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values | warc_filename stringlengths 108 138 | warc_record_offset int32 14.3k 1.61B | warc_record_length int32 798 787k | text stringlengths 97 686k | token_count int32 41 240k | char_count int32 97 686k | metadata stringlengths 439 442 | score float64 3.5 5.06 | int_score int64 4 5 | crawl stringclasses 93
values | snapshot_type stringclasses 2
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value | language_score float64 0.07 0.99 | backtracking_raw stringlengths 0 12.2k | verification_raw stringlengths 0 12.2k | subgoal_setting_raw stringlengths 0 10.2k | backward_chaining_raw stringlengths 0 12.2k |
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https://warreninstitute.org/geometry-parallel-lines-cut-by-a-transversal-worksheet/ | 1,708,699,394,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474412.46/warc/CC-MAIN-20240223121413-20240223151413-00646.warc.gz | 637,850,853 | 22,801 | # Explore the Geometry of Parallel Lines with this Transversal Worksheet!
Welcome to Warren Institute! In today's article, we will dive into the fascinating world of geometry. Specifically, we will explore the concept of parallel lines being cut by a transversal. This interactive worksheet is designed to help students... | 1,426 | 8,242 | {"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, "ma... | 4.40625 | 4 | CC-MAIN-2024-10 | latest | en | 0.904937 | user
## Thoughts
The provided text is an educational article about a worksheet on parallel lines and transversals. It does not contain any instances where the writer realizes a path won't work and explicitly goes back to try a different approach. The text is informative and structured, guiding the reader through the co... | user
## Thoughts
The provided text is an introduction to a worksheet about parallel lines and transversals. It includes explanations, strategies for teaching, and tips for designing worksheets. However, it does not contain any explicit steps where the writer checks their own work or verifies any calculations or results... | user
## Thoughts
The text provided is an overview of a worksheet designed to help students understand the concept of parallel lines cut by a transversal. It outlines different sections of the worksheet, such as understanding the concept, properties of angles, applying angle relationships, and enhancing geometric reason... | user
## Thoughts
The provided text is an introduction to a worksheet about parallel lines and transversals in geometry. It outlines the sections of the worksheet and provides strategies for teaching the concept, designing worksheets, addressing misconceptions, and differentiating instruction. However, the text does not... |
http://photo.portal.prolisok.org/mexf2/losi-8ight-t-nitro-rtr-review-362a4c | 1,632,390,908,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057417.92/warc/CC-MAIN-20210923074537-20210923104537-00620.warc.gz | 47,134,524 | 9,880 | (b) Write 0.000 35 in standard form. Competency Based Curriculum Design Materials Marvel Cinematic Universe Phase 3 Quiz! Three toy cars and 4 toy trains cost $18. Answer question 5 on page 2. Grade 5 maths problems with answers are presented. Here is a list of all of the maths skills students learn in grade 5! She sta... | 5,286 | 21,336 | {"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, "mat... | 4.34375 | 4 | CC-MAIN-2021-39 | latest | en | 0.898932 | assistant ## Thoughts
The provided text is a collection of various math problems and questions aimed at grade 5 students. It does not contain any narrative or discussion that would indicate a writer's thought process or any backtracking behavior. The text simply lists problems and solutions without any indication of a ... | assistant ## Thoughts
The provided text is a collection of various math problems and questions aimed at grade 5 students. It includes problems on standard form, fractions, geometry, and arithmetic. However, the text does not contain any explicit verification steps where the writer checks their work by comparing results... | assistant ## Thoughts
The provided text is a collection of various math problems and questions aimed at grade 5 students. It does not contain any explicit subgoal setting where the writer breaks down the problem into smaller, intermediate goals. Each problem is presented as a standalone question without any step-by-ste... | assistant ## Thoughts
The provided text is a collection of math problems and solutions aimed at grade 5 students. It does not contain any backward-chaining behavior as described in the task. The problems are presented in a straightforward manner, asking for solutions to various math problems without starting from a goa... |
https://economictheoryblog.com/2018/10/17/derivation-of-the-least-squares-estimator-for-beta-in-matrix-notation-proof-nr-1/?replytocom=18970 | 1,618,253,021,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038069133.25/warc/CC-MAIN-20210412175257-20210412205257-00048.warc.gz | 327,099,481 | 23,003 | Derivation of the Least Squares Estimator for Beta in Matrix Notation – Proof Nr. 1
