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# Graphic-solution
• Jul 1st 2009, 11:25 AM
dhiab
Graphic-solution
Give the Graphic-solution of this inequality :
http://www.mathramz.com/xyz/latexren...c070e7fd48.png
• Jul 1st 2009, 02:05 PM
red_dog
$(2x-y-3)(2x-y+3)\leq 0$
The solution is the region between the lines 2x-y-3=0 and 2x-y+3=0.
• Jul 1st 2009, 07:37 PM... |
# A Find the Square Root of a Number B Approximate Square Roots C
```1
Professor Busken – Square Roots and the Pythagorean Theorem
Learning Objectives:
A Find the Square Root of a Number
B Approximate Square Roots
C Use the Pythagorean Theorem
Definition 1. The square of a number is the number times itself.
For instan... |
5-2
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# 5-2 - PowerPoint PPT Presentation
5-2. Bisectors of Triangles. Warm Up. Lesson Presentation. Lesson Quiz. Holt Geometry. Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K . List the congruent segments. Learning Targets.
I am the owner, or... |
# Exponent rules
The quantities are expressed in exponential notation in mathematics for some reasons. For doing some mathematical activities with exponential functions, the fundamental formulas of mathematics may not be useful. Hence, it requires some special properties and they are called the rules of exponents. Now... |
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# Calculator Output
```Simplifying
(y + 9)(y + -2) = 4y
Reorder the terms:
(9 + y)(y + -2) = 4y
Reorder the terms:
(9 + y)(-2 + y) = 4y
Multiply (9 + y) * (-2 + y)
(9(-2 + y) + y(-2 + y)) = 4y
((-2 * 9 + y * 9) + y(-2 + y)) = 4y
((-18 + 9y) + y(... |
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Volume of a Right Circular Cylinder
> ... Math > Circles and Pi > Volume of a Right Circular Cylinder
When we find the volume of a rectangular object, we find the area of the base and multiply it by the height. We do the same thing to find the volume of a cylinder only this time the base is a circle. We find the ... |
# The mean life of a sample of 60 bulbs was 650
Question:
The mean life of a sample of 60 bulbs was 650 hours and the standard deviation was 8 hours. A second sample of 80 bulbs has a mean life of 660 hours and standard deviation 7 hours. Find the overall standard deviation.
Solution:
Given the mean life of a sampl... |
# RD Sharma Solutions Class 12 Straight Line In Space Exercise 28.2
RD Sharma Solutions for Class 12 Maths Chapter 28 Straight Line in Space Exercise 28.2, is provided here for students to prepare for exams at ease. Practising the textbook questions will help you in analysing your level of preparation and knowledge of... |
# Ugly Number II LeetCode Solution
Difficulty Level Medium
## Problem Statement
Ugly Number II LeetCode Solution – An ugly number is a positive integer whose prime factors are limited to `2``3`, and `5`.
Given an integer `n`, return the `n`th ugly number.
```Input: n = 10
Output: 12
Explanation: [1, 2, 3, 4, 5, 6,... |
AP State Syllabus AP Board 6th Class Maths Solutions Chapter 7 Introduction to Algebra InText Questions and Answers.
## AP State Syllabus 6th Class Maths Solutions 7th Lesson Introduction to Algebra InText Questions
Let’s Explore (Page No. 102)
Question 1.
Arrange 2 matchsticks to form the shape Continue the same sh... |
# Examples to find Least Common Multiple by using Prime Factorization Method
Examples to find least common multiple by using prime factorization method are discussed here.
We write the prime factorization of each of the given numbers. Then, the required LCM of these numbers is the product of all different prime facto... |
Chapter 1 Number System R.D. Sharma Solutions for Class 9th Math Exercise 1.4
x
Exercise 1.4
1. Define an irrational number .
Solution
An irrational number is a real number that cannot be reduced to any ratio between an integer p and a natural number q. If the decimal representation of an irrational number is non-te... |
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Math Central Quandaries & Queries
Question from ARUN: dear Sir, please advise me , how to calculate the surface area of a pipe with diameter of 630 mm and thickness of 67 mm which is cut in a angle of 22.5 degree. please show me how to calculate the surface area of the pipe which cut in an angle. Thanking... |
# 05. Matrix multiplication, 2
## 05. Matrix multiplication, 2
### Examples
We're going to do some examples of matrix multiplication.
