text stringlengths 22 1.01M |
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## Section12.4The Two-Body Problem
We will consider motion of two bodies interacting with gravitational force only. We have seen before that motion separates into motion of the center of motion and relative position of the two bodies.
Let $m_1$ and $m_2$ be the masses and $\vec{r}_1$ and $\vec{r}_2$ their positions. ... |
### What’s the Next Number?
We are all familiar with simple mathematical puzzles that give a short sequence and ask “What is the next number in the sequence”. Simple examples would be
$\displaystyle \begin{array}{rcl} && 1, 3, 5, 7, 9, 11, \dots \\ && 1, 4, 9, 16, 25, \dots \\ && 1, 1, 2, 3, 5, 8, \dots \,, \end{arra... |
# Thread: Find sin2x for each given the following condition:
1. ## Find sin2x for each given the following condition:
Find sin2x for each given the following condition:
a) sin x = 4/5 for 90o < x < 180o
b)tan x = -2 for 3pi/2 < x < 2pi
3. ## Re: Find sin2x for each given the following condition:
Hello, alejandro!... |
# McGraw Hill My Math Grade 2 Chapter 8 Lesson 5 Answer Key Dollars
All the solutions provided in McGraw Hill My Math Grade 2 Answer Key PDF Chapter 8 Lesson 5 Dollars will give you a clear idea of the concepts.
## McGraw-Hill My Math Grade 2 Answer Key Chapter 8 Lesson 5 Dollars
Explore and Explain
Teacher Direct... |
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# The mathematical form for three sinusoidal travelling waves are given by Wave 1 : $y\left( {x,t} \right) = \left( {2cm} \right)\sin \left( {3x - 6t} \right)$Wave 2 : $y\left( {x,t} \right) = \left( {3cm} \right)\sin \left( {4x - 12t} \right)$Wav... |
# Median Of Numbers
What is the Median of Numbers?
One of the measures of central tendency is median. Median of numbers is the middlemost value of the given set of numbers. It separates the higher half and the lower half of a given data sample. At least half of the observations are smaller than or equal to median and... |
# What is 70 factorial ?
Steps to calculate factorial of 70
## How to calculate the factorial of 70
To find 70 factorial, or 70!, simply use the formula that multiplies the number 70 by all positive whole numbers less than it.
Let's look at how to calculate the Factorial of Seventy :
70! is exactly : 1197857166996... |
Created By : Abhinandan Kumar
Reviewed By : Rajashekhar Valipishetty
Last Updated : Apr 21, 2023
Surface Area of Box -The surface area of a box is equal to the sum of the areas of each side of the box.
Enter the value of Length(l)
Enter the value of Width(w)
Enter the value of Height(h)
### What is meant by the ... |
### Theory:
There are many techniques to produce more and more irrational numbers between two numbers. But sometimes it is easy to identify the provided number is irrational or not by checking the following properties.
Properties of irrational numbers:
1. Addition, subtraction, multiplication and division of two irrat... |
84 is the amount of pair primes (41 + 43). That is an also composite number that has 2, 3, and also 7 as its prime factors. In this mini lesson, let us learn about the square source of 84, discover out even if it is the square source of 84 is reasonable or irrational, and see how to find the square source of 84 by long... |
# Geometric Constructions - Basics
## Objective and Overview
In this unit, students make formal geometric constructions with Polypad's geometry tools (utensils) while getting a greater insight into geometrical concepts.
In ancient times, geometric constructions of figures and lengths were restricted to the use of on... |
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# If a, b, c in the G.P. and ${{a}^{x}}={{b}^{y}}={{c}^{z}}$ then prove that x, y, z are in H.P
Last updated date: 15th Jul 2024
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Hint: use the basic definition of G.P. i.e. if three te... |
Texas Go Math Grade 7 Lesson 6.2 Answer Key Theoretical Probability of Compound Events
Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 6.2 Answer Key Theoretical Probability of Compound Events.
Texas Go Math... |
Question Video: Finding the Result of Adding Three Fractions with Different Denominators and Expressing It as a Mixed Number | Nagwa Question Video: Finding the Result of Adding Three Fractions with Different Denominators and Expressing It as a Mixed Number | Nagwa
# Question Video: Finding the Result of Adding Three ... |
## Relations Between Roots Solution4
The page relations between roots solution4 is containing solution of some practice questions from the worksheet relationship between roots and coefficients.
