Question

During high tide around 11:00 p.m., the water level is 3 feet above a marker on a pier. The following day, during low tide around 5:12 a.m., the water level has dropped 3 feet below the marker. The height of the water is modeled by the function y=3cos(24πx/149) where x is the time in hours since 11:00 p.m. What is the height of the water at 2:15 a.m.?

Answer 1

To determine the height of the water at 2:15 a.m., we calculate the time elapsed since 11:00 p.m., substitute it into the tide function, and find the result to be approximately 2.61 feet above the marker on the pier.

Step-by-step explanation:

To find the height of the water at 2:15 a.m., we first must calculate the time elapsed since 11:00 p.m. in hours. From 11:00 p.m. to 2:15 a.m. is 3 hours and 15 minutes, which is 3.25 hours. We then substitute this time into the tide model function y=3cos(24πx/149).

The calculation is as follows:

y = 3 cos(π * (24/149) * 3.25)

We use a calculator to evaluate the cosine and then multiply by 3 to get the height of the water above the pier marker. Let's proceed with the calculation:

y = 3 cos(π * (24/149) * 3.25)

y ≈ 3 cos(0.516)

y ≈ 3(0.869)

y ≈ 2.61 feet

Therefore, the height of the water at 2:15 a.m. is approximately 2.61 feet above the marker on the pier.