Quick question

[davyp3]

maths quest ex 6g

A student wanting to catch fish to sell at a local market on Sunday has discovered that
more fish are in the water at the end of the pier when the depth of water is greater than
8.5 metres. The depth of the water (in metres) is given by d = 7 + 3 sin t, where t
hours is the number of hours after midnight on Friday.


e If the student can fish for only two hours at a time, when should she fish in order
to sell the freshest fish at the market from 10.00 am on Sunday morning?

not sure how to approach the question

can someone please help?

[m@tty]

So you're looking for the two hour block where d>8.5 closest to t=10.

First solve

.

.

So now you need to find k such that the end of the fishing time, , is closest to 10.

It happens that places the end time at 8.9 hours after midnight. While the previous time slot ended at 2.61 hours after midnight, and the next high tide comes 5 hours after opening time...

Therefore you want the end time to be at .

And since the student can only fish for two hours at a time she can only begin two hours before this.

So the best time for her to fish is from o'clock to o'clock...

So .

6:54 til 8:54 am.