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url string | text string | date timestamp[s] | meta dict |
|---|---|---|---|
https://www.encyclopediaofmath.org/index.php?title=Complexification_of_a_Lie_algebra&oldid=12632 | Complexification of a Lie algebra
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
over
The complex Lie algebra that is the tensor product of the algebra with the complex field over the field of real numbers :
Thus, the complexification of the Lie algebra is obtained from by extending the ... | 2019-04-21T16:14:24 | {
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https://physics.stackexchange.com/questions/207097/force-on-side-of-pool-from-water | Force on side of pool from water
Given a pool with dimensions $$\ell \times w \times h \, ,$$ I am trying to derive an equation that will yield the force by the water on the sides of the pool, namely $$\ell\times h \quad \mathrm{or} \quad w \times h \, .$$ For the side of the pool with dimensions $\ell \times h$, I st... | 2019-10-22T09:01:24 | {
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https://homework.cpm.org/category/CCI_CT/textbook/int3/chapter/12/lesson/12.2.1/problem/12-80 | ### Home > INT3 > Chapter 12 > Lesson 12.2.1 > Problem12-80
12-80.
Maria Elena is collecting college pennants. She has five fewer pennants from Washington campuses than from California campuses and twice as many pennants from California campuses as from Pennsylvania campuses. She has $40$ pennants in her collection. ... | 2021-09-28T20:37:10 | {
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https://www.shaalaa.com/question-bank-solutions/the-sides-triangle-are-11-cm-15-cm-16-cm-altitude-largest-side-application-of-heron-s-formula-in-finding-areas-of-quadrilaterals_62950 | # The Sides of a Triangle Are 11 Cm, 15 Cm and 16 Cm. the Altitude to the Largest Side is - Mathematics
MCQ
The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to the largest side is
#### Options
• $30\sqrt{7} cm$
• $\frac{15\sqrt{7}}{2}cm$
• $\frac{15\sqrt{7}}{4}cm$
• 30 cm
#### Solution
The area... | 2023-03-27T16:17:53 | {
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http://ceyron.io/state-sovereignty-jatwnj/heat-equation-solution-by-fourier-series-d85d85 | This paper describes the analytical Fourier series solution to the equation for heat transfer by conduction in simple geometries with an internal heat source linearly dependent on temperature. First, we look for special solutions having the form Substitution of this special type of the solution into the heat equation l... | 2021-09-26T02:49:57 | {
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https://cracku.in/15-if-5125-25-1248-4-then-what-is-the-value-of-424-x-ssc-cgl-18-aug-shift-2 | Question 15
# If 5$125 = 25, 12$48 = 4 then what is the value of 4$24 = ? Solution The pattern followed is that for $$a$$$ $$b$$ = $$\frac{b}{a}$$
Eg = 5$125 = $$\frac{125}{5}=25$$ and 12$48 = $$\frac{48}{12}=4$$
Similarly, 4\$24 = $$\frac{24}{4}=6$$
=> Ans - (C) | 2023-03-22T15:52:07 | {
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http://www.scientificlib.com/en/Mathematics/LX/MonomialBasis.html | # .
In mathematics the monomial basis of a polynomial ring is its basis (as vector space or free module over the field or ring of coefficients) that consists in the set of all monomials. The monomials form a basis because every polynomial may be uniquely written as a finite linear combination of monomials (this is an ... | 2022-05-23T00:09:48 | {
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http://mathhelpforum.com/differential-geometry/145771-adjoint-bounded-operators.html | 1. ## Adjoint of Bounded Operators
If $S,T:H\rightarrow H$ are bounded operators, show that $(ST)^*=T^*S^*$.
I'm assuming that $H$ is a Hilbert space, although it doesn't say this in the question. I'm really not sure where to start with this. All I have is that since $S,T$ are bounded there adjoints $S^*$ and $T^*$ e... | 2016-12-07T12:55:51 | {
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https://www.esaral.com/q/find-the-coefficients-of-33091/ | Find the coefficients of
Question:
Find the coefficients of $x^{7}$ and $x^{8}$ in the expansion of $\left(2+\frac{x}{3}\right)^{n}$.
