• Conducting surveys or holding public meetings to gather input from community members. This allows residents to voice their opinions, concerns, and suggestions, which can then be considered during the planning phase.
• Collaborating with local sports clubs, schools, and recreational organizations to understand their requirements and incorporate them into the design. By involving these stakeholders, the converted court can better serve the needs of both organized sports activities and individual play.
• Encouraging public participation through interactive workshops or online platforms where residents can provide feedback on different design options. This approach promotes transparency and inclusivity, making sure that the final conversion project reflects the preferences of the diverse community.
By actively involving stakeholders in decision-making and planning, court conversion projects can provide a space that not only meets the local demand for sports facilities but also fosters a sense of ownership and pride within the community. Ultimately, this collaborative approach creates a win-win situation where the converted court becomes a cherished asset for everyone to enjoy.
## 9. Future Prospects: Potential Advancements and Opportunities in the Field of Court Conversion for Different Sporting Facilities
As the demand for multi-purpose sports facilities continues to grow, the field of court conversion presents exciting prospects for the future. With the ability to transform soccer fields into basketball courts, the potential advancements and opportunities in this field are numerous.
One of the key advantages of court conversion is the maximization of space utilization. Soccer fields are known for their large playing areas, which can be easily converted to accommodate multiple basketball courts. This opens up opportunities for hosting tournaments and events that involve multiple basketball games simultaneously, increasing the overall capacity of the sporting facility. Additionally, court conversion allows for flexibility in scheduling, as different sports can now coexist within the same space, eliminating conflicts and increasing the value of the facility.
• Increased revenue potential through hosting larger events and accommodating more teams
• Ability to attract a wider range of sports enthusiasts by offering various sports options in one location
• Opportunity for cross-training and skill development for athletes in different sports
• Reduced maintenance costs by utilizing existing infrastructure rather than building separate facilities
The future of court conversion looks promising as advancements in technology and design continue to enhance the versatility and functionality of sporting facilities. With the potential to convert soccer fields into basketball courts, the possibilities are endless, offering unique and innovative solutions for organizers, athletes, and fans alike.
## 10. Conclusion: Harnessing the Potential of Court Conversion to Optimize Facility Usage and Promote Sporting Diversity
In conclusion, court conversion is an innovative approach that allows for the optimization of facility usage and the promotion of sporting diversity. By repurposing existing sports fields, such as soccer fields, we can transform them into multi-purpose courts that can accommodate various sports like basketball, volleyball, and even tennis.
This conversion not only maximizes the utilization of space but also opens up opportunities for different sporting activities, catering to a wider range of interests and promoting inclusivity in recreational sports. Instead of having separate dedicated courts for each sport, a converted court offers the flexibility to switch between different sports, making it a cost-effective and efficient solution.
• By harnessing the potential of court conversion, numerous basketball courts can fit within a soccer field, creating a versatile space for athletes and sports enthusiasts alike.
• The ability to adapt the same area for various sports provides a unique opportunity for players to explore different disciplines and enhance their skill sets.
• Furthermore, this initiative encourages individuals from diverse backgrounds and age groups to engage in sports and physical activities, fostering a sense of community and promoting a healthy lifestyle.
Ultimately, court conversion offers a groundbreaking way to optimize facility usage, introduce sporting diversity, and accommodate the ever-evolving needs of athletes and sports enthusiasts.
In conclusion, the conversion of basketball courts in a soccer field varies depending on the size. Key takeaway: A standard soccer field can accommodate approximately 4 to 6 basketball courts, each with their own dimensions and adjustments. #CourtConversion #BasketballOnTheField | 3,935 | 18,987 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2024-33 | latest | en | 0.877032 |
https://lifethroughamathematicianseyes.wordpress.com/tag/research/ | 1,547,736,866,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583658988.30/warc/CC-MAIN-20190117143601-20190117165601-00146.warc.gz | 563,344,805 | 39,124 | Hope you had a good week so far. If you have read my previous post, you were probably expecting this post. While visiting Edinburgh Butterfly & Insect World I have spent some time watching the ants they have there. Looking at their organized trails and how they were carrying things around, I was sure there was some... Continue Reading →
Recently I have posted about my holiday to Romania and what I have visited there. During that journey I have thought at different things that could have transformed it into a maths related one. I feel that every holiday could become a maths-camp if you can find the right questions and use your creativity and... Continue Reading →
Last week on Tumblr I got into an interesting conversation on L'Hopital Rule and I wanted to share with you some of the interesting facts I have found about it. First of all, this rule was one of my favorite during high school and also in the first year of university. If nothing else worked... Continue Reading →
In the last couple of weeks I have been asked a lot about what exactly someone could do with a mathematics degree. I tried my best to explain how beautiful mathematics is and how rewarding it is to have a degree in maths, but then I thought that it would be a great idea to... Continue Reading →
Last week I have shared on Facebook an old post of mine: a quote (anonymous unfortunately) on what good mathematics really means. This is one of all time quotes on mathematics, but I was incredibly surprised by the huge number of reactions I have received and also a great number of comments and messages about... Continue Reading →
This week was a huge mathematical week for a lot of reasons. I don't even what to mention Pi Day anymore, but on Tuesday was the Abel Prize Award and I was incredibly excited for it. Also, this year was one of those few years when I totally know what the winner has been doing... Continue Reading →
This weekend will be full of Pi all over. For those of you that don't know I have organized another event on Facebook: Pi Love, where I invite people to share their love of this day in any way they like. Today I will talking about some historically interesting facts about Pi and then tomorrow will... Continue Reading →
I thought that this would be a good way to finish the event Modern Mathematics. Thank you everyone who participated and helped me find out more about the topics and improve my mathematical knowledge. I have to confess that most of the things were new to me and it was very interesting to find out... Continue Reading →
January brought nice surprises to me. I had no idea that two of my favorite mathematicians are born in January and also the birthdays are so close to each other in term of days, obviously not years. Moreover, I have found another interesting mathematician (new to me) which was also born in January. So I... Continue Reading → | 583 | 2,887 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2019-04 | latest | en | 0.989092 |
rimzaasoft.com | 1,660,652,041,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572304.13/warc/CC-MAIN-20220816120802-20220816150802-00346.warc.gz | 436,938,775 | 20,011 | Home / Battle Strike / What does this signify Seems like (Y Elizabeth Third) in addition to help.
# What does this signify Seems like (Y Elizabeth Third) in addition to help.
When any numbers problem requires, the length of time, it is actually in relation to long distance. Hence to put it differently, if I use the pure logarithm involving e a , I receive back button rear: inside picture type ln(elizabeth a ) Is equal to a, as well as equivalently, ln(exp(x)) Equates to x. Mean is merely a moniker pertaining to ordinary. It’s decimal development goes on eternally and do not repeat. mean: 12-15
median: 14
mode: 14
range: 8 There isn’t any common response.
