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At an amusement park, the pendulum ride's movement from its starting position in meters can be represented by the equation f of x is equal to negative 4 times the cosine of the quantity x over 8 end quantity plus 4 period If x represents time measured in seconds since the ride first began, at what times will the pendulum's movement be 8 meters from its starting position?

At an amusement park the pendulum rides movement from its starting position in meters can be represented by the equation f of x is equal to negative 4 times the class=

Respuesta :

Given

[tex]f(x)=-4\cos(\frac{x}{8})+4[/tex]

To find x when f(x)=8.

Explanation:

It is given that,

[tex]f(x)=-4\cos(\frac{x}{8})+4[/tex]

Then, for f(x)=8,

[tex]\begin{gathered} 8=-4\cos\mleft(\frac{x}{8}\mright)+4 \\ 4\cos(\frac{x}{8})=-4 \\ \cos(\frac{x}{8})=-1 \\ \frac{x}{8}=(2n+1)\pi \\ x=8\pi(2n+1) \\ x=(8\pi+16n\pi)sec \end{gathered}[/tex]

Hence, the answer is

[tex]x=(8\pi+16n\pi)sec[/tex]

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