The height, h , in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t , in seconds can be modeled by the equation h is equal to 15 cosine open paren pi over 20 t close paren How long does it take for the waterwheel to complete one turn?

The waterwheel completes one turn when the cloth returns to the same position and motion, which is one full cycle of the cosine function. For h = 15 cos((π/20)t), the angular frequency is π/20, so the period is 2π ÷ (π/20) = 40 seconds. Therefore, the waterwheel takes 40 seconds to complete one turn.

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