Solve.
-A rectangle that is x feet wide is inscribed in a circle of radius 32 feet. Express the area of the rectangle as a function of x. Graph the function and from the graph determine the value of x, to the Nearest tenth of a foot, which will maximize the area of the rectangle.
A)45.7 feet
B)44.9 feet
C)44.5 feet
D)45.3 feet

Question

Quizplus · Accepted Answer

The diagonal of the rectangle is the diameter of the circle, which is 64 feet. Using the Pythagorean theorem, the length of the rectangle is √(64² - x²). The area of the rectangle is A(x) = x * √(64² - x²). To maximize the area, differentiate A(x) and find the critical points. The maximum area occurs when x is approximately 45.3 feet.

Solve. -A Rectangle That Is X Feet Wide Is Inscribed in in a Circle