SOLUTION: The area of a circle is given by the expression π(16x^2 - 40x + 25). a) What is the diameter of the circle? b) What is its circumference?

Algebra ->  Average -> SOLUTION: The area of a circle is given by the expression π(16x^2 - 40x + 25). a) What is the diameter of the circle? b) What is its circumference?      Log On


   

Question 1138091: The area of a circle is given by the expression π(16x^2 - 40x + 25).
a) What is the diameter of the circle?
b) What is its circumference?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The area of a circle is given by the expression
A=pi%2816x%5E2+-+40x+%2B+25%29

a) What is the diameter of the circle?
A=pi%2816x%5E2+-+40x+%2B+25%29..........since the area of a circle is A=pi%2Ar%5E2

=>pi%2Ar%5E2=pi%2816x%5E2+-+40x+%2B+25%29...simplify
r%5E2=16x%5E2+-+40x+%2B+25...factor completely
r%5E2=16x%5E2+-+20x-20x+%2B+25
r%5E2=%2816x%5E2+-+20x%29-%2820x+-+25%29
r%5E2=4x%284x+-+5%29-5%284x+-+5%29
r%5E2=%284x-5%29%284x+-+5%29
r%5E2=%284x+-+5%29%5E2
r=4x+-+5
then, the diameter of the circle is d=2%284x+-+5%29=>d=8x+-+10

b) What is its circumference?
C=d%2Api
C=pi%288x+-+10%29