Solution:
To find : coefficients of $x^{7}$ and $x^{8}$
Formula : $\mathrm{t}_{\mathrm{r}+1}=\left(\begin{array}{l}\mathrm{n} \\ \mathrm{r}\end{array}\right) \mathrm{a}^{\mathrm{n}-\... | 2022-05-16T15:32:44 | {
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https://homework.cpm.org/category/CC/textbook/cca2/chapter/2/lesson/2.1.1/problem/2-8 | ### Home > CCA2 > Chapter 2 > Lesson 2.1.1 > Problem2-8
2-8.
Consider the sequence with a first term of $256$, followed by $64,16,..$
1. Write the next three terms of this sequence, then find an equation for the sequence.
Note that each number is one-fourth of the preceding number.
Next three terms: $4,1,0.25$
$\... | 2021-10-28T03:03:18 | {
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http://wj32.org/wp/2012/04/09/triangles-in-a-triangle/ | # (How many) triangles in a triangle?
I hope most of you will be familiar with the “how many triangles” puzzle. If you aren’t, here’s a nice demonstration for you.
Given any triangle, let’s call the number of base triangles $$n$$. So the above picture has $$n=7$$. We’ll call the total number of triangles $$c_n$$. The... | 2015-02-27T11:32:33 | {
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... |
https://www.studyadda.com/question-bank/integral-power-of-iota-algebraic-operations-and-equality-of-complex-numbers_q51/1501/114674 | • # question_answer If $\sum\limits_{k=0}^{100}{{{i}^{k}}}=x+iy$, then the values of $x$ and $y$are A) $x=-1,y=0$ B) $x=1,y=1$ C) $x=1,y=0$ D) $x=0,y=1$
$\sum\limits_{k=0}^{100}{{{i}^{k}}=x+iy,}$Þ $1+i+{{i}^{2}}$$+......+{{i}^{100}}=x+iy$ Given series is G.P. Þ $\frac{1.(1-{{i}^{101}})}{1-i}=x+iy$ Þ $\frac{1-i}{1-i}... | 2021-01-20T15:38:12 | {
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"openwebmath_perplexity": 425.99197945522167,
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https://ezeenotes.in/a-car-accelerates-from-rest-at-a-constant-rate-%CE%B1-for-some-time-after-which-it-decelerates-at-a-constant-rate-%CE%B2-and-comes-to-rest-if-the-total-time-elapsed-is-t-then-the-maximum-v/ | # A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate β and comes to rest. If the total time elapsed is t then the maximum velocity acquired by the car is
Question : A car accelerates from rest at a constant rate α for some time, after which it decelerates at a... | 2023-02-08T16:23:38 | {
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"openwebmath_score": 0.9217345714569092,
"openwebmath_perplexit... |
https://math.stackexchange.com/questions/1435074/suppose-that-elements-a-b-and-ab-are-units-in-a-commutative-ring-r-show | # Suppose that elements $a, b$ and $a+b$ are units in a commutative ring $R$. Show that $a^{-1} + b^{-1}$ is also a unit.
Suppose that elements $a, b$ and $a+b$ are units in a commutative ring $R$. Show that $a^{-1} + b^{-1}$ is also a unit.
Here is what I have:
$a+b =b+a$ since $R$ is commutative.
Now,
$$(b+a) \c... | 2019-08-24T20:34:07 | {
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https://stacks.math.columbia.edu/tag/08Z7 | Lemma 47.7.6. Let $(R, \mathfrak m, \kappa )$ be a Noetherian local ring. Let $E$ be an injective hull of $\kappa$ over $R$. Then $E$ satisfies the descending chain condition.
