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# System of differential equation with alternative variables
Let us suppose a system of linear differential equations
\begin{align} \frac{d}{d t}x_1(t)&= -\lambda x_2 (t) \\ \frac{d}{d t}x_2(t)&= \lambda x_1 (t) \end{align}
How this system could be solve analytically ? Because they refer to each other.
-
This can ... |
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Factors
# Factors of 153 | Prime Factorization of 153 | Factor Tree of 153
Written by Prerit Jain
Updated on: 15 Feb 2023
## Factors of 153
Calculate Factors of
The Factors are
https://wiingy.com/learn/math/factors-of-15... |
# How do you write the trigonometric form into a complex number in standard form 6(cos((5pi)/12)+isin((5pi)/12))?
Mar 25, 2018
The complex number in standard form is $\frac{3 \sqrt{6} - 3 \sqrt{2}}{2} + \frac{3 \sqrt{6} + 3 \sqrt{2}}{2} i$.
#### Explanation:
To convert from trig form to standard form, simply comput... |
# Multiplication
Four bags with three marbles per bag gives twelve marbles (4 × 3 = 12).
Multiplication can also be thought of as scaling. Here we see 2 being multiplied by 3 using scaling, giving 6 as a result.
Animation for the multiplication 2 × 3 = 6.
4 × 5 = 20. The large rectangle is composed of 20 squares, each... |
Maharashtra Board Class 8 Maths Solutions Chapter 6 Factorisation of Algebraic Expressions Practice Set 6.3
Maharashtra State Board Class 8 Maths Solutions Chapter 6 Factorisation of Algebraic Expressions Practice Set 6.3
Question 1.
Factorize
i. y³ – 27
ii. x³ – 64y³
iii. 27m³ – 216n³
iv. 125y³ – 1
v. $$8 p^{3}-\fra... |
# Prove inequality: When $n > 2$, $n! < {\left(\frac{n+2}{\sqrt{6}}\right)}^n$
Prove: When $n > 2$, $$n! < {\left(\frac{n+2}{\sqrt{6}}\right)}^n$$
PS: please do not use mathematical induction method.
EDIT: sorry, I forget another constraint, this problem should be solved by algebraic mean inequality.
Thanks.
This ... |
# How do you solve 0=4x^3-20x+16?
Apr 30, 2016
$\left\{\begin{matrix}x = 1 \\ x = - \frac{1}{2} + \frac{\sqrt{17}}{2} \\ x = - \frac{1}{2} - \frac{\sqrt{17}}{2}\end{matrix}\right.$
#### Explanation:
First note that all of the terms are divisible by $4$, so we can separate that out to get:
$0 = 4 {x}^{3} - 20 x + 1... |
### Online College Courses for Credit
4 Tutorials that teach "Either/Or" Probability for Non-Overlapping Events
Common Core: S.CP.7
# "Either/Or" Probability for Non-Overlapping Events
##### Rating:
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Author: Katherine Williams
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Calculate an "OR" probability for non... |
Study Guide
# Quadrilaterals - Trapezoids
## Trapezoids
The last family of quadrilaterals are the outcasts. They're different from the rest of the quadrilaterals, kind of like the socially awkward guest at the quadrilateral party.
While the rest of them have their congruent sides and angles to chitchat about, these... |
# Word Problem: Addition - 2 - Notes | Study Mathematics for Class 3 - Class 3
1 Crore+ students have signed up on EduRev. Have you?
Q.1. Helen the Hippo and her friends are preparing for Thanksgiving at Helen’s house. Let’s find out how much food they have prepared for the party.
Helen baked 435 chocolate chip cook... |
# MATH STUFF #19
## The Standards…Stairsteps to Success
As we finish our second wave of state testing, I am reminded how critically important it is that teachers know and teacher their standards for each math concept. Whether your standards are the CCSS or the Texas TEKS, they are vertically aligned to ensure that co... |
## Fraction Benchmarks
Purpose
In this unit students develop important reference points or benchmarks for zero, one half and one. They use these benchmarks to help compare the relative sizes of fractions, through estimating, ordering and placing fractions on a number line.