In the post that derives the least squares estimator, we make use of the following statement:
$\frac{\partial b'X'Xb}{\partial b} =2X'Xb$
This post shows how one can prove this statement. Let’s start from the statement that we want t... | 1,182 | 3,089 | {"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": 18, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "ma... | 4.4375 | 4 | CC-MAIN-2021-17 | latest | en | 0.464662 | assistant
## Thoughts
The text provided is a mathematical derivation of the least squares estimator for beta in matrix notation. Throughout the derivation, there is a clear and consistent progression of steps without any indication of the writer realizing a mistake or needing to backtrack to a previous step. The writer... | assistant ## Thoughts
The text provided is a detailed derivation of the least squares estimator for beta in matrix notation. It does not contain any explicit verification steps where the author checks their work by comparing results to known values or rechecking calculations. The text focuses on the derivation process ... | assistant
## Thoughts
The text describes a proof for a mathematical statement involving the derivative of a matrix expression. The writer simplifies the problem by labeling $X'X$ as $A$ to make the math easier. The writer then proceeds to compute the partial derivative of $\hat{\beta}'A\hat{\beta}$ with respect to $\ha... | assistant ## Thoughts
The text starts with the statement it wants to prove and then works backward by simplifying and breaking down the problem into smaller parts. It uses the assumption of the statement's truth to guide the steps of the proof, which is a clear example of backward-chaining.
## Does the text exhibit ba... |
https://tutorialcup.com/tag/sap | 1,726,418,786,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651632.84/warc/CC-MAIN-20240915152239-20240915182239-00237.warc.gz | 542,821,946 | 18,559 | ## Binary Search LeetCode Solution
Problem Statement Binary Search LeetCode Solution says that – Given an array of integers nums which is sorted in ascending order, and an integer target, write a function to search target in nums. If target exists, then return its index. Otherwise, return -1. You must write an algorit... | 934 | 3,832 | {"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, "ma... | 3.84375 | 4 | CC-MAIN-2024-38 | latest | en | 0.677803 | userityEngineRecognitionException | userFilterWhere did you find any verification steps in the provided texts? If so, how many? If not, please indicate that as well. | userityEngineer | userityEngineRecognitionException |
https://nrich.maths.org/public/leg.php?code=-985&cl=2&cldcmpid=1140 | 1,558,467,028,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232256546.11/warc/CC-MAIN-20190521182616-20190521204616-00323.warc.gz | 561,529,501 | 7,149 | # Search by Topic
#### Resources tagged with PrimaryResourceful similar to A Puzzling Cube:
Filter by: Content type:
Age range:
Challenge level:
### There are 28 results
Broad Topics > Habits of Mind > PrimaryResourceful
### A Puzzling Cube
##### Age 7 to 11 Challenge Level:
Here are the six faces of a cube - in... | 1,246 | 5,230 | {"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, "ma... | 3.5625 | 4 | CC-MAIN-2019-22 | longest | en | 0.902247 | user
## Thoughts
The provided text is a list of mathematical and logical puzzles and challenges aimed at different age groups. Each entry describes a challenge or problem to be solved, but there is no indication of any backtracking behavior where the writer realizes a path won't work and explicitly goes back to try a d... | assistant ## Thoughts
The provided text is a list of mathematical and logical puzzles or challenges aimed at different age groups. Each challenge describes a problem or task to be solved but does not include any explicit steps for verifying the correctness of the solutions to these problems.
## Does verification?
no
... | user
## Thoughts
The provided text is a list of mathematical and logical problems or challenges aimed at different age groups. Each challenge is described briefly, but there is no detailed explanation or breakdown of the steps needed to solve these problems. Therefore, there is no explicit subgoal setting in the text.
... | assistant ## Thoughts
The provided text is a list of mathematical and logical problems aimed at different age groups. Each problem describes a challenge or a game that requires reasoning and problem-solving skills. However, none of the descriptions explicitly mention starting from a goal and working backward to solve t... |
https://artofproblemsolving.com/wiki/index.php?title=2020_AMC_10B_Problems/Problem_12&diff=next&oldid=117764 | 1,642,822,572,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320303729.69/warc/CC-MAIN-20220122012907-20220122042907-00051.warc.gz | 160,760,262 | 14,405 | During AMC testing, the AoPS Wiki is in read-only mode. No edits can be made.
