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# Alternating series and reciprocal Fibonacci constant
We know that reciprocal Fibonacci constant $$\sum_{n=1}^{\infty} \frac{1}{F_n} = \frac{1}{1} + \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{8} + \frac{1}{13} + \frac{1}{21} + \cdots \approx 3.3598856662 \dots .$$
Evaluate: $$\sum_{n=1}^{\infty... |
Examples of differential equations
Differential equations arise in many problems in physics, engineering, and other sciences. The following examples show how to solve differential equations in a few simple cases when an exact solution exists.
Separable first-order ordinary differential equations
Equations in the for... |
http://www.codinghelmet.com/ Wear a helmet. Even when coding. Follow Zoran Horvat @zoranh75
exercises > reducing-fractions
# Exercise #15 - Reducing Fractionsby Zoran Horvat@zoranh75
## Problem Statement
Given two integers n >= 0 and m > 0, write a function which reduces fraction n/m by producing a pair of relativel... |
# Verbal Reasoning - Direction Sense Test
### Exercise :: Direction Sense Test - Introduction
Introduction:
There are four main directions - East, West, North and South as shown below:
There are four cardinal directions - North-East (N-E), North-West (N-W), South-East (S-E), and South-West (S-W) as shown below:
1.... |
### Row Operation
##### 1. Gaussian elimination and back substitution
To solve a system of linear equations, we first simplify the system and then do backward substitution.
Example In the system
3x1 + x2 - x3 = 2 x1 - x2 + x3 = 2 2x1 + 2x2 + x3 = 6
the variable x1 appears in all 3 equations. We try to eliminate x... |
# Linear Equations
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The unit Linear Equations presents the student with the basics of solving linear equations, including equations that involve a variable on both sides and equati... |
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# Lesson Explainer: Polynomial Long Division without Remainder Mathematics • 10th Grade
In this explainer, we will learn how to perform long division on polynomials.
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# High School Math : Solving Inequalities
## Example Questions
### Example Question #1 : Solving Inequalities
Solve for :
Explanation:
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# How do you factor the expression 56x^3 +43x^2+5x?
Mar 18, 2016
$56 {x}^{3} + 43 {x}^{2} + 5 x = x \left(7 x + 1\right) \left(8 x + 5\right)$
#### Explanation:
First separate out the common factor $x$:
$56 {x}^{3} + 43 {x}^{2} + 5 x = x \left(56 {x}^{2} + 43 x + 5\right)$
To factor the remaining quadratic expres... |
The result follows by applying Rolle’s Theorem to g. ¤ The mean value theorem is an important result in calculus and has some important applications relating the behaviour of f and f 0 . Practice Exercise: Rolle's theorem … We can see its geometric meaning as follows: \Rolle’s theorem" by Harp is licensed under CC BY-S... |
# Unit 12 Trigonometry Homework 1 Pythagorean Theorem Answers
Pythagoras’ theorem is one of the most fundamental mathematical theories of all time, and trigonometry is a branch of mathematics that uses the theorem to solve right-angled triangle problems. Homework 1 for Unit 12 Trigonometry covers the theorem in great ... |
# Volume and Surface Area
Volume and Surface Area: The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of the arc length of one-dimensi... |
# Solve ax²-9(a+b)x+(2a²+5ab+2b²)=0
By BYJU'S Exam Prep
Updated on: September 25th, 2023
Value of x = (a + 2b)/3 or x = (2a + b)/3 for Equation ax²-9(a+b)x+(2a²+5ab+2b²)=0.
