text string | cc-path string | domain string | lang string | lang_score float64 | timestamp timestamp[s] | url string | math_score float64 |
|---|---|---|---|---|---|---|---|
## Step 1: Identify the key elements of the problem.
The problem asks to find a 2x2 matrix A such that [3]' and [-1] are eigenvectors of A with eigenvalues 9 and 3, respectively.
## Step 2: Recall the definition of eigenvectors and eigenvalues.
An eigenvector of a matrix A is a non-zero vector v such that when A multi... | CC-MAIN-2022-40/segments/1664030334942.88/warc/CC-MAIN-20220926211042-20220927001042-00008.warc.gz | itprospt.com | en | 0.789038 | 2022-09-26T22:22:56 | https://itprospt.com/num/6102736/problem-1-2-points-find-2-matrix-such-that-3-x27-and-1-are | 0.948986 |
In determining the price of a home, it's essential to consider the cost of interest on a loan used to finance the home. Interest on any loan is the fee paid to the lender for allowing you to borrow the initial sum of money, known as the principal. The interest rate determines the amount owed on each loan payment and th... | CC-MAIN-2024-46/segments/1730477027987.79/warc/CC-MAIN-20241107083707-20241107113707-00462.warc.gz | unison.com | en | 0.951778 | 2024-11-07T10:47:17 | https://www.unison.com/blog/tips/how-much-interest-to-pay-on-mortgage/var(--white-color) | 0.586384 |
## Step 1: Identify the key elements of the problem
The problem involves determining the precipitate that forms when two solutions are mixed together.
## Step 2: Analyze the chemical reactions
The first reaction is between NaOH(aq) and KNO3(aq). The second reaction is between KOH(aq) and Mn(NO3)2(aq). The third reacti... | CC-MAIN-2023-40/segments/1695233510149.21/warc/CC-MAIN-20230926043538-20230926073538-00419.warc.gz | solvedlib.com | en | 0.847159 | 2023-09-26T06:52:24 | https://solvedlib.com/n/use-the-sum-and-difference-formulas-to-verify-the-identity,7643563 | 0.874327 |
# What is Variance in Statistics?
Variance is a statistical term that measures the spread or dispersion of a set of data points in a dataset. It gives an idea of how far each number in the set is from the mean and, thus, from every other number in the set.
**Understanding the Basics of Statistical Variance**
Varianc... | CC-MAIN-2024-10/segments/1707947474893.90/warc/CC-MAIN-20240229234355-20240301024355-00049.warc.gz | statisticser.com | en | 0.873999 | 2024-03-01T01:54:34 | https://www.statisticser.com/what-is-variance-in-statistics/ | 0.995525 |
To illustrate that measure zero sets can be complex and numerous, consider an uncountable, compact, measure zero subset of [0,1] that contains no intervals. Any x in [0,1] can be expanded in ternary as:
x = ∑[d_n 3^(-n)] from n=1 to ∞, where d_n = 0, 1, or 2.
Define the set C as:
C := {x in [0,1] : x = ∑[d_n 3^(-n)]... | CC-MAIN-2024-33/segments/1722641319057.20/warc/CC-MAIN-20240815235528-20240816025528-00729.warc.gz | jirka.org | en | 0.676948 | 2024-08-16T00:51:18 | https://www.jirka.org/ra/html/sec_outermeasure.html | 0.998735 |
## Square Root
To understand square root, we first need to know about the square of a positive integer. The numbers that can be represented by dot patterns to form a square shape are called square numbers. For example, 1, 4, 9, and 16 are square numbers because they can be represented as a square of dots.
