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The function f(t) = 5 cos(pi over 4t) + 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?

Respuesta :

DeanR

[tex] f(t) = 11 + 5 \cos(\frac \pi 4 t)[/tex]


The period T satisfies [tex]2\pi=\frac \pi 4 T[/tex] so is indeed 8.


We're just asked for


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


Answer: 11 feet


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