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## Simplifying a sum of consecutive cubes
If you were asked to find the sum of the first four cubes, you would easily be able to do so:
$1^3 + 2^3 + 3^3 + 4^3 = 100$
But here you may notice something interesting:
$1^3 + 2^3 + 3^3 + 4^3 = (1+2+3+4)^2$
It turns out that this holds for the sum of the first $n$ cubes ... |
# Radius is half of Diameter
What is a radius of circle?
Radius is the line joining from center to point on circle.
In a particular circle, there can be many radius but they have same length
Given above is the image of a circle with center O
Here OA, OB, OC and OD are the radius since they are straight line joining t... |
# Class 10 Maths Books English Medium chapter 1
CBSE Class 10 Maths Books English Medium chapter 1 Ex 1.1 homework guffo.in
Chapter 1: Real Numbers
Example 1 : Use Euclid’s algorithm to find the HCF of 4052 and 12576.
अध्याय 1: रियल नंबर
उदाहरण 1: 4052 और 12576 के एचसीएफ को खोजने के लिए यूक्लिड के एल्गोरिदम का उपयो... |
### Theory:
Consider the quadratic equation $$ax^2 + bx + c = 0$$, where $$a \ne 0$$.
Let us find the roots of this equation by the method of completing the square.
Divide the equation by $$a$$.
${x}^{2}+\frac{b}{a}x+\frac{c}{a}=0$
Move the constant to the right side.
${x}^{2}+\frac{b}{a}x=-\frac{c}{a}$
Add the ... |
LetsPlayMaths.Com
WELCOME TO THE WORLD OF MATHEMATICS
Class 3 Length
Length
Conversion of Meters into Centimeters
Conversion of Centimeters into Meters
Conversion of Kilometers into Meters
Conversion of Meters into Kilometers
Addition of Meters and Centimeters Without Carrying
Addition of Meters and Centimeter... |
# 180 Days of Math for Fourth Grade Day 119 Answers Key
By accessing our 180 Days of Math for Fourth Grade Answers Key Day 119 regularly, students can get better problem-solving skills.
## 180 Days of Math for Fourth Grade Answers Key Day 119
Directions: Solve each problem.
Question 1.
24 + 29 = __________
24
29
53... |
# AP Statistics Curriculum 2007 Hypothesis Var
(Difference between revisions)
Revision as of 23:12, 6 February 2008 (view source)IvoDinov (Talk | contribs)← Older edit Current revision as of 16:32, 1 May 2008 (view source) (→ General Advance-Placement (AP) Statistics Curriculum - Testing a Claim about a Standard Devi... |
# 9.1 Ratios and Proportions. You will learn to use ratios and proportions to solve problems. 1) ratio 2) proportion 3) cross products 4) extremes 5) means.
## Presentation on theme: "9.1 Ratios and Proportions. You will learn to use ratios and proportions to solve problems. 1) ratio 2) proportion 3) cross products 4)... |
# Question Video: Finding the Solution Set of Root Equations Involving Absolute Value Mathematics • 9th Grade
Find the solution set of the equation √(4𝑥² − 28𝑥 + 49) = |𝑥 + 4|.
03:52
### Video Transcript
Find the solution set of the equation the square root of four 𝑥 squared minus 28𝑥 plus 49 is equal to the a... |
# How do you add 2 different variables?
## How do you add 2 different variables?
How to Add and Subtract Variables
1. Addition. In this equation, you can add all of the coefficients (2, 5, and 4) because the variables are the same (a). 2a + 5a + 4a = 11a.
2. Subtraction. In this equation, you can subtract all of the... |
# Manipulating Surds
## Manipulating Surds
• Understand the definition: Surds are square roots which cannot be simplified to a rational number. They are ‘irrational’ numbers and are often left in surd form to maintain precision.
• Know how to simplify surds: Simplifying a surd involves removing any-square rootable f... |
# Chapter 8: Quadratic Equations Exercise – 8.10
### Question: 1
The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.
