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## Thursday, June 30, 2011
### Solutions to Introduction to Basic Physics, Part 22
We now examine the solutions for the problems in Part 22, on series and parallel circuits.
1)Two resistances of 20 ohms and 5 ohms are connected in parallel by a student. He then connects this combination in series with a 3 ohm resist... |
10.9: Right Triangle Trigonometry
Page ID
129647
### Learning Objectives
After completing this section, you should be able to:
1. Apply the Pythagorean Theorem to find the missing sides of a right triangle.
2. Apply the and right triangle relationships to find the missing sides of a triangle.
3. Apply trigonometric... |
# Scrambled Egg Math
## Curriculum Goal
#### Primary: Number Sense
• Use objects, diagrams, and equations to represent, describe, and solve situations involving addition and subtraction of whole numbers that add up to no more than 50.
## Context
• Educator working with a group of four children.
## Materials
• On... |
# Runge-Kutta Method Calculator
To use Runge-Kutta method calculator, enter the equation, write initial condition, interval values, step size, and click calculate button
Give Us Feedback
## Runge-Kutta Method Calculator
Runge Kutta Method Calculator is used to calculate ordinary differential equations (ODEs) numeri... |
# How do you solve x + y =1 and 2x-y=-2 using substitution?
Jul 10, 2016
By eliminating $x$ in the expression $x + y = 1$, we get
$x = 1 - y$, which we can plug in the second expression:
$2 \left(1 - y\right) - y = - 2$
$2 - 2 y - y = - 2$
$2 - 3 y = - 2$
$- 3 y + 2 = - 2$
$- 3 y = - 4$
$y = \frac{4}{3}$
Know... |
# College Physics 2.52 – Object dropped from a given height
## Solution:
### Part A
We can calculate for the distance traveled in 1 second using the formula
$y=v_ot-\frac{1}{2}gt^2$
Substitute the given values
$y=0-\frac{1}{2}\left(9.80\:m/s^2\right)\left(1\:s\right)^2=-4.9\:m$
The object has traveled 4.9 meters... |
## Pre-Algebra Tutorial
#### Intro
A typical worded math problem is the ‘two working together’ problem, which is described here in detail. This is a classic test problem encountered in algebra and both quick and in-depth explanations are provided. Other examples are included.
#### Sample Problem
Jim can paint a roo... |
# 16. Mensuration
Mensuration is the branch of mathematics which studies the measurement of the geometric figures and their parameters like length, volume, shape, surface area, lateral surface area, etc. Here, the concepts of mensuration are explained and all the important mensuration formulas and properties of differ... |
# Simon's Favorite Factoring Trick
## Contents
Dr. Siman's Favorite Factoring Trick (abbreviated SFFT) is a special factorization first popularized by AoPS user Simon Rubinstein-Salzedo.
## The General Statement
The general statement of SFFT is: ${xy}+{xk}+{jy}+{jk}=(x+j)(y+k)$. Two special common cases are: $xy + ... |
# The Monkey and the Coconuts— Solution
ORIGINAL PUZZLE
Firstly, let’s look at the solution for the original puzzle where a coconut is left over after the final division in the morning so the monkey ends up with 6 coconuts.
1) MATHEMATICAL
Basic algebra gives you this equation: N = {(15625 × F)+ 11529} / 1024 where... |
# Question Video: Telling How Many Times a Specific Hour Comes in the Day Mathematics
How many times a day does the clock show the given time?
02:23
### Video Transcript
How many times a day does the clock show the given time?
The clock that the question’s talking about is shown in the picture. We know that at an ... |
# 4.08 Polynomials
Lesson
## Introduction
An expression of the form Ax^{n}, where A is any number and n is any non-negative integer, is called a monomial. When we take the sum of multiple monomials, we get a polynomial.