Example:
Consider the 90 degree rotation matrix M equals 0, minus 1; 1, 0. We have M squared equals 0, minus 1; 1, 0 times 0, minus 1; 1, 0, which equals minus 1, 0; 0, minus 1.
Th... |
# How do you simplify log_3 27 + 6log_3 9?
Mar 27, 2016
${\log}_{3} 27 + 6 {\log}_{3} 9 = \textcolor{g r e e n}{15}$
#### Explanation:
Always remember when dealing with log functions
$\textcolor{w h i t e}{\text{XXX}} {\log}_{b} a = c \Leftrightarrow {b}^{c} = a$
So
$\textcolor{w h i t e}{\text{XXX}} \textcolor{re... |
# Step By Step Calculus » 2.8 - Rational Functions
Synopsis
A ratio of polynomials is called a rational function. This is a natural analogue of rational numbers. Polynomials have many similarities to the integers: there is a zero polynomial, they factor, there are prime polynomials, and the algebra is similar to that ... |
# GMAT Tip: Counting Problems
Photograph by Michele Constantini
The GMAT Tip of the Week is a weekly column that includes advice on taking the Graduate Management Admission Test, which is required for admission to most business schools. Every week an instructor from a top test prep company will share suggestions for ... |
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# Discrete Probability Distribution : Part 1
## What are discrete random variables and discrete probability distribution?
In probability and statistics, a random variable is a quantitative variable whose value depends on the outcomes of a random phenomenon. For example, let us toss a coin... |
# Lesson 9
Increasing and Decreasing Functions
• Let’s look at what a graph does based on a situation.
### 9.1: Comparing Values
For each pair of numbers, write $$=,<$$, or $$>$$ in the blank to make a true equation or inequality. Be prepared to share your reasoning.
1. -6 $$\underline{\hspace{.5in}}$$ -9
2. $$\fr... |
Cubic polynomials and their roots
# Cubic polynomials and their roots
We have a look at cubic polynomial functions.
Just as for quadratic functions, knowing the zeroes of a cubic makes graphing it much simpler. Typically a cubic function will have three zeroes or one zero, at least approximately, depending on the p... |
$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$... |
GED Mathematical Reasoning: Systems Of Linear Equations | Open Window Learning
Coordinate Plane and Functions
# GED Mathematical Reasoning: Systems Of Linear Equations
A system of linear equations refers to a set of two or more linear equations. Solving a system of linear equations means to find the ordered pair th... |
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# Draw a rough sketch of a quadrilateral . State two pairs of opposite angles.
Last updated date: 13th Jun 2024
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Hint: In this question, first we will draw the rough sketch of a quadrilate... |
# Aptitude - Time and Work
26.
A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :
4 days
6 days
8 days
12 days
Explanation:
(A + B + C)'s 1 day's work = 1 ; 6
(A + B)'s 1 day's work = 1 ; 8
(B + C)'s 1 day's work... |
# How do you solve the following system: x+3y=-2, 5x + 2y = 5 ?
Jun 13, 2018
By arranging the equation
#### Explanation:
Expand the first equation by $- 5$:
$- 5 x - 15 y = 10$
Now add this to the second equation:
$5 x + 2 y = 5$
Yielding:
$- 13 y = 15$
$y = - \frac{15}{13}$
Put this value in the first origi... |
# Ch 7.3: Systems of Linear Equations, Linear Independence, Eigenvalues
## Presentation on theme: "Ch 7.3: Systems of Linear Equations, Linear Independence, Eigenvalues"— Presentation transcript:
Ch 7.3: Systems of Linear Equations, Linear Independence, Eigenvalues
A system of n linear equations in n variables, can b... |
GreeneMath.com - Rounding Whole Numbers Test
Rounding Whole Numbers Test
When we want to get a value that is close but not necessarily exact, we can use an approximation. One method to approximate a number is known as rounding. Rounding allows us to approximate a number to a specific round off place.
Test Objective... |
# Euclidean Algorithm Explained for Elementary School
In number theory, the Euclidean algorithm is a method for getting the greatest common factor (GCF) or highest common factor (HCF) of two positive integers. It is usually used for larger numbers since prime factorization can be used to get the greatest common factor... |
Question Video: Using Variables to Represent Numbers and Write Inequalities When Solving a Real-World Problem | Nagwa Question Video: Using Variables to Represent Numbers and Write Inequalities When Solving a Real-World Problem | Nagwa
# Question Video: Using Variables to Represent Numbers and Write Inequalities When ... |
Find the derivative of sinx using First Principles?
