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Water flowing out of a pipe

  1. Dec 26, 2007 #1
    The problem statement, all variables and given/known data

    t (hours) | R(t) (gallons per hour)
    0 9,6
    3 10,4
    6 10,8
    9 11,2
    12 11,4
    15 11,3
    18 10,7
    21 10,2
    24 9,6​
    The rate at which water flows out of a pipe, in gallons per hour, is given by a differentiable function R of time t. The table above shows the rate as measured every 3 hrs for a 24-hour period.

    (a) Use a midpoint Riemann sum with 4 subdivisions of equal length to approximate [tex]\int_0^{24} R(t) dt[/tex]. Using correct units, explain the meaning of your answer in terms of water flow.

    (b) Is there some time t, 0 < t < 24, such that R´(t) = 0? Justify your answer.

    (c) The rate of water flow R(t) can be approximated by Q(t) = (1/79)(768 + 23t - t^2).
    Use Q(t) to approximate the average rate of water flow during the 24-hour time period. Indicate units of measure.


    P.S.: THIS IS AN AP PROBLEM :(
    P.S.2: SORRY, I DON´T HAVE A CLUE OF WHERE TO START
     
    Last edited: Dec 26, 2007
  2. jcsd
  3. Dec 26, 2007 #2

    NateTG

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    For multi-character limits of integration, you need to use {}'s:
    [tex]\int_0^{24}[/tex]

    The question is basically asking how much water has flowed out of the pipe.

    Do you know what a Riemann sum is?
     
  4. Dec 26, 2007 #3
    no.. i have no idea
     
  5. Dec 26, 2007 #4

    NateTG

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  6. Dec 26, 2007 #5

    NateTG

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    http://mathworld.wolfram.com/LowerSum.html
    http://mathworld.wolfram.com/UpperSum.html

    It's a method for approximating the area under a curve by rectangles.

    You'll want to talk to your teacher/look at your notes before attempting part A then.

    Part B doesn't depend on part A, so you can work on that in the meantime.
     
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