## Parts of polynomials
In the monomial Ax^{n}:
• A is the coefficient
• x is the variable
•... |
## RD Sharma Solutions for Class 7 Maths Chapter 16 Congruence Free Online
Exercise 16.1 Page No: 16.3
1. Explain the concept of congruence of figures with the help of certain examples.
Solution:
Congruent objects or figures are exact copies of each other or we can say mirror images of each other. The relation of two ... |
# Operation on Rational & Irrational Numbers | Q5
###### Number System | Extra Questions For Class 9 Maths Chapter 1 | Polynomial expansion
Question 5: Simplify the following:
(a) {8 + $sqrt{5})}) $${8 - $sqrt{5}$})$b) {10 + $sqrt{3})}) $${6 + $sqrt{2}$})$c) ${$$sqrt {3} + $sqrt {11}$}^2) + ${$$sqrt {3} - \sqrt {11}$... |
# nth root
Calculation results
$\scriptstyle\left.\begin{matrix}\scriptstyle\text{summand}+\text{summand}\\\scriptstyle\text{augend}+\text{addend}\end{matrix}\right\}=$ $\scriptstyle\text{sum}$
Subtraction (−)
$\scriptstyle\text{minuend}-\text{subtrahend}=$ $\scriptstyle\text{difference}$
Multiplication (×)
$\scriptst... |
# Calculus 1 : How to find the meaning of functions
## Example Questions
### Example Question #11 : How To Find The Meaning Of Functions
The derivative of is written . The factorial of is written .
Find the function defined on such that
Explanation:
The MacLaurin series is:
,
which in this case is
.
Th... |
Year 10 Interactive Maths - Second Edition
Dividing a Quantity in a Given Ratio
Consider a line segment AB of length 9 cm, which is divided into two line segments of length 3 cm and 6 cm, as shown in the diagram.
That is, AP = 3 cm and BP = 6 cm.
Conversely, if we know that the point P divides the line segment AB o... |
Keywords: clear search
## Welcome to the Futurama Support Site
The Futurama Support Site is the website where you can find Futurama and Futurama Vision documentation. If you have any questions about the support pages or if you want to provide us feedback please send us an e-mail.
Index Exercise 1: Pythagorean Theore... |
# Find the equation of the line passing through the point (3,-2) with x-intercept -4.
## Question:
Find the equation of the line passing through the point (3,-2) with {eq}x- {/eq}intercept -4.
## Lines:
When we have two points on a line, we can find the line's slope:
{eq}\begin{align*} m &= \frac{\text{rise}}{\tex... |
# McRuffy Math Blog
## Marvelous Multiplication #2
Marvelous Multiplication Trick #2: A Multiplication Challenge Using Easy Squares.
If you haven’t already, check out our previous three blogs:
Quick Math: Find the Squares of Numbers That End With 5
Quick Math: Squaring Numbers 51 to 59
In the previous post (Marve... |
# Long Division - Organized Guessing
So, how does Long Division work?
It works by breaking up the big number and solving it a section at a time.
## Thousands, Hundreds, ...
To illustrate, let us try guessing the answer to 7,698 ÷ 6, but following a special method.
We will start at the thousands, then move to the h... |
# All Factors of 16: Prime Factors, Pair Factors
The factors of 16 are the numbers that completely divide 16 without leaving a remainder. Thus we can say that the factors of 16 are the divisors of 16. In this section, we will learn about the factors of 16 and the prime factors of 16.
Table of Contents
## Highlights ... |
Equation of the tangent line is 3x+y+2 = 0. If you're seeing this message, it means we're having trouble loading external resources on our website. That is to say, you can input your x-value, create a couple of formulas, and have Excel calculate the secant value of the tangent slope. This is a fantastic tool for Stewar... |
## ◂Math Worksheets and Study Guides First Grade. Commutative Property
### The resources above correspond to the standards listed below:
#### Massachusetts Curriculum Frameworks
MA.1.OA. Operations and Algebraic Thinking
1.OA.B. Understand and apply properties of operations and the relationship between addition and ... |
# Factors of 7
Last Updated: May 23, 2024
## Factors of 7
The factors of 7 are the numbers that can divide 7 without leaving a remainder. Since 7 is a prime number, it has exactly two factors: 1 and 7. These factors are significant because they represent the only numbers that can evenly divide 7. Understanding the f... |
Solving Age Problems
Updated on August 6, 2018
Solving Age Problems
One of the most popular applications of linear equations is solving age problems. In this hub I present three word problems of this sort with their complete solution. Hope you will enjoy this hub.
