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# How to write an equation for an exponential graph
R squared is equal to one over nine. Uses function notation incorrectly or not at all. See—this is the same form as the inverse variation function formula. When you do have a coefficient in front of the exponent, you can always get rid of it by manipulating the index... |
### Become an OU student
Everyday maths 2 (Wales)
Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.
# 10.3 Solving ratio problems where the total of one part of the ratio is given
Take a look at the work... |
# Riemann Sum & Table Problems (Type 5)
### AP Questions Type 5: Riemann Sum & Table Problems
Information given in tables may be used to test a variety of ideas in calculus including analysis of functions, accumulation, theory and theorems, and position-velocity-acceleration, among others. Numbers and working with nu... |
# How do you find the length of the curve y^2 = 16(x+1)^3 where x is between [0,3] and y>0?
Feb 24, 2015
The answer is: $L = \frac{1}{54} \left(\sqrt{145} - 37 \sqrt{37}\right)$.
The curve can be written:
$y = \pm 4 \sqrt{{\left(x + 1\right)}^{3}}$, but we need only the branch with $y > 0$, so:
$y = 4 \sqrt{{\left... |
# Find all the zeros of
Question:
Find all the zeros of $2 x^{4}-13 x^{3}+19 x^{2}+7 x-3$ if two of its zeros are $(2+\sqrt{3})$ and $(2-\sqrt{3})$.
Solution:
Let $f(x)=2 x^{4}-13 x^{3}+19 x^{2}+7 x-3$
It is given that $(2+\sqrt{3})$ and $(2-\sqrt{3})$ are two zeroes of $f(x)$
Thus, $f(x)$ is completely divisible... |
Home/Archive/Archive - 2015-16/Std-11, Science, Mathematics, Application of Derivatives
## Std-11, Science, Mathematics, Application of Derivatives
Good afternoon students, today we will study maxima and minima increasing decreasing
functions and other applications of Derivatives. Let us start.
Derivatives are very... |
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# Perpendicular Bisectors
## Intersect line segments at their midpoints and form 90 degree angles with them.
... |
# ISEE Middle Level Math : How to divide fractions
## Example Questions
### Example Question #11 : How To Divide Fractions
Simplify:
Explanation:
Rewrite as a division, then solve:
### Example Question #12 : How To Divide Fractions
Evaluate:
Explanation:
To divide any number by a fraction, we can multiply that... |
Seven Minute Trigonometry
Although it’s not possible to learn everything you need to know to quiz out of college trigonometry in 7 minutes, it is possible for you to understand the basics of trigonometry, sine, cosine, tangent, and theta, in just that short a time.
Yes, thanks to the power of the Mark Clarkson method... |
# My Personal Pizza
2 teachers like this lesson
Print Lesson
## Objective
SWBAT create a pizza and name the different fractions for the slices by using fraction pieces.
#### Big Idea
Different fractions can be used to make up a whole.
## Whole Class Discussion
15 minutes
In today's lesson, the students learn to... |
# 2.6: Chapter 2 Review
Difficulty Level: At Grade Created by: CK-12
## Symbol Toolbox
\begin{align*}\rightarrow\end{align*} if-then
\begin{align*}\land\end{align*} and
\begin{align*}\therefore\end{align*} therefore
\begin{align*}\sim\end{align*} not
\begin{align*}\lor\end{align*} or
Keywords
Inductive Reasoni... |
# Sum of Sequence of Squares
## Theorem
$\displaystyle \forall n \in \N: \sum_{i \mathop = 1}^n i^2 = \frac {n \left({n + 1}\right) \left({2 n + 1}\right)} 6$
## Proof 1
Proof by induction:
For all $n \in \N$, let $P \left({n}\right)$ be the proposition:
$\displaystyle \sum_{i \mathop = 1}^n i^2 = \frac{n \left({... |
# Find the equation of the tangent and normal to the curve y=cosx at x=π/3?
Jun 22, 2018
Tangent's equation is $y = - \frac{\sqrt{3}}{2} x + \frac{\pi}{2 \sqrt{3}} + \frac{1}{2}$
Normal's equation is $y = \frac{2}{\sqrt{3}} x - \frac{2 \pi}{3 \sqrt{3}} + \frac{1}{2}$
#### Explanation:
First, you find the first der... |
# Focus on Math
## Helping children become mathematicians!
### How Many More to Make 30? February 12, 2013
This is an activity I created to use with two grade 2 classes that I work with at Charlie Lake Elementary. In BC, grade two students work extensively with numbers to 100. The activity, like “How many more to ma... |
# Binomial theorem
### Binomial calculator raised to some exponent
The structure of the calculator is as follows:
\left( \text{Monomial 1} + \text{Monomial 2} \right)^{\text{Exponent}} = \text{Result}
• You can enter decimal values, but it is best to only enter whole values
• Do not enter letters or other character... |
Is 13212 a prime number? What are the divisors of 13212?
