Due to the tide, the depth of water at a dock rises and falls over the course of the day. The depth can be modeled by the following equation: f (t) 4sin12) + 7 If you want to tie up your boat at the dock, the water needs to be nine feet deep. If the time is currently t0, at what time will you be able to tie up your boat? Choose the closest time

Question

Nelson Douglas

Mathematics

31 January, 19:07

Due to the tide, the depth of water at a dock rises and falls over the course of the day. The depth can be modeled by the following equation: f (t) 4sin12) + 7 If you want to tie up your boat at the dock, the water needs to be nine feet deep. If the time is currently t0, at what time will you be able to tie up your boat? Choose the closest time

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Answers (1)

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Guillermo Lin · Answer 1

I will be able to tie the boat in 2 hours.

Step-by-step explanation:

f (t) = 4sin (πt/12) + 7

At t=0, f (t) = 7

we must find t in which f (t) = 9, we can replace this and simply solve for t, also, we will be working with radians as units:

9=4sin (πt/12) + 7

2=4sin (πt/12)

1/2=sin (πt/12)

arc sin (1/2) = πt/12

π/6=πt/12

12π/π6=t

2=t

So this is our number. To be sure of this we can replace 2 as t in out oiginal equation

f (2) = 4sin (π2/12) + 7=9