The power output, P, of a solar panel varies with the position of the sun. Let P = 10

Chapter 1, Problem 40

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The power output, P, of a solar panel varies with the position of the sun. Let P = 10 sin watts, where is the angle between the suns rays and the panel, 0 . On a typical summer day in Ann Arbor, Michigan, the sun rises at 6 am and sets at 8 pm and the angle is = t/14, where t is time in hours since 6 am and 0 t 14. (a) Write a formula for a function, f(t), giving the power output of the solar panel (in watts) t hours after 6 am on a typical summer day in Ann Arbor. (b) Graph the function f(t) in part (a) for 0 t 14. (c) At what time is the power output greatest? What is the power output at this time? (d) On a typical winter day in Ann Arbor, the sun rises at 8 am and sets at 5 pm. Write a formula for a function, g(t), giving the power output of the solar panel (in watts) t hours after 8 am on a typical winter day