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url string | text string | date timestamp[s] | meta dict |
|---|---|---|---|
https://math.stackexchange.com/questions/1290771/what-are-the-possible-eigenvalues-of-a-linear-transformation-t-satifying-t/1290772 | # What are the possible eigenvalues of a linear transformation $T$ satifying $T = T^2$ [duplicate]
This question already has an answer here:
Let $T$ be a linear transformation $T$ such that $T\colon V \to V$. Also, let $T = T^2$. What are the possible eigenvalues of $T$?
I am not sure if the answer is only $1$, or $... | 2019-06-25T16:01:47 | {
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https://physics.stackexchange.com/questions/613268/is-there-a-difference-between-instantaneous-speed-and-the-magnitude-of-instantan | Is there a difference between instantaneous speed and the magnitude of instantaneous velocity?
Consider a particle that moves around the coordinate grid. After $$t$$ seconds, it has the position $$S(t)=(\cos t, \sin t) \quad 0 \leq t \leq \pi/2 \, .$$ The particle traces a quarter arc of length $$\pi/2$$ around the un... | 2021-09-28T19:17:40 | {
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http://archiv.siofok.hu/1nura6/87847a-exterior-angle-of-a-polygon | The only constraint is that, together, they sum to 360 deg. A Polygon is any flat shape with straight sides. Drag vertices to create irregular polygons. In the figure shown above, the measure of the exterior angle at vertex C is equal to the sum of the measures of the remote interior angles at vertices A and B. A trape... | 2021-07-31T11:44:31 | {
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https://math.stackexchange.com/questions/3157055/does-the-cantor-set-have-the-cardinality-of-the-continuum?noredirect=1 | Does the Cantor set have the cardinality of the continuum?
I saw somewhere that there are no sets between $$\mathbb Q$$ and $$\mathbb R$$ in the sense that there are no set $$S\subset \mathbb R$$ s.t. $$|\mathbb Q|<|S|$$ but $$|S|<|\mathbb R|$$, i.e. all set $$S\subset \mathbb R$$ s.t. $$|\mathbb Q|<|S|$$ should have ... | 2019-10-20T19:46:11 | {
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"openwebmath_perplexity": 229.05506416988493,
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... |
http://mathoverflow.net/questions/167685/absolute-value-inequality-for-complex-numbers | # Absolute value inequality for complex numbers
I asked this question on stackexchange, but despite much effort on my part have been unsuccesful in finding a solution.
Does the inequality $$2(|a|+|b|+|c|) \leq |a+b+c|+|a+b-c|+|a+c-b|+|b+c-a|$$ hold for all complex numbers $a,b,c$ ? For real values a case analysis wil... | 2015-01-25T14:29:13 | {
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http://mathhelpforum.com/discrete-math/176778-emptyset-function.html | # Math Help - Is emptyset a function?
1. ## Is emptyset a function?
My discrete book is defining a function, f, as a special type of relationship in which if both $(a,b) \in f$ and $(a,c) \in f$, then $b=c$ (and a relation is defined as a set of ordered pairs).
So, is the empty set not a function because it doesn't ... | 2015-03-30T08:00:55 | {
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https://math.stackexchange.com/questions/987146/why-null-space-and-column-space/987657 | # Why null space and column space?
I am not asking this question for WHAT is null space or WHAT is column space. I have finished learning about the definitions of these two concepts for a while. However, to install these concepts in my mind forever, I really want to know what the purposes are for null space and column... | 2019-05-24T09:19:06 | {
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http://edusteps.net/6zisq/998e1f-circumcircle-and-incircle-of-a-triangle | T where {\displaystyle R} A Usually inside a triangle until , unless it's mentioned. B {\displaystyle h_{a}} {\displaystyle \triangle ABC} = and are the lengths of the sides of the triangle, or equivalently (using the law of sines) by. 172-173). and center Incenter & Incircle Action! = B London: Macmillan, pp. c Trilin... | 2021-07-27T02:04:07 | {
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https://www.physicsforums.com/threads/a-question-on-function-equality.246580/ | # A question on function equality
1. Jul 23, 2008
### zenctheo
Hello to every one!
I have a question that came up when I was talking with a fellow mathematician.
I used to say that two functions are equal when the have the same formula and the same domain and codomain.
We read in a book though that two functions are... | 2017-01-24T05:11:13 | {
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https://web2.0calc.com/questions/difficult-logarithmic-equation-without-a-calculator | +0
Difficult logarithmic equation without a calculator
0
682
9
The following equation needs to be done without the use of a calculator and for the life of me I can't figure out how. If anyone has an idea of how to do it, please let me know. Log bases are in square brackets here.
4^(0.5log[4](9) - 0.25log[2](25))
T... | 2018-09-20T17:24:05 | {
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https://math.boisestate.edu/~calhoun/teaching/matlab-tutorials/lab_19/html/lab_19.html | Back to tutorial index
# Finite precision point arithmetic
## Introduction
We all know that when we use the value of pi in Matlab, or compute cos(3.4), we are not getting the "exact" value of $\pi$ or the cosine function, but rather an approximation. In fact, we don't expect to be able to compute any irrational func... | 2018-07-18T03:12:50 | {
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https://math.stackexchange.com/questions/3117696/if-sec-theta-frac1312-then-find-cos-frac-theta2-where-frac | # If $\sec\theta=-\frac{13}{12}$, then find $\cos{\frac{\theta}{2}}$, where $\frac\pi2<\theta<\pi$. The official answer differs from mine.
Given $$\sec\theta=-\frac{13}{12}$$ find $$\cos{\frac{\theta}{2}}$$, where $$\frac\pi2<\theta<\pi$$.
If the $$\sec\theta$$ is $$-\frac{13}{12}$$ then, the $$\cos \theta$$ is $$-\f... | 2022-05-25T23:28:23 | {
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"url": "https://math.stackexchange.com/questions/3117696/if-sec-theta-frac1312-then-find-cos-frac-theta2-where-frac",
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https://stats.stackexchange.com/questions/173922/probability-density-problem | # Probability density problem
Suppose that the random variable $X$ is uniformly distributed on the interval $[0,1]$ (i.e. $X \sim U(0,1)$) and suppose that $$Z=min(2,2X^2+1)$$
(a) Explain why $Z$ does not have a density function.
(b) Find $\mathbf{E}Z$.
Hint: Use the fact that $\mathbf{E}Z=\int_\mathbf{R}{zdF_Z}$
... | 2019-12-07T21:39:17 | {
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https://gateoverflow.in/2273/gate1997-13 | # GATE1997-13
2.3k views
Let $F$ be the set of one-to-one functions from the set $\{1, 2, \dots, n\}$ to the set $\{1, 2,\dots, m\}$ where $m\geq n\geq1$.
1. How many functions are members of $F$?
2. How many functions $f$ in $F$ satisfy the property $f(i)=1$ for some $i, 1\leq i \leq n$?
3. How many functions $f$... | 2020-08-10T01:35:44 | {
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"lm_q1q2... |
http://qdjf.laquintacolonna.it/area-of-rectangle-under-curve-calculator.html | # Area Of Rectangle Under Curve Calculator
Without performance, you are doing nothing. Approximate the area under the curve and above the x-axis using n rectangles. In single-variable calculus, recall that we approximated the area under the graph of a positive function \ (f\) on an interval \ ( [a,b]\) by adding areas... | 2020-06-04T19:34:36 | {
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https://cs.stackexchange.com/questions/138820/why-are-binary-numbers-sometimes-written-with-one-or-more-leading-zeros-that-don | Why are binary numbers sometimes written with one or more leading zeros that don't change the number (quantity) represented?