## Is 13212 a prime number?
No, 13212 is not a prime number.
For example, 13212 can be divided by 2: 13212 / 2 = 6 606.
To be 13212 a prime number, it would have been required that 13212 has only two divisors, i.e., itself and 1.
## Parity of 13212
13212 is... |
# Algebraic Expressions
In these lessons, we will learn what variables, constants, terms, expressions and coefficients are in algebra.
The following diagram gives an example of algebraic expression. Scroll down the page for more examples.
### Algebraic Terms & Expressions
In mathematics, often the value of a certai... |
## The Decimal Point: How a 7-year-old Invented Something Better
By Raphael Kohlberg
The decimal point baffles many children. They often don’t know what it’s for and what the numbers that follow it represent. It doesn’t have to be this way! The best success I’ve had teaching the decimal point has come from guiding my... |
# How do you solve the following system: 7x - y = 10 , 8x - y = 13 ?
Jan 6, 2016
#### Answer:
$x = 3$ and $y = 11$
#### Explanation:
$7 x - y = 10$$\ldots \ldots \ldots \ldots \ldots . . \left(i\right)$
$8 x - y = 13$$\ldots \ldots \ldots \ldots \ldots \ldots \left(i i\right)$
Subtract $\left(i\right)$ from $\le... |
# Solving Simple Inequalities
## Presentation on theme: "Solving Simple Inequalities"— Presentation transcript:
Solving Simple Inequalities
1-5 Solving Simple Inequalities Pre-Algebra Warm Up Solve. 1. x + 6 = 13 2. 8n = 48 3. t 2 = 56 4. 6 = x = 7 n = 6 t = 58 z 6 z = 36 Homework out to check!
Learn to solve and ... |
# 4 Examples Of Rational Numbers
In the context of mathematics, a rational number is a number that can be expressed as the ratio of two integers. A rational number is a number that is equal to the quotient of two integers p and q. In other words, a rational number can be expressed as some fraction where the numerator ... |
Permutation and Combination
# Permutation and Combination
## Concept of Permutation and Combination
Permutation is an arrangement of objects in a specific order. There are n! ways to permute n objects, where n! is the product of all the different permutations of n objects.
Fill Out the Form for Expert Academic Guid... |
Review question
# Can we find the sum of the integers from $2k$ to $4k$ inclusive? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource
Ref: R5849
## Solution
1. The positive integer $k$ is given.
1. Find, in terms of $k$, an expression f... |
Lesson Plan
## Midpoints, Distance, and Slope
• Assessment Anchors
• Eligible Content
• Big Ideas
• Mathematical statements can be justified through deductive and inductive reasoning and proof.
• Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many e... |
## Least Squares Linear Predictor¶
In this section we are going to step away from the bivariate normal distribution and see if we can identify the best among all linear predictors of one numerical variable based on another, regardless of the joint distribution of the two variables.
For jointly distributed random vari... |
# Absolutely
##### Absolute Value
The majority of students learn about absolute value long before high school. That is, they learn a lot of wrong things about absolute value.
• They learn that “the absolute value of a number is the number without its sign” or some such nonsense. All numbers, except zero have a sign!... |
# Making sense of irrational numbers
Hello mathematicians!
Why do I call you a mathematician? Yes, you all are excellent. Since junior and senior KG, you have met with the numbers. White pencil and black slate both were your friend to draw every number and loudly say, “it’s a one, two, …”. Later we learned tables whi... |
Class 10
### Topic Covered
♦ Elimination Method
### Elimination Method
=> Now let us consider another method of eliminating (i.e., removing) one variable. This is sometimes more convenient than the substitution method. Let us see how this method works.
Q 3139578412
The ratio of incomes of two persons is 9 : 7 and ... |
At a Glance - Compound Events
In the world of probability, compound events are probabilities of two or more things happening at once. For example, what is the probability that you forgot to do your homework and there will be a pop quiz in class?
