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Trig Question In Four Parts

    Given: y = cos(Bx − C) + D. Throughout the day the depth of water at the end of a pier varies with the tides. High tide occurs at 4:00 a.m. with a depth of 6 meters. Low tide occurs at 10:00 a.m. with a depth of 2 meters.

1.  Model the problem by using the given trigonometric equation to show the depth of the water hours after midnight, showing all your work.

2.  Solve the problem by finding the depth of the water at noon, explaining your reasoning.

3.  A large boat needs at least 4 meters of water to secure it at the end of the pier.

a.  Determine what span of time after noon, including both a starting and ending time, the boat can first safely be secured, justifying your answer.


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