• Switch in order to Crossbreed Mode
• In lowercase, e will take about any kind of hit-or-miss meaning or perhaps worth as a varied or even constant.
• As an event or maybe modification, E may take with any kind of haphazard meaning.
• E^2 could consult the particular Euclidean place, R^2.
• ?, some sort of back Elizabeth, is a symbol utilised in judgement to indicate the presence of a company in the predicate record.
• E work extremely well rather than “?10^” inside technological notation or even engineering note to ensure that Dollar.Being unfaithful \times 10^5 Dollar is often equivalently published A buck.Hunting for \; \mathrm \; Five Dollar . It is popular in elderly medical online car loan calculator models.
As an example, this downward slope on the operate ex girlfriend or boyfriend will be former mate, and therefore this tend at any point is equal to a y-value with the function. As you are possibly a lot more familiar with the technique of “average” as compared to “measure of fundamental tendency”, We used a lot more comfortable term.) (In case there are twice as many harmful bacteria, then this quantity of microbes develops doubly as fast.) A mathematical rule with the degree of microorganisms following a particular time period is The actual technological definition of that which we frequently refer to as the “average” will be formally termed “the mathematics mean”: accumulating the values after which separating from the number of values.
### What is definitely indicate by simply appearing out in numbers problem-solving?
next back button can be One particular, and also 43908, or 239043248, and not for example -3, because it’s away from the set The style may be the range that is certainly repeated more often than any, hence 14 may be the mode. It lacks something to use degrees, there’s no performance right here. The input suggests the trouble as well as the result suggests the solution! [but never within math] a) consider the maximum amount of points as you can
b) hold aproximation because selection. He has to get at minimum a Seventy nine to the very last check.
This means you might express it “one subtracting ourite to the x”. Here is actually a number of by far the most simple statistical emblems and their matching meanings: “ ” symbolizes above, “=” means equivalent, “?” symbolizes definitely not similar, “?” refers to around similar to, “?” refers to verticle with respect, “°” denotes level, “?” signifies private eye or even Three.17, “?” refers to infinity, “m” signifies the particular mountain of your series, “P” symbolizes circumference, “A” denotes space, “V” symbolizes size, “a:b” refers to ratio, “()” indicates parentheses with regard to bunch, “?” means rectangle actual, “?” indicates summary, “?” denotes a right viewpoint, “| |” indicates total cost, “U” means nation, “?” signifies intersection and “mod” means other parts calculation. The “mean” will be the “average” you happen to be helpful to, that you tally up each of the amounts then split by way of the number of numbers. In case you indicate you are math concepts instructor doesn’t want you with a cellphone with category then its as the texting trend can be a disruption into a lecturers. A few fundamental businesses tend to be denoted because of the right after designs: “+” usually means accessory, “-“ usually means subtraction, “x” means multiplication, plus “/” suggests department. what does indeed range suggest inside finally quality math?
### What will qoutient signify in mathematics?
A solution isn’t going to usually have an average! Sorry I would not know very well what you imply. Page produced inside 2.00013899803161621 xeR is likely : x ? ? funds Age although scaled-down.. a tendency inside mathematics is actually a sample or maybe sequence. y Equates to 1E-06×5 – Zero.0002×4 + 4.0161×3 ( blank ) 4.4893×2 + 7.5295x ( space ) 10.87
Mean, n average, as well as style are usually 3 forms of “averages”. my personal instructor said it is a alternative to “Set connected with true numbers” nevertheless is that proper? My partner and i had written that by using colour also since i could not uncover designs.. The major value is usually Tough luck along with the tiniest is 6 , so the selection is 12 – 7 Implies 5 . cash Ourite but small.. I have come across ebooks who go in any event within this; presently there doesn’t appear to be a opinion about the “right” specification of “mode” while in the above situation.
## Purplemath
The fact is the higher than working out is most likely the mathematics suggest, or maybe often referred to as your necessarily mean typical. Average is really a time period that is utilized, mis-used and quite often overused. If you wish many aproximation within the aspect you can utilize linear function (purple line) wich will provide you with huge oversight in the center. The valuations inside the checklist higher than counseled me full amounts, even so the indicate from the collection was obviously a decimal cost. The range elizabeth is usually, while you point out, irrational. The actual “mode” could be the value proofread and editing services at writingbee.com’s site that develops usually.
### What does indeed no less than suggest in a math dilemma?
So I have told you whatever circumstance the place e can be seen; here is what age is actually. what does quotient necessarily mean around math where misused point equations are authored by strategy for overview. x might be 3280492, or even Zero.32894382, oro 48389.3242, or perhaps -384209482/32490289.3232, or perhaps private eye. So that you would express it “one take away at the towards x”. This list possesses 2 ideals which might be recurring thrice; that is, 15 in addition to 11 , each individual replicated triple.
• E might refer to one within electronic digital calculation, ordinarily the consequence of a division by way of absolutely no or even the look at the purpose away from it has the website. This may also authored “Err”, “Error”, “NaN”, and other notations as being a default expression delivered when a research error happens.
• In lowercase, e may take in any kind of irrelavent significance or perhaps worth to be a variable or maybe continual.
• Linear Mode
• E works extremely well in place of “?10^” in technological note as well as engineering notation such that 1 dollar.In search of \times 10^5 is usually equivalently published One dollar.9 \; \mathrm \; A few Bucks . It is prevalent in more mature clinical car loan calculator models.
• In mensuration, the actual e is an Supposrr que prefix conspicuous while “exa-“, and it’s for being fitted into a component with assess including m (gauge) or perhaps g (g), to make this ingredient actions em (exameter) as well as eg (exagram). The idea signifies a measurement aspect involving 10^18.
• Euler’s range (age) ( blank ) a constant that’s highly important in higher-level mathematics. Otherwise known as Napier’s Frequent or the Healthy Foundation. The actual dramatical perform Bucks e^x might possibly be published Money \exp(a) Money as you move the logarithmic operate Dollar \log_e c Dollar can often be created Buck \ln chemical
Look for instance that graphic: Length Studying
10 Nineteen
15 Twenty-five
20 Twenty-seven
25 30
30 24
35 Thirty eight
40 39
45 49
50 43
55 44 The average may be the t in addition to Some , hence: After that select the key to compare and contrast your answer to Mathway’s. The math name simultaneous show that not one but two wrinkles won’t ever at any time match regardless how long the series is actually. 13, Tough luck, 13, Tough luck, 18, 15, Sixteen, 19, 21 In pc’s along with calculators:
Several standard surgical procedures are usually denoted through the right after signs: “+” usually means addition, “-“ usually means subtraction, “x” suggests multiplication, and “/” means team. (One particular + Two + 4 + 6) ? Some Is equal to 17 ? Four Implies Several.5 a trend around mathematics can be a sample and also collection. where the phase equations are created by strategy for evaluation. (This means that when there is double the amount of money, you’ll gain double desire.) This offers climb towards the blueprint pertaining to desire made worse consistently: Equations suggest a difficulty primarily inside math
• The middle matrix (E) * in straight line algebra, E ordinarily presents a transformation matrix achieving a particular considerations.
