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jedai17 Group Title

can someone answer this quadric surface using completing the square ?thank you :) x^2 + 4y^2 - z^2 - 6x + 8y + 4z = 0

  • one year ago
  • one year ago

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  1. amistre64 Group Title
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    get your like variables together and complete the squares .... which part is giving you pause?

    • one year ago
  2. amistre64 Group Title
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    you can pull it apart into 3 quads if you like .... that might be less data to cull thru.

    • one year ago
  3. jedai17 Group Title
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    i don't know how to solve this..i'm sorry

    • one year ago
  4. amistre64 Group Title
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    do you know how to complete a square?

    • one year ago
  5. jedai17 Group Title
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    it means that it will have a two factors in each variables..all in all it has a 6 factors?

    • one year ago
  6. jedai17 Group Title
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    it is x^2 - 6x , 4y^2 + 8y and z^2 + 4z?

    • one year ago
  7. amistre64 Group Title
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    lets go ahead and split this up into 3 different parts: x^2 + 4y^2 - z^2 - 6x + 8y + 4z = 0 x^2 -6x 4y^2 +8y -z^2 + 4z now that its organized better, you just work each one in its own right .... complete the square for each part

    • one year ago
  8. amistre64 Group Title
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    the key is, do you know how to complete a square? :)

    • one year ago
  9. jedai17 Group Title
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    ah.. its -z^2..

    • one year ago
  10. jedai17 Group Title
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    i'm sorry i forgot how to complete a square..

    • one year ago
  11. amistre64 Group Title
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    basically, you add and subtract a useful form of zero. square half the "x" term ..... for example: x^2 -6x ; the x term is -6, -6/2 = -3, (-3)^2 = 9. Lets add and subtract 9 x^2 -6x + 9 - 9; and condense the square (x-3)^2 - 9

    • one year ago
  12. amistre64 Group Title
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    z will be trick only in that you have to account for the -

    • one year ago
  13. jedai17 Group Title
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    x^2 -6x ; the x term is -6, how it become -6/2?

    • one year ago
  14. amistre64 Group Title
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    we are trying to make a complete square, a perfect square. numbers of the form (a+b)^2 are perfect squares: (2+5)^2 = 49, (3+1)^2 = 16, ... we want to condense this thing back into some (a + b)^2 form, thats all. In order to do that we have to modify its form, but not its value. Since adding zero changes nothing ... its useful to us. BUT what form of zero? lets expand (a+b)^2 = a^2 +2ab + b^2 ; let a=x (x+b)^2 = x^2 +2bx + b^2 notice that the b^2 is missing above. and we know that the "x" term in the middle is equal to 2b. 2b = -6 b = -6/2 = -3 b^2 = 9

    • one year ago
  15. amistre64 Group Title
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    so, adding and subtract 9; 9-9 = 0 right? will allow us to "complete" the square and alter its form ... not its value

    • one year ago
  16. amistre64 Group Title
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    4y^2 +8y 2b = 8 b = 8/2 = 4 b^2 = 16, +16-16 = 0 4y^2 +8y + (16-16) therefore 4y^2 +8y = (2y +4)^2 - 16

    • one year ago
  17. jedai17 Group Title
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    oh..i see. thanks i will solve this..

    • one year ago
  18. jedai17 Group Title
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    btw do you know about contour plotting?

    • one year ago
  19. amistre64 Group Title
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    i would need a little more information to see if i have contour plotting rolling around in my head someplace :)

    • one year ago
  20. jedai17 Group Title
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    do you know what kind of contour plot is this if f(x,y) = \[\sqrt{x^2 + y^2}\] ?

    • one year ago
  21. amistre64 Group Title
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    so the height, or z, is dependent on x and y inputs if we hold one input constant, we can generate a cross section plot and such, are some ideas ive got z = sqrt(x^2+y^2) z^2 = x^2 + y^2 is a circle, and so im gonna extrapolate that this is a sphere or hemisphere as a guess

    • one year ago
  22. amistre64 Group Title
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    http://web.monroecc.edu/manila/webfiles/calcnsf/javacode/calcplot3d.htm might be useful :)

    • one year ago
  23. amistre64 Group Title
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    well it use to work fine, i guess they changed some stuff about

    • one year ago
  24. amistre64 Group Title
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    http://www.wolframalpha.com/input/?i=sqrt%28x%5E2%2By%5E2%29 hmmm, its conic not spherical. it comes to a point at the origin and makes bigger circles as z gets bigger and bigger

    • one year ago
  25. jedai17 Group Title
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    our topic to this is about contour plotting..

    • one year ago
  26. amistre64 Group Title
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    |dw:1361892976311:dw|

    • one year ago
  27. amistre64 Group Title
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    im not up to date on what contour plotting is, this is mostly from an old, decripid memory :)

    • one year ago
  28. amistre64 Group Title
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    for your private message z = k z = x^2 + y for what values of x^2 + y does k = the stated set of values

    • one year ago
  29. amistre64 Group Title
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    x^2 + y = -2 when y=-x^2 -2|dw:1361893200001:dw|

    • one year ago
  30. amistre64 Group Title
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    in other words, the contour follows its reflection in the xy plane if that makes sense

    • one year ago
  31. amistre64 Group Title
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    for any value of k, the reflected graph in the xy plane changes its y intercept so it will float up and down the y axis as needed

    • one year ago
  32. jedai17 Group Title
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    what kind of contour plot is that?

    • one year ago
  33. amistre64 Group Title
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    it looks like a repeition of a parabola to me, so its a type of cylindar right?

    • one year ago
  34. amistre64 Group Title
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    |dw:1361894575970:dw|

    • one year ago
  35. jedai17 Group Title
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    i don't know..but i heard that there is a graph named paraboloid, elliptical paraboloid etc..

    • one year ago
  36. jedai17 Group Title
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    but i think it is elliptical paraboliod because you said that it is cylindar..

    • one year ago
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