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Write a cosine function that has an amplitude of 2, a midline of y=4 and a period of 1/7

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The general form of a cosine function is:

y = A cos (Bx - C) + D

where A is the amplitude, B is the frequency (or 2π divided by the period), C is the phase shift, and D is the vertical shift (or midline).

Using the given information, we can plug in the values to get:

A = 2 (amplitude)

D = 4 (midline)

Period = 1/7

Frequency = 2π / Period = 2π / (1/7) = 14π

So the function is:

y = 2 cos (14πx - C) + 4

where C is the phase shift. Since no phase shift is given, we can assume it to be zero. Therefore, the final equation is:

y = 2 cos (14πx) + 4

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