Binary numbers like '0110', or '00100101' are seen very often in all contexts. What are the leading (left hand side) zeroes for? Why did the writer not write '110' and '100101', respectively?
L... | 2021-11-30T19:24:56 | {
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"openwebmath_score": 0.8383588194847107,
"openwebmath_perplexity": 762.255461973219,
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https://resellernews.pl/me-life-rgnn/factorial-of-0-8029ee | October 22, 2020 . The answer to this lies in how the solution is implemented. The factorial can be seen as the result of multiplying a sequence of descending natural numbers (such as 3 × 2 × 1). = 4 ⋅ 3 ⋅ 2 ⋅ 1 = 24. For example: The factorial of 5 is 120. If you still prefer writing your own function to get the facto... | 2021-10-16T09:20:51 | {
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"url": "https://resellernews.pl/me-life-rgnn/factorial-of-0-8029ee",
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"openwebmath_perplexity": 569.5891442688228,
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"lm_q1_score": 0.982013793196246,
"lm_q2_score": 0.905989819... |
https://math.stackexchange.com/questions/3845996/the-result-of-int-sin3x-mathrmdx | # The result of $\int{\sin^3x}\,\mathrm{d}x$
$$\int{\sin^3x}\,\mathrm{d}x$$
I find that this integration is ambiguous since I could get the answer with different approaches. Are these answers are valid and true? Could someone tell me why and how? And also, is there any proof stating that these two method I use result... | 2022-06-29T01:49:10 | {
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https://mathematica.stackexchange.com/questions/125025/find-the-5566th-digit-after-the-decimal-point-of-7-101?noredirect=1 | # Find the 5566th digit after the decimal point of 7/101
I want to find the 5566th digit after the decimal point of 7/101. I input the following code into Mathematica 11:
Mod[IntegerPart[7/101*10^5566], 10]
The output is 6, which is the correct answer. Is there a better way to find the answer? Thank you very much i... | 2019-10-23T06:53:56 | {
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"openwebmath_perplexity": 3056.217518285138,
"lm_name": "Qwen/Qwen-72B",
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https://math.stackexchange.com/questions/2622650/a-set-of-integers | A set of integers
Assume that there is a set of ordered integers initially containing number $1$ to a given $n$. At each step, the lowest number in the set is removed, if the number was odd, then we go to the next step and if it was even, half of that number is inserted into the set and the cycle repeats until the set... | 2019-08-18T11:58:47 | {
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"url": "https://math.stackexchange.com/questions/2622650/a-set-of-integers",
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"lm_q1_score": 0.9893474872757474,
"lm_q2_score": ... |
https://math.stackexchange.com/questions/372188/should-the-sign-be-reversed-if-i-square-both-sides-of-an-inequality | # Should the sign be reversed if I square both sides of an inequality?
Let us say I have the following:
$$x>y$$
Now, I want to take the square of both sides. Should it result in $$x^2>y^2$$ or $$x^2<y^2$$
I suspect there is no way to give a general answer to this. I would like to know how to analyze this neverthele... | 2023-04-01T00:49:33 | {
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"openwebmath_perplexity": 200.37867968035658,
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"lm_label": "1. YES\n2. YES",
"l... |
https://parulgupta.org/o6cn73w/metric-prefixes-chart-861112 | unit prefixes (pico to Tera); how to convert metric prefixes using dimensional analysis explained & metric prefix numerical relationships tutorial. Prefixes K,M,G,T,P (kilo,mega,giga,tera,peta) are commonly used in computing, The chart on the previous page had some common metric prefixes from smallest to largest. Bulk ... | 2021-09-19T19:30:00 | {
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"url": "https://parulgupta.org/o6cn73w/metric-prefixes-chart-861112",
"openwebmath_score": 0.6746723651885986,
"openwebmath_perplexity": 4372.869184589697,
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"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9658995733060719,
"lm_q2_score": 0.9207... |
https://math.stackexchange.com/questions/2319655/when-is-a-sudoku-like-table-solvable | When is a Sudoku like table solvable
Given a $n\times n$ table is it possible to fill each cell with one of the numbers $1,2,3,\cdots,n$ such that in each column,each row and each diagonal (i.e Denoting $(x,y)$ as number of column and row $(2,1)$ and $(1,2)$ form the first diagonal) every number appears exactly once? ... | 2021-05-17T11:00:27 | {
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"lm_q1_score": 0.9845754506337406,... |
http://www.lofoya.com/Solved/1322/a-race-course-is-400-m-long-a-and-b-run-a-race-and-a-wins-by | # Easy Time, Speed & Distance Solved QuestionAptitude Discussion
Q. A race course is 400 m long. $A$ and $B$ run a race and $A$ wins by 5m. $B$ and $C$ run over the same course and $B$ win by 4m. $C$ and $D$ run over it and $D$ wins by 16m. If $A$ and $D$ run over it, then who would win and by how much?
✔ A. $D$ by ... | 2017-01-20T09:50:15 | {
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https://math.stackexchange.com/questions/2033830/can-the-area-enclosed-by-two-curves-be-infinite | Can the area enclosed by two curves be infinite?
This is a question from my test: Find the area enclosed by the graph of $y=x^3-6x^2+11x-6$ and $y=0$.
This is actually very simple but the way I look at it, I can see two different answers to this question, depending on the answer to my title.
The first is where I ass... | 2019-12-13T13:34:27 | {
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"lm_q1_score": 0.9830... |
http://yourwebexperts.com/fb2pwm/article.php?31d5b2=a-matrix-with-only-one-column-is-called | The following vector q is a 3 × 1 column vector containing numbers: $q=\begin{bmatrix} 2\\ 5\\ 8\end{bmatrix}$ A row vector is an 1 × c matrix, that is, a matrix with only one row. A column vector is an r × 1 matrix, that is, a matrix with only one column. 2. Column and row vectors a matrix with one column, i.e., size ... | 2021-04-23T03:17:12 | {
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"openwebmath_perplexity": 363.4131443754266,
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"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.987568... |
https://math.stackexchange.com/questions/4131809/difference-between-quotient-rule-and-product-rule | # difference between quotient rule and product rule
Product rule :
$$\frac{d}{dx} \big(f(x)\cdot g(x)\big)=f'(x)\cdot g(x)+f(x)\cdot g' (x)$$
Quotient rule :
$$\frac{d}{dx} \frac{f(x)}{g(x)}=\frac{f'(x)\cdot g(x)-f(x)\cdot g'(x)}{[g(x)]^2}$$
Suppose, the following is given in question. $$y=\frac{2x^3+4x^2+2}{3x^2+... | 2021-10-26T23:36:37 | {
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http://mathhelpforum.com/geometry/190201-problem-finding-area.html | # Math Help - Problem finding area
1. ## Problem finding area
i am having a problem finding the area of the three triangles outside the Pitagoras drawing
you can see what i am meaning in this picture
http://i51.tinypic.com/28gxmyd.jpg
so i need the area of all the triangles in the middle of the squares
2. ## Re: Pro... | 2015-08-28T01:45:25 | {
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"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9905874093008835,
"lm_q2_scor... |
https://www.onlycode.in/pascals-triangle/ | # Pascal’s Triangle
In mathematics, Pascal’s triangle is a triangular array of the binomial coefficients. It can also be viewed as: each number in Pascal’s triangle is the sum of the two numbers directly above it as shown:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
Problem statement
Given an integer n a... | 2022-11-26T15:51:47 | {
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"lm_q1_score": 0.985936370890583,
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"lm_q1q2_... |
https://brilliant.org/discussions/thread/approximating-log_107/ | # Approximating $\log_{10}7$
The Moderators have been talking about methods to approximate logarithms given only a little bit of information; namely, $\log_{10}2\approx0.301$ and $\log_{10}3\approx0.477.$ I'm going to go through a couple methods to provide estimates.
