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## UNSW Sydney
Parabola through three points
# A quadratic function through three points
Another application of quadratic functions is t... |
# How do you multiply (4sqrt18)(2sqrt14)?
Jun 18, 2015
$48 \sqrt{7}$
#### Explanation:
You can multiply the numbers outside the roots and them try to manipulate the arguments of the square roots:
$4 \cdot 2 \sqrt{18} \sqrt{14} =$
$= 8 \sqrt{9 \cdot 2} \sqrt{7 \cdot 2} =$
$= 8 \cdot 3 \sqrt{2} \sqrt{7 \cdot 2} =$ ta... |
# Basic facts and techniques of Boats and Streams of Quantitative Aptitude
Boats and Streams is a part of the Quantitative aptitude section. This is just a logical extension of motion in a straight line. One or two questions are asked from this chapter in almost every exam. Today I will tell you some important facts a... |
# How do you differentiate f(x)= 3x^2 (4x - 12)^2 using the product rule?
Nov 12, 2015
Taken you to a point where you should be able to complete the calculation.
#### Explanation:
Let $u = 3 {x}^{2} \text{ }$ then $\frac{\mathrm{du}}{\mathrm{dx}} = 6 x$ ..............(1)
Let $v = {\left(4 x - 12\right)}^{2} \text{... |
# Thearrangement in increasing order for the given numbers.
### Single Variable Calculus: Concepts...
4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
### Single Variable Calculus: Concepts...
4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
#### Solutions
Chapter... |
Lesson Video: Converting Lengths: Meters and Centimeters | Nagwa Lesson Video: Converting Lengths: Meters and Centimeters | Nagwa
# Lesson Video: Converting Lengths: Meters and Centimeters Mathematics
In this video, we will learn how to measure length using mixed units, convert between lengths using partitioning, and... |
# 125% of 16 is what number?
Apr 2, 2018
See a solution process below:
#### Explanation:
"Percent" or "%" means "out of 100" or "per 100", Therefore 125% can be written as $\frac{125}{100}$.
When dealing with percents the word "of" means "times" or "to multiply".
Finally, lets call the number we are looking for "... |
# Portal
You are here: Home » Content » Geometric Sequences
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# Geometric Sequences
Module by: First Last. E-mail the author
Summary: In this section, you will:
• Find the common ratio for a geometric sequence.
• List the terms of a geometric sequ... |
# 5 Parallelogram Problem Solving Techniques for Mastering Geometry
쉬운 목차
## Introduction to Parallelogram Properties
A parallelogram, with its opposite sides parallel and equal in length, serves as a cornerstone of geometric theory, captivating both mathematicians and students. Grasping these characteristics is cru... |
## New Maths Curriculum: Year 2 Multiplication and Division
Year 2 Multiplication and Division
It’s time to start learning those times tables off by heart; beginning with the 2x, 5x and 10x tables.
The statutory requirements for Year 2 Multiplication and division :
Pupils should be taught to:
• recall and use multi... |
Do you want to learn faster and more easily?
Then why not use our learning videos, and practice for school with learning games.
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## How Do You Do Addition and Subtraction?
There are many ways we can do addition and subtraction such as counting on or backwards, using... |
Use adaptive quiz-based learning to study this topic faster and more effectively.
# Acceleration main formula
Like displacement $(s)$ and velocity $(v)$, the acceleration $(a)$ is a vector quantity.
Often we use the symbols $\Tred{u}$ for initial velocity, $\Tblue{v}$ for final velocity and $\Delta v$ for change in ... |
# CAT 2021 Set-2 | Quantitative Aptitude | Question: 6
1 vote
47 views
For a real number $x$ the condition $|3x – 20| + |3x – 40| = 20$ necessarily holds if
1. $9 < x < 14$
2. $6 < x < 11$
3. $7 < x < 12$
4. $10 < x < 15$
retagged
1 vote
Given that, $|3x-20| + |3x-40| = 20 ; x \in \mathbb{R} \quad \longrightarrow ... |
# The median BM of triangle ABC is the diameter of the circle intersecting side BC in its middle. The length of the side AC is 4
The median BM of triangle ABC is the diameter of the circle intersecting side BC in its middle. The length of the side AC is 4. Find the radius of the circumscribed circle of triangle ABC
D... |
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# How to find scale factor
This calculator help us find the scale factor between two lengths, simply enter two lengths, it will automatically calculate the scale factor, supports different length units (mm, cm, m, km, in, ft, yd, mi), in addition corresponding visual graphic and formula, easy understanding... |
# Fractions: Multiplying proper fractions
#### Everything You Need in One Place
Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.