Achievement Objectives
NA3-5: Know fraction... |
# Factoring Quadratics – Definition With Examples
Quadratics are fascinating mathematical expressions that play a vital role in many real-world scenarios. A quadratic is an equation of the form , where and are constants, and is the variable. The power of 2 on the makes it a second-degree polynomial.
The graph of a qu... |
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Question
# Prove that $$5\sqrt { 3 }$$ is an irrational.
Solution
## If possible, let $$5\sqrt{3}$$ is rational.Let its simplest form be $$5\sqrt{3}=\dfrac{a}{b}$$, where a and b are positive integers having no common factor other than 1.Then,$$5\sqrt{3}=\dfrac{a}{b}$$$$\sqrt{3}=\dfrac{a}{5b}$$Since, $$a$$ and $$5b$... |
# Intersection of a Line and a Circle (Part 2)
In this lesson, I’ll be deriving the expression to find the length of a chord intercepted by a circle on a line. We’ll go through two methods again, one involving quadratic equations, and the other involving geometry. Let’s begin!
## Method 1
Let y = mx + c be a given l... |
###### Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
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Introduction to Real Numbers - Problem 1
# Int... |
# IMO Class 1 Chapter 4: Shapes and Spatial Understanding
#### BySchool Connect Online
Jul 15, 2022
The IMO Syllabus for Class 1 covers subjects covered in the academic program. The format of the math olympiad questions, however, is entirely conceptual in order to evaluate students’ capacities for logical reasoning.... |
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# The lines $x - y + z = 1,3x - y - z + 1 = 0$ and $x + 4y - z = 1,x + 2y + z + 1 = 0$ are:A) ParallelB) IntersectingC) Perpendicular and skewD) Non-perpendicular and skew
Last updated date: 13th Jun 2024
Total views: 403.5k
Views today: 4.03k
Ve... |
Factors that 105 are the list of integers that have the right to be evenly separated into 105. There are as whole 8 components of 105 amongst which 105 is the biggest factor and 1, 3, 5, 7, 15, 21, 35, and 105 are positive factors. The amount of all factors of 105 is 192 and its determinants in Pairs are (1, 105), (3, ... |
# How much greater is (17x^2 + 20x + 11) + (15x^2 + 11x + 17)?
Jun 19, 2015
answer 1: = color(red)(2x^2 + 9x -6
answer 2: $= \textcolor{red}{32 {x}^{2}} + \textcolor{b l u e}{31 x} + 28$
#### Explanation:
There are two ways of interpreting this question:
• How much greater is $\left(17 {x}^{2} + 20 x + 11\right)$... |
## Saturday, January 15, 2011
### Solution to the alternating jumps problem
Let me remind about the problem: we alternate jumps to the left and to the right, possible jumps to the left are given as set A, possible jumps to the right are given to set B. Is any integer point reachable?
When we first approach this prob... |
# Rational Mathematics
## Inversive Operations
The idea of an inverse operation that undoes the effect of a given operation is one that is encountered in many different contexts. [In arithmetic we will encounter the inverse operations of addition and subtraction, multiplication and division, raising to a power and ca... |
# Pick’s Theorem To Find The Area Of A Polygon
I have been teaching mathematics in an Australian High School since 1982, and I am a contributing author to mathematics text books.
Sitting languidly at the front of the classroom, head down and pen in hand playing a game of ‘join the dots’, I would occasionally raise my... |
## How To Write The Equation Of An Ellipse
### The Equation Of An Ellipse
Just like a circle, parabola and hyperbola, an ellipse is a cross section of a conical section. In fact, an ellipse is very similar to a circle except that the cross section is taken at an angle to the conical section with gives the ellipse i... |
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### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed y... |
# Solving Basic Logarithmic Equations
To solve a logarithmic equation:
1. Get the logarithm by itself on one side of the equation.
2. Determine the base of the logarithm.
3. Raise both sides of the equation to be a power of that base.
4. Simplify and solve.
Examples:
1)
The logarithm is already by itself. The b... |
Breaking News
What Least Number Must Be Added to 1056?
