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Q5. During a particular tidal the depth of water, d meters, in a harbor t hours after midnight, can be modelled approximately by the function d = cos 30°.

(a) Plot the graph of d = 4 + cos 30°t, 0 £ t £ 10, in intervals of 1 hour.

Suggested scales with landscape orientation: horizontal axis 2 cm = 1

vertical axis 2 cm = 1 (10)

(b) Use the graph drawn in (a) to determine EACH of the following during this period:

(i) the minimum ground clearance of a vessel in the harbor of draught 2.5m;  (2)

(ii) the length of time a vessel of draught 3.8 m may be expected to be around: (3)

(iii) the expected depth of water in the harbor at 0730 hours.  (1)