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

Chapter 1, Problem 40

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The power output, P, of a solar panel varies with the positionof the sun. Let P = 10 sin watts, where is theangle between the suns rays and the panel, 0 .On a typical summer day in Ann Arbor, Michigan, thesun rises at 6 am and sets at 8 pm and the angle is = t/14, where t is time in hours since 6 am and0 t 14.(a) Write a formula for a function, f(t), giving thepower output of the solar panel (in watts) t hoursafter 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 isthe power output at this time?(d) On a typical winter day in Ann Arbor, the sun risesat 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.