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Function of 3 variable help!

  1. Oct 14, 2013 #1
    1. The problem statement, all variables and given/known data

    The problem is given in the picture attached. However we are given the equation of a 4 dimensional shape with certain choice given to explain the shape in that dimension.

    2. Relevant equations

    Equations of different shape such as:

    sphere: √(x^2+y^2+z^2) = r
    Ellipse: (x-h)/a^2 + (y-k)/b^2 = K
    Hyperbola: (x-h)/a^2 - (y-k)/b^2 = 1

    3. The attempt at a solution

    Well for question one and two, I said 1 ( which is w=x^2+y^2+z^2) is a "a collection of equally spaced concentric spheres" and 2 ( w=√(x^2+y^2+z^2) was "a collection of unequally spaced concentric spheres ".Though I know the difference between both is the radius where one is w and the other is √w. But why does have a radius of √w make the sphere unequally spaced?

    My teacher barely touched the topic so I have a hard time figuring out how to visualize these shapes.
     
  2. jcsd
  3. Oct 14, 2013 #2
    I couldn't see my attachment... here it is ( trying again)
     

    Attached Files:

  4. Oct 15, 2013 #3
    You are correct about #1.
     
  5. Oct 15, 2013 #4
    You are correct about #1. I do know the answers to some of the others, and can guess some, but perhaps it would be best to tell you how I would go about this if I had to do the problem.

    Go back to 3 dimensions, and look up the equations of the conic sections. Answer the questions when z is omitted. It has to be similar in 4 dimensions.
     
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