Proof. If $E \supset M_1 \supset M_2 \supset \ldots$ is a sequence of submodules, then
$\mathop{\mathrm{Hom}}\nolimits _ R(E, E) \to \mathop{\... | 2020-06-06T08:36:47 | {
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"lm_q1q2_s... |
https://www.probabilitycourse.com/chapter8/8_2_3_max_likelihood_estimation.php | ## 8.2.3 Maximum Likelihood Estimation
So far, we have discussed estimating the mean and variance of a distribution. Our methods have been somewhat ad hoc. More specifically, it is not clear how we can estimate other parameters. We now would like to talk about a systematic way of parameter estimation. Specifically, we... | 2022-05-17T03:58:59 | {
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http://mathhelpforum.com/calculus/128052-serious-series-problem.html | # Math Help - Serious Series Problem
1. ## Serious Series Problem
What is the sum of:
1/1 + 1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4) + ... + 1/(1+2+3+...+n)
2. Originally Posted by bearej50
What is the sum of:
1/1 + 1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4) + ... + 1/(1+2+3+...+n)
$\sum_{k=1}^{j}k=\frac{j(j+1)}{2}$. And so $\sum... | 2015-07-29T07:59:57 | {
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https://byjus.com/question-answer/for-what-value-of-n-frac-a-n-1-b-n-1-a-n-b/ | Question
# For what value of n, an+1+bn+1an+bn is the arithmetic mean of a and b?
Open in App
Solution
## Since, arithmetic mean of a and b is a+b2, therefore according to the given condition, an+1+bn+1an+bn=a+b2 ⇒ 2an+1+2bn+1=an+1+anb+abn+bn+1 ⇒ 2an+1−an+1−anb=abn+bn+1−2bn+1 ⇒ an+1−anb=abn−bn+1 ⇒ an(a−b)=bn(a−b) ⇒ ... | 2023-01-30T11:17:40 | {
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https://math.stackexchange.com/questions/1191691/solve-a-pde-with-feynman-kac-formula | # Solve a PDE with Feynman-Kac Formula
So there is the following PDE given:
$\frac{\partial}{\partial t}f(t,x) + rx\frac{\partial}{\partial x}f(t,x)+\frac{\sigma^2 x^2}{2}\frac{{\partial}^2}{\partial x^2}f(t,x) = rf(t,x)$
With boundary condition $f(T,x) = x^{\frac{2r}{\sigma^2}}$
Here $r$ and $\sigma$ are positive ... | 2022-05-18T03:51:35 | {
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https://math.stackexchange.com/questions/2538366/for-what-values-of-alpha-does-int-0-infty-times-0-infty-frac | For what values of $\alpha$ does $\int_{(0, +\infty) \times (0, +\infty)} \frac{e^{-y} |\sin (x)|}{(1+xy)^{\alpha}}\: d(x, y)$ converge?
For what values of $\alpha \in \mathbb R$ does
$$\int_{(0, +\infty) \times (0, +\infty)} \frac{e^{-y} |\sin (x)|}{(1+xy)^{\alpha}}\: d(x, y)$$
converge?
What I've tried:
Using th... | 2019-08-23T09:09:59 | {
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"openwebmath_perplexity": 143.69920134969433,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_s... |
https://giasutamtaiduc.com/unit-vector-formula.html | # Unit Vector Formula
5/5 - (1 bình chọn)
Mục Lục
## Unit Vector
Vectors are geometric entities that have magnitude and direction. Vectors have a starting point and a terminal point which represents the final position of the point. Various arithmetic operations can be applied to vectors such as addition, subtractio... | 2023-04-02T02:14:01 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.986777179803135,
"lm_q2_score": 0.661922875849... |
https://www.gradesaver.com/textbooks/math/calculus/calculus-3rd-edition/chapter-15-differentiation-in-several-variables-15-3-partial-derivatives-exercises-page-781/43 | Calculus (3rd Edition)
$$g_u(1,2)= \frac{1}{3}+\ln 3 .$$
Since $g(u,v)=u\ln (u+v)$, then by the product rule, we have $$g_u=\ln (u+v)+u\frac{1}{u+v}=\ln (u+v)+\frac{u}{u+v}.$$ Hence, we get $$g_u(1,2)=\ln (1+3)+\frac{1}{1+2}=\frac{1}{3}+\ln 3 .$$ | 2019-12-16T04:38:56 | {
"domain": "gradesaver.com",
"url": "https://www.gradesaver.com/textbooks/math/calculus/calculus-3rd-edition/chapter-15-differentiation-in-several-variables-15-3-partial-derivatives-exercises-page-781/43",
"openwebmath_score": 0.996089518070221,
"openwebmath_perplexity": 168.9523082871287,
"lm_name": "Qwen/Q... |
https://www.coursehero.com/file/88556361/Module-7-APCalcBC-7-6-Improper-Integralspptx/ | Module 7_ APCalcBC 7-6 Improper Integrals.pptx - 7.6 Improper Integrals 1\/22 Do Now Evaluate 2 2x 4 lim 3 x\u00ae \u00a5 3x x 2 HW Review Improper Integrals \u2022
# Module 7_ APCalcBC 7-6 Improper Integrals.pptx - 7.6...
• 14
This preview shows page 1 - 14 out of 14 pages.