# Difference between revisions of "2020 AMC 10B Problems/Problem 12"
## Problem
The decimal representation of$$\dfrac{1}{20^{20}}$$consists of a string of zeros after the decimal point, followed by a $9$ and then several more digits. How m... | 1,025 | 3,050 | {"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": 63, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "ma... | 4.75 | 5 | CC-MAIN-2022-05 | latest | en | 0.741582 | assistant ## Thoughts
The text provided is a problem statement and several solutions for a math problem from the AMC 10B contest. The solutions provided are straightforward and do not contain any explicit backtracking behavior. There are no instances where the writers realize a path won't work and explicitly go back to... | SupportedContent
5 | URLException | 2 |
https://algorithmsandme.com/sliding-window-problem/ | 1,582,151,847,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875144429.5/warc/CC-MAIN-20200219214816-20200220004816-00173.warc.gz | 276,327,528 | 16,425 | Tags: , , , ,
# Sliding window problem
Given a large integer array of size x, window size of n and a random number k, find smallest k numbers in every window of n elements in array. This is commonly know as sliding window problem. For example: for an array [2,3,1,5,6,4,2,5,4,3,8] k = 2 and n = 6, output should be [1,... | 1,937 | 7,355 | {"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, "ma... | 3.796875 | 4 | CC-MAIN-2020-10 | latest | en | 0.913087 | SupportedContent
5 | 5 | SupportedContent
2 | HeaderCode
HeaderCode
SupportedContentHeaderCode
SupportedContentHeaderCode
SupportedContentHeaderCode
SupportedContentHeaderCode
2 |
https://www.mbatious.com/topic/153/percentage-atreya-roy | 1,513,346,379,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948572676.65/warc/CC-MAIN-20171215133912-20171215155912-00327.warc.gz | 778,530,205 | 18,313 | Percentage - Atreya Roy
• Author: Atreya Roy is pursuing his BTech From Kalyani Government Engineering College, Bengal.
By the term percent we mean value for every 100. If it is said, A gets a profit of 20% of every sale in the company, we can say that for every Rs 100 profit obtained from sale, A will get Rs 20. So ... | 3,564 | 10,972 | {"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, "ma... | 4.53125 | 5 | CC-MAIN-2017-51 | latest | en | 0.904771 | SupportedContent ends here. | SupportedContent | Alicebot | |
https://www.enotes.com/homework-help/int-0-1-cos-x-2-dx-use-power-series-approximate-810583 | 1,670,024,599,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710916.70/warc/CC-MAIN-20221202215443-20221203005443-00424.warc.gz | 796,335,430 | 19,096 | # `int_0^1 cos(x^2) dx` Use a power series to approximate the value of the integral with an error of less than 0.0001.
From the table of power series, we have:
`cos(x) = sum_(n=0)^oo (-1)^nx^(2n)/((2n))!`
`= 1-x^2/(2!)+x^4/(4!)-x^6/(6!)+` ...
To apply this on the given integral `int_0^1 cos(x^2) dx` , we may replac... | 841 | 1,863 | {"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, "ma... | 4.09375 | 4 | CC-MAIN-2022-49 | latest | en | 0.549791 | assistant
## Thoughts
The text provided is a step-by-step solution to an integral using a power series approximation. There is no indication of the writer realizing a mistake or needing to go back to a previous step to try a different approach. The solution proceeds in a linear fashion without any backtracking behavior... | user
## Thoughts
The text describes the process of approximating the value of the integral `int_0^1 cos(x^2) dx` using a power series. It calculates the integral by integrating the power series term by term and then evaluating the result at the limits of integration. However, the text does not explicitly check the resu... | user
## Thoughts
The text describes the process of approximating the integral of `cos(x^2)` using a power series. It breaks down the process into several steps: identifying the power series for `cos(x)`, substituting `x^2` for `x` in the series, integrating the series term by term, and then evaluating the definite inte... | assistant ## Thoughts
The provided text describes the process of approximating the value of the integral `int_0^1 cos(x^2) dx` using a power series. The text does not start from a goal and work backward; instead, it starts with the power series representation of `cos(x)` and then applies it to `cos(x^2)`. The text then... |
https://www.codingninjas.com/codestudio/library/find-the-closest-greater-value-for-every-element-in-the-array | 1,653,549,494,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662604495.84/warc/CC-MAIN-20220526065603-20220526095603-00369.warc.gz | 818,733,724 | 23,728 | # Find the closest greater value for every element in the array
Ayush Tiwari
Last Updated: May 13, 2022
## Introduction
This blog will learn to find the closest greater value for every element in the array. So let's suppose we have an array. We have to find the closest greater value for the element in the array.