Nov 21, 2016
By definition of the derivative $f ' \left(x\right) = {\lim}_{h \rightarrow 0} \frac{f \left(x + h\right) - f \left(x\right)}{h}$
So with $f \left(x\right) = \sin x$ we have;
$f ' \left(x\right) = {\lim}_{h \rightarrow 0} \frac{\sin \left(x + h\right) ... |
# Lesson 6
Area of Parallelograms
Let's practice finding the area of parallelograms.
### 6.1: Missing Dots
How many dots are in the image?
How do you see them?
### 6.2: More Areas of Parallelograms
1.
Calculate the area of the given figure in the applet. Then, check if your area calculation is correct by clicki... |
# Area of Triangle Formula
## Formula
### Summary
The area of a triangle is given by one-half multiplied by the base and height.
Expression Description
The area of the triangle.
The base length of the triangle.
The height length of the triangle.
## Usage
The area of a triangle is calculated using the length of it... |
# Basic Algebra Lessons,Learn Algebra
Basic Algebra builds on the foundation of arithmetic. Featuring the introduction of Mathematical formulas, along with equations that contain letters and symbols, as well as numbers.
The main letters and symbols concerned are called variables, or sometimes unknowns, and they help ... |
# How do you do partial fractions in Laplace transform?
## How do you do partial fractions in Laplace transform?
This technique uses Partial Fraction Expansion to split up a complicated fraction into forms that are in the Laplace Transform table….Solution:
Power of s Equation
s3 0=A1+B
s2 5=2A1+A2+C
s1 8=5A1+2A2
s0 ... |
# Problem of the Week Problem B and Solution The Puzzler
## Problem
The Puzzler is the world’s latest superhero. He uses his immense brain to win all battles by solving a series of math problems. He needs your help to solve the following problems.
Use a calculator to help when needed. You may also want to look up wo... |
# Park Forest Math Team. Meet #5. Algebra. Self-study Packet
Save this PDF as:
Size: px
Start display at page:
## Transcription
1 Park Forest Math Team Meet #5 Self-study Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. Geometry: Angle measures in plane figures including supplements and compl... |
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# wikiHow to Solve Complex Cases of Quadratic Equations
The standard form of a quadratic equation in one variable is ax² + bx + c = 0. Depending on the values of the constants a and c, solving this equation may be simple or may be complicated. To know about the new Diagonal Sum Method, please read the ar... |
## 5. Algebra 2
5.1 – Algebraic Fractions
• Simplifying Fractions:
• Can simplify algebraic fractions using division
• Where possible factorise the numerator and denominator, then cancel common factors.
• E.g. 5x2 – 245
• Addition and Subtraction of Algebraic Fractions:
• To add or subtract algebraic fractions:
... |
Unit circle
File:Unit circle.png
Illustration of a unit circle. t is an angle measure.
In mathematics, a unit circle is a circle with unit radius, i.e., a circle whose radius is 1. Frequently, especially in trigonometry, "the" unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordi... |
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# Algebra 1: A Step-by-Step Approach to Learning Algebra
## Algebra 1: What Is It and Why Is It Important?
Algebra 1 is a branch of mathematics that deals with variables, expressions, equations, functions, graphs, and inequalities. It is often the first math... |
# 数学代写|组合学代写Combinatorics代考|The Bernoulli and Cauchy numbers
#### Doug I. Jones
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couryes-lab™ 为您的留学生涯保驾护航 在代写组合学Combinatorics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写组合学Combinatorics代写方面经验极为丰富，各种代写组合学Combinatorics相关的作业也就用不着说。
• Statistical Infere... |
A few weeks ago, the Mathematical Ninja explained how to divide by 9 on the fly. This week, it’s multiplying that’s on his mind - a more common thing to have to do.
The multiplying method is easier, too. It’s just a case of adding and taking away - and writing a few numbers down. In this version, you work from left to... |
# Geometric Mean
You are probably familiar with the arithmetic mean, also known as the average, which is the sum of n numbers divided by n. The geometric mean is another type of mean where we multiply the numbers together and then take the nth root of the product.
So the geometric mean is formally defined as the nth ... |
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# H.C.F. & L.C.M.
1.
