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Math Help - Word Problems - Calc AB Review related

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    Word Problems - Calc AB Review related

    Snow falls intermittently accumulating on the ground at a rate (inches/hour) given by the equation f(t) = t^2sin{t^3} + 2.5 where t is the number of hours that storm is overhead. To the nearest inch, how much snow will accumulate in the first two hours of the storm?

    Do I just plug in 2 hours into the equation to get 6.46 in? It seems to simple to work like that though.

    The temperature of a city for the 24 hour period starting at 12 noon is given by equation T(t) = 19 + 15sin\frac{x\pi}{12} where t is the number of hours after 12 noon. Find the average temperature of the city to the nearest integer from 12 noon until 6 am the next morning.
    So is t = 18? and I just use the formula favg = \int_{12}^{18}\frac{T(t)}{18 - 12}?
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  2. #2
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    Snow falls intermittently accumulating on the ground at a rate (inches/hour) given by the equation where t is the number of hours that storm is overhead. To the nearest inch, how much snow will accumulate in the first two hours of the storm?

    Do I just plug in 2 hours into the equation to get 6.46 in?
    no ... f(t) is a rate that snow accumulates on the ground.

    amount of snow that will accumulate in the first two hrs is \int_0^2 f(t) \, dt

    ... where t is the number of hours after 12 noon. Find the average temperature of the city to the nearest integer from 12 noon until 6 am the next morning.
    from noon (t=0) to 6AM (t=18)

    T_{avg} = \frac{1}{18-0} \int_0^{18} T(t) \, dt
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  3. #3
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    oh. I see . thanks!
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