We'll go over three different ways to compute these probabilities (organ... |
# Exercise 6.3
### 1. 5x2 × 4x3
#### Solution:
To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices. However, use of these laws is subject to their applicability in the given expressions.
In the present problem, to perform the multiplication, we can proceed as fo... |
# Solving Rational Equations in Algebra
Many word problems about proportions and ratios require you to solve a rational equation. (SEE BOTTOM OF ARTICLE FOR SOLUTION)
A rational function is a fraction where the numerator and denominator are both polynomials. In the context of algebraic equation solving, a rational eq... |
# Elements of the circumference
🏆Practice circle
## What is circumference?
This question is not easy to answer and even more complicated to understand. If you imagine any point on a flat surface and a series of points whose distance from that point is identical, then you are looking at a circle.
## Test yourself o... |
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# Experimental probability for AQA GCSE Maths
1. Understanding randomness
2. Understanding fairness
3. Understanding equally likely events
4. Calculating outcomes of multiple experiments
5. Expected frequencies and theoretical probability
When a random process is occuring, it is rare that the same r... |
# Fractions of an Amount - All Types
## Fractions of an Amount - How it Works - Video with Diagram
### Example 1a
Example 1a:
For this example, the fraction, 2/3, tells us so much. The 2 (numerator) tells us how many equal sections we need and the 3 (denominator) tells us how many total sections we need. The amount... |
# Addition And Subtraction In Vedic Maths
Addition and subtraction in vedic maths
Vedic maths Addition
Usually if we want to add to numbers say 52 and 66 we would add the unit digits. and if there is any remainder we will bring it to the tens digit and atlast we will add the tens digit.
Now we will do it in the ... |
# Lesson 4: Calculating Probabilities for Chance Experiments with Equally Likely Outcomes
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1 Lesson : Calculating Probabilities for Chance Experiments with Equally Likely O... |
Assertion and Reason Questions for Class 9 Maths Chapter 8 Quadrilaterals
Home » CBSE Class 9 Maths » Assertion Reason Questions for Class 9 Maths » Assertion and Reason Questions for Class 9 Maths Chapter 8 Quadrilaterals
Assertion and Reason Questions for Class 9 Maths Chapter Quadrilaterals
Directions:
(a) Assert... |
V.T.U.
Web-Based Education
Engineering Mathematics – I (MAT-11)
By Dr. K.S. Chandrashekhar
Dept. of Mathematics, N.I.E.,
Mysore-8
Lesson 1 Differential Equations
Session – 1
Introduction
Many problems in all branches of science and engineering when analysed for putting in a
mathematical form assumes the form of a diff... |
### Ratio and Proportion
Ratio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of a:b, then it is a ratio whereas a proportion states that two ratios are equal. Here, a and b are any two integers. The ratio and proportion are the two important concepts, and it is the... |
# Simple Interest Questions
FACTS AND FORMULAE FOR SIMPLE INTEREST QUESTIONS
1. Principal: The money borrowed or lent out for a certain period is called the principal or the sum.
2. Interest: Extra money paid for using other's money is called interest
3. Simple Interest (S.I.) : If the interest on a sum borro... |
Free Algebra Tutorials!
Try the Free Math Solver or Scroll down to Tutorials!
Depdendent Variable
Number of equations to solve: 23456789
Equ. #1:
Equ. #2:
Equ. #3:
Equ. #4:
Equ. #5:
Equ. #6:
Equ. #7:
Equ. #8:
Equ. #9:
Solve for:
Dependent Variable
Number of inequalities to solve: 23456789
In... |
## Sunday, April 27, 2014
### Combinations: Arranging Permutations with Three Ascending Consecutive Numbers
Question: How many ways can a digits of a number be arranged so that at least three digits are in (i) ascending order and (ii) consecutive positions?
The Number 1234 (4 digit numbers)
Question: How many way... |
##### Math Word Problems For Dummies
If you need to calculate someone’s salary increase or raise based on the percentage of the raise, you can do this using the distributive property. Here’s an example:
Alison’s salary was \$40,000 last year, and at the end of the year she received a 5% raise. What will she earn this... |
### Counting Factors
Is there an efficient way to work out how many factors a large number has?