Problem Number One :
A mother’s age is five years ... |
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A source of sound is travelling at $\dfrac{{100}}{3}m{s^{ - 1}}$ along a road, towards a point $A$. When the source is $3m$ away from $A$, a person standing at a point $O$ on a road perpendicular to the track hears a sound of frequency $f$. The di... |
# What Does M Stand For In Slope Intercept Form
## The Definition, Formula, and Problem Example of the Slope-Intercept Form
What Does M Stand For In Slope Intercept Form – There are many forms used to depict a linear equation, one that is frequently encountered is the slope intercept form. The formula for the slope-i... |
> #mathematics , #illustrations , #notes , #set-theory > Notes and illustrations on set theory ?
Mar 25
# Notes and illustrations on set theory ?
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Set theory is a branch of mathematical logic that studies sets, which are collections of objects. Sets are typically denoted by curly braces ... |
# Solving Linear Inequalities
An inequality is a statement indicating that two expressions are not equal to one another in a particular way (e.g. one expression is larger or smaller than the other). In the case of a linear inequality, it can be simplified into the form
ax ≥ b, ax b, ax ≤ b, or ax b
where a and b are... |
# Common Core: 6th Grade Math : Understand Independent and Dependent Variables: CCSS.Math.Content.6.EE.C.9
## Example Questions
### Example Question #1 : Understand Independent And Dependent Variables: Ccss.Math.Content.6.Ee.C.9
Select the table of values that represent the relationship between and if
Explanation... |
Content Blocks
Learning Objectives
In this section, you will:
• Determine whether a relation represents a function.
• Find the value of a function.
• Determine whether a function is one-to-one.
• Use the vertical line test to identify functions.
• Graph the functions listed in the library of functions.
A jetliner c... |
# Designing circuits
Robert P. Webber and Don Blaheta, Longwood University
Why are we working on this? The simplest truth tables correspond to individual gates, and as the tables start to get more complex, we link together multiple gates into circuits. As they increase in complexity, trial-and-error becomes difficult ... |
# How many sixth makes a half?
## How many sixth makes a half?
These are the equivalent fractions in the thirds and sixths family. Where is on this line? So how many sixths are the same as one half? Record 1/2 3/6
## How many sixths are in a whole?
It takes two one-sixths to make a third. and we can see that there ... |
# 19 Times Table- Learn Table Of 19 : Multiplication Table Of 19
Safalta expert Published by: Yashaswi More Updated Thu, 19 May 2022 10:48 PM IST
## Highlights
Check out how to learn the 19 Times table easily here at Safalta.com
19 Times Table: Sam asked Joy, "Do you know that there is a Chinese game of Go which is... |
##### SAT
When two lines meet they form an angle. Angles are measured in degrees. On the PSAT/NMSQT, you won’t find any negative or zero angles, and you probably won’t have to deal with fractional angles either (no 45.9°, for example). You do have to know these basic facts:
• A right angle measures 90°. Right angles ... |
Topics in
P R E C A L C U L U S
2
# RATIONAL AND IRRATIONAL NUMBERS
What is a rational number?
CALCULUS IS A THEORY OF MEASUREMENT. The necessary numbers are the rationals and irrationals. But let us start at the beginning.
The following numbers of arithmetic are the counting-numbers or, as they are called, the n... |
# FREE IMO Integers and Data Handling Questions and Answers
0%
#### The temperature in Thrissur was 27°C in the morning which dropped to 17°C in the evening. Find the temperature difference.
Correct! Wrong!
