Question 1125922
A rectangle that is x feet wide is inscribed in a circle of radius 8 ft.
a) Draw an appropriate figure and then express the area of the rectangle as a function of x.
:
We know that the diagonal of a rectangle inscribed in a circle, will be equal to the diameter of the circle. 16'
let w = the width of the rectangle
therefore
x^2 + w^2 = 16^2
w^2 = 256 - x^2
w = {{{sqrt(256-x^2)}}}
A = x*w
replace w
A(x) = {{{x(sqrt(256-x^2))}}} is the area expressed as function of x
:
b) Determine the domain of the function
x: >0, <16
c) Graph the function 
{{{ graph(300, 200, -10, 20, -30, 200, x*(sqrt(256-x^2)), 128) }}} 
green line f(x) = 128
d) What dimensions maximize the area of the rectangle x=11.314
then
w = {{{sqrt(256-11.314^2)}}}
w = 11.313, actually it would be a square as you would expect for max area