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Required number = H.C.F. of $$(91 - 43)$$, $$(183 - 91)$$ and $$(183 - 43)$$
= H.C.F. of $$48, 92$$ and $$140 = 4$$.
Enter details here
2.
The greatest four digit number which is divi... |
Direct Material Quantity Variance
Direct Material Quantity Variance (DMQV) measures how efficiently a manufacturing business can convert its raw materials into the final product.
In this post, I will explain what the direct material quantity variance is, its causes, and the different ways you can calculate it using e... |
# Investigation: Proof of the triangle inequality
Lesson
We will now present a complete paragraph proof of the triangle inequality theorem.
Reading proofs takes much longer than reading text written in everyday language, and that's okay! Follow these tips for understanding and reading proofs:
• Always stop reading ... |
Physically measure the area you are going to sod as estimating could result in ordering too little or too much sod. It is more efficient to take the time required to measure twice and order once. Areas should be measured in square feet.
It is easier and more accurate to measure square or rectangular areas.
If you hav... |
# Fractions, Decimals, And Percentages
Fractions are merely about working with a part of a number. Fractions are breaking whole numbers down into smaller segments or pieces.
Fractions are commonly used in various measurements. Inches are often broken down into 16ths (sixteenths).
Onsego
## Online GED Classes
### G... |
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# ZingPath: Solving Linear Inequalities
Searching for
## Solving Linear Inequalities
Learn in a way your textbook can't show you.
Explore the full path to learning Solving Linear... |
# IS 21 in the 7 times table?
## IS 21 in the 7 times table?
The 7 times table is: 1 × 7 = 7. 2 × 7 = 14. 3 × 7 = 21.
### What are the 24 tables?
24 is a very common number that we use: as 24 carats of gold, 24 hours of a day, 24 major and minor keys in Western tonal music, etc. Hence learning the 24 times table is... |
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• Factor Theorem of Polynomials – Definition, Proof & Examples
Factor Theorem of Polynomials – Definition, Proof & Examples
November 5, 2022
This post is also available in: हिन्दी (Hindi)
Polynomials which are special types of algebraic expressions are used to form polynomial equations, which ... |
How To Find The Area Of The Axial Section Of The Cone | The Science
The Science
# How to find the area of the axial section of the cone
The cone is a geometric body whose base is a circle and the lateral surface - all segments drawn from a point located outside the base plane to the ground. Direct cone, which is... |
## Book: RS Aggarwal - Mathematics
### Chapter: 18. Area of Circle, Sector and Segment
#### Subject: Maths - Class 10th
##### Q. No. 56 of Exercise 18B
Listen NCERT Audio Books to boost your productivity and retention power by 2X.
56
##### In the given figure, PQ = 24 cm, PR = 7 cm and 0 is the centre of the circl... |
What are all the factors, the prime factorization, and factor pairs of 1223?
To find the factors of 1223, divide 1223 by each number starting with 1 and working up to 1223
What is a factor in math ?
Factors are the numbers you multiply together to get another number. For example, the factors of 15 are 3 and 5 becaus... |
# 13.4 Series and their notations
Page 1 / 18
• Use summation notation.
• Use the formula for the sum of the first n terms of an arithmetic series.
• Use the formula for the sum of the first n terms of a geometric series.
• Use the formula for the sum of an infinite geometric series.
• Solve annuity problems.
A couple ... |
# NCERT Solutions For Class 6 Maths Chapter 7 Fractions Exercise 7.5
NCERT Solutions For Class 6 Maths Chapter 7Â Fractions Exercise 7.5 provides students with knowledge about addition and subtraction of like fractions and steps to be followed in solving them. Students can use PDF of NCERT Solutions prepared by subjec... |
##### Algebra I For Dummies
The basics of algebra involve symbols. Algebra uses symbols for quantities, operations, relations, or grouping. The symbols are shorthand and are much more efficient than writing out the words or meanings. But you need to know what the symbols represent, and the following list shares some o... |
Hong Kong
Stage 1 - Stage 3
# Using similarity proportion to solve problems
Lesson
The sides lengths of similar shapes are in the same ratio or proportion. So once we know that two shapes are similar, we can solve any unknown side lengths by using the ratio.
Remember!
You can write the ratio of the big triangle to... |
# Lesson 15
Solving Equations with Rational Numbers
## 15.1: Number Talk: Opposites and Reciprocals (5 minutes)
### Warm-up
The purpose of this number talk is to:
• Remind students that the sum of a number and a number of the same magnitude with the opposite sign is zero.
