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## What is a union in probability?
Union. The union of two sets is a new set that contains all of the elements that are in at least one of the two sets. The union is written as A∪B or “A or B”. Intersection. The intersection of two sets is a new set that contains all of the elements that are in both sets.
What does ∩... |
## Maths - Angle between vectors
How do we calculate the angle between two vectors?
# For 2D Vectors
This is relatively simple because there is only one degree of freedom for 2D rotations. If v1 and v2 are normalised so that |v1|=|v2|=1, then,
angle = acos(v1•v2)
where:
• • = 'dot' product (see box on right of pa... |
## Thinking Mathematically (6th Edition)
The solution set is $\varnothing$(the empty set
The equation is $5-12x=8-7x-\left[ 6\div 3\left( 2+{{5}^{3}} \right)+5x \right]$. Use the order of operations, Work inside parentheses first, \begin{align} & 5-12x=8-7x-\left[ 6\div 3\left( 2+{{5}^{3}} \right)+5x \right] \\ & 5-12... |
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# Algebra 1: 10.2- Graphing Quadratics - PowerPoint PPT Presentation
Algebra 1: 10.2- Graphing Quadratics. Learning Task/Big Idea: Students will learn how to graph quadratic equations by binding the vertex and whether the parabola opens up or down. Notes:. Step 1: First decide if the graph opens UP or DOWN:
I ... |
## Precalculus (6th Edition) Blitzer
$(-∞, -4) ∪ (0, ∞)$
Consider the Rational Inequality as follows: $\frac{x+4}{x}\gt0$ Here are the steps required for Solving Rational Inequalities: Step 1: One side must be zero and the other side can have only one fraction, so we simplify the fractions if there is more than one fr... |
## Want to keep learning?
This content is taken from the National STEM Learning Centre's online course, Maths Subject Knowledge: Fractions, Decimals, and Percentages. Join the course to learn more.
2.8
# Fractions and decimals expressed as percentages
Before we go any further, we need to know what we mean by ‘percen... |
# Advanced Algebra: Absolute Value Inequalities
In advanced algebra, one of the concepts that you must learn is absolute value inequalities. Watch the video below to begin learning this important topic.
## Absolute Value Inequalities
This is a relatively rare topic from the test. So it doesn’t often appear but may a... |
Math + You = 1
# Catalan numbers: Properties and applications
After the numbers of mersenne, here are the Catalan numbers! Catalan numbers are a sequence of natural numbers used in counting. Let's see together their definition, various properties and some applications!
## Definition of Catalan numbers
We can define... |
# Introduction
Welcome to the first lesson in the Straight Line series!
Over the next few (actually many) lessons, I’ll be covering the various forms of equations to a straight line, and a lot of related concepts, formulas and applications.
Without further ado, let’s get started !
To find the equation to a straight... |
## Team 51 School-Home Connection for Math
Place Value
Dear Family,
Your child is learning about place value for very large numbers up to a billion and for decimals with digits in the thousandths place. Each child is learning to compare, order and round these numbers. To do all this, your child must understand the con... |
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# In a flight $50$ people speak Hindi, $20$ speak English and $10$ speak both English and Hindi. The number of people who speak at least one of the two languages is (A) $40$(B) $50$(C) $20$(D) $60$
Last updated date: 14th Jun 2024
Total views: 40... |
# Worksheet on Word Problems on Multiplication of Mixed Fractions | Multiplying Mixed Numbers Word Problems Worksheet
Learn how to solve problems on Multiplying Mixed Numbers in the article on Worksheet on Word Problems on Multiplication of Mixed Fractions. To promote higher level thinking among students we have cover... |
# math
posted by .
Need to solve by substitution
8x - 4y = 16
y = 2x -4
Substitute 2x -4 for y in the first equation and solve the resulting equation for x.
