(5.5) A weather balloon is being filled at a rate of r(t) = 18(1 + 2t) 2 liters per second, starting with a volume of 0 liters at time t = 0

Question

(5.5) A weather balloon is being filled at a rate of r(t) = 18(1 + 2t) 2 liters per second, starting with a volume of 0 liters at time t = 0. What is the volume of the balloon after 1 minute?

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Natalia 3 weeks 2021-09-19T07:58:11+00:00 1 Answer 0

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    2021-09-19T07:59:51+00:00

    Answer:

    78 liters

    Step-by-step explanation:

    The rate of change in volume is given by:

    r(t) =18(1+2t)^2\\r(t) = (4t^2+4t+1)*18\\r(t) = 72t^2+72t+18

    Integrating the expression above from t = 0 to t = 1 minute, gives us the final volume of the balloon after a minute:

    V=\int\limits^1_0 { (72t^2+72t+18}) \, dt \\V=(24t^3+36t^2+18t+c)|_0^1\\V=24+36+18+c-c=78\ liters

    The volume of the balloon after 1 minute is 78 liters.

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45:7+7-4:2-5:5*4+35:2 =? ( )