At a given day, the water at a dock is 5 meters deep at low tide (at 5 am) and 9 meters deep at high tide (at 3 pm). Find the function describing the height of the tide with respect to time.
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Coastal areas experience tides, which is where the ocean periodically gets to high and low points. Tides can be modeled with a sinusoidal (sine or cosine) function. At one beach, the high tide is 10 feet above mean sea level and the low tide is 10 feet below sea level. The length of time between high and low tide is 5 hours. If high tide is at time 0 hours, give the function H(t) that describes the height of the tide relative to sea level hours after the high tide.
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The water level varies from 12 inches at low tide to 52 inches at high tide. Low tide occurs at 9:15 am. High tide occurs at 3:30 pm. What is a cosine function that models the variation in inches above and below the water level as a function of time and hours since 9:15 am?
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