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

Respuesta :

Answer:

1. [tex]Turns = 10000[/tex]

2. [tex]2d\²+3d+1 = (2d+1)(d+1)[/tex]

3. [tex]a\²+7ab+10b\² = (a+5b)(a+2b)[/tex]

Step-by-step explanation:

Solving (1):

Given

[tex]Diameter = 63cm[/tex]

Required

Number of times it turns in a distance of 19.8km

First calculate the circumference of the wheel

[tex]C =\pi D[/tex]

[tex]C =\frac{22}{7} * 63cm[/tex]

Convert cm to km

[tex]C =\frac{22}{7} * 0.00063km[/tex]

[tex]C =\frac{22* 0.00063km}{7}[/tex]

[tex]C =\frac{0.01386km}{7}[/tex]

[tex]C =0.00198km[/tex]

The number of turns is:

[tex]Turns = \frac{19.8km}{0.00198km}[/tex]

[tex]Turns = \frac{19.8}{0.00198}[/tex]

[tex]Turns = 10000[/tex]

Solving (2):

[tex]2d\²+3d+1[/tex]

Expand

[tex]2d\²+3d+1 = 2d\²+2d+d+1[/tex]

Factorize:

[tex]2d\²+3d+1 = 2d(d+1)+1(d+1)[/tex]

[tex]2d\²+3d+1 = (2d+1)(d+1)[/tex]

Solving (3):

[tex]a\²+7ab+10b\²[/tex]

Expand

[tex]a\²+7ab+10b\² = a\²+2ab+5ab+10b\²[/tex]

Factorize:

[tex]a\²+7ab+10b\² = a(a+2b)+5b(a+2b)[/tex]

[tex]a\²+7ab+10b\² = (a+5b)(a+2b)[/tex]