### Solution:
Let the length of one side of the right triangle be x cm then,
the other si... |
# NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.2
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.2 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.2. https://mcqquestions.guru/ncert-s... |
# Operations With Real Numbers SOL 7
## Presentation on theme: "Operations With Real Numbers SOL 7"— Presentation transcript:
Operations With Real Numbers SOL 7
Operations With Real Numbers SOL 7.3 by Lisa Beebe Chincoteague Combined School Commutative Property Associative Property Distributive Property Identity Prop... |
## Stability in Numbers
• Lesson
3-5
1
In this lesson, students apply their knowledge of addition equations to create number sentences using an electronic balance tool.
To begin the lesson, ask students what an addition sentence or addition equation looks like. They might respond with, 9 + 7 = 16. Students should no... |
# Factors of 6
Definition of factors of 6: If a number completely divides 6 without a remainder, then that number is called a factor of 6.
By the above definition, we can say that the factors of 6 are the divisors of 6. In this section, we will learn about the factors of 6 and the prime factors of 6.
## Highlights o... |
# Solve the following quadratic equation by factorization: $\frac{1}{(x-1)(x-2)}+\frac{1}{(x-2)(x-3)}+\frac{1}{(x-3)(x-4)}=\frac{1}{6}$
Given:
Given quadratic equation is $\frac{1}{(x-1)(x-2)}+\frac{1}{(x-2)(x-3)}+\frac{1}{(x-3)(x-4)}=\frac{1}{6}$.
To do:
We have to solve the given quadratic equation.
Solution:
$... |
# How can we prove that a negative number multiplied/divided/subtacted by a negative gives a positive result?
## I've always wondered if we could prove this...
Apr 15, 2018
It's not the case that a negative minus a negative is always positive. For instance, $- 3 - \left(- 2\right) = - 3 + 2 = - 1$, which is still ne... |
Whether mixed numbers have the same denominators or different denominators, adding them is a lot like adding whole numbers: you stack them up one on top of the other, draw a line, and add. For this reason, some students feel more comfortable adding mixed numbers than adding fractions.
Here’s how to add two mixed numbe... |
Online Tution » Important Question » Mean Formula and Meaning in Maths
# Mean Formula and Meaning in Maths
## What is the Definition of Mean?
Mean is the average of all the set of numbers which is used to get the result between the number of numbers. It is calculated by adding together all the numbers in a s... |
# Standards-Aligned Resources for Your Classroom
Manage curriculum, personalize instruction, and detect early warnings with Kiddom
### Kiddom Supports All Standards, Including 3.MD.3
Common Core Mathematics Standards
### 3.MD.3
Draw a scaled picture graph and a scaled bar graph to represent a data set with several... |
# Multiplication Formula
In this page multiplication formula we can find basic formulas in addition, subtraction, multiplication and division using fraction. By using this method we can easily add, subtract, multiply and divide any two fractions.
Difference:
If we want to multiply two fractions we have to multiply t... |
## Question: How To Name A Line In Geometry?
When we draw lines in geometry, we use an arrow at each end to show that it extends infinitely.
1. A line can be named either using two points on the line (for example, ↔AB ) or simply by a letter, usually lowercase (for example, line m ).
2. A segment is named by its two ... |
## College Algebra (11th Edition)
$x=\left\{ -\dfrac{14}{3},8 \right\}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $\log_4[(3x+8)(x-6)]=3 ,$ change to exponential form. Then express the resulting equation in the form $ax^2+bx+c=0.$ Use the Quadratic Formula to solve for the values of the variable. Th... |
# Introduction to Proofs : Functions, Relations, & Cardinality
## Example Questions
← Previous 1
### Example Question #1 : Intro To Proofs
If
Find the cardinality of
Explanation:
The question is asking us to find the number of elements in the intersection of B and B .
