Incredible Online Math

Introduction to Trinomial Notes:

Trinomial notes is a polynomial with three monomial terms. In trinomial notes, sum of three monomials is said to be trinomial. For example, 2x⁵ – 3x² + 3 is a trinomial . An Algebraic expression of the form axⁿ is called a monomial in x, The sum of two monomials is called a binomial and the sum of three monomials is called a trinomial. sum of the finite number of a monomials in term x is called a polynomial of x.

Example :

Factor trinomial notes x² + 3x − 10.

Solution.

The binomial factors will have this form:

(x a)(x b)

What are the factors of 10? they are 2 and 5:

x² + 3x − 10 = (x 2)(x 5).

We have to know how to choose the signs so that, coefficient for middle term will be sum of the outers plus the inners -- will be +3. Choose factors , +5 and −2.

= x² + 3x − 10 Would you like to learn more on angle of elevation

= (x − 2)(x + 5)

When 1 is the coefficient for x², the order of factors it does not matter.

(x − 2)(x + 5) = (x + 5) (x − 2) are same factors keep Math at your fingertips.

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Introduction to Algebra questions and answers

The algebra introduces the concept of the single variable. It is a part of a binary method (binary operators are subtraction ,addition, multiplication, division) is replaced by box. The box is denoted by a letter such as x or y denote a variable, and a, b, or c denote constants. In this topic we shall discuss about some algebra questions and answers.

For Example : X + 3 = 7

Algebra deals with formulas which makes simplification very easy and new techniques to solve expressions. For example the FOIL method is a new way which can be used to simplify multiplication of expressions in an easy and accurate way need algebra 2 homework help. Same way the remainder theorem here is a shortcut method of finding the remainder without actually dividing a polynomial.

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Math is a Game

Radius of a circle from circumference:

The terms radius, diameter & circumference are related to two-dimensional geometric shape named circle. Circle is a two dimensional closed shape with curved edges. The distance from the center of the circle & any point on the circle is always same. Circumference of the circle is 2pi r .where, r is the radius of the circle .

Do you know what is circumference ...?

Circumference is the total distance around the circle. Let us learn about the radius from the circumference of the circle,take a Step Forward to math

Algebra for all the Grades

Introduction to 9^th grade algebra problems:
9^th grade algebra is an Intermediate algebra problems; algebra is the subdivision of mathematics relative to the study of the rules of relations and operations, and the constructions arising from them, together with equations, algebraic expressions, conditions, and polynomials.
It is a number is subtracted ,added or multiplied or divided on both the sides of the scale. In algebra problems numbers are considering as constants.

9th Grade Algebra Problems:

Given the equation

7(-3x - 2) - (-x - 6) = -4(5x + 5) + 12
Multiply factors.
-21x - 14 + x + 6 = -20x - 20 +12
Grouping the terms do you need online algebra tutor.

-20x - 8 = -20x - 8
Add 20x + 8 to both sides, the above equation becomes
0 = 0
All real values are solution to this equation.

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Introduction to ordered indices and Explanation for online indices:

Indices is one of the basic terms in the mathematics. The word indices is plural form of the word index. Even though the word index has many meanings in mathematics but one of the important and the most used. The meaning of the index in the mathematics is that, it indicates the exponential power of a number. In the following topic we will see in detail about the topic ordered indices.

For example, 5⁴ is an example number. In this, the number 5 is called the base number and the number 4 is called as the power. From the above explanation we also said the power as the indices.There are 3 types laws are present in the ordered indices.One is product law, another one is quotient law na the next one is power law do you know what is indices.
Product Law:
An example problem for product law is given below, They are
If suppose p and s are positive integers, then if b 0 means, then the product law is given by,
Example: b^p x b^s = b^p+s . This is example for the product law.
Quotient Law:
An example problem for quotient law is given below, They are
If suppose p and s are positive integers, then if b 0 means, then the product law is given by,
b^p b^s = b^{p - s} . This is example for the quotient law.
Power Law:
An example problem for power law is given below, They are
If suppose p and s are positive integers, then if b 0 means, then the power law is given by,
( b^p )^s = b^ps . Fun learning mathematics This is example for the power law.