• As a flexible utilized in geometry, e may talk about a eccentricity associated with an ellipse or some other conic segment.
• Linear Mode
• The simple matrix (E) * inside straight line algebra, E generally symbolizes a metamorphosis matrix meeting a selected standards.
• E^2 might consider your Euclidean living space, R^2.
xeR is probably : times ? ? maybe shg gives you better outline and much more strategies however you will need to have far more calculations knowledge now (and much less stand out) therefore you should take many yahoo hunting I reckon that. Length Studying
10 Nineteen
15 Twenty-five
20 Twenty-seven
25 30
30 24
35 Thirty eight
40 39
45 49
50 43
55 44 e is at endless decimal, the primary digits ones tend to be 3.71 therefore u find the replies ost Your current Subject matter And that is . the mean means the actual average math points of interest usually are necessarily mean,n average,style,range
## MathHelp.com
Since you are in all probability a lot more experienced with the very idea of “average” than with “measure connected with core tendency”, I oftentimes tried the more comfortable name.) calculating in your mind, typically arithmetic The average is definitely the m + One particular) ? A couple of Means Several.5 various -th benefit; your method is displaying everyone, with that “point-five”, this I’ll ought to ordinary the fifth along with 6 volumes to find the typical. What can greater mean If it means a times 10^ subsequently On the lookout for.0122222900391E-5 is going to be 3.000090122222900391 and that is smaller than 2.00013899803161621 It is decimal extension continues for a long time rather than repeats.
• In lowercase, e might take on any hit-or-miss indicating or perhaps worth as a diverse or constant.
• Switch so that you can Threaded Mode
• In lowercase, e will take for virtually any arbitrary indicating or maybe price to be a diverse or even continual.
Finding a decimal price for that necessarily mean (or the particular median, should you have a good volume of data items) is usually perfectly okay; don’t around your answers to attempt to suit the arrangement of your some other numbers. It lets you know precisely what ideals by may take in. Imply is merely a play name with regard to normal. I’ve exhausted to sort out another formulation. it means a lot more like symbolism Former mate:what does suggest necessarily mean around math concepts meanings or even just what does necessarily mean mean throughout numbers terms .
My question: I personally end up finding that towards the bottom with web sites. It’s got several definitions within arithmetic. The most significant value while in the record is usually 6 , the particular will be A single , in addition to their variation is usually Some , therefore, the vary will be Half a dozen . The “exp” signifies “exponential”.
If you actually get a car or truck in a way of which, after y a long time, you could have moved exactly e^x mile after mile (hence you’ll be increasing continually), then e^x is actually *also* your current quickness immediately after y time! The “range” of a listing a amounts is simply the difference between the best and minutest ideals. 87 + 95 + Seventy six + 88 + x Means 425 Nevertheless is actually not typical, and you should not count on that. 1 + 1/(A person) + 1/(One particular 2 .
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https://wiki-helper.com/question/a-triangle-divided-into-2-a-part-of-the-base-is-7-and-the-other-10-2-the-opposite-is-8-5-find-th-38018590-51/ | 1,632,193,825,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057131.88/warc/CC-MAIN-20210921011047-20210921041047-00175.warc.gz | 651,235,056 | 15,440 | ## a triangle divided into 2, a part of the base is 7 and the other 10.2, the opposite is 8.5 find the top angle of the part that’s 7
Question
a triangle divided into 2, a part of the base is 7 and the other 10.2, the opposite is 8.5 find the top angle of the part that’s 7
in progress 0
1 month 2021-08-16T03:24:44+00:00 1 Answers 0 views 0 | 120 | 345 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2021-39 | latest | en | 0.88235 |
https://www.teachstarter.com/us/blog/best-primary-school-bingo-games-cards-us/ | 1,611,149,886,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703520883.15/warc/CC-MAIN-20210120120242-20210120150242-00449.warc.gz | 1,031,882,877 | 51,245 | # Our Most Popular Classroom Bingo Games!
0
0
## Bingo!
My Year 7 teacher, Mr Elms, used Bingo as a regular Friday afternoon reward. It was our favorite time of the week, and most kids in my class were engaged. There wasn’t a chance we were going to give up an opportunity to score a snake lolly! Little did we know just how educational those repetitive, but always fun, Friday afternoon bingo games were. In fact, they are the reason why I still know that 13 is a “Baker’s Dozen” and that 12 x 13 = 156, even though I left Mr Elms’ classroom a good, well, one and a bit baker’s dozens years ago!
Make your classroom buzz! Subscribe to Teach Starter and access thousands of curriculum-aligned resources and digital learning tools.
Preparing a new bingo game to suit the topic or content takes time. So, we have almost 50 different Bingo games ready for you to download here on the Teach Starter website. The only prep left for you is to print, cut and laminate the classroom bingo games that you and your students love the best so you’ll have them for each Friday afternoon from now until forever!
Here are the ten most popular, most downloaded primary school bingo games in our teacher resources collection.
### 1. Pizza Fraction Bingo
Pull out a fraction card and have students put a marker over the corresponding pizza fraction if they have it on their card. Blank game cards are provided for you to add your own fractions in.
### 2. Australian Currency Bingo
With this layout, your students can decide if they need three squares vertically or five squares horizontally to win.
### 3. 0-1000 Place Value Bingo
We also have Place Value Bingo available with numbers 0 – 10000, and 0 – 100000 as well as two-digit games featuring digits, MAB and pop sticks.
### 4. Contractions Bingo
There are 32 bingo cards in this Contractions Bingo set, including two blank cards so students can create their own!
### 5. CVC Words Bingo
Choose a picture card and either show it to your students or read out the word to them. Students use a counter to cover over the CVC word if they have it on their game card. There are two options provided in this download – picture cards with the CVC words written on them and picture cards with no words.
### 7. 0-12 Times Tables – Multiplication Bingo
Use this set of 32 colorful bingo cards to practice times tables!
### 8. Homophones Bingo
“My brother ate three ice creams and had a big tummy ache!”
Read out these sentences to your students while they identify the homophone and try to find it on their bingo mat.
### 9. 2D Shape Bingo
Rhombus, trapezium, pentagon, circle – these shapes and more are waiting to be called in 2D Shape Bingo!
### 10. Fraction, Decimal and Percentage Bingo
These bingo cards combine digits, symbols and graphs to create a fun and challenging mathematics bingo game.
And that’s the Top Ten!
Whether you are reinforcing concepts in Mathematics or grammar, practising sight words or spelling, Bingo is a fantastic way to support student learning through play. Here are a few more favorites, tried and tested by some of our amazing members.
