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Math Help - Physics / Rate of Change / Velocity

  1. #1
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    Exclamation Physics / Rate of Change / Velocity

    Can't figure this one out! I tried, but I have major doubts about my answer:

    The number of gallons of water in a tank t minutes after the tank has started to drain is Q(t) = 200(30 - t)^2 . How fast is the water running out at the end 10 minutes? What is the average rate at which the water flows out during the first 10 minutes?

    Please respond ASAP! Thanks!
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  2. #2
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    Quote Originally Posted by djalali59 View Post
    Can't figure this one out! I tried, but I have major doubts about my answer:

    The number of gallons of water in a tank t minutes after the tank has started to drain is Q(t) = 200(30 - t)^2 . How fast is the water running out at the end 10 minutes? What is the average rate at which the water flows out during the first 10 minutes?

    Please respond ASAP! Thanks!
    The exact rate at t=10 is the derviative evaluated at t=10

    \frac{dQ}{dt}=400(30-t)(-1)\bigg|_{t=10}=400(30-10)(-1)=-8000

    The average rate of change is just the slope of the line at the points

    (0,Q(0)), (10,Q(10)) so we get

    r_{ave}=\frac{Q(10)-Q(0)}{10-0}=\frac{200(30-10)^2-200(30)^2}{10}=
    20(20^2-30^2)=20(50)(-10)=-10000
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    The exact rate at t=10 is the derviative evaluated at t=10

    \frac{dQ}{dt}=400(30-t)(-1)\bigg|_{t=10}=400(30-10)(-1)=-8000

    The average rate of change is just the slope of the line at the points

    (0,Q(0)), (10,Q(10)) so we get

    r_{ave}=\frac{Q(10)-Q(0)}{10-0}=\frac{200(30-10)^2-200(30)^2}{10}=
    20(20^2-30^2)=20(50)(-10)=-10000
    but i thought for the derivative of the function, you had to multiply everything out, and then figure out each of the derivatives? Or was I mistaken?
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  4. #4
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    Quote Originally Posted by djalali59 View Post
    but i thought for the derivative of the function, you had to multiply everything out, and then figure out each of the derivatives? Or was I mistaken?
    you can do it both ways ... easier to do it the way ES did it using the chain rule for derivatives.
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