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In a tidal river, the time between high and low tide is 7.4 hours. At high tide the depth of water is 17.7 feet, while at low tide the depth is 4.6 feet. Assume the water depth as a function of time can be expressed by a trigonometric function (sine or cosine).
(a) Graph the depth of water over time if there is a high tide at 12:00 noon. Label your graph indicating low and high tide.
Select the letter of the graph which best matches your graph.
Assume that t = 0 is noon.
(b) Write an equation for the depth of the tide (in feet) hours after 12:00 noon.
help (formulas)
(c) A boat requires a depth of 8 feet to set sail, and is docked at 12:00 noon. What is the latest time in the afternoon it can set sail? Round your answer to the nearest minute. For example, if you find when , you would answer at 1:15 PM (since this is 1 and a quarter hours after noon).
The latest the boat can leave is at
: PM
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(Click on a graph to enlarge it)
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