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mathstina Group Title

At what point on the paraboloid y = x^2+z^2 is the tangent plane parallel to the plane x+2y+3z=1?

  • one year ago
  • one year ago

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  1. TuringTest Group Title
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    find the gradient of the surface

    • one year ago
  2. mathstina Group Title
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    <2,-1,2>

    • one year ago
  3. TuringTest Group Title
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    grad f=<2x, -1, 2z>

    • one year ago
  4. mathstina Group Title
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    yes

    • one year ago
  5. TuringTest Group Title
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    ok, now since we can't plug in anything that will change y, let's multiply the gradient by a scalar to get the j-component equal to 2 like it is for the plane

    • one year ago
  6. mathstina Group Title
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    multiply by -2

    • one year ago
  7. TuringTest Group Title
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    right, and so we get?

    • one year ago
  8. mathstina Group Title
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    grad f=<-4x,2y, -4z>

    • one year ago
  9. TuringTest Group Title
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    grad f=<-4x,2,-4z> that y can't just appear from nowhere

    • one year ago
  10. TuringTest Group Title
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    so what value of x makes the i-components equal for the plane and grad f ? what value of z makes the k-components equal?

    • one year ago
  11. mathstina Group Title
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    x=1/2and z= 3/2 ???

    • one year ago
  12. TuringTest Group Title
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    from the equation as we have it we need x=-1/4 and z=-3/4

    • one year ago
  13. mathstina Group Title
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    ok.

    • one year ago
  14. TuringTest Group Title
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    that's all then... boring problem

    • one year ago
  15. mathstina Group Title
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    why qns with sphere have 2 sets of points?

    • one year ago
  16. TuringTest Group Title
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    hm... seems strange that y does not matter. Maybe I messed this one up :P

    • one year ago
  17. TuringTest Group Title
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    sorry? what do you mean?

    • one year ago
  18. mathstina Group Title
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    for qns with sphere has 2 sets of points as ans why?

    • one year ago
  19. TuringTest Group Title
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    what do you mean it has 2 sets of points?

    • one year ago
  20. mathstina Group Title
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    the ans fot this qn is (-1/4, -2,-3/4)

    • one year ago
  21. TuringTest Group Title
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    the way we did it it looks like y does not matter, so (-1/4,y,-3/4) seems strange that y does not matter though, maybe I made a mistake... not sure

    • one year ago
  22. mathstina Group Title
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    so the point for y is 0 or -1?

    • one year ago
  23. TuringTest Group Title
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    neither, the result says y can be anything, so just write y=y

    • one year ago
  24. amistre64 Group Title
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    isnt y a function if x and z to begin with? y = x^2 + z^2; therefore y=1/4

    • one year ago
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