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url string | text string | date timestamp[s] | meta dict |
|---|---|---|---|
https://math.stackexchange.com/questions/1904493/fx-lfloor-x-rfloor-left-x-right-increasing-decreasing-even | # $f(x) = \lfloor x \rfloor - \left\{ x \right\}:$ Increasing, Decreasing, Even , Odd, And/Or Invertible?
Define $\{x\} = x-\lfloor x \rfloor$. That is to say, $\{x\}$ is the "fractional part" of $x$. If you were to expand the number $x$ as a decimal, $\{x\}$ is the stuff after the decimal point. For example $\left\{\... | 2019-07-18T23:57:18 | {
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https://mathhelpboards.com/threads/finding-composition-series-of-groups.2483/ | # Finding Composition Series of Groups
#### Poirot
##### Banned
My sum total of knowledge of composition series is: the definition, the jordan holder theorem and the fact that the product of the indices must equal the order of the group.
With this in mind, can someone help with me with finding a composition series fo... | 2021-07-28T05:17:52 | {
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https://math.stackexchange.com/questions/2879619/what-is-the-cdf-for-a-partially-non-continuous-pdf | # What is the cdf for a partially non-continuous pdf?
Suppose there is a pdf/pmf (?!) which places an atom of size 0.5 on x = 0 and randomizes uniformly with probability 0.5 over the interval [0.5,1].
Such that...
$$f(x)= \begin{cases} 0.5, & \text{if}\ x=0 \\ {1\over (1-0.5)}, & \text{if}\ 0.5 ≤ x ≤ 1 \\ 0, & \text... | 2019-07-23T18:09:22 | {
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"lm_q1_score": 0.98... |
https://math.stackexchange.com/questions/3064391/simplify-sqrt4-frac162x616x4-is-frac3-sqrt42x22 | # Simplify $\sqrt[4]{\frac{162x^6}{16x^4}}$ is $\frac{3\sqrt[4]{2x^2}}{2}$
(I've been posting a lot today and yesterday, not sure if too many posts are frowned upon or not. I am studying and making sincere efforts to solve on my own and only post here as a last resort)
I'm asked to simplify $$\sqrt[4]{\frac{162x^6}{1... | 2021-09-21T15:03:23 | {
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"lm_q1_score": 0.9766... |
https://brilliant.org/discussions/thread/binomial-coefficients-2/ | ×
# Binomial coefficients
$$\text{Binomial coefficients} { n\choose k}, n,k \in \mathbb{N}_0, k \leq n, \text{are defined as}$$
${n \choose i}=\frac{n!}{i!(n-i)!}$.
$\text{They satisfy}{n \choose i}+{n \choose i-1}={n+1 \choose i} \text{ for } i > 0$
$\text{and also} {n \choose 0}+{n\choose 1}+\cdots+{n \choose n}... | 2017-10-17T13:31:04 | {
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"lm_q2_score": 0... |
https://crank.com.br/pages/674a61-how-to-find-irrational-numbers | 1$Find two irrational numbers between two given rational numbers. The ellipsis $(\dots)$ means that this number does not stop. $\sqrt{36}$ The comment about$2^x$still holds for$\sqrt{2}$, but if you were using a larger irrational number you might have to pick a bigger base than$2$. Solution: The numbers you would have ... | 2021-05-08T21:51:09 | {
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"lm_q2_score": 0.8933094096... |
http://math.stackexchange.com/questions/23780/how-does-divisibility-test-using-congruence-work | # How does divisibility test using congruence work?
In the book, it said:
Let $n = a_{k}10^{k} + a_{k-1}10^{k-1} + a_{k-2}10^{k-2} + ... + a_110 + a_0$
Then, because $10 \equiv 0 \pmod{2}$ it follows that $10^j \equiv 0 \pmod{2^j}$
What congruence property did they use in this case? Is that:
If $a \equiv b \pmod{k_1... | 2014-08-01T16:15:27 | {
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https://math.stackexchange.com/questions/4258502/what-is-the-value-of-the-measure-of-the-segment-mn | What is the value of the measure of the segment $MN$?
In an ABC triangle. plot the height AH, then $$HM \perp AB$$ and $$HN \perp AC$$. Calculate $$MN$$. if the perimeter of the pedal triangle (DEH) of the triangle ABC is 26 (Answer:13)
My progress: I made the drawing and I believe that the solution must lie in the p... | 2021-10-25T16:04:25 | {
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https://math.stackexchange.com/questions/2849740/converting-english-to-quantifiers-there-is-no-greatest-prime | # Converting English to Quantifiers: 'There is no greatest prime'
I'm working on an exercise that appears rather simple, but the answer I keep coming up with differs from what the instructor found.
Say I want to convert the sentence 'there is no greatest prime' to quantifier notation, and I'm to work with two english... | 2021-12-01T06:24:22 | {
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"lm_q1_scor... |
https://www.eliterugservices.com/css/unchain-blockchain-geaajfz/archive.php?c53898=how-to-find-radius-from-area | # how to find radius from area
Dimensions of a circle: O - origin, R - radius, D - diameter, C - circumference ( Wikimedia) Area, on the other hand, is all the space contained inside the circle. The diameter is always double the radius. … The radius is half the diameter, so the radius is 5 feet, or r = 5. When we conn... | 2022-10-04T13:58:40 | {
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https://math.stackexchange.com/questions/3797892/if-a-power-series-is-known-to-converge-at-a-point-what-can-we-conclude | # If a Power Series is known to converge at a point, what can we conclude?
If it is known that the series $$\sum_{n=1}^{\infty} a_nx^n$$ is convergent at $$x=4$$. What can we conclude about the series $$\sum_{n=1}^{\infty} a_n(-7)^n$$?
A. Convergent
B. Conditionally Convergent
C. Conditionally Convergent
D. Divergent... | 2023-03-22T05:30:58 | {
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... |
https://math.stackexchange.com/questions/2153769/understanding-a-probability-question-about-order | # Understanding a probability question about order?
A couple is planning to have 3 children. Assuming that having a boy and having a girl are equally likely, and that the gender of one child has no influence on (or, is independent of) the gender of another, what is the probability that the couple will have exactly 2 g... | 2022-05-25T09:24:21 | {
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"lm_q1_score": 0.9825... |
http://mathhelpforum.com/calculus/141578-optimization-help.html | 1. ## Optimization Help!
The problem says...
The trough in the figure is to be made to the dimension shown. Only the angle delta can be varied. What value of delta will maximize the trough's volume. (I attached a picture)
Can someone please show me and explain to me how I would do a problem like this!
2. Originally... | 2017-11-22T10:08:17 | {
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http://math.stackexchange.com/questions/59929/how-to-find-inverse-of-a-composite-function?answertab=oldest | # How to find inverse of a composite function?
I am stuck with this question,
Let $A=B=C=\mathbb{R}$ and consider the functions $f\colon A\to B$ and $g\colon B\to C$ defined by $f(a)=2a+1$, $g(b)=b/3$. Verify Theorem 3(b): $(g\circ f)^{-1}=f^{-1}\circ g^{-1}.$
I have calculated $f^{-1}$, $g^{-1}$, and their composit... | 2016-02-07T17:46:58 | {
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"url": "http://math.stackexchange.com/questions/59929/how-to-find-inverse-of-a-composite-function?answertab=oldest",
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"lm_q1_score":... |
https://math.stackexchange.com/questions/1693923/solving-modulus-inequality-x-1-x-6-le11-geometrically | Solving modulus inequality $|x - 1| + |x - 6|\le11$ geometrically
Find all possible values of $x$ for which $x$ for which the inequality $$|x - 1| + |x - 6|\le11$$ is true.
