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jedai17

  • one year ago

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

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  1. amistre64
    • one year ago
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    get your like variables together and complete the squares .... which part is giving you pause?

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

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

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

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

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

  7. amistre64
    • one year ago
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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

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

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

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

  11. amistre64
    • one year ago
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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

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

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

  14. amistre64
    • one year ago
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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

  15. amistre64
    • one year ago
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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

  16. amistre64
    • one year ago
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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

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

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

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

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

  21. amistre64
    • one year ago
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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

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

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

  24. amistre64
    • one year ago
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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

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

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

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

  28. amistre64
    • one year ago
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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

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

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

  31. amistre64
    • one year ago
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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

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

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

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

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

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

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