In pensacola in june, high tide was at noon. the water level at high tide was 12 feet and 2 feet at low tide. assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve, find an equation for water level in june for pensacola as a function of time (t)

f(t) = 5 cos pi/6 t + 7

Step-by-step explanation:

The information we have given is:

In Pensacola in June, high tide was at noon. The water level at high tide was 12 feet and 2 feet at low tide. Assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve

We have to find:

an equation for water level in June for Pensacola as a function of time (t)

The equation we can use is:

y = A cos bx + c

where A shows the amplitude

b = 2 pi/Period (Period = 12 hrs)

c = midline,

x = t and y = f(t)

A = 1/2 (Xmaximum - Xminimum)

A= 1/2(12-2)

A= 1/2(10)  

A= 5

b = 2 pi / 12 = pi/6  

c = 1/2 (Xmax + Xmin)  

c = 1/2(12+2)

c= 1/2(14)

c= 7

The answer is:

f(t) = 5 cos pi/6 t + 7

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