Explanation:
To find the temperature difference, we subtract the initial temperature from the final temperatu... |
# Solving Systems of Equations by Substitution
Related Topics:
Worksheets to practice solving systems of equations
More Algebra Lessons
These algebra lessons introduce the technique of solving systems of equations by substitution.
In some word problems, we may need to translate the sentences into more than one equat... |
Home >
### (1) Modeling Ratios
Learning Target:
• You will learn how to build bar models to solve word problems that compare quantities using fraction and ratio.
• You will also learn about the link between ratio and fraction by drawing models to organize and solve problems.
Follow along with the videos - take not... |
# Reverse the equation to solve for y
I'm trying to solve for $Y$ in this equation: $\frac {(X-Y)}{Y} = Z.$ I tried applying some of the answers from other questions but I'm having special trouble with figuring out how to get the $Y$ out of the parenthesis. Thanks!
If $Z\not =-1$, then$$\frac{X-Y}{Y}=Z\Rightarrow X-Y... |
# 10.2: Test of Independence
Difficulty Level: At Grade Created by: CK-12
## Learning Objectives
• Understand how to draw data needed to perform calculations when running the chi-square test from contingency tables.
• Run the test of independence to determine whether two variables are independent or not.
• Use the t... |
# Maharashtra Board Class 5 Maths Solutions Chapter 7 Circles Problem Set 28
Balbharti Maharashtra Board Class 5 Maths Solutions Chapter 7 Circles Problem Set 28 Textbook Exercise Important Questions and Answers.
## Maharashtra State Board Class 5 Maths Solutions Chapter 7 Circles Problem Set 28
Question 1.
Draw cir... |
# How do you use synthetic division to show that x=sqrt2 is a zero of x^3+2x^2-2x-4=0?
Jan 24, 2017
By showing that the division gives no remainder, i.e. $r \left(x\right) = 0$.
The basic setup of synthetic division is:
ul(sqrt2" ") "|"" "" "1" "" "2" "" "-2" "" "" "-4
" "+ " "ul(" "" "" "" "" "" "" "" "" "" "" "" ... |
# Unit 3 Part 2 Writing Equations Ax + By = C (standard form) y = mx + b (slope – intercept form)
## Presentation on theme: "Unit 3 Part 2 Writing Equations Ax + By = C (standard form) y = mx + b (slope – intercept form)"— Presentation transcript:
Unit 3 Part 2 Writing Equations Ax + By = C (standard form) y = mx + b... |
# Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis. It can be thought of as a modified Cartesian plane, with the real part of a complex number represented by a displacement along the x-axis,... |
Note: Do not rely on this information. It is very old.
# Trigonometry
Trigonometry derives its name from two Greek words meaning to measure a triangle and originally that was the object of the science. Now, however, its range is much wider; it deals with angles and their measures, with their geometrical properties, ... |
# Mean value theorem – Conditions, Formula, and Examples
The mean value theorem is an important application of derivatives. In fact, it is one of the most important and helpful tools in Calculus, so we need to understand the theorem and learn how we can apply it to different problems.
The mean value theorem helps us ... |
# What is 1/415 as a decimal?
## Solution and how to convert 1 / 415 into a decimal
1 / 415 = 0.002
1/415 or 0.002 can be represented in multiple ways (even as a percentage). The key is knowing when we should use each representation and how to easily transition between a fraction, decimal, or percentage. Both repres... |
# Calculation Short tricks: Calculate Square Roots quickly!
By BYJU'S Exam Prep
Updated on: September 25th, 2023
Calculation tricks to calculate Square roots: In Quantitative Aptitude, calculation short tricks are required to solve the questions quickly and accurately. This minimizes the time of the calculation as w... |
# If the medians of a AABC intersect at G,
Question:
If the medians of a AABC intersect at G, then show that ar (ΔAGB) = ar (ΔAGC) = ar (ΔBGC) = 1/3 ar(ΔABC).