I know this can be easily solved by taking $3$ cases for$x$ and then taking the intersection of those $3$ cases. The solution will be $-2\ge x\le... | 2022-05-18T05:58:31 | {
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"url": "https://math.stackexchange.com/questions/1693923/solving-modulus-inequality-x-1-x-6-le11-geometrically",
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"openwebmath_perplexity": 335.04382080720796,
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"lm_q1_score": ... |
http://languageoption.com/layla-hassan-esdq/page.php?page=f51332-a-correlation-coefficient-is-a-numerical-measure-of-the | A correlation coefficient is a numerical measure of the. If the correlation between two variables is close to 0.01, then there is a very weak linear relation between them. Therefore, correlations are typically written with two key numbers: r = and p =. We will: give a definition of the correlation $$r$$, discuss the ca... | 2021-09-21T11:36:25 | {
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"url": "http://languageoption.com/layla-hassan-esdq/page.php?page=f51332-a-correlation-coefficient-is-a-numerical-measure-of-the",
"openwebmath_score": 0.771691620349884,
"openwebmath_perplexity": 474.46650475997916,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n... |
http://mathhelpforum.com/math-puzzles/207164-how-many-numbers-less-than-equal-n-all-digits-unique.html | # Math Help - how many numbers less than or equal to N with all digits unique
1. ## how many numbers less than or equal to N with all digits unique
Hi all
I am not sure whether this would count as a puzzle but it has puzzled me. I am really bad at combinatorics and need some help. I have stumbled on to the problem w... | 2014-07-28T09:15:46 | {
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"lm_q1_score"... |
https://math.stackexchange.com/questions/1782087/almost-everywhere-vs-almost-sure/1782114 | # almost everywhere Vs. almost sure
I'm reading a book about measure theory and probability (first chapter of Durret's Probability book), and it's starting to switch between the terms "a.e." and "a.s." in different contexts. I'm becoming confused about their meanings. What's the difference between almost everywhere an... | 2022-06-25T02:24:13 | {
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"lm_q1_score": 0.96538115817... |
https://math.stackexchange.com/questions/2702057/proof-of-sum-formula-no-induction | # Proof of sum formula, no induction
$$\sum_{k=1}^n k=\frac{n(n+1)}2$$
So I was trying to prove this sum formula without induction. I got some tips from my textbook and got this.
Let $S=1+2+\cdots+n-1+n$ be the sum of integers and $S=n+(n+1)+\cdots+2+1$ written backwards. If I add these $2$ equations I get $2S=(1+n)... | 2019-06-25T04:28:00 | {
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"lm_q1_score": 0.9920620070720564,
... |
https://www.hpmuseum.org/forum/thread-361.html | Accuracy of HP Financial Calculators - Canadian mortgage
01-08-2014, 03:20 AM (This post was last modified: 01-08-2014 11:39 AM by Jeff_Kearns.)
Post: #1
Jeff_Kearns Member Posts: 147 Joined: Dec 2013
Accuracy of HP Financial Calculators - Canadian mortgage
Having recently adapted an 'accurate' (relative term) TVM rou... | 2020-07-11T14:22:47 | {
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"lm_q1_score": 0.9822876992225169,
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"lm_... |
https://www.physicsforums.com/threads/trig-substitution-with-cosine.854743/ | # Trig Substitution with Cosine
Tags:
1. Jan 30, 2016
### UMath1
I was wondering if you could do a trig substitution with cosine instead of sine. All the textbooks I have referred to use a sine substitution and leave no mention as to why cosine substitution was not used. It seemed that it should work just the same, ... | 2018-01-24T06:40:06 | {
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https://math.stackexchange.com/questions/3445884/solve-2-cos2-x-sin-x-1-for-all-possible-x | # Solve $2 \cos^2 x+ \sin x=1$ for all possible $x$
$$2\cos^2 x+\sin x=1$$
$$\Rightarrow 2(1-\sin^2 x)+\sin x=1$$
$$\Rightarrow 2-2 \sin^2 x+\sin x=1$$
$$\Rightarrow 0=2 \sin^2 x- \sin x-1$$
And so:
$$0 = (2 \sin x+1)(\sin x-1)$$
So we have to find the solutions of each of these factors separately:
$$2 \sin x+1... | 2021-10-25T23:43:05 | {
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"lm_q1_score": 0.977713814460... |
https://coursys.sfu.ca/2018fa-cmpt-383-d1/pages/Exercise8 | # Exercise 8
## Getting Started With Go
You're going to need to get Go code running. Download/install Go tools: a command-line compiler, or IDE, or whatever you like. Start by getting a “hello world” running. (There's one in the lecture slides.)
Download and extract the code skeleton for this exercise. The code incl... | 2018-12-12T21:30:50 | {
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"lm_q1_score": 0.9579122768904644,
"lm_q2_score": 0.92192183378243... |
https://math.stackexchange.com/questions/3550450/which-of-these-answers-is-the-correct-indefinite-integral-using-trig-substitut | # Which of these answers is the correct indefinite integral? (Using trig-substitution or $u$-substitution give different answers)
Answers obtained from two online integral calculators:
\begin{align}\int\dfrac{\sqrt{1 + x}}{\sqrt{1 - x}}\,\mathrm dx &= -\sqrt{\dfrac{x + 1}{1 - x}} + \sqrt{\dfrac{x + 1}{1 - x}}x - 2\ar... | 2021-03-06T12:34:04 | {
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"openwebmath_perplexity": 492.6315629554467,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2.... |
https://math.stackexchange.com/questions/1506759/solve-in-integers-the-equation-2x3y-5/1506772 | Solve in integers the equation $2x+3y = 5$
If I have the following equation $$2x+3y = 5$$ I know all the integer solutions is $$x = 1+3n$$ $$y = 1-2n$$ $$n \in \Bbb Z$$ since I can just plug them in $$2(1+3n)+3(1-2n) = 5+6n-6n = 5$$
but I don't know how to derive the answer from the equation... also is there a name f... | 2019-07-20T11:39:07 | {
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"lm_q1_score": 0.9805806... |
https://etec-radioetv.com.br/tags/j93v1ui.php?page=subsets-of-a-set-06a588 | Problem description . In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set. b) List all the distinct subsets for the set {S,L,E,D}. c) How many of the distinct subsets are proper subsets? A subset that is smaller than t... | 2021-01-20T18:52:15 | {
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"url": "https://etec-radioetv.com.br/tags/j93v1ui.php?page=subsets-of-a-set-06a588",
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"openwebmath_perplexity": 565.9167675346129,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9884918516137419,
"lm_q2_score": 0.8... |
http://math.stackexchange.com/questions/92306/partitions-in-which-no-part-is-a-square?answertab=votes | # Partitions in which no part is a square?
I asked a similar question earlier about partitions, and have a suspicion about another way to count partitions.
Is it true that the number of partitions of $n$ in which each part $d$ is repeated fewer than $d$ times is equal to the number of partitions of $n$ where no part ... | 2014-10-20T22:05:32 | {
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"lm_q1_score": 0.... |
https://math.stackexchange.com/questions/1527968/can-the-roots-of-the-derivative-of-the-polynomial-in-complex-variable-be-as-clos | Can the roots of the derivative of the polynomial in complex variable be as close as we want them to be from the roots of the polynomial itself?
The (probably) famous Gauss-Lucas theorem states that the roots of the derivative $P'(z)$ are contained in the convex hull of the roots of $P(z)$, where $P(z)$ is complex var... | 2021-02-27T19:47:23 | {
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"lm_label": "1. Yes\... |
https://new.procespartner.sk/data/styrene-resin-kwai/article.php?id=0593ed-side-of-rhombus-formula | Diagonals divide a rhombus into four absolutely identical right-angled triangles. The area of the rhombus can be found, also knowing its diagonal. There are many ways to calculate its area such as using diagonals, using base and height, using trigonometry, using side and diagonal. Basic formulas of a rhombus. Then we o... | 2021-05-15T17:13:42 | {
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"openwebmath_perplexity": 423.7974277608552,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9835... |
https://math.stackexchange.com/questions/4059113/time-speed-and-distance-trains-partial-distance | # Time, Speed and Distance : Trains Partial Distance
Two trains $$A$$ and $$B$$ start from station $$X$$ and $$Y$$ towards each other. $$B$$ leaves station $$Y$$ half an hour after train $$A$$ leaves station $$X$$. Two hours after train $$A$$ has started, the distance between train $$A$$ and train $$B$$ is $$\frac{19}... | 2022-01-26T01:00:55 | {
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"openwebmath_perplexity": 478.21906221195735,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9835... |
http://mathhelpforum.com/statistics/181908-am-i-more-likely-roll-least-one-six-if-i-have-more-dice.html | # Thread: Am I more likely to roll at least one six if I have more dice?
