Solving And Calculating

Introduction of solving and calculating:

Introduction of solving and calculating:

In mathematics solving is a process of answering a problem step by step. Same as calculating is also process of answering a problem step by step but the values are given in the question we have to calculate the answer for the question. We shall see some solving problems in algebra and also calculating problems in mathematics.

Solving and Calculating : Problems for Solving Equations:

Ex 1:

Solve: 3x-2y = 4 and 3x+2y = 2, find x and y values?

Sol:

Solving (1) and (2) we get

3x-2y = 4 ------------------(1)

3x+2y = 2 -----------------(2)

6x = 6

'(6x)/6' = '6/6'

x =1 Substitute in (1)

3(1)-2y = 4

3-2y = 4

-2y = 1

y = '-1/2'

Solving the polynomial we get (x,y) as (1,'-1/2' )

Ex 2:

solve 4x - 3y =4, 3x + 2 =3

Sol:

4x - 3y = 4 --------------(1)

3x + 2y = 3 -------------(2)

Solving (1) and (2)

(1) multiply by 2

(2) multiply by -3

8x -6y = 8

-9x -6y =-9

-x = -1

x = 1

Substitute x =1 in (1)

4(1) - 3y = 4

4 -3y =4

-3y = 4-4

-3y =0

y =0

Solving the equation and we get (x,y) as (1,0)

Solving and Calculating : Problems for Calculating Volumes:

Let us see some problems for calculating the values.

Ex 1:

Calculate the volume of a cube with sides = 5cm

Sol:

Given: sides a= 5cm

Calculating volume use the formula

Volume of cube = a3

= 53

=125cm3

Ex 2:

Calculate the volume of a cone with radius =6cm and height = 7cm

Sol:

Given: r=6cm h= 7cm

Calculating volume of cone use the formula

Volume of cone = 1/3 r2 h

= 1/3 3.14 62 7

=1/3 3.14 36 7

= 1/3 791.28

=263.76 cm3

Ex 3:

Calculate the volume of a sphere with radius = 7cm

Sol:

Given: r= 7cm

Calculating volume of sphere use the formula

Volume of cone = '4/3' r3

= '4/3' 3.14 (5)3

='4/3' 392.5

= '1570/3'

=523.33cm3

Solving and Calculating : Practice Problems:

1) Solve: 6x + 2y=3, 3x + 2y =0.

2) Calculate the volume of sphere radius = 9cm?

Answers:

1) (x,y) is (1,-3/2)

2) 3052.08 cm3

by: jeri

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