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https://web2.0calc.com/questions/help_36611 | +0
# help!
0
40
1
Point P is on side $$\overline{AC}$$ of triangle ABC such that $$\angle APB =\angle ABP$$, and$$\angle ABC - \angle ACB = 39^\circ$$ . Find $$\angle PBC$$ in degrees.
Apr 27, 2020 | 2020-06-03 01:25:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000026226043701, "perplexity": 1141.6669800911818}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347426956.82/warc/CC-MAIN-20200602224517-20200603014517-00198.warc.gz"} | 84 |
https://sites.math.rutgers.edu/~bumby/nyntsem/ny201210.html | # Multiplicative representations of integers and Ramsey's theorem
Let ${\mathcal B} = (B_1,\ldots, B_h)$ be an $h$-tuple of sets of positive integers. Let $g_{\mathcal B}(n)$ count the number of representations of $n$ in the form $n = b_1\cdots b_h$, where $b_i \in B_i$ for all $i \in \{1,\ldots, h\}$. It is proved that $\liminf_{n\rightarrow \infty} g_{\mathcal B}(n) \geq 2$ implies $\limsup_{n\rightarrow \infty} g_{\mathcal B}(n) = \infty$.
Mel Nathanson | 2022-07-06 20:10:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9616955518722534, "perplexity": 101.70109716439792}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104676086.90/warc/CC-MAIN-20220706182237-20220706212237-00794.warc.gz"} | 164 |
http://clay6.com/qa/24672/sum-of-n-terms-of-series-s-1-2-2-2-2-3-2-2-4-2-5-2-when-n-is-even-is- | # Sum of n terms of series $\;S=1^2+2(2)^2+3^2+2(4)^2+5^2+\;....\;$ when n is even is :
$(a)\;\frac{1}{4}n(n+2)^2\qquad(b)\;\frac{1}{4}n^2(n+2)\qquad(c)\;\frac{1}{2}n^2(n+1)\qquad(d)\;\frac{1}{2}n(n+1)^2$
Answer : (d) $\;\frac{1}{2}n(n+1)^2$
Explanation : $Let \;n=2m$
$S=\;[1^2+2^2+3^2\;...\;+(2m)^2]+\;[2^2+4^2+6^2+\;...\;(2m)^2]$
$=\frac{1}{6}\;(2m)(2m+1)(4m+1)+\frac{4}{6}\;(m)(m+1)(2m+1)$
$=\frac{1}{3}m(2m+1)\;[4m+1+2m+2]$
$=\frac{1}{2}n(n+1)^2\;.$ | 2018-06-19 19:54:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8310195207595825, "perplexity": 887.5749658217723}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267863119.34/warc/CC-MAIN-20180619193031-20180619213031-00524.warc.gz"} | 283 |
http://mathhelpforum.com/higher-math/217084-help-me-solve-print.html | # Help me solve this
find Z with $z^3 = \frac{1 + i}{\sqrt{2}}$
Change to polar form, then use $\sqrt[3]{r(cos(\theta)+ i sin(\theta))}= r^{1/3}(cos(\theta/3)+ i sin(\theta/3))$ | 2017-12-15 18:37:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9773075580596924, "perplexity": 2812.1774987410017}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948577018.52/warc/CC-MAIN-20171215172833-20171215194833-00382.warc.gz"} | 70 |
http://specialfunctionswiki.org/index.php/Euler_phi | # Euler phi
Jump to: navigation, search
The Euler phi function (not to be confused with the Euler totient) is defined for $q \in \mathbb{C}$ with $|q|<1$ by $$\phi(q) = \displaystyle\prod_{k=1}^{\infty} 1-q^k.$$
# References
Number theory functions | 2018-04-22 04:21:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.989483654499054, "perplexity": 2759.4366076064202}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945493.69/warc/CC-MAIN-20180422041610-20180422061610-00146.warc.gz"} | 82 |
https://www.gradesaver.com/textbooks/math/algebra/algebra-1/chapter-6-systems-of-equations-and-inequalities-cumulative-test-prep-multiple-choice-page-409/13 | Algebra 1
Published by Prentice Hall
Chapter 6 - Systems of Equations and Inequalities - Cumulative Test Prep - Multiple Choice - Page 409: 13
A
Work Step by Step
$y=x+1$ $y=x+2$ The two lines have the same slope but different y-intercepts. The lines don't cross and thus have no solutions.
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 2020-04-02 00:53:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6252148747444153, "perplexity": 1269.5915768095008}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370506477.26/warc/CC-MAIN-20200401223807-20200402013807-00410.warc.gz"} | 116 |
http://www.logic.univie.ac.at/2004/Talk_05-18_a.html | # 2004 seminar talk: Strong Compactness and Stationary Sets
Talk held by John Krueger (KGRC) at the KGRC seminar on 2004-05-18.
### Abstract
I will show how to construct a model in which $\kappa$ is a strongly compact cardinal and the set $S(\kappa,\kappa^+) = \{ a \in P_\kappa \kappa^+ : \ot(a) = (a \cap \kappa)^+ \}$ is non-stationary. | 2020-02-19 20:29:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8014624714851379, "perplexity": 1353.4157192323466}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875144167.31/warc/CC-MAIN-20200219184416-20200219214416-00530.warc.gz"} | 113 |
http://mathhelpforum.com/number-theory/130687-if-n-even.html | # Math Help - if n is even...
1. ## if n is even...
for $n \in \mathbb{Z}$ prove that n is even $\iff \ n -2 [\frac{n}{2}] =0$
2. Originally Posted by flower3
for $n \in \mathbb{Z}$ prove that n is even $\iff \ n -2 [\frac{n}{2}] =0$
Really? $n=2z$ so that $\frac{n}{2}=z$ so that $\left\lfloor\frac{n}{2}\right\rfloor=z\implies2\le ft\lfloor\frac{n}{2}\right\rfloor=2z=n$
3. The other way:
$n-2\lfloor \frac{n}{2} \rfloor = 0 \iff n=2\lfloor \frac{n}{2} \rfloor \implies 2\mid n \implies n$ is even. | 2014-09-16 18:50:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9467847943305969, "perplexity": 1295.3729408858662}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657118950.27/warc/CC-MAIN-20140914011158-00138-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} | 205 |
https://www.aminer.org/pub/5ea6adfa91e011a546871bb3/point-location-and-active-learning-learning-halfspaces-almost-optimally | # Point Location and Active Learning: Learning Halfspaces Almost Optimally
Mahajan Gaurav
Abstract:
Given a finite set $X \subset \mathbb{R}^d$ and a binary linear classifier $c: \mathbb{R}^d \to \{0,1\}$, how many queries of the form $c(x)$ are required to learn the label of every point in $X$? Known as \textit{point location}, this problem has inspired over 35 years of research in the pursuit of an optimal algorithm. Building on the...More
Code:
Data: | 2020-11-28 02:16:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6384004950523376, "perplexity": 781.2778830523572}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141194982.45/warc/CC-MAIN-20201128011115-20201128041115-00715.warc.gz"} | 126 |
https://jeeneetqna.in/1543/relation-between-modulus-modulus-modulus-modulus-rigidity | # Find relation between modulus, If Y → young's modulus, K → Bulk modulus, η → modulus of rigidity
more_vert
Find relation between modulus
If
Y $\to$ young's modulus
K $\to$ Bulk modulus
$\eta$ $\to$ modulus of rigidity
(1) $K={\eta Y\over9\eta-3Y}$
(2) $K={\eta K\over9\eta-3K}$
(3) $K={\eta Y\over9\eta+3Y}$
(4) $K={\eta K\over9\eta+3K}$
more_vert
Properties of solids and liquids, Young's modulus and bulk modulus | 2021-04-20 21:56:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8552802801132202, "perplexity": 5113.347506861331}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039491784.79/warc/CC-MAIN-20210420214346-20210421004346-00549.warc.gz"} | 153 |
http://www.formuladirectory.com/user/formula/200 | HOSTING A TOTAL OF 318 FORMULAS WITH CALCULATORS
## Quick Ratio
The Quick Ratio is used for determining a company's ability to cover its short term debt with assets that can readily be transferred into cash, or quick assets. The Current Liabilities portion references liabilities that are payable within one year
## $\frac{a}{l}$
Here,a=quick assets,l=current liablity
ENTER THE VARIABLES TO BE USED IN THE FORMULA
Similar formulas which you may find interesting. | 2019-02-23 15:10:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6550571322441101, "perplexity": 4181.34205044068}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550249504746.91/warc/CC-MAIN-20190223142639-20190223164639-00242.warc.gz"} | 103 |
https://brilliant.org/problems/a-rather-normal-question/ | # A rather normal question
Calculus Level 4
Let $$P$$ be a point (other than the origin) on the curve $$y = x^{4}$$. Let $$Q$$ be the point where the normal line to the given curve at $$P$$ intersects the $$x$$-axis.