The square ... | CC-MAIN-2024-22/segments/1715971058709.9/warc/CC-MAIN-20240524091115-20240524121115-00454.warc.gz | mathtutory.com | en | 0.876055 | 2024-05-24T09:54:49 | https://mathtutory.com/square-root/ | 0.998979 |
**Addition Within 100 for Grade 1**
The goal is to help Grade 1 kids learn how to add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10. This is achieved by using concrete models or drawings and strategies based on place value, properties of oper... | CC-MAIN-2024-33/segments/1722640380725.7/warc/CC-MAIN-20240803214957-20240804004957-00434.warc.gz | onlinemathlearning.com | en | 0.770047 | 2024-08-03T22:39:35 | https://www.onlinemathlearning.com/grade1-addition.html | 0.993371 |
There are 261 weekdays in a year. To calculate this, we can start by determining the number of weekdays per week, which is 5, and the number of weekdays per month, which is around 20. Multiplying the number of weekdays per month by 12 months gives us 240 weekdays per year. However, this calculation underestimates the a... | CC-MAIN-2024-33/segments/1722640805409.58/warc/CC-MAIN-20240810093040-20240810123040-00451.warc.gz | answerpail.com | en | 0.931768 | 2024-08-10T10:16:35 | https://answerpail.com/index.php/52624/how-many-week-days-are-in-a-year | 0.64229 |
## BoundingBox Class
The BoundingBox class defines the computational domain, which consists of a collection of D-dimensional boxes on a particular length scale `n`. The size of each box is `[2^n]^D`, where higher scales mean smaller boxes, and the scale may be negative. Box translations relative to the world origin mus... | CC-MAIN-2024-10/segments/1707947474690.22/warc/CC-MAIN-20240228012542-20240228042542-00370.warc.gz | readthedocs.io | en | 0.687849 | 2024-02-28T03:06:10 | https://mrcpp.readthedocs.io/en/latest/programmers_manual/BoundingBox.html | 0.710502 |
The simplest form of 594/954 is 33/53.
To simplify the fraction, find the GCD (or HCF) of the numerator and denominator. The GCD of 594 and 954 is 18. Divide both the numerator and denominator by the GCD:
594 ÷ 18 = 33
954 ÷ 18 = 53
Therefore, 594/954 simplified to lowest terms is 33/53.
Equivalent fractions includ... | CC-MAIN-2021-39/segments/1631780057036.89/warc/CC-MAIN-20210920101029-20210920131029-00389.warc.gz | everydaycalculation.com | en | 0.755163 | 2021-09-20T10:54:10 | https://answers.everydaycalculation.com/simplify-fraction/594-954 | 0.999775 |
The chance of getting heads when tossing a dice is 50%, which is symbolically written as "50%" and represents the fraction 50/100 or 1/2. The percent symbol "%" denotes a fraction of 1/100.
To convert a percentage to a fraction, write 100 in the denominator for the percentage symbol. For example, 50% = 50/100 = 1/2, ... | CC-MAIN-2016-18/segments/1461860111313.83/warc/CC-MAIN-20160428161511-00203-ip-10-239-7-51.ec2.internal.warc.gz | math-for-all-grades.com | en | 0.850081 | 2016-04-29T10:00:54 | http://www.math-for-all-grades.com/percentages-1.html | 0.978212 |
The lowest common multiple (LCM) of two or more expressions is the smallest expression that is divisible by each of the given expressions. To find the LCM, first factor each expression completely, then use these factors to write the LCM.
The process involves multiplying all factors included in the factoring of the gi... | CC-MAIN-2018-26/segments/1529267864337.41/warc/CC-MAIN-20180622010629-20180622030629-00133.warc.gz | analyzemath.com | en | 0.874523 | 2018-06-22T01:14:28 | http://www.analyzemath.com/high_school_math/grade_11/LCM_expressions.html | 0.996647 |
# Symbols Describe Mathematical Sentences: Equalities and Inequalities
Equality refers to mathematical equations where the left and right sides are equal, denoted by the symbol " = ". This symbol indicates that the right side is equal to the left side.
In contrast, inequalities occur when the sides are not equal, but... | CC-MAIN-2017-26/segments/1498128320323.17/warc/CC-MAIN-20170624184733-20170624204733-00335.warc.gz | enotes.com | en | 0.883075 | 2017-06-24T19:12:54 | https://www.enotes.com/homework-help/symbols-397268 | 0.998431 |
# 1617.1.1.2 Maximum Seismic Load Effect, EM
The maximum seismic load effect, Em, is used in the special seismic load combinations in Section 1605.4. Em is calculated differently based on whether the effects of seismic ground motion and gravity loads are additive or counteractive.
