Solve Solutions in Math

With the help of Maths we can find the easy solutions to difficult problems. It is a concept of numerically solving with logical understanding. Basic operations in mathematics are addition, subtraction, multiplication, division.Also we solve some problems with the help of identities and formulas. In this article we shall study some more solutions in math. Before solving the maths problems there are some important points to remember. some of them are following.

Read the problem very carefully and find what we have to find ?

If there is any formula start to the solve the problem from there.

If it possible break the problem into 2 or more parts.

Make the an easy equation if possible.

Solve the equation to get the answer.

Some Important Formulas Used to get Solutions in Math

( a + b )2 = a2 + b2 + 2ab

( a - b )2 = a2 + b2 - 2ab

( a + b ) ( a - b ) = a2 - b2

a3 + b3 + c3 = 3abc

Area of perpendicular triangle = 1/2 X base X height

Area of circle = 2pi r

Surface area of cuboid = 2(lb +bh + hl)

volume of cuboid = lbh

mean     =     ("Sum of all Numbers")/(" Total Numbers" )

Examples for Solutions in Math

Ex 1 : Evaluate : 302 + 203 - 503

Sol :Step 1: Let a = 30, b = 20, c = - 50. Then,

a + b + c = 30 + 20 - 50 = 0

Step 2:We know   a3 + b3 + c3 = 3abc

303 + 203 + ( -50 )3 = 3 X 30 X 20 X -50

303 + 203 - 503 =  - 90000  Ans.

Ex 2 : Factorize a4 - b4

Sol :    Step 1: a4 - b4

=  ( a2)2 - ( b2 )2

Step 2:We know ( a + b ) ( a - b ) = a2 - b2

so          =  ( a2)2 - ( b2 )2

= ( a2 + b2 ) ( a2 -  b2)

=  ( a2 + b2 )  (a + b) ( a - b )  Ans.

Ex :3 The radius of a circle is 14 cm . Find the area of the circle.

Sol :         area of circle

Step 1:Radius of circle = 14cm

Step 2:Area of circle = pi r2

=  22/7 14 X 14

=  616 cm2 Ans.
Practice Problems to Find Solutions in Math:

Pro 1: Evaluate :    233 - 173

Ans :   7254

Pro 2: The radius of circle is 35cm. Find the area of circle?

Ans :  3850 cm2

positive Quadrant

Quadrants are the important concept in graph matrix. Positive Quadrant is one of the parts of our Cartesian plane. Usually our Cartesian plane is divided into 4 parts of quadrants.Cartesian plane is the formation of the x and y axis. If the x and y values are positive then that quadrant is called the positive quadrant. It is also called first quadrant. In this article we are going to learn about positive quadrant through problems and diagrams.

Brief Summary about Positive Quadrant

Cartesian Graph plane:

Our Cartesian graph plane is the basic formation of the x and y axis.

X axis:

X axis is the left to right direction line and then it can be divided into 2 parts by the origin.  They are X and x’.  Positive values are marked in the x axis and then the negative values are marked in the x’ axis.

Y axis:

Y axis is the top to bottom direction line and then it can be divided into 2 parts by the origin.  They are Y and y’.  Positive values are marked in the y axis and then the negative values are marked in the y’ axis.

Origin:

The intersection of horizontal axis x and then the vertical axis y is the point origin.

Coordinates:

Coordinates are the major part of graph plane.  It takes the form of (x, y).

Quadrants:

Based on the x and y values it can be marked into the different type of 4 quadrants.

Positive Quadrant:

Positive quadrant is the intersection of positive value of x and positive value of y. The coordinates on the positive quadrant is on the following form (+x, +y).
Example Problems on Positive Quadrant

Example 1:

Shade the following points in the positive quadrant

(5, 2)
(3, 1)
(4, 3)
(6, 2)

Solution:

The graph in the positive quadrant looks like as the following graph,

Example 2:

Identify which points is lies in the positive quadrant from the following list of points

(0,6)
(6,0)
(6,1)
(-2,6)

Solution:

Here (6, 1) is the only point in the positive quadrant.  Because here both 6 and 1 values are positive.