It should be noted that the true value of $\log_{1... | 2020-03-30T23:18:48 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9732407175907055,
"lm_q2_score": 0.91367... |
https://math.stackexchange.com/questions/2429872/a-lily-pad-doubles-in-area-every-second-after-one-minute-it-fills-the-pond-ho/2429893 | # A lily pad doubles in area every second. After one minute, it fills the pond. How long would it take to quarter fill the pond ?
A lily pad doubles in area every second. After one minute, it fills the pond. How long would it take to quarter fill the pond?
To me this seems like we can set up a fraction-like equation:... | 2019-05-19T08:42:16 | {
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"openwebmath_perplexity": 498.64105919092844,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1.... |
https://apimemphis.com/blog/archive.php?id=4ec484-identity-matrix-symbol-latex | L a T e X allows two writing modes for mathematical expressions: the inline mode and the display mode. Pour ajouter un passage à la ligne, ajoutez deux espaces à l'endroit où vous souhaitez que la ligne commence. (Notice that, in the third example, I use the tilde character for a forced space. In this chapter, we wi... | 2022-05-28T11:32:55 | {
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"openwebmath_score": 0.8457075953483582,
"openwebmath_perplexity": 4272.437351296257,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9632305381464927,
"lm_q2... |
https://mathematica.stackexchange.com/questions/78832/log-linear-fitting-of-a-data-e-g-xi-log-yi-and-plotting-the-fit | Log Linear Fitting of a data: e.g. {xi,Log [yi]} and plotting the fit
I have a Log-Linear plot, and i'm unsure about how to fit a line to it. The data represents a I (current) vs V (voltage) curve. The exponential portion of this curve (linear in a Log-Linear plot) is:
data={{0.820667, 0.0123147}, {0.827131, 0.013315... | 2021-12-06T21:28:56 | {
"domain": "stackexchange.com",
"url": "https://mathematica.stackexchange.com/questions/78832/log-linear-fitting-of-a-data-e-g-xi-log-yi-and-plotting-the-fit",
"openwebmath_score": 0.44838935136795044,
"openwebmath_perplexity": 1148.7235940605972,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
... |
https://math.stackexchange.com/questions/913256/the-final-digit-of-fourth-powers | # The final digit of fourth powers
I am working on "Elementary Number Theory" By Underwood Dudley and this is problem 13 in Section 4.
The question is "What can the last digit of a fourth power be?" I got the correct answer but I'm wondering if there is another more elegant way to do it. I'm also wondering if my argu... | 2019-10-15T02:33:19 | {
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"openwebmath_perplexity": 1182.218227273419,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9871787830929849,
"... |
https://stats.stackexchange.com/questions/540290/what-is-the-expected-number-of-marked-fishes-after-7-times | # What is the expected number of marked fishes after 7 times?
Given 10 fishes, each time one fish is chosen randomly, marked and returned to the pool. If a fish is already marked, it constitutes as a turn, and returned the the pool as well.
What is the expected number of marked fishes after 7 times?
Is it:
For each... | 2022-07-06T07:48:31 | {
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"url": "https://stats.stackexchange.com/questions/540290/what-is-the-expected-number-of-marked-fishes-after-7-times",
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"openwebmath_perplexity": 824.4895719356816,
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"lm_label": "1. YES\n2. YES",
"lm_q1_scor... |
https://www.jiskha.com/questions/65902/how-to-do-the-integral-of-ln-x-x-2 | calc
how to do the integral of
(ln(x))/(x^2)
1. 👍
2. 👎
3. 👁
1. Try integration by parts.
Let u = ln x
du = dx/x
dv = 1/x^2 dx
v = -1/x
Integral of lnx/x^2 = Integral of udv
= uv - Integral of vdu
= -(ln x)/x - Integral of -dx/x^2
Take it from there, but check my work also
1. 👍
2. 👎
Similar Questions
1. Calcul... | 2021-02-25T00:03:06 | {
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"url": "https://www.jiskha.com/questions/65902/how-to-do-the-integral-of-ln-x-x-2",
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"lm_q1_score": 0.9811668679067631,
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https://math.stackexchange.com/questions/964624/abstract-algebra-subgroups | # Abstract Algebra : Subgroups
I've been studying about subgroups and I encountered an example with answers and does not have explanation how it is derived and I need help to understand it.
Here is the example:
Example 1.4.20
Determine whether the given subset of the complex numbers is a subgroup of the group $\mat... | 2019-08-22T04:48:09 | {
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"url": "https://math.stackexchange.com/questions/964624/abstract-algebra-subgroups",
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"openwebmath_perplexity": 292.4774185567977,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9811668662546613,
"lm_q2_... |
https://brilliant.org/discussions/thread/1-derivation-of-the-quadratic-formula/ | ×
# 1) Derivation of the quadratic formula
This is note $$1$$ in a set of notes showing how to obtain formulas. There will be no words beyond these short paragraphs as the rest will either consist of images or algebra showing the steps needed to derive the formula mentioned in the title.
Suggestions for other formul... | 2018-02-19T13:46:38 | {
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"url": "https://brilliant.org/discussions/thread/1-derivation-of-the-quadratic-formula/",
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"openwebmath_perplexity": 4455.504473720893,
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"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9918120896142623,
"l... |
http://rnr.rs/eau-de-acpo/e3d36a-what-is-diagonal-in-maths | # what is diagonal in maths
What is the sum of the numbers that are diagonally opposite each other? d1 = long diagonal of kite, d2 = short diagonal of kite, Area = ½ d1d2 . More About Diagonal. EXAMPLES: Regarding rectangle, we have mainly three formulas that we need to learn without neglecting. Diagonal of a Polygon ... | 2021-09-27T01:42:16 | {
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"url": "http://rnr.rs/eau-de-acpo/e3d36a-what-is-diagonal-in-maths",
"openwebmath_score": 0.5840011835098267,
"openwebmath_perplexity": 967.1789921405452,
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"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 0.9715639686018702,
"lm_q2_score": 0.9149009555730... |
https://www.chiaragavuzzi.com/sorrento-rugs-oiatn/618024-big-o-notation | 0 and • Big O is represented using an uppercase Omicron: O(n), O(nlogn), etc. O Big O specifically describes the worst-case scenario, and can be used to describe the execution time required or the space used (e.g. n , read "big Omega". x These individual solutions will often be in the shape of different algorithms or i... | 2021-12-07T09:00:36 | {
"domain": "chiaragavuzzi.com",
"url": "https://www.chiaragavuzzi.com/sorrento-rugs-oiatn/618024-big-o-notation",
"openwebmath_score": 0.8175057768821716,
"openwebmath_perplexity": 812.4109342535271,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9825575173068325,
"lm_q2_sco... |
http://mathhelpforum.com/statistics/81412-balls-problem.html | # Math Help - Balls problem--
1. ## Balls problem--
Hi All,
In a bag there are 10 black balls,8 white balls and 5 Red balls.Three balls are chosen at random and 1 is found to be black. The probability that rest 2 are white is. Find the probability that remaining 2 are white :-
a) 8/23 b) 4/33 c) 10.8.7/23.22.21 d) ... | 2014-07-24T06:52:02 | {
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"url": "http://mathhelpforum.com/statistics/81412-balls-problem.html",
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"openwebmath_perplexity": 759.1571868817398,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9702399026119352,
"lm_q2_score": 0.9161... |
https://math.stackexchange.com/questions/489632/is-every-symmetric-positive-semi-definite-matrix-a-covariance-of-some-multivaria | # Is every symmetric positive semi-definite matrix a covariance of some multivariate distribution?
