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# Law of Sines in Algebra
## Using Trigonometric Rules To Solve Triangles: An Introduction To The Law Of Sines
Trigonometric rules are powerful tools that can help determine various properties and values of right-angled triangles. However, these rules can also be applied to solve non-right-angled triangles by finding... |
#### xaktly | Algebra | Functions
{ factoring }
Quadratic functions are very important.* There's a lot to cover, so the material is broken up into a few sections.
• This section covers all methods of solving quadratic equations.
• Quadratic functions deals with definitions, graphing and transformations of the parabo... |
## Tuesday, December 3, 2013
### How to teach multiplication
The questions and suggestions below pertain to the way multiplication is taught to kids. Examples pertain to multiplication problems involving two two-digit numbers.
Question One: Do you teach kids to multiply right to left or left to right? The standa... |
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# Completing the Square
Say we have a simple expression like x2 + bx. Having x twice in the same expression can make life hard. What can we do?
Well, with a little inspiration from Geometry we can convert it, like this:
As you can see x2 + bx can be rearranged nearly into a square …
… and we can com... |
## Geometry Tutors
Love making paper airplanes, tangram puzzles, and origami? Geometry is the math behind them all. Students begin learning about geometry when they are taught different shapes and angles and how to create new objects from them. They are still interested even when it is time to learn how to determine h... |
## What are extrema of functions?
An extremum (plural extrema) is a point of a function at which it has the highest (maximum) or lowest (minimum) value. A global maximum or minimum is the highest or lowest value of the entire function, whereas a local maximum or minimum is the highest or lowest value in its neighbourh... |
## Prealgebra Problems
This page shows you the types of questions that are covered on the prealgebra section of the Compass mathematics test.
You will find practice prealgebra problems in each section on this page.
The solutions to the prealgebra problems are provided below the questions in each section.
## Calcula... |
SalasSV_10_02_ex
# SalasSV_10_02_ex - 10.2 SEQUENCES OF REAL NUMBERS PROOF 593...
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Unformatted text preview: 10.2 SEQUENCES OF REAL NUMBERS PROOF 593 We will work with the function... |
# 120 cm to Feet: Converting Centimeters to Feet Made Easy
Converting measurements from one unit to another is a common task in various fields, including construction, engineering, and everyday life. One such conversion that often arises is converting centimeters to feet. In this article, we will explore the process o... |
We received concise statements of general rules based on clearly presented evidence:
Matthew, Holly and Isobel from Staunton & Corse C of E School discovered the relationship between the enlargement scale factor and the effect on the area:
We started by writing 5 different dimensions with an area of $20$cm$^2$:
Leng... |
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# A steel rail of length $5\,m$ and area of cross section $40\,c{m^2}$ is prevented from expanding along its length while the temperature rises by $10\,{}^ \circ C$. If coefficient of linear expansion and young’s modulus of steel are $1.2 \times {... |
### I: Students will acquire number sense and perform operations with whole numbers, simple fractions, and decimals.
#### I.1: Demonstrate multiple ways to represent whole numbers and decimals, from hundredths to one million, and fractions.
I.1.a: Read and write numbers in standard and expanded form.
I.1.b: Demonstr... |
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# How do you find the exact value of the following using the unit circle: $\cos \dfrac{{53\pi }}{6}$?
Last updated date: 17th Jun 2024
Total views: 373.5k
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Hint: In the given problem, we are required to fi... |
# 1.2 Algebraic Expressions 8/24/12. Vocabulary Variable: A letter used to represent one or more numbers Exponent: The number or variable that represents.
## Presentation on theme: "1.2 Algebraic Expressions 8/24/12. Vocabulary Variable: A letter used to represent one or more numbers Exponent: The number or variable t... |
# The sum of three consecutive integers is 135. What are the numbers?
Jul 4, 2017
$44 , 45 , 46$
#### Explanation:
$\text{let the first integer be represented by } n$
$\text{then the second integer will be } n + 1$
$\text{and the third integer } n + 2$
$\Rightarrow n + n + 1 + n + 2 = 135 \leftarrow \textcolor{b... |
During AMC testing, the AoPS Wiki is in read-only mode. No edits can be made.
# 1999 AIME Problems/Problem 3
## Problem
Find the sum of all positive integers $n$ for which $n^2-19n+99$ is a perfect square.
