$\text { A petrol car is parked } 35 \text { feet from a long warehouse (see figure). The revolving }$

question 76

Multiple Choice

$\text { A petrol car is parked } 35 \text { feet from a long warehouse (see figure) . The revolving }$ light on top of the car turns at a rate of $\frac { 1 } { 2 }$ revolution per second. The rate at which the light beam moves along the wall is $r = 35 \pi \mathrm { sec } ^ { 2 } \theta \mathrm { ft } / \mathrm { sec }$ . Find the rate $r$ when $\theta$ is $\frac { \pi } { 6 }$ .

• A) \(r = \frac { 140 } { 3 } \mathrm { tt } / \mathrm { sec }\)
• B) \(r = \frac { 70 \sqrt { 3 } \pi } { 3 } \mathrm { ft } / \mathrm { sec }\)
• C) \(r = \frac { 70 \sqrt { 3 } } { 3 } \mathrm { ft } / \mathrm { sec }\)
• D)\(r = \frac { 140 \pi } { 3 } \mathrm { ft } / \mathrm { sec }\)
• E)\(r = \frac { 70 \pi } { 3 } \mathrm { ft } / \mathrm { sec }\)

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Definitions:

Rate of Return

The gain or loss on an investment over a specified period, expressed as a percentage of the investment's initial cost.

Dollar-Weighted Return

A method of calculating an investment's return that takes into account the timing and amount of capital inflows and outflows.

Internal Rate

The internal rate of return (IRR) is a financial metric used to evaluate the profitability of potential investments, representing the discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero.

Geometric Average

A statistical method of determining the average rate of return of a set of values, calculated by multiplying the values together and then taking the root by the number of values.