8x - 4(2x-4) = 16
16 = 16
The two equations are not independent. One can be derived fron the other. There are an infinite number of solutions
## Similar Quest... |
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# fundamental theorem of calculus definite integral
## fundamental theorem of calculus definite integral
The Fundamental Theorem of Calculus now enables us to evaluate exactly (without taking a limit of Riemann sums) any definite integral for which we are able to find an antiderivative of the integrand. This m... |
#### Transcript A1 Algebraic manipulation
```KS4 Mathematics
A1 Algebraic manipulation
1 of 73
Contents
A1 Algebraic manipulation
A A1.1 Using index laws
A A1.2 Multiplying out brackets
A A1.3 Factorization
A A1.5 Algebraic fractions
2 of 73
Multiplying terms
Simplify:
x + x + x + x + x = 5x
x to the power of 5
Simpli... |
Parabola
When you kick a soccer ball (or shoot an arrow, fire a missile or throw a stone) it arcs up into the air and comes down again ... ... following the path of a parabola! (Except for how the air affects it.)
Try kicking the ball:
Definition
A parabola is a curve where any point is at an equal distance from:
... |
# Prime Number Problem
Standard
Following is a problem about prime factorization of the sum of consecutive odd primes. (source: problem 80 from The Green Book of Mathematical Problems)
Prove that the sum of two consecutive odd primes is the product of at least three (possibly repeated) prime factors.
The first thin... |
Inverses
Try to visualize in your mind the graph of a function . We can think of this as either a point of points , , or as a bar graph. In any case, we can look at this graph of and determine
(a) if is injective,
(b) if is surjective,
(c) the inverse , if it exists.
How? Well, from the graph of we can determine t... |
# Measurement in Room 3
### Room 3 have done lots of ‘hands on’ maths.
We started with measurement activities using non-standard units, like hands, feet, blocks and counters. We showed that we had grasped the idea of measuring with these units, and we discussed how we needed units the same size, with no gaps, that we... |
# Lesson 6Be the ChangePractice Understanding
### 1.
Graph the following linear equations on the grid. The equation has been graphed for you. For each new equation explain what the number does to the graph of . Pay attention to the -intercept, the -intercept, and the slope. Identify what changes in the graph and what... |
## Selina Concise Mathematics Class 10 ICSE Solutions Chapter 2 Banking (Recurring Deposit Accounts) Ex 2A
These Solutions are part of Selina Concise Mathematics Class 10 ICSE Solutions. Here we have given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 2 Banking Ex 2A.
Other Exercises
Question 1.
Manish ... |
# What is equilateral?
## What Does equilateral Mean
A triangle is a polygon or figure that has three sides . These sides are made up of segments of different lines that meet at points known as vertices . Triangles meet several conditions: the sum of what two of their sides measure, for example, always exceeds the le... |
## How to Calculate and Solve for Shear Modulus | Mechanical Properties
The image above represents shear modulus.
To compute for shear modulus, two essential parameters are needed and these parameters are Shear Stress (τ) and Shear Strain (γ).
The formula for calculating shear modulus:
G = τ/γ
Where:
G = Shear Mo... |
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Cartesian Coordinate System
• Last Updated : 21 Feb, 2021
A number line can be used to represent a number or solution of an equation that only has one variable. It is sufficient to describe the solution of one-valued equations because they all are single-dimensional. But as the number of variables in ... |
# Math Expressions Grade 1 Unit 3 Lesson 6 Answer Key Subtraction Strategies
Solve the questions in Math Expressions Grade 1 Homework and Remembering Answer Key Unit 3 Lesson 6 Answer Key Subtraction Strategies to attempt the exam with higher confidence. https://mathexpressionsanswerkey.com/math-expressions-grade-1-un... |
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# Solving a difference equation
This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!
A certain smoker has a daily intake of 0.02 milligrams of nicotine. It is assumed that 1% of nicotine is disintegrated by the body per day.