## Solution 1
If $n^2-19n+99=x^2$ for some positive integer $x$, then rearranging we get $n^2-19n+99-x^2=0$. ... |
# Sarin’s family celebrating Hari Raya Puasa part 23 (Math Question)
Standard
The blog postings are about the Singapore Math. The readers can learn from the postings about Solving Singapore Primary School Mathematics. The blog presents the Math Concept, the Math Questions with solutions that teaches in Singapore Prim... |
# Sum of Arithmetic Series
## Arithmetic Series
The series associated with an arithmetic sequence is known as an arithmetic series. For example: 3 + 7 + 11 + 15 + 19 + 23 + 27 + 31 is the arithmetic series associated with the arithmetic sequence: 3, 7, 11, 15, 19, 23, 27, 31.
## Sum of Arithmetic Series
To derive t... |
# Find the percentage of 43 out of 50.
What is 43 out of 50 as a percentage?
In the realm of Mathematics education, understanding percentages plays a crucial role in comprehending various concepts. In this article, we delve into the question of what 43 out of 50 represents as a percentage. By employing simple mathema... |
# What is the practical application of congruence nowadays?
Answer to the comment in Congruences, by dwightisebia
First of all I liked your question. Actually it gave me an idea of adding real life applications of mathematical concepts to my site! Thank you!
Q: What is the practical application of congruence nowaday... |
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# Using CheckedListBox in Multiplication
, 4 Aug 2010
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Ancient Egyptian multiplication and Russian peasants multiplication
## Introduction
When you use your computer or your calculator to do difficult calculations, or when you see your child easily do the following multiplication...
``` 68
x... |
## Variation
### Learning Outcomes
• Define direct variation and solve problems involving direct variation
• Define inverse variation and solve problems involving inverse variation
• Define joint variation and solve problems involving joint variation
So many cars, so many tires.
## Direct Variation
Variation equat... |
# Question: What Happens When You Add 2 Square Roots?
## How do you multiply square roots together?
Explanation: To multiply square roots, we multiply the numbers inside the radical.
Any numbers outside the radical are also multiplied.
We can simplify them if possible..
## What does this sign mean √?
√ is the sym... |
# What is probability in Mathematics OR Explain how do you calculate probability ?
Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes — how likely they are. OR Many events can't be predicted with total certainty. The best we can say is how likely they are to ha... |
We know that all repeating or terminating decimals are rational, but are all rationals either repeating or terminating? If they are, that would by corrolary mean that all irrational numbers do not terminate or repeat.
We'll first consider rationals that have denominators consisting of factors from the base. That is to... |
# Equation with Binomial Expression
Contributed by:
This pdf includes the following topics-
Constant
Terms and expressions
Coefficient of a term
Writing patterns in geometry
Variable
Examples
1. CHRIST SENIOR SECONDARY SCHOOL
CLASS 7
Notes: Chapter 12 ALGEBRAIC EXPRESSIONS
Introduction to Algebraic Expressions
Constan... |
# Solve using quadratic formula solver
## Solving using quadratic formula solver
The solver will provide step-by-step instructions on how to Solve using quadratic formula solver. Long division is the process of calculating a long number in two or more steps. Long division is useful for calculating a large number that... |
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# What percent is Rs $63$ of Rs $90$
Last updated date: 20th Sep 2024
Total views: 413.7k
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Hint: To find what percentage of RS$90$ is RS$63$
First we understand percentage means out of $100$ as there total... |
# Introduction to Addition and Subtraction of Fractions
Fraction is defined as a numerical part of a whole number. Sometimes we want to add or subtract two fractions to find out the total number.
For example, Malini ate 1½ roties for lunch and 2½ roties for dinner. What is the total number of roties Malini ate? In th... |
# College Math Teaching
## August 20, 2018
### Algebra for Calculus I: equations and inequalities
Filed under: basic algebra, calculus, pedagogy — collegemathteaching @ 9:24 pm
It seems simple enough: solve $3x+ 4 = 7$ or $\frac{2}{x-5} \leq 3$.
So what do we tell our students to do? We might say things like “with... |
# Bar Model Approach for Averages of Numbers in Statistics
##### Ho Soo Thong
Abstract
This article illustrates the use of mathematical implications of the Arithmetic Distributive Law for solving problems involving averages at Primary School Level.