One can easily prove that every covariance matrix is positive semi-definite. I come across many claims that the converse is also true; that is,
Every symmetric positive semi-definite matrix is a covariance marix of some... | 2021-09-23T17:04:23 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/489632/is-every-symmetric-positive-semi-definite-matrix-a-covariance-of-some-multivaria",
"openwebmath_score": 0.8837236166000366,
"openwebmath_perplexity": 184.71700561185972,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n... |
https://www.intmath.com/forum/matrices-determinants-20/matrices-ever-be-communitative:39 | IntMath Home » Forum home » Matrices and Determinants » matrices ever be communitative?
# matrices ever be communitative? [Solved!]
### My question
Can matrices ever be communitative? If so can you give an example?
Kim
### Relevant page
6. Matrices and Linear Equations
### What I've done so far
I've read the pa... | 2017-08-20T21:12:27 | {
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"openwebmath_perplexity": 1922.0311801113771,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9740426458162398,
... |
http://chodel.gmina.pl/giant-robot-uxcbi/chebyshev-distance-vs-euclidean-ff48ec | # chebyshev distance vs euclidean
In chess, the distance between squares on the chessboard for rooks is measured in Manhattan distance; kings and queens use Chebyshev distance, andbishops use the Manhattan distance (between squares of the same color) on the chessboard rotated 45 degrees, i.e., with its diag... | 2021-02-28T13:25:48 | {
"domain": "gmina.pl",
"url": "http://chodel.gmina.pl/giant-robot-uxcbi/chebyshev-distance-vs-euclidean-ff48ec",
"openwebmath_score": 0.6235116124153137,
"openwebmath_perplexity": 788.1079260040458,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9688561712637256,
"lm_q2_... |
https://byjus.com/question-answer/the-solution-of-displaystyle-sin-8-x-cos-8-x-frac-17-32-is-displaystyle/ | Question
# The solution of $$\displaystyle \sin ^{ 8 }{ x } +\cos ^{ 8 }{ x } =\frac { 17 }{ 32 }$$ is
A
nπ2±π8
B
nπ±π4
C
nπ±π8
D
No solution
Solution
## The correct option is A $$\displaystyle \frac { n\pi }{ 2 } \pm \frac { \pi }{ 8 }$$$$\sin ^{8}(x)+\cos ^{8}(x)$$ $$=(\sin ^{4}x+\cos ^{4}x)^{2}-2\sin ^{4}x\cos ^... | 2022-01-16T10:03:57 | {
"domain": "byjus.com",
"url": "https://byjus.com/question-answer/the-solution-of-displaystyle-sin-8-x-cos-8-x-frac-17-32-is-displaystyle/",
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"openwebmath_perplexity": 12339.379889706051,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.98... |
https://math.stackexchange.com/questions/3313167/eigenvalues-of-ab-vs-eigenvalues-of-ba-incl-infinite-dimensional-case | # Eigenvalues of $AB$ vs eigenvalues of $BA$ (incl. infinite-dimensional case)
I am reading Curtis - Abstract Linear Algebra to pump up my knowledge a little bit and I found exercise I.F.7 (page 41), where I am asked to prove the following:
If $$V$$ is a vector space over a field $$\mathbb{F}$$ and $$A, B \in End(V)$... | 2021-06-21T10:32:14 | {
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"url": "https://math.stackexchange.com/questions/3313167/eigenvalues-of-ab-vs-eigenvalues-of-ba-incl-infinite-dimensional-case",
"openwebmath_score": 0.9291402697563171,
"openwebmath_perplexity": 162.0189481852395,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
... |
http://mathhelpforum.com/algebra/145937-determinant-simplification.html | # Math Help - Determinant simplification
1. ## Determinant simplification
Hi,
Can anyone see a way of getting from A to B?
A
$
\begin{bmatrix}
1 & z & z+1 \\
z+1 & 1 & z \\
z & z+1 & 1
\end{bmatrix}
$
B
$
2*
\begin{bmatrix}
1 & 0 & z \\
z & 1 & 0 \\
0 & z & 1
\end{bmatrix}
$
So far the best I can do is:
$
2*
\be... | 2014-10-23T00:58:43 | {
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"url": "http://mathhelpforum.com/algebra/145937-determinant-simplification.html",
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"lm_q1_score": 0.9793540740815274,
"lm_q2_sco... |
https://math.stackexchange.com/questions/2504652/geometry-triangles | # Geometry, Triangles
In the figure, $BC$ is parallel to $DE$. If area of ∆ $PDE$ is $3/7$ of area of ∆ $ADE$, then what is the ratio of $BC$ and $DE$?
I tried finding ratios of height of ∆ $ABC$, $PDE$ & $BPC$, and trying to figure out some commonality, but it didn't work out.
P.s. it is not my homework.
Ratio is... | 2020-01-21T21:41:29 | {
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"url": "https://math.stackexchange.com/questions/2504652/geometry-triangles",
"openwebmath_score": 0.9005537629127502,
"openwebmath_perplexity": 167.41540816638258,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9929882056560155,
"lm_q2_score"... |
http://carfol.pl/how-to-ykqtk/f91c3e-argument-of-complex-number | 6. Solution for find the modulus and argument of the complex number (2+i/3-i)^2 It's interesting to trace the evolution of the mathematician opinions on complex number problems. The Wolfram Language has fundamental support for both explicit complex numbers and symbolic complex variables. (1) If z is expressed as a comp... | 2021-08-05T07:17:11 | {
"domain": "carfol.pl",
"url": "http://carfol.pl/how-to-ykqtk/f91c3e-argument-of-complex-number",
"openwebmath_score": 0.8969402313232422,
"openwebmath_perplexity": 641.9323531297422,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 0.9835969655605173,
"lm_q2_score": 0.90329... |
https://math.stackexchange.com/questions/1273151/circle-and-heart-homeomorphic | # Circle and heart homeomorphic?
Is a circle and heart homeomorphic to one another?
Intuitively, I can picture that the one can be "morphed" into the other by bending and stretching and not breaking. But I am unsure if that is correct?
This is not an assignment or anything, I am just thinking about it in general.
C... | 2021-04-18T12:03:03 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1273151/circle-and-heart-homeomorphic",
"openwebmath_score": 0.8569528460502625,
"openwebmath_perplexity": 171.67332975702058,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9835969645988575,
"l... |
https://byjus.com/question-answer/the-coefficient-of-x-in-the-expansion-1-x-1-2x-1-3x-cdots-1-3/ | Question
# The coefficient of x in the expansion (1+x)(1+2x)(1+3x)⋯(1+100x) is also equal to
A
1002992+982972+962952++2212
B
The sum of all 101 A.M.'s inserted between 1 and 99
C
The sum of all 100 A.M.'s inserted between 1 and 99
D
The sum of first 20 terms of the series 1+(1+3)+(1+3+5)+(1+3+5+7)+
Solution
## The ... | 2022-01-28T16:10:27 | {
"domain": "byjus.com",
"url": "https://byjus.com/question-answer/the-coefficient-of-x-in-the-expansion-1-x-1-2x-1-3x-cdots-1-3/",
"openwebmath_score": 0.8778674602508545,
"openwebmath_perplexity": 2119.7889790819067,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.985042915163... |
https://mathoverflow.net/questions/143024/does-every-countably-infinite-interval-finite-partial-order-embed-into-the-integ | # Does every countably infinite interval-finite partial order embed into the integers?