1. ## Am I more likely to roll at least one six if I have more dice?
Hi,
I've had a debate with some friends, about whether I'm more likely to roll at least a single 6 when I have 1000 dice, than I am to roll one with only 1 dice.
I say, the m... | 2018-05-25T02:17:15 | {
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"url": "http://mathhelpforum.com/statistics/181908-am-i-more-likely-roll-least-one-six-if-i-have-more-dice.html",
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"openwebmath_perplexity": 399.29025243412707,
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"lm_q1_score":... |
https://math.stackexchange.com/questions/27719/what-is-gcd0-a-where-a-is-a-positive-integer | # What is $\gcd(0,a)$, where $a$ is a positive integer?
I have tried $\gcd(0,8)$ in a lot of online gcd (or hcf) calculators, but some say $\gcd(0,8)=0$, some other gives $\gcd(0,8)=8$ and some others give $\gcd(0,8)=1$. So really which one of these is correct and why there are different conventions?
• I haven't enco... | 2021-12-01T07:29:30 | {
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"lm_q1_score": 0.9759464527... |
https://math.stackexchange.com/questions/1624236/finding-eigenvectors-of-a-3x3-matrix-7-12-15/1624242 | # Finding Eigenvectors of a 3x3 Matrix (7.12-15)
Please check my work in finding an eigenbasis (eigenvectors) for the following problem. Some of my solutions do not match answers in my differential equations text (Advanced Engineering Mathematics by Erwin Kreyszig, 1988, John Wiley & Sons).
For reference the followin... | 2021-06-21T15:46:59 | {
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"url": "https://math.stackexchange.com/questions/1624236/finding-eigenvectors-of-a-3x3-matrix-7-12-15/1624242",
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"openwebmath_perplexity": 247.0337446583284,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.... |
http://gusx.lampertifashion.it/application-of-laplace-transform-pdf.html | 5 Other transforms. As we saw in the last section computing Laplace transforms directly can be fairly complicated. a signal such that $$x(t)=0$$ for $$x<0$$. Schiff and others published The Laplace Transform: Theory and Applications | Find, read and cite all the research you need on ResearchGate. With the increasing co... | 2020-07-15T11:33:21 | {
"domain": "lampertifashion.it",
"url": "http://gusx.lampertifashion.it/application-of-laplace-transform-pdf.html",
"openwebmath_score": 0.8233507871627808,
"openwebmath_perplexity": 1052.2003106046586,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9883127406273589,
"lm_q2_... |
https://math.stackexchange.com/questions/2291594/a-summation-question-is-s-to-ln-2 | # A summation question ,Is $S \to \ln 2$?
I am in doubt with this question .
let $S=\dfrac{\dfrac12}{1} +\dfrac{(\dfrac12)^2}{2}+\dfrac{(\dfrac12)^3}{3}+\dfrac{(\dfrac12)^4}{4}+\dfrac{(\dfrac12)^5}{5}+...$ Is it converge to $\ln 2$ ?
I tried this $$x=\dfrac12 \to 1+x+x^2+x^3+x^4+...\sim\dfrac{1}{1-x}\to 2$$ by integ... | 2019-09-21T15:59:08 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2291594/a-summation-question-is-s-to-ln-2",
"openwebmath_score": 0.9986375570297241,
"openwebmath_perplexity": 586.628353951528,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9850429116504951,
... |
https://scicomp.stackexchange.com/questions/21867/second-order-derivative-condition-for-convexity/21872 | Second-order derivative condition for convexity
It is written in a book I'm reading that $$\nabla f(x) = \left( \frac{\partial f(x)}{\partial x_1}, \frac{\partial f(x)}{\partial x_2},...,\frac{\partial f(x)}{\partial x_n}\right)$$ and $$\nabla^2 f(x)_{ij} = \frac{\partial^2 f(x)}{\partial x_i ~\partial x_j}, \qquad \f... | 2019-07-18T02:06:15 | {
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"url": "https://scicomp.stackexchange.com/questions/21867/second-order-derivative-condition-for-convexity/21872",
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"openwebmath_perplexity": 387.8944708476335,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": ... |
http://mathhelpforum.com/pre-calculus/62653-negative-exponents.html | Math Help - Negative exponents
1. Negative exponents
Hey guys.
I know that x^-2 is equal to 1/x^2
But, this problem looks like this. It asks me to simplify this (AKA get rid of the negative exponents):
((x^-1)+(y^-1))/((x^-2)-(y^-2))
For some reason I don't think I can just flip the problem around to make it look... | 2015-07-08T01:55:01 | {
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"lm_q1_score": 0.9688561721629776,
"lm_q2_score":... |
https://math.stackexchange.com/questions/1653388/how-many-ways-we-can-choose-items-from-different-boxes | # How many ways we can choose items from different boxes
I searched through the internet but couldn't find my answer, which can either be a very simple or a hard one.
Assume there are $3$ boxes, which carry, respectively, $1$, $4$, $2$ items. My question is how many ways we can select $3$ items from these boxes. I am... | 2019-08-23T11:10:13 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1653388/how-many-ways-we-can-choose-items-from-different-boxes",
"openwebmath_score": 0.843021035194397,
"openwebmath_perplexity": 201.91208405524122,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": ... |
https://math.stackexchange.com/questions/3401393/are-there-a-finite-number-of-trees-with-k-leaves-and-no-vertices-of-degree-2/3401420 | # Are there a finite number of trees with $k$ leaves and no vertices of degree $2$?
Given a fixed positive integer $$k$$. Show that there are only finitely many trees containing $$k$$ leaves and zero vertices of degree $$2$$.
I tried to use the theorem related to rooted trees and tried to prove it by contradiction, b... | 2022-05-25T12:59:50 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/3401393/are-there-a-finite-number-of-trees-with-k-leaves-and-no-vertices-of-degree-2/3401420",
"openwebmath_score": 0.9387131333351135,
"openwebmath_perplexity": 59.10605418348453,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Y... |
http://mathematica.stackexchange.com/questions/39848/probability-of-the-sum-of-the-largest-n-samples?answertab=votes | # Probability of the sum of the largest n samples
15 numbers are randomly chosen from U(0,1), what is the probability that the sum of largest four numbers is greater than 3.5?
With[{f = OrderDistribution[{UniformDistribution[], 15}, #] &},
Probability[a + b + c + d > 3 + 1 / 2,
{a \[Distributed] f[15], b \[Distribute... | 2015-07-04T05:08:11 | {
"domain": "stackexchange.com",
"url": "http://mathematica.stackexchange.com/questions/39848/probability-of-the-sum-of-the-largest-n-samples?answertab=votes",
"openwebmath_score": 0.616093099117279,
"openwebmath_perplexity": 2570.7295486215476,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"l... |
https://www.intmath.com/blog/learn-math/i-heart-math-5179 | # I heart math
By Murray Bourne, 05 Oct 2010
I saw this T-shirt recently.
What does it mean and what's that equation?
