How can I approach these vector valued function problems?

[nirali35]

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

 

[LCKurtz]

Do you know the formulas for velocity, speed, and arc length?

 

[nirali35]

No, I don't.

 

[Juan Pablo]

Then you should go and study and then comeback with some of your work. Nobody will do your homework for you.

 

[nirali35]

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?

 

[HallsofIvy]

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!