Consider, 9x²-9(a+b)x+(2a²+5ab+2b²)=0
First, we have to consider (2a²+5ab+2b²) and factorize it:
= 2a²+4ab+ab+2b²
The above equation can be ... |
Three Act Math Play - School Wheelchair Ramp
starstarstarstarstarstarstarstarstarstar
by Dean Vendramin
| 15 Questions
Note from the author:
Used Formative to collect and share student responses in a vareity of ways for our 3 Act Math Play on Slope
Let's take a look at look at the properties of slope and how they relat... |
# What is 7.15 as a fraction?
7.15 = 143/20
## Converting 7.15 to 143/20
Below is a comprehensive guide for our students to calculate 7.15 to the fraction 143/20. Please reach out with any questions or updates. Use the calculator for other conversions from decimals to fractions.
## Step-by-step Process to Convert 7... |
Math Formula?
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An increasing function is a function where: if x1 > x2, then f(x1) > f(x2) , so as x increases, f(x) increases. A decreasing function is a function which decreases as x increases. Of course, a function may be increasing in some places and decr... |
# Lesson 16
Common Factors
### Lesson Narrative
In this lesson, students use contextual situations to learn about common factors and the greatest common factor of two whole numbers. They develop strategies for finding common multiples and least common multiples. They develop a definition of the terms common factor a... |
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# Graphs of Linear Functions
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Practice Graphs of Linear Functions
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# Finding the Cheapest Cell Phone Plan - Answer Key
## Real World Applications – Algebra I
##... |
Below are the solutions and answers to the Practice Exercises and Problems for the Week 1 Review on LCM and GCD.
Practice Exercises
I. Find the GCD of each of the following.
a.) 6, 10
b.) 18, 42
c.) 12, 48, 60
d.) 56, 72
e.) 225, 75
II. Find the LCM of each of the following.
a.) 3, 4
b.) 2, 5
c.) 3, 6, 8
d.) 3,... |
# Place Value with 3 Digits
Content Place Value with 3 Digits
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Place Value with 3 Digits
CCSS.MATH.CONTENT.2.NBT.A.1
## Place Value in 3-Digit Numbers
Three digit numbers can be confusing at times. But you can use place value charts to display three digit numbers and... |
# What is the Greatest Common Factor (GCF) of 1, 1, 31, and 85?
Are you on the hunt for the GCF of 1, 1, 31, and 85? Since you're on this page I'd guess so! In this quick guide, we'll walk you through how to calculate the greatest common factor for any numbers you need to check. Let's jump in!
First off, if you're in... |
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# 7.2E: The Central Limit Theorem for Sample Means (Exercises)
Use the following information to answer the next six exercises: Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approx... |
# Logarithmic Form: Converting & Overview
Instructor: Kimberlee Davison
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Logarithmic form is useful when you want to solve for a variable in an exponent. In this lesson, y... |
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# What is Chinese remainder theorem?
Chinese remainder theorem– Once a Chinese riddle asks the following question- Is there a positive integer x such that when x is divided by 3 it yields a remainder 2, when x is divided by 5 it yields a remainder 4, and when x is divided by 7 it yields a remainder 6?
I... |
## Thursday, 21 February 2013
### Proving the Chain Rule
The chain rule is a method of differentiating a function within a function, for example $\sin x^2$. If you have studied maths to a sufficient (but not necessary) level it is likely that you will know that \begin{align*}\frac{d}{dx}\left(fg(x)\right) = g'(x)f'g(... |
PERCENTS - FLASH CARD : General GMAT Questions and Strategies
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack
It is currently 04 Dec 2016, 20:43
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest... |
Grade 6 Math Statistics and Probability | Student Handouts
Share the learning joy!
Grade 6 Math: Statistics and Probability
www.studenthandouts.com > Grade 6 > Grade 6 Math > Grade 6 Ratios & Proportional Relationships
Develop understanding of statistical variability.
CCSS.MATH.CONTENT.6.SP.A.1: Recognize a statist... |
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Video solutions to help Grade 8 students learn how to predict the shape of a graph of a linear equation by finding and p... |
Limits and substitution
As in @RobertZ's answer to this question, we often perform substitutions when evaluating limits. For instance, if you're asked to show that $$L = \lim_{t \to 0} \frac{\sin t^3}{t^3} = 1,$$ it's pretty common to say "Let $x = t^3$; then as $t \to 0$, we have $x \to 0$, so $$L = \lim_{x \to 0} \f... |
# Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions. y=1-2x+x^2
Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.
$$\displaystyle{y}={1}... |
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# The Product of Two Consecutive Positive Integers is 306. Find the Integers.
