NEED HELP ASAP GRADE DEPENDS ON THIS (30pts.) The Cobscook Bay tides vary between 4 feet and 20 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 18 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon?
Amplitude = 16 feet; period = 9 hours; midline: y = 8
Amplitude = 16 feet; period = 18 hours; midline: y = 12
Amplitude = 8 feet; period = 9 hours; midline: y = 8
Amplitude = 8 feet; period = 18 hours; midline: y = 12

9514 1404 393

  (d)  Amplitude = 8 feet; period = 18 hours; midline: y = 12

Step-by-step explanation:

The amplitude is half the difference between the low and high, so is ...

  (20 -4)/2 = 16/2 = 8 . . . . amplitude in feet

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The period is the time it takes for one full cycle. The problem statement tells you one full cycle takes 18 hours, so 18 hours is the period.

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The midline is half the sum of the low and high, so is ...

  (20 +4)/2 = 24/2 = 12 . . . . midline in feet

These values are matched by the last choice:

  amplitude 8, period 18, midline 12.

 144 ft²

Step-by-step explanation:

AC = (24 ft)·sin(45°) = 12√2 ft

BC = (24 ft)·cos(45°) = 12√2 ft

Area = 1/2·AC·BC = (1/2)·(12√2 ft)·(12√2 ft) = 144 ft²