In algebraic expressions, we write
a = b + c and na = n... |
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# Class 9 NCERT Solutions Maths Chapter 7 - Triangles
Do you struggle to prove that the two triangles given in a textbook question are congruent? Do you find it difficult to explain the concept of SSS congruence in a Maths problem? If yes, then our NCERT Solutions for CBSE Class 9 Mathematics Chap... |
Greatest Common Gaussian Divisor
Gaussian integers are complex numbers $$\x+yi\$$ such that $$\x\$$ and $$\y\$$ are both integers, and $$\i^2 = -1\$$. The norm of a Gaussian integer $$\N(x+yi)\$$ is defined as $$\x^2 + y^2 = |x+yi|^2\$$. It is possible to define a Euclidean division for Gaussian integers, which means ... |
# Find the angle in a triangle if the distance between one vertex and orthocenter equals the length of the opposite side
Let $O$ be the orthocenter (intersection of heights) of the triangle $ABC$. If $\overline{OC}$ equals $\overline{AB}$, find the angle $\angle$ACB.
-
Position the circumcenter $P$ of the triangle a... |
Home Math Including Numbers in Expanded Kind
### Including Numbers in Expanded Kind
[ad_1]
Study to rearrange for including numbers
in expanded type (briefly type and in lengthy type). The numbers are written in
column type; the digits are organized in expanded type after which lastly discover the
sum of the given n... |
The base of a square pyramid, a three-dimensional solid, is a square. Opposite angles of a square are congruent. 2 2 11 3 2 13 1 2 3 1 0 2 2 13 3 5 1 11 REDUCED ROW ECHELON FORM (rref) Reducing a matrix to reduced row echelon form or rref is a means of solving the equations. In Linear algebra, a determinant is a unique... |
# Factors of 95
The factors of 95 and the prime factors of 95 differ because ninety-five is a composite number. Also, despite being closely related, the prime factors of 95 and the prime factorization of 95 are not exactly the same either. In any case, by reading on you can learn the answer to the question what are th... |
# Difference between revisions of "2008 AIME II Problems/Problem 5"
## Problem 5
In trapezoid $ABCD$ with $\overline{BC}\parallel\overline{AD}$, let $BC = 1000$ and $AD = 2008$. Let $\angle A = 37^\circ$, $\angle D = 53^\circ$, and $M$ and $N$ be the midpoints of $\overline{BC}$ and $\overline{AD}$, respectively. Fin... |
# GRE Math Multi-subject Challenge Question
Once in a while it is fun to take a concept in an official GRE question and run with it. The question below is inspired by a question from the 2nd edition Official Guide. That is not to say it is that similar; I have only extracted a couple of concepts from that problem.
I’... |
# Algebra based Mathematics Notes For CTET Exam : Free PDF
## Algebra
Algebra
It is branch of mathematics that substitutes letters for numbers. Algebra gives different methods of solve equations.
Variables
A variable is represented by either a sign or a letter. Its value may not be the same in every equation.
Exa... |
# Newton’s Second Law Worksheet Answers
An excellent way to teach basic trigonometry skills is to use a Newton’s Second Law Worksheet. The idea is that you learn to work with angles by completing various quantities, such as the angles of a triangle, and by doing so, you learn to calculate the lengths of different line... |
# document2
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Chapter Two FUNCTIONS
2.1 INPUT ---;.,.,.-:"" ANDOUTPUT "__'L_. ._'" """"",C -.-"'"
--
Finding OutputValues:Evaluating Function aEvaluating a function means calculating the value of a fu... |
# How To Solve For Slope Intercept Form
## The Definition, Formula, and Problem Example of the Slope-Intercept Form
How To Solve For Slope Intercept Form – Among the many forms employed to illustrate a linear equation the one most commonly seen is the slope intercept form. You may use the formula of the slope-interce... |
Question Video: Multiplying Complex Numbers Involving Powers of the Imaginary Units | Nagwa Question Video: Multiplying Complex Numbers Involving Powers of the Imaginary Units | Nagwa
# Question Video: Multiplying Complex Numbers Involving Powers of the Imaginary Units Mathematics • First Year of Secondary School
## ... |
• ## Accessibility
Open the accessibility toolbar to change fonts and contrast, access a dictionary, use a ruler and more
One of the golden rules when working with fractions is that you can only add and subtract fractions which have the same denominator.