When the effects are additive, Em is... | CC-MAIN-2022-05/segments/1642320301475.82/warc/CC-MAIN-20220119155216-20220119185216-00212.warc.gz | up.codes | en | 0.739876 | 2022-01-19T16:36:47 | https://up.codes/s/maximum-seismic-load-effect-em | 0.801442 |
In a metric space $(X,d)$ that is compact, every sequence is a lingering sequence. This means that for any sequence $(x_n)_{n=1}^\infty \subseteq X$, there exists a point $x \in X$ such that for all $\epsilon > 0$, the open ball $B_\epsilon(x)$ contains infinitely many terms of the sequence. Mathematically, this can be... | CC-MAIN-2022-49/segments/1669446710869.86/warc/CC-MAIN-20221201185801-20221201215801-00602.warc.gz | kisogo.com | en | 0.763795 | 2022-12-01T20:34:30 | http://www.maths.kisogo.com/index.php?title=Every_sequence_in_a_compact_space_is_a_lingering_sequence | 0.99998 |
CBSE X
Delhi
MATHS PAPER 2009
Time allowed: 180 minutes; Maximum Marks: 90
General Instructions:
1) All questions are compulsory.
2) The question paper consists of thirty questions divided into 4 sections A, B, C and D.
3) All questions in Section A are to be answered in one word, one sentence or as per the exact req... | CC-MAIN-2018-30/segments/1531676590169.5/warc/CC-MAIN-20180718115544-20180718135544-00119.warc.gz | nextgurukul.in | en | 0.770545 | 2018-07-18T12:45:22 | https://www.nextgurukul.in/examCorner/Board-Papers/CBSE/X/Maths/2009/Delhi.htm | 0.999378 |
Statistics can be differentiated from other modes of thinking by its unique approach to uncertainty. To understand this, it's essential to consider the concepts of aleatoric and epistemic uncertainty. Aleatoric uncertainty refers to incomplete knowledge of well-defined states of a carefully constructed system, such as ... | CC-MAIN-2024-33/segments/1722640723918.41/warc/CC-MAIN-20240808062406-20240808092406-00283.warc.gz | github.io | en | 0.957718 | 2024-08-08T07:32:37 | https://rgiordan.github.io/posts/2021-08-23-what_is_statistics.html | 0.813888 |
A new paper, "Henselianity in the language of rings," has been written and published on the arXiv by Franziska Jahnke and the author. The paper explores the relationship between four properties of a field:
* (h) being henselian, which means admitting a nontrivial henselian valuation,
* (eh) being elementarily henseli... | CC-MAIN-2023-06/segments/1674764500074.73/warc/CC-MAIN-20230203185547-20230203215547-00647.warc.gz | wordpress.com | en | 0.800462 | 2023-02-03T20:38:20 | https://sylvyanscombe.wordpress.com/tag/model-theory/ | 0.837368 |
In mathematical terms, a system of equations is a set of two or more equations with the same set of unknown variables, such as x, y, z, where we need to find the values of these variables to solve the equations. To solve a system of equations, we can use functions and the equation solver tool.
**Using Excel Functions*... | CC-MAIN-2021-31/segments/1627046153892.74/warc/CC-MAIN-20210729172022-20210729202022-00608.warc.gz | got-it.ai | en | 0.86364 | 2021-07-29T18:25:20 | https://www.got-it.ai/solutions/excel-chat/excel-tutorial/miscellaneous/how-to-solve-the-system-of-equations-in-excel | 0.999816 |
The basic proof sketch of Gödel's great incompleteness proof is as follows:
1. Take a simple logic, such as a variant of the Principia Mathematica's logic.
2. Show that any statement in the logic can be encoded as a number using an arithmetic process based on the syntax of the logic, known as Gödel numbering.
3. Show ... | CC-MAIN-2022-40/segments/1664030334620.49/warc/CC-MAIN-20220925225000-20220926015000-00185.warc.gz | goodmath.org | en | 0.928704 | 2022-09-26T00:32:22 | http://www.goodmath.org/blog/2014/09/ | 0.981338 |
**Introduction**
The universe is full of mysteries, and numbers hold the key to understanding them. Pythagoras once said, "The world is built on the power of numbers." In school, we learn about the signs of divisibility by 2, 3, 5, 9, and 10. However, this is not enough, and there is a need to expand our knowledge on ... | CC-MAIN-2023-23/segments/1685224648209.30/warc/CC-MAIN-20230601211701-20230602001701-00750.warc.gz | puzedu.com | en | 0.936667 | 2023-06-01T22:23:51 | https://puzedu.com/research-projectsigns-of-the-divisibility-of-numbers/ | 0.99377 |
In the king's gardens in Ardapasia, a miraculous lake has seven lotus flowers that blossom exactly once a year. The flowers bloom in a straight and evenly spaced line. A frog appears when the lotuses bloom and lands on one of the flowers. The frog jumps to other lotus flowers, always by either three or five flowers.