This is an example of an implicit function. When we first learn about functions, they are written explicitly, for example:
f(x) = sin(x) + 4x
This explicit function involves one dependent variable... | 2019-09-19T13:06:28 | {
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"url": "https://www.intmath.com/blog/learn-math/i-heart-math-5179",
"openwebmath_score": 0.7151968479156494,
"openwebmath_perplexity": 1905.423900734085,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.988130881050834,
"lm_q2_score": 0.89330941386542... |
http://stacks.math.columbia.edu/tag/00EC | # The Stacks Project
## Tag 00EC
Lemma 10.20.1. Let $R$ be a ring. Let $e \in R$ be an idempotent. In this case $$\mathop{\rm Spec}(R) = D(e) \amalg D(1-e).$$
Proof. Note that an idempotent $e$ of a domain is either $1$ or $0$. Hence we see that \begin{eqnarray*} D(e) & = & \{ \mathfrak p \in \mathop{\rm Spec}(R) \m... | 2017-04-26T17:44:59 | {
"domain": "columbia.edu",
"url": "http://stacks.math.columbia.edu/tag/00EC",
"openwebmath_score": 1.0000007152557373,
"openwebmath_perplexity": 1124.5804086788503,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9881308791284249,
"lm_q2_score": 0.8933093954028816,
"lm_q1q2... |
https://math.stackexchange.com/questions/497639/predicate-logic-translating-all-but-one | # Predicate Logic Translating “All But One”
I need to translate an English sentence including the phrase "all but one" into predicate logic. The sentence is: "All students but one have an internet connection." I'm not sure how to show "all but one" in logic.
I could say $\forall x ((x \neq a) \rightarrow I(x))$
$I(x... | 2019-08-19T23:51:47 | {
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"url": "https://math.stackexchange.com/questions/497639/predicate-logic-translating-all-but-one",
"openwebmath_score": 0.7436140775680542,
"openwebmath_perplexity": 365.6167340615774,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.96741025194538... |
https://gmatclub.com/forum/sum-of-n-positive-integers-formula-for-consecutive-integers-163301.html | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 21 Mar 2019, 21:17
### GMAT Club Daily Prep
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Customize... | 2019-03-22T04:17:50 | {
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"url": "https://gmatclub.com/forum/sum-of-n-positive-integers-formula-for-consecutive-integers-163301.html",
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"openwebmath_perplexity": 1141.4389797102813,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n",
"lm_q1_score": 0.94659... |
http://mathhelpforum.com/differential-equations/182030-solve-x-2-d-2-dx-2-3x-dy-dx-y-1-x.html | # Math Help - Solve (x^2) ( d^2/dx^2) + 3x(dy/dx) + y = 1/x
1. ## Solve (x^2) ( d^2/dx^2) + 3x(dy/dx) + y = 1/x
(x^2) ( d^2/dx^2) + 3x(dy/dx) + y = 1/x
how can i find the general solution of differential equation?
2. It's a Cauchy-Euler equation. Use that procedure.
3. but right side of equation isn't equal to zer... | 2014-03-16T23:27:28 | {
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"openwebmath_score": 0.8851804733276367,
"openwebmath_perplexity": 559.7885446521278,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9848... |
https://math.stackexchange.com/questions/4267377/length-of-the-curve-displaystyle-3ay2-xx-a2 | # Length of the curve $\displaystyle 3ay^2=x(x-a)^2$
I'm working on finding out the length of the curve $$3ay^2=x(x-a)^2 \tag{1}$$
I ran into a small problem, but was able to end up with an answer that looks right but I'm not entirely sure about it. Here's my approach:
The length of a curve $$f(x)$$ between $$x=a$$ ... | 2023-02-03T22:58:08 | {
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"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.97702262... |
https://math.stackexchange.com/questions/2680258/whats-the-difference-between-mutually-exclusive-and-pairwise-disjoint/2680280 | # What's the difference between MUTUALLY EXCLUSIVE and PAIRWISE DISJOINT?
When I study Statistical Theory, I find that these two concepts confuse me a lot.
By definition, if we say two events are PAIRWISE DISJOINT, that means the intersection of these two event is empty set. If we say that two events are MUTUALLY EXC... | 2020-10-27T09:15:59 | {
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"openwebmath_perplexity": 114.3366865828029,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. ... |
https://www.flypmedia.com/pittosporum-images-lmk/side-of-rhombus-formula-7b2219 | Online calculators and formulas for a rhombus … Area of plane shapes. The area of the rhombus is given by the formula: Area of rhombus = sh. Abhishek241 Abhishek241 19.08.2017 Math Secondary School +5 pts. A rhombus is a type of Parallelogram only. Sitemap. The side of rhombus is a tangent to the circle. Solution: All ... | 2021-04-13T17:47:25 | {
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"url": "https://www.flypmedia.com/pittosporum-images-lmk/side-of-rhombus-formula-7b2219",
"openwebmath_score": 0.7617335915565491,
"openwebmath_perplexity": 481.10646871931215,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 0.9814534376578002,
"... |
https://math.stackexchange.com/questions/1431396/prove-that-any-integer-that-is-both-square-and-cube-is-congruent-modulo-36-to-0 | # Prove that any integer that is both square and cube is congruent modulo 36 to 0,1,9,28
This is from Burton Revised Edition, 4.2.10(e) - I found a copy of this old edition for 50 cents.
Prove that if an integer $a$ is both a square and a cube then $a \equiv 0,1,9, \textrm{ or } 28 (\textrm{ mod}\ 36)$
An outline of... | 2019-05-20T17:03:22 | {
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"openwebmath_perplexity": 85.15460002533804,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2... |
http://adunataalpini-pordenone2014.it/nrwx/graphs-of-sine-and-cosine-functions-answer-key.html | # Graphs Of Sine And Cosine Functions Answer Key
Find arc lengths and areas of. What is the equation for the cosine function graphed here? Gimme a Hint. I can graph the cosine function and its translations. NOW is the time to make today the first day of the rest. To define what these 3 functions, we first have to unde... | 2020-11-25T19:25:16 | {
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"url": "http://adunataalpini-pordenone2014.it/nrwx/graphs-of-sine-and-cosine-functions-answer-key.html",
"openwebmath_score": 0.6496663093566895,
"openwebmath_perplexity": 977.6851453625898,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_scor... |
https://orinanobworld.blogspot.com/2020/02/ | Monday, February 17, 2020
Reversing Differences
Fellow blogger Håkan Kjellerstrand posted an interesting question on OR Stack Exchange recently. Starting from a list of integers, it is trivial to compute the list of all pairwise absolute differences, but what about going in the other direction? Given the pairwise (ab... | 2020-02-22T07:08:49 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9928785710435412,
"lm_q2_score": 0.8887587934924569,
"lm_q1q... |
https://math.stackexchange.com/questions/2671760/why-does-expanding-lim-p-rightarrow-0-frac1-p-1-p31-1-p3-give-a/2671778 | # Why does expanding $\lim_{p \rightarrow 0}\frac{1-p-(1-p)^3}{1-(1-p)^3}$ give a different limit from just substituting?
$$\lim_{p \rightarrow 0}\frac{1-p-(1-p)^3}{1-(1-p)^3}$$
$$= \frac{1-0-(1-0)^3}{1-(1-0)^3}$$
$$=\frac{0}{0}$$
$$\lim_{p \rightarrow 0}\frac{1-p-(1-p)^3}{1-(1-p)^3}$$
$$=\lim_{p \rightarrow 0}\fr... | 2021-02-25T10:33:19 | {
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"openwebmath_perplexity": 218.59312498858014,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",... |
http://vvnn.ecui.pw/latex-symbols-math.html | # Latex Symbols Math
An operator such as the differential operator D^~. Short Math Guide for LATEX, version 2. Even though commands follow a logical naming scheme, you will probably need a table for the most common math symbols at some point. Letters are. = mathrm{C}, LATIN CAPITAL LETTER C. Suppose that you need to t... | 2020-01-18T18:10:10 | {
"domain": "ecui.pw",
"url": "http://vvnn.ecui.pw/latex-symbols-math.html",
"openwebmath_score": 0.9359549880027771,
"openwebmath_perplexity": 2233.4644955099657,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9433475746920261,
"lm_q2_score": 0.935346505335907,
"lm_q1q2_sc... |
https://math.stackexchange.com/questions/2481670/what-is-the-probability-that-player-a-and-b-play-against-each-other | # What is the probability that player A and B play against each other?
