SOLUTION: problem solving question
the depth of water d meters, at a port entrance is given by the function
d(t) = 4.5 + 1.5 sin pi t/12
where t is hours
a certain ship needs the
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the depth of water d meters, at a port entrance is given by the function
d(t) = 4.5 + 1.5 sin pi t/12
where t is hours
a certain ship needs the
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Question 1029598: problem solving question
the depth of water d meters, at a port entrance is given by the function
d(t) = 4.5 + 1.5 sin pi t/12
where t is hours
a certain ship needs the depth at the port entrance to be more than 5 meters. The ship can be loaded and unloaded in and out of the port in 9 hours. assuming the the ship enters the port just as the depth at the entrance passes 5 meters, will the ship be able to exit 9 hours later? How long will it have to spare? or by how many minutes will it miss out?
and can you please show me working out and how you got the answer.
Thankyou Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! d(t) = 4.5 + 1.5 sin pi t/12
:
5 = 4.5 + (1.5 * sin(pi * t/12))
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0.5 = 1.5 * sin(pi * t/12)
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note that pi = 180 degrees
:
1/3 = sin(15t)
:
determine angle from inverse sin function = 1/3
:
15t = 19.471220634
:
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t = 1.298081376 approx 1.3 hours
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we need 9 hours to unload the ship
:
d(10.3) = 4.5 + (1.5 * sin(pi * (10.3)/12)) =
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4.5 + (1.5 * 0.430511097) = 5.145766646 meters
:
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*****yes, the ship will be able to exit 9 hours later
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the sin curve is periodic, here is a graph of the equation
:
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we want to know the value of t when the sin(15t) = 1/3 again *****
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note we subtract 19.471220634 from 180 = 160.528779366
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15t = 160.528779366
:
t = 10.701918624
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***The ship has an addition 24 minutes before it can not sale out of the harbor
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