Thinking Process
Use the property that median of a triangle divides it into two triangles of equal area.
Further, apply above property by considering diffe... |
# CBSE Class 9th Maths Important MCQs from Chapter 14 - Statistics (with Answers)
Get MCQs with answers for CBSE Class 9 Maths Chapter 14 - Statistics. These questions are based on important concepts that must be practiced for the upcoming CBSE Class 9th Term 1 Exam 2021-22.
Created On: Sep 23, 2021 00:34 IST
CBSE Cl... |
# How do you expand (3x-2y)^5?
Jul 13, 2017
$243 {x}^{5} - 810 {x}^{4} y + 1080 {x}^{3} {y}^{2} - 720 {x}^{2} {y}^{3} + 240 x {y}^{4} - 32 {y}^{5}$
#### Explanation:
$\text{using the "color(blue)"binomial theorem}$
•color(white)(x)(x+y)^n=sum_(r=0)^n((n),(r))x^(n-r)y^r
"where" ((n),(r))=(n!)/(r!(n-r)!)
$\text{he... |
Take a Diagnostic Exam - Determine Your Test Readiness - 5 Steps to a 5 AP Statistics 2017 (2016)
## 5 Steps to a 5 AP Statistics 2017 (2016)
### STEP 2
CHAPTER 3 Take a Diagnostic Exam
### Take a Diagnostic Exam
IN THIS CHAPTER
Summary: The following diagnostic exam begins with 40 multiple-choice questions. T... |
# Given the sum of the first 5 terms of an AP as 90 and the first 50 terms as 4275, what is the first term of the series?
giorgiana1976 | College Teacher | (Level 3) Valedictorian
Posted on
We'll apply the formula for the sum of n terms of an A.P.:
Sn = (a1+an)*n/2
We know that the sum of the first 5 terms is 90.
... |
# Minimize the sum of node values by filling a given empty Tree such that each node is GCD of its children
Amarjeet Kumar
Last Updated: May 12, 2022
Difficulty Level :
EASY
## Introduction
In this article we'll look at a problem using Binary Trees to solve it. Binary Trees contain a lot of intriguing qualities, and ... |
# Warm-Up (8/28) Please pick up a warm-up sheet and a fractions chart from the desk in the front of the room and begin working on warm-up #1. Make sure to.
## Presentation on theme: "Warm-Up (8/28) Please pick up a warm-up sheet and a fractions chart from the desk in the front of the room and begin working on warm-up ... |
Open in App
Not now
# Class 12 RD Sharma Solutions- Chapter 32 Mean and Variance of a Random Variable – Exercise 32.1 | Set 1
• Last Updated : 25 Jan, 2021
### Question 1. Which of the following distributions of probabilities of random variables are their probability distributions?
i.
Solution:
We know that the s... |
Addition of Integers – Part 3
# Addition of Integers – Part 3
Fill Out the Form for Expert Academic Guidance!
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• Addition of Two Integers with Same Sign
• Addition of Two Integers with Different Sign
• Summary
• What’s Next?
In the previous ... |
# From a well-shuffled pack of 52 cards, a card is drawn at random.
Question:
From a well-shuffled pack of 52 cards, a card is drawn at random. Find the probability of its being a king or a queen
Solution:
let A denote the event that the card drawn is king and B denote the event that card drawn is queen.
In a pack... |
Trigonometric Differentiation
Learn about trigonometric differentiation, its formula along with different examples. Also find ways to calculate using trigonometric differentiation.
Alan Walker-
Published on 2023-05-26
Introduction to Trigonometric Differentiation
There are six basic trigonometric functions in geom... |
# Math Tutorial 1.6 - Divisibility Rules
Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
There are 21 lessons in this math tutorial covering Divisibility Rules. The tutorial starts with an introduction to Divisibility Rules and is then followed with a list of the separ... |
offers hundreds of practice questions and video explanations. .
or to Clemmonsdogpark GMAT Prep.
