What is a Linear Equation?

Introduction to Linear Equation:

In this section let me help you go though on what is a linear equation. linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.
Linear equations can have one or more variables. Linear equations occur with great regularity in applied mathematics. While they arise quite naturally when modeling many phenomena, they are particularly useful since many non-linear equations may be reduced to linear equations by assuming that quantities of interest vary to only a small extent from some "background" state.

Solving One-step Linear Equations

solve x + 6 = –3

We want to get "x" on one side of the equal sign, and some number on the other side. Since we want x on the one side, this means that we don’t need the "plus six" that's currently on the same side as the x. Here 6 is added to the x, hence we need to subtract to get rid of it. That is, we need to subtract 6 from the x in order to "undo" having added a 6 to it. This could also help us on how to graph linear equations

Solution:

x + 6 = -3

-6 = -6

x =-9

The value of x = -9

how to find standard deviation

Introduction of how to find standard deviation help:

Let us see how to find standard deviation. The idiom of standard deviation is used within the statistics. It is helped to establish the population examples in statistics. The standard deviation is ensuing from the variance of the population. The standard deviation is helped to approximation the many number of populations.

How to Find Standard Deviation:

Let us see how to find standard deviation. Normally, the standard deviation follows some steps, which are shown below. The steps are helped to find the standard deviation.

Step 1: Identify the mean and variance of given data. For example, This can also help us on mobile field solutions

x	M	(x-m)	(x-m)2
5	4	1	1
4	4	0	0
4	4	0	0
3	4	-1	1

Step 2: Identify the sum of (x-m)².
1+1+0+0 = 2.

Step 3: The known number of N=4, Find N-1.

4-1 = 3.

Help on Perimeter of circle

Introduction to Perimeter of Circle:
The Circle is a two dimensional shapes. The out side distance of the circle is know as circumference of the circle. It is also called as perimeter of circle. The distance from the center to points on boundary is constant. That distance called as radius of the circle. The diameter of circle is square of radius. It is also called as chord.

When we look at the figure.. we will come to know how to calculate are of circle perimeter. and this also helps us on what is the circumference of a circle.

The distance around a circle is called the circumference. The distance across a circle through the center point is called diameter. (Pi) is the ratio of the circumference of the circle is called diameter.

Rules of Logarithms

In this section let me help you go through logarithm rules

Definition on Logarithm:-

The logarithm of a number is the exponent to which a base must be raised to equal that number. For example if 5³ = 125, it is said that log₅ 125= 3. Or, in general , if a³ = m, then log_a m =3 . where ‘a’ is called the base of logarithm. Evidently ‘a’ cannot be 1 ( ≠1).

The rules of logarithms are as follows:

Log_a mn = log_a m + log_an, where ‘a’ is any positive number such that a≠1

Log_a m/n= log_a m - log_an , and

Log_a m^b = b log_a m

Where b is any rational number and m and n are positive number.You can apply the same rules on corresponding angles

Example Log15 = Log 5 + Log 3

Log 4/5= Log 4 – Log 5

Log64= Log 4³ = 3 Log 4

Exercise1. convert into exponential form log_m n = p

Options A. n^p = m

B. m^p= n

C. p^m= n

D mⁿ=p

Correct answer B

How to solve Linear Programming Problem

In this session let me help you go through basically on Problems on Linear Programming problems. With the following examples you will come to know how to solve LPP.

Problem 1
Solve the following linear programming problem graphically:
Maximize Z = 4x + y ... (1)
subject to the constraints:
x + y ≤ 50 ....(2)
3x + y ≤ 90 ... (3)
x ≥ 0, y ≥ 0 ... (4)

Solution -
The shaded region in the below figure helps to understand graphical feasible region determined by the system of constraints (2) to (4). We observe that the feasible region OABC is bounded. So,
we now use Corner Point Method to determine the maximum value of Z.
The coordinates of the corner points O, A, B and C are (0, 0), (30, 0), (20, 30) and
(0, 50) respectively. Now we evaluate Z at each corner point. This will also help us in factoring calculator.

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how to solve linear equation in one variable.

