SOLUTION: The depth of water in a harbour as a function of time can be described by cosine function. The maximum depth is 12m and the minimum is 1.5m and at t=0 , the depth is at a minimum.

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Question 1199387: The depth of water in a harbour as a function of time can be described by cosine function. The maximum depth is 12m and the minimum is 1.5m and at t=0 , the depth is at a minimum. In 65 hours, the minimum depth is reached 6 times( including the times at t=0 and t=65 hours)
Write an equation to describe the depth of the water in the harbour as a function of time.
Answer by ikleyn(53937) (Show Source):
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The depth of water in a harbour as a function of time can be described by cosine function.
The maximum depth is 12m and the minimum is 1.5m and at t=0 , the depth is at a minimum.
In 65 hours, the minimum depth is reached 6 times( including the times at t=0 and t=65 hours)
Write an equation to describe the depth of the water in the harbour as a function of time.
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From the condition, the middle / (the average) depth of water is = = 6.75 m. The amplitude of the cosine function is 6.75-1.5 = 5.25 m. In the interval fro t= 0 to t 65 hours, there are 5 periods, so one single period is 65/5 = 13 hours. The minimum depth is reached at t= 0, so we should use the negative cosine function without horizontal shift. Combining everything together, our function for the depth of water is d(t) = . ANSWER

Solved.