7.6 Improper Integrals 1/22 Do Now Evalu... | 2021-06-14T22:19:07 | {
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http://tasks.illustrativemathematics.org/content-standards/HSS/ID/C/7/tasks/1028 | Engage your students with effective distance learning resources. ACCESS RESOURCES>>
Alignments to Content Standards: S-ID.C.7
Medhavi suspects that there is a relationship between the number of text messages high school students send and their academic achievement. To explore this, she asks a random sample of 52 stud... | 2022-08-19T20:09:42 | {
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https://socratic.org/questions/solve-the-equation-4 | # Solve the equation?
## $\sqrt{{x}^{2} + 4 x - 21} + \sqrt{{x}^{2} - x - 6} = \sqrt{6 {x}^{2} - 5 x - 39}$
Jun 25, 2018
$x = 3$
#### Explanation:
$\sqrt{{x}^{2} + 4 x - 21} + \sqrt{{x}^{2} - x - 6} = \sqrt{6 {x}^{2} - 5 x - 39}$
${\left(\sqrt{{x}^{2} + 4 x - 21} + \sqrt{{x}^{2} - x - 6}\right)}^{2} = {\left(\sqr... | 2020-09-19T00:48:09 | {
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https://math.stackexchange.com/questions/3228923/binomial-coefficients-with-variable-in-exponent | Binomial coefficients with variable in exponent
I need to calculate the coefficient of a specific term in a binomial, but how do I do that if the exponent has a variable in it?
For example:
Find the coefficient of $$x^n$$ in the expansion of $$(4x + 5x^2)^{7n}$$
or
Find the coefficient of $$x^5$$ in the expansion ... | 2019-09-15T17:58:01 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.98677... |
https://www.shaalaa.com/question-bank-solutions/in-a-town-there-are-94500-people-2-9-of-them-are-foreigners-6400-are-immigrants-and-the-rest-are-natives-how-many-are-natives-number-system-entrance-exam_106999 | In a town, there are 94500 people. 2/9 of them are foreigners, 6400 are immigrants and the rest are natives. How many are natives? - Mathematics
MCQ
In a town, there are 94500 people. 2/9 of them are foreigners, 6400 are immigrants and the rest are natives. How many are natives?
• 67100
• 27400
• 77600
• 88100
S... | 2022-06-25T16:53:32 | {
"domain": "shaalaa.com",
"url": "https://www.shaalaa.com/question-bank-solutions/in-a-town-there-are-94500-people-2-9-of-them-are-foreigners-6400-are-immigrants-and-the-rest-are-natives-how-many-are-natives-number-system-entrance-exam_106999",
"openwebmath_score": 0.3879140615463257,
"openwebmath_perplexity":... |
https://courses.lumenlearning.com/ivytech-collegealgebra/chapter/section-exercises-34/ | ## Section Exercises
1. With what kind of exponential model would half-life be associated? What role does half-life play in these models?
2. What is carbon dating? Why does it work? Give an example in which carbon dating would be useful.
3. With what kind of exponential model would doubling time be associated? What ... | 2020-02-26T02:10:04 | {
"domain": "lumenlearning.com",
"url": "https://courses.lumenlearning.com/ivytech-collegealgebra/chapter/section-exercises-34/",
"openwebmath_score": 0.6015143990516663,
"openwebmath_perplexity": 569.3432069251597,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.98677717863... |
https://naturale0.github.io/nonparametric/asymptotics_is_strange | Asymptotics is strange...