A partially ordered set $(S,\le)$ is called interval finite if the open intervals $(x,z):=\{y|x\le y\le z\}$ are finite for all choices of $x,z$ in $S$. An embedding $(S,\le)\rightarrow(S',\le')$ of partially ordered sets is an inje... | 2021-12-08T07:21:42 | {
"domain": "mathoverflow.net",
"url": "https://mathoverflow.net/questions/143024/does-every-countably-infinite-interval-finite-partial-order-embed-into-the-integ",
"openwebmath_score": 0.8956851959228516,
"openwebmath_perplexity": 231.81891055183135,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES"... |
https://arbital.greaterwrong.com/p/5r7?l=5r7 | # 0.999...=1
Although some people find it counterintuitive, the decimal expansions $$0.999\dotsc$$ and $$1$$ represent the same real number.
# Informal proofs
These “proofs” can help give insight, but be careful; a similar technique can “prove” that $$1+2+4+8+\dotsc=-1$$. They work in this case because the series co... | 2022-09-28T20:25:22 | {
"domain": "greaterwrong.com",
"url": "https://arbital.greaterwrong.com/p/5r7?l=5r7",
"openwebmath_score": 0.999969482421875,
"openwebmath_perplexity": 251.01399317045588,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9805806546550657,
"lm_q2_score": 0.9059898102301019,
"... |
https://dsp.stackexchange.com/questions/52892/does-the-fourier-series-coefficient-of-ac-components-remains-same-if-dc-componen | # Does the Fourier series coefficient of AC components remains same if DC component is subtracted form the given signal?
Suppose a signal is defined by $$x(t)= \begin{cases} t & 0\leq t \leq 1 \\ 2-t & 1\leq t\leq 2 \\ \end{cases}$$
Since $$x(t)$$ has even symmetry, I can calculate fourier coefficient as $$a_n = \fra... | 2021-06-19T01:14:14 | {
"domain": "stackexchange.com",
"url": "https://dsp.stackexchange.com/questions/52892/does-the-fourier-series-coefficient-of-ac-components-remains-same-if-dc-componen",
"openwebmath_score": 0.9961004853248596,
"openwebmath_perplexity": 743.008559337098,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. Y... |
https://math.stackexchange.com/questions/3667337/how-to-solve-3-lfloor-x-rfloor-lfloor-x2-rfloor-2-x | How to solve $3\lfloor x \rfloor - \lfloor x^{2} \rfloor = 2\{x\}$?
I am trying to solve the following question involving floor/greatest integer functions.
$$3\lfloor x \rfloor - \lfloor x^{2} \rfloor = 2\{x\}$$ with the notations $$\lfloor x \rfloor$$ denoting the greatest integer less than or equal to $$x$$ and $$\... | 2022-06-28T03:29:43 | {
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"url": "https://math.stackexchange.com/questions/3667337/how-to-solve-3-lfloor-x-rfloor-lfloor-x2-rfloor-2-x",
"openwebmath_score": 0.9364206194877625,
"openwebmath_perplexity": 115.84082149276317,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.... |
https://math.stackexchange.com/questions/1419302/is-the-matrix-a-positive-negative-semi-definite | Is the matrix $A$ positive (negative) (semi-) definite?
Given, $$A = \begin{bmatrix} 2 &-1 & -1\\ -1&2 & -1\\ -1& -1& 2 \end{bmatrix}.$$
I want to see if the matrix $A$ positive (negative) (semi-) definite.
Define the quadratic form as $Q(x)=x'Ax$.
Let $x \in \mathbb{R}^{3}$, with $x \neq 0$.
So, $Q(x)=x'Ax = \beg... | 2019-08-21T00:42:29 | {
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https://math.stackexchange.com/questions/3139209/validity-of-geometric-series-formula-for-r-0 | # Validity of geometric series formula for $r=0$
I can convince myself of the geometric series formula
$$\sum_{n=0}^{\infty} r^n = \frac{1}{1-r}$$
for $$0<|r|<1$$, but not for $$|r|<1$$ because I don't believe the formula for $$r=0$$.
If $$r=0$$, we have
$$\sum_{n=0}^{\infty} r^n = 0^0 + 0^1 + 0^2 + \ldots$$
It i... | 2019-09-21T08:56:57 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9658995... |
https://www.physicsforums.com/threads/rational-inequality.767248/ | # Homework Help: Rational inequality
1. Aug 23, 2014
### mafagafo
1. The problem statement, all variables and given/known data
Find all integer roots that satisfy (3x + 1)/(x - 4) < 1.
3. The attempt at a solution
I would do this:
Make it an equation and find x such that (3x + 1)/(x - 4) = 1.
3x + 1 = x - 4
2x = ... | 2018-07-21T00:40:57 | {
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http://math.stackexchange.com/questions/306425/expected-value-function | # Expected Value Function
My text-book defines expected value as $$E(X) = \mu_x = \sum_{x \in D} ~x \cdot p(x)$$ And so, if I was to find the expected value of a random variable $X$, where $X = 1,2,3$, then it would resemble this: $$E(X)= \sum_{x=1}^3~ x \cdot p(x)= 1\cdot p(1) + 2\cdot p(2) + 3 \cdot p(3)$$ Furthermo... | 2015-03-01T12:31:48 | {
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"url": "http://math.stackexchange.com/questions/306425/expected-value-function",
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"openwebmath_perplexity": 282.1667617092513,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9848109538667758,
"lm_q2_scor... |
https://math.stackexchange.com/questions/2826887/in-how-many-ways-can-integers-a-1a-2a-3a-4-be-chosen-from-the-integers-1-2 | # In how many ways can integers $a_1<a_2<a_3<a_4$ be chosen from the integers $1,2,3,…,26$ such that $5 \le a_i - a_{i-1} \le 7$
In how many ways can $4$ integers $a_1<a_2<a_3<a_4$ be chosen from the integers $1,2,3,...,26$ such that $5 \le a_i - a_{i-1} \le 7$ for all $i = 2,3,4$?
I'm not sure what I'm missing in my... | 2019-09-20T10:10:28 | {
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"openwebmath_perplexity": 138.67493532858055,
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"lm_label": "1. YES\n2. YE... |
https://math.stackexchange.com/questions/1845079/verify-the-meaning-of-the-closure-of-a-set-in-a-finite-non-metric-space | verify the meaning of the closure of a set in a finite/non-metric space.
My motivation behind this question is to better under the fundamental concepts of topology in their general sense.
I understand what a set closure when dealing with real numbers and a euclidean metric. So if the space is $\mathbb{R}$ with euclid... | 2022-01-18T05:59:33 | {
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"openwebmath_score": 0.8761559724807739,
"openwebmath_perplexity": 286.67442385994866,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",... |
https://cs.stackexchange.com/questions/80415/why-is-binary-search-using-this-weird-thing-to-calculate-middle/97738 | # Why is binary search using this weird thing to calculate middle?