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Introduction about pentagonal prism:
 
The vertices are the corners points of the 3 dimensional object. The pentagonal prism has the 10 vertices. Pentagonal prism is a 3 dimensional object. Generally the flat surface of the pentagonal prism is called as its face. The shape of pentagonal prism is shown in below. In which A, A’, B, B’, C, C’, D, D’ and E, E’ are the 10 vertices. Let us see how to calculate the volume of pentagonal prism using the vertex point.
Do you know what is vertices in math

Formula to Find the Volume of Pentagonal Prism:

Volume of the pentagonal prism (A) = 1.72 a² h cubic units
a – side length
h – Height
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Introduction to area of the circle:

A circle is a simple form consisting of those points in a plane which are equidistant from a given point called the center. The common distance between the points of a circle from its center is called its radius.Circle can be divide into two regions with simple curves an interior and an exterior. The following figure represents the circle

"r" represents the radius of the circle

Here we are gong to study about how to find the area of the circle and its example problems.

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Area of the Circle – Example Problems

Example: 1

Find the area of the circle with radius 14 meter

Solution:
Here r = 14 meter, = 3.14, substitute r and value in the above formula we get

Area = 3.14 * 14²

Area = 3.14 *14*14

Simplify the above we get

Area = 615.44 meter square There is one solution to all your problems Geometry World

Therefore the area of the circle is 615.44 meter ²

Growing up with Mathematics

Do You Know How to calculate ratio:

In mathematics, The magnitude of quantities relative to each other. with the ratio expression Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient.

Example:

For every Spoon of sugar, you need 2 spoons of flour (1:2)

Some Simple Operation in Ratios:
The ration of two numbers a and b(b≠0) is the quotient of the numbers. The numbers a and b referred to as the terms of the ratio.Have you heard about chronometric ratio

1. Compounded ratios
2. Duplicate ratios
3. Triplicate ratios

Compounded ratios:
General format for compounded ratio is
*=
Example for compounded ratios:
Example 1:
How to Find ratios: X = or or 25:4
Amazing is in it also find some interesting topics on Precalculus help

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Let us learn how to draw an ogive
The other name for Ogive curve is cumulative frequency curve.
Cumulative frequency curve or ogive is used to obtain the following information from a set of grouped data.

• median
• lower quartiles
• upper quartile
• inner quartile range

Cumulative frequency table is first step in constructing ogive.
Box and whisker plot can also constructed Using a cumulative frequency curve or ogive.

How to Draw an Ogive - Cumulative Frequency Curve or Ogive

Steps to learn how to draw ogive
Ogive or cumulative frequency curve looks like this:-

The cumulative frequency is the basic step in calculating ogive it is obtained by adding up the frequencies as you go along to give a 'running total'.
Do you Know what is line graph generator
Before drawing the cumulative frequency curve or ogive, we need to work out on the cumulative frequencies. This is done by adding the frequencies in turn.
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Algebra linear calculator is used to find the values of variables without manual calculation. free online algebra tutor. These calculators are very useful for the students who are not well with the math formulas and arithmetic operations. Many websites provides free online linear algebra 2 online equations calculator for solving the problems. When the required values are entered in the online solver, it automatically generates the output value. The picture of linear calculator is shown below,

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Mean formula

Mean Formula

In general sample mean (A.M) or average of n observations x₁, x₂, …, x_n is defined to be the number x such that the sum of the deviations of the observations from x is 0. That is, the arithmetic mean x of n observations x₁, x₂, …, x_n is given by the equation

(x₁ − x) +(x₂ − x) + ^... +(x_n − x) = 0

Hence sample mean formula = x₁+x₂+x₃+…….x_n / n

sample mean formula= sum of elements / number of elements

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Sample Mean Example

Following steps used to calculate the sample mean value

Step1: find the sum of the numbers

Step2: Calculate the total numbers

Step3: Using the formula finding the mean

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Solving System of Equations

In mathematics, a system of linear equations is a collection of linear equations involving the same set of variables. For example,

is a system of three equations in the three variables . A solution to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by

since it makes all three equations valid.so this is specially for linear equations in two variables or more than two variables.

