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posted by  niqua on 10/27/2009 7:01:16 PM  |  status: Live  |  Earned Karma: 36

derivative as an instantaneous rate of change

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Electrical Engineering N/A N/A N/A 10/27/2009 at 10:00:00 PM
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A tank containing 6000L of water drains out in 30 min. The volume V of water in the tank after t min of draining is V=6000(1-t/30)2. Find the instantaneous time rate of change of V after 15 min draining.

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Sage
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posted by Gort on 11/5/2009 6:50:37 AM  |  status: Live
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A tank containing 6000L of water drains out in 30 min. The volume V of water in the tank after t min of draining is V=6000(1-t/30)2. Find the instantaneous time rate of change of V after 15 min draining.
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01.   V = 6000*[1 - t/15 + (1/900)*t2 ]
02.   γ = dV/dt = 6000*[-1/15 + (1/450)*t]
03.   γ(t = 15) = 6000*[-1/15 + 15/450] = 6000*(-15/450) = -200 Liters/minute @ t = 15 minutes
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Gort
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