I noticed that in many books calculation of midpoint for binary search uses this:
int mid = left + (right - left) / 2;
Why not use
int mid = (left + right) / 2;
• The only "advantage" is that your calculation never exceeds the value of right. Aug... | 2023-03-25T07:45:12 | {
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"url": "https://cs.stackexchange.com/questions/80415/why-is-binary-search-using-this-weird-thing-to-calculate-middle/97738",
"openwebmath_score": 0.5031972527503967,
"openwebmath_perplexity": 1916.0203639991316,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm... |
http://yo-site.biz/isoborneol-vs-pstyrfa/cnmm5i.php?page=0a408b-logarithmic-differentiation-problems | Problems. (3) Solve the resulting equation for y′ . Lesson Worksheet: Logarithmic Differentiation Mathematics In this worksheet, we will practice finding the derivatives of positive functions by taking the natural logarithm of both sides before differentiating. (3x 2 – 4) 7. Using the properties of logarithms will some... | 2021-06-18T03:28:05 | {
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"url": "http://yo-site.biz/isoborneol-vs-pstyrfa/cnmm5i.php?page=0a408b-logarithmic-differentiation-problems",
"openwebmath_score": 0.9247481822967529,
"openwebmath_perplexity": 570.5269978655537,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.971... |
http://www.southernglowtans.com/kids-desk-xefgmli/bccf95-permutation-matrix-inverse | # permutation matrix inverse
The array should contain element from 1 to array_size. Inverse Permutation is a permutation which you will get by inserting position of an element at the position specified by the element value in the array. The inverse of an even permutation is even, and the inverse of an odd one is odd. ... | 2021-05-07T13:44:06 | {
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"url": "http://www.southernglowtans.com/kids-desk-xefgmli/bccf95-permutation-matrix-inverse",
"openwebmath_score": 0.8973594307899475,
"openwebmath_perplexity": 401.4975871929007,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.990874361532886... |
https://math.stackexchange.com/questions/1273112/intuitively-understanding-sum-i-1ni-n1-choose2 | # Intuitively understanding $\sum_{i=1}^ni={n+1\choose2}$
It's straightforward to show that
$$\sum_{i=1}^ni=\frac{n(n+1)}{2}={n+1\choose2}$$
but intuitively, this is hard to grasp. Should I understand this to be coincidence? Why does the sum of the first $n$ natural numbers count the number of ways I can choose a pa... | 2019-11-12T13:27:24 | {
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"url": "https://math.stackexchange.com/questions/1273112/intuitively-understanding-sum-i-1ni-n1-choose2",
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"openwebmath_perplexity": 272.603581655035,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9861513... |
http://math.stackexchange.com/questions/119911/proving-formula-involving-eulers-totient-function | # Proving formula involving Euler's totient function
This question is motivated by lhf's comment here .
"It'd be nice to relate this formula with the natural mapping $U_{mn} \to U_m \times U_n$ by proving that the kernel has size $d$ and the image has index $\varphi(d)$."
I'm trying to prove the formula $$\varphi(mn... | 2016-02-14T06:15:40 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.98308... |
http://openstudy.com/updates/55d713cfe4b02663346b5874 | ## anonymous one year ago I need help to prove that $$\binom{n}{0}^2 + \binom{n}{1}^2 + \cdots + \binom{n}{n}^2 = \binom{2n}{n}.$$ using committee forming...
1. ganeshie8
suppose there are $$n$$ men and $$n$$ women and you want to choose a committee consisting of $$n$$ people
2. anonymous
thats 2n choose n
3. gane... | 2016-10-27T17:13:33 | {
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"lm_q2_score": 0.901920685756612... |
http://hurdman.net/ekli2a6u/776769-what-is-the-cube-root-of-125 | A cube root of a number a is a number x such that x3 = a, in other words, a number x whose cube is a. So, in this case the cube root of 125 is 5. Thus, each edge of the cube is 5 cm long. The length of a side (edge) of a cube is equal to the cube root of the volume. 125 is said to be a perfect cube because 5 x 5 x 5 is... | 2021-02-26T09:29:08 | {
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"openwebmath_perplexity": 354.3765989599167,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9744347905312772,
"lm_q2_score": 0.9111797... |
https://math.stackexchange.com/questions/2513458/setting-of-this-induction-proof?noredirect=1 | # setting of this induction proof [duplicate]
I would like to see if this is a correct induction proof and whether or not this is a good setting out of it
A sequence is defined by $$a_n = a_{n-1} + a_{n-2} + a_{n-3}$$ for $n\geq 3, a_0 = 1, a_1 = 2, a_2 = 4$.
Prove that $a_n \leq 4^n$ for all $n\in\mathbb{N}$.
Let $P... | 2020-12-02T08:44:03 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9828232... |
https://mathhelpboards.com/threads/finding-the-area-bounded-by-the-curve.7787/ | # Finding the Area bounded by the curve
#### shamieh
##### Active member
Find the area bounded by the curve $$\displaystyle x = 16 - y^4$$ and the y axis.
I need someone to check my work.
so I know this is a upside down parabola so I find the two x coordinates which are
$$\displaystyle 16 - y^4 = 0$$
$$\displaysty... | 2020-11-25T07:42:12 | {
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"l... |
https://lectures.quantecon.org/jl/linear_algebra.html | Code should execute sequentially if run in a Jupyter notebook
# Linear Algebra¶
## Overview¶
Linear algebra is one of the most useful branches of applied mathematics for economists to invest in
For example, many applied problems in economics and finance require the solution of a linear system of equations, such as
... | 2018-11-15T08:08:19 | {
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"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9937100989807552,
"lm_q2_score": 0.89330939682... |
https://www.jiskha.com/questions/1733918/a-bag-contains-only-red-and-blue-marbles-yasmine-takes-one-marble-at-random-from-the-bag | Math
A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red marble is 1 in 5. Yasmine returns the marble to the bag and adds five more red marbles to the bag. The probability that she takes one red marble at random is now 1 in 3. How many red marb... | 2021-09-25T05:38:18 | {
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"url": "https://www.jiskha.com/questions/1733918/a-bag-contains-only-red-and-blue-marbles-yasmine-takes-one-marble-at-random-from-the-bag",
"openwebmath_score": 0.8535917401313782,
"openwebmath_perplexity": 430.02246614616513,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES... |
https://s140450.gridserver.com/hrm9dhkd/e5439e-decomposition-of-antisymmetric-tensor | (antisymmetric) spin-0 singlett, while the symmetric part of the tensor corresponds to the (symmetric) spin-1 part. This means that traceless antisymmetric mixed tensor $\hat{T}^{[ij]}_{k}$ is equivalent to a symmetric rank-2 tensor. Since det M= det (âMT) = det (âM) = (â1)d det M, (1) it follows that det M= 0 if... | 2021-05-18T16:43:10 | {
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"url": "https://s140450.gridserver.com/hrm9dhkd/e5439e-decomposition-of-antisymmetric-tensor",
"openwebmath_score": 0.8882725834846497,
"openwebmath_perplexity": 1127.1270849276234,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9902915238050521,
... |
https://www.themathdoctors.org/what-is-a-trapezoid-more-on-inclusive-definitions/ | # What Is a Trapezoid? More on Inclusive Definitions
A month ago, I wrote about classifying shapes, discussing inclusive and exclusive definitions, and variations in different contexts. I promised to return to the subject, moving on to the specific issue of trapezoids, and some other related topics. Now is the time.
... | 2021-07-23T21:13:05 | {
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"openwebmath_perplexity": 622.3495079181878,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9825575129653769,
... |
https://math.stackexchange.com/questions/4205201/why-does-the-n-1-rule-not-work-in-all-cases-of-circular-permutations | # Why does the $(n-1)!$ rule not work in all cases of circular permutations? [duplicate]
$$5$$ Boys and $$5$$ girls sit alternatively around a round table. In how many ways can this be done?
I solved it like this : $$5$$ boys can be arranged in $$(5-1)!$$ ways. After that the $$5$$ girls can be arranged in the gaps i... | 2022-10-05T06:04:35 | {
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"openwebmath_score": 0.5905911922454834,
"openwebmath_perplexity": 212.14852990839736,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
... |
https://math.stackexchange.com/questions/4451310/probability-of-pair-of-gloves-selection | # Probability of pair of gloves selection
In his wardrobe, Fred has a total of ten pairs of gloves. He had to pack his suitcase before a business meeting, and he chooses eight gloves without looking at them. We assume that any set of eight gloves has an equal chance of being chosen.
