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

question 44

Multiple Choice

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) \(A ( x ) = \frac { 160 x - 4 x ^ { 2 } - \pi x ^ { 2 } } { 2 }\)

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Definitions:

Static Budget

A fixed budget that does not change or adjust to variations in business activity levels, often used for control purposes in stable environment operations.

Flexible Budget

A budget that adjusts or flexes with changes in the volume or activity level.

Direct Labor

The wages or salaries paid to employees who are directly involved in producing goods or providing services.

Electric Power

Electric power is the rate at which electrical energy is transferred by an electric circuit, commonly utilized for domestic, commercial, and industrial activities.