With point $$O$$ being the origin, form the triangle $$OPQ$$. Over all such triangles, what is the minimum value of the ratio of the base length $$OQ$$ to the height of $$\Delta OPQ$$?
× | 2017-10-20 23:48:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8214098215103149, "perplexity": 169.45421476846363}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824471.6/warc/CC-MAIN-20171020230225-20171021010225-00435.warc.gz"} | 113 |
http://clay6.com/qa/52114/if-the-density-of-some-lake-water-is-1-25g-ml-and-contains-92-g-of-na-ions- | Browse Questions
# If the density of some lake water is $1.25g mL^{–1}$ and contains 92 g of $Na^+$ ions per kg of water, calculate the molality of $Na^+$ ions in the lake.
$\begin{array}{1 1}4m\\5m\\6m\\7m\end{array}$
Number of molality = $\large\frac{\text{Mole of }Na^+\text{ ions}}{\text{Mass of water(kg)}}$
92g of $Na^+$ ions =$\large\frac{929}{23gmol^{-1}}$
$\Rightarrow 4$ mole
Therefore molality = 4m | 2017-01-20 16:06:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7555987238883972, "perplexity": 3524.0736468385353}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280835.60/warc/CC-MAIN-20170116095120-00105-ip-10-171-10-70.ec2.internal.warc.gz"} | 148 |
https://cracku.in/13-for-a-sequence-of-real-numbers-x_1x_2x_n-if-x_1-x_-x-cat-2021-slot-2-quant | Question 13
# For a sequence of real numbers $$x_{1},x_{2},...x_{n}$$, If $$x_{1}-x_{2}+x_{3}-....+(-1)^{n+1}x_{n}=n^{2}+2n$$ for all natural numbers n, then the sum $$x_{49}+x_{50}$$ equals
Solution
Now as per the given series :
we get $$x_1=1+2\ =3$$
Now $$x_1-x_2=\ 8$$
so$$x_2=-5$$
Now $$x_1-x_2+x_3\ =\ 15$$
so $$x_3\ =7$$
so we get $$x_n\ =\left(-1\right)^{n+1}\left(2n+1\right)$$
so $$x_{49}\ =\ 99$$ and $$x_{50}\ =-101$$
Therefore $$x_{49\ }+x_{50}\ =-2$$ | 2022-08-13 10:08:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9602159857749939, "perplexity": 212.73981478101288}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571911.5/warc/CC-MAIN-20220813081639-20220813111639-00015.warc.gz"} | 229 |
http://clay6.com/qa/37717/in-a-class-of-50-students-15-are-girls-5-of-the-girls-and-large-frac-of-the | Browse Questions
Home >> AIMS
# In a class of 50 students,15 are girls,5 of the girls and $\large\frac{2}{7}$ of the boys were chosen to represent their class in a game.The total number of students chosen is
$\begin{array}{1 1}(A)\;12&(B)\;15\\(C)\;19&(D)\;25\end{array}$
The total number of students chosen is 15
Hence (B) is the correct answer. | 2017-03-27 04:39:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9850996732711792, "perplexity": 531.2162438991722}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189403.13/warc/CC-MAIN-20170322212949-00146-ip-10-233-31-227.ec2.internal.warc.gz"} | 114 |
http://atekihcan.github.io/CLRS/E04.03-03/ | We saw that the solution of $T(n) = 2T(\lfloor n/2 \rfloor) + n$ is $O(n \lg n)$. Show that the solution of this recurrence is also $\Omega(n \lg n)$. Conclude that the solution is $\Theta(n \lg n)$.
Let us assume $T(n) \ge c (n + b) \lg (n + b)$ for all $n \ge n_0$, where $b$, $c$, and $n_0$ are positive constants.
The last step holds as long as $(n - cn - dc) \ge 0 \implies n \ge cd / (1 - c)$. For example, $d = 0$, $n \ge 1$, and $% $. | 2017-08-17 23:03:52 | {"extraction_info": {"found_math": true, "script_math_tex": 13, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9925447702407837, "perplexity": 23.653864289526553}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886104172.67/warc/CC-MAIN-20170817225858-20170818005858-00071.warc.gz"} | 168 |
https://bigdave1583.wordpress.com/2015/08/ | # Taxi from HELL!!
Ok so I’m running a little late for work so I’m like fuck it! I don’t want to take the subway because it will take to long so I thought I’ll just jump into a cab so I can get there faster. I WAS SOOOOOO WRONG!!!!!!!!!!! This dumb ass cab took the Westside highway at rush hour. FUCKING DUMB ASSSSSSSSSS!!!!!!!! I’m like what the FUCK!! Are you doing? he’s like this is the quickest way. Quickest way my ass this is why Urber is taking over and these cabs are going to be long forgotten. | 2021-10-28 05:27:48 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8418068885803223, "perplexity": 3277.7850437024726}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588257.34/warc/CC-MAIN-20211028034828-20211028064828-00080.warc.gz"} | 136 |
https://www.gradesaver.com/textbooks/math/calculus/calculus-10th-edition-anton/chapter-1-limits-and-continuity-1-2-computing-limits-exercises-set-1-2-page-70/35 | ## Calculus, 10th Edition (Anton)
Let $f(x) = x, \, g(x) = x^2$. $\lim\limits_{x \to 0} f(x) = \lim\limits_{x \to 0} g(x) = \infty$. But, $$\lim\limits_{x \to 0} \frac{f(x)}{g(x)} = \lim\limits_{x \to 0} \frac {x}{x^2} = \lim\limits_{x \to 0} \frac 1x = \infty$$ That is, $\lim\limits_{x \to 0} \frac{f(x)}{g(x)} \ne 1$. | 2019-11-15 15:46:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9975611567497253, "perplexity": 3151.479549850326}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668682.16/warc/CC-MAIN-20191115144109-20191115172109-00527.warc.gz"} | 160 |
https://economics.stackexchange.com/tags/game/new | # Tag Info
The intersection itself is not terribly interesting, what matters here is only that it is not empty- that it contains some state. To know event $E$ means that one does not consider it possible that the event $E$ does not obtain and that $E$ does indeed obtain. Since the true state is always considered possible, that $i$ knows $E$ at $\omega$ means that \$\... | 2021-01-19 20:42:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.39069756865501404, "perplexity": 355.99401397206844}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703519784.35/warc/CC-MAIN-20210119201033-20210119231033-00168.warc.gz"} | 87 |
http://mathhelpforum.com/algebra/72484-binomial-expansion.html | # Math Help - Binomial expansion
1. ## Binomial expansion
Is this the correct expansion $(2 - x)^{-1} = \frac{1}{2} + x + \frac{x^2}{4}$
2. No.
$(2-x)^{-1}=\frac{1}{2-x}$
3. I mean when you expand it up to x^2 using binomial expansion | 2015-03-28 14:58:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.769931972026825, "perplexity": 4339.120611687419}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131297587.67/warc/CC-MAIN-20150323172137-00068-ip-10-168-14-71.ec2.internal.warc.gz"} | 85 |
http://mathoverflow.net/revisions/106880/list | MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
The proof of Brouwer fixed point theorem by using fundamental group of $S^1$ is equal to $\mathbb{Z}$, while the fundamental group of $D^2$ is trivial. | 2013-06-19 15:12:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7514677047729492, "perplexity": 323.4527834186589}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368708808767/warc/CC-MAIN-20130516125328-00092-ip-10-60-113-184.ec2.internal.warc.gz"} | 80 |
http://answers.gazebosim.org/questions/12562/revisions/ | I have a robotic arm in Gazebo from which I am already reading the angles (i.e. GetAngle(0).Radian()) as well as the velocity (i.e. GetVelocity(0)) from each joint. Now I also need to get the acceleration from the joints. | 2020-02-22 11:19:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8014712929725647, "perplexity": 707.4270361403862}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145657.46/warc/CC-MAIN-20200222085018-20200222115018-00438.warc.gz"} | 59 |
https://proofwiki.org/wiki/Set_Equivalence_of_Regular_Representations | Set Equivalence of Regular Representations
Theorem
If $S$ is a finite subset of a group $G$, then:
$\card {a \circ S} = \card S = \left|{S \circ a}\right|$
That is, $a \circ S$, $S$ and $S \circ a$ are equivalent: $a \circ S \sim S \sim S \circ a$.
