Luis DP FP Rough Sketch

1. Jim and Bob are racing from the origin to the point (5, 10). Let t be the number of seconds after the start of the race. Jim's position at any time t is given by the parametric equations x = t, y = 2t. Bob's position at any time t is given by the parametric equations x = 5t, y = 10t. Who will win the race? How long does it take each competitor to finish the race?
2. The following plane curve is a circle: x = 2 cos(t), y = 2 sin(t), 0≤t < 2π. Is its orientation clockwise or couterclockwise? What happens when you reverse the parametric equations, so that x = 2 sin(t), y = 2 cos(t)?
3. Given a point in rectangular coordinates (x, y), express it in polar coordinates (r, θ) two different ways such that 0≤θ < 2π: (x, y) = (- 7, - 7).
4. Given a point in polar coordinates (r, θ), express it in rectangular coordinates (x, y): (r, θ) = (1, 2π/3).