Question

1)A bicycle wheel has a diameter of 63cm. Calculate how many times the wheel turns in traveling 19.8km. Use the value 3¹/7. 2) Solve these quadratic expressions: 2d²+3d+1 a²+7ab+10b²

Answer 1

1.
`Turns = 10000`

2.
`2d\²+3d+1 = (2d+1)(d+1)`

3.
`a\²+7ab+10b\² = (a+5b)(a+2b)`

Explanation:

Solving (1):

Given

`Diameter = 63cm`

Required

Number of times it turns in a distance of 19.8km

First calculate the circumference of the wheel

`C =\pi D`

`C =(22)/(7) * 63cm`

Convert cm to km

`C =(22)/(7) * 0.00063km`

`C =(22* 0.00063km)/(7)`

`C =(0.01386km)/(7)`

`C =0.00198km`

The number of turns is:

`Turns = (19.8km)/(0.00198km)`

`Turns = (19.8)/(0.00198)`

`Turns = 10000`

Solving (2):

`2d\²+3d+1`

Expand

`2d\²+3d+1 = 2d\²+2d+d+1`

Factorize:

`2d\²+3d+1 = 2d(d+1)+1(d+1)`

`2d\²+3d+1 = (2d+1)(d+1)`

Solving (3):

`a\²+7ab+10b\²`

Expand

`a\²+7ab+10b\² = a\²+2ab+5ab+10b\²`

Factorize:

`a\²+7ab+10b\² = a(a+2b)+5b(a+2b)`

`a\²+7ab+10b\² = (a+5b)(a+2b)`