url
stringlengths 13
5.21k
| text
stringlengths 100
512
| date
stringlengths 19
19
| metadata
stringlengths 1.05k
1.1k
| token_length
int64 11
539
|
---|---|---|---|---|
https://homework.cpm.org/category/CCI_CT/textbook/calc/chapter/1/lesson/1.2.4/problem/1-71 | ### Home > CALC > Chapter 1 > Lesson 1.2.4 > Problem1-71
1-71.
1. Find the domain of each of the following functions. Homework Help ✎
1. f(x) = log (x − 4)
$\text{If the domain of the parent graph, } y=\sqrt{x}, \text{ is } x \geq 0,\text{ what is the domain of }f(x)?$
$\text{If the domain of the parent graph, } y=\frac{1}{x}, \text{ is } x \neq 0,\text{ what is the domain of }f(x)?$
$\text{If the domain of the parent graph, } y=\text{ log}{x}, \text{ is } x > 0,\text{ what is the domain of }f(x)?$ | 2020-01-17 22:23:57 | {"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": 0.6602946519851685, "perplexity": 6384.429875431311}, "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/1579250591234.15/warc/CC-MAIN-20200117205732-20200117233732-00450.warc.gz"} | 182 |
https://socratic.org/questions/how-do-you-solve-using-the-quadratic-formula-x-2-5x-14-0 | # How do you solve using the quadratic formula x^2-5x-14=0?
May 16, 2015
$y = {x}^{2} - 5 x - 14 = 0$
D = d^2 = 25 + 56 = 81 -> d = +-9
x = 5/2 + 9/2 = 14/2 = 7
x = 5/2 - 9/2 = -4/2 = -2
There is another way that is faster. (new AC Method)
Find 2 numbers knowing product (-14) and sum (7). Compose factor pairs of (-14): (-1, 14)(-2, 7). This last sum is 5 = -b. Then the 2 real roots are: -2 and 7 | 2020-09-28 16:22:21 | {"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": 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": 0.7992181181907654, "perplexity": 1173.1823299688165}, "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/1600401601278.97/warc/CC-MAIN-20200928135709-20200928165709-00401.warc.gz"} | 178 |
http://clay6.com/qa/67137/shweta-ate-large-frac-of-a-pizza-and-her-friend-george-ate-large-frac-of-th | Answer
Comment
Share
Q)
# Shweta ate $\large\frac{3}{11}$ of a pizza and her friend George ate $\large\frac{13}{22}$ of the pizza. How much total pizza did they eat altogether?
( A ) $\large\frac{19}{11}$
( B ) $\large\frac{22}{19}$
( C ) $\large\frac{11}{19}$
( D ) $\large\frac{19}{22}$ | 2020-08-10 19:36:58 | {"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": 0.7830217480659485, "perplexity": 5529.938304302237}, "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-2020-34/segments/1596439737168.97/warc/CC-MAIN-20200810175614-20200810205614-00037.warc.gz"} | 103 |
http://legisquebec.gouv.qc.ca/en/showversion/cs/I-8.1?code=se:103_4&pointInTime=20210906 | ### I-8.1 - Act respecting offences relating to alcoholic beverages
103.4. In proceedings for contravention of section 103.1 or 103.2, the permit holder shall incur no penalty if he proves that he used reasonable diligence to ascertain the age of the person and that he had reasonable ground for believing that that person was of full age or if he proves that he had reasonable ground for believing that it was a case contemplated in the second paragraph of section 103.2.
1979, c. 71, s. 128. | 2021-10-25 08:46:39 | {"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": 0.8366407155990601, "perplexity": 2790.266276743814}, "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/1634323587655.10/warc/CC-MAIN-20211025061300-20211025091300-00139.warc.gz"} | 115 |
https://www.gradesaver.com/textbooks/math/algebra/elementary-and-intermediate-algebra-concepts-and-applications-6th-edition/chapter-4-polynomials-4-7-polynomials-in-several-variables-4-7-exercise-set-page-286/106 | ## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
$$=P-2Pr+Pr^2$$
In order to find a polynomial that gives the amount after two years, we plug in 2 for t and multiply out the expression to obtain: $$P\left(1-r\right)^2 \\ P\left(r^2-2r+1\right) \\ =P-2Pr+Pr^2$$ | 2019-10-21 08:17:58 | {"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": 0.4987066388130188, "perplexity": 394.7427045666538}, "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-2019-43/segments/1570987763641.74/warc/CC-MAIN-20191021070341-20191021093841-00317.warc.gz"} | 92 |
http://nrich.maths.org/344/index?nomenu=1 | I am searching for fractions with values between $\sqrt{56}$ and $\sqrt{58}$. I'm told there are an infinite number of possibilities...
Find some fractions with small denominators, say less than $10$ or $20$.
Have you found any denominators which won't yield a fraction between $\sqrt{56}$ and $\sqrt{58}$?
Send us any examples you find of denominators which don't work, and a justification that all other denominators will work! | 2016-08-27 15:13:13 | {"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": 0.6418215036392212, "perplexity": 500.52255605090994}, "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-2016-36/segments/1471982921683.52/warc/CC-MAIN-20160823200841-00102-ip-10-153-172-175.ec2.internal.warc.gz"} | 100 |
https://proofwiki.org/wiki/Mathematician:David_Borwein | # Mathematician:David Borwein
## Mathematician
Canadian mathematician of Lithuanian origin, best known for his research in the summability theory of series and integrals.
Also working in measure theory and probability theory, number theory, and approximate subgradients and coderivatives, and the properties of single- and many-variable sinc integrals.
Father of Jonathan Michael Borwein and Peter Benjamin Borwein. | 2020-08-03 17:30:12 | {"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": 0.8455008864402771, "perplexity": 5322.153834313859}, "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/1596439735823.29/warc/CC-MAIN-20200803170210-20200803200210-00322.warc.gz"} | 87 |
https://www.encyclopediaofmath.org/index.php/Median_(of_a_triangle) | Median (of a triangle)
A straight line (or its segment contained in the triangle) which joins a vertex of the triangle with the midpoint of the opposite side. The three medians of a triangle intersect at one point, called the centre of gravity, the centroid or the barycentre of the triangle. This point divides each median into two parts with ratio $2:1$ if the first segment is the one that starts at the vertex. The centroid lies on the Euler line. | 2020-02-23 20:47:24 | {"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": 0.6273155808448792, "perplexity": 110.41766501903172}, "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-2020-10/segments/1581875145839.51/warc/CC-MAIN-20200223185153-20200223215153-00116.warc.gz"} | 98 |
https://socratic.org/questions/how-do-you-write-the-equation-of-a-line-in-point-slope-form-that-is-parallel-to--1 | # How do you write the equation of a line in point slope form that is parallel to y=2x-6 and goes through (2,3)?
$y - 3 = 2 \left(x - 2\right)$
$y - {y}_{0} = m \left(x - {x}_{0}\right)$
$y - 3 = 2 \left(x - 2\right)$ | 2022-01-21 06:29:24 | {"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": 0.7502787709236145, "perplexity": 233.17781335065104}, "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/1642320302723.60/warc/CC-MAIN-20220121040956-20220121070956-00189.warc.gz"} | 89 |
http://clay6.com/qa/48630/a-parallel-plate-capacitor-with-air-between-the-plates-has-a-capacitance-of | Browse Questions
# A parallel plate capacitor with air between the plates has a capacitance of $9 \;pF$. The separation between its plates is d. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_1 = 3$ and thickness $\large\frac{d}{3}$ while the other one has dielectric constant $K_2 = 6$ and thickness $\large\frac{2d}{3}$ . Capacitance of the capacitor is now
$(C) 40.5 pF$ | 2017-06-25 19:02:39 | {"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": 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": 0.8954192996025085, "perplexity": 260.8015353927952}, "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/1498128320570.72/warc/CC-MAIN-20170625184914-20170625204914-00527.warc.gz"} | 124 |
http://clay6.com/qa/70333/count-the-number-of-parallelogram-in-the-given-figure- | Comment
Share
Q)
# Count the number of parallelogram in the given figure.
$(A) 8 \\ (B) 11 \\(C)12 \\ (D)15$ | 2019-09-20 16:50:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 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": 0.5495256781578064, "perplexity": 4031.3458501672376}, "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-2019-39/segments/1568514574050.69/warc/CC-MAIN-20190920155311-20190920181311-00123.warc.gz"} | 41 |
https://socratic.org/questions/how-do-you-factor-15x-3-21x-2-20x-28 | # How do you factor 15x^3-21x^2+20x-28?