By BYJU'S Exam Prep
Updated on: September 25th, 2023
17 and 18 are two consecutive positive integers whose product is 306. To calculate this solution, we will consider two numbers a and a+1, as both numbers are consecutive. By using algebr... |
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Perform the indicated divisions of polynomials by monomials. $\frac{-24{x}^{6}+36{x}^{8}}{4{x}^{2}}$
A polynomial is an expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a non-negative integral power.
Here the given polyno... |
# Learning to Count Again
Let’s define an event A, flipping heads on the flip of a coin for example. What is the probability of that event occurring? I will use the common notation of P(A) to represent the probability of an event A. The basic way to calculate a probability is to divide the number of ways A can occur b... |
# How to Find the Difference Between Two Numbers
How to Find the Difference Between Two Numbers
To find the difference between two numbers, subtract the smaller number from the larger number.
• To find the difference between two numbers, subtract the smaller number from the larger number.
• 5 – 3 = 2 and so, the dif... |
### Subsection3.4.4Whirlwind Tour of Summation Notation
In the remainder of this section we will frequently need to write sums involving a large number of terms. Writing out the summands explicitly can become quite impractical — for example, say we need the sum of the first 11 squares:
\begin{gather*} 1 + 2^2 + 3^2 +... |
# RD Sharma Solutions for Class 11 Chapter 8 - Transformation Formulae Exercise 8.2
In this exercise, we shall discuss problems based on formulae to transform the sum or difference into a product. The solutions prepared by our expert tutors are in an interactive manner to make it easy for the students to understand th... |
# Probability 1 answer below »
An urn holds 5 white and 3 black marbles. If 2 marbles are to be drawn at random without replacement and "x" denotes the number of white marbles, find the probability distribution for x.
Piyanka D
In an urn, there are 5 white and 3 black marbles. From it, 2 balls are drawn at random. He... |
Tutoring high school maths and sciences, unit conversions are prevalent. The math tutor offers an example of converting between common units.
Hello: hope your summer is going great. As I’ve implied over the previous few weeks, my activities have shifted from day-to-day tutoring towards maintenance and research.
One... |
## How do you find the domain of an equation?
A function with a fraction with a variable in the denominator. To find the domain of this type of function, set the bottom equal to zero and exclude the x value you find when you solve the equation. A function with a variable inside a radical sign.
## How do you find the ... |
# 101 is what percent of 104?
## (101 is 97.1154 percent of 104)
### 101 is 97.1154 percent of 104. Explanation: What does 101 percent or 101% mean?
Percent (%) is an abbreviation for the Latin “per centum”, which means per hundred or for every hundred. So, 101% means 101 out of every 100.
### Methods to calculate ... |
# Qnt 561 Week 6
1144 Words5 Pages
Answers to Week Two Homework Assignment ( Assignment 1) Chapter 7 Exercise 13 You should choose a sample size of 1000 people. Although the law of averages tells you that the average of 1000 people is very likely to be close to 60 inches -- and thus under 65 inches tall -- here you ar... |
# Row in Math
Home » Math Vocabulary » Row in Math
## What Is a Row in Math?
A row is simply the horizontal arrangement of objects, side by side, from left to right. It could be people, numbers, or others, placed alongside each other.
Have you observed how the desks and chairs are arranged in a classroom? How does ... |
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# Linear equations
10 CHAPTER
## Here are four examples of equations.
3x 5 17 2(a 3) 18
5(3y 1) 13y 4
16 x 1 x
4
An equation must always have an sign because one side of an equation is always equal to the
other side.