We simply find the common elements of the t... |
### Standard Deviation
Consider the following data about the heights of plants in Jonathan's garden:
3cm, 4cm, 5cm, 7cm, 11cm
Now, let's calculate the mean - μ - of these values.
μ = (3 + 4 + 5 + 7 + 11)/5 = 6cm
If we use this value to describe the mean height of plants, we immediately run into difficulties; because... |
# Problem of the Week Problem B and Solution 'Temp'ting Crickets
## Problem
Crickets can help determine the temperature, in degrees Celsius. One possible way to make this calculation is to follow the steps below.
• Step 1: Count the number of chirps in $$25$$ seconds.
• Step 2: Divide the number from Step 1 by $$3$... |
Question 1: Find the modulus and argument of the following complex numbers and hence express each one of them in polar form:
$\displaystyle \text{i) } 1+i \hspace{1.0cm} \text{ii) } \sqrt{3}+i \hspace{1.0cm} \text{iii) } 1-i \hspace{1.0cm} \text{iv) } \frac{1-i}{1+i} \hspace{1.0cm} \text{v) } \frac{1}{1+i}$
$\display... |
1. ## Dice session :-)
10 dice is rolled, what is the probability of:
a) getting one & two once and all other numbers exactly twice
b) getting one & two exactly 3 times
c) getting four even and six odd numbers
d) getting one & three two times, if we know that two appeared once and five 3 times
2. The correct answer ... |
### AVERAGE
1. Explanation :
There are five prime numbers between 30 and 50. They are 31,37,41,43 and 47.Therefore the required average=$$\frac{(31+37+41+43+47)}{5}$$=$$\frac{199}{5}$$ =39.8.
1. Explanation :
sum of first n natural numbers=n(n+1)/2; So,sum of 40 natural numbers=$$\frac{(40*41)}{2}$$=820.
Therefore ... |
The additive inverse, or opposite, of a number n is the number which, when added to n, yields zero. The additive inverse of n is denoted −n.
For example:
• The additive inverse of 7 is −7, because 7 + (−7) = 0;
• The additive inverse of −0.3 is 0.3, because −0.3 + 0.3 = 0.
Thus by the last example, −(−0.3) = 0.3.
T... |
# 7.07 Dot plots
Lesson
The dot plot is a useful way to express discrete data in a visually simple manner. The main advantages of the dot plot are that we can find the mode and range very easily, as well as quickly see how the data is distributed. The main disadvantages are that we need to count each dot when finding... |
# Cofunction identity of sin function
## Formula
Sexagesimal System
$\sin{(90^\circ-\theta)} \,=\, \cos{\theta}$
$\sin{\Big(\dfrac{\pi}{2}-x\Big)} \,=\, \cos{x}$
In this formula, the angle in degrees is denoted by Theta ($\theta$) and the angle in radians is denoted by $x$.
The angle of sin function is an allied an... |
Part 3: Multiplication
# 3.4: Word problems for multiplying fractions
Notes
In the following, “A/B” represents the fraction “A over B.” For example, “2/3” refers to the fraction “2 over 3” or “two-thirds.”
Word problems for the multiplication problem, A/B x C/D, have the form “A/B of C/D of a unit is how much of a ... |
# rhombus perimeter formula
° rad. The formula for rhombus perimeter is as given perimeter = 4a, where a is the side length as shown in Figure 1. Since all four sides of a rhombus are equal, much like a square, the formula for the perimeter is the product of the length of one side with 4 $$P = 4 \times \text{side}$$ A... |
(Analysis by Benjamin Qi)
Subtask 1: $P=1$
Let's start by computing the following quantity $Q$: the minimum number of moves to move all of liquid $1$ to tube $1$ and all of liquid $2$ to tube $2$. Once we know how to compute this quantity, we can compute $Q'$, the minimum number of moves to move all of liquid $1$ to ... |
Mister Exam
# Graphing y = y=(0.2x^3-0.3x^2+0.1)(-0.1x^5+0.4x^2+4)+0.3
v
from to
does show?