#### Learn and Practice With Ease
Our proven video lessons ease you through probl... |
# Square of a Trinomial Expansion | Perfect Square Trinomial Definition, Formula & Solved Examples
Do you want to expand trinomials easily without any confusion and hassle? You should refer to this page. Here, we have explained how to expand the Square of a Trinomial and perfect square trinomial definition and formula... |
# All You Need to Know About Hailstone Sequence in Python
Lets us first understand what a sequence is in the hailstone sequence python. A sequence is an ordered series of numbers that follows a particular pattern. A sequence can be something as simple as a series of odd numbers. A hailstone sequence is a series of num... |
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# Probability
### Example 3: using the probability rules
A treasure chest contains $$30$$ diamonds, $$10$$ gold coins, $$20$$ sapphires and $$5$$ silver medallions. If an item is selected at random, find the probability that it is:
a) a gold coin?
b) not a sapphire?
c) either a gold coin... |
# Common Core: High School - Functions : Symmetry and Periodicity of Trigonometric Functions: CCSS.Math.Content.HSF.TF.B.4
## Example Questions
← Previous 1
### Example Question #1 : Symmetry And Periodicity Of Trigonometric Functions: Ccss.Math.Content.Hsf.Tf.B.4
Find the following trigonometric exact value.
Expl... |
# Law of Cosines by Ancient Sliding
### What Might This Be About?
20 November 2014, Created with GeoGebra
### The Law of Cosines
As is common, we shall denote the sides of $\Delta ABC$ opposite vertices $A,B,C$ as $a,b,c$ and the enclosed angles as $\alpha,\beta,\gamma.$
$c^{2}=a^{2}+b^{2}-2ab\cos\gamma.$
### Pro... |
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# Measuring the Distance between Two Lines in Geometry
In geometry, it is important to be able to accurately measure the distance between two lines. This skill can come in handy when solving complex equations and making calculations. To measure the distance between two lines, you need to know wha... |
# How do you simplify 4|3-(-3)| + (-1)?
The absolute value acts as a bracket, so analyze what's inside there first, then it's order of operations as normal, to get to $23$.
#### Explanation:
Starting with the original:
$4 | 3 - \left(- 3\right) | + \left(- 1\right)$
The absolute value acts as a set of brackets, so... |
# Vertex of Absolute Value Equations
by FARAWAY
(PA)
CALCULATING THE VERTEX OF AN ABSOLUTE VALUE OF THE EQUATION
WRITE DOWN WHAT IS INSIDE THE ABSOLUTE VALUE SYMBOL AND SET EQUAL TO ZERO
SOLVE FOR "X"
SUBSTITUTE THE VALUE OF X INTO THE ORIGINAL EQUATION AND SOLVE FOR "Y"
WRITE THE ORDERED PAIR
Y=(X)-2
y=-10(X=4... |
# Calculating Simple Compound Interest Simple Interest Simple interest
• Slides: 8
Calculating Simple & Compound Interest
Simple Interest ¡ Simple interest (represented as I in the equation) is determined by multiplying the interest rate by the principal by the number of periods. (Same amount every year)
¡ ¡ ¡ Prin... |
# Class 8 NCERT Solutions – Chapter 9 Algebraic Expressions and Identities – Exercise 9.3
• Last Updated : 20 Nov, 2020
### Question 1. Carry out the multiplication of the expressions in each of the following pairs.
(i) 4p, q + r
Solution:
(4p) * (q + r) = 4pq + 4pr
(ii) ab, a – b
Solution:
(ab) * (a – b) = a2 ... |
# Reduce the equation
Question:
Reduce the equation 2x – 3y – 5 = 0 to slope-intercept form, and find from it the slope and y-intercept.
Solution:
Given equation is $2 x-3 y-5=0$
We can rewrite it as 2x – 5 = 3y
$\Rightarrow 3 y=2 x-5$
$\Rightarrow y=\frac{2}{3} x-\frac{5}{3}$
This equation is in the slope-inte... |
# Coordinate Graphing of Real World Problems
Patterns are all around you. From the six-pack of sodas to the dozen eggs you might buy, there is something to notice everywhere you look.