• Remind students that the product of a nu... |
During AMC testing, the AoPS Wiki is in read-only mode. No edits can be made.
# Difference between revisions of "2019 AMC 8 Problems/Problem 3"
## Problem 3
Which of the following is the correct order of the fractions $\frac{15}{11},\frac{19}{15},$ and $\frac{17}{13},$ from least to greatest?
$\textbf{(A) }\frac{15... |
# Vectors and Scalars in Physics
Vectors and scalars allow us to describe physical quantities. Scalars are used for quantities that can be described completely using only one number and one unit. Vectors, on the other hand, have both a magnitude and a direction.
Examples of scalar quantities include mass, temperature... |
Paul's Online Notes
Home / Calculus III / Line Integrals / Green's Theorem
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape m... |
# How do you factor 4c^3-2c^2-6c?
Aug 30, 2016
$4 {c}^{3} - 2 {c}^{2} - 6 c = c \left(2 c - 3\right) \left(2 c + 2\right)$
#### Explanation:
Note that all of the terms are divisible by $c$, so we can separate that out as a factor first.
We can then factor the remaining quadratic by completing the square and using ... |
# Question: What Are The Types Of Function In Math?
## What are the 4 types of functions?
The various types of functions are as follows:
• Many to one function.
• One to one function.
• Onto function.
• One and onto function.
• Constant function.
• Identity function.
• Quadratic function.
• Polynomial function.
## ... |
# Statements Reasons
1. 3x - 7 = -4 1.
2. 3x - 7 + 7 = -4 + 7 2.
3. 3x + 0 = -4 + 7 3.
4. 3x + 0 = 3 4.
5. 3x = 3 5.
6. (1/3) 3x = 3 (1/3) 6.
7. (1/3) 3x = 1 7.
8. 1x = 1 8.
9. x = 1 9.
8 months ago
## To understand how each statement is justified, let's go through each step:
1. Starting with the equation 3x - 7 = ... |
Given continuous function f(x)=1, x<=0, f(x) =2^xa, 0<x<=1, f(x) = (x^2-2x+b)/(-x+2), 1<x<=2, what is b^(a+2)? domain of f (-infinite,2)
embizze | Certified Educator
Given `f(x)={[1,x<=0],[2^x a,0<x<=1],[(x^2-2x+b)/(-x+2),1<x<2]}`
where f(x) is continuous, find the values of a and b.
** There is a typo in the probl... |
# gaussian elimination
Imagine you have a puzzle with different colored blocks that you need to sort in a certain order. You have a set of simple rules that tell you how to move the blocks around, like "you can switch the places of two blocks" or "you can add or subtract a certain amount of blocks from each other."
G... |
## Mrs. Ashe is planning to take her study group on a field trip to an amusement park. The regular cost is \$7.00 per person. There is a party s
Question
Mrs. Ashe is planning to take her study group on a field trip to an amusement park. The regular cost is \$7.00 per person. There is a party special that costs \$4.0... |
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# 1.1: Points, Lines, and Planes
Difficulty Level: At Grade Created by: CK-12
## Learning Objectives
• Understand the terms point, line, and plane.
• Draw and label terms in a diagram.... |
# 008A Sample Final A, Question 6
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Question: Sketch ${\displaystyle 4x^{2}+9(y+1)^{2}=36}$. Give coordinates of each of the 4 vertices of the graph.
Foundations
1) What type of function is this? What type of graph is this?
2) What can you say ... |
## Precalculus (6th Edition) Blitzer
Published by Pearson
# Chapter 6 - Review Exercises - Page 798: 19
#### Answer
The two airplanes would be $861\text{ miles}$ apart.
#### Work Step by Step
The distance traveled by the first airplane in $2$ hours is: $325\times 2=650\text{ miles}$ The distance covered by the se... |
Associated Topics || Dr. Math Home || Search Dr. Math
### How Many Chickens and Ducks?
Date: 8/16/96 at 10:22:45
From: Leong Theng Kwong
Subject: How Many Chickens and Ducks?
