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Vector Valued Funcations

  1. Oct 22, 2009 #1
    Hey,

    Can anyone please help me sove these problems:

    These are two different problems form different sections.

    1. Show that one arch of the cycloid r(t) = <t-sint, 1-cost> has length 8. Find the value of t in [0,2pi] where the speed is at a maximum.

    2. Find a parametization of the curve. The intersection of the surfaces z=x^2-y^2 and z=x^2+xy-1

    Thanks
     
  2. jcsd
  3. Oct 22, 2009 #2

    LCKurtz

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    Do you know the formulas for velocity, speed, and arc length?
     
  4. Oct 22, 2009 #3
    No, I don't.
     
  5. Oct 22, 2009 #4
    Then you should go and study and then comeback with some of your work. Nobody will do your homework for you.
     
  6. Oct 23, 2009 #5
    Actually this is no a homework question, its from a placement practice exam. So I didn't really know where to look for things. But, I think I have solved the 2nd. So Now just need help with 1st.

    The attempt at a solution
    2. z=x^2-y^2 and z=x^2+xy-1
    x^2-y^2 = x^2+xy-1
    ...
    x=(1/y) - y

    z=(1/y)-y-y^2

    Set y=t

    Ans. r(t)=<(1/t)-t, t, (1/t)-t-t^2>

    1. I have no clue where to start. Although, I did find formulas for it.
    But can anyone please guide me on where to start?
     
  7. Oct 23, 2009 #6

    HallsofIvy

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    This is a placement test?

    If you honestly have no idea how to approach such a problem, the last thing you want to do is to "trick" the people scoring the placement test to think that you do. The result would be that you wind up in a course where they expect you to already be able to do things you have no idea how to do!
     
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