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  • one year ago

5x^2+y^4 = -9 Evaluate y'' at x=2, y=1 --- This question seems to have an answer, but does the answer actually mean anything?

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  1. dan815
    • one year ago
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    it depends do u want it to mean anything

  2. anonymous
    • one year ago
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    he wants acceleration at that point (2,1) I guess.

  3. pujan20
    • one year ago
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    @dan815 i agree with fbi2015

  4. dan815
    • one year ago
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    who says its d^2y/dt^2

  5. anonymous
    • one year ago
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    well if x is time

  6. Empty
    • one year ago
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    y'' = d^2y/dx^2 here

  7. imqwerty
    • one year ago
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    wait a sec i got the answer :)

  8. Empty
    • one year ago
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    There is an "answer" no problem. But that's not what I care about.

  9. anonymous
    • one year ago
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    true that, you can swabb answer from wolfram all day everyday

  10. ikram002p
    • one year ago
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    @dan815 yeah it mean something in complex maybe xD

  11. dan815
    • one year ago
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    |dw:1440371299983:dw|

  12. imqwerty
    • one year ago
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    u have to double differentiate the equation with respect to x nd then u'll get an equation in x nd y then u jst put the values nd get the answer LOL

  13. Empty
    • one year ago
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    Stop solving it, I don't care, I only care about this: x=2, y=1 \[5x^2+y^4=-9\] \[5*4+1 \ne -9\]

  14. dan815
    • one year ago
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    i see

  15. Empty
    • one year ago
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    \[y'' = 12.5\] I believe, just so no one else tries to solve it haha

  16. dan815
    • one year ago
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    maybe in complex plane

  17. dan815
    • one year ago
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    like what does it mean to have complex routes

  18. dan815
    • one year ago
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    roots*

  19. Empty
    • one year ago
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    I don't think so, because although there are complex solutions to \(5x^2+y^4=-9\) x=2 and y=1 are still not solutinos

  20. dan815
    • one year ago
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    like can we try a simpler example Y=x^3 y'=3x^2 y''=12x what does y''(0,2) mean? 0,2 is not a solution yo y=x^3 but at the same time it just works because 0 can be put in for x

  21. dan815
    • one year ago
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    maybe something similiar to that is happening here

  22. Empty
    • one year ago
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    Yeah that looks good

  23. dan815
    • one year ago
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    the way the 2nd derivative behaves is just not a function of the y domain so with other functions maybe u can get it to not be functions of some lines and the point 2,1 happens to be on that line

  24. dan815
    • one year ago
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    the way the 2nd derivate behaves in this case*

  25. dan815
    • one year ago
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    the point (2,1) could belong to some other function too, a function along which the 2nd derivative is constant

  26. dan815
    • one year ago
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    you can try to think of a function where the 2nd derivative will be cosntant along some other curves

  27. dan815
    • one year ago
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    |dw:1440372327851:dw|

  28. Empty
    • one year ago
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    Ok I kinda see what you're saying, add a constant value to our original equation and we have a family of curves: \[5x^2+y^4+C = -9\] This will have all the same derivatives as the original case C=0 but now we can also find the curve that satisfies x=2 and y=1. I guess this would be a way to think of it?

  29. dan815
    • one year ago
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    ya that makes sense

  30. dan815
    • one year ago
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    what would the gradient and the gradient field of this function look like for example could be an example

  31. dan815
    • one year ago
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    but i see what u mean this only works out if theres a constant and some variation so that this function exists everywhere over the space

  32. dan815
    • one year ago
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    what would the gradient and the gradient of the gradient* field of this function look like for example could be an example

  33. dan815
    • one year ago
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    im not really satisfied with that lol but ya

  34. dan815
    • one year ago
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    also i was thinking about that complex root stuff with a parabola

  35. dan815
    • one year ago
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    |dw:1440373563511:dw|

  36. dan815
    • one year ago
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    |dw:1440373638686:dw|

  37. Empty
    • one year ago
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    Hmmm I don't really understand what you mean

  38. dan815
    • one year ago
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    its gonna give us a complex answer in uv plane but what does that complex value mean in x,y plane

  39. dan815
    • one year ago
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    like suppose you have a transformation of coordinates and you tried to solve for the complex roots

  40. dan815
    • one year ago
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    like okay for example x^2+y^2=1 is not a well defined function with a simple x domain or y domian it has to have both x,y domain, its a 1:1 function in theta:r so im saying if u take your given function and do some transformation of coordiantes where its 1:1 and then fiding complex roots in that domain what does that complex number mean in x,y domain?

  41. dan815
    • one year ago
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    so technically for example your function 5x^2+y^2=-9 we werent able to thjink about this as having complex routes

  42. dan815
    • one year ago
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    but for some transformation of coordinates u can think about complex roots

  43. dan815
    • one year ago
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    i dunno =.=

  44. Empty
    • one year ago
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    Well wait I think there's a difference here between complex answers and nonsense answers. For example, a set of complex values that work for \(x^2+y^2=1\) would be x=2 and \(y=i \sqrt{3}\) A set of nonsense values that don't work are x=2 and y=2.

  45. dan815
    • one year ago
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    ya i was thinking about that lol, but who says complex root arent just nonsense too

  46. Empty
    • one year ago
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    Me, I say that they aren't

  47. dan815
    • one year ago
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    lol

  48. Empty
    • one year ago
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    lol

  49. dan815
    • one year ago
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    it has a use so they arent nonsense all of a sudden

  50. dan815
    • one year ago
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    what if these will have uses later then

  51. Empty
    • one year ago
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    complex answers are just expanding your domain and range, nonsense answers are just picking values that don't satisfy the equation. So we can pick a pair of complex nonsense answers or a pair of real nonsense answers.

  52. dan815
    • one year ago
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    okay himm hoow about this argument

  53. dan815
    • one year ago
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    is it possible that some non parabolic functions can be defined in sum of an infinite set of parabolic functions

  54. dan815
    • one year ago
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    okay well the way i see it is that

  55. dan815
    • one year ago
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    this complex value came because someone wanted to see the intersection of a parabola with the y=0 line

  56. dan815
    • one year ago
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    but we can pick other lines for other functions

  57. dan815
    • one year ago
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    it will still give specific answers, for each line and which domain you pick, but yet every point can be covered depending on how u change your domain and what line you pick

  58. dan815
    • one year ago
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    im just saying random stuff right now :>

  59. Empty
    • one year ago
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    hmmm so wait give an example cause I'm not seeing these parabolas or something like wanna start a twiddla or cosketch or whatever

  60. Empty
    • one year ago
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    http://cosketch.com/Rooms/hkedsyu

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