The depth of water in a tank oscilliates sinusoidally once every 6 hours. If the smallest depth is 5.5 feet and the largest depth is 8.5 feet, find a possible formula for the depth of time inhours.

I say f(x)=6.75+1.25sin(pi/3)

Am I right

Correct.

I believe it should have been

y = 7 + 1.5sin(pi/3)t

To determine if your formula for the depth of time in hours is correct, let's analyze the given information. We are told that the depth of water in the tank oscillates sinusoidally once every 6 hours, with the smallest depth being 5.5 feet and the largest depth being 8.5 feet.

The general formula for a sinusoidal function is:
f(x) = A + Bsin(Cx + D)

In this case, we can assign the following values to the variables in the formula:
A = average depth = (smallest depth + largest depth) / 2 = (5.5 + 8.5) / 2 = 7 feet
B = amplitude = (largest depth - smallest depth) / 2 = (8.5 - 5.5) / 2 = 1.5 feet
C = frequency = 2π / period = 2π / 6 = π/3 (since the period is 6 hours and 2π represents a complete cycle)
D = phase shift = 0 (since we are not given any specific starting point)

Substituting these values into the general formula, we get:
f(x) = 7 + 1.5sin(π/3x)

Comparing this with your proposed formula f(x) = 6.75 + 1.25sin(π/3), we can see that they are quite similar, but there are slight differences in the constant terms. The average depth should be exactly 7 feet, not 6.75 feet, and the amplitude should be 1.5 feet, not 1.25 feet.

Therefore, the correct formula for the depth of time in hours would be:
f(x) = 7 + 1.5sin(π/3x)

So, your formula is close but not entirely accurate.