Question 1113618: suppose that the water level varies 70 inches between low tide at 8:.40 AM and high tide at 2:55PM .what he cosine function that models the variation in inches above and below the average water level as a function of the number of hours since 8:40AM .at what point in the cycle does the function cross the midline.what does the midline represent.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! suppose that the water level varies 70 inches between low tide at 8:40 AM and high tide at 2:55 PM. what he cosine function that models the variation in inches above and below the average water level as a function of the number of hours since 8:40AM.
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1455 - 0840 = 7:15 hours for a half-cycle (notice the arithmetic is easy by not using AM & PM for times)
The period is 2x that = 14:30 = 14.5 hours
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The amplitude = 70/2 = 35 inches, ie, 35 above the mean and 35 below.
h(t) = 35*cos(2pi*t/14.5) --> cosine function with max at t = 0
h(t) = 35*cos(4pi*t/29 + 180) --> function of the tides, t in hours
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at what point in the cycle does the function cross the midline.
At t = 0840 + 7.25 hours + 14.5*n hours where n = integer
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what does the midline represent.
It's the x axis and MSL, Mean Sea Level
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