### The solution
You have entered [src]
/ 3 2 \ / 5 2 \
|x 3*x 1 | | x 2*x | 3
f(x) = |-- - ---- + --|*|- -- + ---- + 4| + --
\5 10 10/ \ 10 5 / 10
$$f{\left(x \r... |
## Friday, November 1, 2013
### Counting I : Ways to Avoid Over Counting or Under Counting
Check out Mathcounts here, the best competition math program for middle school students.
Download this year's Mathcounts handbook here.
Question #1: How many ways to count a triple of natural numbers whose sum adds up to 12
if... |
## Precalculus (6th Edition) Blitzer
$(1,-1,1)$
Step 1. Writing a matrix based on the given system of equations, we have $\begin{bmatrix} 1 & -2 & -1 & | & 2 \\ 2 & -1 & 1 & | & 4 \\ -1 & 1 & -2 & | & -4 \end{bmatrix} \begin{array} ..\\-2R1+R2\to R2\\ R1+R3\to R3 \end{array}$ Step 2. Perform row operations given to th... |
Tamil Nadu Board of Secondary EducationHSC Commerce Class 12th
Determine an initial basic feasible solution to the following transportation problem by using least cost method Destination Supply D1 D2 D3 S1 9 8 5 25 Source S2 6 8 4 35 S3 7 6 9 40 Requirement - Business Mathematics and Statistics
Chart
Sum
Determine a... |
Utah Math 2 - 2020 Edition
7.05 Proving triangles congruent
Lesson
Now that we know the criteria for identifying congruent triangles, the next step is to find a way to communicate that knowledge in the form of a proof. Recall two commonly used proof forms, the two-column proof and the paragraph proof.
### Two-column ... |
# For a linear function f, f(-1)=3 and f(2)=4 find an equation for fplease answer soon, I need help badly
mcetner | Certified Educator
Another way to answer this question is that you know any linear function can always be written y = mx + b, where m is the slope.
Find m first, (4 - 3)/(2 - -1)=1/3.
Then plug in one... |
# Binomial Theorem Aptitude Important Formulas, Definitions, & Examples:
#### Overview:
Topic Included: Formulas, Definitions & Exmaples. Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Permutation and Combination Aptitude Notes & Questions. Questions for practice: 10 Questions & Answers with Sol... |
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# Suppose ${a_2},{a_3},{a_4},{a_5},{a_6},{a_7}$ are integers such that,$\dfrac{5}{7} = \dfrac{{{a_2}}}{{2!}} + \dfrac{{{a_3}}}{{3!}} + \dfrac{{{a_4}}}{{4!}} + \dfrac{{{a_5}}}{{5!}} + \dfrac{{{a_6}}}{{6!}} + \dfrac{{{a_7}}}{{7!}}$ Where, $0 \leqsla... |
# 2017 AMC 8 Problems/Problem 18
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
## Problem
In the non-convex quadrilateral $ABCD$ shown below, $\angle BCD$ is a right angle, $AB=12$, $BC=4$, $CD=3$, and $AD=13$. What is the area of quadrilateral $ABCD$?
$[asy]draw((0,0)--(2.4,3.6)--(0,5)... |
Evaluate the integral or show that it is divergent?
Jan 4, 2018
The improper integral converges and equals $\frac{32}{3}$.
Explanation:
First note that
$\int \frac{\mathrm{dx}}{x + 2} ^ \left(\frac{1}{4}\right) = \int {\left(x + 2\right)}^{- \frac{1}{4}} \mathrm{dx} = \frac{4}{3} {\left(x + 2\right)}^{\frac{3}{4}}... |
# How do you solve the inequality 16 - 2c < 14?
Dec 30, 2015
Step by step solution of solving the linear inequality is given below. Please go through the explanation.