So the question is: "What do we do when they don't have the sa... |
# HCF and LCM Calculator
HCF and LCM, often referred to as the building blocks of arithmetic, play a crucial role in various mathematical operations. Understanding these concepts is fundamental for both students and individuals dealing with mathematical challenges in their everyday lives.
## What is HCF (Highest Comm... |
# Pythagorean Theorum RevisedPage 1
#### WATCH ALL SLIDES
Slide 1
The Pythagorean Theorem Mr. Clutter VMS Library
Slide 2
## Pythagoras
Lived in southern Italy during the sixth century B.C.
Considered the first true mathematician
Used mathematics as a means to understand the natural world
First to teach that t... |
# 7.1: Linear Systems by Graphing
Difficulty Level: At Grade Created by: CK-12
## Learning Objectives
• Determine whether an ordered pair is a solution to a system of equations.
• Solve a system of equations graphically.
• Solve a system of equations graphically with a graphing calculator.
• Solve word problems usin... |
Question Video: Recognizing the Seven Times Table | Nagwa Question Video: Recognizing the Seven Times Table | Nagwa
# Question Video: Recognizing the Seven Times Table Mathematics • Third Year of Primary School
Notice how each row is 7 more than the previous one. 1 × 7 = 7, 2 × 7 = 14, 3 × 7 = 21. Find the result of ... |
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# How to solve radical equations
The solver will provide step-by-step instructions on How to solve radical equations. So let's get started!
## How can we solve radical equations
We can do your math homework for you, and we'll make sure that you understand How to solve radical equations. Negative exponents in fractio... |
# Estimating Sum and Difference
The procedure of estimating sum and difference are in the following examples.
Working Rules for Estimating Sum or Difference:
Step I: First we need to find the smaller number.
Step II: Then round off the all given numbers to the highest place value of that of the smaller number.
Ste... |
### Kirchhoff’s First Law
The physicist Gustav Robert Kirchhoff (1824–1887) was a researcher and experimentalist in a time when little was understood about how electric currents flow. Nevertheless, he used certain commonsense notions to deduce two important properties of dc circuits.
Kirchhoff reasoned that dc ought ... |
Exponential and Logarithmic Functions
Evaluate and Graph Logarithmic Functions
Learning Objectives
By the end of this section, you will be able to:
• Convert between exponential and logarithmic form
• Evaluate logarithmic functions
• Graph Logarithmic functions
• Solve logarithmic equations
• Use logarithmic models... |
My Math Forum System of equations
Algebra Pre-Algebra and Basic Algebra Math Forum
March 1st, 2015, 10:01 AM #1 Member Joined: Aug 2014 From: Lithuania Posts: 60 Thanks: 3 System of equations I need to solve for a and b: $\displaystyle 10a+b-7=3a+3b$ $\displaystyle a^2+b^2-ab=10a+b$ I can't find a way how to do i... |
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# A committee of seven has to be formed from 9 boys and 4 girls. In how many ways this can be done when the committee consists of1. Exactly 3 girls.2. At least 3 boys.3. At most 3 girls.
Last updated date: 13th Jun 2024
Total views: 413.4k
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# An algebra of orders
Did you know that you can add and multiply orders? For any two order structures $A$ and $B$, we can form the ordered sum $A+B$ and ordered product $A\otimes B$, and other natural operations, such as the disjoint sum $A\sqcup B$, which make altogether an arithmetic of orders. We combine orders wi... |
# How to prove this formula for counting sub-sequences?
A sequence $(s_i)_0^{N+2m}$ of ones and zeroes has ones on $s_0$ and $s_{N+2m}$ and it's subsequence $(s_i)_1^{N+2m-1}$ that lies in between contains $N+m-1$ ones and $m$ zeroes, where $N\in \mathbb{N}$ and $m\in \mathbb{N}_0$. Such a sequence $(s_i)$ can be spli... |
## Глосарій
Виберіть одне з ключових слів ліворуч ...
