What is the depth of water at 7:30 am? And at what time will the depth of water reach 9 metres for the first time?

Question

Description:Because of the tide the depth of water in a Harbour is modeled by the equation d=-2.5cos30t+7.5, where do reps the depth of water in metres and the reps the number of hours after midnight (t=0 @midnight, t=1 at 1 am and so on) 

 

How would I find depth at 7:30 am and time depth reaches 9 metres for the first time? ,If you could please show steps that would help.

Answer 1

Given that, d=-2.5cos30t+7.5, where do represents the depth of water in metres and t represents the number of hours after midnight (t=0 @midnight, t=1 at 1 am and so on)bstituting d
  Thus at 7:30 AM t=7.5, substituting 7.5 for t in the given equation we get, d=-2.5cos30*7.5t+7.5 = -2.5* 0.866*7.5+7.5 =-8.738 meters

the negative sign denotes the opposite (of depth), i.e., height of wayer level

 

Again substituting 9 meters for d in the given expression, 9=-2.5cos30t+7.5

=>1.5=-2.5cos30t ..... subtracting 7.5 from both sides

=>t=1.5/(-2.5cos30) .... dividing both sides by -2.5cos30

=t=-0.69 =41 minutes 24 second before midnight, because of negative sign it is decided to be before midnight that is at 11:18:36 PM.

Answer 2

What do you mean by the word "reps"?