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Cant work this out, why is it happening, please help

  1. Nov 14, 2008 #1
    cant work this out, why is it happening, please help!!

    y(t)=22t-4t[tex]^{2}[/tex]
    x(t)=30t-t[tex]^{3}[/tex]

    find x(y) or y(x)
    what i did was say

    y-22t+4t[tex]^{2}[/tex]=0

    t=[tex]\frac{22+\sqrt{484-16y}}{8}[/tex]=[tex]\frac{11+\sqrt{121-4y}}{4}[/tex]

    x=30*[tex]\frac{11+\sqrt{121-4y}}{4}[/tex]-([tex]\frac{11+\sqrt{121-4y}}{4}[/tex])[tex]^{3}[/tex]


    which works for every value for y(t) i plug in except for t=2s
    where i get, from the original equations, x=52 y=28
    but from my equation when y=28, x=62.125
    why is this happening?
     
  2. jcsd
  3. Nov 14, 2008 #2

    Mark44

    Staff: Mentor

    Re: cant work this out, why is it happening, please help!!

    Did you remember to cube the 4 in the denominator when you substituted for t^3? x=30IOW, the second term in your value for x should be:
    [tex]\frac{(11+\sqrt{121-4y})^3}{4^3}[/tex]

    Also, you are omitting the [tex]\pm[/tex] in your value for t, but this is a more minor problem.
     
  4. Nov 14, 2008 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: cant work this out, why is it happening, please help!!

    The equation [itex]4t^2- 22t+ y= 0[/itex] has two solutions! Choosing the positive root means that you are assuming that t> 11/4= 2.75 and your formula will be correct only for t> 2.75

     
  5. Nov 16, 2008 #4
    Re: cant work this out, why is it happening, please help!!

    thanks, that works perfectly, but why do you say specifically 11/4, because of 11/4 in the fraction or because when the sqrt=0, t=11/4
     
  6. Nov 16, 2008 #5

    Mark44

    Staff: Mentor

    Re: cant work this out, why is it happening, please help!!

    Because your value for t is 11/4 + a positive quantity (i.e., sqrt(121 - 4y)/4 ). By omitting the other solution, you are losing sight of the fact that there is a solution for t < 11/4.
     
  7. Nov 16, 2008 #6
    Re: cant work this out, why is it happening, please help!!

    thanks
     
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