#### Explanation:
To solve the inequality $16 - 2 c < 14$
Start by isolating the term containing the variable. This part is done as we do for equali... |
Explain the Hamming Codes in Error Correction
The Hamming code can be used to the data units of any length when we consider the two codewords which have the same length. The Hamming distance between two codewords is represented as the number of positions in which their specific item differs.
Example
Hamming Distance... |
Precalculus by Richard Wright
Are you not my student and
has this helped you?
This book is available
At that time people will see the Son of Man coming in clouds with great power and glory. Mark 13:26 NIV
# 4-10 Applications of Right Triangle Trigonometry
Summary: In this section, you will:
• Solve proble... |
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# Find the derivative of the function.$y = \sqrt {x + \sqrt {x + \sqrt {x}}}$
## $$\frac{1}{2 \sqrt{x}}+1\\\frac{2 \sqrt{x+\sqrt{x}}+1}{2 \sqrt{x+\sqrt{x+\sqrt{x}}}}$$
Derivatives
Differentiation
### Di... |
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# The angle of depression of the top and the bottom of a 7m tall building from the top of tower are ${45^ \circ }$ and ${60^ \circ }$ respectively, find the height of the tower.
Last updated date: 09th Aug 2024
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# Step deviation Method for Finding the Mean with Examples
Statistics is a discipline of mathematics that uses quantified models and representations to gather, review, analyze, and draw conclusions from data. The most commonly... |
# How can you simplify this expression?
$$\frac{(n+1)!}{k! \cdot (n-k+1)!}$$
I don't have any clue. Can $(n-k+1)!$ be simplified into $(n+1)!(k)!$
I am not too familiar with this symbol: !.
• Relevant reading: Factorial and Binomial_coefficient – user2468 Nov 1 '12 at 16:33
• The symbol $!$ refers to factorial. – S... |
# Integers and their Opposites
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Integers and their Opposites
CCSS.MATH.CONTENT.6.NS.C.6.A
## Integers and Their Opposites
Understanding integers and their opposites is like having a superpower in math! Imagine being able to represent any whole number, positive or neg... |
Browse Questions
# Bag I contains 3 red and 4 black balls and bag II contains 4 red and 5 black balls. One ball is transferred from bag I to bag II and then a ball is drawn from bag II at random. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.
Toolbox:
• Accord... |
# Lesson Percentage Word Problems (discount)
Algebra -> Algebra -> Percentage-and-ratio-word-problems -> Lesson Percentage Word Problems (discount) Log On
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides s... |
> > > Geometric Mean Formula
# Geometric Mean Formula
We have used the arithmetic mean in many data-related problems. Here we will see another such term frequently used with data analysis. A geometric mean formula is used to calculate the geometric mean of a set of numbers. It is a type of mean that indicates the cen... |
# Mastering multiplication. Expert tips for fractions with whole numbers
## Crush Math Class with These Expert Tips on Multiplying Fractions with Whole Numbers
Are you struggling to understand how to multiply fractions with whole numbers in your math class? Don't worry, you're not alone! This topic can be tricky for ... |
# Algebra Worksheets
In this page you can get free algebra worksheets for the topic algebra. It will be very useful to students who are in7th,8th and 9th grade students. The students must practice this kind of worksheets to get clear knowledge in algebra. You can find many different questions in these worksheets.
One... |
# The Art of Partitioning a Line Segment!
In geometry, the simple act of drawing a line segment can lead to deeper, fascinating explorations. One such exploration is the partitioning of a line segment. Imagine dividing a chocolate bar into pieces, ensuring each friend gets an equal share, or maybe one gets twice as mu... |
# Matrix Multiplication – Method, Definition With Examples
At Brighterly, we strive to make math enjoyable and accessible to children. Today, we’re diving into a fascinating and fundamental mathematical concept: matrix multiplication. Matrices might seem intimidating initially, but they are actually quite interesting ... |
# Finding Total Volume: Methods and Formulas
January 23, 2024 by JoyAnswer.org, Category : Mathematics
How do you find total volume? Explore methods and formulas for finding total volume. This article provides insights into mathematical approaches for calculating the total volume of different shapes and objects.