# Euclidean GeometryEuclid’s Axioms
Час читання: ~25 min
Before we can write any proofs, we need some common terminology that will make it easier to talk about geometric objects. These are not particularly exciting, but you should already know most of them:
A p... |
Students of Grade 3 Module 3 can get a strong foundation on mathematics concepts by referring to the Eureka Math Book. It was developed by highly professional mathematics educators and the solutions prepared by them are in a concise manner for easy grasping. To achieve high scores in Grade 3, students need to solve all... |
# If One Zero of Polynomial 3x2-8x+2k+1 in Seven Times other Find the Zero and the Value of the k
By Mohit Uniyal|Updated : May 16th, 2023
If one zero of polynomial 3x2-8x+2k+1 in seven times other find the zero and the value of the k
To find the zero and the value of k in the polynomial 3x^2 - 8x + 2k + 1, given th... |
# The North American Arithmetic: Uniting Oral and Written Exercises, in Corresponding Chapters. Part second
Russell, Odiorne & Company, 1833 - 191 σελίδες
### Τι λένε οι χρήστες -Σύνταξη κριτικής
Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
### Περιεχόμενα
Ενότητα 1 1 Ενότητα 2 2 Ενότητα 3 5 Ενότητα 4 6 Ενότ... |
# What is the standard form of the equation of a circle with centre is at point (5,8) and which passes through the point (2,5)?
Jan 5, 2016
${\left(x - 5\right)}^{2} + {\left(y - 8\right)}^{2} = 18$
#### Explanation:
standard form of a circle is ${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$
where... |
# 6. Maths Trigonometry
Trigonometry is based on triangles. The point of trigonometry is to find either the unknown side or angle of a triangle, when we know a side and an angle.
Here is a little diagram to get you started (pretty isnt it).
Now:
O stands for opposite.
H stands for hypotenuse.
alpha is the angle in t... |
Do you ever find yourself in a situation where you need to add two really large numbers but don’t have access to an easy-to-use calculator? You will always be able to effortlessly add two numbers together with this addition calculator, whether they are positive or negative, large or tiny. We describe how our addition c... |
# How do you solve (x-1)(x-2)(x-3)(x-4) = 24?
Apr 19, 2016
$x = \left\{\begin{matrix}0 \\ 5 \\ \frac{5}{2} \pm \frac{\sqrt{15}}{2} i\end{matrix}\right.$
#### Explanation:
Let $f \left(x\right) = \left(x - 1\right) \left(x - 2\right) \left(x - 3\right) \left(x - 4\right)$
Then:
f(0) = (-1)(-2)(-3)(-4) = 4! = 24
f... |
# Factors of 325
Are you looking for all the factors of 325? If yes, you are in the right page to get answers factors of 325. Here in this page we have given brief discussion behind this article, so that students will get complete idea to find the answers.
## Factors of 325:
Topic Factors Number 325 Roman Numeral ... |
# RS Aggarwal Solutions Class 9 Maths Chapter 19 Probability (Updated For 2021-22)
RS Aggarwal Solutions Class 9 Maths Chapter 19 Probability: Your Class 9 Maths exam preparation is incomplete by studying the RS Aggarwal Solutions Class 9 Maths. You can always rely on the RS Aggarwal Solutions Class 9 Maths Chapter 19... |
# 3.2 Solving Systems of Equations Algebraically Substitution Method Elimination Method.
## Presentation on theme: "3.2 Solving Systems of Equations Algebraically Substitution Method Elimination Method."— Presentation transcript:
3.2 Solving Systems of Equations Algebraically Substitution Method Elimination Method
S... |
# The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
Given:
The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420.
To do:
We have to find its common difference.
Solution:
Let $a$ be the first term, ... |
Question Video: Simplifying Expansions Using the Binomial Theorem | Nagwa Question Video: Simplifying Expansions Using the Binomial Theorem | Nagwa
# Question Video: Simplifying Expansions Using the Binomial Theorem Mathematics • Third Year of Secondary School
## Join Nagwa Classes
Simplify ππΆ0 + 17 Γ ππ... |
Visual Explanations in Mathematics
## 2. Casselman's visual proof
The incommensurability of side and diagonal in a regular pentagon
In this regular pentagon, call the side length s and the length of the diagonal d. Our job is to show that s and d are incommensurable. First notice that in a regular pentagon, a diago... |
Hovedinnhold
# Middelværdisætningen
## Video transkripsjon
Let's see if we can give ourselves an intuitive understanding of the mean value theorem. And as we'll see, once you parse some of the mathematical lingo and notation, it's actually a quite intuitive theorem. And so let's just think about some function, f. So... |
## Step by step tutorial: How to draw a perfect square
When we construct our drawings we often find ourselves having to draw primitives. Let’s explore how to draw a perfect square with just a few easy steps!