Set up a di... |
Common Core: 1st Grade Math : Place Value and Properties of Operations to Add and Subtract
Example Questions
← Previous 1 3 4 5 6 7 8 9 10 11
Example Question #1 : Add A Two Digit Number To A One Digit Number, And Two Digit Number And A Multiple Of 10: Ccss.Math.Content.1.Nbt.C.4
Explanation:
When we add two digit... |
Calculating Horizontal Cylinder Volume
To find the volume of a horizontal cylinder, we must 1) Calculate the entire area of one cylinder "end". 2) Calculate the segment area - (the blue area) by: subtracting triangle Area AOB from the sector area (sector area is the blue area plus the red area) 3) Divid... |
# NCERT Solutions for Class 5 Maths Chapter 13 – Ways to Multiply and Divide
#### Question 1:
• Use Bela’s method to multiply these numbers.
(a) 32 × 46
(b) 67 × 18
32×46 192 ¯ 32×6+—- 32×40
67×18 — ¯ 67×8+ 6 7 0 67×_ _• Do these in your notebook using Bela’s method.
(a) 4... |
Hawkes Learning Systems: College Algebra
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Hawkes Learning Systems: College Algebra - PowerPoint PPT Presentation
Hawkes Learning Systems: College Algebra. Section 1.6: The Complex Number System. Objectives. The imaginary unit and its properties. The algebra of complex numbers. Roots and complex numbers. The Im... |
WHOLE NUMBERS AND DECIMAL NUMBERS
Difference between Whole Numbers and Decimal Numbers
Whole number is a number without fraction. For example 1, 2, 3, 41000, 38888 are examples of whole numbers.71/2 is not a whole number. A decimal number is a fractional number less than 1. It is smaller to a whole number. Examples –... |
# The Explicit Formula for Fibonacci Sequence
First, let's write out the recursive formula: $a_{n+2}=a_{n+1}+a_n$ where $a_{ 1 }=1,\quad a_2=1$
Now, the expression will be modified in 2 different, but similar, ways.
First modification: $a_{n+2}-\alpha a_{n+1}=\beta (a_{n+1}-\alpha a_ n)$ Define a new sequence like t... |
# 3.09 Variables and exponents
Lesson
## Multiplying terms with exponents
When multiplying a number by itself repeatedly, we are able to use exponent notation to write the expression more simply. Here we are going to look at a rule that allows us simplify products that involve the multiplication of exponent terms.
... |
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# Rate of Interest in Simple Interest
Reviewed by:
Last updated date: 04th Aug 2024
Total views: 192.9k
Views today: 5.92k
## An Overview
The rate of interest is the percentage of principal that a lender charges to a borrower. Different banks p... |
# Euler’s Formula with jubes and toothpicks
Learning Intention: To distinguish between prisms and other three-dimensional shapes and to work out the relationship between vertices, edges and faces (Euler’s Formula).
These two Year 7 students are making three-dimensional models with jubes and toothpicks (or satay stick... |
# Square and Cubic Root Calculator
The roots calculator provides an easy-to-use interface for calculating roots for any number. It allows users to understand how to calculate roots, whether they are square roots, cubic roots, or any other type.
## Roots are calculated as follows:
• The value under the root raised to... |
### Grade 6: Rate, Ratio and Proportional Reasoning
Rating:
#### Common Core Standards
Content Standards
6.RP.1 - Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
6.RP.2 - Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠... |
## Precalculus (6th Edition) Blitzer
The required values are $C=162{}^\circ,a\approx 33.8$, and $b\approx 67.3$.
At first we will find C. Property of a triangle: Sum of three angles is $A+B+C=180{}^\circ$ \begin{align} & A+B+C=180{}^\circ \\ & 6{}^\circ +12{}^\circ +C=180{}^\circ \\ & C=180{}^\circ -18{}^\circ \\ & C=... |
## Graph piecewise-defined functions
Sometimes, we come across a function that requires more than one formula in order to obtain the given output. For example, in the toolkit functions, we introduced the absolute value function $f\left(x\right)=|x|$. With a domain of all real numbers and a range of values greater than... |
# Multiplying Powers in Algebra
Powers can be multiplied together.