... | CC-MAIN-2022-40/segments/1664030335362.18/warc/CC-MAIN-20220929163117-20220929193117-00756.warc.gz | medium.com | en | 0.927064 | 2022-09-29T18:06:44 | https://medium.com/@rashmiabbigeri/puzzle-frog-and-the-lotus-path-c25fc4a0d0bc?source=post_internal_links---------0---------------------------- | 0.903501 |
**Word Problems For Absolute Value**
Absolute value word problems can cover various topics, including distances, weights, and quantities. Each word problem comes with an absolute value equation or inequality that needs to be solved. The absolute value symbol, denoted by vertical bars (| |), represents the magnitude or... | CC-MAIN-2024-30/segments/1720763514724.0/warc/CC-MAIN-20240715224905-20240716014905-00780.warc.gz | denizen.io | en | 0.698411 | 2024-07-16T00:39:23 | https://denizen.io/words/word-problems-for-absolute-value.html | 0.997515 |
Rational Expressions are the ratio of two polynomials, similar to a fraction. They can be simplified, and it is essential to identify excluded values. The domain of a rational expression can be found, and simplifying these expressions is crucial. A rational expression is any expression or function with a polynomial in ... | CC-MAIN-2017-22/segments/1495463607813.12/warc/CC-MAIN-20170524112717-20170524132717-00476.warc.gz | slidesearchengine.com | en | 0.88273 | 2017-05-24T11:54:52 | http://www.slidesearchengine.com/slide/rational-expressions | 0.997914 |
## How to Calculate Growth Rate
To calculate the average growth rate, organize your data in a table and use a growth rate equation that takes into account the number of time intervals in your data. The compound annual growth rate (CAGR) metric smoothes out lumpy growth to calculate a theoretical annual growth rate.
#... | CC-MAIN-2023-14/segments/1679296945282.33/warc/CC-MAIN-20230324113500-20230324143500-00162.warc.gz | netlify.app | en | 0.874753 | 2023-03-24T12:49:30 | https://topbtcxhqtt.netlify.app/yax34435rit/how-to-get-the-average-growth-rate-326.html | 0.979315 |
I began using Jon Corippo's 8 p*ARTS last year and saw great success with the repetition. To replicate this success in Math, I developed a similar plan for 5th grade, which can be easily modified for other grades.
The plan consists of the following daily activities:
- Today's Number: The student of the day chooses a ... | CC-MAIN-2020-50/segments/1606141735600.89/warc/CC-MAIN-20201204101314-20201204131314-00191.warc.gz | nowatechie.com | en | 0.909858 | 2020-12-04T10:34:53 | https://nowatechie.com/tag/daily-review/ | 0.922999 |
# Understanding and Implementing Binary Search in JavaScript
To illustrate the concept of binary search, let's consider a game where you think of a number between 1 and 100, and I try to guess it by asking questions.
## First Approach: Linear Search
In this approach, I would ask you if your number is 1, then 2, and ... | CC-MAIN-2021-10/segments/1614178357935.29/warc/CC-MAIN-20210226175238-20210226205238-00141.warc.gz | medium.com | en | 0.855906 | 2021-02-26T17:59:02 | https://akibur-rahman.medium.com/understand-and-implement-binary-search-in-javascript-c0df874e0cc5 | 0.749733 |
111 is a composite number because it has factors other than 1 and itself. The 4 factors of 111 are 1, 3, 37, and 111. The factor pairs of 111 are 1 x 111 and 3 x 37. The proper factors of 111 are 1, 3, and 37, or, if the definition excludes 1, they are 3 and 37. The prime factors of 111 are 3 and 37, and the prime fact... | CC-MAIN-2024-30/segments/1720763518579.47/warc/CC-MAIN-20240725053529-20240725083529-00323.warc.gz | answers.com | en | 0.933056 | 2024-07-25T06:06:22 | https://math.answers.com/basic-math/Factors_of_111 | 0.999613 |
A body has **non-uniform circular motion** when its trajectory is a circumference and its angular acceleration is constant. In this section, we study non-uniform circular motion graphs.