$\left(5 x - 7\right) \left(3 {x}^{2} + 4\right)$
$15 {x}^{3} - 21 {x}^{2} + 20 x - 28$ | 2021-12-08 15:35:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 2, "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": 0.25450748205184937, "perplexity": 8523.29417067636}, "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-2021-49/segments/1637964363515.28/warc/CC-MAIN-20211208144647-20211208174647-00601.warc.gz"} | 74 |
https://dsp.stackexchange.com/questions/23143/adaptive-filter-gradient-descent | • @user1832413: If you have a quadratic form $x^TAx+b^Tx$, and if the matrix $A$ is positive (semi-)definite (as is the case with an autocorrelation matrix), then the function defined by the quadratic form is convex and has a minimum. A saddle point can only occur if the matrix $A$ is indefinite. – Matt L. May 3 '15 at 20:00 | 2019-09-18 12:23:37 | {"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": 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": 0.9716269969940186, "perplexity": 145.443954643754}, "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-2019-39/segments/1568514573284.48/warc/CC-MAIN-20190918110932-20190918132932-00475.warc.gz"} | 93 |
https://proofwiki.org/wiki/Electric_Charge/Quantum/Examples | Electric Charge/Quantum/Examples
$60 \ \mathrm W$ Bulb at $200 \ \mathrm V$
Consider a $60 \ \mathrm W$ light bulb running at $200 \ \mathrm V$.
Approximately $2 \times 10^{18}$ units of elementary charge flow along the filament of the light bulb every second. | 2022-01-20 20:55:26 | {"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": 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": 0.8943676948547363, "perplexity": 1439.10177809967}, "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-2022-05/segments/1642320302622.39/warc/CC-MAIN-20220120190514-20220120220514-00640.warc.gz"} | 72 |
http://www.euro-math-soc.eu/node/4003 | ## Riemann, Einstein and geometry
Sep 18 2014 - 09:00
Sep 20 2014 - 12:30
Venue:
Institut de Recherche Mathématique Avancée, University of Strasbourg (France)
Short description of the event:
The conference is part of a series of bi-annual conferences "Encounter between Mathematicians and Theoretical Physicists" and it is addressed to a large audience.
Athanase Papadopoulos : athanase.papadopoulos$math.unistra.fr Sumio Yamada : yamada$math.gakushuin.ac.jp | 2014-03-07 09:00:25 | {"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": 0.7580703496932983, "perplexity": 13252.943875181329}, "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-2014-10/segments/1393999639602/warc/CC-MAIN-20140305060719-00025-ip-10-183-142-35.ec2.internal.warc.gz"} | 131 |
https://math.stackexchange.com/questions/850029/rayleigh-quotient-variant | # Rayleigh Quotient variant?
If $A$ is a covariance matrix and I want to get
$\max X^TAX$ where each value of $x$ is between -1 and 1.
Is there a closed-form solution for this?
I understand when $X^TX = 1$ this becomes the original Rayleigh quotient problem.
• Is $X$ a random column vector? – Omnomnomnom Jun 28 '14 at 4:33
• @Omnomnomnom: Right, X is an n x 1 vector – user40923 Jun 28 '14 at 4:45 | 2019-05-25 23:12:02 | {"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": 0.9404663443565369, "perplexity": 434.59922249905475}, "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-2019-22/segments/1558232258453.85/warc/CC-MAIN-20190525224929-20190526010929-00023.warc.gz"} | 132 |
https://socratic.org/questions/oxides-of-most-metals-combine-with-water-to-form-what | # Oxides of most metals combine with water to form what?
Nov 15, 2016
$N {a}_{2} O$ + ${H}_{2} O$ ------> $2 N a O H$.
$M g O$ + ${H}_{2} O$ ------> $M g {\left(O H\right)}_{2}$.
$A {l}_{2} {O}_{3}$ + $3 {H}_{2} O$ ------> $2 A l {\left(O H\right)}_{3}$. | 2019-11-15 10:21:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 9, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.520042359828949, "perplexity": 11042.288305253145}, "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-2019-47/segments/1573496668618.8/warc/CC-MAIN-20191115093159-20191115121159-00469.warc.gz"} | 113 |
https://www.gradesaver.com/textbooks/science/physics/fundamentals-of-physics-extended-10th-edition/chapter-3-vectors-questions-page-56/13e | ## Fundamentals of Physics Extended (10th Edition)
$\vec{A}$ is a vector $\vec{B}\cdot\vec{C}$ is a scalar. (vector) + (scalar) has no meaning as we can not add scalars and vectors. | 2019-03-18 17:50:57 | {"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": 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": 0.6945178508758545, "perplexity": 1013.3542255497701}, "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-2019-13/segments/1552912201521.60/warc/CC-MAIN-20190318172016-20190318194016-00028.warc.gz"} | 54 |
https://puzzling.stackexchange.com/questions/80400/get-2-liters-from-4-and-5-liter-buckets/80402 | # Get 2 liters from 4 and 5 liter buckets [duplicate]
You have a 4 liter bucket and a 5 liter bucket and an (infinite) supply of liquid.
How do you get 2 liters? | 2020-04-09 05:13:05 | {"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": 0.8790210485458374, "perplexity": 1853.674623205523}, "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-2020-16/segments/1585371829677.89/warc/CC-MAIN-20200409024535-20200409055035-00520.warc.gz"} | 47 |
https://web2.0calc.com/questions/two-circles-again | +0
# two circles again
0
57
1
The smaller circle in the diagram is internally tangent to the larger circle. The area of the gray region is $100\pi$ square units. The perimeter of the gray region (include both inner and outer boundaries) is $100\pi$ units. What is the distance in units between the centers of the two circles?
Feb 20, 2021 | 2021-04-13 08:28:16 | {"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": 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": 0.9446906447410583, "perplexity": 267.6824718846954}, "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/1618038072175.30/warc/CC-MAIN-20210413062409-20210413092409-00636.warc.gz"} | 86 |
https://www.gradesaver.com/textbooks/math/algebra/college-algebra-7th-edition/chapter-1-equations-and-graphs-section-1-10-modeling-variation-1-10-exercises-page-164/17 | College Algebra 7th Edition
$\displaystyle R= \frac{kP^{2}t^{2}}{b^{3}}$
Since $R$ is directly (jointly) proportional to the squares of $P$ and $t$, but inversely proportional to the cube of $b$, we have: $\displaystyle R= \frac{kP^{2}t^{2}}{b^{3}}$ (where $k$ is a constant.) | 2018-07-19 14:09:18 | {"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": 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": 0.9953418374061584, "perplexity": 221.88575288996975}, "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-2018-30/segments/1531676590901.10/warc/CC-MAIN-20180719125339-20180719145339-00033.warc.gz"} | 96 |
https://www.esaral.com/q/solve-this-following-25422/ | Solve this following
Question:
Compound $\mathrm{A}\left(\mathrm{C}_{9} \mathrm{H}_{10} \mathrm{O}\right)$ shows positive iodoform test. Oxidation of $\mathrm{A}$ with $\mathrm{KMnO}_{4} / \mathrm{KOH}$ gives acid $\mathrm{B}\left(\mathrm{C}_{8} \mathrm{H}_{6} \mathrm{O}_{4}\right)$. Anhydride of $\mathrm{B}$ is used for the preparation of phenolphthalein. Compound $\mathrm{A}$ is :-
Correct Option: 1
Solution: | 2022-06-29 00:27:37 | {"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": 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": 0.8681351542472839, "perplexity": 7043.388731214367}, "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/1656103619185.32/warc/CC-MAIN-20220628233925-20220629023925-00530.warc.gz"} | 139 |
https://forum.math.toronto.edu/index.php?PHPSESSID=1u0iucfle60t5k23oom8iace62&topic=385.0 | ### Author Topic: Writing the quiz with another section (Read 1496 times)
#### Victor Ivrii
• Administrator
• Elder Member
• Posts: 2563
• Karma: 0
##### Writing the quiz with another section
« on: September 15, 2014, 10:57:17 AM »
Students of one evening section are allowed to write Quiz with another evening section but not with a day section.
Students of the day section are allowed to write a Quiz with one of the evening sections. | 2021-09-28 01:42:50 | {"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": 0.9002169370651245, "perplexity": 13565.537339092305}, "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-2021-39/segments/1631780058589.72/warc/CC-MAIN-20210928002254-20210928032254-00582.warc.gz"} | 112 |
http://ringtheory.herokuapp.com/keywords/keyword/15/ | # Keyword: matrix ring
Description: Given a ring $R$ and a natural number $n$, the set $M_n(R)$ with ordinary matrix operations. | 2018-11-19 06:12:25 | {"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": 0.9416454434394836, "perplexity": 394.02314774324077}, "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-2018-47/segments/1542039745281.79/warc/CC-MAIN-20181119043725-20181119065725-00375.warc.gz"} | 33 |
https://brilliant.org/problems/again-a-good-problem/ | # This can't be that Short!
Algebra Level 4
$\displaystyle \sum_{k=1}^m \left [ (k^2 + 1) \ k! \right ] = 1999 \times 2000!$
What value of $$m$$ satisfies the above summation?