## ... |
# Two Tangent Circles and a Square- Problem With Solution
You are givn the perimeter of a small circle to find the radius of a larger circle inscribed within a square.
Problem : In the figure below, the small circle with center B and the larger circle with center C are tangent at point T. A is the vertex of the squa... |
Challenge: Solving the Task Using Inclusion-Exclusion Principle | Probability of Complex Events
Probability Theory Basics
Course Content
Probability Theory Basics
Probability Theory Basics
1. Basic Concepts of Probability Theory
2. Probability of Complex Events
3. Commonly Used Discrete Distributions
4. Commonly Us... |
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# Is 19 A Prime Number?
• Yes the number 19 is a prime number.
• It's a prime because nineteen has no positive divisors other than 1 and itself.
## Prime Factorization Of 19
• Prime factors of 19: 1 * 19
## How To Calculate Prime Number Factors
• How do you calcu... |
Newton's Laws: Chapter Outline || About the Tutorial || Tutorial Topics || Usage Policy || Feedback
## Lesson 2: Force and Its Representation
### Determining the Net Force
If you have been reading through Lessons 1 and 2, then Newton's first law of motion ought to be thoroughly understood.
An object at rest tends t... |
High School Physics + more
# How to use Pascal’s principle (or Pascal’s law) in Hydraulic Car Lift?
Last updated on September 9th, 2021 at 02:06 pm
We will first see what Pascal’s Principle or Pascal’s Law states. Then we will find out with formula and diagram how to apply Pascal’s Law to explain the operating princ... |
# How do you find 1 significant figure?
## How do you find 1 significant figure?
To round to a significant figure:
1. look at the first non-zero digit if rounding to one significant figure.
2. look at the digit after the first non-zero digit if rounding to two significant figures.
3. draw a vertical line after the p... |
# U1A4 Textbook Questions
```In Summary
Key Idea
• Polynomials can be divided in much the same way that numbers are divided.
Need to Know
• A polynomial can be divided by a polynomial of the same degree or less.
• Synthetic division is a shorter form of polynomial division. It can only be used
when the divisor is line... |
It"s really common when learning about fractions to desire to understand how convert a portion like 30/200 into a percentage. In this step-by-step guide, we"ll show you how to revolve any portion into a portion really easily. Let"s take a look!
Want to easily learn or present students exactly how to convert 30/200 to ... |
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# How to calculate a ladder?
Blondel's rule for determining the rise and tread of a staircase The best known ratio is that: 2 a + p = 62/65 cm. This ratio is also known as Blondel's rule and is the one that is commonly used the most.
## How do you calculate the length of a stair?
This will be the number of s... |
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# ZingPath: Representing Linear Inequalities and Two Quantities
Searching for
## Representing Linear Inequalities and Two Quantities
Learn in a way your textbook can't show you.
... |
# 23 Times Table
In 23 times table we will learn how to read and write multiplication table of 23.
We read twenty three times table as:
One time twenty three is 23
Two times twenty three are 46
Three times twenty three are 69
Four times twenty three are 92
Five times twenty three are 115
Six times twenty three ... |
Mathematics » Introducing Integers » Solve Equations Using Integers, The Division Property of Equality
# Modeling the Division Property of Equality
## Modeling the Division Property of Equality
All of the equations we have solved so far have been of the form $$x+a=b$$ or $$x-a=b.$$ We were able to isolate the variab... |
## Engage NY Eureka Math 4th Grade Module 4 Lesson 9 Answer Key
### Eureka Math Grade 4 Module 4 Lesson 9 Problem Set Answer Key
Question 1.
