Question

The function t(t)=5 cos(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?

a. 8 feet
b. 10 feet
c. 12 feet
d. 14 feet

Answer 1

The height of the tide after six hours is approximately 15.8905 feet.

Step-by-step explanation:

To find the height of the tide after six hours, we can substitute t = 6 into the function t(t) = 5cos(4t) + 11.

So for t = 6, we have:

t(6) = 5cos(4*6) + 11.

Simplifying further, we get:

t(6) = 5cos(24) + 11.

Using a calculator, we find that cos(24) is approximately 0.9781. Plugging this value into the equation:

t(6) = 5(0.9781) + 11.

Calculating further, we get:

t(6) ≈ 4.8905 + 11.

Adding the two values, we find:

t(6) ≈ 15.8905 feet.