Players with same skill take part in a competition. The probability of winning each game is 0.5. At first, we divide a group of $2^n$ people to random pairs that play against each other. Then we will do the same for $2^{n-1}$ winners and this conti... | 2019-12-14T13:59:01 | {
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"openwebmath_score": 0.9961243867874146,
"openwebmath_perplexity": 336.79968621321535,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"... |
http://gmatclub.com/forum/to-find-the-units-digit-of-a-large-number-155363.html | Find all School-related info fast with the new School-Specific MBA Forum
It is currently 30 Aug 2015, 00:00
### GMAT Club Daily Prep
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C... | 2015-08-30T08:00:57 | {
"domain": "gmatclub.com",
"url": "http://gmatclub.com/forum/to-find-the-units-digit-of-a-large-number-155363.html",
"openwebmath_score": 0.32343626022338867,
"openwebmath_perplexity": 2334.657257537312,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n",
"lm_q1_score": 0.9738443862008362,
"lm_... |
https://mathhelpboards.com/threads/find-all-the-integer-values-of-k-for-x-3-kx-k-11-0-has-at-least-one-positive-integer-solution.25900/ | # Find all the integer values of k for x^3 - kx + (k + 11) = 0 has at least one positive integer solution
#### Taran
##### New member
Hi, this question was in a year 11 extension maths textbook in the enrichment section. I have the answer as k>17 and k<-11 because I graphed it on GeoGebra. The Graph can be found here... | 2020-06-04T04:50:00 | {
"domain": "mathhelpboards.com",
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"openwebmath_score": 0.7407698035240173,
"openwebmath_perplexity": 254.31747904766357,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "... |
https://math.stackexchange.com/questions/955294/prove-that-int-0-pi-frac-cos-x21-cos-x-sin-x-mathrmdx-i | # Prove that $\int_0^{\pi} \frac{(\cos x)^2}{1 + \cos x \sin x} \,\mathrm{d}x =\int_0^{\pi} \frac{(\sin x)^2}{1 + \cos x \sin x} \,\mathrm{d}x$
In a related question the following integral was evaluated $$\int_0^{\pi} \frac{(\cos x)^2}{1 + \cos x \sin x} \,\mathrm{d}x =\int_0^{\pi} \frac{\mathrm{d}x/2}{1 + \cos x \sin... | 2019-06-27T10:41:05 | {
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"url": "https://math.stackexchange.com/questions/955294/prove-that-int-0-pi-frac-cos-x21-cos-x-sin-x-mathrmdx-i",
"openwebmath_score": 0.9998661279678345,
"openwebmath_perplexity": 1534.2748462268687,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score":... |
http://stats.stackexchange.com/questions/32824/how-to-minimize-residual-sum-of-squares-of-an-exponential-fit | # How to minimize residual sum of squares of an exponential fit?
I have the following data and would like to fit a negative exponential growth model to it:
Days <- c( 1,5,12,16,22,27,36,43)
Emissions <- c( 936.76, 1458.68, 1787.23, 1840.04, 1928.97, 1963.63, 1965.37, 1985.71)
plot(Days, Emissions)
fit <- nls(Emission... | 2013-05-24T01:16:46 | {
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"url": "http://stats.stackexchange.com/questions/32824/how-to-minimize-residual-sum-of-squares-of-an-exponential-fit",
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"openwebmath_perplexity": 980.0923183511632,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_scor... |
https://scicomp.stackexchange.com/questions/37372/is-there-a-general-threshhold-for-which-a-large-condition-number-becomes-proble/37379 | Is there a general threshhold for which a large condition number becomes “problematic?”
I think the answer is probably no in the linear algebra community, but I'd say anything above $$10^8$$ and you're starting to lose too much precision, making the situation problematic. In some statistics settings, where they use OL... | 2021-06-15T01:03:25 | {
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"openwebmath_score": 0.793489396572113,
"openwebmath_perplexity": 277.9344189141476,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. ... |
https://themortgagestudent.com/tag/550a36-what-is-the-cube-root-of-125 | # what is the cube root of 125
The cube root of -8 is written as $$\sqrt[3]{-8} = -2$$. ... ∛125: 5 ∛216: 6 ∛1,000: 10 ∛1,000,000: 100 ∛1,000,000,000: 1000: The calculations were performed using this cube root calculator. When did organ music become associated with baseball? 5³ = 5 * 5 * 5 = 25 * 5 = 125 So the cube r... | 2021-01-19T15:22:30 | {
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"url": "https://themortgagestudent.com/tag/550a36-what-is-the-cube-root-of-125",
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"openwebmath_perplexity": 636.7021015367188,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9843363512883316,
"lm_q2... |
https://math.stackexchange.com/questions/2853732/prove-log-2x-log-xy-log-y8-geq-sqrt381 | # Prove: $\log_2(x)+\log_x(y)+\log_y(8)\geq \sqrt[3]{81}$
Prove that for every $x$,$y$ greater than $1$: $$\log_2(x)+\log_x(y)+\log_y(8)\geq \sqrt[3]{81}$$
What I've tried has got me to:
$$\frac{\log_y(x)}{\log_y(2)}+\log_x(y)+3\log_y(2)\geq \sqrt[3]{81}$$
I didn't really get far.. I can't see where I can go from h... | 2020-02-23T11:52:03 | {
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"url": "https://math.stackexchange.com/questions/2853732/prove-log-2x-log-xy-log-y8-geq-sqrt381",
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"openwebmath_perplexity": 535.426234789077,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.987568348415041... |
https://math.stackexchange.com/questions/560816/find-the-sum-of-the-series-sum-frac1nn1n2 | # Find the sum of the series $\sum \frac{1}{n(n+1)(n+2)}$
I got this question in my maths paper
Test the condition for convergence of $$\sum_{n=1}^\infty \frac{1}{n(n+1)(n+2)}$$ and find the sum if it exists.
I managed to show that the series converges but I was unable to find the sum. Any help/hint will go a long w... | 2019-05-20T09:03:44 | {
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"url": "https://math.stackexchange.com/questions/560816/find-the-sum-of-the-series-sum-frac1nn1n2",
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"openwebmath_perplexity": 804.6634061231066,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.987568346951... |
http://nyvb.ilcampanileborgo.it/analytic-trigonometry-pdf.html | # Analytic Trigonometry Pdf
Trigonometry is a special subject of its own, so you might like to visit: Introduction to Trigonometry; Trigonometry Index. Most of the topics that appear here have already been discussed in the Algebra book and often the text here is a verbatim copy of the text in the other book. Find the ... | 2020-07-06T23:09:17 | {
"domain": "ilcampanileborgo.it",
"url": "http://nyvb.ilcampanileborgo.it/analytic-trigonometry-pdf.html",
"openwebmath_score": 0.5778871178627014,
"openwebmath_perplexity": 2061.6495554520557,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9908743631497862,
"lm_q2_score": 0... |
https://math.stackexchange.com/questions/2186634/how-to-draw-a-sublattice-to-exhibit-diagonalization/2186851 | # How to draw a sublattice to exhibit diagonalization?
Given the matrix:
$$A=\begin{pmatrix} 3 & 1 \\ -1 & 2 \\ \end{pmatrix}.$$
Let $V =\mathbb Z^2$ and $L = AV$. We want to find basis for $V$ and $L$ and draw the sublattice that exhibit the diagonalization.