Proof
Follows immediately from the fact that both the left and right regular representation are permutations, and therefore bijections.
$\blacksquare$ | 2020-06-01 07:13:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9575698375701904, "perplexity": 254.547352983503}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347415315.43/warc/CC-MAIN-20200601071242-20200601101242-00261.warc.gz"} | 119 |
https://wikieducator.org/Cubic_identity_1 | # Cubic identity 1
Objective
To verify $(a+b)^3 = a^3+3a^2b+3ab^2+b^3$ using unit cubes
27 Unit cubes
## What is a unit cube?
A unit cube is nothing but a cube all of whose sides are 1 unit long as shown below.
This is a unit cube
1. We say its dimension is 1 X 1 X 1.
2. The volume of a 3-dimensional unit cube is 1 cubic unit.
3. By joining unit cubes we can form cubes and cuboids of varied dimension. | 2021-01-25 06:20:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6789743900299072, "perplexity": 1030.2152083454089}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703565376.63/warc/CC-MAIN-20210125061144-20210125091144-00763.warc.gz"} | 127 |
https://www.physicsforums.com/threads/conservative-electric-field.634094/ | # Conservative electric field
## Homework Statement
Is the field (given below) in a simply connected region of space conservative
E=A[yex+xey]
## The Attempt at a Solution
What is a conservative electric field & how do I find whether it is . . . . .
## Answers and Replies
Ah!
If a vector field is conservative then the integral round a closed loop in the domain is zero.
Oops, sorry. | 2021-05-17 19:42:07 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8440797924995422, "perplexity": 779.876538296789}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243992440.69/warc/CC-MAIN-20210517180757-20210517210757-00263.warc.gz"} | 88 |
http://mathhelpforum.com/math-topics/125058-how-pronounce-cesaro.html | # Thread: How to pronounce "Cesàro"?
1. ## How to pronounce "Cesàro"?
That is, the name in "Cesàro summability". Thanks!
2. Originally Posted by zzzhhh
That is, the name in "Cesàro summability". Thanks!
Check this out. I often want to know how to pronouce names, so I go here...
Pronunciation Guide for Mathematics | 2018-04-22 05:42:05 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8398310542106628, "perplexity": 9995.799674075339}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945493.69/warc/CC-MAIN-20180422041610-20180422061610-00312.warc.gz"} | 91 |
https://www.studypug.com/algebra-help/sigma-notation | # Sigma notation - Sequences and Series
### Sigma notation
Don't you find it tiring when we express a series with many terms using numerous addition and/or subtraction signs? Don't you wish that we have something to symbolise this action? Well we have a solution, introducing the "Sigma Notation"! In this section, we will learn how to utilise the sigma notation to represent a series, as well as how to evaluate it. | 2020-01-22 16:55:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 20, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9040955305099487, "perplexity": 964.8296472748646}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250607314.32/warc/CC-MAIN-20200122161553-20200122190553-00007.warc.gz"} | 90 |
https://byjus.com/question-answer/what-will-be-the-slope-of-line-having-the-equation-as-y-2x-5-1/ | Question
# What will be the slope of line having the equation as $$(y+2x)=5$$ ?
Solution
## $$y+2x=5$$ can be written as $$y=-2x+5$$ which is of form $$y=mx+c$$ Comparing we get, $$m=-2$$So slope is$$(-2)$$Physics
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View More | 2022-01-21 08:49:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5614970326423645, "perplexity": 2009.2358454560563}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320302740.94/warc/CC-MAIN-20220121071203-20220121101203-00335.warc.gz"} | 97 |
https://answerriddle.com/answer-which-one-of-the-following-jazz-musicians-served-in-the-u-s-army-in-the-1940s-and-helped-form-wolfpack-one-of-first-integrated-bands-in-the-u-s-military/ | # Answer: Which one of the following jazz musicians served in the U.S. Army in the 1940s and helped form Wolfpack, one of first integrated bands in the U.S. Military?
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The Answer: Dave Brubeck. | 2021-05-07 09:25:21 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8656054139137268, "perplexity": 3708.024402653616}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988775.80/warc/CC-MAIN-20210507090724-20210507120724-00526.warc.gz"} | 113 |
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https://www.physicsforums.com/threads/transformation-that-takes-all-point-on-parabola-onto-unit-circle.312638/ | # Transformation that takes all point on parabola onto unit circle
## Homework Statement
Show that the transformation
Code:
_ __ _ __
| 0 -2 1 || x |
| -2 2 0 || y |
|_2 -2 1 _||_ 1_|
takes all points on parabola y2=x onto the unit circle x2+y2=1
## The Attempt at a Solution
I can't find out what to do I just need a hint about how to get started about doing this. | 2021-04-18 20:26:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22586607933044434, "perplexity": 831.7239442768222}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038860318.63/warc/CC-MAIN-20210418194009-20210418224009-00537.warc.gz"} | 124 |
https://boredofstudies.org/threads/electromagnetism-help.391444/ | # Electromagnetism help (1 Viewer)
#### zacn
##### New Member
Anyone help with this question please.
#### Canteen
##### New Member
$\bg_white \frac{F}{\ell}=k\frac{I^2}{d} \implies I=\sqrt{\frac{Fd}{\ell k}}\ \ \left(\textrm{where } k\textrm{ is } \frac{\mu_0}{2\pi}\right)$
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https://brainiak.in/491/c-the-mass-of-an-atom-of-hydrogen-is-1-008-u-what-is-the-mass-of-18-atoms-of-hydrogen | 0 votes
6 views
4 ) solve problems
C. The mass of an atom of hydrogen is 1.008 u. What is the mass of 18 atoms of hydrogen.
reopened | 6 views
## 1 Answer
0 votes
Best answer
Given : mass of hydrogen = 1.008 u
To find : mass of 18 atoms of hydrogen
Solution :
mass of 18 atoms of hydrogen = 18 $$\times$$ mass of hydrogen
=$$18\times 1.008 u=18.144u$$
$$\therefore$$ mass of 18 atoms of hydrogen is 18.144 u
by (5.4k points) | 2021-06-15 09:47:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3808462917804718, "perplexity": 5712.851565832943}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487620971.25/warc/CC-MAIN-20210615084235-20210615114235-00610.warc.gz"} | 148 |
https://www.gradesaver.com/textbooks/math/algebra/algebra-a-combined-approach-4th-edition/chapter-12-section-12-7-common-logarithms-natural-logarithms-and-change-of-base-practice-page-885/2 | ## Algebra: A Combined Approach (4th Edition)
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https://brilliant.org/problems/quadratic-non-residues/ | Find the smallest $$n$$ such that for some prime $$p$$, at least $$20$$ of the numbers $$1,2,...,n$$ are quadratic non-residues modulo $$p$$.
Details and assumptions
$$k$$ is a quadratic residue modulo $$p$$ if there exists an integer $$j$$ such that $$j^2 \equiv k \pmod{p}$$.
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× | 2017-07-28 15:06:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.957099199295044, "perplexity": 36.33779788712526}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500550969387.94/warc/CC-MAIN-20170728143709-20170728163709-00057.warc.gz"} | 126 |
http://mathhelpforum.com/trigonometry/176389-help-isolate.html | # Math Help - Help to isolate θ
1. ## Help to isolate θ
Isolate θ
cos 2θ = cos y cos x
I have no clue where to start, some help would be great.