To multiply powers, add the exponents together.
This is a law of exponents.
# How to Multiply Powers in Algebra
Multiplying powers in algebra is easy.
#### An Example Question
Use the law of exponents to multiply the powers below.
Step 1
Check ... |
# 2-1
Télécharger la présentation
## 2-1
- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
##### Presentation Transcript
1. Solving Equations by Adding or Subtracting 2-1 Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz
2. 3 1 2 2 2 3 3 3 3 2 3 ... |
# 1997 USAMO Problems/Problem 5
## Problem
Prove that, for all positive real numbers $a, b, c,$
$(a^3+b^3+abc)^{-1}+(b^3+c^3+abc)^{-1}+(a^3+c^3+abc)^{-1}\le(abc)^{-1}$.
## Solution 2
Outline:
1. Because the inequality is homogenous, scale $a, b, c$ by an arbitrary factor such that $abc = 1$.
2. Replace all $abc$... |
# Calculus
## What is Calculus?
Technically, calculus is the study of rates of change. However, if you’ve never taken calculus before, “rates of change” might have too much meaning to you. Calculus is actually two separate categories: differentiation and integration. Differentiation is a tool where you can find an ob... |
AP Statistics Lectures
by Arnold Kling
Geometric Distribution
Suppose that I am at a party and I start asking girls to dance. Let X be the number of girls that I need to ask in order to find a partner. If the first girl accepts, then X=1. If the first girl declines but the next girl accepts, then X=2. And so on.
Whe... |
Скачать презентацию Section 6 2 Applications of Right Triangles Copyright
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• Количество слайдов: 23
Section 6. 2 Applications of Right Triangles Copyright © 2013, 2009, 2006, 2001 Pearson Education, Inc.
Objectives · · Solve right triangles. Solve applied problems involving right... |
20.109(F22):M1D7
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
20.109(F22): Laboratory Fundamentals of Biological Engineering
Introduction
Today is the final laboratory session for Module 1! You have completed all of the bench work for your research; however, there is still data analysis... |
## Saturday, 9 August 2014
### chapter 10 Worked Out Examples
Example: 1
Evaluate the following limits
(a) $\mathop {\lim }\limits_{x \to 2} \left( {\dfrac{2}{{x(x - 2)}} - \dfrac{1}{{{x^2} - 3x + 2}}} \right)$ (b) $\mathop {\lim }\limits_{n \to \infty } \left[ {(1 + x)(1 + {x^2})(1 + {x^4})\ldots(1 + {x^{{2^n}}})}... |
User:
# Solve a quadratic equation by completing the square
With quadratic equations (ax2 + bx + c = 0), you can solve by completing the square.
Step 1: Make sure that the left side of the equation looks like x2 + bx.
Step 2: Add $(\frac{b}{2})^2$ to both sides.
Step 3: Factor the left side as $(x+\frac{b}{2})^2$
... |
# How do you simplify 5sqrt12-2sqrt48-7sqrt75?
Oct 30, 2016
$- 33 \sqrt{3}$
#### Explanation:
$5 \sqrt{12} = 5 \sqrt{4 \times 3} = 5 \times 2 \sqrt{3} = 10 \sqrt{3}$
$2 \sqrt{48} = 2 \sqrt{16 \times 3} = 2 \times 4 \sqrt{3} = 8 \sqrt{3}$
$7 \sqrt{75} = 7 \sqrt{25 \times 3} = 7 \times 5 \sqrt{3} = 35 \sqrt{3}$
Th... |
# Geometry Math Problems - Perimeters
In these lessons, we will learn to solve geometry math problems that involve perimeter.
Geometry word problems involves geometric figures and angles described in words. You would need to be familiar with the formulas in geometry.
