Classifying math diagrams - Square

Classifying math diagrams - Square:

• Square has four equal sides.
• The side length of the square is denoted as S.
• Total angle of the square is 360°
• All the four sides have the same angle 90°
• Square has two diagonals and both the diagonals are equal in length
• Area of the square is s²

Theorem of MatrIces

Theorem of Matrice:
From the definition of inverse of a matrix, we have (AB)(AB)^-1 = I

or A^-1 (AB)(AB)^-1 = A^-1 I (Pre-multiplying both sides by A^-1)

or (A^-1A) B (AB)^-1 = A^-1 (Since A^-1 I = A^-1)

or I B (AB)^-1 = A^-1

or B (AB)^-1 = A^-1

or (B^-1B)(AB)^-1 =B^-1A^-1

or I(AB)^-1= B^-1A^-1

or (AB)^-1 = B^-1A^-1

Properties of Arithmetic

Properties of Arithmetic:

The properties of arithmetic define when the order of operations can be changed in an initial calculation, so that we can get a second calculation which is equal to the first obtained result. The arithmetic operations that involving real numbers and/or real extents that uses the properties of arithmetic.

There are three types of arithmetic properties. They are,

• Associative property
• Commutative property
• Distributive property

The addition or multiplication of a group of values is similar to the how the numbers are grouped. There are three or more values involved in associative property. The parenthesis refers the terms that are considered one unit. The combination (Associative Property) are within the parenthesis. Therefore, the values are 'associated' together. For multiplication, the product is always same as the grouping. In Associative Property grouping the brackets are done first.

Associative property of addition:

a+(b+c)=(a+b)+c

Associative property for multiplication:

a×(b×c)=(a×b)×c

Example:

Find the associative property of 2+(3+9) and 2(85)

Solution:

2+(3+9)=(2+3)+9

2×(8×5)=(2×8)×5)

Commutative property is the property that altering the order of the values and does not alter the final result. It is a basic property of many binary operations. Many mathematical proofs based on it.

Distributive property of addition:

a+b=b+a

Distributive property for multiplication:

ab=ba

Example:

Find the Commutative property for 4+6 and 6×9

Solution:

4+6=6+4

6×9=9×6

Distributive properties used to distributing something or we can split something or broken up into parts.

This is defined as,

a(b+c)=ab+ac

Example:

Multiply 3 x 17 by using the distributive law.

Solution:

Given 3 x 17
=3(10 +7)
=3(10) + 3(7)
=30 + 21
Therefore 3 x 17=51.

Introduction to arithmetic terms

Introduction to arithmetic terms:
In mathematics the arithmetic terms are the basic one. It is used for calculating the additional, difference operations and etc. The arithmetic functions also used to computer science for writing coding. The basic math functions are including in this arithmetic terms. Here we will see about the basic four functions.

Functions:

The following 4 functions is the arithmetic terms.

• Addition
• Subtraction
• Multiplication
• Division

Trigonometry application

Trigonometry application:

Triangulation technique is used in astronomy to measure the distance of nearby stars.

• It is also used to measure the distance between the landmarks.
• It is used to calculate the oscillation (the waves that moves in a space. There are so many waves like sound waves, earthquake waves, matter waves and the light waves)
• The most important wave is the sin wave. It turns up all over the place, these wave forms can always be broken down into a series of superimposed sin waves of various frequencies. So this process is called as Fourier transform.

Table of Trigonometric identities

Table of Trigonometric identities:

reciprocal Identities: sin u = \frac{1}{csc u} cos u = \frac{1}{sec u} tan u = $\frac{1}{cot u}

csc u = \frac{1}{sin u} sec u = \frac{1}{cos u} cot u = \frac{1}{tan u}

sin u is the inverse function of cosec u

cos u is the inverse function of sec u

Tan u is the inverse function of Cot u

Cosec u is the inverse function of Sin u

Sec u is the inverse function of Cos u

Cot u is the inverse function of Tan u

Examples for Solve Length of side fire Triangle

Examples for Solve Length of side fire Triangle:

1) Solve the length of two side’s fire triangle is 29 cm and 30cm. If perimeter of the fire triangle is 81 cm, what is the length of third side of the fire triangle?

Solution:

Let third side length of the triangle is x cm then,

20 + 30 + x = 81

50+ x = 81

x = 81 -50

x = 31cm

Therefore length of third side of the fire triangle is 31cm.