# How to draw a perfect square
A square is nothing more than 4 lines of equal length touching each other’s be... |
Jun 18, 2023
I. Introduction
Calculating percent increase is crucial in analyzing and interpreting statistical and financial data. This process assesses the shifting trend and helps to predict the future trend. Accurate knowledge of percent increase is essential for budgeting, comparing financial results, and identif... |
6.3 Normal distributions and heights
In the (NNS) (conducted with the 1995 National Health Survey (NHS)), trained nutritionists measured the heights of the respondents .
The values quoted are used for modelling purposes, and are essentially the population means $$\mu$$ and standard deviations $$\sigma$$.
1. Take a w... |
# Origin of the Displacement and Acceleration Equation
Here we will take a look at the derivation of the following kinematics equation:
The above equation solves for the displacement of an object when it is undergoing a constant acceleration. You need to know the original velocity, vo, the constant acceleration, a, a... |
Paul's Online Notes
Home / Calculus I / Derivatives / Differentiation Formulas
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landsca... |
Operations The verbs of mathematics.. Subtraction Same as: adding a negative number. 4 - 3 = 4 + (-3)
Presentation on theme: "Operations The verbs of mathematics.. Subtraction Same as: adding a negative number. 4 - 3 = 4 + (-3)"— Presentation transcript:
Operations The verbs of mathematics.
Subtraction Same as: addi... |
## Related Articles
• NCERT Solutions for Class 11 Maths
# Class 11 NCERT Solutions- Chapter 11 Conic Section – Exercise 11.4
• Difficulty Level : Hard
• Last Updated : 09 Mar, 2021
### Question 1. = 1
Solution:
Comparing the given equation with = 1
we conclude that transverse axis is along x-axis.
a2 = 16 and... |
Math Skills: How to Calculate, Convert, and Use Percents
What is Percent?
If you listen to the radio, watch the television, or read a newspaper you can't help but hear or see phrases like "25% off today only" or "all merchandise 10% off" or "going out of business mark-downs of 50%." What does all this mean?
Percent... |
### Theory:
1. Dividing a fraction by another fraction:
To divide a fractional number with another fractional number, follow the steps below:
Step 1: Take the reciprocal of the divisor.
Step 2: Multiply the reciprocal of the divisor with the dividend to get the new numerator and denominator of the fraction.
Recipro... |
# How do you simplify (4+ 2i) /( -1 + i)?
May 2, 2018
$\frac{4 + 2 i}{- 1 + i} | \cdot \left(- 1 - i\right)$
$\frac{\left(4 + 2 i\right) \left(- 1 - i\right)}{\left(- 1 + i\right) \left(- 1 - i\right)}$
$\frac{- 2 {i}^{2} - 6 i - 4}{1 - {i}^{2}}$
$\frac{2 - 6 i - 4}{1 + 1}$
$\frac{- 2 - 6 i}{2}$
$= - 1 - 3 i$
#... |
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# Tutor profile: Rhoda A.
Rhoda A.
Math and Statistics tutor
## Questions
### Subject:Basic Math
TutorMe
Question:
1/5 + 3/5= ?
Rhoda A.
To solve this fraction, we will first note that the fractions have a common denominator (5). A denominator is the number on the bottom of a fraction, w... |
## Book: RS Aggarwal - Mathematics
#### Subject: Maths - Class 10th
##### Q. No. 35 of Exercise 10E
Listen NCERT Audio Books to boost your productivity and retention power by 2X.
35
##### In a class test, the sum of the marks obtained by P in mathematics and science is 28. Had he got 3 more marks in mathematics and... |
# Decimals
## Contents
#### Addition and Subtraction of Decimals
To add or subtract decimals, simply line them up so their decimal points are in the same place, and then add or subtract as usual. Sometimes one of the numbers will have more decimal places than the other. Because adding zeros to the end of a decimal d... |
# Nim and simple mathematical proofs 1/3
A few weeks ago I discussed a game called Nim. In studying Nim, with the help of Thomas S. Ferguson’s book Game Theory, I have again found great joy in mathematical thinking, proving theorems and using logical thinking to come to conclusions.