Adding numbers together is a foundation skill in mathematics. It is important to understand the basic concepts of addition in order to answer questions like “what least number must be added to 1056?”. The key to addition is understanding that when you add two num... |
# How do you differentiate f(x)=cos5x * cot3x using the product rule?
Jul 16, 2016
$- 5 \sin 5 x \cot 3 x - 3 {\csc}^{2} \left(3 x\right) \cos 5 x$
#### Explanation:
The derivative of a product is stated as follows:
$\textcolor{b l u e}{\left(u \left(x\right) \cdot v \left(x\right)\right) ' = u ' \left(x\right) \cd... |
Transcript Geometry Section 2.2 Notes
```CHAPTER
2
2.2 Proofs Involving
Congruence
Slide 4-1
Congruent Segments
Two segments that have the same length are called
congruent segments. The symbol ≅ means
congruent.
We mark congruent segments in a figure with
exactly the same number of tick marks.
Slide 4-2
Definition
Two... |
How Do You Construct An Angle With Compass And Ruler
Construction Of An Angle Using Compass And Ruler
To draw an angle equal to a given angle
In this section, we will learn how to construct angles of 60º, 30º, 90º, 45º and 120º with the help of ruler and compasses only.
Construction Of Some Standard Angles
Constru... |
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# Algebra of Matrices
LIVE
Join Vedantu’s FREE Mastercalss
## What is a Matrix?
A matrix is a rectangular matrix of numbers arranged in columns and rows. Arrays are usually enclosed in square brackets. The horizontal and vertical rows of the matr... |
# Factorise 2c2 + 8c + 8.
• 563 views
Factorise 2c2 + 8c + 8.
Use the following steps to factorise a quadratic:
-Take out a common factor
-Split into two brackets with the x term at the start of each bracket
-Write out the factor pairs of the last number
-Identify the pair that can be added or subtracted to give... |
# Some Applications of Trigonometry Class 10 Maths Formulas
For those looking for help on Some Applications of Trigonometry Class 10 Math Concepts can find all of them here provided in a comprehensive manner. To make it easy for you we have jotted the Class 10 Some Applications of Trigonometry Maths Formulae List all ... |
# 2020 AMC 8 Problems/Problem 5
## Problem 5
Three fourths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of $5$ cups. What percent of the total capacity of the pitcher did each cup receive?
$\textbf{(A) }5 \qquad \textbf{(B) }10 \qquad \textbf{(C) }... |
# 1819 C2X §6.1
Which exercises/theories should we discuss on the board?
1 / 20
Slide 1: Mind map
WiskundeMiddelbare schoolhavo, vwoLeerjaar 2
This lesson contains 20 slides, with interactive quiz and text slides.
Lesson duration is: 50 min
## Items in this lesson
Which exercises/theories should we discuss on the ... |
# How do you find the derivative of sqrt(e^(2x) +e^(-2x))?
Jul 22, 2016
(dy)/(dx) = (e^(2x) - e^(-2x))/(sqrt(e^(2x) + e^(-2x))
#### Explanation:
$y = {\left({e}^{2 x} + {e}^{- 2 x}\right)}^{\frac{1}{2}}$
We need to use the chain rule as we have $y \left(u \left(x\right)\right)$.
In this case $\frac{\mathrm{dy}}{\... |
# Filling the board with 0s and 1s
You are given a $9\times9$ grid board.
You have 40 "$1$"s and 41 "$0$"s. You can put these numbers wherever you want on the board.
After that, you will take the sum of the numbers in each row and column and as a result there will be $18$ sums at the end.
1. Is it possible to have ... |
# Integral of Inverse Cosecant
The integral of inverse cosecant ${\csc ^{ – 1}}x$ it is an important integral function, but it has no direct method to find. We shall find the integration of inverse cosecant by using the integration by parts method.
The integral of inverse cosecant is of the form
$I = \int {{{\csc }^{... |
# Truncation
Here we will learn about truncation including how to truncate numbers to powers of 10, decimals and significant figures.
There are also truncation worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
## What is truncation?
Trunc... |
# Surface Area of Prisms & Cylinders Geometry Mr. Westlove Summer 2009.
## Presentation on theme: "Surface Area of Prisms & Cylinders Geometry Mr. Westlove Summer 2009."— Presentation transcript:
Surface Area of Prisms & Cylinders Geometry Mr. Westlove Summer 2009
Objectives/Assignment Find the surface area of a p... |
# What is the slope of the line normal to the tangent line of f(x) = 1/x+x^3 at x= 2 ?
Sep 17, 2016
$- \frac{4}{47}$
#### Explanation:
The slope of the line tangent to the curve $y = f \left(x\right)$ at $x = 2$ is given by $f ' \left(2\right)$.
