Question 1138091

The area of a circle is given by the expression 

{{{A=pi(16x^2 - 40x + 25)}}}
 

a) What is the diameter of the circle?

{{{A=pi(16x^2 - 40x + 25)}}}..........since the area of a circle is {{{A=pi*r^2}}}
 
=>{{{pi*r^2=pi(16x^2 - 40x + 25)}}}...simplify

{{{r^2=16x^2 - 40x + 25}}}...factor completely

{{{r^2=16x^2 - 20x-20x + 25}}}

{{{r^2=(16x^2 - 20x)-(20x - 25)}}}

{{{r^2=4x(4x - 5)-5(4x - 5)}}}

{{{r^2=(4x-5)(4x - 5)}}}

{{{r^2=(4x - 5)^2}}}

{{{r=4x - 5}}}

then, the diameter of the circle is {{{d=2(4x - 5)}}}=>{{{d=8x - 10}}}


b) What is its circumference? 

{{{C=d*pi}}}

{{{C=pi(8x - 10)}}}