Nvm i figured it out
2. Take inverse $\cos$ of both sides then divide by 2.
What do you get? | 2015-03-29 16:10:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7548320293426514, "perplexity": 2131.1105043604416}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131298576.76/warc/CC-MAIN-20150323172138-00056-ip-10-168-14-71.ec2.internal.warc.gz"} | 76 |
http://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-6th-edition/chapter-5-section-5-5-the-greatest-common-factor-and-factoring-by-grouping-exercise-set-page-295/63 | Chapter 5 - Section 5.5 - The Greatest Common Factor and Factoring by Grouping - Exercise Set: 63
(2x + 3y)(x + 2)
Work Step by Step
1. Rearrange 2$x^{2}$ + 3xy + 4x + 6y = 2$x^{2}$ + 4x + 3xy + 6y 2. Factor out the GCF from the two groups of two monomials. 2x(x + 2) + 3y(x + 2) 3. Use the distributive property to simplify. (2x + 3y)(x + 2)
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 2017-03-27 10:57:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5507827401161194, "perplexity": 1115.185062451349}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189471.55/warc/CC-MAIN-20170322212949-00206-ip-10-233-31-227.ec2.internal.warc.gz"} | 178 |
https://qsimfp.org/feedback/add | # Give us some feedback
• Enter a few-word description of the feedback
• Enter a the feedback description here | 2022-05-20 13:15:55 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9682134985923767, "perplexity": 8777.902250414361}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662532032.9/warc/CC-MAIN-20220520124557-20220520154557-00720.warc.gz"} | 23 |
https://www.gradesaver.com/textbooks/math/algebra/algebra-and-trigonometry-10th-edition/chapter-2-2-1-linear-equations-in-two-variables-2-1-exercises-page-170/49 | ## Algebra and Trigonometry 10th Edition
y = -$\frac{1}{2}$x - 2
Point: [2,-3]; m = $-\frac{1}{2}$ y - (-3) = $-\frac{1}{2}$(x-2) y + 3 = $-\frac{1}{2}$ + 1 y = -$\frac{1}{2}$x - 2 | 2020-09-27 04:24:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23596473038196564, "perplexity": 3148.477013009751}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400250241.72/warc/CC-MAIN-20200927023329-20200927053329-00335.warc.gz"} | 92 |
http://openstudy.com/updates/55c4a088e4b0f6bb86c3d9e2 | ## anonymous one year ago can someone help me find an equation for the inverse of the function. f(x)=2x -3^x/4
1. anonymous
Is this your equation? $$\huge f(x) = -3^{\frac{x}{4}} + 2x$$ Or is it this one $$\huge f(x) = -\frac{3^{x}}{4} + 2x$$
2. anonymous
Or is this your equation $$\huge f(x) = \frac{-3^{x} + 2x}{4}$$
Find more explanations on OpenStudy | 2017-01-20 16:17:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5877249240875244, "perplexity": 1805.624856907995}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280835.60/warc/CC-MAIN-20170116095120-00572-ip-10-171-10-70.ec2.internal.warc.gz"} | 128 |
http://www.piday.org/calculators/compound-interest-calculator/ | Compound Interest Calculator
I want to calculate:
Input known variables:
VariablePeriod
% per year
Show me the solution without an explaination
Explanation
Problem
Problem goes here
Result
Result goes here
Explanation
$${A = P(1 + \frac{r}{n})^{n.t} }$$
A = total amount
P = principal or amount of money deposited,
r = annual interest rate
n = number of times compounded per year
t = time in years
In this example we have
After plugging the given information we have: | 2019-07-15 17:57:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8000019788742065, "perplexity": 7872.810830091278}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195523840.34/warc/CC-MAIN-20190715175205-20190715201205-00208.warc.gz"} | 117 |
https://web2.0calc.com/questions/urgent-please-help-discounts | +0
+1
120
1
An item is regularly priced at \$65. It is now priced at a discount of 55% off the regular price. Find the price now.
Jan 25, 2019
$$55\% \text{ off means you pay }(100\%-55\%) = 45\%\\ 45\% \text{ of }\65 = (0.45)65 = \29.25$$ | 2019-06-18 07:47:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2886596918106079, "perplexity": 3689.9768718260952}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998690.87/warc/CC-MAIN-20190618063322-20190618085322-00406.warc.gz"} | 95 |
http://mathhelpforum.com/statistics/91883-cube.html | # Math Help - Cube
1. ## Cube
Select up 3 vertices of a cube. What is the probability that they belong to the same face?
2. Originally Posted by Apprentice123
Select up 3 vertices of a cube. What is the probability that they belong to the same face?
There are eight vertices of a cube..
How many set of three vertices are there?
How many of those 3-sets have all three vertices in the same face of the cube? | 2015-05-27 07:59:37 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8165097236633301, "perplexity": 356.96606874727905}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207928923.21/warc/CC-MAIN-20150521113208-00286-ip-10-180-206-219.ec2.internal.warc.gz"} | 98 |
https://www.physicsforums.com/threads/help-with-a-riemann-surface.368162/ | Help with a Riemann surface
1. Jan 8, 2010
wofsy
I am having trouble describing the Riemann surface of log(z) + log(z-a)
2. Jan 9, 2010
mathman
I am very rusty on this subject, but did you try working with the combined log ?
[log(z2 - za)]
Last edited: Jan 9, 2010 | 2017-10-20 18:19:00 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8689578771591187, "perplexity": 2086.766999920377}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824293.62/warc/CC-MAIN-20171020173404-20171020193404-00772.warc.gz"} | 89 |
https://www.gradesaver.com/textbooks/math/algebra/elementary-algebra/chapter-3-equations-and-problem-solving-3-3-more-on-solving-equations-and-problem-solving-problem-set-3-3-page-115/50 | ## Elementary Algebra
The formula for the volume of a right circular cone is: V = $\frac{1}{3}$ $\times$ $\pi$ $\times$ $r^{2}$ $\times$ h Substitute 324$\pi$ for V and 9 for r to obtain: 324$\pi$ = $\frac{1}{3}$ $\times$ $\pi$ $\times$ $9^{2}$ $\times$ h 324$\pi$ = $\frac{1}{3}$ $\times$ $\pi$ $\times$ 81 $\times$ h Multiply both sides by 3 972$\pi$ = $\pi$ $\times$ 81 $\times$ h Divide both sides by 81$\pi$ h = 12 | 2018-12-16 06:45:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8177433609962463, "perplexity": 269.48093237454935}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376827281.64/warc/CC-MAIN-20181216051636-20181216073636-00024.warc.gz"} | 155 |
https://cameramath.com/expert-q&a/Algebra/Determine-the-axis-of-symmetry-of-the-function-below-Determine-the-axis | ### Still have math questions?
Algebra
Question
Determine the axis of symmetry of the function below
$$y=x^2-7x+12$$
$$x=\frac{7}{2}$$ | 2022-01-21 17:01:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4749504029750824, "perplexity": 3208.7936348674925}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303512.46/warc/CC-MAIN-20220121162107-20220121192107-00617.warc.gz"} | 44 |
https://csedoubts.gateoverflow.in/2777/tspgecet-2019-cse-18 | Given $R = ABCDE$ and FD set $\left\{\begin{matrix} Ab \rightarrow CD,\\ E \rightarrow A,\\ D \rightarrow E\end{matrix}\right.$. If we decompose into BCNF how many tables will we get?
1. $3$
2. $5$
3. $4$
4. $2$ | 2019-08-23 22:31:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9613962173461914, "perplexity": 1999.7663256233166}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027319082.81/warc/CC-MAIN-20190823214536-20190824000536-00443.warc.gz"} | 77 |
https://math.stackexchange.com/questions/3221497/red-black-tree-insertion-deletion-complexity-proof | Red-Black-Tree Insertion & Deletion Complexity proof
I'm struggling with two propositions in my algorithms book. I'm unsure how to proof this. The insertion is abolutely logical that it takes up to O(log(n)) recoloring and at most one restructuring (as the BT is already soerted befor its inserted). However, I'm unsure how to proof this. Can someone help?
Tarjan, Robert. (1983). Updating a balanced search tree in O(1) rotations. | 2019-07-17 08:51:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8772047758102417, "perplexity": 3009.1299926429874}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525133.20/warc/CC-MAIN-20190717081450-20190717103450-00117.warc.gz"} | 104 |
https://socratic.org/questions/an-isotope-of-iron-has-28-neutrons-if-the-atomic-mass-of-the-isotope-is-54-how-m | # An isotope of iron has 28 neutrons. If the atomic mass of the isotope is 54, how many protons does it have?
Nov 1, 2016
The iron atom is characterized by an atomic number, "Z=26. That is every iron nucleus contains $26$ protons, 26, massive, positively charged, nuclear particles, by definition.