First, find $f ' \left(x\right)$.
$f ' \left(x\right) = \frac{d}{\... |
# AP SSC 10th Class Maths Solutions Chapter 9 Tangents and Secants to a Circle Ex 9.3
AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 9 Tangents and Secants to a Circle Ex 9.3 Textbook Questions and Answers.
## AP State Syllabus SSC 10th Class Maths Solutions 9th Lesson Tangents and Secants... |
### fun.contest.id's blog
By fun.contest.id, 16 months ago,
### Problem statement
We need to find any number in the range $[l, r]$ with the least luckiness
Luckiness of a number is defined as the difference between its maximum and minimum digit
So for $n = 369$ the luckiness will be 9 — 3 = 6
### Solution
#### B... |
# Day 25 – Congruence 2, Isosceles Triangles
Last time we learned about the SAS Theorem, which is used as a shortcut to show that two triangles are congruent. In fact, this is not the only “shortcut” of this type — there are three others, which we will learn about today. They are called angle side angle (ASA), angle... |
# Solving Optimization Problems
One type of problem that calculus gives us the ability to solve is optimization problems. You may recognize that the word “optimization” is similar to the word “optimal.” This is because optimization problems are typically about finding the measurements or circumstances that ensure the ... |
# How do you divide (n^3+6n^2+4n-2)div(n+1) using synthetic division?
Nov 3, 2016
$\left({n}^{3} + 6 {n}^{2} + 4 n - 2\right) \div \left(n + 1\right)$
$= {n}^{2} + 5 n - 1 \text{ } r e m - 1$
#### Explanation:
The method is very easy, but the process is a bit difficult to explain.
(n^3+6n^2+4n-2)div(n+1) = ??????... |
# Products and Factoring
Understanding Factors and Products
When multiplying two or more numbers together the result obtained is called product. Therefore, any numbers once multiplied are called: factors of the product.
Example 1
3 , a , x can be considered as factors to product 3ax.
Example 2
4, y, x can also be... |
Home » Math Theory » Algebra » Properties of Addition
## Introduction
The properties of addition are fundamental concepts in mathematics that help students develop a strong foundation in arithmetic and algebra. This article presents an overview of the topic, its key concepts, and real-life applications. We will explo... |
# An Easy Guide to Understanding Quadrilaterals – Properties & Types with Examples
Quadrilaterals are fundamental shapes in geometry, consisting of four sides and four angles. Understanding their properties and types is crucial for anyone delving into the world of geometry. In this comprehensive guide, we will explore... |
# Lesson 5
Coordinate Moves
### Lesson Narrative
Students continue to investigate the effects of transformations. The new feature of this lesson is the coordinate plane. In this lesson, students use coordinates to describe figures and their images under transformations in the coordinate plane. Reflections over the $... |
# Limits of Functions
The theory of limits of functions is the cornerstone of calculus because these are the limits upon which the notion of a derivative depends. What is a Limit? Let us understand the definition of “limit” with the help of an example, consider the function f(x). Let the independent variable x take va... |
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# Single Variable Multiplication Equations
## Solve one - step equations using division.
%
Progress
Practice Single Variable Multiplication Equations
Progress
%
Single Variable Mult... |
# wikiHow to Learn Algebra
This wikiHow will give you lots of tips and pointers on how to learn algebra. You will need basic math skills, such as adding, subtracting, multiplying, and dividing.
## Key Points
• Know and use the order of operations by following the acronym: PEMDAS. More ↓
• Understand negative numbers... |
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# Systems of Linear Equations. Solve a System of Equations by Graphing Objectives: Solve a System of Equations by Graphing Standards: Learn and apply geometric.
## Presentation on theme: "Systems of Linear Equations. Solve a System of Equations by Graphing Objectives: Solve a Sys... |
Mutually Exclusive Events - Formula & Examples
# Mutually Exclusive Events
A set of outcomes is referred to as event. When two events cannot occur at the same time, then we say that the events are mutually exclusive else the events are said to be not mutually exclusive. For example: when we flip a coin then either he... |
# Lesson: Simple Interest and Compound Interest
## Comment on Simple Interest and Compound Interest
### in this above question how
in this above question how did u get the value of c=12
### c = the # of times the
c = the # of times the interest is compounded each year.