You may not have realized it before, but your powers of observation are a mathematical skill. By graphing your observations on a coord... |
# How do you simplify 3sqrt[3] + 2sqrt[27] –sqrt[12]?
Apr 8, 2016
$7 \sqrt{3}$
#### Explanation:
Given an expression to simply
$3 \sqrt{3} + 2 \sqrt{27} - \sqrt{12}$
Factorize second and third terms as
3sqrt3+2sqrt(3xx3xx3)-sqrt(2xx2xx3
We know that if there are 2 same digits/numbers under the square root symbol,... |
# Tower of Hanoi
The Tower of Hanoi is a simple mathematical problem or puzzle. You are given three rods and a number of discs of different sizes. The puzzle starts with all discs on a single rod. Your aim is to move all of them to a different rod according to various rules:
• Only one disc can be moved at a time
• N... |
Evaluating Exponents with Negative Bases | KS3 Maths Resources
## What you need to know
Things to remember:
• If the base number is negative and the power is odd, the answer will be negative.
• If the base number is negative and the power is even, the answer will be positive.
An exponent is a number written to the ... |
# Roman Numbers: Learn 7 Roman Symbols
Roman numbers are a part of a numeral system that was used in ancient Rome to represent any number using 7 different symbols. The seven different symbols used to represent any number in the roman number system include I, V, X, L, C, D, and M. The roman symbols:
• I indicate 1
• ... |
# 2007 AIME II Problems/Problem 8
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
## Problem
A rectangular piece of paper measures 4 units by 5 units. Several lines are drawn parallel to the edges of the paper. A rectangle determined by the intersections of some of these lines is called ba... |
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## Introduction to Multiplication Strategies
In our previous grades, we have read about the concept of multiplication. Let's revise with an example: you visit a bakery shop and buy 19 cakes for 3 rupees each. It'... |
## Plotting Points on the Coordinate Plane
### Learning Outcomes
• Define the components of the Cartesian coordinate system.
• Plot points on the Cartesian coordinate plane.
An old story describes how seventeenth-century philosopher/mathematician René Descartes invented the system that has become the foundation of a... |
Introductory Statistics
# 9.6Hypothesis Testing of a Single Mean and Single Proportion
Introductory Statistics9.6 Hypothesis Testing of a Single Mean and Single Proportion
## Stats Lab
### Hypothesis Testing of a Single Mean and Single Proportion
Class Time:
Names:
Student Learning Outcomes
• The student will se... |
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Probability amplitude wikipedia, lookup
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History of statistics wikipedia, lookup
Inducti... |
# 180 Days of Math for First Grade Day 105 Answers Key
By accessing our 180 Days of Math for First Grade Answers Key Day 105 regularly, students can get better problem-solving skills.
## 180 Days of Math for First Grade Answers Key Day 105
Directions: Solve each problem.
Question 1.
Count the dots in the frame. How... |
# How do you simplify ((3x^-2 y)^-2)/( 4xy^-2)^-1 ?
##### 1 Answer
Mar 15, 2018
color(red)(((3x^-2 y)^-2)/( 4xy^-2)^-1 = color(blue)((4x^5)/(9y^4)
#### Explanation:
Given:
color(red)(((3x^-2 y)^-2)/( 4xy^-2)^-1 Expression 1
We can simplify the above exponent problem as follows:
color(green)(Step" 1"
Rule 1
c... |
# Video: Differentiating a Combination of Trigonometric and Linear Functions
Chris O’Reilly
Given that 𝑦 = 10𝑥 − 2 cos 9𝑥, determine 𝑑𝑦/𝑑𝑥.
02:18
### Video Transcript
Given that 𝑦 equals 10𝑥 minus two cos nine 𝑥, determine 𝑑𝑦 𝑑𝑥.
Well in order to solve this problem, we can actually differentiate eac... |
Edit Article
# wikiHow to Solve a Linear Diophantine Equation
Solving a linear Diophantine equation means that you need to find solutions for the variables x and y that are integers only. Finding integral solutions is more difficult than a standard solution and requires an ordered pattern of steps. You must first fin... |
# Algebra 1 : How to find the slope of parallel lines
## Example Questions
← Previous 1 3
### Example Question #1 : How To Find The Slope Of Parallel Lines
What is the slope of a line parallel to the line described by 3x + 8y =16?
Explanation:
First, you should put the equation in slope intercept form (y = mx + b... |
# Weighted MeanWeighted Average Formula
The mean page showed how to work out the arithmetic mean/average of a set of values.