GMAT Sets: Venn Diagrams
Learn this technique to master set questions of GMAT Quant word problem.
Practice questions
First, try these challenging practice questions.
1) Of the 80 houses in a development, 50 have a two... |
New
New
Year 3
# Estimate the position of 3-digit numbers on unmarked number lines
I can estimate the position of 3-digit numbers on an unmarked number line.
New
New
Year 3
# Estimate the position of 3-digit numbers on unmarked number lines
I can estimate the position of 3-digit numbers on an unmarked number line.... |
# Perimeter and Area Class 7 Extra Questions Maths Chapter 11
Perimeter and Area Class 7 Extra Questions Maths Chapter 11
### Perimeter and Area Class 7 Extra Questions Maths Chapter 11
Extra Questions for Class 7 Maths Chapter 11 Perimeter and Area
### Perimeter and Area Class 7 Extra Questions Very Short Answer T... |
# 9R Elimination w Multiplication - MrNappiMHS
```Do Now
Solve using elimination:
3x + 2y = – 19
– 3x – 5y = 25
Homework Solutions
1)
x – y = 1
+ x + y = 3
2x
= 4
x = 2
2+ y = 3
y = 1
Solution: (2, 1)
Homework Solutions
3)
x + 4y
– x – 6y
10y
y
= 11
= 11
= 0
= 0
x + 4(0) = 11
x = 11
Solution: (11, 0)
Homework Solution... |
### Infant Maths Evening
```Infant Maths Evening
Helping Your Child with Their Maths at Home
Maths in the Infants
Progression in number work
Methods we use for the operations
Other maths in the infants
Counting using Objects
•The first step in children’s number work is counting up to 10 and
beyond.
• Children th... |
# What Is 71/100 as a Decimal + Solution With Free Steps
The fraction 71/100 as a decimal is equal to 0.71.
Long division is a mathematical operation that enables you to solve challenging and intricate division-related problems. The Long division approach simplifies difficult division by breaking enormous numbers int... |
# Book I. Propositions 33 and 34
Problems
Back to Propositions 33, 34.
11. a) State the hypothesis of Proposition 33.
Do the problem yourself first!
Straight lines join the extremities on the same side of two equal and parallel straight lines.
12. b) State the conclusion.
Those straight lines are themselve... |
# Video: AQA GCSE Mathematics Foundation Tier Pack 1 • Paper 3 • Question 18
Two function machines are shown. Both function machines have the same input. Work out the value of the input such that the output of A is two times the output of B.
04:01
### Video Transcript
Two function machines are shown. A: input multi... |
# Math Snap
## One of the following sets is not closed in $\mathbb{R}$. Select one: a. $\mathbb{Z}$ b. $\left\{\frac{\tan ^{-1}(n)}{n}: n \in \mathbb{N}\right\} \cup\{0\}$ c. $\left\{(-1)^{n}\left(1-\frac{1}{n}\right): n \in \mathbb{N}\right\} \cup\{0,1\}$ d. N e. None of them
#### STEP 1
Assumptions 1. We are worki... |
Section 4: Inverse Functions
# Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)
• Notes
• davidvictor
• 12
This preview shows pages 1–3. Sign up to view the full content.
Section 8.4 Inverse Functions 803 Version: Fall 2007 8.4 Inverse Functions As we saw in the last section, in order to solve app... |
# Lesson: Fractions: Adding and Subtracting Like Fractions
12 Views
8 Favorites
### Lesson Objective
SWBAT find the sum or difference of fractions with like denominators.
### Lesson Plan
Materials Needed: scrap paper for DN and GP, Example Like Denominator Chart, white board, dry erase markers, pencils, and IND Wo... |
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# How do you simplify ${{\left( 2+5\iota \right)}^{2}}$?