(5) If α and β are the roots of 2 x² - 3 x - 5 = 0, form a quadratic equation whose roots are α² and β².
Solution:
General... |
The statement $3 \times 4 = 12$ has two parts: the numbers that are being multiplied, and the answer. The number that are being multiplied are factors, and the answer is the product. We say that $3$ and $4$ are factors of $12$.
The factors of a number are those number whose continued product is the number: thus $4$ an... |
2 Vectors
# 2.2 Coordinate Systems and Components of a Vector
### Learning Objectives
By the end of this section, you will be able to:
• Describe vectors in two and three dimensions in terms of their components, using unit vectors along the axes.
• Distinguish between the vector components of a vector and the scala... |
# A plane goes through $A:(0,1,2), \ B:(3,2,1)$ and $C:(4,-1,0).$ Determine the equation of the plane in affin form.
Solution:
The vectors $\vec{AB}=(3,2,1)-(0,1,2)=3,1,-1$ and $\vec{AC}=(4,-1,0)-(0,1,2)=(4,-2,-2),$ are two direction vectors of the plane. A normal vector $\vec{n}$ to the plane is then given by $$\vec... |
# Calculus/Fundamental Theorem of Calculus/Solutions
1. Evaluate ${\displaystyle \int _{0}^{1}x^{6}dx}$. Compare your answer to the answer you got for exercise 1 in section 4.1.
${\displaystyle \int _{0}^{1}x^{6}dx={\frac {x^{7}}{7}}{\biggr |}_{0}^{1}={\frac {1^{7}}{7}}-{\frac {0^{7}}{7}}=\mathbf {{\frac {1}{7}}=0.{\o... |
# How do you simplify (3x^2y)(10x^5y^3)?
Jan 3, 2017
Multiply each like term in each of the parenthesis. See full explanation below.
#### Explanation:
We will multiply each common term in parenthesis with the common term in the other parenthesis:
$\left(\textcolor{red}{3} \textcolor{b l u e}{{x}^{2}} \textcolor{g ... |
Pre-Calc Exam Notes 98
# Pre-Calc Exam Notes 98 - 0.775 rad ⇒ ∠ CBD = 2(0.775 =...
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98 Chapter 4 Radian Measure §4.3 Example 4.13 The centers of two circles are 7 cm apart, with one circle having a radius of 5 cm and the other a radius of 3 cm. Find the are... |
# How do you find critical points of a logarithmic function y = e^x - 2e^(-x) - 3x?
Oct 29, 2015
Correction: That is not a logarithmic function, but here is how to find the critical numbers for the function.
#### Explanation:
$f \left(x\right) = {e}^{x} - 2 {e}^{- x} - 3 x$
Note that "Dom:(f) = (-oo,oo)
$f ' \lef... |
# How to Find the Square Root of 197?
What does square root mean? By definition, the square root of 197 is the number that, multiplied by itself, produces the given number 197. In this case, that number is 14.0357.
Square root of 197 = 14.0357
11972
The symbol √ is called
radix, or radical sign
The number below
th... |
# R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 14 Height and Distance
## Chapter 14 – Height and Distance Exercise Ex. 14
Question 1
A tower stands vertically on the ground. From a point on the ground which is 20 m away from the foot of the tower, the angle of elevation of its top is found to b... |
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# NCERT Exemplar Class 6 Maths Chapter 3 Solutions: Integers
NCERT Exemplar Solutions Class 6 maths Chapter 3 ‘Integers’ will help you understand what negative numbers and positive numbers are. NCERT Exemplar Class 6 Maths Chapter 3 contains a comprehensive as well as a s... |
## How to Multiply Matrices
### Matrices Operations
The basic operations on a matrix are addition, subtraction, and multiplication. For matrices to be added or subtracted, they must be in the same order. For matrices to be multiplied, the number of columns in the first Matrix must equal the number of rows in the seco... |
# Finding the Sum and Difference of Two Matrices
To solve a problem like the one described for the soccer teams, we can use a matrix, which is a rectangular array of numbers. A row in a matrix is a set of numbers that are aligned horizontally. A column in a matrix is a set of numbers that are aligned vertically. Each ... |
Optimizing Simple Systems
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# ANGLE MEASURES IN POLYGONS
There are two types of angle measures in polygons.