But there is also what is known as a "weighted mean" or "weighted average".
Which differs slightly from the arithmetic mean in regards to how we obtain the value.
There is a weighted averag... |
# Conditional probability & distribution
Contents:
## What is conditional probability?
Conditional probability is the probability of an event occurring, given that another event has already occurred. It is used to determine the probability of one event happening when we have information about the occurrence of a rel... |
# Event planners are planning a fireworks display for the 4th of July. The fireworks will launch from a boat in the bay, and must land in a designated "fire-safe" zone 100 meters away. To be visible above the buildings, the fireworks must reach at least 30 meters high. Write an equation that could model the path of the... |
# Video: Pack 2 • Paper 1 • Question 7
Pack 2 • Paper 1 • Question 7
02:46
### Video Transcript
A student drew this for the graph of 𝑦 equals 𝑥 squared minus two. Identify one error that the student made.
Well, the first thing we’re gonna do to actually help solve this problem is work out some 𝑥 and 𝑦 values t... |
# How to Calculate 4/10 Plus 6/10
Are you looking to work out and calculate how to add 4/10 plus 6/10? In this really simple guide, we'll teach you exactly what 4/10 + 6/10 is and walk you through the step-by-process of how to add two fractions together.
To start with, the number above the line in a fraction is calle... |
# How Will Alex O’Loughlin Fare Today? (01/16/2020)
How will Alex O’Loughlin get by on 01/16/2020 and the days ahead? Let’s use astrology to undertake a simple analysis. Note this is for entertainment purposes only – don’t get too worked up about the result. I will first calculate the destiny number for Alex O’Loughli... |
Sequences
Sequences
Definition: A Sequence $\{ a_n \}_{n=1}^{\infty}$ is an ordered list of numbers $a_1, a_2, ...$ where $a_j$ denotes the $j^{\mathrm{th}}$ term of the sequence.
One of the most famous sequences is the Fibonacci Sequence that is recursively defined by $f_{1} = 1$, $f_{2} = 1$, and $f_{n} = f_{n-1}... |
# Vectors
This is a vector:
A vector has magnitude (size) and direction:
The length of the line shows its magnitude and the arrowhead points in the direction.
We can add two vectors by joining them head-to-tail:
And it doesn't matter which order we add them, we get the same result:
### Example: A plane is flying ... |
# Divisibility Rule by 3
If the sum of all digits of a given umber is multiple of 3 or is exactly divisible by 3 then we can say that the given number is divisible by 3.
Lets take an example to understand this point more clearly.
Example - Is 543 divisible by 3?
Solution -
Let's sum the all digits i.e. 5 + 4 + 3 =... |
# How do you solve 2( 9t - 1) + 3= 13?
Jun 10, 2017
See a solution process below:
#### Explanation:
First, subtract $\textcolor{red}{3}$ from each side of the equation to isolate the term with parenthesis while keeping the equation balanced:
$2 \left(9 t - 1\right) + 3 - \textcolor{red}{3} = 13 - \textcolor{red}{3... |
# Domain and Range of a Function
A step by step tutorial, with detailed solutions, on how to find the domain and range of real valued functions is presented. First the definitions of these two concepts are presented. A table of domain and range of basic functions might be useful to answer the questions below.
## Defi... |
# How do you simplify x^2-5x+3(x^2+7x)?
Apr 18, 2018
Distribute and combine like terms.
#### Explanation:
Distribute the 3 among the terms inside parentheses:
${x}^{2} - 5 x + 3 \left({x}^{2} + 7 x\right) = {x}^{2} - 5 x + 3 {x}^{2} + 21 x$
Combine like terms.
${x}^{2} - 5 x + 3 {x}^{2} + 21 x = 4 {x}^{2} + 16 x... |
## Series Solutions: Hermite's Equation
Hermite's Equation of order k has the form
y''-2ty'+2ky=0,
where k is usually a non-negative integer.
We know from the previous section that this equation will have series solutions which both converge and solve the differential equation everywhere.
Hermite's Equation is our... |
Imaginary and Complex Numbers
Complex numbers
Real and imaginary parts
The complex plane
The set of all complex numbers C
Absolute value, modulus of a complex number
Complex conjugates
Addition and subtraction of complex numbers
Multiplication and division of complex numbers
Complex numbers
A complex number is the sum ... |
# A function f(x) is defined as,
Question:
A function f(x) is defined as,
$f(x)=\left\{\begin{array}{rr}\frac{x^{2}-x-6}{x-3} ; & \text { if } \quad x \neq 3 \\ 5 & ; \text { if } x=3\end{array}\right.$
Show that f(x) is continuous that x = 3.