## Non-uniform circular motion graphs
### Angular position - time (φ-t) graph
The angular position-time graph represents time on th... | CC-MAIN-2020-05/segments/1579250608062.57/warc/CC-MAIN-20200123011418-20200123040418-00524.warc.gz | fisicalab.com | en | 0.770887 | 2020-01-23T01:49:22 | https://www.fisicalab.com/en/section/non-ucm-graphics | 0.977222 |
Per-mille or per-mil refers to parts per thousand. One per-mille is equal to 1/1000 fraction: 1‰ = 1/1000 = 0.001. Similarly, 10‰ = 10/1000 = 0.01, 100‰ = 100/1000 = 0.1, and 1000‰ = 1000/1000 = 1.
To calculate per-mille of a value, multiply the per-mille fraction by the value. For example, what is 40 per-mille of $70... | CC-MAIN-2020-45/segments/1603107866404.1/warc/CC-MAIN-20201019203523-20201019233523-00212.warc.gz | allcalculators.net | en | 0.692701 | 2020-10-19T20:53:08 | https://allcalculators.net/mathematics/numbers/per-mille/ | 0.89001 |
A machine is rolling a metal cylinder under pressure. The radius of the cylinder is decreasing at a constant rate of 0.05 inches per second, and the volume V is 128 cubic inches. At what rate is the length H changing when the radius r is 2.5 inches?
Given:
- Volume V = 128 cubic inches
- Rate of change of radius (dr/d... | CC-MAIN-2017-51/segments/1512948581033.57/warc/CC-MAIN-20171216010725-20171216032725-00329.warc.gz | mathhelpforum.com | en | 0.867945 | 2017-12-16T02:04:25 | http://mathhelpforum.com/calculus/17963-rate-change.html | 0.953933 |
When multiplying by 10, a pattern emerges where the product of each number multiplied by 10 is that number with a zero on the end. This can be observed in the following examples:
1 × 10 = 10
2 × 10 = 20
3 × 10 = 30
4 × 10 = 40
5 × 10 = 50
6 × 10 = 60
7 × 10 = 70
8 × 10 = 80
9 × 10 = 90
Applying this pattern, adding a... | CC-MAIN-2017-13/segments/1490218189589.37/warc/CC-MAIN-20170322212949-00419-ip-10-233-31-227.ec2.internal.warc.gz | learningfarm.com | en | 0.872225 | 2017-03-28T02:18:56 | http://www.learningfarm.com/web/practicePassThrough.cfm?TopicID=907 | 0.998529 |
**Radius of a Circle Calculator**
Our radius of a circle calculator finds the radius from the values of circumference, area, or diameter. A circle is a well-known geometrical figure, and the distance from its center to any point on the circumference is known as the radius.
In geometry, a circle is defined by several ... | CC-MAIN-2022-49/segments/1669446711396.19/warc/CC-MAIN-20221209112528-20221209142528-00057.warc.gz | calculator-online.net | en | 0.790145 | 2022-12-09T12:57:58 | https://calculator-online.net/radius-of-a-circle-calculator/ | 0.986964 |
# y = -6x + 2 and -12x - 2y = -4, how many solutions does this linear system have?
**Solution:**
Given two equations:
1. y = -6x + 2
2. -12x - 2y = -4
Substitute the value of y from equation (1) into equation (2):
-12x - 2(-6x + 2) = -4
-12x + 12x - 4 = -4
-4 = -4
This result indicates that the two equations repres... | CC-MAIN-2022-49/segments/1669446710733.87/warc/CC-MAIN-20221130060525-20221130090525-00237.warc.gz | cuemath.com | en | 0.874548 | 2022-11-30T08:17:36 | https://www.cuemath.com/questions/y-6x-2-and-12x-2y-4-how-many-solutions-does-this-linear-system-have/ | 1.000005 |
## Step 1: Complete the table using existing knowledge
To complete the table, we need to convert the given numbers into decimal fractions and then into a combined decimal format. For example, given the numbers 3, 6, we can convert them into a decimal fraction as 3 $\frac{6}{10}$, which simplifies to 3.6.
## Step 2: Fi... | CC-MAIN-2018-51/segments/1544376828501.85/warc/CC-MAIN-20181217091227-20181217113227-00400.warc.gz | quizover.com | en | 0.833618 | 2018-12-17T10:58:12 | https://www.quizover.com/course/section/activity-5-tables-and-checks-to-arrange-and-record-data-by-openstax | 0.934771 |
Quaternions are used to represent rotations in a compact and efficient manner, avoiding gimbal lock and allowing for easy interpolation. Unity relies on Quaternions to represent all rotations internally. Although they are based on complex numbers and can be challenging to understand intuitively, they provide a powerful... | CC-MAIN-2024-10/segments/1707947474526.76/warc/CC-MAIN-20240224080616-20240224110616-00633.warc.gz | unity3d.com | en | 0.844156 | 2024-02-24T09:14:25 | https://docs.unity3d.com/460/Documentation/ScriptReference/Quaternion.html | 0.919154 |
# NSW Extension 1 (Year 11 3 Unit) Mathematics
The course is divided into 172 lessons, covering various topics in mathematics. The main topics include:
1. **Study Plan**: Creating a tailored study plan based on formative assessment results.