1. Interior Angles
2. Exterior Angles
## Measures of Interior and Exterior Angles
Interior Angle :
An interior angle of a polygon is an angle inside the polygon at each of its vertices.
Exterior Angle :
An exterior angle of a polyg... |
# Vertex of the graph of a quadratic polynomial
This is what a website states:
Before graphing a quadratic function we rearrange the equation, from this:
$f(x) = ax^2 + bx + c$
To this:
$f(x) = a(x-h)^2 + k$
Where:
$h = -b/2a$
$k = f( h )$
In other words, calculate h$(=-b/2a)$, then find $k$ by calculating the ... |
Overview
The fact that many quadratic equations have two solutions has the potential to be confusing. Bear in mind, however, that we are normally looking for just one solution to a particular problem. Choosing the correct solution from two possible answers is usually a matter of recognising which of the answers is app... |
Paul's Online Notes
Home / Calculus II / Series & Sequences / Convergence/Divergence of Series
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How to work out the arc length and perimeter of a sector (part of the circumference of a circle)
Updated on March 28, 2013
Arc Length Of A Sector Video
If you take a part of the circumference of a circle then the distance along this arc is called the arc length. So since the arc length is part of the circumference o... |
Prealgebra 2e
4.5Add and Subtract Fractions with Different Denominators
Prealgebra 2e4.5 Add and Subtract Fractions with Different Denominators
Learning Objectives
By the end of this section, you will be able to:
• Find the least common denominator (LCD)
• Convert fractions to equivalent fractions with the LCD
• A... |
### Is the relation a function?
```Formalizing Relations
and Functions
Objectives:
To determine whether a relation is
a function
To find domain and range and use
function notation
Relation:
a pairing of numbers in one set with
numbers in another set
Domain:
the set of x-values
Range:
the set of y-values
Problem #1: Id... |
What Do The Stars Say About Lamar Odom? (11/03/2019)
How will Lamar Odom fare on 11/03/2019 and the days ahead? Let’s use astrology to undertake a simple analysis. Note this is not scientifically verified – take it with a grain of salt. I will first work out the destiny number for Lamar Odom, and then something simila... |
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
11.2: The One-Way ANOVA Test
Difficulty Level: At Grade Created by: CK-12
Learning Objectives
• Understand the shortcomings of comparing multiple means as pairs of hypotheses.
• Unders... |
# 2: Vectors in Space
Learning Objectives
• Describe three-dimensional space mathematically.
• Locate points in space using coordinates.
• Write the distance formula in three dimensions.
• Write the equations for simple planes and spheres.
• Perform vector operations in (mathbb{R}^{3}).
Vectors are useful tools for ... |
# Question Video: Solving Word Problems by Finding the General Term of a Sequence Mathematics
Emma started a workout plan to improve her fitness. She exercised for fourteen minutes on the first day and increased the duration of her exercise plan by six minutes each subsequent day. Find, in terms of π, the πth te... |
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# Chapter 8, Part 2
## Copyright 2010 Pearson Education, Inc.
DO NOW PICK 2
1) What is a linear model and what does it help us understand? 2) How do we find the residual value? 3) How do we find the line of best fit?
Slide 8 - 3
## AIM AND HOMEWORK
How do we plot and understand l... |
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# Binompdf Function
## Using binompdf(n,p,a) on the TI calculator to evaluate P(X=a) = nCa x p^a x q^(n-a)
Es... |
How to Use the Power Rule for Derivatives. Examples and Interactive Practice Problems.
# How to Use the Power Rule for Derivatives
### Quick Overview
• Power Rule for Derivatives: $$\displaystyle \frac d {dx}\left( x^n\right) = n\cdot x^{n-1}$$ for any value of $$n$$.
• This is often described as "Multiply by the ... |
# lecture 3 Slides.pptx
28 de May de 2023
1 de 13
### lecture 3 Slides.pptx
• 1. Lecture 3 Topics: Outlier in Box Plot Mean, Median and Spread data SADAF SALEEM Department of Computer Sciences GIFT University, Pakistan Course Title: Probability Theory Course Code: MATH-313 Program: BS MATH Semester: Spring 2023
• 2.... |
## Monday, October 25, 2021
### Projectile Motion When Vertical Displacement Is Not Zero
Where are we going with this? The information on this page relates to the skills needed to investigate and evaluate the graphical and mathematical relationship (using either manual graphing or computers) of one-dimensional kinema... |
GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 26 May 2019, 19:35
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
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Paul's Online Notes
Home / Algebra / Common Graphs / Parabolas
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## Mathematics that I learned – By Angela
NATURAL NUMBERS
Natural numbers – We know , we use 1, 2, 3, 4,……when we begin to count. They come naturally when we start counting . Hence, mathematicians call the counting numbers as natural numbers.