Solution:
Given:
$f(x)=\left\{\begin{array}{l}\frac{x^{2}-x-6}{x-3}, ... |
Rs Aggarwal 2020 2021 Solutions for Class 10 Maths Chapter 18 Mean, Median, Mode Of Grouped Data, Cumulative Frequency Graph And Ogive are provided here with simple step-by-step explanations. These solutions for Mean, Median, Mode Of Grouped Data, Cumulative Frequency Graph And Ogive are extremely popular among Class 1... |
Princess Erika Vegafria
2022-10-04
determine the following functions (v/g)x
v= x² + 5x+4 g= x² + 2x-8
alenahelenash
To determine the value of the function $\left(v/g\right)x$, we need to substitute the given expressions for v and g into the function and simplify the result.
Given:
$v={x}^{2}+5x+4$
$g={x}^{2}+2x... |
Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
Solutions for Session 8, Part C
See solutions for Problems: C1 | C2 | C3 | C4 | C5 | C6 | C7
Problem C1 The triangle with hypotenuse 4: By similarity with the original... |
Lesson Objectives
• Demonstrate an understanding of rational expressions
• Demonstrate an understanding of how to find the LCM
• Demonstrate the ability to factor a polynomial
• Learn how to find the LCD for a group of rational expressions
## How to Find the LCD for a Group of Rational Expressions
In our pre-algebra ... |
# OU on the BBC: The Code - Prima Pizzeria hints and tips
Updated Tuesday 5th July 2011
Improve your chances with the Prima Pizzeria game with these hints and tips from our maths academics on prime numbers as well as further links to improve your learning.
1. Prima Pizzeria is about prime numbers. A prime number is ... |
# How do you simplify sqrt (27 / 64)?
Feb 8, 2016
$\frac{3 \sqrt{3}}{8}$
#### Explanation:
We can begin be re writing the square root as:
$\sqrt{\frac{27}{64}} = \frac{\sqrt{27}}{\sqrt{64}}$
Luckily, 64 is a square number so that will allow us to get rid of the square root on the bottom:
$= \frac{\sqrt{27}}{8}$
... |
# 2012 AIME II Problems/Problem 14
## Problem 14
In a group of nine people each person shakes hands with exactly two of the other people from the group. Let $N$ be the number of ways this handshaking can occur. Consider two handshaking arrangements different if and only if at least two people who shake hands under on... |
Lesson 1ª
Operations with Algebraic Fractions
10.1 Calculate the result of the sum:
1st. Calculate the least common multiple (l.c.m.) of the denominators: We find that the l.c.m.(2, 3, 4) = 12
2nd. Divide the l.c.m. by each denominator (the value below the fraction), then, multiply the quotient times the numerator... |
# Equations with Variables on Both Sides
4 teachers like this lesson
Print Lesson
## Objective
To solve equations with variables and integers on both sides.
#### Big Idea
Use of a pan balance to explain solving equations with integers on both sides
## Do Now
15 minutes
Students enter the class silently accordin... |
# Is 7 8 9 a triangle?
Can 7 8 and 9 be sides of a triangle
lengths can form a triangle. Therefore, it is possible to form a triangle with side lengths of 8, 7 and 9 cm.
What type of triangle is 7 8 9
scalene triangle
Hence the triangle with sides 7 cm, 8 cm and 9 cm is a scalene triangle.
What is a 7cm 8cm 9cm t... |
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# How to Solve a Math Problem
There... |
# Triangle inequality
Jump to navigation Jump to search
{{#invoke:Hatnote|hatnote}}
Three examples of the triangle inequality for triangles with sides of lengths x, y, z. The top example shows the case when there is a clear inequality and the bottom example shows the case when the third side, z, is nearly equal to t... |
Word Problems For Linear Inequalities
Word Problems For Linear Inequalities - Web quiz unit test about this unit we will now equate two algebraic expressions and think about how it might constrain what value the variables can take on. Given he saves \$20 every week, find the amount of. Inequalities word problems with ... |
Home | | Maths 12th Std | Continuous Distributions
# Continuous Distributions
In this section we learn (i) Continuous random variable (ii) Probability density function (iii) Distribution function (Cumulative distribution function). (iv) To determine distribution function from probability density function. (v) To dete... |