It is a useful trick to “flip” the denominator into numerator when it comes to proving asymptotic properties of errors. Here’s how to do so. Consider a form
$\frac{1}{b_0 + b_1 h + o(h)},$
where $h \to 0$ and $b_i$’s are non-zero constants. Then
\begin{aligned} &\frac{1}{b_0 + b_1 h + o(h... | 2021-05-06T15:53:11 | {
"domain": "github.io",
"url": "https://naturale0.github.io/nonparametric/asymptotics_is_strange",
"openwebmath_score": 1.000006914138794,
"openwebmath_perplexity": 1082.2505742136825,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9867771786365549,
"lm_q2_score": 0.66192287... |
https://math.stackexchange.com/questions/2834183/minimum-generator-set-for-matrix-algebras | # Minimum generator set for matrix algebras
Let $A\subseteq M_n(\mathbb{R})$ a finite set, where $M_n(\mathbb{R})$ is the set of all $n\times n$ matrices. Let $S(A)$ the generated algebra by $A$.
What is the minimun number of elements of $A$ in order that $S(A)=M_n(\mathbb{R})$?
In other words: what is the minimum $... | 2019-11-20T15:13:41 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2834183/minimum-generator-set-for-matrix-algebras",
"openwebmath_score": 0.7896981835365295,
"openwebmath_perplexity": 43.07784985390621,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.98677717824... |
https://mc-stan.org/docs/2_23/functions-reference/multivariate-gaussian-process-distribution.html | This is an old version, view current version.
## 21.4 Multivariate Gaussian Process Distribution
### 21.4.1 Probability Density Function
If $$K,N \in \mathbb{N}$$, $$\Sigma \in \mathbb{R}^{N \times N}$$ is symmetric, positive definite kernel matrix and $$w \in \mathbb{R}^{K}$$ is a vector of positive inverse scales,... | 2020-08-08T17:29:36 | {
"domain": "mc-stan.org",
"url": "https://mc-stan.org/docs/2_23/functions-reference/multivariate-gaussian-process-distribution.html",
"openwebmath_score": 0.769591212272644,
"openwebmath_perplexity": 1614.1877777597072,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.986777... |
https://mdtpmodules.org/linr/linr-2/linr-1-lesson-4-writing-the-equation-of-a-line/linr-1-lesson-4-try-this-convert-equations-to-standard-form/linr-1-lesson-4-try-this-converting-between-slope-intercept-and-standard-form-solutions/ | # LINR 1 | Lesson 4 | Try This! (Converting between Slope-Intercept and Standard Form Solutions)
Investigate this idea to develop a process for isolating a variable.
1. Use the equation $$3x-2y=6$$.
• Substitute the value $$x=4$$ into the equation $$3x-2y=6$$. Isolate the variable $$y$$ by solving the equation for $... | 2021-01-19T03:21:34 | {
"domain": "mdtpmodules.org",
"url": "https://mdtpmodules.org/linr/linr-2/linr-1-lesson-4-writing-the-equation-of-a-line/linr-1-lesson-4-try-this-convert-equations-to-standard-form/linr-1-lesson-4-try-this-converting-between-slope-intercept-and-standard-form-solutions/",
"openwebmath_score": 0.9586004614830017,
... |
https://blog.zilin.one/2015/02/25/an-upper-bound-on-stirling-number-of-the-second-kind/ | # An Upper Bound on Stirling Number of the Second Kind
We shall show an upper bound on the Stirling number of the second kind, a byproduct of a homework exercise of Probabilistic Combinatorics offered by Prof. Tom Bohman.
Definition. A Stirling number of the second kind (or Stirling partition number) is the number of... | 2019-08-22T18:50:53 | {
"domain": "zilin.one",
"url": "https://blog.zilin.one/2015/02/25/an-upper-bound-on-stirling-number-of-the-second-kind/",
"openwebmath_score": 0.9968483448028564,
"openwebmath_perplexity": 135.92065209767253,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9867771782476948,
"... |
https://deeplearningmath.org/logistic-regression-type-neural-networks.html | # 2 Logistic Regression Type Neural Networks
Learning outcomes from this chapter
• Logistic regression view as a shallow Neural Network
• Maximum Likelihood, loss function, cross-entropy
• Softmax regression/ multinomial regression model as a Multiclass Perceptron.
