Results 1 to 2 of 2

Math Help - Parametric Equation

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    36

    Parametric Equation

    Consider the parametric curve given by the equations:

    y(t) = t^2 +30 t +15
    x(t) = t^2 +30 t +46

    How many units of distance are covered by the point P(t) = (x(t),y(t)) between t=0, and t=3 ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by derekjonathon View Post
    Consider the parametric curve given by the equations:

    y(t) = t^2 +30 t +15
    x(t) = t^2 +30 t +46

    How many units of distance are covered by the point P(t) = (x(t),y(t)) between t=0, and t=3 ?
    There are few ways to do this problem

    1: use the arc length fromula

    \int_{t_0}^{t_1}\sqrt{(\frac{dx}{dt})^2+(\frac{dy}  {dt})^2}dt


    This gives

    \int_{0}^{3}\sqrt{(2t+30)^2+(2t+30)^2}dt

    Just simplify and integrate and you are done.

    2: subtract the equations from each other to get

    y-x=-31 \iff y=x-31

    Note that x(0)=46 \text{ and } x(3)=145

    Since the above is a line with slope one we can use the pythagorean theorem. So both sides have length 99

    c=\sqrt{(99)^2+(99)^2}=99\sqrt{2}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cartesian Equation and Parametric Equation
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 29th 2010, 08:33 PM
  2. [SOLVED] Parametric equation / Cartesian equation
    Posted in the Trigonometry Forum
    Replies: 9
    Last Post: July 21st 2010, 11:54 AM
  3. Replies: 2
    Last Post: May 23rd 2010, 10:46 AM
  4. Help me !Parametric equation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 22nd 2009, 11:32 PM
  5. Parametric Equation to Cartesian Equation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 26th 2008, 11:19 AM

Search Tags


/mathhelpforum @mathhelpforum