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Homework Help: Please Help Soon thanks

  1. Nov 29, 2007 #1
    Please Help Soon!!!!!thanks

    A river follows the path y = f(z) where x, y are in kilometers. Near the
    sea, it widens into a lagoon, then narrows again at its mouth. At the point
    (x, y), the depth of the lagoon is given by D(x, y) = 40−160(y−f(x))2 − 40x2 meters. The lagoon itself is described by D(x, y)  0. What is the
    volume of the lagoon in cubic meters?

    so far i got that this problem needs to use transformation and the jacobian.
    i put x=u^2-v^2
    y=2uv
    find the trans using the matrix getting
    4u^2+4v^2
    double integral (2uv)(4u^2+4v^2)dudv
    if what i did so far was right could anyone tell me how to find the limits or at least enlighten me in the right direction
     
  2. jcsd
  3. Nov 29, 2007 #2

    HallsofIvy

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    Science Advisor

    I'm sorry but I have no idea what "D(x, y)  0" means. What that "box" a special symbol?
     
  4. Nov 29, 2007 #3
    sorry i wrote it down wrong
    D(x,y)>=0
     
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