Complete the table.
Refer to the below table.
Explanation:
In pattern block A, the total number that fit around one vertex is 4 and the interior angle measurement is 360° ÷... |
# Question
Abi spent of her money on 2 identical bookmarks and some identical pens. The cost of each bookmark to the cost of each pen was 2:3. She bought some more bookmarks with 2/5 of her remaining money and had 24 bookmarks in the end How many pens did she buy at first?
Source: Ang Mo Kio Primary
Here is how I wo... |
# How do you solve 7( x - 1) + 5= - 2( 3- 4x ) + 5?
Aug 1, 2017
$x = - 1$
Refer to the explanation for the process.
#### Explanation:
Solve:
$7 \left(x - 1\right) + 5 = - 2 \left(3 - 4 x\right) + 5$
Expand.
$7 x - 7 + 5 = - 6 + 8 x + 5$
Simplify.
$7 x - 2 = - 1 + 8 x$
Subtract $7 x$ from both sides.
$- 2 = ... |
# Quant Data Sufficiency for IBPS RRB Officer and Assistant Mains Exam
The Quantitative Aptitude section for IBPS RRB Mains examination consists of 40 questions which constitutes twenty-five percentage of the total weightage in the exam. Data sufficiency is an important topic of this section which tests a candidate’s ... |
How do you find the equation of the XY plane?
XY plane is perpendicular to z-axis and passes through origin, So its equation is , (r −0 ).( z )=0.YZ plane is perpendicular to x-axis and passes through origin, So its equation is , (r −0 ).( x )=0.ZX plane is perpendicular to y-axis and passes through origin, So its equ... |
## Inequalities
7.1 Inequalities
Definition The relationship between two quantities that do not have the same value.
Symbol Meaning $$\gt$$ Greater than $$\lt$$ Less than
Example From the number line above, $$–2$$ lies to the left of $$3$$. So, $$–2$$ is less than $$3$$. Thus, the inequality is $$–2 < 3$$.
Ex... |
# Lesson 14
Surface Area of Right Prisms
### Lesson Narrative
In grade 6, students used nets made up of rectangles and triangles to find the surface area of three-dimensional figures. In this lesson they find surface areas of prisms, and see that structure of a prism allows for shortcuts in adding up the areas of th... |
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# What's Half Of 27?
## Introduction
When it comes to math, we often encounter problems that require us to divide numbers. One of the most common questions that people ask is “what’s half of 27?” While this may seem like a simple question, it can sometimes be confusing, especially for those who are not... |
UPSC > Introduction, Basic Concepts & Formulae: Mensuration- 2
# Introduction, Basic Concepts & Formulae: Mensuration- 2 Video Lecture - CSAT Preparation - UPSC
## CSAT Preparation
197 videos|151 docs|200 tests
## FAQs on Introduction, Basic Concepts & Formulae: Mensuration- 2 Video Lecture - CSAT Preparation - U... |
Double 47 is 94.
This Math quiz is called 'Addition and Subtraction 2' and it has been written by teachers to help you if you are studying the subject at elementary school. Playing educational quizzes is an enjoyable way to learn if you are in the 3rd, 4th or 5th grade - aged 8 to 11.
It costs only \$12.50 per month ... |
# Exponential Growth and Decay
### Exponential growth can be amazing!
Let us say we have this special tree.
It grows exponentially , following this formula (e is Euler's number):
Height (in mm) = ex
• At 1 year old it is: e1 = 2.7 mm high ... really tiny!
• At 5 years it is: e5 = 148 mm high ... as high as a cup
•... |
## Introduction
### Introduction
There are three main characteristics of a geometric experiment.
1. Repeating independent Bernoulli trials until a success is obtained. Recall that a Bernoulli trial is a binomial experiment with number of trials n = 1. In other words, you keep repeating what you are doing until the f... |
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# Work
## There are three key ingredients to work - force, displacement, and cause.
Estimated16 minsto complete
%
Progress
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Welcome back! We’re glad you made it to Part 2 of this series. Let’s dive right in.