I found the diagonal form of the matrix to be:
$$\begin... | 2019-06-17T19:18:49 | {
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"url": "https://math.stackexchange.com/questions/2186634/how-to-draw-a-sublattice-to-exhibit-diagonalization/2186851",
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"openwebmath_perplexity": 195.23123817738258,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_sc... |
https://stonedynamicsco.com/what-does-oiypld/topological-sort-problems-b4c8cf | A topological sort takes a directed acyclic graph and produces a linear ordering of all its vertices such that if the graph $$G$$ contains an edge $$(v,w)$$ then the vertex $$v$$ comes before the vertex $$w$$ in the ordering. Also try practice problems to test & improve your skill level. if the graph is DAG. The approa... | 2021-07-30T08:06:16 | {
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"url": "https://stonedynamicsco.com/what-does-oiypld/topological-sort-problems-b4c8cf",
"openwebmath_score": 0.3852830231189728,
"openwebmath_perplexity": 931.7901930903615,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9736446440948805,
"l... |
http://milanoporteeserramenti.it/tec/circumference-of-a-semicircle-calculator.html | Circumference C= Diameter Area Radius π Learn the formula for circumference: πd Learn the formula for the area of a circle: A= πr 2 Learn the value of pi correct to d. Calculate the circumference of a circle. Calculate the area of the square, and divide that by the surface area of the facing-out side of a brick. How to... | 2020-10-25T04:54:43 | {
"domain": "milanoporteeserramenti.it",
"url": "http://milanoporteeserramenti.it/tec/circumference-of-a-semicircle-calculator.html",
"openwebmath_score": 0.8478139638900757,
"openwebmath_perplexity": 427.07611142392966,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9907319871... |
http://math.stackexchange.com/questions/95562/how-to-calculate-z4-frac1z4-if-z2-z-1-0/95596 | # How to calculate $z^4 + \frac1{z^4}$ if $z^2 + z + 1 = 0$?
Given that $z^2 + z + 1 = 0$ where $z$ is a complex number, how do I proceed in calculating $z^4 + \dfrac1{z^4}$?
Calculating the complex roots and then the result could be an answer I suppose, but it's not quite elegant. What alternatives are there?
-
Fr... | 2015-10-06T21:04:42 | {
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"openwebmath_score": 0.9703070521354675,
"openwebmath_perplexity": 417.32785874465696,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.987375050... |
http://mathematica.stackexchange.com/questions/22349/mathematica-for-teaching-orthographic-projection | # Mathematica for teaching orthographic projection
Edit: All the four answers to this question are great, and if you're interested, you should take a look at all the answers. Nevertheless, belisarius' code was accepted since it was closest to what I had in mind.
I'm trying to use Mathematica to help students better u... | 2015-05-25T13:45:40 | {
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"url": "http://mathematica.stackexchange.com/questions/22349/mathematica-for-teaching-orthographic-projection",
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"openwebmath_perplexity": 2193.327691647778,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0... |
https://math.stackexchange.com/questions/2998130/matrix-representation-of-mixed-derivatives | # Matrix representation of Mixed derivatives
Imagine we have the problem
$$\begin{cases} -\frac{d^2u}{dx^2} = f(x), x \in [0,L] \\ u(0) = 0 \\ u(L) = 0 \end{cases}$$
We know that we can approximate the second derivative using this formula:$$\frac{d^2u(x)}{dx^2} \approx \frac{u(x+h)-2u(x)+u(x-h)}{h^2}$$
if we define... | 2019-05-22T11:39:46 | {
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"url": "https://math.stackexchange.com/questions/2998130/matrix-representation-of-mixed-derivatives",
"openwebmath_score": 0.9938884377479553,
"openwebmath_perplexity": 169.78465940030057,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.984093605... |
https://math.stackexchange.com/questions/1610277/how-to-solve-an-initial-value-problem-if-my-function-is-implicit | # How to solve an initial value problem if my function is implicit?
I have the differential equation:
$\dfrac{dy}{dt} = \dfrac{1}{2y+3}$
with the initial value of $y(0) = 1$
So I solve the diffeq via separation of variables:
$y^2 + 3y = t + c$
But from here, how do I solve for the function? Am I "allowed" to use ... | 2019-08-21T23:13:49 | {
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"url": "https://math.stackexchange.com/questions/1610277/how-to-solve-an-initial-value-problem-if-my-function-is-implicit",
"openwebmath_score": 0.8892452120780945,
"openwebmath_perplexity": 188.69460773115534,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_... |
https://math.stackexchange.com/questions/2944252/finding-the-probability-that-someone-has-the-disease-given-they-test-positive-o | # Finding the probability that someone has the disease, given they test positive on two tests
This question is from the textbook "Introduction to Probability - Blitzstein & Hwang."
I was studying for a class when I came across an example problem that I solved, but got a slightly different result than the textbook. He... | 2019-06-18T15:20:13 | {
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"url": "https://math.stackexchange.com/questions/2944252/finding-the-probability-that-someone-has-the-disease-given-they-test-positive-o",
"openwebmath_score": 0.739641547203064,
"openwebmath_perplexity": 311.0663614422447,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2.... |
https://math.stackexchange.com/questions/1591534/for-numerical-integration-is-it-true-that-higher-degree-of-precision-gives-bett | # For numerical integration, is it true that higher degree of precision gives better accuracy always?
In case of numerical integration, is it true that higher degree of precision always gives better accuracy? Justify your answer.
I know the definition of degree of precision. For Trapezoidal and Simpson's 1/3 rule the... | 2019-07-23T16:52:40 | {
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"url": "https://math.stackexchange.com/questions/1591534/for-numerical-integration-is-it-true-that-higher-degree-of-precision-gives-bett",
"openwebmath_score": 0.8301143646240234,
"openwebmath_perplexity": 292.14336287453494,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n... |
https://mathhelpboards.com/threads/find-all-pairs-m-k-of-integer-solutions.6882/ | Find all pairs (m,k) of integer solutions
anemone
MHB POTW Director
Staff member
Find all solutions to $(m^2+k)(m+k^2)=(m-k)^3$, where $m$ and $k$ are non-zero integers.
Opalg
MHB Oldtimer
Staff member
Find all solutions to $(m^2+k)(m+k^2)=(m-k)^3$, where $m$ and $k$ are non-zero integers.
Multiply out the brackets... | 2020-09-22T22:49:35 | {
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"openwebmath_score": 0.9229340553283691,
"openwebmath_perplexity": 200.91971747974273,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9808759593358226,
... |
https://mathhelpboards.com/threads/review-my-solution-trigonometry-proof.5778/ | TrigonometryReview my solution: Trigonometry proof
sweatingbear
Member
For a triangle with sides $$\displaystyle a$$, $$\displaystyle b$$, $$\displaystyle c$$ and angle $$\displaystyle C$$, where the angle $$\displaystyle C$$ subtends the side $$\displaystyle c$$, show that
$$\displaystyle c \geqslant (a+b) \sin \le... | 2021-01-25T15:07:22 | {
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"url": "https://mathhelpboards.com/threads/review-my-solution-trigonometry-proof.5778/",
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"openwebmath_perplexity": 213.6857001573631,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9905874101345136,
"lm... |
http://mathhelpforum.com/discrete-math/93273-divide-3-a.html | # Math Help - divide by 3?
1. ## divide by 3?
hi folks,
I hope this is the right place to post this! I have no idea how to proceeed with the following question:
Show that for all positive integral values of n
[HTML]7 <sup>n</sup> + 2 <sup>2n+1</sup>[/HTML]
is divisible by 3.
I tried a few terms as follows:
n = ... | 2015-11-26T12:07:11 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9888419710536894,
"lm_q2_score": 0.8918... |
https://mathhelpboards.com/threads/another-solid-of-revolution-problem.1116/ | # [SOLVED]Another Solid of Revolution problem
##### Member
I'm finding myself stuck again. This time it is more in the set up then the solving.
Find the volume of the following solid of revolution.
The region bounded by $$\displaystyle y=\frac{1}{x^2}$$, y=0, x=2, x=8, and revolved about the y-axis.
