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# IAL differentiation(?) question

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1. The height of sea water, h metres, on a harbour wall at time t hours after midnight is given by
h = 3.7 + 2.5cos(30t – 40)°, 0 < t < 24

(a) Calculate the maximum value of h and the exact time of day when this maximum first occurs.

Fishing boats cannot enter the harbour if h is less than 3

(b) Find the times during the morning between which fishing boats cannot enter the harbour. Give these times to the nearest minute

Okay, how on Earth are you supposed to do this?
2. (Original post by jessyjellytot14)
The height of sea water, h metres, on a harbour wall at time t hours after midnight is given by
h = 3.7 + 2.5cos(30t – 40)°, 0 < t < 24

(a) Calculate the maximum value of h and the exact time of day when this maximum first occurs.

Fishing boats cannot enter the harbour if h is less than 3

(b) Find the times during the morning between which fishing boats cannot enter the harbour. Give these times to the nearest minute

Okay, how on Earth are you supposed to do this?
You should be familiar with these sort of Rcos(x - a) questions.

Cosine is bounded between -1 and 1.

-2.5 < 2.5 cos (anything) < 2.5

So 3.7 -2.5 < 3.7 + 2.5 cos (anything) < 3.7 + 2.5

That's yur maximum right there. This occurs when cos (anything) = 1 (for part(b)) so solve thatz.
3. (Original post by Zacken)
You should be familiar with these sort of Rcos(x - a) questions.

Cosine is bounded between -1 and 1.

-2.5 < 2.5 cos (anything) < 2.5

So 3.7 -2.5 < 3.7 + 2.5 cos (anything) < 3.7 + 2.5

That's yur maximum right there. This occurs when cos (anything) = 1 (for part(b)) so solve thatz.
Oh okay, so is it basically a graph transformation question where y=h and x=t ?
4. (Original post by jessyjellytot14)
Oh okay, so is it basically a graph transformation question where y=h and x=t ?
If you want to think of it that way, yeah.

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