To add a natural number of any digit write the number below one another. ... |
### Math Notes
Subjects
#### Algebra Solutions
##### Topics || Problems
If an object is shot vertically from the surface of the earth with an initial velocity of $$v$$ feet per second, and if air resistance and other disturbing factors are neglected, it is found that $$s = vt - 0.5gt^2$$, where $$s$$ feet is the he... |
# Lesson Video: Equation of a Straight Line: Vector Form Mathematics
In this video, we will learn how to find the equation of a straight line in vector form.
18:28
### Video Transcript
In this video, we will learn how to find the equation of a straight line in vector form. There are many different ways that we can ... |
# How many times is 3 75?
The number that multiplies by 3 to give 75 is 25. To answer the question of what times 3 equals 75, we need to find a number x, such that the See full answer below.
## What multiplication answer is 75?
75 = 1 x 75, 3 x 25, or 5 x 15.
## What times 15 gives you 75?
Thus, the answer to “15 ... |
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# Derivatives Study Guide
(not rated)
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Updated on Oct 1, 2011
## Derivatives
Straight lines may be ideal to human beings, but most functions have curved graphs. This does not stop us from projecting straight lines on them! For example, at the point marked x on the graph in Figur... |
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# The V - I graph for a conductor at temperature ${T_1}$ and ${T_2}$ are as shown in the figure. The term $({T_2} - {T_1})$ is proportional to:A) $\dfrac{{\sin 2\theta }}{{{{\sin }^2}\theta }}$B) $\dfrac{{\cot 2\theta }}{{{{\sin }^2}\theta }}$C) $... |
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## Largest Area of Triangle | AIME I, 1992 | Question 13
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Largest Area of Triangle.
## Area of Triangle – AIME I, 1992
Triangle ABC has AB=9 and BC:AC=40:41, find the largest area that this triangle ... |
# How do you graph f(x)=3^(x - 2)?
May 4, 2018
$\text{ }$
#### Explanation:
$\text{ }$
Given the exponential function: color(red)(f(x)=3^(x-2)
Before graphing this function, create a data table:
The table should contain values for color(red)(x, corresponding values for color(red)(y=3^x) and color(red)(y=3^(x-2)
... |
Last time I focused on some basics about learning the number bonds (combinations) of 10 as well as adding 10 to any number. Today I want to show the benefits of making a 10 when adding numbers with sums greater than 10 (such as 8 + 5). Then I’ll show how to help students add up to apply that to addition and subtractio... |
#### need solution for RD Sharma maths class 12 chapter Inverse Trignometric Functions exercise 3.7 question 4 sub question (v)
Answer: $\frac{\pi }{5}$
Hint: The range of principal value of $\sec ^{-1}$ is $\left [ 0,\pi \right ]-\left [ \frac{\pi }{2} \right ]$
Given: $\sec ^{-1}\left(\sec \frac{9 \pi}{5}\right)... |
### Theory:
In this section, let us discuss different types of matrices.
1. Row matrix
A matrix is a row matrix when it is made up of just one row and '$$n$$' number of columns. Row matrices are also called row vectors.
For a matrix $$A = \begin{bmatrix} a_{11} & a_{12} & a_{13} & … & a_{1n} \end{bmatrix}$$, the order... |
# Algebra and General Mathematics: Set Theory
Review notes in set theory topic in Algebra and General Mathematics. This will help you prepare in taking the Engineering Board Exam or simply reviewing for your Algebra subject.
Set theory is the branch of mathematical logic that studies sets, which informally are collec... |
Set Theory: Venn Diagrams And Subsets
Free Roman Numeral Games
Set Operations & Venn Diagrams Venn Diagram Examples Set Worksheets
What Is A Venn Diagram?
A Venn Diagram is a pictorial representation of the relationships between sets.
