?Suppose that the number of hours of daylight on a given day in Seattle is modeled by

Chapter 5, Problem 198

(choose chapter or problem)

Suppose that the number of hours of daylight on a given day in Seattle is modeled by the function \(-3.75 \cos \left(\frac{\pi t}{6}\right)+12.25\), with t given in months and t=0 corresponding to the winter solstice.

(a) What is the average number of daylight hours in a year?

(b) At which times \(t_{1}\) and \(t_{2}\), where \(0 \leq t_{1}<t_{2}<12\), do the number of daylight hours equal the average number?

(c) Write an integral that expresses the total number of daylight hours in Seattle between \(t_{1}\) and \(t_{2}\).

(d) Compute the mean hours of daylight in Seattle between \(t_{1}\) and \(t_{2}\), where \(0 \leq t_{1}<t_{2}<12\), and then between \(t_{2}\) and \(t_{1}\), and show that the average of the two is equal to the average day length.

Text Transcription:

-3.75 cos(pi t/6)+12.25

t_1

t_2

0 leq t_1<t_2<12