### Time Bingo Cards @teacher.tess
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### Fractions Bingo Game @missfloydsclassroom
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### Multiplication and Division Bingo Game @teach.create.dominate
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### Vowel Diagraph Bingo @miss.bs.monsters
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p.s. We really do try to reduce your prep time as much as possible, though laminating is one symptom of ‘Teach Starter Bingo-itis’ that we can’t promise you’ll avoid!
## Check out the full Teach Starter collection of primary school Bingo games and cards here!
Make your classroom buzz! Subscribe to Teach Starter and access thousands of curriculum-aligned resources and digital learning tools. | 908 | 4,031 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2021-04 | latest | en | 0.949067 |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=34&t=35507&p=117258 | 1,606,192,982,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141171077.4/warc/CC-MAIN-20201124025131-20201124055131-00293.warc.gz | 377,047,394 | 10,981 | ## s vs d orbital
Nicole Garrido 2I
Posts: 52
Joined: Fri Sep 28, 2018 12:18 am
### s vs d orbital
Why are some elements written with a d^10 rather than s^2 and d^8?
Germar G 4F
Posts: 38
Joined: Fri Sep 28, 2018 12:28 am
### Re: s vs d orbital
This situation usually happens with Zn 2+. Since we want to avoid having two half-filled orbitals when there are 2 electrons that could be used in the outer 4s shell, we take the electrons from s2 and give them to d8, so that this way the orbital is at fully filled with electrons (d10).
Shash Khemka 1K
Posts: 38
Joined: Fri Sep 28, 2018 12:18 am
### Re: s vs d orbital
It is preferable for orbitals to be fully filled. We can do this by taking 2 electrons from s2 and give it to d8. This allows the d orbital to be fully filled and "happy". | 248 | 796 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2020-50 | latest | en | 0.922009 |
https://forum.dynamobim.com/t/python-order-a-list-based-in-another-list/49893/6 | 1,653,114,638,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662538646.33/warc/CC-MAIN-20220521045616-20220521075616-00240.warc.gz | 319,032,369 | 7,302 | # PYTHON - order a list based in another list
Hello everyone,
beginners question here
I am trying to get a list of points (x,y,z) ordered based in the z value.
As a beginner, I thought I could use two lists (xyz and only z) to create a dictionary, then sort it, then create a new list with the sorted positions x,y,z. Why is it not working and is there another better method to achieve what I am trying to?
Cheers!
To sort by Z then X then Y use the following:
``````import clr
orglst = IN[0]
orglst.sort(key = lambda orglst: (orglst.Z, orglst.X, orglst.Y))
OUT = orglst
``````
3 Likes
that is beautiful, and it works indeed.
As a beginner, I would like to understand what I am doing though, and this lambda expression was a bit too much. I tried to translate it into a function and was not successful. Would you mind helping me with that as well?
import clr
orglist = IN[0
def reorder(elem):
return elem.Z
orglist.sort(key=reorder)
OUT = orglist
Thanks a lot!
Loud and clear
Dialing this right back… the simplest way to sort by one part of an XYZ is to use a List.SortByFunction node. Then use the re-ordered list to get the Elements in order
3 Likes
for some reason that didnt work here, but I am really curious to understand whats the mistake I am doing with the function in python. I would be interested in understanding how to translate the lambda into a function, if that makes sense? Just as a way to understand what the lambda is doing… Thanks a lot!
To sort by Z then X then Y as a function in a Python the input and return needed to be adjusted to work as a definition.
``````import clr
def sortbyZXY(orglst):
orglst.sort(key = lambda orglst: (orglst.Z, orglst.X, orglst.Y))
return orglst
input = IN[0]
result = []
for i in input:
result.append(sortbyZXY(i))
OUT = result``````
3 Likes | 462 | 1,817 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2022-21 | latest | en | 0.90233 |
https://orangekitchens.net/bakeing/frequent-question-how-long-does-it-take-to-cook-a-25-lb-ham.html | 1,660,089,183,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571090.80/warc/CC-MAIN-20220809215803-20220810005803-00598.warc.gz | 422,823,533 | 20,006 | # Frequent question: How long does it take to cook a 25 lb ham?
Contents
Put the ham, flat-side down, on a rack in a roasting pan. Pour 1/4 inch water into the bottom of the pan. Transfer to the oven and roast until a thermometer inserted into the thickest part of the ham registers 130 degrees F, about 2 hours, 30 minutes (about 15 minutes per pound).
## Do you cook a ham at 325 or 350?
For boneless hams, bake at 325 degrees; for 6- to 8-pound hams, about 20 minutes per pound. For a bone-in ham, cook at 325 degrees; for up to 14 to 16 pounds, about 12 minutes per pound. For canned ham, bake at 325 degrees; cook a 3-pound ham about 21 minutes per pound.
## Do you cover a ham when you bake it?
Cover either the ham itself or the pan with foil. Make sure it is covered well so the ham doesn’t dry out. Set the oven to 350 degrees and bake the ham, basting every 15-20 minutes. Uncover the ham when you baste it, but then cover it back up when you put it back in the oven.
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## How long do I cook a precooked ham for?
HOW DO I COOK A PRECOOKED HAM? A precooked ham should be cooked in the oven at 325 degrees F for 10 minutes per pound, or until it reaches 145 degrees F, according to the USDA.
## How long do you cook a 20 lb ham?
Preheat the oven to 325°F. To heat the ham, place it on a rack in a shallow roasting pan, and bake uncovered. For a whole ham, allow 15 to 18 minutes to the pound; for a half, 18 to 24 minutes per pound.
## How long do you bake a ham per pound?
Put the ham, flat-side down, on a rack in a roasting pan. Pour 1/4 inch water into the bottom of the pan. Transfer to the oven and roast until a thermometer inserted into the thickest part of the ham registers 130 degrees F, about 2 hours, 30 minutes (about 15 minutes per pound).
## What temperature do you cook ham to?
A fully cooked ham needs to be cooked to 140°F (basically just to heat it) where as a “cook before eating” ham needs to be cooked to 160°F. When cooking ham, you’ll want to preheat your oven and place the ham cut side down. Cover the ham in foil and crimp the foil around your roasting pan (I use a 9×13 pan) to seal it.
## What happens if you overcook ham?
Heating above 135 degrees will only detract from taste and tenderness. Re-cooking or prolonged heating will always make cooked meat tough and in the case of cured hams, the meat will be crumbly. … That is simply because those meats contain much more water and fat. Water and excess fat buffer the effects of over cooking.
## Do you wrap ham in foil to bake?
Tightly wrap and seal the ham with foil so none of the juices escape. Place the ham in a baking pan and cook for approximately 20 to 25 minutes per pound, or follow the directions on the package for cooking times. A fully cooked ham will be done when the internal temperature reaches 130 degrees F to 140 degrees F.
