SOLUTION: The rate filled a tank with water is represented by the the equation r(t)=6t^2+3t-2 gallons per second. how many gallons of water will be in the tank for the first 5 seconds?

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Question 1042692: The rate filled a tank with water is represented by the the equation r(t)=6t^2+3t-2 gallons per second. how many gallons of water will be in the tank for the first 5 seconds?
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The rate filled a tank with water is represented by the the equation r(t)=6t^2+3t-2 gallons per second. how many gallons of water will be in the tank for the first 5 seconds?
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f(5) = 6(5^2) + 3(5)-2 = 6*25+15-2 = 150+15-2 = 133 gallons
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Cheers,
Stan H.
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Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
The rate filled a tank with water is represented by the the equation r(t)=6t^2+3t-2 gallons per second.
how many gallons of water will be in the tank for the first 5 seconds?
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Integral of r(t) from 0 (zero) to 5 seconds.


Which is V(t) = 2t%5E3+%2B+1.5t%5E2+-+2t at t = 5.


Which is 2%2A5%5E3+%2B+1.5%2A5%5E2+-+2%2A5 =  2*125 + 1.5*25 - 10 = 277.5 gallons.