2. **Rules for Indices/Exponents**: Lessons 2-7 cover the rules for adding, s... | CC-MAIN-2019-43/segments/1570986697439.41/warc/CC-MAIN-20191019164943-20191019192443-00324.warc.gz | futureschool.com | en | 0.870056 | 2019-10-19T18:16:18 | https://www.futureschool.com/australian-curriculum/new-south-wales/mathematics-extension-1-year-11-3-unit/ | 0.99996 |
# Quaternions
Quaternions are mathematical objects used to describe geometry. This introduction provides key properties and definitions, particularly for geometric applications. For further information, readers can refer to online resources such as Wikipedia and MathWorld articles.
## Definitions
A quaternion can be... | CC-MAIN-2017-26/segments/1498128321309.25/warc/CC-MAIN-20170627101436-20170627121436-00091.warc.gz | bealto.com | en | 0.78759 | 2017-06-27T10:24:05 | http://www.bealto.com/geo-quaternions.html | 0.997279 |
It follows that any triangle in which the sides satisfy this condition is a right triangle. The calculator solves the triangle specified by three of its properties. The perimeter of a triangle is the distance covered around the triangle and is calculated as the sum of all the three sides of it. The circumcenter of the ... | CC-MAIN-2021-39/segments/1631780055808.78/warc/CC-MAIN-20210917212307-20210918002307-00670.warc.gz | gridserver.com | en | 0.868454 | 2021-09-17T22:17:44 | http://s141453.gridserver.com/constitution-of-nhyd/boxing-north-bay-ontario-68d19a | 0.999356 |
Mental multiplication is a crucial topic in primary and secondary school, and mastering the times tables is essential for academic success. To improve mental multiplication skills, learning the times tables by heart is the easiest way, and practicing regularly can help master the concept.
The times tables from 1 x 1 ... | CC-MAIN-2017-30/segments/1500549425737.60/warc/CC-MAIN-20170726002333-20170726022333-00307.warc.gz | ultimatemaths.com | en | 0.919211 | 2017-07-26T00:50:51 | http://www.ultimatemaths.com/multiplication-and-division.htm | 0.986583 |
Definition 87.4.8. Let $A$ be a linearly topologized ring. An element $f \in A$ is called *topologically nilpotent* if $f^n \to 0$ as $n \to \infty$. A *weak ideal of definition* for $A$ is an open ideal $I \subset A$ consisting entirely of topologically nilpotent elements. The ring $A$ is said to be *weakly pre-admiss... | CC-MAIN-2024-26/segments/1718198861606.63/warc/CC-MAIN-20240615190624-20240615220624-00161.warc.gz | columbia.edu | en | 0.861494 | 2024-06-15T21:36:23 | https://stacks.math.columbia.edu/tag/0AMV | 0.816136 |
# Calculus and Vectors
This course extends students' understanding of rates of change, introducing derivatives of various functions and integral calculus. Students will apply these concepts to model real-world relationships and solve problems involving vectors and lines in three-space. The course is intended for stude... | CC-MAIN-2023-14/segments/1679296945248.28/warc/CC-MAIN-20230324051147-20230324081147-00570.warc.gz | uwaterloo.ca | en | 0.909881 | 2023-03-24T05:43:28 | https://courseware.cemc.uwaterloo.ca/11?gid=106 | 0.999993 |
A wireless phone company's cell towers are arranged in a regular hexagonal structure. If each tower's coverage radius is exactly half the length of a side of the regular hexagon, what percentage of the hexagon's area will not be covered by the towers?
To solve this problem, we'll treat it like a shaded region question... | CC-MAIN-2023-14/segments/1679296948684.19/warc/CC-MAIN-20230327185741-20230327215741-00547.warc.gz | pwntestprep.com | en | 0.904897 | 2023-03-27T19:28:01 | https://pwntestprep.com/2012/07/weekend-challenge-dead-zones/ | 0.925828 |
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