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On September 17, 2008, high tide in Portland was at midnight. The water level at high tide was 10.3 feet; later, at low tide, it was 0.3 feet. Assuming the next high tide is exactly at 12 noon and that the height of the water is given by a sine or cosine curve, find a formula for the water level in Portland as a function of time, where y is the water level in feet, and t is the time measured in hours from midnight

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HomertheGenius
The height of the water is given by a cosine curve.
A function is:
y = a cos ( b t ) + c
where: a = ( 10.3 - 0.3 ) : 2 = 10 : 2 = 5
c = 10.3 - 5 = 4.3
2 π / b = 12
b = 2 π / 12 = π / 6
Answer:
y = 5 cos ( π/6 · t ) + 4.3

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