subject: Solving And Calculating [print this page] 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
