A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below.If the perimeter of the window is 40 ft, express the area, A, as a function of the width, x, of the window.
A) $A ( x ) = \frac { 160 x - 4 x ^ { 2 } - \pi x ^ { 2 } } { 8 }$
B) $A ( x ) = \frac { 80 x - x ^ { 2 } } { 2 }$
C) $A ( x ) = \frac { 80 x - 2 x ^ { 2 } - \pi x ^ { 2 } } { 4 }$
D) $A ( x ) = \frac { 80 x + ( 2 - \pi ) x ^ { 2 } } { 4 }$
E) $A ( x ) = \frac { 160 x - 4 x ^ { 2 } - \pi x ^ { 2 } } { 2 }$

Question

A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below.If the perimeter of the window is 40 ft, express the area, A, as a function of the width, x, of the window. 
A) $A ( x ) = \frac { 160 x - 4 x ^ { 2 } - \pi x ^ { 2 } } { 8 }$ 
B) $A ( x ) = \frac { 80 x - x ^ { 2 } } { 2 }$ 
C) $A ( x ) = \frac { 80 x - 2 x ^ { 2 } - \pi x ^ { 2 } } { 4 }$ 
D) $A ( x ) = \frac { 80 x + ( 2 - \pi ) x ^ { 2 } } { 4 }$ 
E) $A ( x ) = \frac { 160 x - 4 x ^ { 2 } - \pi x ^ { 2 } } { 2 }$

Quizplus · Accepted Answer

The Answer of A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below.If the perimeter of the window is 40 ft, express the area, A, as a function of the width, x, of the window. 
A) $A ( x ) = \frac { 160 x - 4 x ^ { 2 } - \pi x ^ { 2 } } { 8 }$ 
B) $A ( x ) = \frac { 80 x - x ^ { 2 } } { 2 }$ 
C) $A ( x ) = \frac { 80 x - 2 x ^ { 2 } - \pi x ^ { 2 } } { 4 }$ 
D) $A ( x ) = \frac { 80 x + ( 2 - \pi ) x ^ { 2 } } { 4 }$ 
E) $A ( x ) = \frac { 160 x - 4 x ^ { 2 } - \pi x ^ { 2 } } { 2 }$

A Norman Window Has the Shape of a Rectangle Surmounted A(x)=160x−4x2−πx28A ( x ) = \frac { 160 x - 4 x ^ { 2 } - \pi x ^ { 2 } } { 8 }A(x)=8160x−4x2−πx2​

A Norman Window Has the Shape of a Rectangle Surmounted $A ( x ) = \frac { 160 x - 4 x ^ { 2 } - \pi x ^ { 2 } } { 8 }$