I am trying to ... | 2021-07-30T16:28:33 | {
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"url": "https://mathhelpboards.com/threads/another-solid-of-revolution-problem.1116/",
"openwebmath_score": 0.7557286024093628,
"openwebmath_perplexity": 170.146418740701,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9777138092657496,
"lm_q... |
http://math.stackexchange.com/questions/56688/please-help-me-to-prove-the-convergence-of-gamma-n-1-frac12-frac1 | Please help me to prove the convergence of $\gamma_{n} = 1+\frac{1}{2}+\frac{1}{3}+…+\frac{1}{n}-\ln n$
Please help me to prove that $\gamma_{n} = 1+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{n}-\ln n$ converge and it's limit $\gamma \in [0,1]$. Then, using $\gamma_{n}$ find the sum: $\sum_{n=1}^{\infty}(-1)^{n+1}\frac{1}{... | 2015-09-03T18:06:03 | {
"domain": "stackexchange.com",
"url": "http://math.stackexchange.com/questions/56688/please-help-me-to-prove-the-convergence-of-gamma-n-1-frac12-frac1",
"openwebmath_score": 0.9519006013870239,
"openwebmath_perplexity": 601.6958971091595,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_... |
http://mathhelpforum.com/algebra/164881-word-problem.html | # Math Help - word problem.
1. ## word problem.
hi ! im having a difficult time answering this word problem.
"Alvin set out from a certain point and travelled at the rate of 6 kph. After Alvin had gone for two hours, Ben set on to overtake him and went 4km the first hour, 5 km the second hour, 6 km the third hour an... | 2016-05-05T14:49:30 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9822877049262134,
"lm_q2_score": 0.89769528... |
https://math.stackexchange.com/questions/3140502/do-the-12-lines-of-a-bingo-card-have-equal-chance-of-winning | # Do the 12 lines of a bingo card have equal chance of winning?
You have a $$5 \times 5$$ bingo card filled with $$25$$ distinct numbers, one per square. There is also a pot containing each number once and you draw them out one by one without replacement.
A line is any of the $$5$$ rows, $$5$$ columns, or $$2$$ main ... | 2019-06-19T16:41:30 | {
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"url": "https://math.stackexchange.com/questions/3140502/do-the-12-lines-of-a-bingo-card-have-equal-chance-of-winning",
"openwebmath_score": 0.5851178765296936,
"openwebmath_perplexity": 759.8442247230166,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_sc... |
https://math.stackexchange.com/questions/59943/if-n-323232-cdots-50-text-digits-9-i-e-in-base-9-then-how-to-find-t?noredirect=1 | # If $N= (323232 \cdots 50 \text{ digits})_9$ (i.e in base $9$) then how to find the remainder when this $N$ is divided by $8$?
If $N= (\underbrace{323232 \cdots}_{50 \text{ digits}})_9$ (i.e in base $9$) then how to find the remainder when this $N$ is divided by $8$?
I am looking for a "fast" approach that could be ... | 2019-06-17T11:27:27 | {
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"openwebmath_score": 0.8038354516029358,
"openwebmath_perplexity": 185.7710300479582,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2.... |
http://cms.math.ca/Competitions/MOCP/2001/sol_feb.mml | location:
61.
Let $S=1!2!3!\dots 99!100!$ (the product of the first 100 factorials). Prove that there exists an integer $k$ for which $1\le k\le 100$ and $S/k!$ is a perfect square. Is $k$ unique? (Optional: Is it possible to find such a number $k$ that exceeds 100?)
Solution 1. Note that, for each positive integer $j... | 2014-03-07T20:05:46 | {
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"lm_q1_score": 0.9838471618625457,
"lm_q2_score": 0.8962513752119936,
"... |
http://mathhelpforum.com/advanced-algebra/133902-proving-group.html | # Math Help - Proving that this is a group
1. ## Proving that this is a group
Hello, I would really appreciate any help with the following problem:
Prove that $(G, *)$ is a group, where $G=<-1,1>$ and $a*b=\dfrac{a+b}{1+ab}$,.... $\forall a, b \in G$.
_______________________________
To prove that this is a group, ... | 2015-02-28T19:25:58 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9732407175907054,
"lm_q2_score":... |
https://math.stackexchange.com/questions/1469820/area-under-quarter-circle-by-integration | # Area under quarter circle by integration
How would one go about finding out the area under a quarter circle by integrating. The quarter circle's radius is r and the whole circle's center is positioned at the origin of the coordinates. (The quarter circle is in the first quarter of the coordinate system)
From the eq... | 2021-11-28T08:29:47 | {
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"openwebmath_perplexity": 623.0111737277325,
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"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.993807011309... |
https://math.stackexchange.com/questions/2243997/find-the-2-digits-in-front-of-the-number-14-so-that-the-4-digit-number-we-get-i/2244024 | # Find the 2 digits in front of the number 14, so that the 4-digit number we get is divisible by 26.
I know that 26=13.2. The last digit of the number is 4, it is divisible by 2. I have to remove the last digit and check out if the remaining digits are divisible by 13 or?
• what do you mean by '2 digits in front of t... | 2020-10-24T20:20:18 | {
"domain": "stackexchange.com",
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"openwebmath_score": 0.8078303933143616,
"openwebmath_perplexity": 145.0054071910057,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1... |
https://math.stackexchange.com/questions/1767217/does-the-infinite-series-sum-k-1-infty-frac14-1kk-converge | # Does the infinite series $\sum_{k=1}^{\infty} \frac{1}{(4+(-1)^k)^k}$ converge?
I have been wondering if this infinite series converges $$\sum_{k=1}^{\infty} \frac{1}{(4+(-1)^k)^k}$$
I tried to put it in wolfram alpha but it says that the ratio test is inconclusive, but when I do the ratio test I get: Let first $a_... | 2019-04-25T21:56:00 | {
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"openwebmath_score": 0.9552393555641174,
"openwebmath_perplexity": 419.01548789766053,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_sco... |
http://pobarabanu.com.ua/414yquca/elnfm.php?57d14b=system-of-linear-equations-matrix-conditions | Solving systems of linear equations. This calculator solves Systems of Linear Equations using Gaussian Elimination Method, Inverse Matrix Method, or Cramer's rule.Also you can compute a number of solutions in a system of linear equations (analyse the compatibility) using Rouché–Capelli theorem.. First, we need to find ... | 2021-03-05T01:00:55 | {
"domain": "com.ua",
"url": "http://pobarabanu.com.ua/414yquca/elnfm.php?57d14b=system-of-linear-equations-matrix-conditions",
"openwebmath_score": 0.8119489550590515,
"openwebmath_perplexity": 560.0163132020501,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9688561694652... |
https://math.stackexchange.com/questions/3483283/whats-wrong-in-my-calculation-of-int-frac-sin-x1-sin-x-dx | What's wrong in my calculation of $\int \frac{\sin x}{1 + \sin x} dx$?
I have the following function:
$$f: \bigg ( - \dfrac{\pi}{2}, \dfrac{\pi}{2} \bigg ) \rightarrow \mathbb{R} \hspace{2cm} f(x) = \dfrac{\sin x}{1 + \sin x}$$
And I have to find $$\displaystyle\int f(x) dx$$. This is what I did:
$$\int \dfrac{\sin... | 2021-06-15T14:12:00 | {
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"url": "https://math.stackexchange.com/questions/3483283/whats-wrong-in-my-calculation-of-int-frac-sin-x1-sin-x-dx",
"openwebmath_score": 0.8357511758804321,
"openwebmath_perplexity": 278.8970099780308,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score... |
http://mathhelpforum.com/discrete-math/95124-easy-easy-question-print.html | # easy, easy question
• Jul 14th 2009, 07:06 AM
billym
easy, easy question
How many ways are there to seat 10 people, consisting of 5 couples, in a row of seats (10 seats wide) if all couples are to get adjacent seats?
• Jul 14th 2009, 07:20 AM
Soroban
Hello, billym!