In mathematics, the theory of linear systems is a branch of linear algebra, a subject which is fundamental to modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra, and such methods play a prominent role in engineering, physics, chemistry, computer science, and economics. A system of non-linear equations can often be approximated by a linear system (see linearization), a helpful technique when making a mathematical model or computer simulation of a relatively complex system.This is how linear equations explained ,let's see a example on this now from linear algebra tutoring online.
Question:-

Solve the system of equations

8x-z=4

y+z=5

11x+y=15

Answer:-

8x-z=4 ----- eq1

y+z=5 ---- eq2

11x+y=15 -----eq3

add eq1 and eq2

we get 8x+y=9 ----- eq4

subtract eq4 from eq3

11x+y=15
-8x+y=9
-----------
3x = 6

x =2

putting this value in eq1

8x-z =4

16-z=4

z=12

putting this value in eq2

y+z = 5

y = -7

so x=2 , y= -7 and z=12

How to find the arc length of a curve

The arc length is a topic from 10 grade math geometry,lets see the general definition for arc length after which we can see what is the arc length formula and how to use it.
A curve in, say, the plane can be approximated by connecting a finite number of points on the curve using line segments to create a polygonal path. Since it is straightforward to calculate the length of each linear segment (using the theorem of Pythagoras in Euclidean space, for example), the total length of the approximation can be found by summing the lengths of each linear segment.

This free online tutoring math will discuss this in more detail like,
If the curve is not already a polygonal path, better approximations to the curve can be obtained by following the shape of the curve increasingly more closely. The approach is to use an increasingly larger number of segments of smaller lengths. The lengths of the successive approximations do not decrease and will eventually keep increasing—possibly indefinitely, but for smooth curves this will tend to a limit as the lengths of the line segments get arbitrarily small.

For some curves there is a smallest number L that is an upper bound on the length of any polygonal approximation. If such a number exists, then the curve is said to be rectifiable and the curve is defined to have arc length

The arc length formula is s=rθ

where s is the arc , r is the radius of the circle and θ is the angle .

Commutative and Distributive Number Properties

Number properties are
Associative property applies to both addition and multiplication: a+(b+c)=(a+b)+c, a*(b*c)=(a*b)*c.
Distributive property ties addition and multiplication together. Distributive property can be written as: a*(b+c) = a*b + a*c.
Commutative property means that operands can switch places: a+b=b+a, a*b=b*a.

For Example:
Question 1 :- Distributive PropertyThe property demonstrated in the equation -(3n - 5) = -3n + 5 is:
a. associative b. commutative c. distributive d. Neither side of the equation is equal to the other.
Answer:
-1(3n-5) = -3n+5
(-1) (3n) + (-1) (-5)
= -3n+5 (Distributive Property)

Question 2 :- Associative Property
property demonstrated in the equation (5 + n) - 2 = 5 + (n - 2) is:
Answer:
(5+n)-2 = 5+(n-2)
Here the grouping that is the parentheses has changed.so it a (Associative Property)

Question 3 :- Commutative Property
property is this one 7 - 4 + 2 = 7 + 2 – 4
Answer:
7 - 4 + 2 . 7 + 2 - 4
Here the order - 4 + 2 has become 2 + - 4. So it is a (Commutative Property)

All metric units

Topic:-Metric Units

The metric system is the common system of measuring units used by most of the world. It exists in several variations, with different choices of fundamental units, though the choice of base units does not affect its day-to-day use. Metric units are widely used around the world for personal, commercial and scientific purposes.

Few basic metric units for you.

