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The function f(t) = 5 cos(pi over 6t) + 7 represents the tide in Stanley Sea. It has a maximum of 12 feet when time (t) is 0 and a minimum of 2 feet. The sea repeats this cycle every 12 hours. After four hours, how high is the tide?



11.3 feet


9.5 feet


4.5 feet


2.6 feet

Respuesta :

The function for the height is
[tex]f(t) = 5cos( \frac{ \pi }{6} t)+7[/tex]

f(0) = 5 cos(0) + 7 = 5 + 7 = 12  (verified)
The period is T  = 12 hours.

After 4 hours (t = 4), the height is
[tex]f(4) = 5cos( \frac{ 4\pi }{6} )+7 = 5*(-0.5)+7=4.5[/tex]

A graph of f(t) confirms the answer.

Answer: 4.5 ft
Ver imagen Аноним
MrRoyal

Based on the function equation, the tide is 4.5 feet high after 4 hours

How to determine the height after 4 hours?

The function is given as:

f(t) = 5 cos((π/6)t) + 7

After 4 hours, the value of t is:

t = 4

So, we have:

f(4) = 5 cos((π/6)*4) + 7

Evaluate the product

f(4) = 5cos(2π/3) + 7

Evaluate the expression

f(4) = 4.5

This means that, the tide is 4.5 feet high after 4 hours

Read more about cosine functions at:

https://brainly.com/question/17075439

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