A man bought 20 chickens and ducks altogether, with a \$2 discount per
chicken and 50 cent discount per duck. He saved \$22 in all. How many
c... |
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# If $\left| z \right| = \left| \omega \right|,\omega \ne 0$and$\arg \left( z \right) + \arg \left( \omega \right) = \pi$, then $z =$${\text{a}}{\text{. }} - \omega \\ {\text{b}}{\text{. }}\omega \\ {\text{c}}{\text{. }}\varpi \\ {\text{d}}{\text{. }}... |
# SOLVING INEQUALITIES BY CLEARING THE FRACTIONS
To solve for the variable indicated in the question, we have to isolate the variable term in one side. For that, we will use inverse operations.
• Inverse operation for addition is subtraction.
• Inverse operation for subtraction is addition.
• Inverse operation for mu... |
In sports such as athletics (or swimming, …) the gold medal is awarded to the person who finishes first, ie the person who reaches the finish line in the shortest time, and we call that movement the fast runner. the fastest (or the fastest swimmer).
Watching: What is Velocity
So what is the quantity to know how fast ... |
# Introduction to Probability and Statistics Chapter 6 The
• Slides: 30
Introduction to Probability and Statistics Chapter 6 The Normal Probability Distribution
Continuous Random Variables • Continuous random variables can assume infinitely many values corresponding to points on a line interval. • Examples: – Height... |
# If P(x) is divided by (x-a)(x-b) where a!=b, a,b in RR, can you prove that the remainder is: ((P(b)-P(a))/(b-a))xx(x-a)+P(a)?
Feb 24, 2017
See below.
#### Explanation:
$P \left(x\right)$ can be represented as
$P \left(x\right) = Q \left(x\right) \left(x - a\right) \left(x - b\right) + {r}_{1} x + {r}_{2}$ where ... |
# Numerical Solution of Linear Equations
## Presentation on theme: "Numerical Solution of Linear Equations"— Presentation transcript:
Numerical Solution of Linear Equations
Lecture 2 Chapter 3 Numerical Solution of Linear Equations
Linear System of Equations
In matrix–vector notation
Numerical methods for the solut... |
# Multiplication up to 5
Multiplication up to 5
A Guide to Learning Multiplication Basics
Method:
Multiplication is a mathematical operation that involves multiplying two numbers together. It is one of the four basic operations in mathematics, along with addition, subtraction, and division. To learn multiplication up... |
# Derivative of Arcsin
The derivative of the arcsin function (also denoted as sin^(-1)(x) or asin(x)) can be found using differentiation techniques. Let’s denote y = arcsin(x), where -1 ≤ x ≤ 1.
To find the derivative dy/dx, we can differentiate both sides of the equation y = arcsin(x) with respect to x. Using the ch... |
# SAT Math : Spheres
## Example Questions
### Example Question #771 : Sat Mathematics
A cube with volume 27 cubic inches is inscribed inside a sphere such that each vertex of the cube touches the sphere. What is the radius, in inches, of the sphere?
√3/2 (approximately 1.73)
9
(3√3)/2 (approximately 2.60)
8.5
(... |
## College Algebra (10th Edition)
Published by Pearson
# Chapter 5 - Section 5.6 - Complex Numbers; Quadratic Equations in the Complex Number System - 5.6 Assess Your Understanding: 31
#### Answer
The zeros of the given function are: $\color{blue}{\left\{1, \dfrac{-1}{2} - \dfrac{\sqrt3i}{2}, \dfrac{-1}{2} + \dfrac... |
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# 1.1: Equations and Graphs
Difficulty Level: At Grade Created by: CK-12
## Learning Objectives
A student will be able to:
• Find solutions of graphs of equations.
• Find key properti... |
# Subtraction Word Problems
## Overview
Subtraction helps us to find the difference. Subtraction can tell us how many are left.
Subtraction is easy to do! Subtraction is the opposite of addition.
We can use subtraction in word, or story, problems.
Subtraction skills can help us solve correctly!
For example:
Let’s ... |
# Is ln 2x the same as ln x 2?
## How do you find the derivative of y ln x 2?
ln2x is simply another way of writing (lnx)2 and so they are equivalent.
## Is ln 2x the same as ln x 2?
In normal mathematical usage lnx2 means ln(x2); both are equal to 2lnx and have derivative 2x. Of course (lnx)2 is something altogeth... |
Games That Involve Geometric Probability
By Josh Turner
Jupiterimages/Comstock/Getty Images
Geometric probability deals with likelihood and chance. Traditionally, it attempts to find the odds of a certain outcome when using geometric objects. This works when dealing with games that involve geometric shapes. Many of t... |
# What is the derivative of x^sin(x)?
Dec 20, 2016
$\frac{\mathrm{dy}}{\mathrm{dx}} = {x}^{\sin} x \left(\cos x \ln x + \sin \frac{x}{x}\right)$
#### Explanation:
$y = {x}^{\sin} x$
Take the natural logarithm of both sides.