The question tells us that interest is compou... |
# Maharashtra Board 12th Commerce Maths Solutions Chapter 8 Differential Equation and Applications Ex 8.5
Balbharati Maharashtra State Board Std 12 Commerce Statistics Part 1 Digest Pdf Chapter 8 Differential Equation and Applications Ex 8.5 Questions and Answers.
## Maharashtra State Board 12th Commerce Maths Soluti... |
Which of the
following names can be used to describe the
geometric shape below? So the first name in
question is a quadrilateral. And a quadrilateral is
literally any closed shape that has four sides. And this is definitely a closed
shape that has four sides. So it is definitely
a quadrilateral. Next, we have to think ... |
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How to Find Lcd
## Pair of Fractions With a Common Denominator Calculator
A pair of fractions with a common denominator is a fraction with numerator D and denominator D. The easiest pairs of fractions with a common denominator for denominator D are 1/2 and 3/4, 8/9 and 5/6, and 7/8 and 4/5.
### Common
... |
# 2.01 Operations with decimals
Lesson
You already know how to work with positive decimals using various combinations of operations. Now we will use and extend this knowledge by looking at questions that involve negative decimals.
Last year you learned the rules for adding, subtracting, multiplying, and dividing dec... |
# How to Use the Fractional-Part-of-a-Number Equation
Instructor: Laura Pennington
Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.
This lesson will cover how to use the fractional part of a number equation. We will see how to set up this equation and how to use this equation ... |
# Logarithm Rules (Properties)
Logarithm rules are the properties or the identities of the logarithm that are used to simplify complex logarithmic expressions and solve logarithmic equations involving variables. They are derived from the exponent rules, as they are just the opposite of writing an exponent.
Here is th... |
# Math in Focus Grade 4 Chapter 6 Practice 2 Answer Key Subtracting Fractions
Practice the problems of Math in Focus Grade 4 Workbook Answer Key Chapter 6 Practice 2 Subtracting Fractions to score better marks in the exam.
## Math in Focus Grade 4 Chapter 6 Practice 2 Answer Key Subtracting Fractions
Find the equiva... |
Mathematics is a subject that requires attention to detail, logical thinking, and problem-solving skills. Students often come across various formulas that they need to understand and apply effectively. One such formula that can be particularly challenging is the (A-B)³ formula. In this article, we will delve into the d... |
# Angle of Intersection of Two Curves
Here you will learn angle of intersection of two curves formula with examples.
Let’s begin –
## Angle of Intersection of Two Curves
The angle of intersection of two curves is defined to be the angle between the tangents to the two curves at their point of intersection.
Let $$C... |
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# How to Add and Subtract Positive and Negative Numbers
## Numbers Can be Positive or Negative:
Negative Numbers (-) Positive Numbers (+) (This is the Number Line, read about Using The Number Line)
"-" is the negative sign. "+" is the positive
## No... |
## Sunday, August 9, 2015
### Farey Fractions and Funny Farey Fraction Addition
8/09/2015
8,092,015 is a 19,933-gonal and 809,203-gonal number.
Farey Fractions and Funy Farey Fraction Addition:
The 775 fractions in the box below are “Farey Fractions”:
They are all fractions between zero and one, written in numeric ... |
# Solve by substitution solver
We can do your math homework for you, and we'll make sure that you understand how to Solve by substitution solver. We can help me with math work.
## Solving by substitution solver
When you try to Solve by substitution solver, there are often multiple ways to approach it. This may seem ... |
# To match: The graph of f with graph of its derivative with proper explanation.
### 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
##... |
# A person spent Rs. 564 in buying pens and pencils if cost of each pen is Rs. 7 and each pencil is Rs. 3 and if the total number of things bought was 108, how many of each type did he buy?
Given:
A person spent Rs. 564 in buying pens and pencils.
The cost of each pen is Rs. 7 and each pencil is Rs. 3.