Making a sketch of the geometric figure is often ... |
Question
Mohan is able to write 20 words in one hour. How many words would he be ableto write in 10 minutes?
Hint: Use the unitary method to find the answer. First find the number of words he can write in 1 minute. Then multiply this by 10 to find the number of words he can write in 10 minutes.
Complete step by step... |
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Math 109 T8-Trigonometric Identities
Page 1
MATH 109 – TOPIC 8
TRIGONOMETRIC IDENTITIES
I. Using Algebra in Trigonometric Forms Practice Problems II. Verifying Identities
Practice Problems
I. Using Algebra in Trigonometric Form This topic will focus mainly on identities and how they ca... |
# How do you solve n^2-4=77?
Aug 4, 2016
$n = 9$
#### Explanation:
color(magenta)("Let's add 4 to both sides of the equation:"
${n}^{2} - \cancel{4} = 77$
$\textcolor{w h i t e}{a a} + \cancel{4}$ $\textcolor{w h i t e}{a} + 4$
On the left side of the equation you're left with ${n}^{2}$ since $\left(- 4\right) + ... |
## The Clock Arithmetic and Modular Systems Series
This is a series of posts that explains modular systems starting from an intuitive introduction using clocks. I wrote this for high school students of average mathematical ability.
I hope you find the series easy to read and student friendly.
The Series
This post i... |
# Find the area of the triangle formed by the lines
Question:
Find the area of the triangle formed by the lines x = 0, y = 1 and 2x + y = 2.
Solution:
The given equations are
$x=0 \ldots(\mathrm{i})$
$y=1 \ldots(\mathrm{ii})$
and $2 x+y=2 \ldots$ (iii)
Let eq. (i), (ii) and (iii) represents the sides AB, BC and... |
Q:
# The linear function graphed below represents the value of a comic book since Lucy purchased it. What was the value of the comic book when Lucy bought it?
Accepted Solution
A:
Answer:C. $25Step-by-step explanation:We will find,The slope of the function using $$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$.Taking the points ... |
# One, Two, Buckle My Shoe: Math and Literacy for Preschoolers
Math is all around, even for our youngest learners. By providing a home rich in language and where thinking is encouraged, you can help your preschooler develop important numeracy and literacy skills. Below are four examples of ways to integrate language a... |
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The graph of a quadratic function is called a parabola.
A quadratic graph is the graph of a quadratic function. This module describes the graphing of quadratic functions. A quadratic function has the form $$y=ax^{2}+bx+c$$ where $$a\neq0$$ .
The graph of a quadratic function is called a parabola.
To sketch a parabol... |
## Friday, December 22, 2006
### James G's Percentage Growing Post (Question 6)
Question 6
Use a hundred grid (unit square) to illustrate the following questions. Once you have explained and illustrated what the question means solve it.
a) 16 is 40% of what number?
40/40=1%
40/100=0.4
0.4x100=40
40/100 = 16/40
b)
W... |
NCERT Solutions for Class 9th: Ch 1 Number Systems Maths
NCERT Solutions for Class 9th: Ch 1 Number Systems Maths
Page No: 5
Exercise 1.1
1. Is zero a rational number? Can you write it in the form p/q, where p and q are integers and q ≠ 0?
Yes. Zero is a rational number as it can be represented as 0/1 or 0/2.