× | 2017-10-23 15:42:33 | {"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": 0.9432784914970398, "perplexity": 4574.029062233722}, "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/1508187826114.69/warc/CC-MAIN-20171023145244-20171023165244-00190.warc.gz"} | 67 |
http://mathhelpforum.com/differential-geometry/111861-homeomorphism.html | # Math Help - Homeomorphism
1. ## Homeomorphism
Show that (a,b) is homeomorphic to R..
Thank you in advance
2. Originally Posted by math.dj
Show that (a,b) is homeomorphic to R..
Thank you in advance
You've left out a lot! Are we to assume that (a, b) is an interval in R with the "usual topology"? If so, you basically need to find a one-to-one function from (a,b) onto R. You should be able to find a rational function that maps a to $-\infty$ and b to $\infty$. | 2014-04-18 22:59:14 | {"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": 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": 0.6146227121353149, "perplexity": 764.5891418843324}, "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-2014-15/segments/1397609535095.9/warc/CC-MAIN-20140416005215-00097-ip-10-147-4-33.ec2.internal.warc.gz"} | 132 |
https://brilliant.org/problems/fun-with-maths-3/ | # Fun with Maths
Algebra Level 4
If the roots of $$10x^3- cx^2-54x-27=0$$ are in harmonic progression then find $$c$$.
× | 2017-09-26 14:51:27 | {"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": 0.4140471816062927, "perplexity": 2088.921185756664}, "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/1505818696182.97/warc/CC-MAIN-20170926141625-20170926161625-00350.warc.gz"} | 43 |
https://socratic.org/questions/how-do-you-solve-x-80-19 | How do you solve x + 80 = -19?
Jan 20, 2016
$x = - 99$
Explanation:
$x + 80 = - 19$
move from LHS to the RHS all the therms without the $x$, changing their sign
$x = - 19 \textcolor{g r e e n}{- 80}$
$x = - 99$ | 2019-09-18 18:09:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "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": 0.9417382478713989, "perplexity": 1688.977645002624}, "config": {"markdown_headings": false, "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-2019-39/segments/1568514573323.60/warc/CC-MAIN-20190918172932-20190918194932-00202.warc.gz"} | 83 |
https://www.transtutors.com/questions/change-the-order-of-integration-to-dz-dx-dy-for-it-s-next-to-impossible-to-draw-out--1348002.htm | # Change the order of integration to dz dx dy for: It's next to impossible to draw out a 3D version of
Change the order of integration to dz dx dy for:
It's next to impossible to draw out a 3D version of the figure, so I tried drawing the region(s) on the xy, zy, zx planes... not sure if I've done it correctly though -- I get | 2021-06-18 01:39:09 | {"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": 0.9346845746040344, "perplexity": 499.12078869776394}, "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-2021-25/segments/1623487634616.65/warc/CC-MAIN-20210618013013-20210618043013-00267.warc.gz"} | 85 |
https://unacademy.com/course/hindi-solution-and-explanation-of-memory-based-questions-gate-2019/ML9O1D6E | Hindi
(Hindi) Solution and Explanation of Memory-Based Questions: GATE 2019
6 ratings
Deep Sangeet Maity
In this Course, The Educator will discuss the solution of GATE 2019 Questions of Mechanical Branch. The questions are developed by the feedback of students who attempted GATE 2019 (ME). | 2020-07-05 08:26:47 | {"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": 0.8806295990943909, "perplexity": 6166.8111377536325}, "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-2020-29/segments/1593655887046.62/warc/CC-MAIN-20200705055259-20200705085259-00150.warc.gz"} | 71 |
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&tp=&arnumber=6462165&contentType=Books+%26+eBooks | This chapter contains sections titled: The Problem, The Nineteenth Century, The Twentieth Century, Conclusion | 2017-11-24 13:37:47 | {"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": 0.8225895762443542, "perplexity": 1735.9996642292517}, "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-2017-47/segments/1510934808133.70/warc/CC-MAIN-20171124123222-20171124143222-00215.warc.gz"} | 21 |
http://mathhelpforum.com/trigonometry/189160-sinusoidal-functions-print.html | # Sinusoidal Functions
• Sep 29th 2011, 06:07 PM
lakers784
Sinusoidal Functions
Hi i need help with this problem my test is tomorrow and i am trying to figure out if i am right i have attached the file and the problem is number 13
i got y=-1+8cos pi/35(x-5)
• Sep 29th 2011, 06:14 PM
pickslides
Re: Sinusoidal Functions
Sounds fair to me.
• Oct 1st 2011, 05:06 AM
niggawut
yes you are absolutely correct (Rofl)
no kidding, I've worked it out.
$y = ({8})( {cos\frac{\pi(x-5)}{\35})} -1$ (Rofl) | 2017-08-18 22:06:28 | {"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": 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": 0.7003374099731445, "perplexity": 3886.720049812781}, "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/1502886105187.53/warc/CC-MAIN-20170818213959-20170818233959-00707.warc.gz"} | 177 |
http://www.gradesaver.com/founding-brothers/q-and-a/chapter-one-the-duel-302453 | # Chapter One, The Duel?
Chapter one, thesis
In order to understand the true significance and aftermath of the duel between Hamilton and Burr, one must first consider the personalities of the assailants, and the argument that brought them to that fateful place. | 2017-10-19 07:44:47 | {"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": 0.8136900067329407, "perplexity": 3425.6541766595346}, "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-2017-43/segments/1508187823255.12/warc/CC-MAIN-20171019065335-20171019085335-00094.warc.gz"} | 52 |
https://mathematica.stackexchange.com/revisions/161524/2 | 2 of 2 edited tags
# log plot problems
Why does the following code give me two different curves?
a = 100;
b = -0.1;
s = a n^b;
LogLogPlot[{s, a n^b}, {n, 1000, 1000000}] | 2020-07-14 07:04:15 | {"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": 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": 0.6088894605636597, "perplexity": 12924.605918710904}, "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-2020-29/segments/1593657149205.56/warc/CC-MAIN-20200714051924-20200714081924-00280.warc.gz"} | 65 |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-10th-edition/chapter-12-sequences-induction-the-binomial-theorem-chapter-review-review-exercises-page-839/33 | ## Precalculus (10th Edition)
$84$
According to the Binomial Theorem, the term containing $x^j$ in the expansion of $(ax+b)^n$ is given by: ${n\choose n-j}a^jb^{n-j}x^j.$ Hence, the coefficient of $x^2$ is ${7\choose 7-2}2^2(1)^{7-2}=84$ | 2019-11-18 07:04:51 | {"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": 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": 0.8954875469207764, "perplexity": 151.88351971017914}, "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/1573496669454.33/warc/CC-MAIN-20191118053441-20191118081441-00226.warc.gz"} | 93 |
https://socratic.org/questions/what-is-a-polynomial-function-with-the-roots-1-2-and-3 | # What is a polynomial function with the roots -1, 2, and 3?
Sep 20, 2015
It is a cubic IE.(it has 3 roots)
(x+1)(x-2)(x-3)
#### Explanation:
Lets define a cubic;
3 ROOTS$\to \alpha , \beta , \gamma$
So we can say that a cubic is
$\left(x - \alpha\right) \left(x - \beta\right) \left(x - \gamma\right)$
We are given ;
$\alpha = - 1 , \beta = 2 , \gamma = 3$
Finally substituting;
We get our cubic function to be
$f \left(x\right) = \left(x + 1\right) \left(x - 2\right) \left(x - 3\right)$ | 2019-02-19 04:56:44 | {"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": 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": 0.809803307056427, "perplexity": 3434.265594173885}, "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-2019-09/segments/1550247489343.24/warc/CC-MAIN-20190219041222-20190219063222-00636.warc.gz"} | 180 |
http://mathhelpforum.com/business-math/203167-checking-my-answer-calculating-expenses.html | # Thread: Checking my answer: Calculating expenses
1. ## Checking my answer: Calculating expenses
What are the total amount of expenses shown in the picture?
I get: 186,200. Because there is a service revenue of 541,100, there is a net income of 354,900.
Is that correct?
Thank You | 2017-04-30 00:46:51 | {"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": 0.8194360733032227, "perplexity": 4569.273675645968}, "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-2017-17/segments/1492917123632.58/warc/CC-MAIN-20170423031203-00232-ip-10-145-167-34.ec2.internal.warc.gz"} | 71 |
https://brilliant.org/problems/a-calculus-problem-by-avineil-jain/ | Deducing From The Integral
Calculus Level 5
A differentiable function $$f$$ is defined on the positive real numbers such that
$\int_{1}^{xy} f(t) \, dt = y\int_{1}^{x} f(t) \, dt + x\int_{1}^{y} f(t) \, dt.$
If $$f(1) = 3$$, what is $$f(e)$$?
×
Problem Loading...
Note Loading...