We can represent sets using Venn diagrams. In a Venn diagram, the sets are repres... |
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# Class 10 NCERT Solutions- Chapter 3 Pair of Linear Equations in Two Variables – Exercise 3.6
• Last Updated : 07 Nov, 2021
### (i)
Solution:
Lets, take 1/x = a and 1/y = b
Here, the two given equation will be as follows:
+ = 2
Multiply it by 6, we get
3a + 2b = 12 -(1)
and,
... |
Associated Topics || Dr. Math Home || Search Dr. Math
### Volume of Soil
```
Date: 02/16/99 at 09:05:17
From: Amy Atteberry
Subject: Volume of soil needed for a trapezoidal bed
I am building some planting beds in a trapezoidal shape. The beds will
be 8" deep. The dimensions of the trapezoidal bed are 2 x 6 x 4 x 4'
... |
# What is the LCM of 10 and 14?
70
#### Explanation:
LCM, or Lowest Common Multiple, is the number which is both a multiple of 10 and 14 and is the first number that is.
Many students will look at the two numbers, in this case 10 and 14 and say: "If I multiply 10 and 14, I'll get 140 and that is for sure a multiple... |
# Properties of a quadratic equation
In the quadratic equation form ax2+bx+c=0, x stands for the unknown value and a, b and c the numbers that are known such that a will never be equal to zero. If in case a is zero, then that equation is not a quadratic equation but a linear equation. a, b and c are the coefficients o... |
# How to use the Z Table (With Examples)
A z-table is a table that tells you what percentage of values fall below a certain z-score in a standard normal distribution.
A z-score simply tells you how many standard deviations away an individual data value falls from the mean. It is calculated as:
z-score = (x – μ) / σ
... |
# denominator 74 results
denominator - The bottom portion of a fraction. For a/b, b is the denominator
1, 1/2, 1/4, 1/8, 1/16 The next number in the sequence is 1/32. What is the function machine you wou
1, 1/2, 1/4, 1/8, 1/16 The next number in the sequence is 1/32. What is the function machine you would use to fin... |
# Linear Algebra/Introduction to Matrices and Determinants
(Redirected from Linear Algebra/Introduction to Determinants)
The determinant is a function which associates to a square matrix an element of the field on which it is defined (commonly the real or complex numbers).
## Matrices
Organization of a matrix
Info... |
Question
# If ${{\text{S}}_1}$ and ${{\text{S}}_2}$ are respectively the sets of local minimum and local maximum points of the functions $f\left( x \right) = 9{x^4} + 12{x^3} - 36{x^2} + 25,x \in R$, then write the elements contained by the two sets ${{\text{S}}_1}$ and ${{\text{S}}_2}$.${\text{A}}{\text{. }}{{\text{S... |
### 1 Changing variables in multiple integrals
When the method of substitution is used to solve an integral of the form ${\int }_{a}^{b}f\left(x\right)\phantom{\rule{0.3em}{0ex}}dx$ three parts of the integral are changed, the limits, the function and the infinitesimal $dx$ . So if the substitution is of the form... |
## Asymptotic Expansion of an integral
Problem: find the asymptotic expansion of the following integral:
$$I_n=\int_0^1\exp(x^n)dx$$
as $n \to \infty$. This expansion, while at first pedestrian-seeming, turns out to have a very interesting set of coefficients.
You can expand the exponential in a Taylor series quite... |
# 2.21: Conversions of Length, Mass, Capacity in Metric Units
Difficulty Level: At Grade Created by: CK-12
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... |
# Quick Answer: What Is Greatest To Least?
## Are fractions with different denominators?
If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator . To do this, you need to find the least common multiple (LCM) of the two denominators. To add fractions with unli... |
# How do you solve abs(-2r-1)=11?
Oct 30, 2017
$r = - 6 , r = 5$
#### Explanation:
This is an absolute value equation meaning that we need to split this into two equations; the original equation and the opposite of it:
$- 2 r - 1 = 11$ and $- 2 r - 1 = - 11$
Notice that the $11$ became $- 11$.