2. ... |
# LIAL HORNSBY SCHNEIDER
## Presentation on theme: "LIAL HORNSBY SCHNEIDER"— Presentation transcript:
LIAL HORNSBY SCHNEIDER
COLLEGE ALGEBRA LIAL HORNSBY SCHNEIDER
2.4 Linear Functions Graphing Linear Functions
Standard Form Ax + By = C Slope Average Rate of Change Linear Models
Linear Function A function is a li... |
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# Scientific Notation
## Writing and reading scientific notation
Estimated10 minsto complete
%
Progress
Practice Scientific Notation
MEMORY METER
This indicates how strong in your memo... |
# Fraction and Fraction Calculators Online
Fraction in Mathematics:
Fraction is one of the ‘basic terms’ in mathematics, Fraction can simply be defined as:
The part of whole number
Or it can be defined as,
“Representation of a whole number in a different way”
Example:
• 5 can be written as 2 ½
• 10 can be Writte... |
Factors
# Factors of 9 | Prime Factorization of 9 | Factor Tree of 9
Written by Prerit Jain
Updated on: 12 Aug 2023
### Factors of 9 | Prime Factorization of 9 | Factor Tree of 9
When two numbers are multiplied together to get the result of 9, they are called factors of 9. The factors of 9 can be written in either... |
# Recurrence Relation
In an Analysis of Algorithm, recurrence relations are used to analyze the running time of a recursive function. The running time of a recursive function is denoted by $T(n)$ where $n$ is the size of the input. In recurrence relation, the running time of a recursive function of input size $n$ is e... |
1.- Addition of fractions with the same denominator.
We have one piece of cake (1/5) and we add 2 pieces (2/5). Finally we have three pieces (3/5).
To add fractions with the same denominator, we must add the numerators, keeping the same denominator.
Examples: 2/7 + 3/7 + 1/7 = 6/7; 5/9 + 8/9 = 13/9
Solve these sums... |
# Similar and Dissimilar Surds
We will discuss about similar and dissimilar surds and their definitions.
Definition of Similar Surds:
Two or more surds are said to be similar or like surds if they have the same surd-factor.
or,
Two or more surds are said to be similar or like surds if they can be so reduced as to ... |
+0
# Six children are each offered a single scoop of any of \$3\$ flavors of ice cream from the Combinatorial Creamery. In how many ways can each c
+1
35
1
+15
Six children are each offered a single scoop of any of 3 flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavo... |
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# Block on Block Problems - Friction | JEE Important Topic
Last updated date: 22nd Jul 2024
Total views: 91.2k
Views today: 2.90k
## Friction Problems: Overview
Mechanics is the branch of science that deals with the forces and their effects on ... |
How to recognise the digit multiplication, subtraction or addition when checking for divisibility by 7, 11, 13, 17 and 19?
I was studying this page Divisibility by prime numbers under 50 to check for the divisibility by 7, 11, 13, 17, 19 etc. Is there any way to recognise whether to add or sub the given times of unit ... |
# Absolute-value problems
Consider how the absolute value of a real number x relates to a fixed positive number, say 4:
On the inside is one region where |x| < 4, on the outside are two regions where |x| > 4, and these regions are separated by two points where |x| = 4. Using this picture it's easy to solve these equat... |
Title
College Algebra
Tutorial 51: Systems of Linear Equations
and Problem Solving
Learning Objectives
After completing this tutorial, you should be able to: Use Polya's four step process to solve various problems involving systems of linear equations in both two and three variables.
Introduction
Hey, lucky you,... |
Name: ___________________Date:___________________
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### Grade 6 - Mathematics12.11 Linear Equations - 2
Examples: 2x + 8 = 14 Then x = ? 2x + 8 = 14 subtracting 8 from both sides 2x + 8 - 8 = 14 - 8 2x = 6 Dividing both... |
ML Aggarwal Class 7 Solutions Chapter 16 Perimeter and Area Ex 16.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.
## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Ex 16.1
Question 1.