Set Loading... | 2017-07-27 08:54:50 | {"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": 0.9499044418334961, "perplexity": 2748.447998643541}, "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-2017-30/segments/1500549427750.52/warc/CC-MAIN-20170727082427-20170727102427-00106.warc.gz"} | 107 |
http://openstudy.com/updates/504c13bae4b0985a7a58d1b7 | ## mostfinnest 3 years ago In 1980, median family income was about $19,000, and in 2000 it was about$40,000. Find the slope of the line passing through points (1980, 19000) and (2000,40000) m=
$slope=m=\frac{ y _{2} - y _{1}}{ x _{2} - x _{1}}$
If you treat (1980, 19000) as $(x _{1}, y _{1})$ and (2000,40000) as $(x _{2}, y _{2})$ | 2016-05-01 23:17:39 | {"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": 2, "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": 0.509418249130249, "perplexity": 3672.017165121596}, "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-2016-18/segments/1461860117244.29/warc/CC-MAIN-20160428161517-00117-ip-10-239-7-51.ec2.internal.warc.gz"} | 138 |
https://www.cs.toronto.edu/~frossard/topics/gradient-descent/ | Introduction Linear regression is a method used to find a relationship between a dependent variable and a set of independent variables. In its simplest form it consist of fitting a function $\boldsymbol{y} = w.\boldsymbol{x}+b$ to observed data, where $\boldsymbol{y}$ is the dependent variable, $\boldsymbol{x}$ the independent, $w$ the weight matrix and $b$ the bias. Illustratively, performing linear regression is the same as fitting a scatter plot to a line. | 2019-12-12 16:54:54 | {"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": 0.35073670744895935, "perplexity": 172.0903388674977}, "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-2019-51/segments/1575540544696.93/warc/CC-MAIN-20191212153724-20191212181724-00533.warc.gz"} | 103 |
https://www.gradesaver.com/textbooks/math/algebra/introductory-algebra-for-college-students-7th-edition/chapter-1-review-exercises-page-110/100 | # Chapter 1 - Review Exercises: 100
10
#### Work Step by Step
Plug in -2 for x and simplify the expression. -x$^2$-7x -(-2)$^2$-7(-2) -(4)-7(-2) -4-7(-2) -4-(-14) -4+14 10
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. | 2018-06-18 21:14:22 | {"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": 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": 0.5685453414916992, "perplexity": 7552.402970931077}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2018-26/segments/1529267861163.5/warc/CC-MAIN-20180618203134-20180618223134-00534.warc.gz"} | 111 |
https://mathsgee.com/36392/subset-finite-dimensional-linear-spaces-rightarrow-linear | 0 like 0 dislike
272 views
Let $U \subset V$ and $W$ be finite dimensional linear spaces and $L: V \rightarrow W$ a linear map. Show that
$\operatorname{dim}\left(\left.\operatorname{ker} L\right|_{U}\right) \leq \operatorname{dim} \operatorname{ker} L=\operatorname{dim} V-\operatorname{dim} \operatorname{Im}(L)$
| 272 views
1 like 0 dislike
1 like 0 dislike
2 like 0 dislike
1 like 0 dislike
0 like 0 dislike
2 like 0 dislike
1 like 0 dislike
1 like 0 dislike
0 like 0 dislike | 2023-02-02 01:56:29 | {"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": 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": 0.7644431591033936, "perplexity": 7767.020106384212}, "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-2023-06/segments/1674764499954.21/warc/CC-MAIN-20230202003408-20230202033408-00424.warc.gz"} | 161 |
https://www.gradesaver.com/textbooks/science/chemistry/introductory-chemistry-5th-edition/chapter-13-solutions-exercises-problems-page-479/34 | ## Introductory Chemistry (5th Edition)
According to the given data, A $KCl$ solution containing 42 g of $KCl$ per 100 g of water is cooled from 60 °C to O °C. The solubility of $KNO_3$ at 60 °C = 45 g / 100 g of water. So, the given solution acts as an unsaturated solution at this temperature. The solubility of $KNO_3$ at 0 °C = 27 g / 100 g of water. At this temperature, the given solution acts as a supersaturated solution. So, cooling down from 60 °C to 0 °C results in the recrystallization of $KCl$. | 2019-06-16 12:50:19 | {"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": 0.783599317073822, "perplexity": 591.361965375319}, "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/1560627998238.28/warc/CC-MAIN-20190616122738-20190616144738-00203.warc.gz"} | 158 |
https://www.ideals.illinois.edu/handle/2142/16340/browse?value=Feuerman%2C+Kenneth+Edward&type=author | # Browse Dissertations and Theses - Mathematics by Author "Feuerman, Kenneth Edward"
• (1991)
The Hanna Neumann Conjecture states that if two subgroups of a finitely generated free group have finite ranks m and n, then their intersection has rank N which satisfies $N$ $-$ 1 $\leq$ ($m$ $-$ 1)($n$ $-$ 1). The current ...
application/pdf
PDF (4MB) | 2017-07-22 09:00:25 | {"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": 0.4870796203613281, "perplexity": 1426.9147757696587}, "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-2017-30/segments/1500549423927.54/warc/CC-MAIN-20170722082709-20170722102709-00201.warc.gz"} | 99 |
https://www.physicsforums.com/threads/cabibbo-theory.236431/ | # Cabibbo Theory
Hi,
I'm trying to cover the basics of Cabibbo theory, yet the materials Ive been presented with give a very jumbled description, and I'd just like to ask here to obtain some clarity...
Is it fair to say that the Cabibbo angle is a means of quantifying the different coupling strengths between different generations of quarks?
Or is this too much a simplification or just plain ol wrong?
Regards
Luke | 2021-03-03 18:35:57 | {"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": 0.8198843002319336, "perplexity": 1102.0608707329943}, "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/1614178367183.21/warc/CC-MAIN-20210303165500-20210303195500-00636.warc.gz"} | 93 |
https://socratic.org/questions/what-is-the-relationship-between-diatomic-molecules-and-diatomic-elements | # What is the relationship between diatomic molecules and diatomic elements?
So ${O}_{2}$ is a diatomic element (and thus a diatomic molecule)
$H C l$ is a diatomic molecule, but not a diatomic element. | 2020-01-29 20:09:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 2, "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": 0.7772149443626404, "perplexity": 1320.2249595090705}, "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/1579251802249.87/warc/CC-MAIN-20200129194333-20200129223333-00162.warc.gz"} | 51 |
http://math.stackexchange.com/questions/215646/if-i-have-n-choose-k-how-can-i-rewrite-it-to-be-something-that-ends-in-choose | # If I have (n choose k) how can I rewrite it to be something that ends in “choose k+1”?
See title for question; just trying to rewrite a combinatoric
-
Suppose that $k\ne n$. Then $$\binom{n}{k}=\frac{n!}{k!(n-k)!}=(k+1)\frac{n!}{(k+1)!(n-k)!}=\frac{k+1}{n-k}\frac{n!}{(k+1)!(n-k-1)!}.$$ It follows that $$\binom{n}{k}=\frac{k+1}{n-k}\binom{n}{k+1}.$$ | 2014-11-22 16:31:45 | {"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": 0.9704585075378418, "perplexity": 377.57288505377187}, "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-2014-49/segments/1416400378429.52/warc/CC-MAIN-20141119123258-00221-ip-10-235-23-156.ec2.internal.warc.gz"} | 145 |
https://socratic.org/questions/how-do-you-solve-2x-5-3-4x-5-1-5#159449 | # How do you solve (2x/5) + 3 - (4x/5) = 1/5?
$x = 7$
Rearrange to make $x$ the subject:
$\left(2 \frac{x}{5}\right) + 3 - \left(4 \frac{x}{5}\right) = \frac{1}{5}$ => $- 2 \frac{x}{5} = - \frac{14}{5}$ => $x = 7$ | 2021-10-17 12:53:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "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": 0.9085005521774292, "perplexity": 2144.528828898978}, "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/1634323585177.11/warc/CC-MAIN-20211017113503-20211017143503-00020.warc.gz"} | 106 |
https://www.authorea.com/users/5705/articles/62619-the-complexity-of-probability-distribution-functions/_show_article | # The complexity of probability distribution functions
AbstractThis is the abstract section. The abstract should be one section and count less than 200 words.
# Introduction
Main text paragraph. Citing a journal paper (Lastname 2008). And now citing a book reference (Lastname 2007).
Main text paragraph. | 2017-07-22 08:52:36 | {"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": 0.9885864853858948, "perplexity": 7232.04171277518}, "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-2017-30/segments/1500549423927.54/warc/CC-MAIN-20170722082709-20170722102709-00091.warc.gz"} | 65 |
http://mathcentral.uregina.ca/QQ/database/QQ.09.10/h/sarah3.html | SEARCH HOME
Math Central Quandaries & Queries
Question from Sarah, a student: what is pi + pi?
Hi Sarah,
$\pi + \pi$ is the same as $2 \times \pi.$ $\pi$ is approximately 3.1416 so $\pi + \pi$ is approximately 6.2832.