One of the most important statistical concepts is the distribution curve. A distribution curve is a graph that shows the different frequencies of a certain variable. For example, if I were to make a distribution curve of scores receive... |
NCERT Solutions for Class 11 Chapter 7- Permutations and Combinations
*According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 6.
NCERT Solutions Class 11 Maths Chapter 7 Permutations and Combinations prepared in accordance with the latest update on CBSE Syllabus for 2023-24 have been prov... |
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# Exponents and Roots Practice Problems: GED Math (page 2)
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Updated on Mar 23, 2011
1. e. 72 = 7 × 7, and 7 × 7 = 49.
2. d. When there is a negative exponent, take the reciprocal of the base and raise it to the positive power. 2–3, = , and .
3. b. is the cube root of 27; wh... |
## Trigonometry (11th Edition) Clone
The solution set is $$\{\frac{\pi}{12},\frac{5\pi}{12},\frac{13\pi}{12},\frac{17\pi}{12}\}$$
$$\sin x\cos x=\frac{1}{4}$$ over interval $[0,2\pi)$ This equation features both sine and cosine of the same functions of $x$, and they are in the position of a multiplication. In fact, it... |
# What is Factorial of Hundred
Factorial of hundred, denoted as 100!, is the product of all positive integers from 1 to 100. This number is quite large, with 158 digits in total. Factorial of hundred is often used in mathematics and computer science, and it has various applications in statistics, probability, and comb... |
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On a particular day, the rainfall recorded in the terrace is 6m long and 5m board is $15cm$. The quantity of water collected in then terrace isA) $300{\text{ }}litres$B) $450{\text{ }}litres$C) $3000{\text{ }}litres$D) $4500{\text{ }}litres$s
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# Find the area of the quadrant of a circle whose circumference is 44 cm.
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Hint: In circles, if we have a circle of radius r then the circumference of t... |
# How do you find the derivative of f(x)= x/(x-1)?
Apr 26, 2016
$f ' \left(x\right) = - \frac{1}{x - 1} ^ 2$
#### Explanation:
We can use the Quotient Rule to find the derivative, which states:
$y ' = \frac{g \left(x\right) h ' \left(x\right) - h \left(x\right) g ' \left(x\right)}{g \left(x\right)} ^ 2$
Where in... |
# Revision Notes on Areas Related to Circles
## Perimeter and Area of a Circle
The perimeter of all the plain figures is the outer boundary of the figure. Likewise, the outer boundary of the circle is the perimeter of the circle. The perimeter of circle is also called the Circumference of the Circle.
Circumference =... |
# HiSET Math Practice Test Questions
Taking the HiSET Math test? Try the following FREE HiSET Math sample questions. Reviewing practice questions is the best way to brush up on your Math skills and prepare for the HiSET Math test. Here, we walk you through solving 10 common HiSET Math practice problems covering the mo... |
What is the solution of the differential equation dy/dx = 2y(5-3y) with y(0)=2?
Dec 21, 2017
$y = \frac{10 {e}^{10 x}}{6 {e}^{10 x} - 1}$
Explanation:
We have:
$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 y \left(5 - 3 y\right)$
This is a First Order Separable ODE, so we can "separate the variables" to get
$\int \setm... |
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To better understand certain problems involving rockets and propulsion it is necessary to use some mathematical ideas from trigonometry, the study of triangles. On another page we have introduced the trigonometric functions sine, cosine, and tangent of the angles o... |
# 12 HOUR CLOCK ARITHMETIC
In modular arithmetic, if the divisor is 12, it is called as 12 hour clock arithmetic.
Because the divisor is 12, the remainders must be less than or equal to 11.
So, the remainder are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
"0" corresponds to the hour "12"
"1" corresponds to the hour "1"
... |
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