# How to “make up a formula” of a sum: $S=2+7+12+\cdots+(5n-3)$?
Determine a formula for the following sum with $n\in\mathbb N$:
$$S=2+7+12+\cdots+(5n-3)$$
I had no clue about what to do about it. I just wrote, for the sake of doing something, the following:
$$\sum_{i=0}^n(5i-3) = \left(\sum_{i=0}^n(5i) - 3n\right)... |
# Mathematics
### Solving Trigonometric Equations
E.g.1
Solve sin x = 0.5 for 0 ≤ x ≤ 360
sin x = 0.5
x = 300
Since y = 0.5 line crosses the sine curve at two points, there are two solutions.
Now, look at the symmetry of the graph; the two values of x are 300 and 1500.
x = 30 and 150.
E.g.2
Solve cos x = -0.5 for ... |
Probability
```Probability
Example and Definitions:
Question: A spinner has 4 equal sectors colored yellow, blue,
green and red. What are the chances of landing on blue after
spinning the spinner? What are the chances of landing on red?
Solution: The chances of landing on red are 1 in 4, or one fourth.
This problem as... |
# 3.2 - Identifying Outliers: IQR Method
3.2 - Identifying Outliers: IQR Method
Some observations within a set of data may fall outside the general scope of the other observations. Such observations are called outliers. In Lesson 2.2.2 you identified outliers by looking at a histogram or dotplot. Here, you will learn... |
# Parasitic number
(Redirected from Parasitic numbers)
An n-parasitic number (in base 10) is a positive natural number which can be multiplied by n by moving the rightmost digit of its decimal representation to the front. Here n is itself a single-digit positive natural number. In other words, the decimal representat... |
# Using the Property a B = a K B K , Fill in the Blanks Substituting Proper Numbers in the Following. - Algebra
Sum
Using the property a/b = (ak)/(bk) , fill in the blanks substituting proper numbers in the following.
9/14 = 4.5/(.......) = (........)/ 42 = (......) /3.5
#### Solution
4.5 = 9 × 0.5, 42 = 14 × 3, 3.... |
# Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name of the property that says "3 + 4 = 4 + 3" or "2 × 5 = 5... |
# What makes something a linear operator?
## What makes something a linear operator?
A linear transformation is a function from one vector space to another that respects the underlying (linear) structure of each vector space. A linear transformation is also known as a linear operator or map. The two vector spaces mus... |
# Difference between revisions of "2012 AMC 8 Problems/Problem 20"
## Problem
What is the correct ordering of the three numbers $\frac{5}{19}$, $\frac{7}{21}$, and $\frac{9}{23}$, in increasing order?
$\textbf{(A)}\hspace{.05in}\frac{9}{23}<\frac{7}{21}<\frac{5}{19}\quad\textbf{(B)}\hspace{.05in}\frac{5}{19}<\frac{7... |
# How do you write an equation in standard form given a line that passes through (4,-3) with m=2?
Jun 4, 2015
The equation in standard form is $2 x - y = 5$.
The general equation for the standard form of a line is $\text{A"x+"B"y="C}$, where $\text{A}$ and $\text{B}$ are integers, and $\text{A} \ne 0$, and $\text{B}... |
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# In the equation ${{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0$ represents a circle with X-axis as a diameter and radius a, then which of the following is possible.A. $f=2a,g=0,c=3{{a}^{2}}$ B. $f=0,g=a,c=3{{a}^{2}}$ C. $f=0,g=-2a,c=3{{a}^{2}}$ D. none of the... |
# Optimization Problems in Calculus
Contents:
More optimization problems:
## General Optimization Steps
Optimization problems in calculus often involve the determination of the “optimal” (meaning, the best) value of a quantity. For example, we might want to know:
• The biggest area that a piece of rope could be ti... |
# Solving for Xmas: how to make mathematical Christmas cards
With less than a month to go before Christmas Day, it’s time to start thinking about cards. Here Oxford maths don Vicky Neale explains how to impress your friends with these stunning geometrical designs. It’s Christ-maths time, and there’s no need to be afra... |