Fo... | 1,390 | 5,460 | {"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, "ma... | 4.375 | 4 | CC-MAIN-2022-21 | latest | en | 0.806104 | user
## Thoughts
The text provided is a tutorial on finding the closest greater value for every element in an array. It describes two approaches: a naive approach using nested loops and an optimal approach using sets. The text does not contain any instances where the writer realizes a path won't work and explicitly goe... | assistant ## Thoughts
The text provided is a tutorial on finding the closest greater value for every element in an array. It discusses two approaches: a naive approach and an optimal approach using sets. The text provides algorithms, code implementations, and complexity analysis for both approaches. However, there are ... | assistant
## Thoughts
The text describes two approaches to solving the problem of finding the closest greater value for every element in an array. The naive approach and the optimal approach both have algorithms described in a step-by-step manner, which can be considered as subgoal setting. However, the steps are not e... | assistant ## Thoughts
The text provided is a tutorial on finding the closest greater value for every element in an array. It discusses two approaches: a naive approach and an optimal approach using sets. The text does not exhibit backward-chaining behavior as it does not start from a goal and work backward to achieve i... |
https://janeljs.github.io/brute%20force/%EB%B0%B1%EC%A4%80-14888%EB%B2%88-%EC%97%B0%EC%82%B0%EC%9E%90-%EB%81%BC%EC%9B%8C%EB%84%A3%EA%B8%B0/ | 1,643,440,311,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320300573.3/warc/CC-MAIN-20220129062503-20220129092503-00658.warc.gz | 371,650,247 | 70,601 | # 백준 14888번 연산자 끼워넣기
## Solution
import sys
n = int(input())
nums = list(map(int, input().strip().split()))
ops_count = list(map(int, input().strip().split()))
save = [0] * sum(ops_count)
min_v = 1e9
max_v = -1e9
def calculate(prev, i, next):
if i == 0:
return prev + next
if i == 1:
return prev - next
if i == 2:
r... | 1,018 | 3,185 | {"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, "mat... | 3.703125 | 4 | CC-MAIN-2022-05 | latest | en | 0.275076 | user
## Thoughts
The provided text is a code snippet with three different implementations (Python, Python模范解答, and Java) for a problem involving inserting operators. The code does not contain any explicit statements indicating backtracking behavior such as "Let me try again", "Wait", "I made a mistake", or "we need to ... | assistant
## Thoughts
The provided text contains code snippets in Python and Java for solving a problem related to inserting operators between numbers. The code includes recursive functions that calculate the maximum and minimum values of expressions formed by inserting operators. However, there are no explicit steps w... | user
## Thoughts
The provided text contains code snippets in Python and Java for solving a problem involving inserting operators between numbers to find the maximum and minimum possible values. The code includes recursive functions that break down the problem into smaller steps, but there is no explicit textual descrip... | assistant ## Thoughts
The provided text is a code snippet for solving a problem where the goal is to find the maximum and minimum values of an expression by inserting operators between given numbers. The code uses a recursive function to explore all possible combinations of operators. However, the code does not exhibit... |
https://math.stackexchange.com/questions/2400080/derivative-of-matrix-valued-function-with-respect-to-matrix-input | 1,723,320,919,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640822309.61/warc/CC-MAIN-20240810190707-20240810220707-00871.warc.gz | 291,535,222 | 38,350 | # Derivative of matrix-valued function with respect to matrix input
I have the expression
$$\bf \phi = \bf X W$$
where $\bf X$ is a $20 \times 10$ matrix, $\bf W$ is a $10 \times 5$ matrix.
How can I calculate $\frac{d\phi}{d\bf W}$? What is the dimension of the result?
• Have you tried anything so far? What are y... | 625 | 1,867 | {"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, "mat... | 3.515625 | 4 | CC-MAIN-2024-33 | latest | en | 0.80424 | assistant```markdown
## Thoughts
The text provided does not contain any explicit instances where the writer realizes a path won't work and goes back to try a different approach. The text is more of a discussion and explanation of a mathematical concept without any indication of backtracking or correction of a previous ... | assistant ## Thoughts
The text provided is a discussion about the derivative of a matrix-valued function with respect to a matrix input. It does not contain any explicit steps where the writer checks their work or verifies the correctness of their calculations or results. The text is more focused on explaining the conc... | assistant
## Thoughts
The text does not provide a clear breakdown of the problem into smaller, intermediate goals. It introduces the problem and provides some context and related information, but it does not outline a step-by-step approach to solving the problem.