Let me help you go through what is all about linear equations and how to solve linear equation in one variable.
what is linear Equation?
A set of linear equations having a regular solution set is called system of coincident linear equations.Find values of three unknowns, given three linear equations in the three unknown variables. Linear equation in three unknowns x, y, z is report of parity of form ax + by + cz + d = 0 where a, b, c, d are real numbers with a ≠ 0, b ≠ 0 and c ≠ 0.
Solving linear equations in one variable
Find the following examples on linear equation in one variable
Examples -
Mr.R is seven times as old as his son. 10 years hence, he will be three times as old as his son. Find their ages.

Solution -
Let the son's age be x years.
Mr.R's age is 7x years.
After 10 years, his son's age will be = (x + 10) years
After 10 years, Mr.R's age will be = (7x + 10) years
By the given condition of the problem
(7x + 10) = 3(x + 10)
7x + 10 = 3x + 30
7x - 3x = 30 - 10
4x = 20 or x = 5
Son's age is 5 years.
Mr.R's age is 7 5 = 35 years
Mr.R's age is 35 years and his son's age is 5 years

what is matrix

let me give you brief introduction to matrix & types of matrices,

Definition : A matrix is an ordered rectangular array of numbers or functions. The
numbers or functions are called the elements or the entries of the matrix.
We denote matrices by capital letters. The following are some examples of matrices:
In the above examples, the horizontal lines of elements are said to constitute, rows
of the matrix and the vertical lines of elements are said to constitute, columns of the
matrix. Thus A has 3 rows and 2 columns, B has 3 rows and 3 columns while C has 2
rows and 3 columns.

Trigonometry help on domain and range

This Trigonometry help explains about domain and range.

Domain is the set of values that t can take.

here t can take any real value.

so domain is the set of real numbers.

interval notation,domain =(-∞,∞)

we have different trigonometry formulas to solve all kinds trigonometric problems ,
let's how to get the range values.


range of a function f (denoted by ran f ) is the set of all "output" values produced by f. Sometimes it is called the image, or more precisely, the image of the domain of the function. If a function is a surjection then its range is equal to its codomain. In a representation of a function in an xy Cartesian coordinate system, the range is represented on the ordinate (on the y axis).
Now the range of sin t is given by:

-1 ≤ sin t ≤ 1

multiplying by 3,we get

-3 ≤ 3Sint ≤ 3


In interval notation

Range=[-3,3]

Problem on solving a quadrtic equation

Topic:-quadratic equation

A quadratic equation is equation is a polynomial equation of the second degree. The general form is

where x represents a variable, and a, b, and c, represent constants, with a ≠ 0. (If a = 0, the equation becomes a linear equation.)
The constants a, b, and c, are called respectively, the quadratic coefficient, the linear coefficient and the constant term or free term. Quadratic comes from quadratus, which is the Latin word for "square."
This math help gives a example as well.


Question:-

x2-12x+27       x+9
---------  *  -------
x2-81           3-x

Answer:-

Let's start with simplifying the quadratic expression

x2-12x+27

x2-3x-9x+27

x(x+3)-9(x-3)

(x-3)(x-9)

Let's substitute it back in the given equation


(x-3)(x-9)      x+9
---------  *  -------
x2-81          3-x



(x-3)(x-9)      x+9
----------  *  -------
(x+9)(x-9)      3-x


Cancel the similar terms on numerator with denominator

We get

 x-3
-------
 3-x

We can write 3-x as -(x-3)

So     x-3
   ------- = -1
   -(x-3)

So -1 is the answer.

Question on Angular Speed/Angular Velocity at which Earth Rotates

Planet earth in the universe rotates and revolve on its own orbit in the solar system. The study of earth revolution is a part of geometry construction and as well as a geological reasoning

Topic : Angular Speed of Earth

Angular speed or angular velocity is a rate of change of angular displacement with respect to time.

Question : Each point on Earth's surface (except the poles) moves in a circle as earth rotates on its axis. What is the angular speed in a radians per second of the point where your located?

Solution :
Earth rotates once about its axis in 24 hours.
that is 2 radians in 24 hours.
Therefore angular speed = 2π/24 rad/hr
= 2π/24*60*60 rad/sec
= 7.272X10^-5rad/sec
So angular speed at which earth rotates is 7.272X10^-5rad/sec