Last updated date: 19th Jul 2024
Total views: 383.7k
Views today: 9.83k
Verified
383.7k+ views
Hint: In this problem, we have to find the square of a complex number. This can also be done b... |
A resource for profoundly gifted middle school students, their parents, and teachers
MATHEMATICS CONCEPTS
### Cantor-Bernstein Therorem
Two sets A and B have the same cardinality if there is a 1-1 and onto mapping or correspondence from A to B. Often, it is easier to find a 1-1 mapping rather than one that is 1-1 an... |
# FIND QUOTIENT AND REMAINDER USING SYNTHETIC DIVISION
## About "Find Quotient and Remainder Using Synthetic Division"
Find Quotient and Remainder Using Synthetic Division :
Here we are going to see some practice questions to understand the concept of finding quotient and remainder using synthetic division.
## Find... |
# We have DeltaABCand the point M such that vec(BM)=2vec(MC).How to determinate x,y such that vec(AM)=xvec(AB)+yvec(AC)?
May 10, 2017
The answer is $x = \frac{1}{3}$ and $y = \frac{2}{3}$
#### Explanation:
We apply Chasles' relation
$\vec{A B} = \vec{A C} + \vec{C B}$
Therefore,
$\vec{B M} = 2 \vec{M C}$
$\vec{... |
# 2.7 Linear inequalities and absolute value inequalities
Page 1 / 11
In this section you will:
• Use interval notation.
• Use properties of inequalities.
• Solve inequalities in one variable algebraically.
• Solve absolute value inequalities.
It is not easy to make the honor role at most top universities. Suppose s... |
# Ex.13.6 Q7 Surface Areas and Volumes Solution - NCERT Maths Class 9
## Question
A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is $$7 \; \rm mm$$ and the diameter of the graphite is $$1\; \rm mm$$. If the length of the pencil is $$14... |
# Difference between revisions of "2011 AIME II Problems/Problem 13"
## Problem
Point $P$ lies on the diagonal $AC$ of square $ABCD$ with $AP > CP$. Let $O_{1}$ and $O_{2}$ be the circumcenters of triangles $ABP$ and $CDP$ respectively. Given that $AB = 12$ and $\angle O_{1}PO_{2} = 120^{\circ}$, then $AP = \sqrt{a} ... |
What is the formula for the volume of a rectangular prism?
A rectangular prism, also known as a cuboid, is a solid geometric shape that has six faces, all of which are rectangles. The volume of a rectangular prism can be found by multiplying the length, width, and height of the prism.
Formula for the Volume of a Rect... |
## How many right angles does a obtuse triangle have?
An obtuse triangle (or obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90°) and two acute angles. Since a triangle’s angles must sum to 180° in Euclidean geometry, no Euclidean triangle can have more than one obtuse angle.
## Can an obtus... |
# Important Formulas on Streams
### Streams - Important Aptitude formulas, shortcut methods and tricks:
Theorem: (1). If α km/hr be the man’s rate in still water and β km/hr be the rate of the current, then
α + β = man’s rate with current
α - β = man’s rate against current
Note: (i) A man’s rate in still water is ha... |
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# System of Linear Equations in three variables using Cramer’s Rule
Cramer’s rule: In linear algebra, Cramer’s rule is an explicit formula for the solution of a system of linear equations with as many equations as unknown variables. It expresses the solution in terms of the... |
# ORDER OF OPERATIONS WORKSHEETS
## About "Order of operations worksheets"
Order of operations worksheets are much useful to the kids who would like to practice problems on the binary operations like add, subtract, multiply, divide, squaring,etc.
When we have two or more operations in the same expression, we may hav... |
HBSE 7th Class Maths Solutions Chapter 10 Practical Geometry InText Questions
Haryana State Board HBSE 7th Class Maths Solutions Chapter 10 Practical Geometry InText Questions and Answers.
Haryana Board 7th Class Maths Solutions Chapter 10 Practical Geometry InText Questions
Think, Discuss & Write (Page No. 195):
Q... |
# More Cake Halves
6 teachers like this lesson
Print Lesson
## Objective
SWBAT create halves of squares and cakes. SWBAT explain that a whole split in halves has two equal pieces.