ABCD is a square of side 24 cm... |
# Difference between revisions of "2002 AMC 10A Problems/Problem 20"
## Problem
Points $A,B,C,D,E$ and $F$ lie, in that order, on $\overline{AF}$, dividing it into five segments, each of length 1. Point $G$ is not on line $AF$. Point $H$ lies on $\overline{GD}$, and point $J$ lies on $\overline{GF}$. The line segment... |
# Mensuration Problems
Home > Lesson > Chapter 35
5 Steps - 3 Clicks
# Mensuration Problems
### Introduction
Mensuration Problems deals with the area, perimeter, diagonal, height, circumference etc. of figures like square, rectangle, parallelogram, rhombus, trapezium, triangle, equilateral triangle, cube, cuboid, c... |
# Local maximum from the left implies left-hand derivative is nonnegative if it exists
This article describes a test that can be used to determine whether a point in the domain of a function gives a point of local, endpoint, or absolute (global) maximum or minimum of the function, and/or to narrow down the possibiliti... |
# Square root of 81
The square root of 81 is a number when multiplied by itself will be 81. It is the positive solution of the quadratic equation x2=81. The square root of 81 is denoted by the symbol √81. In this section, we will learn how to find the value of √81.
Note that if a square has an area of 81 unit2, then ... |
# Time to Teach Presents Year 5 (National Numeracy Strategy) (Based on DFEE Sample Lessons) www.timetoteach.co.uk.
## Presentation on theme: "Time to Teach Presents Year 5 (National Numeracy Strategy) (Based on DFEE Sample Lessons) www.timetoteach.co.uk."— Presentation transcript:
Time to Teach Presents Year 5 (Natio... |
## Section9.3Logarithmic Functions and Their Graphs
The inverse of a simple exponential function, $f(x)=b^x, b \gt 0, b \neq 1\text{,}$ is called a logarithmic function. The inverse of $f(x)=b^x$ is symbolized as
\begin{equation*} f^{-1}(x)=\log_b(x) \end{equation*}
which is read aloud as "f-inverse of x equals the ... |
## How do you find the magnitude and angle of a vector?
MAGNITUDE AND DIRECTION OF A VECTOR Given a position vector →v=⟨a,b⟩,the magnitude is found by |v|=√a2+b2. The direction is equal to the angle formed with the x-axis, or with the y-axis, depending on the application. For a position vector, the direction is found ... |
# Learn How to Round to The Nearest Tenth
• Published On:
Life gets easy once you learn decimal rounding methods, and using them every day will become a part of your routine. Whether you are estimating your shopping bills, balancing accounts or rounding numbers saves time. In this blog post, you will learn how to rou... |
# 1760 Pots of Gold and Rainbows
### Today’s Puzzle:
Write the numbers 1 to 12 in the first column and again in the top row so that those numbers are the factors that make the given clues. It’s a level 6, so it won’t be easy. Finding a leprechaun’s pot of gold isn’t easy either. Still, if you can solve this puzzle, t... |
# How to easily retrieve operation table of group elements from this Cayley diagram?
• Nov 17th 2012, 02:30 PM
x3bnm
How can I retrieve operation table of group elements from this Cayley diagram?
There's a math problem in Pinter's Abstract Algebra book on pp. 52(exercise G):
Exercise:
Every finite group may be repre... |
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# Section P.3 – Functions and their Graphs
## Presentation on theme: "Section P.3 – Functions and their Graphs"— Presentation transcript:
Section P.3 – Functions and their Graphs
Functions A relation such that there is no more than one output for each input A B C W Z Algebraic Function Can be written as finite sums,... |
# Why Does The 9 Hand Trick Work?
## What is the 9 trick in math?
A Mathemagical Trick Start by thinking of a number, any number.
Now, multiply that number by 9.
If the result is a multi-digit number, add its digits together to come up with a new number.
If that new number is still a multi-digit number, add its di... |
# Question #b7e2c
Feb 5, 2016
You would like to prove that
$2 \left({\sin}^{6} \Theta + {\cos}^{6} \Theta\right) - 3 \left({\sin}^{4} \Theta + {\cos}^{4} \Theta\right) + 1 = 0$
This can be proven by starting at the left side and transforming until we have the right side, so in this case, $0$.
