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The function f(t) = 5*cos ((pi/4)*t) + 11 represents the tide in Dark Sea. It has a maximum of 16 feet when time (t) is 0 and a minimum of 6 feet. The sea repeats this cycle every 8 hours. After six hours, how high is the tide?

A. 11 feet
B. 6 feet
C. 8.5 feet
D. 10.5 feet

Respuesta :

merlynthewhizz
Given [tex]t = 6[/tex]
Substitute this value of 't' into the function

[tex]f(6) = 5 cos( \frac{6 \pi }{4})+11 [/tex]
[tex]f(6)=11 feet[/tex]

After six hours, the tide is 11 feet high.

What is function?

  • "It defines a relation between input and output values."
  • "In function, for each input there is exactly one output."

For given question,

We have been given a function [tex]f(t)=5\times cos((\frac{\pi}{4} )t)+11[/tex]

which represents the tide in Dark Sea and t represents the time in hours.

We need to find the height of the tide after 6 hours.

For t = 6, we need to find the value of function f(t)

[tex]\Rightarrow f(6)=5\times cos((\frac{\pi}{4} )6)+11\\\\\Rightarrow f(6)=5\times cos((\frac{3\pi}{2} ))+11\\\\\Rightarrow f(6)=0+11\\\\\Rightarrow f(6)=11[/tex]

Therefore, after six hours, the tide is 11 feet high.

Learn more about the function here:

https://brainly.com/question/13461298

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