Quote:
How many ways are there to seat 10 people... | 2016-12-04T06:38:07 | {
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"lm_q2_... |
https://math.stackexchange.com/questions/1792266/two-methods-of-implicit-differentiation-dont-correspond | # Two methods of implicit differentiation don't correspond
I recently attempted a question on implicit differentiation twice. I differentiated using one method in the first attempt and then another method in the second attempt but they do not correspond when I plug in values for the variables x and y. Please look at t... | 2020-02-27T18:43:30 | {
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"url": "https://math.stackexchange.com/questions/1792266/two-methods-of-implicit-differentiation-dont-correspond",
"openwebmath_score": 0.6070007085800171,
"openwebmath_perplexity": 169.3289375081391,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score":... |
http://bernardklima.cz/hyq2s1h/d7c474-permutation-matrix-inverse | Led
01
And every 2-cycle (transposition) is inverse of itself. Every permutation n>1 can be expressed as a product of 2-cycles. Sometimes, we have to swap the rows of a matrix. A permutation matrix is an orthogonal matrix • The inverse of a permutation matrix P is its transpose and it is also a permutation matrix and ... | 2021-06-19T03:39:08 | {
"domain": "bernardklima.cz",
"url": "http://bernardklima.cz/hyq2s1h/d7c474-permutation-matrix-inverse",
"openwebmath_score": 0.9370395541191101,
"openwebmath_perplexity": 369.1545041757962,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9820137868795702,
"lm_q2_score": ... |
https://mathhelpboards.com/threads/combinatorics-question-involving-6-6-sided-dice.3756/ | # Combinatorics question involving 6 6-sided dice
#### wittysoup
##### New member
When rolling 6 6-sided dice, how many different ways can you have exactly 4 different numbers?
I tried solving this like so,
the first dice has a possible 6 numbers, the second has a possible 5, the third has a possible 4, and the fou... | 2021-08-01T17:35:59 | {
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"url": "https://mathhelpboards.com/threads/combinatorics-question-involving-6-6-sided-dice.3756/",
"openwebmath_score": 0.7834502458572388,
"openwebmath_perplexity": 675.7231009233019,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.971563965308... |
https://math.stackexchange.com/questions/1558133/different-function-with-the-same-derivative | # Different function with the same derivative
Today at school I entered in a problem when the professor asked us to differentiate the following function:
$$f(x)=\arctan\left(\frac {x-1}{x+1}\right)$$
With the basic rules of differentiation I came to a confusing result:
$$f'(x)=\frac 1{1+x^2}$$
And the teacher agre... | 2021-09-17T21:32:53 | {
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"url": "https://math.stackexchange.com/questions/1558133/different-function-with-the-same-derivative",
"openwebmath_score": 0.885212779045105,
"openwebmath_perplexity": 205.54974554083205,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.986777178... |
https://mathhelpboards.com/threads/sets.5984/ | # Sets
#### bergausstein
##### Active member
1.are the following sets a finite sets? if yes why? if no why?
a. the set of points on a given line exactly one unit from a given point on that line.
b. the set of points in a given plane that are exactly one unit from a given point in that plane.
i'm confused with the pa... | 2021-09-16T16:20:27 | {
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"url": "https://mathhelpboards.com/threads/sets.5984/",
"openwebmath_score": 0.790042519569397,
"openwebmath_perplexity": 388.7327711655853,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9918120905823452,
"lm_q2_score": 0.8887587920192298,
... |
https://math.stackexchange.com/questions/1479483/when-does-the-inverse-of-a-covariance-matrix-exist | # When does the inverse of a covariance matrix exist?
We know that a square matrix is a covariance matrix of some random vector if and only if it is symmetric and positive semi-definite (see Covariance matrix). We also know that every symmetric positive definite matrix is invertible (see Positive definite). It seems t... | 2019-05-23T14:57:35 | {
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"url": "https://math.stackexchange.com/questions/1479483/when-does-the-inverse-of-a-covariance-matrix-exist",
"openwebmath_score": 0.9590762257575989,
"openwebmath_perplexity": 99.61419093271385,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.98... |
https://math.stackexchange.com/questions/1737564/conditional-probability-question-understanding-mistake | # Conditional probability question (understanding mistake)
I'm trying to understand the following question:
An engineer conducts tests to find out if circuits of a certain type are prone to overheating. 30% of all such circuits are prone to overheating. If the circuit is prone to overheating, the test will report it ... | 2021-09-18T16:03:14 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1737564/conditional-probability-question-understanding-mistake",
"openwebmath_score": 0.8229305148124695,
"openwebmath_perplexity": 424.64601854916737,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score":... |
https://math.stackexchange.com/questions/2624208/counting-particular-odd-length-strings-over-a-two-letter-alphabet | # Counting particular odd-length strings over a two letter alphabet.
OEIS sequence A297789 describes
The number of [equivalence classes of] length $2n - 1$ strings over the alphabet $\{0, 1\}$ such that the first half of any initial odd-length substring is a permutation of the second half.
Two strings are in the sam... | 2020-01-28T20:16:47 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2624208/counting-particular-odd-length-strings-over-a-two-letter-alphabet",
"openwebmath_score": 0.9548411965370178,
"openwebmath_perplexity": 298.4569757127717,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_... |
https://math.stackexchange.com/questions/3305462/sum-of-digits-divisible-by-27 | # Sum of digits divisible by $27$
I know that every third number is divisible by $$3$$ and hence, sum of its digits is divisible by $$3$$. Same holds for $$9$$ also. But how do we generalise it? We know that the divisibility condition for higher powers of $$3$$ is not about the sum of digits. How can we find $$n$$ suc... | 2019-09-20T20:20:15 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/3305462/sum-of-digits-divisible-by-27",
"openwebmath_score": 0.8824615478515625,
"openwebmath_perplexity": 90.64754032392688,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9883127409715955,
"lm... |
https://math.stackexchange.com/questions/1371759/prove-sum-limits-i-0n-binomnii-binom2n1n1 | # Prove $\sum\limits_{i=0}^{n}\binom{n+i}{i}=\binom{2n+1}{n+1}$ [duplicate]
I'm trying to prove this algebraically: $$\sum\limits_{i=0}^{n}\dbinom{n+i}{i}=\dbinom{2n+1}{n+1}$$
Unfortunately I've been stuck for quite a while. Here's what I've tried so far:
1. Turning $\dbinom{n+i}{i}$ to $\dbinom{n+i}{n}$
2. Turning ... | 2019-05-24T11:14:26 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1371759/prove-sum-limits-i-0n-binomnii-binom2n1n1",
"openwebmath_score": 0.8197067379951477,
"openwebmath_perplexity": 547.5101587479361,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.97283076610... |
http://terabook.info/diy-rattan-kiluwab/symmetric-closure-of-a-relation-ada95c | # symmetric closure of a relation
0. Finally, the concepts of reflexive, symmetric and transitive closure are The reflexive, transitive closure of a relation R is the smallest relation that contains R and that is both reflexive and transitive. Reflexive and symmetric properties are sets of reflexive and symmetric bina... | 2021-02-28T06:50:21 | {
"domain": "terabook.info",
"url": "http://terabook.info/diy-rattan-kiluwab/symmetric-closure-of-a-relation-ada95c",
"openwebmath_score": 0.7278335690498352,
"openwebmath_perplexity": 526.8847190002843,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.978712651931994,
"lm_... |
https://mymathforum.com/threads/how-do-i-find-the-modulus-of-the-average-force-a-sphere-gets-from-colliding-with-the-ground.347560/ | # How do I find the modulus of the average force a sphere gets from colliding with the ground?
#### Chemist116
The problem is as follows:
A ball of $1\,kg$ in mass is thrown with a speed of $-10\vec{j}\,\frac{m}{s}$ from a height of $15\,m$ to a horizontal floor. Find the modulus of the average force in $N$ that the... | 2020-02-16T23:05:23 | {
"domain": "mymathforum.com",
"url": "https://mymathforum.com/threads/how-do-i-find-the-modulus-of-the-average-force-a-sphere-gets-from-colliding-with-the-ground.347560/",
"openwebmath_score": 0.7999904751777649,
"openwebmath_perplexity": 612.2589436959513,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n... |
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