1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Equations systems

  1. Nov 6, 2008 #1
    given x(t)=30t-t[tex]^{3}[/tex]
    what i need to do in this excercise is fine an equation with x as a function of y x(y) or the opposite y(x)---- 1 function without any variable t.
    i have managed up till now by finding an expression for t and plugging that in instead of t in the 2nd equation, problem here is the extra t's, sqared and cubed, tried dividing both by t-not much help.. any ideas?
  2. jcsd
  3. Nov 6, 2008 #2


    User Avatar
    Science Advisor

    There won't be one way to do that because the two functions are not one-to-one: x(0)= 0 and x([itex]\sqrt{30})= 0[/itex]. There is no single function that will give both of those.
    Similarly, y(0)= y(11/2)= 0.

    What you can do is, for example, is treat the second equation as a quadratic equation in t: 4t2- 22t+ y= 0 and use the quadratic formula to solve for t:
    [tex]t= \frac{22\pm\sqrt{(22)^2- 4(4)y}}{8}= \frac{22\pm\sqrt{484- 16y}}{8}[/tex]
    It's that "[itex]\pm[/itex]" that is the problem. Choose either "+" or "-" and put that value of t into the equation x= 30t- t3 to get x as a function of y.
  4. Nov 7, 2008 #3
    Do you mean like composition y(t) [itex]\circ[/itex] x(t) = h(t), or y(x(t))=h(t).

    For y(30t-t3)=22(30t-t3)-4(30t-t3)2

    Can you continue out of here?
  5. Nov 8, 2008 #4
    no, cant continue from there, i dont see how you got there either, from what i see you did was placed (30t-t^3) in place of "t", which doesnt seem right to me, i need an equation that will be y as a function of x, that i can plug in a given y/x and find the other.
  6. Nov 8, 2008 #5


    User Avatar
    Science Advisor

    No, that's not what you want to do: you want to convert parametric equations to a Cartesian equation, not find a composition. The simplest thing to do is to solve for t as a function of y, as I showed and then replace t by that expression in the formula for x.
  7. Nov 8, 2008 #6
    so what would i do to solve that, cant see what youre doing from here
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Equations systems
  1. System of Equations (Replies: 4)

  2. System of equations (Replies: 1)

  3. System of Equations (Replies: 1)

  4. System of Equations (Replies: 6)

  5. System of equations (Replies: 3)