$\ln y = \ln \left({x}^{\sin} x\right)$
Use laws of logarithms to simplify.
$\ln y = \si... |
# Mastering Matrix Math: Fixing Singular Matrices and Calculating Determinants with NumPy
Matrix math is an essential component of many fields, including data science, computer science, and engineering. It allows us to represent complex systems and make predictions about their behavior.
One of the most fundamental op... |
Quartiles & Quantiles | Calculation, Definition & Interpretation
Quartiles are three values that split sorted data into four parts, each with an equal number of observations. Quartiles are a type of quantile.
• First quartile: Also known as Q1, or the lower quartile. This is the number halfway between the lowest numb... |
# Inter 2nd Year Maths 2A Probability Solutions Ex 9(a)
Practicing the Intermediate 2nd Year Maths 2A Textbook Solutions Inter 2nd Year Maths 2A Probability Solutions Exercise 9(a) will help students to clear their doubts quickly.
## Intermediate 2nd Year Maths 2A Probability Solutions Exercise 9(a)
I. In the experi... |
# How do you integrate int xsqrt(2x^2+7) using substitution?
Jan 22, 2017
I got: $\int x \sqrt{2 {x}^{2} + 7} \mathrm{dx} = \frac{1}{6} \left(2 {x}^{2} + 7\right) \sqrt{2 {x}^{2} + 7} + c$
#### Explanation:
Let us set:
$2 {x}^{2} + 7 = t$
derive:
$4 x = \mathrm{dt}$
let us use this inside our integral (red):
$\int ... |
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### Finding Pythagorean Triplets
```Date: 02/02/2006 at 17:07:24
From: Faizan
Subject: Pythagorean triplets
Without using the standard a = n^2 - m^2, b = 2nm, c = n^2 + m^2, how
can you work out primitive Pythagorean triplets?
For example, you can work out an eq... |
# How do you graph y=xabs(2x+5)?
Jan 19, 2018
#### Explanation:
Let's think of it this way:
$\left\mid a \right\mid = a$ and $\left\mid - a \right\mid = a$
For our first case, we are just bringing out $a$ outside the absolute value.
For the second case, we are finding the opposite of whatever was inside the absolut... |
# Why does dividing by zero give us no answer whatsoever?
I've heard about this and I know that division can be used in one way like this:
For example, if I want to do $30$ divided by $3$, how many times can I subtract $3$ from $30$ to get to $0$? Well, I can do it this way: $30-3=27-3=24-3=21-3=18-3=15-3=12-3=9-3=6-... |
4.01 Multiplication
Lesson
When we need to solve multiplication problems, we have many methods we could use. Which method we choose depends on our problem, how many digits our numbers have, and the method we are more comfortable with.
Idea summary
Methods used in multiplication:
• double-double
• area model
• pa... |
# Powers of Coprime Numbers are Coprime
## Theorem
Let $a, b$ be coprime integers:
$a \perp b$
Then:
$\forall n \in \N_{>0}: a^n \perp b^n$
In the words of Euclid:
If two numbers be prime to one another, and each by multiplying itself make a certain number, the products will be prime to one another; and if the o... |
HANDS-ON ACTIVITY 3.2: THE EXTREME VALUE THEOREM - Limits and Continuity - AP CALCULUS AB & BC REVIEW - Master AP Calculus AB & BC
## Master AP Calculus AB & BC
Part II. AP CALCULUS AB & BC REVIEW
CHAPTER 3. Limits and Continuity
HANDS-ON ACTIVITY 3.2: THE EXTREME VALUE THEOREM
NOTE. The intervals of continuity... |
# A proof of Pythagoras' Theorem (Investigation)
Lesson
The study of mathematics is like a huge pyramid, with things which are proven forming the base of more complicated work above it. The great thing about math is that once someone has proven something, you can take it as completely true and never have to doubt its... |
9140 minus 35 percent
This is where you will learn how to calculate nine thousand one hundred forty minus thirty-five percent (9140 minus 35 percent). We will first explain and illustrate with pictures so you get a complete understanding of what 9140 minus 35 percent means, and then we will give you the formula at the... |
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