Question

If the depth of the water at a pier on a given day can be modeled using the function d(t)= 5sin (0.25t-π )+9 , in which t represents the number of hours since midnight, what is the depth of the water at 11 am? (Give your answer rounded to the nearest tenth.)

Answer 1

To find the depth of the water at 11 am, we calculate d(11) using the function d(t) = 5sin(0.25t-π)+9. Substituting t with 11 hours and evaluating the expression, we get a result of approximately 7.1 meters after rounding to the nearest tenth.

Step-by-step explanation:

To find the depth of the water at the pier at 11 am using the function d(t) = 5sin(0.25t-π)+9, first calculate the value of t at 11 am. Since t represents the number of hours since midnight, at 11 am, t would be 11 hours. Substituting 11 for t into the function, we get:

d(11) = 5sin(0.25×11-π)+9

After performing the calculations inside the sine function:

d(11) = 5sin(2.75-π)+9

And using a calculator to find the sine value:

d(11) = 5sin(-0.3917)+9

d(11) = 5×(-0.3827)+9

d(11) = -1.9135+9

We round the answer to the nearest tenth:

The depth of the water at 11 am is approximately 7.1 meters.