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How do you find a level surface representing another surface?

  1. Feb 1, 2012 #1
    1. The problem statement, all variables and given/known data
    The surface S is the graph of f(x,y) = sqrt(25-x^2)

    a)Find a level surface g(x,y,z) = c Representing S.
    b) with C=?



    2. Relevant equations



    3. The attempt at a solution
    I have no idea what to do with this question. How should I find g(x,y,z)? Do I let sqrt(25-x^2) = C? I tried this method and the answer is wrong. Am I on the right track?And what does it mean by C=?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 1, 2012 #2

    Simon Bridge

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    http://math.arizona.edu/~calc/Text/Section12.5.pdf [Broken]
    ... but surely you've covered this?

    Don't know what it means by C=?
    Does not look like a general notation.
     
    Last edited by a moderator: May 5, 2017
  4. Feb 1, 2012 #3
    I missed 2 weeks of lectures because I was sick, so I am having a really difficult time to catch up...
    So basically I take sqrt(25-x^2)-z and solve it for Z?
     
    Last edited by a moderator: May 5, 2017
  5. Feb 1, 2012 #4

    Simon Bridge

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    Ah - then you should read through that link I gave you.
    It is very hard to give you hints without doing the thing for you it's that basic - the link covers the concepts and has examples.

    Basically, you put g(x,y,z) = z-f(x,y) = c which gives you a family of 3D surfaces... now, if c=0, you get a simplification that will tell you the basic shape of the surface in 3D.
     
  6. Feb 1, 2012 #5

    HallsofIvy

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    First, [itex]f(x,y)= \sqrt{25- x^2}[/itex] is not a surface in a xyz-coordinate system because you need a coordinate representing z. Rather [itex]z= \sqrt{25- x^2}[/itex] is a surface. And that is the same as [itex]\sqrt{25- x^2}- z= 0[/itex].
     
  7. Feb 1, 2012 #6

    Simon Bridge

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    Its badly phrased isn't it?
    I got my interpretation by googling for similar phrasing ... JIC.
    shalanheyyo really needs to check with someone else on the course.

    It could be the intent is that one put [itex]z=f(x,y)[/itex] then rearrange that so all the "constant" terms are on the RHS and all the terms with x or y or z in them are on the LHS. This would have form g(x,y,z)=c, and it would make sense to ask what c is.
     
  8. Feb 1, 2012 #7
    I emailed my Prof and the question is actually really simple. I guess I got confused by how the question is worded
     
  9. Feb 1, 2012 #8

    Simon Bridge

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    So are you going to enlighten us?
     
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