The expression before the equals sign is called t... |
Radicals allow us to reverse exponent operations. For example, squaring a number such as 5, or (-5) will give us 25. If we take the square root of 25, we get back to 5 or (-5). The same process occurs when we look at higher level roots. A cube root will undo cubing a number. A fourth root will undo raising a number to ... |
## Section2.4Equations and Inequalities as True/False Statements
###### ObjectivesPCC Course Content and Outcome Guide
This section introduces the concepts of algebraic equations and inequalities, and what it means for a number to be a solution to an equation or inequality.
### Subsection2.4.1Equations, Inequalities... |
# Class 8 Maths MCQ – Finding Square Roots through Repeated Subtraction
This set of Class 8 Maths Chapter 6 Multiple Choice Questions & Answers (MCQs) focuses on “Finding Square Roots through Repeated Subtraction”.
1. Find the square root of 25 by repeated subtraction method.
a) 5
b) 4
c) 6
d) 2
Explanation: The sum... |
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# Question Video: Finding the Argument of a Complex Number in Radians Mathematics
What is the argument of the complex number 4π?
02:42
### Video Transcript
What is the argument of the complex number four π?
In this question, weβre asked to find the argument of the complex number four π. To answer this q... |
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# Coterminal Angles in Geometry
Coterminal angles are angles that have the same terminal side. In other words, they share the same endpoint. Coterminal angles are often used in geometry and trigonometry, and it's important to be able to identify them and understand how they work. Let's take a clo... |
# How do you factor 18x^2-2?
Jun 20, 2017
$2 \left(3 x + 1\right) \left(3 x - 1\right)$
#### Explanation:
First look for common factors
$18 {x}^{2} - 2 = 2 \left(9 {x}^{2} - 1\right)$
then see if the bracket can be factorised
we note difference of squares hence
$2 \left(9 {x}^{2} - 1\right) = 2 \left(3 x + 1\ri... |
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# Is 42 Divisible By 2?
• Yes, 42 is divisible by 2. It will leave no comma spot.
• Divisibilty rule for 2 is: Units are divisible by two if the last digit is even. Even numbers for 2 are (0,2,4,6,8).
## What Is 42 Divided By 2
• Forty-two divided by two is 21. Mat... |
Mixture Problems
Solving Mixture Problems
Any problem in which two or more quantities are combined to produce a different quantity, or a single quantity is separated into different quantities may be considered a mixture problem.
One type of mixture problem involves mixing liquids or solutions and evaluating the cont... |
# 1’s Complement Subtraction Explained with Examples
Last Updated on October 25, 2023 by Electricalvolt
This article describes the complement arithmetic using 1’s complement binary subtraction. Complement arithmetic is a mathematical process used for subtraction. This operation includes two types of complements, name... |
Instruction
1
If a large number is zero, then division by it any smaller (i.e. negative) values it is impossible to determine.
2
If you want to share any positive value by exceeding its value, then the result is sure to be a fractional number. Because there are several versions of writing fractions, you should start wi... |
# Difference between revisions of "Circumradius"
The circumradius of a cyclic polygon is the radius of the circumscribed circle of that polygon. For a triangle, it is the measure of the radius of the circle that circumscribes the triangle. Since every triangle is cyclic, every triangle has a circumscribed circle, or a... |
# ISEE Upper Level Quantitative : How to find the area of a square
## Example Questions
← Previous 1
### Example Question #1 : How To Find The Area Of A Square
The perimeter of a square is one yard. Which is the greater quantity?
(a) The area of the square
(b) square foot
(b) is greater.
