Question
a rectangle that is x feet wide is inscribed in a circle of radius 7 ft....
a rectangle that is x feet wide is inscribed in a circle of radius 7 ft. .
a)express the area of the rectangle as a function of x.
b) find the domain of the function
c) graph the function with a graphing calculator
d) what dimensions mazimize the area of the rectangle
a(x) =
Homework Answers
Answer #1
width of rectangle = x feet
radius of circle = 7 feet
diameter of the circle = 2*7 = 14 feet
which is hypotenuse of the rectangle
now applying pythagorean theorem to find the length
length = sqrt ( 14^2 - x^2 )
= sqrt ( 196 - x^2 )
area = length * width
a(x) = x sqrt ( 196 - x^2 )
b) domain of the function is
196 - x^2 >= 0
x^2 <= 196
x <= 14
domian is [-14 , 14 ]
c) graph shown below
d) dimensions that maximizes the area is length = 9.899 feet and width = 9.899 feet
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