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Vector Analysis ifferential Calculus

  1. Aug 28, 2008 #1
    Vector Analysis:Differential Calculus

    1. The problem statement, all variables and given/known data

    The height of a certain hill(in feet) is given by

    h(x,y)=10(2xy-3x^2-4y^2-18x+28y+12)

    where y is the distance (in miles) north, x the distance east of South Hadley

    a)Where is the top of the hill located

    b) How high is the hill?




    2. Relevant equations

    grad T=dT/dx xhat+dT/dy yhat+ dT/dz zhat

    3. The attempt at a solution

    a) I need to find the distance in the x direction , so I would take the derivative of h(x,y) with respect to x

    dh/dx=20*x-12=0=> x=3/5 feet

    b) same algorithm, only I am now ask to calculate how high the hill is and so I would take the derivative of h(x,y) with respect to y:

    dh/dy=y=3*x+9=3*(.6)+9=10.8 feet

    or maybe I should calculate h(x,y) in order to determine the height of the hill. Therefore , I'd plugged x and y into h(x,y) right?
     
    Last edited: Aug 28, 2008
  2. jcsd
  3. Aug 29, 2008 #2

    tiny-tim

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    Hi Benzoate! :smile:

    (have a curly d: ∂ :smile:)
    Nooo … :cry:

    Your ∂h/∂x and ∂h/∂x are completely wrong …

    for example, ∂h/∂x should start with 20*y, not 20*x

    and what happened to all the other terms (and all the other 10s)?

    You need to go back to your book and look again at how to do partial derivatives … :smile:
     
  4. Aug 29, 2008 #3
    Re: Vector Analysis:Differential Calculus

    wow I messed up big time with calculating my partial derivatives.

    Anyway, dh/dx= 20y-90x-180= and dh/dy= 20x-80y+280 =0. once I calculate my values for x and y , I would be able to calculate the height which is h(x,y), correct?
     
  5. Aug 29, 2008 #4

    tiny-tim

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    (what happened to that ∂ I gave you? :smile:)

    erm … 90x is wrong :rolleyes:

    and the equations would be a lot more manageable if you'd divided them by 20 :wink:
    That's right! :smile:
     
  6. Aug 29, 2008 #5

    HallsofIvy

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    Re: Vector Analysis:Differential Calculus

    Why is this listed under "physics" rather than "mathematics"?
     
  7. Aug 29, 2008 #6
    Re: Vector Analysis:Differential Calculus

    well because the problem came from my intro to Electrodynamics textbook
     
  8. Aug 30, 2008 #7

    tiny-tim

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    it's field theory …

    :biggrin: The hill was part of a field! :biggrin:
     
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