## Does subgoal setting?
no
## Number of subgoal setti... | user5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555... |
http://math.stackexchange.com/questions/618832/solve-6x-36-cdot-9-75x-2 | 1,466,949,432,000,000,000 | text/html | crawl-data/CC-MAIN-2016-26/segments/1466783395346.6/warc/CC-MAIN-20160624154955-00036-ip-10-164-35-72.ec2.internal.warc.gz | 198,401,915 | 17,384 | # Solve $6^x=36\cdot (9.75)^{x-2}$
I try to solve the following equation:
$6^x=36\cdot (9.75)^{x-2}$
I tried:
$1=6\cdot (9.75)^{x-2}$
But this is obviously wrong!
I think it would be smarter to bring the whole expression on one side. How should I proceed instead?
-
Try $\log$ on both sides – Shuchang Dec 26 '13 ... | 515 | 1,032 | {"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, "mat... | 4.4375 | 4 | CC-MAIN-2016-26 | latest | en | 0.667993 | assistant
## Thoughts
The writer initially attempts to solve the equation by simplifying it incorrectly, realizing the mistake, and then decides to take a different approach by bringing the whole expression on one side and using logarithms. This is a clear instance of backtracking. Additionally, the writer acknowledges... | assistant ## Thoughts
The text provided does not contain any explicit verification steps where the writer checks their work by substituting the answer back into the original equation, differentiating, or testing with a simple case. The text is a series of comments and solutions to the equation, but none of the solution... | assistant ## Thoughts
The text provided does not contain a clear breakdown of the problem into smaller, intermediate goals. Instead, it presents a series of attempts and hints towards solving the equation, but does not explicitly outline a step-by-step plan with subgoals.
## Does subgoal setting?
no
## Number of subg... | assistant ## Thoughts
The text provided does not exhibit backward-chaining behavior. The solutions provided start from the given equation and work towards solving for \(x\), rather than starting from the goal and working backward. The solutions involve algebraic manipulations and the use of logarithms to isolate \(x\),... |
https://artofproblemsolving.com/wiki/index.php?title=Roots_of_unity&diff=prev&oldid=9666 | 1,653,589,412,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662619221.81/warc/CC-MAIN-20220526162749-20220526192749-00364.warc.gz | 152,946,509 | 12,319 | # Difference between revisions of "Roots of unity"
The Roots of unity are a topic closely related to trigonometry. Roots of unity come up when we examine the complex roots of the polynomial $x^n=1$.
## Solving the equation
First, we note that since we have an nth degree polynomial, there will be n complex roots.
No... | 812 | 2,669 | {"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": 31, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "ma... | 4.5625 | 5 | CC-MAIN-2022-21 | latest | en | 0.862479 | user
## Thoughts
The text provided is an explanation of the mathematical concept of roots of unity. It does not contain any instances where the writer realizes a mistake or a dead-end in their approach and decides to backtrack to try a different method. The explanation flows logically from the definition of roots of un... | user
## Thoughts
The text provided is an explanation of the concept of roots of unity, their derivation, and some of their properties. It does not contain any explicit steps where the writer checks their work or verifies the correctness of the results derived. The text is purely expository and does not include any veri... | user
## Thoughts
The text describes the process of solving for the roots of unity in a step-by-step manner. It starts by noting the number of roots, then converts the equation to polar form, solves for the magnitude and angle, and finally provides the solutions. This breakdown into steps indicates subgoal setting.
## ... | 提供的文本中没有表现出反向链接的行为。文本主要描述了单位根的概念、求解方法、几何性质、属性以及应用，但没有从目标结果反向推导的过程。
## Does the text exhibit backward chaining?
no
## Number of backward chaining instances
<count>0</count> |
https://stats.stackexchange.com/questions/270979/generalized-linear-model-confused-by-definition?noredirect=1 | 1,600,810,601,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400206763.24/warc/CC-MAIN-20200922192512-20200922222512-00425.warc.gz | 627,321,907 | 29,846 | # Generalized linear model - confused by definition [duplicate]
I'm beginning with the regression analysis and I'm quite confused with the generalized linear regression.