## Do you add water when cooking a ham?
Gently cook the ham with at least 1/2 cup of water, wine, or stock in the pan and cover it with foil to make sure the ham won’t dry out (until you’ve applied the glaze—then, the foil comes off).
## How do you reheat Ham without drying it out?
Place in an oven-safe baking dish. Cover top of ham with loosely wrapped aluminum foil to keep moisture in. Bake at 275 degrees F at 10 minutes per pound–or until meat thermometer reads 135 – 140 degrees.
## Can I cook the ham the day before Thanksgiving?
Can I Cook the Ham The Day Before Thanksgiving? Yes, you absolutely CAN cook the ham the day before and then refrigerate overnight.
## How do you heat up a precooked ham without drying it out?
Cover the slices with foil and heat in the oven. Or cover and reheat in a microwave. “It’s just fine to reheat it, just don’t overheat it,” Becker said. According to www.honeybaked.com, their hams should be reheated in a 275-degree oven, covered with foil for 10 minutes per pound.
## Is a Budaball ham fully cooked?
Budaball hams are fully cooked, and heating time depends upon the size and style of the ham. A bone-in ham needs to heat in a preheated 325-degree-Fahrenheit oven for 14 to 17 minutes per pound.
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## Is a smoked ham fully cooked?
The answer, in short, is if it is cured, smoked or baked, ham is considered “pre-cooked,” and would not technically need to be cooked. This includes the ham that is purchased at the deli. In fact, most ham that is sold to consumers is already cured, smoked or baked.
## How do you know if a ham is done?
How do you know if a ham is done? A ham is ready to heat when a thermometer inserted into the thickest part of the ham registers 145 degrees F. Your thermometer should not be touching any bone, as this will produce an inaccurate reading. | 1,211 | 4,812 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2022-33 | latest | en | 0.866536 |
http://myriverside.sd43.bc.ca/keng2015/tag/week2/ | 1,621,223,370,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991557.62/warc/CC-MAIN-20210517023244-20210517053244-00550.warc.gz | 36,116,827 | 8,985 | # Math 10 Week #2
this week we learned how to simplify mixed and entire radicals.
you first find the perfect square that multiplies to your radical then separate your perfect square and and radicand. the perfect square always stay in the outside
like so…
so $\sqrt{75}$ equals $5\sqrt{3}$ in simple form | 74 | 308 | {"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": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2021-21 | latest | en | 0.876892 |
http://filterdom.com/find-out-whos-talking-about-mathematics-of-origami-and-why-you-need-to-be-concerned/ | 1,680,324,672,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949701.0/warc/CC-MAIN-20230401032604-20230401062604-00229.warc.gz | 17,351,053 | 20,652 | ## Mathematics of Origami — the Story
This is apparently an excellent size for modular origami. Reflection A 2×2 matrix is sufficient to symbolize a reflection. If possible, use different kinds of origami paper to modify the appearance of the finished origami and have fun with it! I wished essay help to learn origami but the few times in my personal life which I tried I couldn’t understand the directions. Some would say that this kind of origami is easily the most mathematical one. Discover how to produce easy origami with these basic instructions and diagrams.
Framer’s learning curve depends upon how comfortable you’re with code. The marvels of mathematical origami is easily seen in its application. The perfect way to find out regarding the benefits of origami is to do it yourself! Utilize congruency, trigonometry, and proofs to figure out the surface https://www.thefreedictionary.com/teaching region of your origami creations!
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The effect might be short term or may endure for a life time. But hope continues while there’s possibility for positive shift. The change in direction needs to be taken while it’s still possible.
## Things You Won’t Like About Mathematics of Origami and Things You Will
It’s a lot more effective! Even in the event you do still love her or him, you don’t need to act on it. They love you once you could be happy or sad, as soon as you are angry or frustrated. Please I would like to know what you believe.
## The Dirty Facts on Mathematics of Origami
The few of basic origami folds can be combined in a range of strategies to create intricate designs. If you’d love to do so, please create another heading within this section. Temporary Temples is an internet image library of crop circles, and it’s among the best on the net. Just unfold it and have a look!
Additionally, there are standard named bases that are employed in a diverse range of models, for example the bird base is an intermediate stage in the building of the flapping bird. For example, when you fold the standard waterbomb base, you have produced a crease pattern with eight congruent right triangles. This crease pattern has the secret of the way the paper has the capability to fold in the bird and that secret is math.
This is a task that one needs to do just in your mind. I discovered this surprising since working with their hands and very good visualization skills should be their forte. You should produce the commitment to correct this issue quickly by communicating with each other deeply. Drinking plenty of water will force you to wish to visit the bathroom a whole lot, and that is going to offer you minimal exercise in preventing back muscle strain. If you own a therapist, ask them if there’s a group (for ladies, women’s groups, for men, men’s groups) which you can join. You require professional assistance.
## Mathematics of Origami
Parents may use the worksheets for additional practice of their kids. To fully grasp how digital computers do math, we will need to understand a bit about how they think. It’s best if a dedicated venue is readily available for the complete whole-day or half-day session.
There are a lot of recent very powerful effects in origami mathematics. Where you choose to teach the true lesson plan i.e. math, craft etc is all up to you but it fits many educational locations. The individual who is both a mathematics teacher (or at the very least a teacher who’s comfortable teaching mathematical ideas) and a seasoned folder will find the best use from LMWO.
A beginning geometry student might want to work out the varieties of triangles on the paper. Fractals are a lovely subset of geometry which use numbers and equations to create complex and attractive patterns with infinite heights of complexity. You enter the corner, where it’s always 90 degrees. The Sonobe unit is an easy example unit from modular origami that’s both easy to fold and compatible for constructing a wide variety of models.
## Mathematics of Origami at a Glance
Lily is a good add-on to our loved ones. It’s not true that in the event that you adopt a dog you can’t get a puppy or perhaps a purebred dog. They are very smart, too.
Understand what the fractions are. Know that you won’t always feel this manner. Paper crafts are created from the heavy paper sheets. Washi() is the classic origami paper employed in Japan.
## The Number One Question You Must Ask for Mathematics of Origami
These complicated ideas are presented in a manner that young people are able to understand and start to experiment with. Often in assignments, there’s 1 set answer and one approach to receive there. Obviously, you don’t need to spend 20 on a storage bin and you may not need to.
## Up in Arms About Mathematics of Origami?
If you enjoy these sorts of projects, I want to know in the comments. Unfortunately, a lot of the above-mentioned work is new, and at the right time of this writing there are not many excellent references for this kind of information. We didn’t enjoy the folks, the group was awful, nobody liked us. Curricular connections are supplied for educators.