I hope this helps,
Penny
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. | 2017-10-22 22:59:15 | {"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": 0.7000290155410767, "perplexity": 1899.8636192885224}, "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/1508187825473.61/warc/CC-MAIN-20171022222745-20171023002745-00024.warc.gz"} | 95 |
http://soft-matter.seas.harvard.edu/index.php?title=Limit_cycle&direction=prev&oldid=11394 | # Limit cycle
A limit cycle in a dynamical system is a closed orbit in phase space, which is the limiting behavior of some trajectories either as $t->\infty$ or $t->-\infty$ | 2022-12-07 11:33:33 | {"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": 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": 0.8647662997245789, "perplexity": 206.41797555716812}, "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-2022-49/segments/1669446711151.22/warc/CC-MAIN-20221207085208-20221207115208-00298.warc.gz"} | 45 |
https://www.vcalc.com/wiki/DavidC/Fugacity+of+component+i+in+Vapor+phase | # Fugacity of component i in Vapor phase
Not Reviewed
hatf_i^V =
DavidC.Fugacity of component i in Vapor phase
The fugacity coefficient hatvarphi_i, for component i in the vapor is calculated from an equation of state (e.g., Virial). Sometimes it is approximated by a pure component value from a correlation. The fugacity coefficient is a correction for vapor phase non-ideality. Often at pressures close to atmospheric, hatvarphi_i= 1 | 2019-05-20 01:31:00 | {"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": 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": 0.9234142899513245, "perplexity": 6653.461342889303}, "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/1558232255251.1/warc/CC-MAIN-20190520001706-20190520023706-00200.warc.gz"} | 108 |
http://www.ams.org/mathscinet-getitem?mr=306566 | MathSciNet bibliographic data MR306566 33A30 Wong, R.; Rosenbloom, E. Series expansions of \$W\sb{k,\,m}(Z)\$$W\sb{k,\,m}(Z)$ involving parabolic cylinder functions. Math. Comp. 25 (1971), 783–787. Article
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews. | 2016-08-25 14:33:56 | {"extraction_info": {"found_math": true, "script_math_tex": 1, "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": 0.9994025230407715, "perplexity": 9671.080431538216}, "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-2016-36/segments/1471982293468.35/warc/CC-MAIN-20160823195813-00121-ip-10-153-172-175.ec2.internal.warc.gz"} | 112 |
https://homework.cpm.org/category/CC/textbook/cc2/chapter/1/lesson/1.2.2/problem/1-74 | ### Home > CC2 > Chapter 1 > Lesson 1.2.2 > Problem1-74
1-74.
Read this lesson’s Math Notes box about scaling axes. Then, on your paper, copy the incomplete axes below and write the missing numbers on each one. Homework Help ✎
1.
See the Math Notes box below for this lesson.
Look at the two ticks labeled $60$ and $100$. What is the difference of $60$ and $100$? How many spaces are between them?
See the number line below.
1.
See part (a).
1.
See the number line below.
1. See part (a). | 2019-09-20 10:25:01 | {"extraction_info": {"found_math": true, "script_math_tex": 4, "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": 0.5270220041275024, "perplexity": 3311.978831711024}, "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/1568514573988.33/warc/CC-MAIN-20190920092800-20190920114800-00405.warc.gz"} | 136 |
https://brilliant.org/problems/for-my-friend-nihar-mahajan-happy-birthday-man/ | For My Friend Nihar Mahajan (Happy Birthday Man)
Algebra Level 5
$\large{{ x }_{ n+1 }=\left\lfloor \sqrt [ 3 ]{ { x }_{ n }^{ 3 }-\left\lfloor \sqrt [ 3 ]{ { x }_{ n } } \right\rfloor } \right\rfloor }$
Let there be a sequence defined by above rule for $$n \ge 1$$. For $$n \ge k$$ the value of $$a_{n}$$ will be $$0$$, for some positive integer $$k$$. Find the value of $$k$$, if $$a_{1}=839475687$$.
× | 2017-05-22 23:32:23 | {"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": 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": 0.8132408857345581, "perplexity": 536.9970611747656}, "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-2017-22/segments/1495463607242.32/warc/CC-MAIN-20170522230356-20170523010356-00567.warc.gz"} | 150 |
http://docs.itascacg.com/pfc700/pfc/pfcmodule/doc/manual/ball_manual/ball_commands/cmd_ball.accumulate-stress.html | # ball accumulate-stress command
Syntax
ball accumulate-stress b
Specify that stresses are accumulated and stored during cycling. This slows performance by ~15% but allows the current stress state to be queried and used in contact models during force-displacement computations. By default, the ball stresses are not accumulated but are computed when queried. | 2021-10-18 16:49:58 | {"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": 0.6599735617637634, "perplexity": 8695.694507729548}, "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/1634323585204.68/warc/CC-MAIN-20211018155442-20211018185442-00020.warc.gz"} | 67 |
https://hackage-origin.haskell.org/package/summoner-1.2.0/candidate/docs/Summoner-Text.html | summoner-1.2.0: Tool for scaffolding completely configured production Haskell projects.
Summoner.Text
Synopsis
# Documentation
Creates module name from the name of the package Ex: my-lovely-projectMyLovelyProject
intercalateMap :: Text -> (a -> Text) -> [a] -> Text Source #
Converts every element of list into Text and then joins every element into single Text like intercalate.
tconcatMap :: (a -> Text) -> [a] -> Text Source #
Convert every element of a list into text, and squash the results | 2022-10-07 12:44:07 | {"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": 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": 0.21839125454425812, "perplexity": 8154.598924585832}, "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-2022-40/segments/1664030338073.68/warc/CC-MAIN-20221007112411-20221007142411-00277.warc.gz"} | 120 |
https://learn.careers360.com/ncert/question-write-a-pair-of-integers-whose-product-is-minus-12-and-there-lies-seven-integers-between-them-excluding-the-given-integers/?question_number=114.0 | # Get Answers to all your Questions
#### Write a pair of integers whose product is –12 and there lies seven integers between them (excluding the given integers).
The integers -2 and 6 are such that
$(-2) \times 6=-12$
There are seven integers i.e-1,0,1,2,3,4,5 which lie between them. | 2023-03-23 00:53:33 | {"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": 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": 0.484296590089798, "perplexity": 1237.666894058577}, "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-2023-14/segments/1679296944606.5/warc/CC-MAIN-20230323003026-20230323033026-00511.warc.gz"} | 81 |
https://www.lessonplanet.com/teachers/one-two-three-isaac-newton-and-me-9th-12th | # One Two three Isaac Newton and Me
Young scholars discover that the learning cycle develops the concepts of Newton's Laws and applies these concepts to travel in space. | 2018-11-18 04:25:02 | {"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": 0.9362950325012207, "perplexity": 1633.1498929015647}, "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-2018-47/segments/1542039743963.32/warc/CC-MAIN-20181118031826-20181118053826-00302.warc.gz"} | 32 |
https://www.wyzant.com/resources/answers/262075/bus_calc_dimensions | Lexi D.
# Bus. Calc dimensions
For reasons too complicated to explain, I need to create a rectangular orchid garden with an area of exactly 169 sq. ft. abutting my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $4 per foot, and the fencing for the east and west sides costs$2 per foot. What are the dimensions of the orchid garden with the least expensive fence? | 2021-08-02 05:54:32 | {"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": 0.1800849884748459, "perplexity": 2933.0446582573286}, "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-2021-31/segments/1627046154304.34/warc/CC-MAIN-20210802043814-20210802073814-00195.warc.gz"} | 93 |
http://www.pacm.princeton.edu/node/632 | # Low-Rank Covariance for Cryo-EM Clustering
Speaker:
Joakim Anden
Date:
Apr 5 2016 - 12:30pm
Event type:
Cryo-electron microscopy (cryo-EM) provides 2D projections of 3D molecules by measuring electron absorption. Due to very high noise, a large
demonstrating its effectiveness for clustering heterogeneous cryo-EM samples. | 2017-09-24 15:38:26 | {"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": 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": 0.27436941862106323, "perplexity": 14435.073832788068}, "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-2017-39/segments/1505818690035.53/warc/CC-MAIN-20170924152911-20170924172911-00304.warc.gz"} | 90 |
https://barneyshi.me/2021/08/18/power-of-three/ | # Leetcode 326 - Power of three
Note: It’s not that hard but there are some traps in this problem.
method 1:
method 2: | 2022-10-05 00:07:03 | {"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": 0.4305623173713684, "perplexity": 3354.3265364632416}, "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-2022-40/segments/1664030337529.69/warc/CC-MAIN-20221004215917-20221005005917-00362.warc.gz"} | 34 |
http://spot.pcc.edu/math/orcca/knowl/exercise-1063.html | ###### Exercise17
Use the associative property of multiplication to write an equivalent expression to $${4\!\left(5m\right)}\text{.}$$
in-context | 2018-10-17 18:11:23 | {"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": 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": 0.9476216435432434, "perplexity": 2565.308695002809}, "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-2018-43/segments/1539583511206.38/warc/CC-MAIN-20181017174543-20181017200043-00252.warc.gz"} | 37 |
http://openstudy.com/updates/55b54e71e4b0ce105661620f | ## anonymous one year ago Solve for x: |3x + 12| = 18 x = 2, x = –10 x = 2, x = –2 x = 10, x = –10 x = –2, x = 10
$\huge~\rm~3x + 12 = 18$ $\huge~\rm~3x + 12= -18$ Now solve for x you end up with 2 answers | 2016-10-22 18:17:07 | {"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": 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": 0.20207743346691132, "perplexity": 245.5868255189564}, "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-2016-44/segments/1476988719033.33/warc/CC-MAIN-20161020183839-00485-ip-10-171-6-4.ec2.internal.warc.gz"} | 97 |
https://www.cableizer.com/documentation/d_b3/ | # Distance c of multi-layer backfill
Distance c to calculate the resistance of multi-layer backfill.