1.Weight
l kg = l,000gms

2.Length
l cm=10mm
1 decimeter = 10 centimeter
1 meter = 100 centimeters
1 Kilometers = 1,000 meters
Capacity
l liter = 1,000ml

3.Calendar
1 week=7days
1 year = 52 weeks
1 year = 12 months
l year = 365 days
1 leap year = 366 days
1 decade = 10 years
1 century = 100 years
1 millionaire 1,000 years

word problem on percentages

Topic:-Percentages

a percentage is a way of expressing a number as a fraction of a number (per cent meaning "per hundred"). It is often denoted using the percent sign, "%". For example, 45% (read as "forty-five percent") is equal to 45 / 100, or 0.45.
Percentages are used to express how large one quantity is, relative to another quantity. The first quantity usually represents a part of, or a change in, the second quantity, which should be greater than zero.
This percentages help  with give you an example as well.

Question:-

How many liters of water must be added to 20 liters of a 24% acid solution to make it 8 % acid.


Answer:-
20 L ,24% acid

needs to be 8% acid

So 24% of 20 is 4.8

Let x be the number of liters of water

(20+x)(8%)=4.8 liters

(20+x)(0.08)=4.8 liters

1.6+0.08x=4.8

0.08x=4.8-1.6

x=40 liters of water is the Answer.



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problem on elimination methos

Topic:- Elimination method

When we are solving equations in algebra ,We can add or subtract the equations ,So that
We can simplify the equations , This is called elimination method

Here we have a simple example to show you ,how this methos works.

This algebra help shows ,how to solve equations as well.

Question :

x+y = 7 and x-y = 9

Solve for 'x',By using elimination method.

Answer:-

Let's add both the equations

      x + y = 7
      x - y = 9
 ------------------
        2x = 16


Divide with 2 on both sides


       2x     16
      ---- = -----
       2       2


        x = 8


So 8 is the answer


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Converting an algebraic expression into dependent variables of a single variable

Here is an algebra question where in a given algebraic expression like terms are on one side and unlike term on another side, this problem is all about making into different subject.

Topic : Making into different subject

This example would clearly explain what making into different subject exactly mean.

Problem : Let f = uv / (u + v) Make “v” as the subject

Solution :

f = uv / (u + v)
Multiplying by (u + v) on either sides of the equation
f (u + v) = uv
fu + fv = uv
Subtract fv on both the sides
fu = uv – fv
fu = v(u – f)
fu / (u – f) = v

Hope the meaning on coverting to different subject is well understood by above example, for more algebra questions like this contact algebra help.

Question on Integration and Application of Fundamental Theorem of Calculus

Here is a Multi choice problem on Integration, Integrating a trigonometric functions and finding its derivative. You can find similar set of questions at Tutor Vista Blogs.

Topic : Integrating Trigonometric value.

Calculation in the solution will help you to identify correct choice and get reasons for, why remaining choices are incorrect.

Problem : If y = ₀∫^x2Cos t dt, then dy/dx = ?
a. 2x Cos(x²)
b. Cos(x²)
c. 2x Sin (x²)
d. Sin (x²)
Solution :

choice a is correct.

y = ₀∫^x2Cos t dt

Let u = x<sup>2




= Cos (u) * 2x
= 2x Cos (x2)

Choice b is incorrect because of applying the fundamental theorem of calculus without using the chain rule.

Choice c is incorrect because of wrong application of fundamental theorem of calculus.

Choice d is incorrect because of wrong application of fundamental theorem of calculus.</sup>

Question to Find Equation of Tangent Line to the Ellipse

Topic : Equation of Tangent

Question : Find the equation of the tangent line to the ellipse 25 x² + y² = 109 at the point (2,3).

Solution :
In the above equation, consider y as a function of x:
25 x² + y(x)² = 109,
and use the techniques of differentiation, to get
From this, we obtain

which implies that at the point (2,3). So the equation of the tangent line is given by
or equivalently

3y + 50 x = 109.