Math

The average depth of the water at the end of the dock is 6 feet. High tide occurs at 6 am and low tide occurs at 6 pm. The depth of the water at high tide is 9 feet. The information can be graphed using a sinusoidal function. Your boat needs at least 4.5 feet of water to come into the dock. What times of the day is the water going to be too low to come into the dock?

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1. model this as depth of water:
D=6 -3sin wt w=PI/12 and t is in Universal 24 hr time (6am is 6, 6PM is 18)

so when is D<4.5
4.5=6-3sin(PI*t/12)
sin(PI*t/12)=1/2
PI*t/12=(30 deg)=PI*t/6
t=2, so by symettry, at low tide +- 2hrs, the boat wont float. That is 4Pm to 8PM

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bobpursley
2. Wow thank you so much :)

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