# 2.3 graphing linear equations in slope-intercept form · 2009-09-18 · 2.3 62 chapter 2 graphing...
of 6 /6
2.3 62 Chapter 2 Graphing Linear Equations and Linear Systems Graphing Linear Equations in Slope-Intercept Form 2.3 How can you describe the graph of the equation y = mx + b? Work with a partner. Graph the equat... |
# NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Straight Lines
#### NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Straight Lines
The NCERT Solutions for Class 11 Maths Chapter 9, covering Straight Lines, are a helpful resource for students preparing for their Math board exams. The chapter covers impor... |
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# Harry's Job at a Candy Store
Media Type:
Video
Running Time: 3m 27s
Size: 9.5 MB
or
Source: Cyberchase: “A Fraction of a Chance”
### Collection Developed by:
Collection Credits
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# When calculating to find the mean and standard deviation of these two sets of numbers: (a)4 0 1 4 3 6 (b)5 3 1 3 4 2 Which data set is more spread out?
Sep 16, 2016
Data-set (a) is more spread out.
#### Explanation:
Both the given data sets have exactly $6$ data points and their sum is too $18$, hence mean of bot... |
## Computing Limits II: The Squeeze Theorem – Application Proof
Posted: 9th February 2013 by seanmathmodelguy in Lectures
One very important application of the squeeze theorem is the proof that $$\displaystyle \lim_{\theta \to 0} \frac{\sin \theta}{\theta} = 1$$. We present this proof next.
This proof is for the lim... |
## Trigonometry (11th Edition) Clone
Published by Pearson
# Chapter 5 - Trigonometric Identities - Section 5.1 Fundamental Identities - 5.1 Exercises - Page 200: 34
#### Answer
$$\sin\theta=-\frac{2}{5}$$ $$\cos\theta=-\frac{\sqrt{21}}{5}$$ $$\tan\theta=\frac{2\sqrt{21}}{21}$$ $$\cot\theta=\frac{\sqrt{21}}{2}$$ $$\... |
How to Calculate Fractional Exponents
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The Basics
Fractional exponents can look intimidating, but they’re much simpler than they seem. Remember that ½ is really the reciprocal – or the “opposite” of 2. That’s why multiplying 3 times 2 gives you 6, so if you want to get from 6 back to 3, you need to multi... |
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# Fractions
Children begin to learn about fractions in Year One when they understand that a fraction is an equal part of a whole. Initially, children learn about halves and quarters. They use shapes to se... |
# 3.4 Composition of functions (Page 6/9)
Page 6 / 9
## Finding the domain of a composite function involving radicals
Find the domain of
Because we cannot take the square root of a negative number, the domain of $\text{\hspace{0.17em}}g\text{\hspace{0.17em}}$ is $\text{\hspace{0.17em}}\left(-\infty ,3\right].\tex... |
# Factors of 21
The factors of 21 are the numbers that produce the result as 21 when a pair factor is multiplied together. A factor of a number divides the original number uniformly.
The factors of 21 are 1, 3, 7 and 21.
Factor pairs of the number 21 are the numbers that result in the original number multiplying the... |
Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
Observing Student Reasoning and Proof
Introduction | Inscribed Triangles | Problem Reflection #1 | Inscribed Triangle Continued | Problem Reflection #2 | Classroom Prac... |
# Interest Formula: Days
Solving for the unknown factor for the formula when time is stated in whole days using either ordinary interest dating or exact interest dating: All Example 1 will use ordinary interest dating and All Example 2 will use exact interest dating in this handout. PXRXT=I P = Principle (The amount b... |
# How do you use implicit differentiation to find dy/dx given xe^y-y=5?
Mar 5, 2017
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{{e}^{y}}{1 - x {e}^{y}}$
#### Explanation:
When we differentiate $y$ wrt $x$ we get $\frac{\mathrm{dy}}{\mathrm{dx}}$.
However, we cannot differentiate a non implicit function of $y$ wrt $x$... |
Solve for b
## Share
a+b=-4 ab=4
To solve the equation, factor b^{2}-4b+4 using formula b^{2}+\left(a+b\right)b+ab=\left(b+a\right)\left(b+b\right). To find a and b, set up a system to be solved.
-1,-4 -2,-2
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all s... |
# Equation Solver
## Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.
We can say equation solver is a kind of tool to solve the equation. We can say an equation is of the form A = B. Here A and B are expressions having unknowns. For example, 3 is th... |
# Special Matrices: Triangular, Symmetric, Diagonal
We have seen that a matrix is a block of entries or two dimensional data. The size of the matrix is given by the number of rows and the number of columns. If the two numbers are the same, we called such matrix a square matrix.
To square matrices we associate what we... |
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