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27 August, 19:47

The water level in a tank can be modeled by the function h (t) = 8cos (pi t / 7) + 11.5, where t is the number of

hours since the water level is at its maximum height, h. How many hours pass between two consecutive times when the water in the tank is at its maximum height?

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  1. 27 August, 20:10
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    NO amount of hour passed between two consecutive times when the water in the tank is at its maximum height

    Step-by-step explanation:

    Given the water tank level modelled by the function h (t) = 8cos (pi t / 7) + 11.5. At maximum height, the velocity of the water tank is zero

    Velocity is the change in distance with respect to time.

    V = {d (h (t) }/dt = - 8π/7sin (πt/7)

    At maximum height, - 8π/7sin (πt/7) = 0

    -Sin (πt/7) = 0

    sin (πt/7) = 0

    Taking the arcsin of both sides

    arcsin (sin (πt/7)) = arcsin0

    πt/7 = 0

    t = 0

    This shows that NO hour passed between two consecutive times when the water in the tank is at its maximum height
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