Now we can solve th... |
# Divide by 10, 100 and 1000 Divisors
We will learn how to divide by 10, 100 and 1000 divisors to find the quotient and remainder. Let us consider some examples:
So, 3458 ÷ 10 = 345 with remainder 8 So, 9396 ÷ 10 = 939 with remainder 6
When we divided a number by 10 then the very first digit from the extreme right ... |
# Sides of a Right-angled Triangle
$$(2n + 1)^2 + (2n^2 + 2n)^2 = (2n^2 +2n +1)^2$$
It can be used to generate infinitely many sides of right-angled triangles with integer lengths by putting values of $$n = 1, 2, 3, ...$$
I wanted to know that how we came to this equation. How do we know that putting n = 1, 2, 3, … ... |
# Integral of the absolute Value of $$x$$: $$\int |x| dx$$
Evaluate the integral $\int |x| \; dx$ Rewrite as $\int |x| \; dx = \int 1 \cdot |x| \; dx \quad (I)$
Note that $$|x| = \sqrt {x^2}$$ and hence $$\dfrac{d(|x|)}{dx} = \dfrac{d( \sqrt {x^2})}{dx} = \dfrac{x}{\sqrt {x^2}} = \dfrac{x}{|x|} \quad (II)$$
Apply ... |
# Identify Parallel Lines
Related Topics:
Lesson Plans and Worksheets for Grade 4
Lesson Plans and Worksheets for all Grades
Examples, solutions, and videos to help Grade 4 students learn how to identify, define, and draw parallel lines.
Common Core Standards: 4.G.1
### New York State Common Core Math Grade 4, Modu... |
Ex 11.1
Chapter 11 Class 10 Constructions [Deleted]
Serial order wise
Β
This video is only available for Teachoo black users
Get live Maths 1-on-1 Classs - Class 6 to 12
### Transcript
Ex 11.1, 3 Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding... |
Free Algebra Tutorials!
Try the Free Math Solver or Scroll down to Tutorials!
Depdendent Variable
Number of equations to solve: 23456789
Equ. #1:
Equ. #2:
Equ. #3:
Equ. #4:
Equ. #5:
Equ. #6:
Equ. #7:
Equ. #8:
Equ. #9:
Solve for:
Dependent Variable
Number of inequalities to solve: 23456789
Ine... |
# Lagrange multipliers
## Lagrange multipliers :
Lagrange multipliers are a mathematical tool used to find the maximum or minimum value of a function subject to constraints. Essentially, they allow us to find the optimal solution to a problem by combining multiple equations and constraints.
For example, let’s say we ... |
What Is 11 Out Of 15?
Are you curious to know what is 11 out of 15? You have come to the right place as I am going to tell you everything about 11 out of 15 in a very simple explanation. Without further discussion let’s begin to know what is 11 out of 15?
In various contexts, you might encounter expressions like “11 ... |
Lesson: Input/Output Tables: 2 Step Rules
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Lesson Objective
SWBAT use a rule to complete an input/output table
Lesson Plan
Materials Needed: white board, dry erase markers, DN worksheet, Example Problem, scrap paper, pencils, GP worksheet, IND practice worksheet
Vocabulary: input, output, numer... |
# Factors Of 40 | With Easy Division and Prime Factorization
Contents
In maths, factors of 40 are the numbers that divide the original number 40 and produce the whole number in quotient form. You can find the original number by multiplying any two factors in pairs. Likewise, multiples of 40 are the lengthened version... |
Polynomials (Chapter 2, Exercise 2.2) – Class 10 Maths Solutions NCERT
This page consists of the solutions of the Exercise 2.2, Chapter 2 of Class 10 Mathematics under NCERT Syllabus. The Chapter 2 of Class 10 Mathematics is about the Polynomials. The Exercise 2.2 deals with the questions based on the Relationship bet... |
Tips & Tricks: Probability
# Probability Tips and Tricks for Government Exams
## Introduction
• Probability is the section of mathematics, that deals with the results of random events. The word probability means chance or possibility of an outcome. It explains the possibility of a particular event occurring. We ofte... |
# 2012 AMC 12B Problems/Problem 17
## Problem
Square $PQRS$ lies in the first quadrant. Points $(3,0), (5,0), (7,0),$ and $(13,0)$ lie on lines $SP, RQ, PQ$, and $SR$, respectively. What is the sum of the coordinates of the center of the square $PQRS$?