Of course, the nucleus also contains 28 neutrons, 28 neutral, massive nuclear particles, to give the ""^54Fe isotope, which is about 4% abundant, check on this. | 2019-09-21 06:48:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 3, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4044952094554901, "perplexity": 2721.976930411846}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574286.12/warc/CC-MAIN-20190921063658-20190921085658-00105.warc.gz"} | 123 |
http://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-12th-edition/chapter-4-section-4-4-multiplying-polynomials-4-4-exercises-page-304/13 | ## Intermediate Algebra (12th Edition)
$18k^4+12k^3+6k^2$
Using $a(b+c)=ab+ac$ or the Distributive Property, the product of the given expression, $6k^2(3k^2+2k+1) ,$ is \begin{array}{l}\require{cancel} 6k^2(3k^2)+6k^2(2k)+6k^2(1) \\\\= 18k^4+12k^3+6k^2 .\end{array} | 2018-02-21 01:37:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.995492696762085, "perplexity": 9960.011379676178}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813187.88/warc/CC-MAIN-20180221004620-20180221024620-00174.warc.gz"} | 126 |
http://jokerwang.com/wp-content/one/278.html | In trapezoid $$ABCD$$, leg $$\overline{BC}$$ is perpendicular to bases $$\overline{AB}$$ and $$\overline{CD}$$, and diagonals $$\overline{AC}$$ and $$\overline{BD}$$ are perpendicular. Given that $$AB=\sqrt{11}$$ and $$AD=\sqrt{1001}$$, find $$BC^2$$.
(第十八届AIME2 2000 第8题) | 2017-06-27 17:16:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6703083515167236, "perplexity": 456.0896954970325}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128321497.77/warc/CC-MAIN-20170627170831-20170627190831-00370.warc.gz"} | 109 |
https://socratic.org/questions/is-sulfur-a-nonmetal | # Is sulfur a nonmetal?
Sulfur is an abundant non-metal, and one of the few elements that can found naturally in its elemental form. Under normal conditions, sulfur occurs as the ${S}_{8}$ molecule, a bright yellow powder. | 2020-10-28 03:15:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 1, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5184661746025085, "perplexity": 4132.344560504943}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107896048.53/warc/CC-MAIN-20201028014458-20201028044458-00282.warc.gz"} | 51 |
https://www.gktoday.in/question/a-and-b-can-do-a-piece-of-work-in-12-days-b-and-c | A and B can do a piece of work in 12 days. B and C in 8 days and C and A in 6 days. How long would B take to do the same work alone ?
[A] 24 days
[B] 32 days
[C] 40 days
[D] 48 days | 2018-05-23 03:38:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 7, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35813963413238525, "perplexity": 317.62534338110237}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794865411.56/warc/CC-MAIN-20180523024534-20180523044534-00386.warc.gz"} | 65 |
http://mathhelpforum.com/algebra/34607-simultaneous-equation-help-please.html | 1. ## Simultaneous Equation Help Please!
y=2x+3
x²+y²=2
i get
x²+(2x+3)=2 then,
x²+(2x+3)(2x+3)=2 then,
x²+4x²+12x+9=2
Then im stuck i realise it's a quadratic equation (4x²+12x+9) but i don't know where to go from here.
Help greatly appreciated x
2. Hello,
(4x²+12x+9)
this is equal to:
(2x)²+2*3*2x+3²
If a=2x and b=3
You have a²+2ab+b², which is (a+b)²
3. Move everything to one side:
$5x^{2} + 12x + 7 = 0$
Factor and see what you get
4. thanks | 2013-12-06 07:12:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5495392680168152, "perplexity": 7813.919013181457}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163049948/warc/CC-MAIN-20131204131729-00027-ip-10-33-133-15.ec2.internal.warc.gz"} | 202 |
https://socratic.org/questions/what-is-formal-charge-how-is-it-found | # What is formal charge? How is it found?
Aug 16, 2016
#### Answer:
Formal charge is the charge left on an atom when all the bonding electrons are removed. | 2019-08-25 05:16:44 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8620205521583557, "perplexity": 3424.8666592329873}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027323067.50/warc/CC-MAIN-20190825042326-20190825064326-00270.warc.gz"} | 40 |
https://www.thejournal.club/c/paper/55086/ | #### Lower bounds for testing digraph connectivity with one-pass streaming algorithms
##### Glencora Borradaile, Claire Mathieu, Theresa Migler
In this note, we show that three graph properties - strong connectivity, acyclicity, and reachability from a vertex $s$ to all vertices - each require a working memory of $\Omega (\epsilon m)$ on a graph with $m$ edges to be determined correctly with probability greater than $(1+\epsilon)/2$.
arrow_drop_up | 2022-08-11 02:33:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5885886549949646, "perplexity": 1829.9139168956642}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571232.43/warc/CC-MAIN-20220811012302-20220811042302-00136.warc.gz"} | 101 |
https://brilliant.org/problems/something-interesting-on-cubes/ | # Something interesting in cubes
Algebra Level 4
$\large 8x^{3}-12x^{2}-6x-1=0$
If the value of a real root that satisfy the equation above can be expressed as
$\large \dfrac{\sqrt[3]{a}+\sqrt[3]{b}+1}{c}$
where $$a,b$$ and $$c$$ are positive integers, find the value of $$a+b+c$$.
× | 2017-05-30 10:55:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9318976998329163, "perplexity": 250.04256940453234}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463615093.77/warc/CC-MAIN-20170530105157-20170530125157-00430.warc.gz"} | 98 |
https://ask.sagemath.org/questions/7826/revisions/ | # Revision history [back]
### latex typesetting for derivatives like g'
When i try:
f(x) = function('f',x)
g = diff(f(x),x)
latex(g)
I get: D[0]\left(f\right)\left(x\right)
But i would like to get something like: g'\left(x\right)
How can i do this with sage? | 2021-10-24 20:51:45 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9391584396362305, "perplexity": 12395.161280884839}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587606.8/warc/CC-MAIN-20211024204628-20211024234628-00415.warc.gz"} | 81 |
http://clay6.com/qa/tag/p195 | # Recent questions tagged p195
Questions from:
### Find the equation of the curve through the point (1,0) if the slope of the tangent to the curve at any point (x,y) is $\Large \frac{y-1}{x^2+x}.$
To see more, click for the full list of questions or popular tags. | 2019-11-15 13:27:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19962969422340393, "perplexity": 273.7204929339274}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668644.10/warc/CC-MAIN-20191115120854-20191115144854-00009.warc.gz"} | 73 |
https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-fractions-on-the-number-line/e/fractions_on_the_number_line_2 | Unit fractions on the number line
Use unit fractions to think about the location of other fractions on the number line.
Problem
Move the dot to start fraction, 2, divided by, 4, end fraction on the number line. | 2016-10-01 13:58:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5516324639320374, "perplexity": 1319.655311972566}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738662882.88/warc/CC-MAIN-20160924173742-00030-ip-10-143-35-109.ec2.internal.warc.gz"} | 48 |
https://brilliant.org/wiki/if-the-derivative-of-fx-is-fx-is-it-true-that-int/?subtopic=sequences-and-limits&chapter=common-misconceptions-calculus | # If F(x) is the antiderivative of f(x), is it true that $\int_a^b$f(x)dx=F(b)-F(a)?
Cite as: If F(x) is the antiderivative of f(x), is it true that $\int_a^b$f(x)dx=F(b)-F(a)?. Brilliant.org. Retrieved from https://brilliant.org/wiki/if-the-derivative-of-fx-is-fx-is-it-true-that-int/
× | 2022-06-27 02:38:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 27, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.717947781085968, "perplexity": 1974.4112733818902}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103324665.17/warc/CC-MAIN-20220627012807-20220627042807-00525.warc.gz"} | 100 |
https://homework.cpm.org/category/CC/textbook/cca2/chapter/4/lesson/4.2.1/problem/4-73 | ### Home > CCA2 > Chapter 4 > Lesson 4.2.1 > Problem4-73
4-73.
Solve the following absolute value inequalities. Homework Help ✎
1. $| x - 4 | < 9$
2. $| \frac { 1 } { 2 } x - 45 | \geq 80$
3. $| 2 x - 5 | \leq 2$
See problem 4-66 for additional examples.
