The Smaller the Curvature in a Bend of a Road $y = \frac { 1 } { 3 } x ^ { 3 } ( x \text { and } y \text { are measured in miles) can safely go } 25 \text { miles per hour at }$

question 75

Multiple Choice

The smaller the curvature in a bend of a road, the faster a car can travel. Assume that the maximum speed around a turn is inversely proportional to the square root of the curvature. A car Moving on the path $y = \frac { 1 } { 3 } x ^ { 3 } ( x \text { and } y \text { are measured in miles) can safely go } 25 \text { miles per hour at }$ $\left( 1 , \frac { 1 } { 3 } \right)$ . How fast can it go at $\left( \frac { 5 } { 2 } , \frac { 125 } { 24 } \right)$ ? Round your answer to two decimal places.

• A) \(259.31 \mathrm { mi } / \mathrm { h }\)
• B) \(149.71 \mathrm { mi } / \mathrm { h }\)
• C) \(119.77 \mathrm { mi } / \mathrm { h }\)
• D) \(75.30 \mathrm { mi } / \mathrm { h }\)
• E) \(299.42 \mathrm { mi } / \mathrm { h }\)

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Definitions:

Authoritarian

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Exerting power or influence over situations or individuals often to achieve a desired outcome, sometimes at the expense of others' autonomy.

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