Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 67 and 83 degrees du

Question

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 67 and 83 degrees during the day and the average daily temperature first occurs at 8 AM. How many hours after midnight, to two decimal places, does the temperature first reach 71 degrees?

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Ximena 4 weeks 2021-09-19T02:46:15+00:00 1 Answer 0

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    2021-09-19T02:47:36+00:00

    Answer:

    Step-by-step explanation:

    given that outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 67 and 83 degrees during the day and the average daily temperature first occurs at 8 AM.

    Max = 83 and min = 67

    Hence amplitude = 8,

    At 8 am, temp = average = 75

    So we can take 8 a.m. as 0 time

    Period = 24 hours

    Equation would be

    T(t) = 75+8sin pi t/12

    So when t =0 at 8 am. we have average temperature = 75

    When T(t) = 71

    we have sin pit/12 = -4/8

    Or pit/12 = 11pi/6

    t=22

    i.e. at 8+22 = 6 a.m. the temperature would be 71 degrees.

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