Solve the Problem $\frac { \text { width } } { \text { height } } = \frac { 16 } { 8 + 3 \pi }$

question 379

Multiple Choice

Solve the problem.
-A window is in the form of a rectangle surmounted by a semicircle. The rectangle is of clear glass, whereas the semicircle is of tinted glass that transmits only one-fourth as much light per unit area as clear glass does. The total perimeter is fixed. Find the proportions of the window that will admit the most light. Neglect the thickness of the frame.

• A) \(\frac { \text { width } } { \text { height } } = \frac { 16 } { 8 + 3 \pi }\)
• B) \(\frac { \text { width } } { \text { height } } = \frac { 4 } { 8 + 3 \pi }\)
• C) \(\frac { \text { width } } { \text { height } } = \frac { 16 } { 8 + \pi }\)
• D) \(\frac { \text { width } } { \text { height } } = \frac { 16 } { 4 + 3 \pi }\)

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Definitions:

Midpoint Method

A technique used in economics to calculate the elasticity of demand or supply by taking the average of the starting and ending prices and quantities.

Price Elasticity

A measure of how much the quantity demanded of a good responds to a change in the price of that good, indicating how prices can affect consumer purchasing decisions.

Equation

A mathematical statement that asserts the equality of two expressions, represented by the symbol "=".

Luxury

Goods or services that are considered non-essential but desirable, often associated with high quality and high price.