−5 < x < 13
See part (a).
x ≥ 250 or x ≤ −70
See part (a). | 2019-08-21 14:06:05 | {"extraction_info": {"found_math": true, "script_math_tex": 3, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4711969792842865, "perplexity": 14408.921025041005}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027316021.66/warc/CC-MAIN-20190821131745-20190821153745-00409.warc.gz"} | 134 |
https://www.giancolianswers.com/giancoli-physics-7th-edition-solutions/chapter-8/problem-70 | ## You are here
Hi aheumangutman, the position of the axis of rotation affects which equation to use. The textbook has some good illustrations on pg. 210 in Figure 8-20. This particular question says the axis of rotation is positioned at the center of the rod, which is what makes the equation $I=\dfrac{1}{12}ML^2$. | 2022-08-15 18:24:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2527123987674713, "perplexity": 224.48606808626857}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572198.93/warc/CC-MAIN-20220815175725-20220815205725-00409.warc.gz"} | 81 |
https://socratic.org/questions/54b17273581e2a2c83c2bf1c | # A sphere made out of a material that has a density of "2.7 g cm"^(-3) has a mass of "82 g". What is the radius of the sphere?
Jan 10, 2015
$\mathrm{de} n s i t y = \frac{m a s s}{v o l u m e}$
$V o l u m e = \frac{m a s s}{\mathrm{de} n s i t y}$
$V o l u m e = \frac{82}{2.7} = 30.37 c {m}^{3}$
The volume of a sphere is given by:
$V = \frac{4}{3} \pi {r}^{3}$
So ${r}^{3} = \frac{3 V}{4 \pi} = \frac{3 \times 30.37}{4 \times 3.142} = 1.274$
$r = 1.084 c m$ | 2019-11-20 19:03:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5357965230941772, "perplexity": 703.6133238431792}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670601.75/warc/CC-MAIN-20191120185646-20191120213646-00463.warc.gz"} | 213 |
https://community.wolfram.com/groups/-/m/t/2158533?p_p_auth=6as0VAZ7 | # Custom attributes to variables/ Defining custom domains?
Posted 1 year ago
1294 Views
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3 Total Likes
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Hi, I'm looking to see if there is a way to add custom attributes to variables in Mathematica. Or alternately being able to define manifolds. For instance, I want to see I can add assumptions such as, x \in S^2 or R \in SO(3)Then later define operations suitable to the domain type. Any help is appreciated! Thank you | 2022-01-28 05:01:50 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9626548886299133, "perplexity": 1390.7249514477858}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305420.54/warc/CC-MAIN-20220128043801-20220128073801-00086.warc.gz"} | 106 |
https://freshergate.com/arithmetic-aptitude/numbers/discussion/321 | Home / Arithmetic Aptitude / Numbers :: Discussion
### Discussion :: Numbers
1. What least number must be subtracted from 13601, so that the remainder is divisible by 87 ?
2. A. 23 B. 31 C. 29 D. 37 E. 49
Explanation :
87) 13601 (156
87
----
490
435
----
551
522
---
29
---
Therefore, the required number = 29.
Be The First To Comment | 2022-08-11 15:05:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34228673577308655, "perplexity": 4555.632595826697}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571472.69/warc/CC-MAIN-20220811133823-20220811163823-00284.warc.gz"} | 104 |
https://www.cymath.com/blog/2020-07-06 | # Problem of the Week
## Updated at Jul 6, 2020 10:17 AM
How can we solve for the derivative of $${v}^{6}+7v$$?
Below is the solution.
$\frac{d}{dv} {v}^{6}+7v$
1 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$6{v}^{5}+7$Done6*v^5+7 | 2020-08-07 23:24:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5812157988548279, "perplexity": 3252.8209959068336}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439737233.51/warc/CC-MAIN-20200807231820-20200808021820-00041.warc.gz"} | 111 |
https://brilliant.org/problems/wished-to-have-a-transformation-formula-for/ | # Transforming Tangents?
Geometry Level 3
$\large \tan70^\circ - \tan50^\circ + \tan10^\circ$
The expression above has a closed form, find this closed form.
Give your answer to 2 decimal places.
× | 2020-06-06 05:45:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5353964567184448, "perplexity": 5003.3291775785365}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348509972.80/warc/CC-MAIN-20200606031557-20200606061557-00132.warc.gz"} | 54 |
http://gooddownloadsoftwarefast.us/2018/01/13/adelle-font-download-zip_so/ | Posted on
And what I assume you shall assumeLinks to Japanese typography compiled by adelle font download zip Luc Devroye 1 I celebrate myself. For every atom belonging to me as good belongs to you. .I loafe and invite my soul
Links to Japanese typography compiled by Luc Devroye 1 I celebrate myself. And what I assume you shall assume For every adelle font download zip atom belonging to me as good belongs to you. .I loafe and invite my soul and sing myself | 2018-01-17 23:37:14 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9531278014183044, "perplexity": 13162.766490099853}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887024.1/warc/CC-MAIN-20180117232418-20180118012418-00529.warc.gz"} | 103 |
https://datascience.stackexchange.com/questions/66638/pretrained-handwritten-ocr-model/66885 | # Pretrained handwritten OCR model
I've been looking around for pretrained models dedicated to handwritten OCR. So far I've found very little. Could you please share, if you know any? I find tesseract hard to parse anything that isn't arial and perfectly captured.
## 1 Answer
Discover open-source deep learning code and pretrained models at Model Zoo
These are pre-trained sources available in the Github.
Some Helpful Resources: | 2020-07-03 20:15:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.211028054356575, "perplexity": 7669.149742263332}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655882934.6/warc/CC-MAIN-20200703184459-20200703214459-00293.warc.gz"} | 87 |
http://mathhelpforum.com/calculus/35374-parametric-plane-equation-print.html | # Parametric Plane Equation
• April 21st 2008, 11:55 AM
Del
Parametric Plane Equation
Find the parametric equations for the line through the point P = (0, 1, -3) that is perpendicular to the plane https://webwork.math.lsu.edu/webwork...c0ae5b1b41.png
Use "t" as your variable, t = 0 should correspond to P, and the velocity vector of the line should be the same as the standard normal vector of the plane.
x = ?
y = ?
z = ?
If $ax+by+cz+d=0$ is a plane then $$ is its normal vector. | 2014-08-23 01:53:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6558125019073486, "perplexity": 388.5598980475167}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500824990.54/warc/CC-MAIN-20140820021344-00434-ip-10-180-136-8.ec2.internal.warc.gz"} | 144 |
https://en.zdam.xyz/problem/12703/ | #### Problem 67E
67. Boyle’s Law states that when a sample of gas is compressed at a constant temperature, the pressure $P$ of the gas is inversely proportional to the volume $V$ of the gas.
(a) Suppose that the pressure of a sample of air that occupies $0.106 \mathrm{~m}^{3}$ at $25^{\circ} \mathrm{C}$ is $50 \mathrm{kPa}$. Write $V$ as a function of $P$.
(b) Calculate $d V / d P$ when $P=50 \mathrm{kPa}$. What is the meaning of the derivative? What are its units? | 2022-08-10 01:46:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.920375645160675, "perplexity": 112.53921034892576}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571097.39/warc/CC-MAIN-20220810010059-20220810040059-00095.warc.gz"} | 140 |
https://proofwiki.org/wiki/Sequence_of_Imaginary_Reciprocals/Interior | # Sequence of Imaginary Reciprocals/Interior
## Theorem
Consider the subset $S$ of the complex plane defined as:
$S := \set {\dfrac i n : n \in \Z_{>0} }$
That is:
$S := \set {i, \dfrac i 2, \dfrac i 3, \dfrac i 4, \ldots}$
where $i$ is the imaginary unit.
No point of $S$ is an interior point.
## Proof
From Sequence of Imaginary Reciprocals: Boundary Points, every $z \in S$ is a boundary point of $S$.
Thus no $z \in S$ is an interior point.
$\blacksquare$ | 2021-03-06 17:07:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9398163557052612, "perplexity": 434.54031179957104}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178375274.88/warc/CC-MAIN-20210306162308-20210306192308-00256.warc.gz"} | 158 |
https://www.esaral.com/q/if-p-and-q-are-two-prime-number-52281/ | If p and q are two prime number,
Question:
If p and q are two prime number, then what is their HCF?