Many people, as far as I know, hav... |
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You are reading an older version of this FlexBook® textbook: CK-12 Algebra - Basic Go to the latest version.
# 12.5: Multiplication and Division of Rational Expressions
Difficulty Level: At Grade Created by: CK-12
Because a rational expression is really a f... |
# Ask Uncle Colin: Evil in integral form
Dear Uncle Colin,
I've been set an evil integral: $\int_0^\piby{4} \frac{\sqrt{3}}{2 + \sin(2x)}\d x$. There is a hint to use the substitution $\tan(x) = \frac{1}{2}\left( -1 + \sqrt{3}\tan(\theta)\right)$, but I can't see how that helps in the slightest.
— Let's Integrate Ev... |
NCERT Solutions for class 10 Maths Chapter 13- Exercise 13.2
NCERT Solutions for Class 10 Maths Chapter 13, Surface Areas and Volumes, Exercise 13.2, are available here in downloadable PDF format. The problems in this exercise have been answered by our Maths experts, to make students understand the theories in a bette... |
# What is Power Set – Definition, Formula and Examples
Here you will learn what is power set and its definition with examples.
Let’s begin –
## What is Power Set ?
Definition : Let A be a set. Then the collection or family of all subsets of A is called the power set of A and is denoted by P(A).
That is, P(A) = { ... |
# Problems on Calculating Time
Here we will learn to solve different types of problems on calculating time.
We know, the formula to find out time = distance/speed
Word problems on calculating time:
1. A car travel 60 km in 30 minutes. In how much time will it cover 100 km?
Solution:
Using the unitary method;
Tim... |
# How do you integrate int x^2/sqrt(x^2+1) by trigonometric substitution?
May 26, 2018
$\int \frac{{x}^{2} \cdot \mathrm{dx}}{\sqrt{{x}^{2} + 1}} = \frac{x}{2} \cdot \sqrt{{x}^{2} + 1} - \frac{1}{2} {\sinh}^{-} 1 x + C$
#### Explanation:
$\int \frac{{x}^{2} \cdot \mathrm{dx}}{\sqrt{{x}^{2} + 1}}$
After using $x = ... |
# How do you find the slope and intercept of y=(5-x)/10?
Mar 10, 2018
See a solution process below
#### Explanation:
Rewrite the equation in slope intercept form. The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$
Where $\textcolor{red}{m}$ is the slope and $\text... |
# What is 0.45 as a Fraction?
If you’re wondering what 0.45 is as a fraction, you’re in luck. We’ve got the answer, along with a handy explanation of how to arrive at it.
Checkout this video:
## Introduction
When we talk about fractions, we usually think of numbers like 1/2, 3/4, or 5/8. These fractions have a nume... |
# What is the solution of the system of equations?y = -3x + 7y = 2x – 8
What is the solution of the system of equations?
y = -3x + 7
y = 2x - 8
## This Post Has 10 Comments
1. jbug6780 says:
y = -2
x = 3
Step-by-step explanation:
Solve using elimination
1. Rearrange the equations to make it easier to solve
y =... |
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# Counting Techniques
## Number of ways to choose (and potentially arrange) k objects from a group of n object... |
## Division within 10 000
2.4 Division within 10 000
There are various methods for solving appropriate divisions operations for numbers up to 10 000
Examples of division operation questions and solutions
We put 45 small stones equally into 3 jars. Calculate the number of small stones in one jar.
Mathematical sente... |
Home | | Maths 10th Std | Pythagoras Theorem
# Pythagoras Theorem
Among all existing theorems in mathematics, Pythagoras theorem is considered to be the most important because it has maximum number of proofs. There are more than 350 ways of proving Pythagoras theorem through different methods.
Pythagoras Theorem
Am... |
# How to Find Friction Force
## What is Friction
Definition: Frictional force is a force that opposes the motion between two surfaces in contact with each other. The coefficient of static friction, μ is defined as the ratio of the limiting frictional force (F) to the normal reaction (R). The frictional force is measu... |
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