mcr 3u exam review.5 - 3 Because of the tide the depth of the water in a harbour is modelled by the equation d = 2.5 cos 30t 7.5 where d represents the

# mcr 3u exam review.5 - 3 Because of the tide the depth of...

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360 720 90 180 270 450 540 630 –90 –180 θ 1 2 3 –1 –2 –3 y 360 720 90 180 270 450 540 630 –90 –180 θ 1 2 3 –1 –2 –3 y (midnight, 5 m) (3 a.m., 7.5 m) (6 a.m., 10 m) (9 a.m., 7.5 m) (noon, 5 m) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 t 2 4 6 8 10 d 3. Because of the tide, the depth of the water in a harbour is modelled by the equation 5 . 7 t 30 cos 5 . 2 d + - = , where d represents the depth of the water in metres and t represents the number of hours after midnight. (i.e. t = 0 means midnight, t = 1 means 1 A.M., and so on.) a) Sketch the graph for one cycle, showing five ordered pairs. b) What is the depth of the water (to the nearest centimeter) at 7:30 a.m.? c) At what time will the depth of the water reach 9 metres for the first time? 4. The population of frogs in a particular swamp in Ontario follows a yearly cycle. This cycle can be modelled as a sinusoidal function. The maximum population of 300 frogs occurs at the beginning of October. The minimum population of 60 frogs occurs 6 months later, at the beginning of April.

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