### Repeaters
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
### Oh! H... |
# Law of Sines
## Definition
The Law of Sines is a relationship linking the sides of a triangle with the sine of their corresponding angles. The statement is as follows: Given triangle $$ABC$$, with corresponding side lengths $$a, b$$ and $$c$$ and corresponding angles $$\alpha, \beta$$ and $$\gamma$$, and $$R$$ as t... |
## Modeling and Finding Equivalent Fractions
### Learning Outcomes
• Model equivalent fractions
• Find equivalent fractions
Let’s think about Andy and Bobby and their favorite food again. If Andy eats ${\Large\frac{1}{2}}$ of a pizza and Bobby eats ${\Large\frac{2}{4}}$ of the pizza, have they eaten the same amount ... |
# Completing the Square: Two Geometrical Proofs
On this website I previously showed you why the formulas used to complete the square work – and how they can be used to derive formulas such as the quadratic equation. Now, I’ll be doing something different, but related… On this post, I’ll be showing you how to come up w... |
Serviceline Industrial Sensors
Serviceline Explosion Protection
# Did You Find Out? Get the Answer to the Riddle of E-News Issue No. 6, November 2019
2019-11-13
## Field Trip to Industry 4.0
How old is the chemical plant and the automation technology it uses?
A group of students goes on a field trip to a chemical ... |
<meta http-equiv="refresh" content="1; url=/nojavascript/">
# Medians
## Line segment that joins a vertex and the midpoint of the opposite side of a triangle.
%
Progress
Practice Medians
Progress
%
Medians
What if your art teacher assigned an art project involving triangles? You decide to make a series of hanging t... |
# 10.3 | Finding and Using Taylor Series
Find the Taylor series representation for $$\displaystyle f(x) = \frac{1}{1+x}$$ at $$x=2$$.
\begin{aligned} f(x) & = \frac{1}{1+x} = \frac{1}{3+(x-2)} \\ & = \frac{1}{3 \left[ 1 + \left( \frac{x-2}{3} \right) \right]} = \frac{1}{3} \frac{1}{1-\left(-\frac{x-2}{3} \right)} \\ ... |
# NCERT Solutions For Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.2
Here, Below you all know about NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.2 Question Answer. I know many of you confuse about finding Chapter 14 Mathematical Reasoning Ex 14.2 Of Class 11 NCERT Solutions. So,... |
# A positive integer is of the form $3q+1$, $q$ being a natural number. Can you write its square in any form other than $3m+1$, $3m$ or $3m+2$ for some integer $m$? Justify your answer.
Given: A positive integer of the form $3q\ +\ 1$.
To prove: Here we have to check if the square of $3q\ +\ 1$ is in any form other t... |
# How To Calculate The Mean, Median, And Mode
How To Calculate The Mean, Median, And Mode? Mean, Median, and Mode are 03 types of averages. There are many averages in statistics, but Mean, Median, and Mode are the most common. Use the below given Formula and Shortcut Tricks to calculate the Mean, Median, And Mode in a... |
# Video: AQA GCSE Mathematics Higher Tier Pack 5 • Paper 2 • Question 13
Here is some information about the time spent in a week reading fiction books by students in a school. Shortest time: 15 minutes, longest time: 8 hours, lower quartile: 1 hour 15 minutes, interquartile range: 3 hours 30 minutes, median time: 3 ho... |
# Applications of Differentiation
A LevelAQAEdexcelOCR
## Applications of Differentiation
In this section, we’ll look at how to use differentiation in mechanics and practical problems.
Make sure you are happy with the following topics before continuing.
A LevelAQAEdexcelOCR
## Finding Maximum and Minimum Values o... |
Tamilnadu State Board New Syllabus Samacheer Kalvi 8th Maths Guide Pdf Chapter 3 Algebra Ex 3.3 Text Book Back Questions and Answers, Notes.
## Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 3 Algebra Ex 3.3
Question 1.
Expand
(i) (3m + 5)2
(ii) (5p – 1)2
(iii) (2n – 1)(2n + 3)
(iv) 4p2 – 25q2
(i) (3m + 5)2
Co... |
# Quadrilateral with equal opposite sides is a parallelogram
In this chapter we will prove that “any quadrilateral with equal opposite sides is actually a parallelogram.
Given:
Consider quadrilateral ABCD in which opposite sides are equal.
AB = CD and AD = BC
To Prove:
Prove that the quadrilateral is parallelogram.