I am told to calculate the likelih... | 2022-06-26T12:29:19 | {
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"openwebmath_perplexity": 170.38671993740866,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.986979509503... |
https://math.stackexchange.com/questions/1831270/different-ways-of-evaluating-int-0-pi-2-frac-cosx-sinx-cosxdx | Different ways of evaluating $\int_{0}^{\pi/2}\frac{\cos(x)}{\sin(x)+\cos(x)}dx$
My friend showed me this integral (and a neat way he evaluated it) and I am interested in seeing a few ways of evaluating it, especially if they are "often" used tricks.
I can't quite recall his way, but it had something to do with an id... | 2021-10-18T08:42:22 | {
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"url": "https://math.stackexchange.com/questions/1831270/different-ways-of-evaluating-int-0-pi-2-frac-cosx-sinx-cosxdx",
"openwebmath_score": 0.8823049664497375,
"openwebmath_perplexity": 818.8913197919615,
"lm_name": "Qwen/Qwen-72B",
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"lm_q1_s... |
https://math.stackexchange.com/questions/2445462/the-probability-that-a-hits-a-target-is-frac14-and-that-of-b-is-frac13-if/2445467 | # The probability that A hits a target is $\frac14$ and that of B is $\frac13$. If they fire at once and one hits the target, find $P(\text{A hits})$
The probability that A hits a target is 1/4 and the probability that B hits a target 1/3. They each fire once at the target.
If the target is hit by only one of them, w... | 2019-10-17T01:22:44 | {
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"openwebmath_score": 0.9966638088226318,
"openwebmath_perplexity": 459.21869390506856,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES... |
https://mathematica.stackexchange.com/questions/94621/how-to-plot-slices-of-a-surface-of-an-iterative-function-parametrized-by-the-ite | # How to plot slices of a surface of an iterative function parametrized by the iterator k?
I am trying to plot a surface of
$$z=\sin^{(k)}(x),\text{where (k) means nesting the function k times}$$
to visualise the fixed points and their neighbourhood to visually analyse their behaviour.
Currently, the following (ada... | 2020-02-24T12:57:31 | {
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"url": "https://mathematica.stackexchange.com/questions/94621/how-to-plot-slices-of-a-surface-of-an-iterative-function-parametrized-by-the-ite",
"openwebmath_score": 0.22005541622638702,
"openwebmath_perplexity": 2846.4024987592734,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1... |
https://infinityinfoway.com/bruce-venables-dwqvm/794d5a-exponential-function-formula | . There are three kinds of exponential functions: Thus, the exponential function also appears in a variety of contexts within physics, chemistry, engineering, mathematical biology, and economics. In particular, when Population growth can be modeled by an exponential equation. t It is used everywhere, if we talk about t... | 2021-03-02T08:24:46 | {
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"url": "https://infinityinfoway.com/bruce-venables-dwqvm/794d5a-exponential-function-formula",
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"openwebmath_perplexity": 645.2781477594338,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.982287697148445... |
https://nicoguaro.github.io/posts/putnam_prob/ | # Probability that a random tetrahedron over a sphere contains its center
I got interested in this problem watching the YouTube channel 3Blue1Brown, by Grant Sanderson, where he explains a way to tackle the problem that is just … elegant!
I can't emphasize enough how much I like this channel. For example, his approac... | 2022-05-20T04:33:24 | {
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"lm_q1_score": 0.9822877033706601,
"lm_q2_score": 0.9032941995446778,
"lm_q... |
http://mathcentral.uregina.ca/QQ/database/QQ.09.12/h/r.m.1.html | SEARCH HOME
Math Central Quandaries & Queries
Question from r.m, a student: question from calculus exam: what is the figure obtained having eqn.r=10cos(t) in cylindrical coordinates? i know it is a cylinder with center (5,0) ,but can't the equation represent two cylinders, one with center (5,0) and the other with cen... | 2023-02-02T21:13:09 | {
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"openwebmath_perplexity": 162.56082261370122,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9899864293768269,
"lm_q2_score": 0.8962513... |
https://math.stackexchange.com/questions/2776158/is-the-blue-area-greater-than-the-red-area/2776166 | Is the blue area greater than the red area?
Problem:
A vertex of one square is pegged to the centre of an identical square, and the overlapping area is blue. One of the squares is then rotated about the vertex and the resulting overlap is red.
Which area is greater?
Let the area of each large square be exactly $1$ ... | 2019-10-17T12:52:35 | {
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"url": "https://math.stackexchange.com/questions/2776158/is-the-blue-area-greater-than-the-red-area/2776166",
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"openwebmath_perplexity": 527.2969854243514,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.98... |
https://math.stackexchange.com/questions/1969751/is-it-possible-to-cover-a-8-times8-board-with-2-times-1-pieces | # Is it possible to cover a $8 \times8$ board with $2 \times 1$ pieces?
We have a $8\times 8$ board, colored with two colors like a typical chessboard. Now, we remove two squares of different colour. Is it possible to cover the new board with two-color pieces (i.e. domino pieces)?
I think we can, as after the removal... | 2021-10-17T20:12:02 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_... |
https://www.whitman.edu/mathematics/calculus_online/section11.05.html | As we begin to compile a list of convergent and divergent series, new ones can sometimes be analyzed by comparing them to ones that we already understand.
Example 11.5.1 Does $\ds\sum_{n=2}^\infty {1\over n^2\ln n}$ converge?
The obvious first approach, based on what we know, is the integral test. Unfortunately, we c... | 2022-05-18T22:53:15 | {
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"lm_q2_score": 0.89... |
http://mathhelpforum.com/math-topics/39580-finding-sides-giant-wooden-cube-print.html | # Finding sides on giant wooden cube
• May 25th 2008, 01:49 PM
annie3993
Finding sides on giant wooden cube
A giant wooden cube is painted green on all 6 sides and then cut into 125identical, smaller cubes. How many of these smaller cubes are painted on exactly two faces?
i got 72, but I don't think its right...
THA... | 2016-12-04T14:56:03 | {
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https://math.stackexchange.com/questions/2022700/in-how-many-ways-can-the-letters-in-wondering-be-arranged-with-exactly-two-conse | # In how many ways can the letters in WONDERING be arranged with exactly two consecutive vowels
In how many ways can the letters in WONDERING be arranged with exactly two consecutive vowels
I solved and got answer as $90720$. But other sites are giving different answers. Please help to understand which is the right a... | 2020-03-29T10:15:42 | {
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"openwebmath_perplexity": 385.5642050212766,
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https://rstudio-pubs-static.s3.amazonaws.com/572818_27642d4e2cf64ec98cb4d8bf3a7ca1e2.html | ## Problem Set 1
#### Part 1
Show that $$A^TA \neq AA^T$$ in general. (Proof and demonstration.)
Assume $$A^T A = A A^T$$ Consider matrix $$A_{m\times n}$$ where $$m \ne n$$. So $$A^T$$ will be the size of $$n \times m$$. Also $$AA^T$$ will be a matrix of size $$m\times m$$ and $$A^TA$$ will be a matrix of size $$n ... | 2020-06-04T06:15:35 | {
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"openwebmath_perplexity": 3537.9408199576937,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.980580655790071... |
https://mathhelpboards.com/threads/evaluate-the-sum-of-the-reciprocals.8286/ | # Evaluate the sum of the reciprocals
#### anemone
##### MHB POTW Director
Staff member
Given
$p+q+r+s=0$
$pqrs=1$
$p^3+q^3+r^3+s^3=1983$
Evaluate $\dfrac{1}{p}+\dfrac{1}{q}+\dfrac{1}{r}+\dfrac{1}{s}$.