Solution:
It is given that p and q are two prime numbers; we have to find their HCF.
We know that the factors of any prime number are 1 and the prime number itself.
For example, let $p=2$ and $q=3$
Thus, the factors are as follows
$p=2 \times 1$
And
$q=3 \times 1$
Now, the HCF of 2 and 3 is 1.
Thus the HCF of p and is 1 | 2022-01-26 07:30:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8252757787704468, "perplexity": 235.49123337309118}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304928.27/warc/CC-MAIN-20220126071320-20220126101320-00279.warc.gz"} | 144 |
https://www.onooks.com/tag/let-textbfx-x_1/ | Categories
## Vector of multivariate normal distribution
Let $\textbf{X} = (X_1, X_2, X_3)^T$ and $\textbf{Y} = (Y_1, Y_2, Y_3)^T$ be independent vectors with multivariate normal distribution, with means $\mu_X$ and $\mu_Y$ and covariance matrices $\Sigma_X$ and $\Sigma_Y$ with non-zero determinant. Let $A_{2 \times 3}$ and $B_{3 \times 3}$ be lineary independent matrices. Find distribution of $(\textbf{X}^TA^T, \textbf{Y}B^T)^T$. This is what I’ve done […] | 2020-04-08 11:51:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8358428478240967, "perplexity": 133.0571994799747}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371813538.73/warc/CC-MAIN-20200408104113-20200408134613-00096.warc.gz"} | 153 |
https://meta.discourse.org/t/do-unreviewed-translations-ship-into-releases/18171 | # Do unreviewed translations ship into releases?
(Anton) #1
As I got the reviewer rights, it’s now interesting to know if non-reviewed translations get included automatically into releases of Discourse?
(Erick Guan) #2
Yes, it is. Everything changes fast.
(Jonathan Feist) #3
Check out the Swedish locale. Incomplete and apparently not perfectly translated where it has been translated. So I guess some are not fully reviewed but we are not yet at version 1 so I suppose this is to be expected. | 2018-06-21 17:36:06 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8639013767242432, "perplexity": 4902.509503077276}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864256.26/warc/CC-MAIN-20180621172638-20180621192638-00297.warc.gz"} | 113 |
https://www.gradesaver.com/textbooks/math/prealgebra/prealgebra-7th-edition/chapter-7-section-7-1-percents-decimals-and-fractions-exercise-set-page-475/26 | ## Prealgebra (7th Edition)
$\dfrac{1}{50}$
To write a percent as a fraction, drop the % symbol and multiply by $\dfrac{1}{100}$. $2\% \rightarrow 2 \rightarrow \dfrac{2}{100} = \dfrac{1}{50}$ | 2018-09-25 23:01:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8037353157997131, "perplexity": 4261.128513522195}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267162563.97/warc/CC-MAIN-20180925222545-20180926002945-00508.warc.gz"} | 69 |
https://vrcacademy.com/formulas/z-test-p-value/ | ## Z-test p Value Calculator
Use this calculator to compute the p-value of test based on normal distribution.
## $p$-Value of Z-test
If the test statistic $Z$ has standard normal distribution, then the $p$-value of the test
a. left-tailed hypothesis is $p$-value = $P(Z\leq z_{obs})$.
b. right-tailed hypothesis is $p$-value = $P(Z\geq z_{obs})$.
c. two-tailed hypothesis is $p$-value = $2P(Z\geq |Z_{obs}|)$. | 2020-04-08 09:13:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8076297640800476, "perplexity": 2952.561810173284}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371810807.81/warc/CC-MAIN-20200408072713-20200408103213-00152.warc.gz"} | 132 |
https://byjus.com/question-answer/if-a-and-b-are-two-matrices-such-that-ab-b-ba-a-then-a/ | Question
# If $$A$$ and $$B$$ are two matrices such that $$AB = B, BA = A$$ then $$[A$$ and $$B$$ are not null matrices].
A
A2=A
B
B2=0
C
AB is idempotent
D
AB is nilpotent
Solution
## The correct option is A $$A^{2} = A$$$$AB=B$$ $$\&$$ $$BA=A$$$$\Rightarrow AB=B$$$$\Rightarrow (BA)B=B$$$$\Rightarrow B(AB)=B$$$$\Rightarrow B.B=B$$$$\Rightarrow B^2=B$$Similarly, $$A^2=A$$Hence, the answer is $$A^2=A.$$Maths
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View More | 2022-01-21 02:34:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8812011480331421, "perplexity": 2567.820760684384}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320302715.38/warc/CC-MAIN-20220121010736-20220121040736-00138.warc.gz"} | 173 |
https://brilliant.org/problems/derivative-of-composition-of-functions/ | Derivative of Composition of Functions
There is a certain function $f$ such that the tangent line at $x=\frac{1}{2}$ is $y=2x+1.$
Given that $g(x)=f(\sin x),$ find the sum of all possible values of $\frac{dg}{dx}$ when evaluated at $x=\frac{\pi}{6}$.
× | 2021-12-03 16:26:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 12, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5898910164833069, "perplexity": 70.40200130340783}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362891.54/warc/CC-MAIN-20211203151849-20211203181849-00622.warc.gz"} | 80 |
https://istopdeath.com/find-the-derivative-d-dx-y3ex/ | # Find the Derivative – d/dx y=3e^x
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Exponential Rule which states that is where =.
Find the Derivative – d/dx y=3e^x
Scroll to top | 2022-12-06 08:09:05 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9480265974998474, "perplexity": 1519.6571912434133}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711074.68/warc/CC-MAIN-20221206060908-20221206090908-00507.warc.gz"} | 63 |
http://mathsci.kaist.ac.kr/home/ | ## Problem of the week
### 2018-23 Game of polynomials
Two players play a game with a polynomial with undetermined coefficients $1 + c_1 x + c_2 x^2 + \dots + c_7 x^7 + x^8.$ Players, in turn, assign a real number to an undetermined coefficient until all coefficients are determined. The first player wins if the polynomial has no real zeros, and the second player wins if the polynomial has at least one real zero. Find who has the winning strategy. | 2019-01-22 10:16:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28355154395103455, "perplexity": 200.91419767244815}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583835626.56/warc/CC-MAIN-20190122095409-20190122121409-00108.warc.gz"} | 112 |
http://mathhelpforum.com/pre-calculus/219720-find-angle-between-vector-print.html | # Find Angle Between Vector
• June 10th 2013, 10:57 AM
Mc3
Find Angle Between Vector
<3,1> x <4,-5>
• June 10th 2013, 11:33 AM
Plato
Re: Find Angle Between Vector
Quote:
Originally Posted by Mc3
<3,1> x <4,-5>
The angle between $\vec{A}~\&~\vec{B}$ is $\arccos \left( {\frac{{\vec{A}\cdot\vec{B}}}{{\|\vec{A}\|~\|\vec{ B}\|}}} \right)$
• June 10th 2013, 04:13 PM
Mc3
Re: Find Angle Between Vector
I tried cos^1 7/ square root 10 x square root 41 but it says error on my calc?
• June 10th 2013, 04:30 PM | 2015-08-31 20:25:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9209287166595459, "perplexity": 10937.46018575279}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644066586.13/warc/CC-MAIN-20150827025426-00086-ip-10-171-96-226.ec2.internal.warc.gz"} | 208 |
https://www.gradesaver.com/textbooks/math/geometry/elementary-geometry-for-college-students-5th-edition/chapter-2-section-2-5-convex-polygons-exercises-page-105/7b | ## Elementary Geometry for College Students (5th Edition)
Published by Brooks Cole
# Chapter 2 - Section 2.5 - Convex Polygons - Exercises: 7b
#### Answer
1440$^{\circ}$
#### Work Step by Step
S=(10-2)$\times$180 S=(8)$\times$180 S=1440$^{\circ}$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 2018-08-18 01:42:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5926805734634399, "perplexity": 6528.376113130438}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221213247.0/warc/CC-MAIN-20180818001437-20180818021437-00165.warc.gz"} | 116 |
http://openmoodle.conted.ox.ac.uk/mod/forum/discuss.php?d=2305&parent=12823 | ## Therapeutic cloning forum
### Euthanasia
Re: Euthanasia
It is because every case has it's own unique character that we might want to distinguish between rules about euthanasia and acts of euthanasia - deciding perhaps that although individual acts are acceptable (perhaps) the law that disbars it is also a good one.