... |
# Difference between revisions of "2004 AMC 12B Problems/Problem 14"
## Problem
In $\triangle ABC$, $AB=13$, $AC=5$, and $BC=12$. Points $M$ and $N$ lie on $AC$ and $BC$, respectively, with $CM=CN=4$. Points $J$ and $K$ are on $AB$ so that $MJ$ and $NK$ are perpendicular to $AB$. What is the area of pentagon $CMJKN$?... |
TOPICS
Exercise - 12.1
Question-1 :- A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
Solution :-
``` Side of traffic signal board = a
Peri... |
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# Let the integral $I = \int\limits_0^1 {\dfrac{{{x^3}\cos 3x}}{{2 + {x^2}}}dx}$. Then which condition on $I$ holds true$\left( a \right){\text{ }}\dfrac{{ - 1}}{2} < I < \dfrac{1}{2} \\ \left( b \right){\text{ }}\dfrac{{ - 1}}{3} < I < \dfrac{1}{... |
# Linear Algebra
```A LEVEL PURE MATHS REVISON NOTES
1 ALGEBRA AND FUNCTIONS
a) INDICES
Rules to learn :
π₯ π × π₯ π = π₯ π+π
π₯ π ÷ π₯ π = π₯ π−π
3
(π₯ π )π = π₯ ππ
1
π₯ −π =
π
1
π₯π
π
π
π
π₯ π = √π₯ π = ( √π₯ )
Solve 3... |
# rational number
The set of rational numbers, usually denoted by $$\mathbb{Q}$$, is the subset of real numbers that can be expressed as a ratio of integers, that is, as ratios of positive or negative whole numbers, like $$\frac{2}{3}$$ or $$\frac{-13}{5}$$. Real numbers that cannot be so expressed are called irration... |
Distance Point Construction
Historical records show that besides Alberti’s construction, there were other methods for constructing pavimenti. One of them was known as the distance point construction, and was found in the treatise of Jean Pelerin (1445 – 1522), also known as the Viator. Entitled De Artificiali Perspe... |
# 5+3/4n+8=-2/4n+8
## Simple and best practice solution for 5+3/4n+8=-2/4n+8 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so dont hesitate to use it as a solution of your homework.
If it's not what You are looking for type in the equation solver your own... |
# Signals & Systems Questions and Answers – Basics of Linear Algebra
This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Basics of Linear Algebra”.
1. Find the values of x, y, z and w from the below condition.
$$5\begin{bmatrix} x & z \\ y & w \\ \end{bmatrix} = \begin{bmatrix} 2 & 10... |
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# Tutor profile: Dylan H.
Inactive
Dylan H.
Tutor for 5 years
Tutor Satisfaction Guarantee
## Questions
### Subject:SAT
TutorMe
Question:
$$a^2–26a+69=0$$. If $$a–5>0$$, what is the value of a? A. 3 B. 5 C. 18 D. 23
Inactive
Dylan H.
There are two methods for solving this problem. First ... |
# The Method of Partial Fractions
## Introduction
Early in Algebra you learn how to combine "simple'' fractions into a "more complicated'' one. Here is a typical example:
The Method of Partial Fractions does the opposite: It dissects a complicated fraction into a sum of simple fractions. While this is a little more ... |
# 2013 AMC 10A Problems/Problem 7
## Problem
A student must choose a program of four courses from a menu of courses consisting of English, Algebra, Geometry, History, Art, and Latin. This program must contain English and at least one mathematics course. In how many ways can this program be chosen?
$\textbf{(A)}\ 6\q... |
#### xaktly | Mathematics
Trigonometric functions
### From a black box to a function
So far we've looked at trig functions as ratios of sides, and where those are known, that's easy to calculate. The other way we've used them is as "black boxes" — we put a number into a calculator and we get one back out. Here's a t... |
# How to convert Binary to Octal?
To convert a binary number to octal, start by multiplying each digit of the binary number by 2 raised to the nth power, where n is the position of the digit from the right.
For example, if the binary number is 1011, then you would multiply 1 by 2^3, 0 by 2^2, 1 by 2^1, and 1 by 2^0. ... |
# 7.08 Division where answers are decimals
Lesson
We've previously learned how to use a division algorithm with short division . Let's practice this concept.
### Examples
#### Example 1
Find the value of 856\div8.
Worked Solution
Create a strategy
Use short division.