Symbol
$d_{b3}$
Unit
m
Formulae
$\sqrt{{s_{b3}}^2+{w_{b4}}^2}$
Related
$s_{b3}$
$w_{b4}$
Used in
$R_{q11}$
$R_{q21}$ | 2022-01-24 07:43:58 | {"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": 0.8181958198547363, "perplexity": 14198.510523859666}, "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/1642320304515.74/warc/CC-MAIN-20220124054039-20220124084039-00678.warc.gz"} | 88 |
https://homework.cpm.org/category/CCI_CT/textbook/apcalc/chapter/7/lesson/7.1.1/problem/7-10 | Home > APCALC > Chapter 7 > Lesson 7.1.1 > Problem7-10
7-10.
Sketch the region bounded by $y = x^4$ and $y = 1$. Calculate the exact area of the region.
What are your limits of integration? Which function has higher $y$-values and which has lower? | 2021-09-26 03:19:09 | {"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": 0.8511502742767334, "perplexity": 1464.4991570389286}, "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-2021-39/segments/1631780057796.87/warc/CC-MAIN-20210926022920-20210926052920-00420.warc.gz"} | 75 |
https://proofwiki.org/wiki/Parseval%27s_Theorem | # Parseval's Theorem
## Theorem
Let $f$ be a function square-integrable over $\left[-\pi \ldots \pi\right]$ given by the Fourier series,
$\displaystyle f(x) \cong \frac {a_0} 2 + \sum_{n=1}^\infty \left(a_n \cos\left(nx\right) + b_n\sin\left(nx\right)\right)$
Then,
$\displaystyle \frac 1 \pi \int_{-\pi}^\pi \left|f^2(x)\right|\mathrm dx = \frac {a_0^2} 2 + \sum_{n=1}^\infty \left(a^2_n + b^2_n\right)$
## Source of Name
This entry was named for Marc-Antoine Parseval. | 2018-02-24 19:40:38 | {"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": 0.7820825576782227, "perplexity": 5487.432633450625}, "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/1518891815934.81/warc/CC-MAIN-20180224191934-20180224211934-00190.warc.gz"} | 183 |
http://mathhelpforum.com/calculus/58535-stationary-points.html | # Math Help - Stationary points
1. ## Stationary points
Prove that the polynomial
$f=(x^2+y^2)(x^2+y^2+1)z+z^3+x+y$
doesn't have real stationary points.
Thanks!!!
2. Originally Posted by roporte
Prove that the polynomial
$f=(x^2+y^2)(x^2+y^2+1)z+z^3+x+y$
doesn't have real stationary points.
Thanks!!!
Start by calculating the partial derivatives and equating them to zero. Can you do that? Post your answers. | 2015-09-01 04:11:37 | {"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": 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": 0.8762442469596863, "perplexity": 3916.3481251942617}, "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-2015-35/segments/1440645151768.51/warc/CC-MAIN-20150827031231-00099-ip-10-171-96-226.ec2.internal.warc.gz"} | 125 |
https://socratic.org/questions/given-the-first-term-and-the-common-dimerence-er-an-arithmetic-sequence-how-do-y-2 | # Given the first term and the common dimerence er an arithmetic sequence how do you find the 52nd term and the explicit formula: a_1=12, d=-20?
Dec 7, 2017
${a}_{52} = - 1008$
#### Explanation:
We can write the nth term of the sequence:
${a}_{n} = {a}_{1} + d \cdot \left(n - 1\right)$
So, we have ${a}_{n} = 12 - 20 \cdot \left(n - 1\right)$.
To find the 52nd term we now substitute 52 for n:
${a}_{52} = 12 - 20 \cdot \left(52 - 1\right) =$
$= 12 - 20 \left(51\right) = 12 - 1020 = - 1008$ | 2019-11-17 03:02:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "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": 0.9819767475128174, "perplexity": 1675.5948093957848}, "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/1573496668782.15/warc/CC-MAIN-20191117014405-20191117042405-00426.warc.gz"} | 190 |
https://homework.cpm.org/category/CC/textbook/cca2/chapter/8/lesson/8.2.1/problem/8-71 | ### Home > CCA2 > Chapter 8 > Lesson 8.2.1 > Problem8-71
8-71.
Explain why $i^{3} = –i$. What does $i^{4}$ equal?
$i ^{3} = i ^{2} · i$. What does $i ^{2}$ equal?
How can you rewrite $i ^{4}$ as a product of $i ^{2}$ and/or $i$ factors? | 2020-12-01 18:18:14 | {"extraction_info": {"found_math": true, "script_math_tex": 7, "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": 0.5336148738861084, "perplexity": 2376.678863377428}, "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-2020-50/segments/1606141681209.60/warc/CC-MAIN-20201201170219-20201201200219-00307.warc.gz"} | 100 |
https://www.gradesaver.com/textbooks/science/physics/university-physics-with-modern-physics-14th-edition/chapter-44-particle-physics-and-cosmology-problems-discussion-questions-page-1519/q44-2 | University Physics with Modern Physics (14th Edition)
It is possible to momentarily create particle-antiparticle pairs of energy $\Delta E$ for a short time $\Delta t$ as long as Heisenberg’s uncertainty principle for matter is obeyed. Empty space is not truly empty. | 2019-11-20 14:02:04 | {"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": 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": 0.1863218992948532, "perplexity": 325.11467606780946}, "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-2019-47/segments/1573496670559.66/warc/CC-MAIN-20191120134617-20191120162617-00111.warc.gz"} | 58 |
https://web2.0calc.com/questions/inequality_122 | +0
# Inequality
0
121
2
Solve the inequality 2x - 5 < -x - 12. Give your answer as an interval.
Dec 20, 2021
#1
+179
+1
$$\left(-\infty \:,\:-\frac{7}{3}\right)$$One of these 2 should be correct
Dec 20, 2021
#2
+13724
+1
$$x\in \mathbb R\ |\ x<-\frac{7}{3}$$
asinus Dec 20, 2021 | 2022-06-29 22:28:07 | {"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": 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": 0.9714916348457336, "perplexity": 8811.715679320752}, "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/1656103645173.39/warc/CC-MAIN-20220629211420-20220630001420-00266.warc.gz"} | 134 |
https://www.gradesaver.com/textbooks/math/calculus/calculus-8th-edition/appendix-d-trigonometry-d-exercises-page-a32/14 | # Appendix D - Trigonometry - D Exercises - Page A32: 14
$4\pi$ centimeters
#### Work Step by Step
We use the formula $s=θr$ $θ$ must be in radians. It is given in degrees. We convert from radians to degrees: $72°\times\frac{\pi}{180}=\frac{2\pi}{5}$ Plug in given values and simplify: $s=\frac{2\pi}{5}(10)=4\pi$ centimeters
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. | 2019-11-17 09:40:32 | {"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": 0.7904466986656189, "perplexity": 1699.9777962571673}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2019-47/segments/1573496668910.63/warc/CC-MAIN-20191117091944-20191117115944-00102.warc.gz"} | 144 |
https://socratic.org/questions/how-many-moles-are-present-in-454-grams-of-co-2 | # How many moles are present in 454 grams of CO_2?
Moles of $C {O}_{2}$ $=$
(454*g)/(44*g*mol^(-1)) = ?? mol | 2019-08-18 21:58:00 | {"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": 0.4730672240257263, "perplexity": 4652.86145985315}, "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/1566027314130.7/warc/CC-MAIN-20190818205919-20190818231919-00514.warc.gz"} | 44 |
https://brilliant.org/problems/trailing-zeroes-of-a-sum/ | # Trailing zeroes of a sum
How many trailing zeroes are in the decimal representation of $n=1+\displaystyle{\sum_{k=1}^{2013}k!(k^3+2k^2+3k+1)}?$
× | 2017-03-29 19:18:29 | {"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": 0.6082990765571594, "perplexity": 1002.9540190631503}, "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/1490218191353.5/warc/CC-MAIN-20170322212951-00494-ip-10-233-31-227.ec2.internal.warc.gz"} | 55 |
http://math.stackexchange.com/questions/334341/prod-k-0-infty-p-k-0-rightarrow-sum-k-0-infty-1-p-k-infty | # $\prod_{k=0}^\infty p_k > 0 \Rightarrow \sum_{k=0}^\infty (1-p_k) < \infty$
Let $\{p_k\}$ be a probability mass sequence. Is it true that if $\prod_{k=0}^\infty p_k > 0$ then $\sum_{k=0}^\infty (1-p_k) < \infty$?