We’ve been using this program from the start and it has not disappointed. The lessons generally consist of a design for those students to make, together with either one or a string of questions or goals that are linked to the design. Mass-advertising sells this item. A significant advantage of this project is the deficiency of resources necessary. In your class, show a form and ask students to produce a means to make it. | 1,244 | 6,010 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2023-14 | longest | en | 0.944479 |
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# Identifying the Key Changing Conditions of the Earth System (Grades 10-12)
In this unit, students investigate temperature cycles, tree rings, CO2 records, and the effects of CO2 on temperature, precipitation and cloud cover to determine the impacts of changing climate on forests. After gathering and analyzing local data,... (View More)
# SDO Project Suite Module 2: How and Why Do We Study the Sun
This is the second module in the Solar Dynamic Observatory (SDO) Project Suite curriculum. Each activity is self-directed by students or student teams and uses online videos, data from the SDO satellite and hands-on activities to explore, research... (View More)
# SDO Project Suite Module 3: How Does the Sun Affect the Earth?
This is the third module in the Solar Dynamic Observatory (SDO) Project Suite curriculum. Each activity is self-directed by students or student teams and utilizes online videos, data from the SDO satellite and hands-on activities to explore,... (View More)
# Powering the Satellite
In this lesson, learners will first use computers to research and learn how solar panels convert sunlight into electricity. Next, they will calculate the surface area of solar panels board a satellite and their total power generated in various... (View More)
# MRC: Brainstorm and Preliminary Design (Grades 6-8)
Learners will identify, become familiar with and use the Engineering Design Process, use the engineering design process to sketch a reasonable drawing of the rover that will be built, use the steps of the engineering design process to build a Mars... (View More)
Audience: Middle school
# S'COOL Lesson: Clouds - a Multidisciplinary Study
Clouds serve as a theme in a series of linked introductory explorations in math, language arts, and science. After participating in a demonstration of cloud formation, students are directed to create an acrostic poem (a poem that uses the letters in... (View More)
# Finding Other Effects on the Earth
This is an activity about cause and effect. Learners will investigate various online sources to find data and other pertinent information regarding reported effects on Earth for the solar events they identified in the previous activities in this... (View More)
Audience: Elementary school, Middle school, High school
Materials Cost: Free
# IMAGE Satellite 1/4-scale Model
This is an activity about scale model building. Learners will use mathematics to determine the scale model size, construct a pattern, and build a one-fourth size scale model of the IMAGE (Imager for Magnetopause-to-Aurora Global Exploration)... (View More)
1 | 642 | 3,037 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2018-47 | latest | en | 0.848315 |
https://www.physicsforums.com/threads/discharging-capacitor-half-life.472399/ | 1,590,751,527,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347402885.41/warc/CC-MAIN-20200529085930-20200529115930-00026.warc.gz | 857,203,117 | 16,613 | # Discharging capacitor half life
## Main Question or Discussion Point
What is meant by discharging capacitor half life (the description). I seem to be getting different description, I would just like for someone to confirm it here for me please.
Related Other Physics Topics News on Phys.org
uart
If discharged through a resistor the capacitor voltage reduces exponentially via the equation
$$v = V_0 \, e^{-\frac{t}{RC}}$$
Mathematically it's easy to represent an exponential of one base in other other base.
In this case the above exponential can be re-written as
$$v = V_0\, 2^{-\frac{t}{\log(2) \, RC}}$$
where "log" is the natural logarithm.
From the above equation you can see that the "half life" is $RC/\log_e(2)$
Last edited:
Thanks Uart,
I understand that, how would you describe half life (not mathematically or through equations).
If discharged through a resistor the capacitor voltage reduces exponentially via the equation
$$v = V_0 \, e^{-\frac{t}{RC}}$$
Mathematically it's easy to represent an exponential of one base in other other base.
In this case the above exponential can be re-written as
$$v = V_0\, 2^{-\frac{t}{\log(2) \, RC}}$$
where "log" is the natural logarithm.
From the above equation you can see that the "half life" is $RC/\log_e(2)$
uart
Thanks Uart,
I understand that, how would you describe half life (not mathematically or through equations).
Well obviously, it's the time that you have to wait until the voltage is half of it's original value. That's how I'd describe it.
Delta2
Homework Helper
Gold Member
Half life of a quantity is the time it needs so that the quantity is reduced to half of its original value.
In the example of Uart, half life of the voltage is the time it gets for the voltage to reduce to the half of its starting value , that is the time it needs to go from $$V_0$$ to $$\frac{V_0}{2}$$
Thanks.
sophiecentaur
you can see that the "half life" is $RC/\log_e(2)$
Just correcting a typo above. That should of course have been $RC \, \log_e(2)$ | 528 | 2,028 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.671875 | 4 | CC-MAIN-2020-24 | longest | en | 0.926269 |
https://forum.ansys.com/discussion/13999/average-heat-loss-in-regolith-furnace | 1,611,220,668,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703524270.28/warc/CC-MAIN-20210121070324-20210121100324-00284.warc.gz | 336,250,538 | 12,803 | # Average Heat Loss in Regolith Furnace
Member
Hey guys,
I am doing a simulation of a small regolith furnace for a student experiment. The furnace is heated with a heating wire, which is wrapped around a center surface (labeled 2) and at a constant 1300C, just like the entire inside of the furnace with the molten regolith. I have modelled the outside surface of the furnace with a radiation coefficient of 0,9. The outer shell of the furnace (labeled 1) is a steel cylinder, which is coated from the inside to have a radiation coefficient of 0,1. The outside of the cylinder (labeled 3) is cooled with air at about 40C with a thermal convectivity of 10.
The empty space will be filled with a vacuum container or an insulation material, but for now the assumption of empty space is fine.
I am now interested in the heat loss of the system, meaning the average heat flux over the outer surfaces of the cylinder, since this heat loss will determine how much power we will have to put into the heating wires to keep the inside temperature constant.
I am using ansys 16.2 and haven't found a method to calculate this heat loss of the system.