Apply the idea
Set up the short division.... |
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# Systems Using Substitution
## Solve for one variable, substitute the value in the other equation
0%
Progres... |
## How do you get 30% of 80?
Percent means per one-hundred and hence 30% is 30/100. Thus 30% of 80 is (30/100) x 80 = 24.
## What number is 35% of 80?
28
How do you find 70 percent of a number?
Example 1. Find 70% of 80. Following the shortcut, we write this as 0.7 × 80. Remember that in decimal multiplication, yo... |
225-Notes02
225-Notes02 - Stat 225 Lecture Notes "Counting Techniques"...
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Stat 225 Lecture Notes “Counting Techniques” Ryan Martin Spring 2008 1 Basic Counting Rule Recall that in the classical probability model, the probability of an event E is P ( E )... |
1.4: Calculating Limits with Limit Laws
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$... |
# What Is The Median Of These Numbers?
## How do you find the mean median and mode?
– Mode-The most repetitive number.
– Median:The number in the MIDDLE when they are IN ORDER.
– Mean- The AVERAGE OF ALL NUMBERS: You add up all the numbers then you divide it by the TOTAL NUMBER of NUMBERS.
– Range – THE BIGGEST mi... |
# Tips for Teaching Ratios and Rates in 6th, 7th and 8th Grade Math
Are your students hitting a bit of a roadblock when it comes to wrapping their heads around ratios and rates? Need a fun and colorful way to dive into these math essentials? Well, you’re in for a treat! In this blog post, I’m about to unveil how I tea... |
# SOLUTION: How do I graph 1/2x-4y=6?
Algebra -> Algebra -> Linear-equations -> SOLUTION: How do I graph 1/2x-4y=6? Log On
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Alge... |
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```Chapter 6
Continuous Random Variables
McGraw-Hill/Irwin
Continuous Random
... |
# Lesson 3Reasoning about Contexts with Tape Diagrams (Part 2)
Let’s see how equations can describe tape diagrams.
### Learning Targets:
• I can match equations and tape diagrams that represent the same situation.
• If I have an equation, I can draw a tape diagram that shows the same relationship.
## 3.1Find Equiva... |
## Fractions
2.1 Fractions
We will learn to solve basic operations involving fractions. An improper fraction is a fraction with the numerator equal to or greater than the denominator. As example, $$\dfrac{24}{5}$$ is an improper fraction because the value of the numerator ($$\color{red}{24}$$) is greater than the va... |
# Linear Programming in Excel
This tutorial demonstrates how to use Excel to tackle integer linear programming problems. With the Solver add-in in Microsoft Excel, users may find the solution for an integer linear program rapidly. We will walk through this process in simple, straightforward steps today. The final port... |
# Aptitude Logical Reasoning Time and Distance 2019 CMAT Part 5
1. A boy goes to his school from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming. The distance between his house and school is?
A. 5 km
B. km
C. 6 km
D. km
Ans: C
Explanation:
Average speed... |
# Missing Number Math Test: If You Are A Genius, What Is The Missing Number?
Missing Number Math Test: If you would like to know your intelligence level, take a short break and solve this riddle.
Today’s challenge will stimulate your thinking. In the image appearing on your screen, there is a mathematical challenge. ... |
# Dividing Fractions
Consider the two fractions with same or different denominators. These two fractions can be divided by taking the reciprocal of second fraction and multiply this fraction with the first fraction. That is,
Steps to divide fractions:
Step 1: Take the reciprocal of the divisor.
Step 2: Multiply the... |
Lesson Video: Simplifying Trigonometric Expressions Using Trigonometric Identities | Nagwa Lesson Video: Simplifying Trigonometric Expressions Using Trigonometric Identities | Nagwa
# Lesson Video: Simplifying Trigonometric Expressions Using Trigonometric Identities Mathematics
In this video, we will learn how to sim... |
# Difference between revisions of "2004 AMC 10B Problems/Problem 21"
## Problem
Let $1$; $4$; $\ldots$ and $9$; $16$; $\ldots$ be two arithmetic progressions. The set $S$ is the union of the first $2004$ terms of each sequence. How many distinct numbers are in $S$?
$\mathrm{(A) \ } 3722 \qquad \mathrm{(B) \ } 3732 \... |
Integration Using Euler's Formula
Get Integration Using Euler's Formula essential facts below. View Videos or join the Integration Using Euler's Formula discussion. Add Integration Using Euler's Formula to your PopFlock.com topic list for future reference or share this resource on social media.