I will use the follow... |
# How do you solve -2( n - 5) = 20?
##### 1 Answer
May 27, 2018
$n = - 5$
#### Explanation:
$- 2 \left(n - 5\right) = 20$
First, use the distributive property shown below to simplify/expand $- 2 \left(n - 5\right)$:
Following this image, we know that:
$\textcolor{b l u e}{- 2 \left(n - 5\right) = \left(- 2 \cdot ... |
How do you solve 4x - 24= - 5x + 12?
Jun 22, 2018
$x = 4$
Here's how I did it:
Explanation:
$4 x - 24 = - 5 x + 12$
First, add $\textcolor{b l u e}{24}$ to both sides:
$4 x - 24 \quad \textcolor{b l u e}{+ \quad 24} = - 5 x + 12 \quad \textcolor{b l u e}{+ \quad 24}$
$4 x = - 5 x + 36$
Now add $\textcolor{b l u... |
# why is sin(90-θ) = cosθ?
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why is sin(90-θ) = cosθ?
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Imagine a rectangle with a diagonal drawn bottom left to top right. The angle the diagonal makes with the horizontal base is theta and the length of the base is d.cos(theta) where d is the length of the diagonal. Adjacent over hypotenuse is cosine... |
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The concepts of mathematics are very integral. They are used in almost all fields and help people in day-to-day lives also. Many concepts like Algebra, Venn diagrams, Geometry, Standard deviation, etc are widely used. They must be well understood from the beginning only.
Standard deviation is one important con... |
# PERMUTATIONS AND COMBINATIONS for Class 11 MATHS
## INTRODUCTION TO TRIGONOMETRY :
Permutation and combination are the ways to represent a group of objects by selecting them in a set and forming subsets. It defines the various ways to arrange a certain group of data. When we select the data or objects from a certai... |
Mathematical operators
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The mathematical operators perform basic math operations, such as addition and subtraction. The values that the operators act on are called operands.
Syntax and Operation
Addition
The addition operator + (plus sign) returns the sum of two values (i.e., it add... |
Distance between Two Points in Polar Co-ordinates
How to find the distance between two points in polar Co-ordinates?
Let OX be the initial line through the pole O of the polar system and (r₁, θ ₁) and (r₂, θ₂) the polar co-ordinates of the points P and Q respectively. Then, OP₁ = r₁, OQ = r₂, ∠XOP = θ₁ and ∠XOQ = θ₂,... |
# What is the slope of f(t) = (t^2-tsqrtt,t/2) at t =3?
Jun 15, 2017
$m = - 8.0386$
#### Explanation:
This parametric equation says that the $x$ value of the function $f$ is
$x \left(t\right) = {t}^{2} - t \sqrt{t}$
When $t = 3$
$x \left(3\right) = {3}^{2} - 3 \sqrt{3} = 9 - 3 \sqrt{3} \approx 3.8038$
The deriv... |
# PLAYING WITH NUMBERS
Mathematics is a subject with full of fun, magic and wonders. Here we are going to enjoy with some of this fun and wonder.
## Numbers in General Form
Let us take the number 42 and write it as
42 = 40 + 2 = 10 × 4 + 2
Similarly, the number 27 can be written as
27 = 20 + 7 = 10 × 2 + 7
In ge... |
# Z=1/6as for a?
Sep 18, 2017
$a = \frac{1}{6 s z}$
#### Explanation:
$z = \frac{1}{6 a s}$
Multiply both sides by $\textcolor{red}{6 a s}$
$z \cdot \textcolor{red}{6 a s} = \frac{1}{6 a s} \cdot \textcolor{red}{6 a s}$
We cancel 6as from the right side then we will have $1$ as the remaining
$6 a s z = 1$
To find $... |
# Quadratic Inequalities
In this section, I'll consider quadratic inequalities. I'll solve them using the graph of the quadratic function. I'll also look at other inequalities, which I'll solve using sign charts.
A quadratic function is a function of the form . The graph of a quadratic function is a parabola.
If , t... |
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