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)

Algebra ->  Surface-area -> 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)      Log On


   

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) About Me  (Show Source):
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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%28256-x%5E2%29
A = x*w
replace w
A(x) = x%28sqrt%28256-x%5E2%29%29 is the area expressed as function of x
:
b) Determine the domain of the function
x: >0, <16
c) Graph the function
+graph%28300%2C+200%2C+-10%2C+20%2C+-30%2C+200%2C+x%2A%28sqrt%28256-x%5E2%29%29%2C+128%29+
green line f(x) = 128
d) What dimensions maximize the area of the rectangle x=11.314
then
w = sqrt%28256-11.314%5E2%29
w = 11.313, actually it would be a square as you would expect for max area