FEBRUARY 20, 2015 (15 points) Eachday th etide in a harboreontinuously goes inan
ID: 3196544 • Letter: F
Question
FEBRUARY 20, 2015 (15 points) Eachday th etide in a harboreontinuously goes inand out raising And lowering a boat an- chored there At low tide, the bont is only 2 feet above the ocean floor. Then 6 hours later, at peak high MTH 131 ExAM 1 tide, the bost is 20 feet above the ocean fBoor. Suppose the boat is at low tide at midnight. (a) Sketch and label two cycles of a periodic function D(t) modeling the boat's distance above the ocean Min 2ft (D) ft- 24 20 18 16 12 10 246 810 12 14 10 18 20 22 24 20 28 30im(hvs) (b) Find a formula for -9 cos (hot)+Il 2. 3 2. Answer: D(t)=-9 cos ( (vt) til (e) Use your formula to find the boat's distance above the ocean the first decimal place and include units in your answer. floor 2pm. Round your answer to Agos(t%-14) +11 bs 05 AnswerExplanation / Answer
as
D(t) = -9 cos(t*pi/6) + 11
for 2 PM, t =14
=> D(14) = -9 cos(14*pi/6) + 11
= -9 cos(2*pi + 2*pi/6) +11
= -9 cos( 2*pi/6) + 11 { cos(2pi+x) = cos(x) }
= -9 cos(pi/3) + 11
= -9 *1/2 + 11
= 11-4.5
= 6.5 feet (answer)
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