-
Actually, I just noticed that my question does not make sense, because if $\{p_k\}$ is a probability mass sequence, then $\sum_{k=0}^\infty p_k = 1$, but then $\prod_{k=0}^\infty p_k$ cannot be greater than $0$. I'm sorry. – user67398 Mar 20 '13 at 1:59 | 2016-05-01 23:54:12 | {"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": 0.955426037311554, "perplexity": 99.43609365424109}, "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-2016-18/segments/1461860117244.29/warc/CC-MAIN-20160428161517-00006-ip-10-239-7-51.ec2.internal.warc.gz"} | 180 |
https://www.esaral.com/q/solve-this-following-42643 | # Solve this following
Question:
If $2\left(\begin{array}{cc}3 & 4 \\ 5 & x\end{array}\right)+\left(\begin{array}{ll}1 & y \\ 0 & 1\end{array}\right)=\left(\begin{array}{cc}7 & 0 \\ 10 & 5\end{array}\right)$
A. $(x=-2, y=8)$
B. $(x=2, y=-8)$
C. $(x=3, y=-6)$
D. $(x=-3, y=6)$
Solution: | 2023-02-01 13:29:10 | {"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": 0.7952053546905518, "perplexity": 6971.525819888254}, "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-2023-06/segments/1674764499934.48/warc/CC-MAIN-20230201112816-20230201142816-00691.warc.gz"} | 137 |
https://www.gradesaver.com/textbooks/science/chemistry/chemistry-and-chemical-reactivity-9th-edition/chapter-2-atoms-molecules-and-ions-study-questions-page-95a/18 | ## Chemistry and Chemical Reactivity (9th Edition)
All but $_{18}^{9}X$ are isotopes of X.
Since the element has an atomic number of 9, all species with an atomic number of 9 are X's isotopes, so all but $_{18}^{9}X$ are isotopes of X. | 2018-06-18 04:32:52 | {"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": 0.6236510276794434, "perplexity": 1362.9732828621243}, "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/1529267860041.64/warc/CC-MAIN-20180618031628-20180618051628-00324.warc.gz"} | 72 |
http://www.gradesaver.com/textbooks/math/calculus/calculus-10th-edition/chapter-3-applications-of-differentiation-3-3-exercises-page-186/92 | # Chapter 3 - Applications of Differentiation - 3.3 Exercises: 92
False.
#### Work Step by Step
Let $h(x)=f(x)\times g(x)$ and $f'(x)gt;0; g'(x)gt;0$ over some interval $(a, b).$ Then $h'(x)=f'(x)g(x)+g'(x)f(x)$ which is not necessarily positive over the interval $(a, b)$ since we do not know the values of $f(x)$ and $g(x).$
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. | 2017-03-24 08:36:49 | {"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": 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": 0.7557439208030701, "perplexity": 372.3543037841425}, "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-2017-13/segments/1490218187744.59/warc/CC-MAIN-20170322212947-00344-ip-10-233-31-227.ec2.internal.warc.gz"} | 149 |
https://www.mathplanet.com/education/act/problems-21-40/32-what-is-the-value-of-cos-theta | # 32. What is the value of cos theta?
$\begin{array}{lcl} The\;angle\;\theta\;lies\;in\;the\;second\\ quadrant\;and\;\sin \theta = \frac{4}{5}.\;What\;is\;the\\ value\;of\;\cos \theta ?\\ \\ (F)\; \frac{1}{5}\\ \\ (G)\; \frac{3}{5}\\ \\ (H)\; -\frac{3}{5}\\ \\ (J)\; -\frac{1}{5}\\ \\ (K)\; \frac{2}{5}\\ \end{array}$ | 2023-02-04 11:51:11 | {"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": 0.582552969455719, "perplexity": 1105.0604491379536}, "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-2023-06/segments/1674764500126.0/warc/CC-MAIN-20230204110651-20230204140651-00349.warc.gz"} | 145 |
https://proofwiki.org/wiki/Definition:Multiplicative_Identity | Definition:Multiplicative Identity
Definition
Let $\left({F, +, \times}\right)$ be a field.
Then the identity element of the multiplicative group $\left({F^*, \times}\right)$ of $F$ is called the multiplicative identity of $F$.
It is often denoted $e_F$ or $1_F$, or, if there is no danger of ambiguity, $e$ or $1$.
Note that the multiplicative identity of $F$ is the unity of the ring that $\left({F, +, \times}\right)$ is by definition of a field. | 2020-01-18 22:34:30 | {"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": 0.9919002056121826, "perplexity": 61.79137892567198}, "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-2020-05/segments/1579250593994.14/warc/CC-MAIN-20200118221909-20200119005909-00506.warc.gz"} | 128 |
https://www.physicsforums.com/threads/circumference-of-a-4-sphere.675800/ | # Circumference of a 4-sphere
What is the circumference of a four dimensional sphere?
$2\pi R$, I guess. | 2020-10-24 04:09:09 | {"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": 0.9813919067382812, "perplexity": 1969.1104201784306}, "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/1603107881640.29/warc/CC-MAIN-20201024022853-20201024052853-00135.warc.gz"} | 30 |
http://openstudy.com/updates/50e4c46be4b0e36e35149417 | ## mtmb11 2 years ago What is the simplified form of the expression.
1. mtmb11
2. RainbowsandCats
Dude type the question the link doesn't show on my computer
3. mtmb11
$\sqrt{1}\over 121$
4. RainbowsandCats
is that a i where the square root is or ....
5. mtmb11
the square root is over the whole equation
6. RainbowsandCats
ohh okay the square root of 121 is 11 so i think it would be |dw:1357170094551:dw|
7. RainbowsandCats
im not really sure 0.0
8. mtmb11
l0l its ok | 2015-04-19 17:51:16 | {"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": 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": 0.7196729183197021, "perplexity": 2777.80466303711}, "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-2015-18/segments/1429246639325.91/warc/CC-MAIN-20150417045719-00219-ip-10-235-10-82.ec2.internal.warc.gz"} | 159 |
https://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-for-college-students-7th-edition/chapter-9-section-9-3-logarithmic-functions-exercise-set-page-700/48 | ## Intermediate Algebra for College Students (7th Edition)
$(-6, +\infty)$.
RECALL: The domain of the logarithmic function $f(x) = \log_a{x}$ is $x \gt 0$. Thus, the domain of the given function is the set of all real numbers such that: $x+6 \gt 0$. Solve the inequality to obtain: $x + 6 \gt 0 \\x \gt 0-6 \\x \gt -6$ Therefore, the domain of the given function is $(-6, +\infty)$. | 2018-07-18 03:33:01 | {"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": 0.9003852605819702, "perplexity": 122.13091864901985}, "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-2018-30/segments/1531676590046.11/warc/CC-MAIN-20180718021906-20180718041906-00510.warc.gz"} | 125 |
http://openstudy.com/updates/4e4482fa0b8b3609c72033af | ## anonymous 5 years ago solve for the indicated letter a = 5b the solution is b =
1. anonymous
b=a/5
2. anonymous
$\frac{a}{5}$
3. KatrinaKaif
Divide by 5 on both sides to get b alone so a/5 = b | 2016-10-26 23:29:04 | {"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": 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": 0.48008793592453003, "perplexity": 2826.7093462270072}, "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-2016-44/segments/1476988721008.78/warc/CC-MAIN-20161020183841-00274-ip-10-171-6-4.ec2.internal.warc.gz"} | 66 |
http://ahay.org/blog/2006/11/01/claerbouts-nmo/ | Moveout, velocity, and stacking, another chapter from Jon Claerbout‘s book Basic Earth Imaging is added to the collection of reproducible papers. There are some slight modifications due to substituting Madagascar programs. | 2020-02-18 06:43:46 | {"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": 0.8988760709762573, "perplexity": 5609.510867073129}, "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/1581875143635.54/warc/CC-MAIN-20200218055414-20200218085414-00228.warc.gz"} | 42 |
http://www.ams.org/mathscinet-getitem?mr=1765876 | MathSciNet bibliographic data MR1765876 37A30 (28D05 37E10 60F15 60G10 60H25) Ruffino, Paulo R. C. A sampling theorem for rotation numbers of linear processes in ${\bf R}^2$${\bf R}^2$. Random Oper. Stochastic Equations 8 (2000), no. 2, 175–188. Article
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews. | 2017-01-18 16:22:56 | {"extraction_info": {"found_math": true, "script_math_tex": 1, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9880372285842896, "perplexity": 10906.406741763727}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280308.24/warc/CC-MAIN-20170116095120-00323-ip-10-171-10-70.ec2.internal.warc.gz"} | 136 |
https://brilliant.org/problems/a-simple-sum/ | # A Simple Sum
Logic Level 2
$\array{\hspace{.5cm}XXXX\\ \hspace{.5cm}YYYY\\ + ZZZZ\\ \hline YXXXZ}$
In the sum above, each letter represents a digit (0,1,2,3,4,5,6,7,8,9).