Robin
Btw. in the picture: Strahlung means radiation and the other 2 boundaries should be clear. | 286 | 1,243 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2021-04 | latest | en | 0.938991 |
http://wiki.tcl.tk/330 | 1,534,364,195,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221210304.2/warc/CC-MAIN-20180815200546-20180815220546-00374.warc.gz | 437,623,480 | 3,935 | Updated 2011-05-08 02:08:45 by RLE
# -*- tcl -*-
``` # test = intersection + differences
set max 50
proc testA {a b} {
if {[llength \$a] == 0} {
return [list {} {} \$b]
}
if {[llength \$b] == 0} {
return [list {} \$a {}]
}
set res_is {}
set res_ab {}
set res_ba {}
set a [lsort \$a]
set b [lsort \$b]
while {1} {
# Store lindex/0,1 in var, access later faster ?
set n [string compare [lindex \$a 0] [lindex \$b 0]]
if {\$n == 0} {
# A = B => element in both, add to intersection.
lappend res_is [lindex \$a 0]
set a [lrange \$a 1 end]
set b [lrange \$b 1 end]
} elseif {\$n > 0} {
# A > B, remove B, we are beyond the element.
# This element in B is part of B-A.
lappend res_ba [lindex \$b 0]
set b [lrange \$b 1 end]
} else {
# A < B, remove A, we are beyond the element.
# This element in A is part of A-B.
lappend res_ab [lindex \$a 0]
set a [lrange \$a 1 end]
}
if {[llength \$a] == 0} {
foreach e \$b {
lappend res_ba \$e
}
return [list \$res_is \$res_ab \$res_ba]
}
if {[llength \$b] == 0} {
foreach e \$a {
lappend res_ab \$e
}
return [list \$res_is \$res_ab \$res_ba]
}
}
return [list \$res_is \$res_ab \$res_ba]
}
proc testC {a b} {
if {[llength \$a] == 0} {
return [list {} {} \$b]
}
if {[llength \$b] == 0} {
return [list {} \$a {}]
}
set res_i {}
set res_ab {}
set res_ba {}
foreach e \$b {
set ba(\$e) .
}
foreach e \$a {
set aa(\$e) .
}
foreach e \$a {
if {![info exists ba(\$e)]} {
lappend res_ab \$e
} else {
lappend res_i \$e
}
}
foreach e \$b {
if {![info exists aa(\$e)]} {
lappend res_ba \$e
} else {
lappend res_i \$e
}
}
list \$res_i \$res_ab \$res_ba
}
proc Intersect2 {a b} {
if {[llength \$a] == 0} {
return {}
}
if {[llength \$b] == 0} {
return {}
}
set res {}
if {[llength \$a] < [llength \$b]} {
foreach \$b {.} {break}
foreach e \$a {
if {[info exists \$e]} {
lappend res \$e
}
}
} else {
foreach \$a {.} {break}
foreach e \$b {
if {[info exists \$e]} {
lappend res \$e
}
}
}
return \$res
}
proc diff {a b} {
if {[llength \$a] == 0} {
return {}
}
if {[llength \$b] == 0} {
return \$a
}
set res {}
foreach \$b {.} {break}
foreach e \$a {
if {![info exists \$e]} {
lappend res \$e
}
}
return \$res
}
proc testB {a b} {
list [Intersect2 \$a \$b] [diff \$a \$b] [diff \$b \$a]
}
# IS_NE -> a, b random, unsorted, intersection almost always empty
# IS_EQ -> a = b, random
set fa1 [open "|./2nep IS_A_NE Ar.dat X.dat" w]
set fa2 [open "|./2nep IS_A_EQ Ae0.dat X.dat" w]
set fb1 [open "|./2nep IS_B_NE Br.dat X.dat" w]
set fb2 [open "|./2nep IS_B_EQ Be0.dat X.dat" w]
set fc1 [open "|./2nep IS_C_NE Cr.dat X.dat" w]
set fc2 [open "|./2nep IS_C_EQ Ce0.dat X.dat" w]
set fx [open "|./2nep IS_X X.dat" w]
set a0 {}
set b0 {}
puts stdout " ______________________________" ; flush stdout
puts stdout " ISECT| ......A ......B ......C" ; flush stdout
for {set i 0} {\$i <= \$max} {incr i} {
set ix [format %03d \$i]
puts stderr " * \$ix (a0) = \$a0" ; flush stderr
puts stderr " * \$ix (b0) = \$b0" ; flush stderr
set ra1 [lindex [time {testA \$a0 \$b0} 1000] 0]
set ra2 [lindex [time {testA \$a0 \$a0} 1000] 0]
set rb1 [lindex [time {testB \$a0 \$b0} 1000] 0]
set rb2 [lindex [time {testB \$a0 \$a0} 1000] 0]
set rc1 [lindex [time {testC \$a0 \$b0} 1000] 0]
set rc2 [lindex [time {testC \$a0 \$a0} 1000] 0]
puts stdout " ______________________________" ; flush stdout
puts stdout " \$ix NE [format %7d \$ra1] [format %7d \$rb1] [format %7d \$rc1]"
puts stdout " \$ix EQ [format %7d \$ra2] [format %7d \$rb2] [format %7d \$rc2]"
puts \$fa1 \$ra1
puts \$fa2 \$ra2
puts \$fb1 \$rb1
puts \$fb2 \$rb2
puts \$fc1 \$rc1
puts \$fc2 \$rc2
puts \$fx \$i
lappend a0 [string range [lindex [split [expr {rand()}] .] 1] 0 4]
lappend b0 [string range [lindex [split [expr {rand()}] .] 1] 0 4]
}
puts stderr "----" ; flush stderr
puts stdout " ______________________" ; flush stdout
close \$fa1
close \$fa2
close \$fb1
close \$fb2
close \$fc1
close \$fc2
close \$fx``` | 1,514 | 3,957 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2018-34 | latest | en | 0.242897 |
http://mathhelpforum.com/number-theory/19843-help-university-algebra-problems-print.html | 1,524,300,561,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125945082.84/warc/CC-MAIN-20180421071203-20180421091203-00372.warc.gz | 209,073,207 | 3,172 | # Help with University Algebra Problems
• Oct 1st 2007, 08:44 PM
Joey123
Help with University Algebra Problems
Hello everyone,
Can anyone help me with the problems below, it's very urgent.
1. R is a ring with property that x^2=x for each x in R.
a) Show that each element of R equals its own negative. (Hint: Consider (x+x)^2)
b) Hence show that R is a commutative ring.
2. Find a factorisation of 9+4sqrt(3) into irreducibles, in Z[sqrt(3)]
• Oct 2nd 2007, 08:04 AM
red_dog
Quote:
Originally Posted by Joey123
Hello everyone,
Can anyone help me with the problems below, it's very urgent.
1. R is a ring with property that x^2=x for each x in R.
a) Show that each element of R equals its own negative. (Hint: Consider (x+x)^2)
b) Hence show that R is a commutative ring.
a) We have $\displaystyle (x+x)^2=x+x$
But, $\displaystyle (x+x)^2=(x+x)(x+x)=x^2+x^2+x^2+x^2=x+x+x+x$.
Then, $\displaystyle x+x+x+x=x+x\Rightarrow x+x=0\Rightarrow x=-x$.
b) We have $\displaystyle (x+y)^2=x+y$.
On the other side, $\displaystyle (x+y)^2=(x+y)(x+y)=x^2+xy+yx+y^2=x+xy+yx+y$.
Then $\displaystyle x+xy+yx+y=x+y\Rightarrow xy+yx=0\Rightarrow xy=-yx=-(-yx)=yx$.
• Oct 2nd 2007, 03:23 PM
Joey123
Thank you so much red_dog for helping me with Q1, I finally understand it now.
