Question

The water depth in a harbor rises and falls over time. the function f(t) = 4.1 sine (startfraction pi over 6 endfraction t minus startfraction pi over 3 endfraction) 19.7 models the water depth, in feet, after t hours. during the first 24 hours, at what times does the water depth reach a maximum? at 5 and 17 hours at 11 and 23 hours at 2, 8, 14, and 20 hours at 5, 11, 17, and 23 hours

Answer 1

Step-by-step explanation:

A function assigns the value of each element of one set to the other s/p

Answer 2

The water depth in the harbor reaches its maximum at 5, 11, 17, and 23 hours during the first 24 hours.

Step-by-step explanation:

The water depth reaches its maximum when the sine function in the model reaches its peak value of 1. In the given function, f(t) = 4.1 sin(π/6 t - π/3) + 19.7, the sine function reaches its peak every time the argument (π/6 t - π/3) is an odd multiple of π/2.

Within the first 24 hours (t = 0 to 24):

At t = 5, π/6 t - π/3 = π/2, making sin(π/6 t - π/3) = 1 and f(t) reaches its maximum.

Similarly, at t = 11, 17, and 23, the argument of the sine function becomes 3π/2, 5π/2, and 7π/2, respectively, each leading to a peak value of sin(π/6 t - π/3) and a maximum for f(t).

Therefore, the water depth in the harbor reaches its maximum at 5, 11, 17, and 23 hours during the first 24 hours.