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Math Help - Temperature

  1. #1
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    Temperature

    The temperature on New Year's Day in Hinterland was given by T(h) = -a - bcos(PiH/12), where T is the temperature in degreen Fahrenheit and h is the number of hours from midnight from 0 to 24.

    The initial temperature at midnight T(0) was -15F and at noon, T(12) was 5F. Find a and b.

    -What do I do?

    Find the average temperature for the first 10 hours.
    -DO I just use the Average value theorem?

    Use the trapezoid Rule with 4 subdivisions to estimate integral from 0 to 8 of T(h)dh.

    Find an expression for the rate that the temperature is changing with respect to h
    Last edited by mr fantastic; January 3rd 2009 at 12:26 PM. Reason: Modified potentially offensive expression
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  2. #2
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    The initial temperature at midnight T(0) was -15F and at noon, T(12) was 5F. Find a and b.
    T(h) = -a - b\cos\left(\frac{\pi h}{12}\right)

    T(0) = -15

    -15 = -a - b\cos(0)

    -15 = -a - b

    T(12) = 5

    5 = -a - b\cos(\pi)

    5 = -a + b

    a = 5 ... b = 10


    Find the average temperature for the first 10 hours.
    T_{avg} = \frac{1}{10-0} \int_0^{10} T(h) \, dh


    Use the trapezoid Rule with 4 subdivisions to estimate integral from 0 to 8 of T(h)dh.
    \int_0^8 T(h) \, dh \approx 1[T(0) + 2T(2) + 2T(4) + 2T(6) + T(8)]


    Find an expression for the rate that the temperature is changing with respect to h
    \frac{d}{dh} \left[-5 -10\cos\left(\frac{\pi h}{12}\right)\right]
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