I understand, that the ordinary linear models can be described with a formula
$$y_i = \beta_1 x_1 + \beta_2 x_2 + \cdots + \beta_n x_n + \epsilon_i... | 851 | 2,902 | {"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, "mat... | 3.578125 | 4 | CC-MAIN-2020-40 | latest | en | 0.832985 | user
## Thoughts
The text provided does not contain any explicit instances where the writer realizes a path won't work and goes back to try a different approach. The text is a question and an answer about the definition of a generalized linear model, and there is no indication of backtracking in the explanation or the ... | assistant ## Thoughts
The text provided is a discussion about the definition of a generalized linear model (GLM) and does not contain any explicit steps where the writer checks their own work or verifies the correctness of their calculations or statements. The text is more explanatory in nature, clarifying the concept ... | assistant ## Thoughts
The text provided is a discussion about the confusion regarding the definition of a generalized linear model (GLM). The writer is asking for clarification on the role of the expected value in the GLM formula. The response given by Tim explains the concept of GLM and clarifies the confusion. Howeve... | assistant ## Thoughts
The text provided is a discussion about the definition and understanding of generalized linear models (GLMs). It does not contain any instances where the writer starts from a goal and works backward to achieve it. The text is more focused on explaining and clarifying the concept of GLMs and addres... |
https://study.com/academy/lesson/translating-piecewise-functions.html | 1,576,044,230,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540529955.67/warc/CC-MAIN-20191211045724-20191211073724-00124.warc.gz | 546,971,895 | 41,530 | # Translating Piecewise Functions
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• 0:05 Understanding…
• 1:19 Unknown ... | 1,071 | 4,719 | {"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, "ma... | 4.25 | 4 | CC-MAIN-2019-51 | longest | en | 0.953149 | assistant
## Thoughts
The text provided does not contain any instances where the writer realizes a path won't work and explicitly goes back to try a different approach. The content is instructional and explains the concept of translating piecewise functions without any indication of backtracking or correction of a prev... | assistant ## Thoughts
The text provided is a lesson on translating piecewise functions. It explains the concept and provides examples of how to translate piecewise functions without explicitly checking the results of the translations. There are no explicit verification steps where the author checks the correctness of t... | assistant ## Thoughts
The text does not contain explicit subgoal setting where the writer breaks down the problem into smaller, intermediate goals. The content is more instructional and descriptive, explaining concepts and transformations of piecewise functions without delineating a step-by-step process to achieve a sp... | assistant ## Thoughts
The text provided does not contain any instances of backward-chaining behavior. The content is focused on explaining the concept of translating piecewise functions and does not start from a goal and work backward to achieve it. Instead, it provides a general explanation and examples of how to tran... |
http://nzmaths.co.nz/resource/astronomical-proportions | 1,369,313,502,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368703317384/warc/CC-MAIN-20130516112157-00094-ip-10-60-113-184.ec2.internal.warc.gz | 185,504,228 | 12,503 | Te Kete Ipurangi
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Level Five > Number and Algebra
# Astronomical Proportions
Keywords:
Student Activity:
Click on the image to enlarge it. Click again to close. Download PDF (743 KB)
Purpose:
This is a level 5 number activity from the Figure It Out series. It... | 2,173 | 8,812 | {"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, "ma... | 4.09375 | 4 | CC-MAIN-2013-20 | longest | en | 0.926749 | assistant
## Thoughts
The provided text does not contain any instances of backtracking behavior. The text is a structured educational material that outlines activities and solutions for mathematical problems related to astronomical proportions. It does not include any self-correction or realization of errors that would... | assistant
## Thoughts
The text provided contains several instances where the writer checks their work or verifies the results of calculations. These verification steps are primarily found in the explanations for the activities and answers, where the writer explicitly checks the results by comparing them to known values... | assistant ## Thoughts
The text provided contains several instances where subgoal setting is evident. These instances are primarily found within the "Activity One" and "Activity Two" sections, where the text breaks down the problem-solving process into smaller, intermediate steps to guide the reader through the solution... | assistant ## Thoughts
The text provided is a set of educational activities and their solutions, focusing on astronomical proportions and mathematical problem-solving. The text does not exhibit backward-chaining behavior as described in the task description. The activities and solutions provided are more about direct pr... |
https://calconcalculator.com/math/arcsin-calculator-inverse-sine/ | 1,726,487,790,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651697.32/warc/CC-MAIN-20240916112213-20240916142213-00792.warc.gz | 135,568,233 | 20,884 | The mathematics of trigonometry is complex and, at times, confusing. To make this topic understandable to you, you will get a detailed explanation through this article of inverse sine, trigonometric functions, and other relationships. Accordingly, we present you with our arcsin calculator and the principle of operation... | 1,044 | 4,246 | {"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, "ma... | 4.84375 | 5 | CC-MAIN-2024-38 | latest | en | 0.909269 | user
## Thoughts
The provided text is an explanation of the arcsine function, its calculation, and its relationships with other trigonometric functions. There is no indication of the writer realizing a mistake or needing to go back to a previous step to try a different approach. The text flows smoothly without any back... | user
## Thoughts
The provided text explains the concept of arcsine, how to calculate it, and its relationships with other trigonometric functions. However, it does not contain any explicit steps where the writer checks their work or verifies the correctness of the calculations or explanations provided.