Q2. Find a factorisation of 9+4squareroot(3) into irreducibles, in Z[squareroot(3)]
Your input will be appreciated, Thank you.
• Oct 2nd 2007, 05:42 PM
ThePerfectHacker
Quote:
Originally Posted by Joey123
Q2. Find a factorisation of 9+4squareroot(3) into irreducibles, in Z[squareroot(3)]
A very bad I see how to procede is to write,
$\displaystyle 9+4\sqrt{3} = (a+b\sqrt{3})(c+d\sqrt{3})$
Thus,
$\displaystyle (ac+3bd)=9$.
Thus,
$\displaystyle (ad+bc)=4$.
And now try to solve for integers. Guessing is the best way it seems. I played around with these for a few minutes but I did not find anything, maybe you do better. | 637 | 1,896 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2018-17 | latest | en | 0.879122 |
https://www.jagranjosh.com/articles/how-to-solve-trigonometry-questions-quickly-in-ssc-examinations-1480071585-1 | 1,653,688,602,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652663006341.98/warc/CC-MAIN-20220527205437-20220527235437-00756.warc.gz | 945,505,924 | 39,177 | # How to solve trigonometry questions quickly in SSC exams?
In this article, prospective syllabus and tips for cracking it are explained. Our SSC team of experts have prepared these strategies after analysing various topics. so, to get familiar with it go through the article.
Updated: Feb 6, 2019 17:01 IST
SSC Trigonometry Tips
SSC Examinations are very popular in India because of the large number of vacancies and the prestige associated with the jobs to be offered through the recruitment exercise. Quantitative Aptitude plays a very vital role in the recruitment exercise and in order to succeed in this exam, you need to be well versed with this section.
Trigonometry questions are very common in this section apart from arithmetic, algebra, geometry and Mensuration. You are going to find at least 5-7 questions in any examination conducted by SSC and having mathematics on this section of quantitative aptitude. In this article, we are going to see how to tackle the trigonometry part of the mathematics section in SSC examinations.
Why analysis of Previous Year Paper is important to crack SSC Exams?
SSC Exams: Syllabus of Trigonometry
In almost all SSC examinations, you are going to find questions on trigonometry from the following chapters and you have to be very well conversant in it to crack these examinations with good enough marks to secure a job in the highly competitive market of government jobs.
Triangles and their properties
This is the basic thing of trigonometry since you are going to find questions on the relation between Sin, Cos and Tan on the basis of triangles and the relation between the various sides of the triangle. In this chapter, you need to understand the basic concepts and relationships between Sin, Cos, Tan, Cosec, Sec and Cot.
The values that matter
The next important thing that matters in SSC is the value of Sin, Cos, Tan etc on the basis of various angles attributed to it. You are going to find questions based on the values of these quantities and unless you know the same, you will have no choice but to leave the question at the examination hall.
Relationship between trigonometric identities
You are certainly going to find questions based on the internal relationship between all these and you need to be very prompt in understanding this since the direct questions will ask from you the relationships between these. You need to be very good in this section to score high marks.
How to crack SSC Reasoning in just 30 days?
Height and Distance Problems
This is like the most favorite problem of SSC as you are certainly going to find at least one question from this chapter in any SSC examination. This is important since you need to understand the situation and draw the same in order to solve the question quickly. Otherwise, you will find it difficult to answer these questions.
SSC Examination: How to master Trigonometry
Once we are done with the syllabus, the next important thing is to know the way you should approach the subject in order to score as much as possible in these examinations. Let us see the ideal approach to be adopted by an average student:
Go through the basics
This is the first and foremost thing to be done by you in order to have a fighting chance to score as much as possible in the examination in this section. First, pick up any good book on the subject and grasp all the basic things about the topic. You need to understand the topics first in order to be able to remember it properly.
Make a mind map or any other way
Trigonometry demands from you a lot of things such as you have to remember a number of formulae, relations, values etc if you want to score much in this section. In order to do this successfully, you need to devise your own strategy to remember things.
Why Trigonometry is in SSC CGL but not in IBPS?
Height and distance should be very important
This is because you are certainly going to find one question based on this and you need to have very good concept on this subject in order to attempt problems based on this subject. So, prepare this chapter properly and attempt the sure shot questions.
Practice is the last word
This is true for almost each and everything under the sun and trigonometry is no different. You need to practice hard in order to understand the basics and values etc and the next thing is to remember them properly at the time of the examination. So, practice as much as possible once you are done and then you will see wonders happening
Trigonometry section is very easy for those who have made efforts to master the same in the preparation days but at the same time, if you are not very good at it, you will have to leave the questions based on trigonometry in your examination. This is going to affect your marks since you have to score as much as possible and leaving questions for lack of preparation is certainly not going to help your cause. So, prepare your heart out and give your best in the examination
How to solve Quantitative Aptitude section in SSC Examinations quickly?
रोमांचक गेम्स खेलें और जीतें एक लाख रुपए तक कैश
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Disclaimer: Comments will be moderated by Jagranjosh editorial team. Comments that are abusive, personal, incendiary or irrelevant will not be published. Please use a genuine email ID and provide your name, to avoid rejection. | 1,121 | 5,395 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2022-21 | latest | en | 0.956697 |
https://uk.mathworks.com/matlabcentral/cody/problems/44299-vector-element-multiplication/solutions/2358763 | 1,603,501,792,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107881551.11/warc/CC-MAIN-20201023234043-20201024024043-00212.warc.gz | 572,245,451 | 17,070 | Cody
# Problem 44299. Vector Element Multiplication
Solution 2358763
Submitted on 24 May 2020 by Karl Ezra Pilario
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
x = [1 2 3 4 5]; y = [1 2 3 4 5]; ele_mult_vec = [1 4 9 16 25]; assert(isequal(your_fcn_name(x,y),ele_mult_vec))
2 Pass
x = ones(1,10); y = ones(1,10); ele_mult_vec = ones(1,10); assert(isequal(your_fcn_name(x,y),ele_mult_vec))
3 Pass
x = ones(1,10); y = 10:10:100; ele_mult_vec = 10:10:100; assert(isequal(your_fcn_name(x,y),ele_mult_vec))
4 Pass
x = 10:10:100; y = 0.1*ones(1,10); ele_mult_vec = 1:10; assert(isequal(your_fcn_name(x,y),ele_mult_vec))
5 Pass
x = 1:3; y = 4:6; ele_mult_vec = [4 10 18]; assert(isequal(your_fcn_name(x,y),ele_mult_vec))
6 Pass
x = mod(1:100,2); y = mod([2:100,1],2); ele_mult_vec = zeros(1,100); assert(isequal(your_fcn_name(x,y),ele_mult_vec))
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Start Hunting! | 395 | 1,106 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2020-45 | latest | en | 0.588424 |
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