The total nu... |
# A stone of mass 1kg is tied with a string and it is whirled in a vertical circle of radius 1 m. If tension at the highest point is 14 N, then velocity at lowest point will be
A
3m/s
B
4m/s
C
6m/s
D
8m/s
Video Solution
Text Solution
Generated By DoubtnutGPT
## To find the velocity of the stone at the lowest ... |
To find fractions equivalent to a given fraction
## Objective
To find fractions equivalent to a given fraction
### Fraction
• A fraction is a number representing part of a whole.
• The whole may be a single object or a group of objects.
• A number expressed as a quotient, in which a numerator is divided by a deno... |
# Which is the easiest method for muliplication
2
by shanisharakharma
2016-03-28T00:04:16+05:30
There are 5 easiest way to do multiplication are as follow:
Tip #1: Multiplying by Powers of 5There are times in life when you just get lucky. It turns out that one of those lucky little moments occurs each and every time... |
## The Orthocenter of a Triangle Formula: Explained and Illustrated
Triangles are fundamental shapes in geometry, and understanding their properties is essential for various mathematical applications. One of the key concepts related to triangles is the orthocenter, which plays a significant role in triangle analysis a... |
# Fifth Root (5√) Calculator
A number’s fifth root is a number that, when multiplied by itself five times, returns the original number. Use this fifth root calculator to find the 5√ of any number.
``````<iframe src="https://calculatorhub.org/?cff-form=107" style="width:100%;height:100%;"></iframe>
``````
We will use... |
# What are all the factors, the prime factorization, and factor pairs of 108?
To find the factors of 108, divide 108 by each number starting with 1 and working up to 108
## What is a factor in math ?
Factors are the numbers you multiply together to get another number. For example, the factors of 15 are 3 and 5 becau... |
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# Find the sum of the first 22 terms of the AP 1,4,7,10,…. ?
Last updated date: 16th Jul 2024
Total views: 449.1k
Views today: 10.49k
Verified
449.1k+ views
Hint- Here, we will be using the formula for the sum of first n terms of an arithmetic pr... |
Study Guide
## Rhombi
Now that we've covered the most common type of quadrilateral that we come across, we can bust out our shovels and dig a little deeper for rarer quadrilaterals. How will we know if a quadrilateral is common or rare? Well, we should look for quadrilaterals that are somehow different and have speci... |
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# What are the 4 steps to solve by elimination?
## What are the 4 steps to solve by elimination?
To Solve a System of Equations by Elimination
1. Write both equations in standard form.
2. Make the coefficients of one variable opposites.
3. Add the equations resulting... |
# Combinatorics - Mathematics for Computer Scientists
Document Sample
``` Mathematics for Computer Scientists
Lecture notes for the module G51MCS
Venanzio Capretta
University of Nottingham
School of Computer Science
Chapter 6
Combinatorics
6.1 Quantifiers
When we want to say that each element of a set satis... |
# Gravitational acceleration on the Moon and Mars
There are plenty of formulas that use gravity acceleration of Earth. This is represented with the symbol $g$. In my school work (I am a high school student) we usually take it as $g= 9,8 \,\text m/\text s^2$.
This thing is obviously a number that is only usable on Ear... |
# Essay Title
1259 words - 5 pages
Lecture 1: An Introduction to Boolean Algebra
The operation of almost all modern digital computers is based on two-valued or binary systems. Binary systems were known in the ancient Chinese civilisation and by the classical Greek philosophers who created a well structured binary sys... |
# What’s new for the US?
## An update on our new content for the United States (Jan to Mar 2018)
#### Elementary
The distributive property for multiplication is introduced to students in Grade 3 through the idea of the area model for multiplication. Students identify that the area of 9 x 27 is the same as the area f... |
# If the side of a square is doubled, then find its perimeter
• Last Updated : 20 Nov, 2021
Square is a geometrical figure which is formed of four equal sides. It is a regular quadrilateral where all the angles are right angles. Basically, it can be considered as a special case of a rectangle, where all the sides are... |
# Lesson 8
Conditional Probability
### Problem 1
Jada rolls one standard number cube, then she rolls another standard number cube.