Or some variation on this theme. The fact is that the type-token distinction here is crucial (see some of the other postings).
M | 2017-09-24 04:46:57 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.878778874874115, "perplexity": 2713.8749122501245}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818689874.50/warc/CC-MAIN-20170924044206-20170924064206-00356.warc.gz"} | 99 |
https://www.physicsforums.com/threads/is-the-component-of-a-vector-still-a-vector.340555/ | Is the component of a vector still a vector?
1. Sep 26, 2009
Red_CCF
I know that a vector has magnitude and direction. But what about its components? Are they still considered vectors? Thanks in advance
2. Sep 26, 2009
mikelepore
Yes, if the unit vector is part of the term. For vector v=3i+4j, 3i is a vector, 4j is a vector. The 3 and 4 are not vectors. | 2018-03-22 22:45:11 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.847745954990387, "perplexity": 667.9308359817826}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257648003.58/warc/CC-MAIN-20180322205902-20180322225902-00214.warc.gz"} | 111 |
https://jax.readthedocs.io/en/stable/_autosummary/jax.lax.stop_gradient.html | jax.lax.stop_gradient(x)[source]
Operationally stop_gradient is the identity function, that is, it returns argument x unchanged. However, stop_gradient prevents the flow of gradients during forward or reverse-mode automatic differentiation. If there are multiple nested gradient computations, stop_gradient stops gradients for all of them.
For example:
>>> jax.grad(lambda x: x**2)(3.)
array(6., dtype=float32) | 2021-05-16 17:23:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7030531167984009, "perplexity": 6981.254084530694}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991178.59/warc/CC-MAIN-20210516171301-20210516201301-00025.warc.gz"} | 85 |
https://web2.0calc.com/questions/homework-help-me-understand | +0
# homework help me understand
-1
24
1
Simplify each expression when x = 2 and y = 3
7x + 3y -48
Im so confused .
Apr 29, 2022
#1
+1351
+2
Substitute it like this: $$(7 \times 2) +(3 \times 3)-48$$
Apr 29, 2022
Substitute it like this: $$(7 \times 2) +(3 \times 3)-48$$ | 2022-05-19 01:36:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9880094528198242, "perplexity": 4989.879545638153}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662522741.25/warc/CC-MAIN-20220519010618-20220519040618-00331.warc.gz"} | 119 |
https://www.gradesaver.com/textbooks/math/algebra/algebra-2-common-core/chapter-1-expressions-equations-and-inequalities-get-ready-page-1/15 | ## Algebra 2 Common Core
$-\frac{14}{3}$
Simplify the terms to $\frac{8}{3}-\frac{22}{3}$ Since both terms have the same denominator (the number on the bottom), simply subtract 8 by 22. $8-22 = -14$ Add back the denominator $-\frac{14}{3}$ | 2020-05-28 04:31:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9289259910583496, "perplexity": 896.6090161212842}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347396495.25/warc/CC-MAIN-20200528030851-20200528060851-00476.warc.gz"} | 77 |
https://notstatschat.rbind.io/2018/06/05/new-blog-home/ | I’m not actually worried by that: one of the key features of a git repository is that it doesn’t have the only copy of any of your stuff. The main motivation for switching was to use blogdown rather than Tumblr, because my blog is mostly text. | 2019-05-22 15:47:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34207963943481445, "perplexity": 668.5837836611801}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256858.44/warc/CC-MAIN-20190522143218-20190522165218-00189.warc.gz"} | 53 |
https://gateoverflow.in/303592/grammar-doubt | 47 views
L is regular <=> there exists a linear grammar for L.
Which way is it true and which way is it false?
| 47 views
0
The biconditional is true. (which means it correct both ways)
https://gateoverflow.in/303591/cfg-doubt
and more over if
Let L is: A-> a (RG) and also Linear G
and S-> aSb | epsilon (which is linear. But for it we can't drive any RG)
by Active (1.5k points) | 2020-01-26 10:00:55 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8059635758399963, "perplexity": 14221.213713033096}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251687958.71/warc/CC-MAIN-20200126074227-20200126104227-00232.warc.gz"} | 131 |
https://brilliant.org/problems/a-problem-by-swapnil-das-4/ | # 1 equation 3 variables
Algebra Level 2
$\large 2^{x} = 3^{y} = 12^{z}$
If the equation above is fulfilled for non-zero values of $$x,y,z,$$ find the value of $$\frac { z(x+2y) }{ xy }$$.
×
Problem Loading...
Note Loading...
Set Loading... | 2017-03-27 04:54:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5997189879417419, "perplexity": 4275.542334077438}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189403.13/warc/CC-MAIN-20170322212949-00446-ip-10-233-31-227.ec2.internal.warc.gz"} | 81 |
https://brilliant.org/problems/inspired-by-arturo-presa/ | # Inspired By Arturo Presa
Calculus Level 5
What can we say about the function $$f: \mathbb{R}^+ \rightarrow \mathbb{R}$$ which satisfies
$f(xy) = f(x) + f(y) ?$
×
Problem Loading...
Note Loading...
Set Loading... | 2017-09-24 08:42:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3631236255168915, "perplexity": 14743.615538207276}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818689900.91/warc/CC-MAIN-20170924081752-20170924101752-00592.warc.gz"} | 67 |
https://www.esaral.com/q/a-diverging-lens-of-focal-length-62332 | A diverging lens of focal length
Question:
A diverging lens of focal length $20 \mathrm{~cm}$ and a converging mirror of focal length $10 \mathrm{~cm}$ are placed coaxially at a separation of $5 \mathrm{~cm}$. Where should an object be placed so that a real image is formed at the object itself?
Solution: | 2023-02-05 13:24:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9374554753303528, "perplexity": 297.1142272175161}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500255.78/warc/CC-MAIN-20230205130241-20230205160241-00423.warc.gz"} | 78 |
https://socratic.org/questions/how-do-you-evaluate-20p2 | # How do you evaluate 20P2?
Mar 5, 2017
Steps and result are outlined below...
#### Explanation:
The general formula for a permutation is
""_nP_r = (n!)/(n-r!)
In this case, $n = 20$ and $r = 2$, so our equation becomes
""_20P_2 = (20!)/(18!) = (20xx19) = 380 | 2020-02-28 23:58:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 4, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9324063062667847, "perplexity": 4198.078803420176}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875148163.71/warc/CC-MAIN-20200228231614-20200229021614-00228.warc.gz"} | 92 |
https://socratic.org/questions/how-do-you-find-domain-and-range-for-y-sqrt-x-2 | # How do you find domain and range for y=sqrt(x- 2)?
The domain is $x \ge 2$ or $D \left(f\right) = \left[2 , + \infty\right)$ and the range is
$y = \sqrt{x - 2} \ge 0 \implies y \ge 0$ or $R \left(f\right) = \left[0 , + \infty\right)$ | 2019-11-20 21:50:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 4, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3653736412525177, "perplexity": 494.0734037059598}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670635.48/warc/CC-MAIN-20191120213017-20191121001017-00115.warc.gz"} | 99 |
https://stats.meta.stackexchange.com/questions/660/the-404-not-found-image-is-not-unique | # The 404 not found image is not unique
This site's 404 not found image is not unique. It's shared with TeX SE.
It's entirely possible that this is intentional, but since most sites don't have the same image, I thought it was reasonable to suspect that it was a bug.
Sister bug report:
on Meta TeX | 2022-01-24 14:00:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.995294988155365, "perplexity": 1966.1833505799987}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304570.90/warc/CC-MAIN-20220124124654-20220124154654-00202.warc.gz"} | 73 |
http://www.chegg.com/homework-help/questions-and-answers/completely-filled-barrel-contents-combined-weight-200-lb-cylinder-c-connected-barrel-heigh-q2491283 | A completely filled barrel and its contents have a combined weight of 200 lb. A cylinder C is connected to the barrel at a height h = 22 in. as shown. Knowing $$\mu_{s}= 0.40$$ and $$\mu_{k}=0.35$$ , determine the maximum weight of C so the barrel will not tip. | 2015-03-04 21:26:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.753072202205658, "perplexity": 327.18620577185254}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936463658.66/warc/CC-MAIN-20150226074103-00320-ip-10-28-5-156.ec2.internal.warc.gz"} | 73 |