## Does verific... | PostalCodesBot | SupportedContent
SupportedContent |
https://mikepawliuk.ca/tag/analogies/ | 1,685,668,637,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224648245.63/warc/CC-MAIN-20230602003804-20230602033804-00787.warc.gz | 452,895,582 | 22,703 | ## How does modern AI work? – Math for my mom
This is part of a series of posts aimed at helping my mom, who is not a scientist, understand what I’m up to as a mathematician.
Lately, Artificial Intelligence (AI) has made some remarkable milestones. There are computers that are better than humans at the strategy board... | 991 | 4,460 | {"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": 11, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "ma... | 3.640625 | 4 | CC-MAIN-2023-23 | latest | en | 0.951137 | user
## Thoughts
The provided text does not contain any explicit backtracking behavior. The content is a series of introductions to different topics, including an explanation of how modern AI works, a practical guide to using countable elementary submodels, and a discussion on simulations. None of these sections show a... | assistant
## Thoughts
The provided text does not contain any explicit verification steps. It discusses concepts related to set theory and simulations but does not include any steps where the author checks their work or verifies a result through comparison or testing.
## Does verification?
no
## Number of answer verif... | assistant
## Thoughts
The provided text does not contain any explicit subgoal setting. The text discusses the concept of countable elementary submodels in set theory and provides an analogy to explain the idea of forcing without delving into the technical details of subgoal setting in a mathematical proof or problem-so... | assistant
## Thoughts
The provided text does not contain any backward-chaining behavior. The content discusses the concept of artificial intelligence and provides a practical guide to using countable elementary submodels in set theory, as well as a discussion on simulations. None of the examples or explanations provide... |
http://www.algebra.com/algebra/homework/word/numbers/Numbers_Word_Problems.faq.question.157926.html | 1,371,663,930,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368709000375/warc/CC-MAIN-20130516125640-00079-ip-10-60-113-184.ec2.internal.warc.gz | 308,574,465 | 5,075 | # SOLUTION: Find two numbers such that twice the first exceeds three times the second by 1, and three times the first exceeds twice the second by 14.
Algebra -> Algebra -> Customizable Word Problem Solvers -> Numbers -> SOLUTION: Find two numbers such that twice the first exceeds three times the second by 1, and th... | 354 | 1,313 | {"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, "ma... | 3.796875 | 4 | CC-MAIN-2013-20 | latest | en | 0.83185 | assistant
## Thoughts
The text provided is a solution to a system of linear equations. The writer does not explicitly state any backtracking behavior such as realizing a mistake or needing to try a different approach. The solution proceeds in a straightforward manner, solving the equations and then checking the solutio... | assistant ## Thoughts
The text provided contains a problem-solving process for finding two numbers based on given conditions. At the end of the solution, the solver checks the answers by substituting them back into the original equations to verify if they satisfy the conditions. This is a clear example of a verificatio... | assistant
## Thoughts
The text provided is a solution to a word problem involving two numbers. The solver sets up two equations based on the conditions given in the problem. However, the solution does not explicitly break down the problem into smaller, intermediate goals. Instead, it directly sets up and solves the equ... | assistant ## Thoughts
The solution provided does not start from the goal and work backward. Instead, it sets up the equations based on the given conditions and solves them step by step. The process described is a forward approach to solving the system of equations, not backward chaining.