Find the value of $$Z$$.
By the way $$X,Y$$ and $$Z$$ are not equal.
× | 2017-05-24 09:56:28 | {"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": 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": 0.7900927066802979, "perplexity": 1053.697175237534}, "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-2017-22/segments/1495463607811.15/warc/CC-MAIN-20170524093528-20170524113528-00198.warc.gz"} | 100 |
http://www.chegg.com/homework-help/questions-and-answers/a-charge-of-876mc-is-placed-at-each-corner-of-a-square-0420m-on-a-side-a-determine-the-mag-q3578765 | ## Find the Magnitude of the Force on Each Charge
A charge of 8.76mC is placed at each corner of a square 0.420m on a side. (A) Determine the magnitude of the force on each charge. (B) Determine the direction of the force on each charge: 1. From the center of the square towards the charge 2. From the charge towards the center of the square OR 3. Another direction | 2013-05-25 19:29:57 | {"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": 0.8408920168876648, "perplexity": 253.00804578809525}, "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-2013-20/segments/1368706121989/warc/CC-MAIN-20130516120841-00053-ip-10-60-113-184.ec2.internal.warc.gz"} | 94 |
https://www.physicsforums.com/threads/integration-and-trigonometricfunctions.464104/ | # Integration and trigonometricfunctions
howsockgothap
## Homework Statement
Integrate: 3sec3x(3sec3x+2tan3x)dx
## The Attempt at a Solution
Ok I just multiplied out and obviously got the integrals of both to be tan3x +c and 6sec3x+c
My question is does that make my final answer tan3x+6sec3x +c or +2c?
I swear this is the last integration question I will ask. For awhile. | 2022-08-19 06:05:07 | {"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": 0.8062633275985718, "perplexity": 3726.3125041830194}, "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/1659882573623.4/warc/CC-MAIN-20220819035957-20220819065957-00436.warc.gz"} | 113 |
https://proofwiki.org/wiki/Primitive_of_Root_of_a_squared_minus_x_squared | # Primitive of Root of a squared minus x squared
$\ds \int \sqrt {a^2 - x^2} \rd x = \frac {x \sqrt {a^2 - x^2} } 2 + \frac {a^2} 2 \arcsin \frac x a + C$
$\ds \int \sqrt {a^2 - x^2} \rd x = \frac {x \sqrt {a^2 - x^2} } 2 - \frac {a^2} 2 \arccos \frac x a + C$ | 2023-02-08 19:53:18 | {"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": 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": 0.9698591232299805, "perplexity": 774.1297926289777}, "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-2023-06/segments/1674764500904.44/warc/CC-MAIN-20230208191211-20230208221211-00330.warc.gz"} | 127 |
https://learnzillion.com/resources/72203-rewrite-an-expression-to-understand-how-the-quantities-are-related-7-ee-a-2 | # Rewrite an expression to understand how the quantities are related (7.EE.A.2)
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05". | 2019-12-07 10:01:11 | {"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": 0.9110566973686218, "perplexity": 563.5036407554514}, "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-2019-51/segments/1575540497022.38/warc/CC-MAIN-20191207082632-20191207110632-00046.warc.gz"} | 83 |
https://www.gradesaver.com/textbooks/math/algebra/algebra-and-trigonometry-10th-edition/chapter-1-1-2-linear-equations-in-one-variable-1-2-exercises-page-87/15 | ## Algebra and Trigonometry 10th Edition
$x=4$
$x+11=15\\x+11-11=15-11\\x=4$ Checking the solution: $4+11=15$, which is true. | 2020-02-16 21:34:14 | {"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": 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": 0.9302284121513367, "perplexity": 2071.781931146873}, "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/1581875141430.58/warc/CC-MAIN-20200216211424-20200217001424-00191.warc.gz"} | 50 |
https://socratic.org/questions/a-sample-of-rock-is-found-to-contain-100-grams-ion-a-parent-isotope-how-many-gra | # A sample of rock is found to contain 100 grams ion a parent isotope. How many grams of the parent isotope will remain after two half lives?
After one half life 50 grams $\frac{100}{2} = 50$
After two half lives 25 grams $\frac{50}{2} = 25$ | 2019-07-22 12:48:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 2, "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": 0.1935151368379593, "perplexity": 1309.2451943124195}, "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-2019-30/segments/1563195528013.81/warc/CC-MAIN-20190722113215-20190722135215-00351.warc.gz"} | 69 |
https://homework.cpm.org/category/CON_FOUND/textbook/mc1/chapter/9/lesson/9.2.2/problem/9-69 | ### Home > MC1 > Chapter 9 > Lesson 9.2.2 > Problem9-69
9-69.
Find the area and perimeter of the figure at right. All angles are right angles. Show your work.
Use the new side labels to help you find both the area and the perimeter of this figure.
Remember that area is the space within a shape and perimeter is the distance around a shape.
To find the area, add the areas of the separate sections, as labeled in red.
$37.8 + 19.74 = 57.54$ square units | 2022-06-25 11:36:06 | {"extraction_info": {"found_math": true, "script_math_tex": 1, "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": 0.618738055229187, "perplexity": 1064.5496620635263}, "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/1656103034930.3/warc/CC-MAIN-20220625095705-20220625125705-00507.warc.gz"} | 120 |
https://ifc43-docs.standards.buildingsmart.org/IFC/RELEASE/IFC4x3/HTML/lexical/Qto_SlabBaseQuantities.htm | # 6.1.5.13 Qto_SlabBaseQuantities
## 6.1.5.13.1 Semantic definition
Base quantities that are common to the definition of all occurrences of slabs. | 2023-03-26 02:37:49 | {"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": 0.8096998929977417, "perplexity": 8101.398796540309}, "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-2023-14/segments/1679296945381.91/warc/CC-MAIN-20230326013652-20230326043652-00747.warc.gz"} | 46 |
http://clay6.com/qa/45904/a-potential-difference-of-250-volt-is-applied-across-the-plates-of-a-capaci | # A potential difference of $250\; volt$ is applied across the plates of a capacitor of $10\; pF$. Calculate the charge on the plates of the capacitor.
## 1 Answer
Here,$V= 250 V$
$C= 10 \;p$
$F= 10 \times 10^{-12} F= 10^{-11}F$
$Q= CV=10^{-11} \times 250=2.5 \times 10^{-9}$
Hence A is the correct answer.
answered Jun 13, 2014 by
1 answer
1 answer | 2018-06-19 19:47:11 | {"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": 0.6473622918128967, "perplexity": 792.8789065631371}, "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-2018-26/segments/1529267863119.34/warc/CC-MAIN-20180619193031-20180619213031-00335.warc.gz"} | 128 |
https://insignificancegalore.net/2007/03/all-gone/ | # All gone
Managed to find the structure of the poles in my marginal “cirkus tent” distribution. Before and after graphs: | 2021-05-13 00:28:06 | {"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": 0.9287798404693604, "perplexity": 4154.807173694315}, "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/1620243991413.30/warc/CC-MAIN-20210512224016-20210513014016-00170.warc.gz"} | 28 |
http://bandicoot.mit.edu/docs/reference/generated/bandicoot.network.assortativity_attributes.html | # assortativity_attributes¶
bandicoot.network.assortativity_attributes(user)
Computes the assortativity of the nominal attributes.
This indicator measures the homophily of the current user with his correspondants, for each attributes. It returns a value between 0 (no assortativity) and 1 (all the contacts share the same value): the percentage of contacts sharing the same value. | 2018-12-15 01:09:12 | {"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": 0.19014039635658264, "perplexity": 3044.889093985412}, "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/1544376826530.72/warc/CC-MAIN-20181214232243-20181215014243-00233.warc.gz"} | 80 |
https://api-project-1022638073839.appspot.com/questions/how-do-you-solve-log-x-2-2 | # How do you solve log x^2 =2?
##### 1 Answer
Oct 5, 2015
$x = \pm 10$
#### Explanation:
Assuming that's the common log, take the base 10 exponential of both sides, that is, the "sideth" power of 10.
$\log \left({x}^{2}\right) = 2$
${x}^{2} = {10}^{2}$
Take the root
$x = \pm 10$
Since ${x}^{2}$ is positive for all values of $x$ the only value of $x$ we can't have is $0$, so both answers are okay. | 2021-10-26 17:24:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 8, "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": 0.8923617005348206, "perplexity": 1137.4008725591382}, "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-2021-43/segments/1634323587915.41/warc/CC-MAIN-20211026165817-20211026195817-00346.warc.gz"} | 144 |