SOLUTION: 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.
b)
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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.
b) Determine the domain of the function.
c) Graph the function
d) What dimensions maximize the area of the rectangle
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 =
A = x*w
replace w
A(x) = is the area expressed as function of x
:
b) Determine the domain of the function
x: >0, <16
c) Graph the function
green line f(x) = 128
d) What dimensions maximize the area of the rectangle x=11.314
then
w =
w = 11.313, actually it would be a square as you would expect for max area
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