Question

The depth of water near a boat dock is collected by a buoy. The data shows that the water level reached 11 feet during high tide at 2:00am and a level of 8 feet during low tide at 9:00am. The depth can be modeled by a sinusoidal function. How deep will the water be at noon? Round your answer to the nearest hundredth. HINT: The equation that models this is y=1.5sin (25.72(x+1.5))+9.5

Answer 1

The water will be approximately 8.32 feet deep at noon.

Step-by-step explanation:

To find how deep the water will be at noon, we can substitute the value of x = 10 into the given equation.

So, y = 1.5sin(25.72(10+1.5))+9.5

y ≈ 1.5sin(227.32)+9.5

y ≈ 1.5(-0.586)+9.5

y ≈ 8.321

Therefore, the water will be approximately 8.32 feet deep at noon.

Answer 2

9514 1404 393

Answer:

9.17 ft

Step-by-step explanation:

Put x=12 in the equation and evaluate. (The sine argument is in degrees.)

y = 1.5·sin(25.72(12 +1.5)) +9.5 = 1.5·sin(347.22) +9.5

y = -0.33 +9.5 = 9.17

The water will be 9.17 feet deep at noon.