It is impossible to te... |
# and Perpendicular Lines 5 2 Parallel and Perpendicular
• Slides: 21
and Perpendicular Lines 5 -2 Parallel and Perpendicular Lines Warm Up Problem of the Day Lesson Presentation Pre-Algebra
5 -2 Parallel and Perpendicular Lines Warm Up Complete each sentence. 1. Angles whose measures have a sum of 90° are ________.... |
# How do you solve the following system?: 1/3y = 3/4x + 5 , 3/2x - 8y = 2
Apr 1, 2018
$x = - \frac{244}{33}$ $y = - \frac{18}{11}$
#### Explanation:
$\left(\frac{1}{3}\right) y = \left(\frac{3}{4}\right) x + 5$----(1)
$\left(\frac{3}{2}\right) x - 8 y = 2$----(2)
Multiply (2) by $\left(\frac{1}{2}\right)$
$\left(... |
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# Georgia Department of Education
## Common Core Georgia Performance Standards Framework
Fourth Grade Mathematics x Unit 3
STANDARDS FOR MATHEMATICAL CONTENT
MCC4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining... |
What are the solutions of a polynomial?
Table of Contents
What are the solutions of a polynomial?
A solution of a polynomial system is a tuple of values of (x1., xm) that satisfies all equations of the polynomial system. The solutions are sought in the complex numbers, or more generally in an algebraically closed fi... |
# What is the factor tree of 108?
## What is the factor tree of 108?
Factors of 108 are the integers that can divide the original number evenly. There are a total of twelve factors of 108, they are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54 and 108….Pair Factors of 108.
Positive Factors of 108 Positive Pair Factors of 108... |
# What Is The 30Th Term Of The Arithmetic Series 4, 7, 10, €¦?
Contents
## What Is The 30th Term Of The Arithmetic Series 4 7 10 €¦??
The 30th term of the arithmetic progression is 91.
## How do you find the 30th term in a sequence?
1. Given: arithmetic series 2 5 8.
2. d= the common difference.
3. d=a2−a1=a3−a2... |
# NCERT solution class 9 chapter 12 Heron’s Formula exercise 12.1 mathematics
## EXERCISE 12.1
#### Question 1:
A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of t... |
# Friday Morning Math Problem
## Fifty Coins
Find the number of ways that change can be made for \$1.00, using exactly 50 coins.
Solution
Denote the number of pennies, nickels, dimes, quarters, and fifty-cent pieces as x1, x5, x10, x25, x50
Now, we know already that x50 = 0, since having even one fifty-cent piece w... |
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Simplify: $\dfrac{x-2}{{x}^{2}-4}+\dfrac{{x}^{2}}{x-2}-\dfrac{{x}^{3}+x-4}{{x}^{2}-4}, ~~(x \neq \pm2)$.
| ... |
# 2020 AMC 12B Problems/Problem 13
## Problem
Which of the following is the value of $\sqrt{\log_2{6}+\log_3{6}}?$
$\textbf{(A) } 1 \qquad\textbf{(B) } \sqrt{\log_5{6}} \qquad\textbf{(C) } 2 \qquad\textbf{(D) } \sqrt{\log_2{3}}+\sqrt{\log_3{2}} \qquad\textbf{(E) } \sqrt{\log_2{6}}+\sqrt{\log_3{6}}$
## Solution 1 (P... |
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# If ${{x}^{2}}+x+1=0$, then the value of ${{\left( x+\dfrac{1}{x} \right)}^{2}}+{{\left( {{x}^{2}}+\dfrac{1}{{{x}^{2}}} \right)}^{2}}+.....+{{\left( {{x}^{27}}+\dfrac{1}{{{x}^{27}}} \right)}^{2}}$ isA $27$B $72$C $45$D $54$
Last updated date: 17... |
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### Number Differences
##### Stage: 2 Challenge Level:
Place the numbers from 1 to 9 in the squares below so that the difference between jo... |
# Mixed Numbers Calculator
Mixed Numbers Calculator is designed to perform the arithmetical operations like addition, subtraction, multiplication and division on any two mixed numbers easily. You have to enter the mixed numbers in the input fields, select any one operation, and press on the calculate button to check t... |
# How to find position vector between two points
It’s important to keep them in mind when trying to figure out How to find position vector between two points.
