Solve the Problem $$\sqrt { r ( 29000 + 41000 \tan \theta ) }$$

question 28

Multiple Choice

Solve the problem.
-A racetracks curve is banked so that the outside of the curve is slightly elevated or inclined above the inside of the curve. This inclination is called the elevation of the track. The maximum speed on the track in miles per hour is given by
$$\sqrt { r ( 29000 + 41000 \tan \theta ) }$$
where $r$ is the radius of the track in miles and $\theta$ is the elevation in degrees. Find the maximum speed for a racetracks with an elevation of $27 ^ { \circ }$ and a radius of $0.5$ miles. Round to the nearest mile per hour.

• A) 35,278 miles per hour
• B) \(- 74,403\) miles per hour
• C) 158 miles per hour
• D) 188 miles per hour

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Definitions:

Long-Run Average Cost Curve

A graphical representation showing the minimum cost per unit at which a firm can produce any given level of output in the long run when all inputs are variable.

Diseconomies of Scale

The phenomenon where, as a firm becomes too large, its costs per unit increase due to inefficiencies, leading to a decrease in overall productivity or cost-effectiveness.

Long-Run Average Cost Curve

A graphical representation used in economics to show the lowest average cost of production at which any given level of output can be produced in the long run, when all inputs are variable.

ATC

Average Total Cost, which refers to the total cost per unit of output produced, calculated by dividing the total cost by the quantity of output.