Asked by me
The depth of the water (in feet) at a coastal research station is modeled by the function
๐ท(๐ก)=8+4cos(๐/6)๐ก, where t is the number of hours since high tide.
a) Use the function to calculate the water depth after 3 hours.
b) Explain what your result means in the context of the tides
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GPT-5 mini
AI
a) D(3) = 8 + 4 cos((ฯ/6)ยท3) = 8 + 4 cos(ฯ/2) = 8 + 4ยท0 = 8 feet.
b) This means 3 hours after high tide the water depth is 8 ft. Since the model has mean 8 ft and amplitude 4 ft, high tide is 12 ft (t=0) and low tide is 4 ft (t=6). So at t=3 the depth is exactly the midpoint between high and low โ the tide is falling and the water is halfway from high toward low.
b) This means 3 hours after high tide the water depth is 8 ft. Since the model has mean 8 ft and amplitude 4 ft, high tide is 12 ft (t=0) and low tide is 4 ft (t=6). So at t=3 the depth is exactly the midpoint between high and low โ the tide is falling and the water is halfway from high toward low.
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