• Optimisation procedure: gradient descent, stochast... | 2021-03-04T21:37:10 | {
"domain": "deeplearningmath.org",
"url": "https://deeplearningmath.org/logistic-regression-type-neural-networks.html",
"openwebmath_score": 0.935717761516571,
"openwebmath_perplexity": 1866.591018964998,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9867771778588348,
"lm_q... |
https://socratic.org/questions/what-is-the-sum-of-all-odd-numbers-between-0-and-100 | # What is the sum of all odd numbers between 0 and 100?
##### 1 Answer
Sep 17, 2015
First, notice an interesting pattern here:
$1 , 4 , 9 , 16 , 25 , \ldots$
The differences between perfect squares (starting at $1 - 0 = 1$) is:
$1 , 3 , 5 , 7 , 9 , \ldots$
The sum of $1 + 3 + 5 + 7 + 9$ is $25$, the ${5}^{\text{t... | 2019-10-14T23:46:45 | {
"domain": "socratic.org",
"url": "https://socratic.org/questions/what-is-the-sum-of-all-odd-numbers-between-0-and-100",
"openwebmath_score": 0.8993134498596191,
"openwebmath_perplexity": 148.05599096771894,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9867771778588348,
"l... |
https://www.xarg.org/proof/svg-arc-to-gcode-g2-and-g3/ | # Proof: SVG Arc to GCode G2 and G3
The SVG arc command consists of
A rx ry x-axis-rotation large-arc-flag sweep-flag x y
• rx: Ellipse radius of x-axis
• ry: Ellipse radius of y-axis
• x-axis-rotation: Coordinate system rotation in degrees
• large-arc-flag: Flag if large or small circle should be taken
• sweep-flag:... | 2023-01-29T18:14:40 | {
"domain": "xarg.org",
"url": "https://www.xarg.org/proof/svg-arc-to-gcode-g2-and-g3/",
"openwebmath_score": 0.7041487693786621,
"openwebmath_perplexity": 3121.1318181593106,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9867771778588348,
"lm_q2_score": 0.6619228758499942,
... |
https://math.stackexchange.com/questions/1967156/question-about-induction | Prove by induction $w_k = w_{k−2} + k$, for all integers $k \ge 3, w_1 = 1,w_2 = 2$ has an explicit formula $$w_n = \begin{cases} \frac{(n+1)^2}{4}, & \text{if n is odd} \\ \frac n2(\frac n2 + 1), & \text{if n is even} \end{cases}$$
Inductive step for when $n$ is odd:
Suppose $w_k = \frac{(k+1)^2}{4}$ if $k$ is odd. ... | 2020-12-04T00:11:57 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1967156/question-about-induction",
"openwebmath_score": 0.9744769334793091,
"openwebmath_perplexity": 89.45954808242983,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9867771774699746,
"lm_q2_s... |
https://yourgametips.com/miscellaneous/what-is-the-probability-of-drawing-an-ace-from-a-deck-of-52-cards/ | # What is the probability of drawing an ace from a deck of 52 cards?
## What is the probability of drawing an ace from a deck of 52 cards?
The probability of picking up an ace in a 52 deck of cards is 4/52 since there are 4 aces in the deck.
## What is the probability of getting either a spade or a jack when drawing... | 2023-01-27T01:50:46 | {
"domain": "yourgametips.com",
"url": "https://yourgametips.com/miscellaneous/what-is-the-probability-of-drawing-an-ace-from-a-deck-of-52-cards/",
"openwebmath_score": 0.8371797204017639,
"openwebmath_perplexity": 199.34001458755725,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score"... |
https://entucnesi.web.app/954.html | On ideals of rings of fractions and rings of polynomials nai, yuan ting and zhao, dongsheng, kodai mathematical journal, 2015. A ring all of whose ideals are principal is called a principal ideal ring, two important cases are z and kx, the polynomial ring over a field k. In s, we have studied those prime left principal... | 2021-09-18T03:58:05 | {
"domain": "web.app",
"url": "https://entucnesi.web.app/954.html",
"openwebmath_score": 0.8363492488861084,
"openwebmath_perplexity": 229.812329795307,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9867771770811147,
"lm_q2_score": 0.6619228758499942,
"lm_q1q2_score": 0.65... |
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