#### mente oscura
##### Well-known member
Given
$p+q+r+s=0$
$pqrs=1$
$p^3+q^3+r^3+s^3=1983$
Evaluate $\dfr... | 2021-01-19T08:03:06 | {
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"url": "https://mathhelpboards.com/threads/evaluate-the-sum-of-the-reciprocals.8286/",
"openwebmath_score": 0.932515025138855,
"openwebmath_perplexity": 6902.302822776169,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9881308817498917,
"lm_q... |
https://discusstest.codechef.com/t/sprnmbrs-editorial/11791 | # SPRNMBRS - Editorial
Author: Kanstantsin Sokal
Tester: Jingbo Shang
Editorialist: Lalit Kundu
Easy-medium
### PREREQUISITES:
number theory, euler totient
### PROBLEM:
\phi(N) is defined as the number of positive integers less than or equal to N that are coprime with N. Let’s call a positive integer N a super nu... | 2021-07-24T17:42:09 | {
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"url": "https://discusstest.codechef.com/t/sprnmbrs-editorial/11791",
"openwebmath_score": 0.7449960112571716,
"openwebmath_perplexity": 1493.2496313921472,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9790357591818725,
"lm_q2_score": 0.905989827... |
http://casinos-mit-paypal.com/downtown-boston-lfc/a5b033-how-to-find-the-period-of-a-wave | wavelength/2 A wave is a shallow water wave if depth < wavelength/20 To figure out whether it's a deep or shallow water wave, you need to find its wavelength. Its frequency equals 21 divided by 3, which is 7 Hz. A wave travelling at the same speed with half the period of the given wave. Periodic Wave Examples. I made t... | 2021-10-22T09:48:57 | {
"domain": "casinos-mit-paypal.com",
"url": "http://casinos-mit-paypal.com/downtown-boston-lfc/a5b033-how-to-find-the-period-of-a-wave",
"openwebmath_score": 0.6891902685165405,
"openwebmath_perplexity": 617.9520816993594,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9585377... |
https://gateoverflow.in/3538/gate-it-2006-question-1 | 5,224 views
In a certain town, the probability that it will rain in the afternoon is known to be $0.6$. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to $25°C$, the probability that it will rain in the afternoon is $0.4$. The temperature at noon is equally likely to be a... | 2023-02-05T14:46:36 | {
"domain": "gateoverflow.in",
"url": "https://gateoverflow.in/3538/gate-it-2006-question-1",
"openwebmath_score": 0.7255260348320007,
"openwebmath_perplexity": 1981.7403981863722,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9927672349125561,
"lm_q2_score": 0.8933093989533... |
https://mathhelpboards.com/threads/combination-problem.2923/ | # Combination Problem
#### schinb65
##### New member
Thirty items are arranged in a 6-by-5 array. Calculate the number of ways to form a set of three distinct items such that no two of the selected items are in the same row or same column.
I am told the answer is 1200.
I do not believe that I am able to use the sta... | 2021-07-24T21:17:09 | {
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"url": "https://mathhelpboards.com/threads/combination-problem.2923/",
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"openwebmath_perplexity": 397.8135993777976,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9802808695883038,
"lm_q2_score": 0.904... |
https://math.stackexchange.com/questions/970719/question-about-complete-metric-on-manifolds/3337838 | # Question about complete metric on manifolds
I've recently been wondering about whether non-complete metrics on manifolds can be transformed into complete metrics on manifolds and whether all manifolds have complete metrics. After some googling I came across this link and the first comment says that any metric is act... | 2022-06-25T20:12:23 | {
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"openwebmath_perplexity": 130.59506968950893,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.99... |
https://math.stackexchange.com/questions/1385989/has-anyone-heard-of-this-maths-formula-and-where-can-i-find-the-proof-to-check-m/1385998 | # Has anyone heard of this maths formula and where can I find the proof to check my proof is correct? $\sum^n_{i = 1}i + \sum^{n-1}_{i=1}i = n^2$
The formula basically is:
The sum of all integers before and including $n$, plus all the integers up to and including $n-1$.
This will find $n^2$.
$$\sum^n_{i = 1}i + \su... | 2021-12-04T19:37:33 | {
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"openwebmath_score": 0.9676469564437866,
"openwebmath_perplexity": 857.6873540672635,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "... |
https://math.stackexchange.com/questions/2154537/is-there-a-pattern-to-expression-for-the-nested-sums-of-the-first-n-terms-of-a?noredirect=1 | # Is there a pattern to expression for the nested sums of the first $n$ terms of an expression? [duplicate]
Apologies for the confusing title but I couldn't think of a better way to phrase it. What I'm talking about is this:
$$\sum_{i=1}^n \;i = \frac{1}{2}n \left(n+1\right)$$ $$\sum_{i=1}^n \; \frac{1}{2}i\left(i+1\... | 2019-10-22T10:54:51 | {
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"url": "https://math.stackexchange.com/questions/2154537/is-there-a-pattern-to-expression-for-the-nested-sums-of-the-first-n-terms-of-a?noredirect=1",
"openwebmath_score": 0.8492360711097717,
"openwebmath_perplexity": 160.51146579699576,
"lm_name": "Qwen/Qwen-72B",
"lm_label... |
http://mathhelpforum.com/algebra/25343-inequality-set-real-numbers.html | # Math Help - inequality on the set of real numbers
1. ## inequality on the set of real numbers
Solve the following inequality on the set of real numbers
$x^2-3\sqrt{x^2+3}\leq1$
2. Originally Posted by perash
Solve the following inequality on the set of real numbers
$x^2-3\sqrt{x^2+3}\leq1$
$x^2-3\sqrt{x^2+3}\leq... | 2016-06-24T20:37:41 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9877587250685455,
"lm_q2_scor... |
https://math.stackexchange.com/questions/853000/what-is-the-truth-table-for-demorgans-law | # What is the truth table for demorgan's law?
From Demorgan's law:
$(A \cup B)^c = A^c \cap B^c$
I constructed the truth table as follows:
$$\begin{array}{cccccc|cc} x\in A & x \in B & x \notin A & x \notin B & x \in A^c & x \in B^c & x\notin A \text{ or } x \notin B & x \in A^c \text{ and } x \in B^c & \\ \hline T... | 2019-10-14T11:39:25 | {
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"url": "https://math.stackexchange.com/questions/853000/what-is-the-truth-table-for-demorgans-law",
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"openwebmath_perplexity": 414.3442369745594,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.978712647585... |
https://www.freemathhelp.com/forum/threads/find-the-numbers.115989/ | Find the Numbers
Status
Not open for further replies.
Full Member
There are two numbers whose sum is 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers?
Set up:
Let x = large number
Let y = small number
x + y = 53...Equation A
3y = x + 19....Equation B
x + y = 53
... | 2019-08-24T11:54:03 | {
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"lm_q1_score": 0.9861513889704252,
"lm_q2_score":... |
http://mathhelpforum.com/number-theory/124509-help-proof-print.html | Help with a proof.
• Jan 19th 2010, 07:26 PM
seven.j
Help with a proof.
Hi, I'm stuck at proving the following question...
Prove that for all n>0,
1/2 + 2/2^2 + 3/2^3 + ... + n/2^n = 2 - (n+2)/2^n
I've tried all sorts of different ways of solving this, but to no avail.
Any help is appreciated :)
• Jan 19th 2010, 0... | 2016-10-25T21:04:18 | {
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"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9875683473173829,
"lm_q2_sco... |
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