1. What is the probability that she rolls a 5 on both number cubes?
2. What is the probability that the second roll is a 5 under the condition that the first roll is a 6?
3. What is the... |
Some dose-response curves are steeper or shallower than the standard curve. The rise is 2 units. Graphically, a negative slope means that as the line on the line graph moves from left to right, the line falls. Then, they asked about the physical meaning of the slope of the graph: tan( angle) as a function of n( number ... |
```Question 116018
b)
<b>Description of transformation</b>:
Looking at {{{h(x)=e^(-x)}}}, notice how the exponent is negated. So let's see what affect this transformation has on {{{f(x)=e^x}}},
{{{h(-2)=e^(-(-2))}}} Plug in x=-2
{{{h(-2)=e^(2)}}} Negate {{{-(-2)}}} to get 2
Notice if we plug in x=2 into {{{f(x)=... |
# 2020 AMC 8 Problems/Problem 25
Rectangles $R_1$ and $R_2,$ and squares $S_1,\,S_2,\,$ and $S_3,$ shown below, combine to form a rectangle that is 3322 units wide and 2020 units high. What is the side length of $S_2$ in units?
$[asy] draw((0,0)--(5,0)--(5,3)--(0,3)--(0,0)); draw((3,0)--(3,1)--(0,1)); draw((3,1)--(3,... |
One of the great things about mathematics is its ability to bring together apparently completely unrelated phenomena, and explain them all with the same simple concept. It turns out that a very basic mathematical idea — power laws — describes the economics of pizza, limitations on the sizes of insects, income inequalit... |
# How do you eliminate a parameter with sin and cos?
## How do you eliminate a parameter with sin and cos?
To eliminate the angle parameter, rewrite the parametric equations in terms that can be substituted into a trigonometric identity. To eliminate the angle parameter of the two parametric equations above, rewrite ... |
# 0.4 Transverse waves (Page 8/10)
Page 8 / 10
The key is to understand that a standing wave must be created in the medium that is oscillating. There are restrictions as to whatwavelengths can form standing waves in a medium.
For example, if we consider a rope that can move in a pipe such that it can have
• both ... |
## Linear Algebra and Its Applications, Exercise 3.3.15
Exercise 3.3.15. Suppose $P$ is a projection matrix that projects vectors onto a line in the $x$$y$ plane. Describe the effect of the reflection matrix $H = I-2P$ geometrically. Why does $H^2 = I$? (Give both a geometric and algebraic explanation.)
Answer: When ... |
# Math > Year 2
## Adding and subtracting three 1-digit numbers
What are one-digit numbers?
One-digit numbers are the numbers made up of only one digit i.e., ones.
For example, 1, 2, 3 etc.
2 + 4 + 1
2 + 4 = 6
6 + 1 = 7
So, 2 + 4 + 1 = 7
Changing order
For adding 3 one-digit numbers, we can change the order of t... |
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# Introduction to probability
In this article we introduce some basic concepts in probability.
## Variables
A variable refers to a value that can change between measurements/examples such as quantity or state. This could be a discrete variable such as Risk with possible values {Red, Amber, Gre... |
# Video: Calculating Currents and Voltages in a Five-Resistor Circuit
The total current in the circuit below is 100 mA. a) Calculate, to the nearest ohm, the total resistance of the parallel combination of resistors. b) What is the total resistance in this circuit to the nearest ohm? c) What is the voltage across the ... |
# What is the prime factorization of 35100?
## What is the prime factorization of 35100?
The orange divisor(s) above are the prime factors of the number 35,100. If we put all of it together we have the factors 2 x 2 x 3 x 3 x 3 x 5 x 5 x 13 = 35,100. It can also be written in exponential form as 22 x 33 x 52 x 131.
... |
# completing the square
• Jul 11th 2008, 06:45 PM
princess_anna57
completing the square
Solve by completing the square:
x^2 - 3x + 2 = 0
Please show step-by-step instructions because this is the first time I've come across this concept and I've looked through some examples but I can't determine the number that turns... |
Author:
Material Type:
Lesson Plan
Level:
Middle School
6
Provider:
Pearson
Tags:
6th Grade Mathematics, Greatest Common Factor, Models
Language:
English
Media Formats:
Interactive, Text/HTML
# Lesson Overview
Students use a geometric model to investigate common multiples and the least common multiple of two numbers.... |
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