## Does the text exhibit backw... |
https://secondsminutes.com/217403-seconds-in-minutes | 1,686,152,831,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224653930.47/warc/CC-MAIN-20230607143116-20230607173116-00359.warc.gz | 564,523,190 | 6,728 | # 217403 seconds in minutes
## Result
217403 seconds equals 3623.39 minutes
You can also convert 217403 seconds to minutes and seconds or to hours and minutes
## Conversion formula
Multiply the amount of seconds by the conversion factor to get the result in minutes:
217403 s × 0.0166667 = 3623.39 min
## How to c... | 1,101 | 4,482 | {"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, "ma... | 4.15625 | 4 | CC-MAIN-2023-23 | latest | en | 0.734015 | assistant```markdown
## Thoughts
The provided text is a straightforward conversion of seconds to minutes, detailing the process and providing additional information such as a conversion table and definitions of the units involved. There is no indication of any backtracking behavior where the writer realizes a mistake o... | 55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555... | assistant
## Thoughts
The text provided is a detailed explanation of the conversion of seconds to minutes, including the formula and a step-by-step process to convert 217403 seconds to minutes. However, the text does not break down the problem into smaller, intermediate goals or subgoals. It directly explains the conve... | 2 |
https://familychristianhomeschoolers.org/science-literacy-essay/completing-the-square-notes-essay.php | 1,603,550,101,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107883636.39/warc/CC-MAIN-20201024135444-20201024165444-00374.warc.gz | 307,641,514 | 17,998 | familychristianhomeschoolers.org
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# Completing the square notes essay
### Worked case study 6: Fixing quadratic equations by just performing your square
It’s very a great deal a confirm who you’ll find quadratic equations about the particu... | 3,379 | 16,400 | {"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, "ma... | 3.59375 | 4 | CC-MAIN-2020-45 | latest | en | 0.922737 | userHeaderCodegentTriggerInput
assistantHeaderCodegentTriggerInputUAGE_ERRORInParameterValue | assistant
## Thoughts
The text provided does not contain any explicit verification steps. The content is an explanation and example of how to solve quadratic equations by completing the square, but it does not include any steps where the writer checks their work or verifies the correctness of the solution.
## Does ver... | assistant
## Thoughts
The text provided is a detailed explanation of how to solve quadratic equations by completing the square. It breaks down the process into several steps, each of which represents a subgoal in the overall process of solving the equation. The steps include identifying the missing constant, using the ... | assistant
## Thoughts
The provided text does not contain any backward-chaining behavior. The text is a detailed explanation of the method of completing the square to solve quadratic equations. It does not start from a goal and work backward; instead, it provides a step-by-step forward approach to solving quadratic equa... |
https://www.freemathhelp.com/forum/threads/find-the-equation-for-a-line-which-goes-thorugh-origo.70757/ | 1,553,332,101,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912202781.33/warc/CC-MAIN-20190323080959-20190323102959-00144.warc.gz | 762,637,854 | 11,346 | # Find the equation for a line which goes thorugh origo
#### Anna55
##### New member
Decide the equation for the line which goes through origo and are perpendicular against the line x-y+1=0
#### Denis
##### Senior Member
Anna55 said:
...perpendicular against the line x-y+1=0
Can you calculate the slope of that line... | 606 | 2,253 | {"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, "ma... | 4.5625 | 5 | CC-MAIN-2019-13 | latest | en | 0.897217 | user
## Thoughts
The text provided does not contain any explicit instances where the writer realizes a path won't work and goes back to try a different approach. The discussion revolves around solving a math problem, and while there are explanations and corrections, there is no indication of backtracking in the sense o... | user
## Thoughts
The text provided does not contain any explicit verification steps where the writer checks their own work by comparing the result to a known value or by checking the result of a calculation. The text is more focused on guiding the user through the process of solving the problem and does not include a s... | user
## Thoughts
The text contains a clear example of subgoal setting in the response by mmm4444bot. The problem is broken down into three steps: determining the slope of the given line, finding the slope of the perpendicular line, and using the Point-Slope formula to write the equation. Additionally, wjm11 also provid... | user
## Thoughts
The text does not contain any instances where the writers start from the goal and work backward. Instead, the discussion revolves around finding the slope of a given line and then determining the slope of a line that is perpendicular to it. The process described is forward-chaining, where the steps are... |
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