Problem

The depth of water in a harbour

t

hours after midnight is

D(t) = 4 \cos\left(\frac{\pi}{6}t\right) + 6

metres. a. Sketch the graph of

D

against

t

for

0 \le t \le 24

. b. Find the highest and lowest depths of the water, and the times at which they occur. c. A boat requires a water depth of 5 metres to sail in. Will the boat be able to enter the harbour at 8 pm?

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