Answer Happy

In the theory of biorhythms, a sine function of the form P(t) = 50 sin (ot) + 50 is used to measure the percent P of a person's potential at time t, where t is measured in days and t=0 is the person's birthday. Three characteristics are commonly measured: physical potential with a period of 23 days, emotional potential with a period of 28 days, and intellectual potential with a period of 33 days. (a) Find for each characteristic. For physical potential, @= (Simplify your answer. Type an exact answer in terms of x. Use integers or fractions for any numbers in the expression.) For emotional potential, = (Simplify your answer. Type an exact answer in terms of x. Use integers or fractions for any numbers in the expression.) B For intellectual potential, = (Simplify your answer. Type an exact answer in terms of x. Use integers or fractions for any numbers in the expression.) (b) Using a graphing utility, graph all three functions on the same screen. Choose the correct answer below. All graphs are shown in [0,50,10] by [0,100,10] viewing windows. OA. OB. C O C. O D. Q Q MXX XXXXX M² XXXXX Q Q 5 2

(c) Is there a time t when all three characteristics have 100% potential? When is it? OA. Yes; t = OB. No (d) Suppose that a person is 28 years old today (t = 10,227 days). Describe this person's physical, emotional, and intellectual potential for the next 30 days. The next time this person's physical potential peaks is days after the person's birthday. (Round up to the nearest day.) The next time this person's emotional potential peaks isdays after the person's birthday. (Round up to the nearest day.) The next time this person's intellectual potential peaks is days after the person's birthday. (Round up to the nearest day.)