#### Big Idea
Students will continue to explore the concept of half.
## Warm Up
5 minutes
I have the students gather in a circle on ... |
# Prime Numbers of 20
Let us know about Prime Numbers of 20.
There are 20 prime numbers under 8: 2, 3, 5, 7, 11, 13, 17 and 19 .
Similarly, how do you find the factorization of 20? 20 = 1 x 20, 2 x 10 , or 4 x 5. Factors of 20: 1, 2, 4, 5, 10, 20. Prime factors: 20 = 2 x 2 x 5, also written as 20 = 2² x 5 can go. Wh... |
# 2016 AMC 12A Problems/Problem 7
## Problem
Which of these describes the graph of $x^2(x+y+1)=y^2(x+y+1)$ ?
$\textbf{(A)}\ \text{two parallel lines}\\ \textbf{(B)}\ \text{two intersecting lines}\\ \textbf{(C)}\ \text{three lines that all pass through a common point}\\ \textbf{(D)}\ \text{three lines that do not all... |
# Basics of Circle
You might already know that Circles have the least surface area but did you ever think about the geometry which makes it so? Well yes, like straight lines, circles have geometry too and trust me when I say, it is as easy as its linear counterpart. After all, how difficult is it to understand a curv... |
# Special Right Triangles
The special right triangle is a right triangle whose sides are in a particular ratio. According to the special right triangle rules, it is not necessary to use the Pythagorean theorem to get the size of a side.
## A step-by-step guide to solving Special Right Triangles
• Two special right t... |
I have already discussed a concept - Quadratic Equations of quantitative aptitude. Today I will discuss some examples of simple equations which have been proved to be a very important topic for various competitive exams. The problems of linear equations can be easily solved by using simple tricks. Lets discuss how.
##... |
ME495+Statistics+Homework+Solutions
# ME495+Statistics+Homework+Solutions - ME495 Statistics...
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ME495 Statistics Homework Solutions 1. Single-factor ANOVA In an experiment to compare the quality of four different brands of recording tape, five reels of ... |
# Buffon's Needle
Buffon's Needle
The Buffon's Needle problem is a mathematical method of approximating the value of pi $(\pi = 3.1415...)$involving repeatedly dropping needles on a sheet of lined paper and observing how often the needle intersects a line.
# Basic Description
The method was first used to approximate... |
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# Vedic Math Sutra: Sutra-14 Ekanyunena Purvena
## |
Since mathematics has always been essential to our lives, kids must have a... |
# AP Statistics Curriculum 2007 Bayesian Normal
## Probability and Statistics Ebook - Normal Example
### Motivational example
It is known that the speedometer that comes with a certain new sports car is not very accurate, which results in an estimate of the top speed of the car of 185 mph, with a standard deviation ... |
# Understanding the Basics of Ohm’s Law
To work as an electrician, you need to have a good understanding of Ohm’s law.
With it, you can understand the relations between the three electrical variables: current, voltage, and resistance.
Search Electrician Programs
Get information on Electrician programs by entering y... |
# Binary Tree | Set 2 (Properties)
• Difficulty Level : Easy
• Last Updated : 19 Oct, 2021
We have discussed Introduction to Binary Tree in set 1. In this post, the properties of a binary tree are discussed.
1) The maximum number of nodes at level ‘l’ of a binary tree is 2l
Here level is the number of nodes on the p... |
# 221_Chapter5_Student
Document Sample
``` 5.1 Review and Preview
In this chapter we combine the methods of descriptive statistics presented in Chapters 2 and 3 and those of
probability presented in Chapter 4. We will be constructing probability distributions by presenting possible
outcomes along with the relativ... |
# 4.7: Parametric Equations
Learning Objectives
• Plot a curve described by parametric equations.
• Convert the parametric equations of a curve into the form (y=f(x)).
• Recognize the parametric equations of basic curves, such as a line and a circle.
• Recognize the parametric equations of a cycloid.
In this section... |
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