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The Chesapeake Bay tides vary between 4 feet and 6 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 12 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon? Amplitude = 1 foot; period = 12 hours; midline: y = 5 Amplitude = 2 feet; period = 6 hours; midline: y = 1 Amplitude = 2 feet; period = 12 hours; midline: y = 5

2 Answers

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Answer:

A. Amplitude = 1 foot; period = 12 hours; midline: y = 5

User Jpmarindiaz
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5 votes

Answer:

The correct option is 1.

Explanation:

The general cosine function is


y=A\cos (Bx+C)+D

where, A is amplitude,
(2\pi)/(B) is period, C is phase shift and D is midline.

It is given that the Chesapeake Bay tides vary between 4 feet and 6 feet. it means the minimum value is 4 and maximum value is 6.

Amplitude of the function is


Amplitude=(Maximum-Minimum)/(2)


Amplitude=(6-4)/(2)


Amplitude=1

Therefore the amplitude of the function is y=5.

Midline of the function is


Mid line=(Maximum+Minimum)/(2)


Mid line=(6+4)/(2)=5

Therefore the midline of the function is y=5.

It completes a full cycle in 12 hours.


Period=12 hours


(2\pi)/(B)=12

Period of the function is 12 hours. Therefore the correct option is 1.

User Xeye
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5.9k points