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November 01, 2025, 07:03:56 am
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Author Topic: Calc 2 Mixing Question  (Read 672 times)  Share 

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mikehepro

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Calc 2 Mixing Question
« on: September 20, 2015, 11:30:04 pm »
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Hey guys!
I'm struggling with a). Any help would be greatly appreciated!!!
I tried setting up a equation and using separable ODE and then using integration by parts,however i'm getting a weird answer.

Whisky consists mainly of water and alcohol. Before bottling, the alcohol is diluted with water to the standard bottle concentration of (44−46)%. Suppose a 2500 gallon tank initially contains 600 gallons of pure alcohol. An alcohol-water mix of (1+cos t)/6 % alcohol is fed in at 6 gallons per minute and the mixture stirred; simultaneously the mixture is withdrawn at 3 gallons per minute.

(a) Find the amount of alcohol (in %) in the tank at time t.
(b) Approximately how many hours will it take for the mixture in the tank to reach 44%?
(c) Approximately how many hours will it take for the mixture in the tank to overflow?

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