$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 6.2\qquad\textbf{(C)}\ 6.4\q... |
# Variance of a Data Set
## The mean of the squares of the deviation of data values
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Calculating Variance
If you were told that the mean ... |
# Degree (graph theory) explained
In graph theory, the degree (or valency) of a vertex of a graph is the number of edges that are incident to the vertex; in a multigraph, a loop contributes 2 to a vertex's degree, for the two ends of the edge.[1] The degree of a vertex
v
is denoted
\deg(v)
or
\degv
. The maximum... |
# How do you find an ordered pair for 3x - 4y = 18 and 5y = x - 28?
#### Answer:
Solve for x in one equation in order to substitute it into the other equation and you'll work through to get (-2,-6)
#### Explanation:
Let's start with the original equations:
$3 x - 4 y = 18$
$5 y = x - 28$
We can solve the 2nd equa... |
# The IntMath Newsletter - 21 Sep 2008
By Murray Bourne, 21 Sep 2008
In this Newsletter:
1. Math tip - Hexadecimal Numbers
2. Encryption - and a challenge
3. Current IntMath Poll - Math Anxiety
4. From the math blog
5. Final thought
## 1. Math tip - Hexadecimal Numbers
First, so we can better understand hexadecima... |
# square root
Graph of the square root function ${\ displaystyle y = {\ sqrt {x}}}$
In the logarithmic representation , the graph of the square root function becomes a straight line with a slope of 12 .
The square root (colloquially root; English square root , just sqrt ) a non-negative number is that (uniquely dete... |
# Ascending Order
Ascending order is a method of arranging numbers from smallest value to largest value. The order goes from left to right. Ascending order is also sometimes named as increasing order. For example, a set of natural numbers are in ascending order, such as 1 < 2 < 3 < 4 < 5 < 6 < 7 < 8… and so on. The le... |
# Difference between revisions of "1997 AHSME Problems/Problem 26"
## Problem
Triangle $ABC$ and point $P$ in the same plane are given. Point $P$ is equidistant from $A$ and $B$, angle $APB$ is twice angle $ACB$, and $\overline{AC}$ intersects $\overline{BP}$ at point $D$. If $PB = 3$ and $PD= 2$, then $AD\cdot CD =$... |
# Area Of Square Using Diagonals
The area of a square can be calculated using its diagonals. Apart from the traditional method of finding the area of a square by squaring the sides, this is one of the most useful methods to compute the area of a square if the diagonal length is given.
## Formula to Calculate Area of ... |
# Vertex Form
Pronunciation: /ˈvɜr.tɛks fɔɹm/ Explain
Click on the blue points in the figure and drag them to change the figure. How can you change the figure so that the parabola opens downwards? Manipulative 1 - Vertex Form of a Quadratic Equation Created with GeoGebra.
The vertex form of a quadratic equation is ... |
# If $A (-3, 5), B (-2, -7), C (1, -8)$ and $D (6, 3)$ are the vertices of a quadrilateral $ABCD$, find its area.
Given:
$A (-3, 5), B (-2, -7), C (1, -8)$ and $D (6, 3)$ are the vertices of a quadrilateral $ABCD$.
To do:
We have to find the area of the quadrilateral.
Solution:
Join $A$ and $C$ to get two triangl... |
Graphing
3.1 Understanding Proportional Relationships (Extra Lesson)UNIT 3 • LESSON 1 UNDERSTANDING PROPORTIONAL RELATIONSHIPS adybug and ant move at constant speeds. The diagrams with tick marks show their positions at different times. Each tick mark represents 1 centimeter.
1. Lines uu and v also show the positions ... |
# Statistics Outlier Function – lesscss
By | April 24, 2019
# Statistics – Outlier Function
An outlier in a probability distribution function is a number
that is more than 1.5 times the length of the data set away from
either the lower or upper quartiles. Specifically, if a number is
less than \${Q_1 – 1.5 times IQR... |
Game Development Reference
In-Depth Information
equation using what are known as the inverse trig functions. The
names of these functions match their counterparts, but prefixed
with the word arc . In this case, we need to use arctangent to find
the value of each of these angles.
B
A
=
arctan
15/20
ð
Þ
90 °
A
B
=
arctan... |
# How do you solve for x: 6(x+1)=12(x-3)?
Feb 4, 2017
See the entire solution process below:
#### Explanation:
First, expand all the terms in exponents:
$\left(6 \times x\right) + \left(6 \times 1\right) = \left(12 \times x\right) - \left(12 \times 3\right)$
$6 x + 6 = 12 x - 36$
Next, subtract $\textcolor{red}{... |
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# The vertex of a variable $\Delta ABC$ are $a(3,4)$, $b(5\cos t,5\sin t)$, and $c(5\sin t, - 5\cos t)$. Find the locus of orthocentres of $\Delta ABC$.
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