Integration Using Euler'... |
Algebra 1 Online! Henrico County Public Schools, Virginia
Module - Polynomials
Introduction - Animal Populations
Lessons 1- Multiplying Monomials 2- Dividing Monomials 3- Scientific Notation 4- Degree, Ascending, and Descending Order 5- Adding and Subtracting Polynomials 6- Multiplying Polynomials by Monomials 7- Mu... |
# Fractal Geometry
## Fractal Dimension
Ordinary dimension is always given as an integer. For instance, a line is one-dimensional, a square is two-dimensional, and a cube is three-dimensional. However, fractal dimension can be a non-integer, i.e. fractal dimension can be a fraction!
To understand why fractal dimensi... |
# What is the antiderivative of x^3/(1+x^2)?
Jul 7, 2016
$\frac{1}{2} \left\{{x}^{2} + 1 - \ln \left({x}^{2} + 1\right)\right\} + C .$
OR
$\frac{1}{2} \left\{{x}^{2} - \ln \left({x}^{2} + 1\right)\right\} + {C}_{1} ,$ where ${C}_{1} = C + \frac{1}{2.}$
#### Explanation:
Let $I = \int {x}^{3} / \left(1 + {x}^{2}\r... |
# Series - Parallel Resistances the Combination
Whenever we work with circuits in the real world, they are seldom as straightforward as a simple series or parallel circuit. Normally, they are a combination of the two, called a SERIES-PARALLEL circuit. While they look forbidding at first, you must keep in mind that ALL... |
## What is the slope of 4x 3y 12?
Therefore the slope is 4/3.
## What type of border line should the inequality have 4x 3y 12?
The boundary line will be solid because the inequality operator contains an “or equal to” clause.
## Is 4x 3y 12 a linear equation in two variables?
The equation 4x – 3y = 12 is a linear e... |
# What is the slope of any line perpendicular to the line passing through (16,6) and (-2,-13)?
Apr 3, 2018
$- \frac{18}{19}$
#### Explanation:
Let's first find the slope of the line passing through the aforementioned points
$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} \rightarrow$ Finding a slope via two points fo... |
# Transpose of a matrix - properties and formulas -
Definition
- Definition
- Examples
Properties
- Product
- Inverse
- Determinant
- Trace
- Linearity
Definition
A matrix in which the row and column elements of a matrix are exchanged is called the transposed matrix of that matrix. The transpose of a matrix $A$ is ... |
Set (mathematics)
Informally, a set is thought of as any collection of distinct elements. The relevant formal definitions are given in a branch of mathematics known as set theory.
Introduction
The basic property of sets is that they are solely determined by the elements they contain (this is called extensionality). ... |
## NCERT Solutions For Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.1
Free download NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.1, Ex 5.2, Ex 5.3, Ex 5.4, Ex 5.5, Ex 5.6 and Ex 5.7, 5.8 and 5.9 Understanding Elementary Shapes PDF for CBSE 2020 Exams.
### Understanding Elementary Shapes Clas... |
# Math
• ### Eureka Math – 3rd – Lesson 7
Compare fractions – How can we compare fractions? Join Ms. Roose as she partitions wholes into unit fractions and reasons about their size.
• ### Eureka Math – 3rd – Lesson 8
Compare fractions with different wholes – How can we compare fractions when our wholes are differen... |
# Evaluate the following integrals:
Question:
Evaluate the following integrals:
Solution:
Let $t=\sin ^{2} x$
$d t=2 \sin x \cos x d x$
we know $\sin 2 x=2 \sin 2 x \cos 2 x$
therefore, $d t=\sin 2 x d x$
$\int \frac{\sin 2 x}{\sqrt{\sin ^{4} x+4 \sin ^{2} x-2}} d x=\int \frac{d t}{\sqrt{t^{2}+4 t-2}}$
Add and... |
# RD Sharma Class 10 Solutions Chapter 9 Arithmetic Progressions Exercise 9.5 (Updated for 2021-22)
RD Sharma Class 10 Solutions Chapter 9 Exercise 9.5: The selection of terms in an A.P. is the main focus of the RD Sharma Class 10 Maths Solutions chapter 9 exercise 9.5. Kopykitab created answers to these exercise prob... |
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