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The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 a.m. and 3:30 p.m., with a depth of 3.25 meters, while high tides occur at 7:45 a.m. and 11:15 p.m., with a depth of 8.75 meters. Which of the following equations models d, the depth of the water in meters, as a function of time, t, in hours? Let t = 0 be 12:00 a.m.

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Answer:

C

Step-by-step explanation:

took the review and got it right

lhmarianateixeira

In this exercise we have to calculate the value of the water depth, so we have:

[tex]d=5.5cos(12t)+6[/tex]

Putting together some information given in the statement we have:

  • The minimum depth of 3.25 m occurs at 12:00 am and at 3:30 pm.
  • Therefore the period t=0 will be  12:00 am.
  • The maximum depth of 8.75 m occurs at 7:45 am and at 11:15 pm.

Knowing that the formula will be given by an equation similar to:

[tex]d = acos(bt) + k[/tex]

Where:

  • d = depth, m
  • t = time, hours
  • a= amplitude

The amplitude difference is given by:

[tex]8.75-3.25= 5.5m[/tex]

The mean depth is:

[tex]k = (3.25 + 8.75)/2 = 6.0 m[/tex]

Then writing the equation with;

[tex]d = acos(bt) + k\\d=5.5cos(12t)+6[/tex]

See more about functions at brainly.com/question/4450545

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