## Precalculus : Find a Direction Vector When Given Two Points
Example 1: Given two points P = (-4, 6) and Q = (5, 11), determine the position vector PQ. Solu... |
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## Number Properties - Official Questions on Rounding
Some weeks back, we looked at some rounding rules. Today, let’s go over some official questions on rounding. They are quite sim... |
11.7 Solving systems with inverses (Page 2/8)
Page 2 / 8
Show that the following two matrices are inverses of each other.
$A=\left[\begin{array}{rrr}\hfill 1& \hfill & \hfill 4\\ \hfill -1& \hfill & \hfill -3\end{array}\right],B=\left[\begin{array}{rrr}\hfill -3& \hfill & \hfill -4\\ \hfill 1& \hfill & \hfill 1\en... |
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How do get 24 out of 8 5 6 4?
Updated: 9/17/2023
Wiki User
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6 * 4 + 80 - 50 = 24
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How do you make 24 by using 3 4 5 6?
5+3=8 8-4=4 4*6=24
Can you make 24 using 5 4 8 8?
24 is the same as 6x... |
Semicircle perimeter formula explained
Learn and know how we find the semicircle perimeter. For calculating this we have a formula, so learn it and find the perimeter.
Generally, all the students will think that as area of semicircle is half of the area of circle, in the similar manner they think that perimeter of th... |
# 3.2 Vector addition and subtraction: graphical methods (Page 5/15)
Page 5 / 15
## Conceptual questions
Which of the following is a vector: a person’s height, the altitude on Mt. Everest, the age of the Earth, the boiling point of water, the cost of this book, the Earth’s population, the acceleration of gravity?
... |
# Partial fraction of $\frac{x^n}{(1-x)(1-2x)(1-3x)\ldots(1-nx)}$
How should you break $\displaystyle \frac{x^n}{(1-x)(1-2x)(1-3x)\ldots(1-nx)}$ into partial fractions?
First you have to take out a multiple of the denominator to make the degree of the numerator smaller than that of the denominator:
$$\frac{x^n}{(1-x... |
Home » Importance of Trigonometry formulas
# Importance of Trigonometry formulas
Many difficulties in trigonometry have formulas that can help you work them out. Trigonometric identities (sin, cos, tan, sec, cosec, and cot), Pythagorean identity, product identities, etc., could be at play here. With the Trigonometry ... |
# How does Hanoi Tower Work?
Contents
Tower of Hanoi consists of three pegs or towers with n disks placed one over the other. The objective of the puzzle is to move the stack to another peg following these simple rules. Only one disk can be moved at a time. No disk can be placed on top of the smaller disk.
## What i... |
Total Surface Area - the trick to getting it right
How to Find the Surface Area of a Box
Three Methods:
Finding the surface area of a box is easy as long as you know the length of the sides. Once you know how long the sides are, you simply have to plug them into a basic equation to get your answer. You can even find... |
# MENSURATION
Mensuration means measurement. It is being done in our life in many situations. For example, Length of cloth we need for stitching, the area of a wall which is being painted, perimeter of a rectangular plot to be fenced, quantity of water needed to fill the tank etc. For these kinds of activities, we are... |
# How to Simplify Polynomials
To simplify polynomials, you need to find ‘like’ terms and combine them. Here you can learn how to simplify polynomials.
## Step by step guide to simplifying polynomials
• Find “like” terms. (they have same variables with same power).
• Add or Subtract “like” terms using order of operat... |
Solve 3x^3+6x^2+x+2=0 | Uniteasy.com
# Solve the cubic equation:
## $$3x^3+6x^2+x+2=0$$
Since the discriminant $$\Delta >0$$, the cubic equation has one real root and two conjugate complex roots.
$$\Delta=0.2318244170096$$
$$\begin{cases} x_1=-2 \\ x_2=\dfrac{1}{\sqrt{3}}i \\ x_3=-\dfrac{1}{\sqrt{3}}i \end{cases... |
# How do you write a quadratic equation with x-intercepts: -4,3 ; point: (-5,16)?
Sep 11, 2016
$y = 2 {x}^{2} + 2 x - 24$
#### Explanation:
Use the form $y = k \left(x - a\right) \left(x - b\right)$
where k is a constant, and a and b are the zeros (x coordinate of the x-intercepts).
