Determine the Quadratic Function Whose Graph Is Given $= \frac { 120 } { \pi + 4 } \approx 16.8$

question 66

Multiple Choice

Determine the quadratic function whose graph is given.
-Alan is building a garden shaped like a rectangle with a semicircle attached to one short side along its diameter. The diameter of the semicircle is equal to the width of the short side of the rectangle. If he has 60 feet of fencing
To go around the garden, what dimensions will give him the maximum area in the garden?

• A) width \(= \frac { 120 } { \pi + 4 } \approx 16.8\), length \(= 8.4\)
• B) width \(= \frac { 60 } { \pi + 4 } \approx 8.4\), length \(= 16.8\)
• C) width \(= \frac { 120 } { \pi + 4 } \approx 16.8\), length \(= 21.6\)
• D) width \(= \frac { 120 } { \pi + 8 } \approx 10.8\), length \(= 16.1\)

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Definitions:

Georg Simmel

Georg Simmel was a German sociologist and philosopher known for his contributions to social theory and for his analysis of the dynamics of social relationships and urban life.

Louis Wirth

A sociologist known for his work on urban life and social structures, particularly his studies on urbanization and its effects on social behavior.

Herbert Gans

An influential sociologist known for his work on urban issues, culture, and the concept of public space in American society.

Urbanism

The study of the characteristic ways of interaction of inhabitants in urban areas, which are distinct from rural areas.