Question

every day there are two low and two high tides of the ocean. at the cove near a lighthouse, the high tide is 4 feet above average sea level and the low tide is 4 feet below average sea level. the function that models this situation is shown where g(t) represents the height, in feet, of the water level relative to the average sea level and t represents the number of hours elapsed since the water height was equal to the average sea level after a low tide. g(t) = 4 sin(π/6 t) five hours have elapsed since the water height was equal to the average sea level after a low tide. what is the height, in feet, of the water level relative to the average sea level? a. 2 feet b. 4 feet c. 0.5 foot d. 2.5 feet

Explanation:

Step1: Substitute \( t = 5 \) into the function

We are given the function \( g(t)=4\sin(\frac{\pi}{6}t) \). Substitute \( t = 5 \) into the function: \( g(5)=4\sin(\frac{\pi}{6}\times5) \).

Step2: Calculate the sine value

First, calculate \( \frac{\pi}{6}\times5=\frac{5\pi}{6} \). We know that \( \sin(\frac{5\pi}{6})=\frac{1}{2} \).

Step3: Calculate the value of \( g(5) \)

Since \( g(5)=4\sin(\frac{5\pi}{6}) \) and \( \sin(\frac{5\pi}{6})=\frac{1}{2} \), then \( g(5)=4\times\frac{1}{2} \).

Answer:

A. 2 feet