On Dolphin Beach, the high tide is 2.2 meters and only occurs at 12 a.m. and 12 p.m. The low tide is 1 meter and only occurs at 6 a.m. and 6 p.m.
Which function models the height of the tide t hours after 12 a.m.?

h(t) = 0.6 sin (πt/6) + 1.6
h(t) = 1.6 sin (πt/3) + 2.2
h(t) = 1.2 cos (πt/3) + 1
h(t) = 0.6 cos (πt/6) + 1.6

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UgandanChungus UgandanChungus · Answer 1 · 2019-04-08T00:23:19+02:00

Answer:

D

Step-by-step explanation:

maximum at 12am which is time, t = 0 and 12pm which is time, t = 12

so we’ll use a cosine function since no phase shift is given.

period, T: 1 cycle = 2π and time taken to complete one cycle is 12hrs

T = 2π/(12) = ⅙π

med-line = ½(1 + 2.2) = 1.6

and thus amplitude = 1.6 - 1 = 0.6 or 2.2 - 1.6 = 0.6

h(t) = 0.6 cos(⅙πt ) + 1.6

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