Pa-help po kuya. Pre-calculus. Salamat po ng marami.
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Pa-help po kuya. Pre-calculus. Salamat po ng marami.
Pa-help po kuya. Pre-calculus. Salamat po ng marami.
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Problem:
A floating dock on the coast measures the depth of water below it
d(t) = 2.4cos(πt/8) + 7.2
where t is the time after midnight
1.) What is the depth of water at midnight? 8am? 2:40am?
Solution:
depth of water at midnight
d(t) = 2.4cos(πt/8) + 7.2
d(t) = 2.4cos(π(0))/8 + 7.2
d(t) = 2.4(1) + 7.2
d(t) = 2.4 + 7.2
d(t) = 9.6m
depth of water at 8am
d(t) = 2.4cos(πt/8) + 7.2
d(t) = 2.4cos(π(8)/8) + 7.2
d(t) = 2.4cosπ + 7.2
d(t) = 2.4(-1) + 7.2
d(t) = -2.4 + 7.2
d(t) = 4.8m
depth of water at 2:40am
2:40am = 2 hrs and 40mins ; 40 mins = 40/60 = 2/3
2:40am = 8/3 hrs
d(t) = 2.4cos(πt/8) + 7.2
d(t) = 2.4cos(π(8/3)/8) + 7.2
d(t) = 2.4cosπ/3 + 7.2
d(t) = 2.4(0.5) + 7.2
d(t) = 1.2 + 7.2
d(t) = 8.4m
2.) How many hours is a full tidal cycle?
16 hours or at 4pm
3.) Sketch one cycle of the graph
Please see attached file
4-5.) Use the graph to estimate when the water is 5m? 8m? For the first time
d(t) = 2.4cos(πt/8) + 7.2
5 = 2.4cos(πt/8) + 7.2
t = 6.95 hrs or 6:57am or by estimate 7am
at 7am, the water is 5m
d(t) = 2.4cos(πt/8) + 7.2
8 = 2.4cos(πt/8) + 7.2
t = 3.13hrs or 3:08am or by estimate 3:10am
at 3:10am the water is 8m
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