$a = - 4$ and $b = 3$
$y = k \... |
# Average Problems
Home > Lesson > Chapter 7
5 Steps - 3 Clicks
# Average Problems
### Introduction
Average is a straight- forward concept and it can be solved easily by equal distribution method.
### Methods
Average: Average is the sum of all the elements in a given data set divided by the total number of eleme... |
# NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry
Written by Team Trustudies
Updated at 2021-05-07
## NCERT solutions for class 10 Maths Chapter 7 Coordinate Geometry Exercise 7.1
Q1 ) Find the distance between the following pairs of points:
(i) (2, 3), (4, 1)
(ii) (-5, 7), (-1, 3)
(iii) (a, b), (- ... |
# Equivalent Fractions Calculator
Created by Wojciech Sas, PhD
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Jan 18, 2024
This equivalent fractions calculator is a great tool that helps you find equivalent fractions for any fraction you wish. This is the right place to learn what is an equivalent fraction of ... |
# Types of Matrices with Examples
In this article, we will define different types of matrices along with examples.
Matrix: A matrix is a form of a rectangular array of m rows and n columns. These elements are multiplied during matrix multiplication keeping in mind some basic matrix multiplication properties.
Element... |
Lesson Objectives
• Demonstrate an understanding of how to factor a polynomial
• Learn how to identify a rational expression
• Learn how to find the restricted value(s) for a rational expression
• Learn how to simplify a rational expression
## What is a Rational Expression?
Since pre-algebra, we have seen real number... |
# Finding limits algebraically - direct substitution
### Finding limits algebraically - direct substitution
Graphically finding the limit of a function is not always easy, as an alternative, we now shift our focus to finding the limit of a function algebraically. In this section, we will learn how to apply direct sub... |
# 5. The Ellipse
## Why study ellipses?
Orbiting satellites (including the earth and the moon) trace out elliptical paths.
Many buildings and bridges use the ellipse as a pleasing (and strong) shape.
One property of ellipses is that a sound (or any radiation) beginning in one focus of the ellipse will be reflected ... |
# What are the best criteria for assessing a research question?
## What are the best criteria for assessing a research question?
In this section, we consider two criteria for evaluating research questions: the interestingness of the question and the feasibility of answering it….Is it interesting?Doubt. If the answer ... |
Properties of Convergent Series
# Properties of Convergent Series
We will now look at some very important properties of convergent series, many of which follow directly from the standard limit laws for sequences.
Theorem 1: Let $\sum_{n=1}^{\infty} a_n$ be convergent to the sum $A$ and let $\sum_{n=1}^{\infty} b_n$... |
# How do you find a standard form equation for the line with (-6, 0) and (2, -9)?
Aug 24, 2016
$y = - \frac{9}{8} x - \frac{27}{4}$
#### Explanation:
The equation of a line in $\textcolor{b l u e}{\text{slope-intercept form}}$ is
$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor... |
# ISEE Middle Level Math : How to find length of a line
## Example Questions
### Example Question #11 : Lines
The coordinates of on the rectangle are and . Find the length of the diagonal.
Explanation:
A rectangle has two diagonals with the same length. Therefore, use the distance formula to calculate the distan... |
+0
# trigonometry
0
168
1
if a circle has a radius of 8 centimeters, what is the exact length of the arc intercepted by a central angle of 90 degrees.
May 15, 2018
#1
+2339
+1
An accompanying diagram is an asset geometrists use to condense large amounts of information into something more manageable and visual. I ... |
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