A particle moves along the x-axis according to the equation below for seven seconds.

x(t) = t³ – 11t² + 38t – 30

1. Write a set of parametric equations to model the path of the particle and set the Graph Style to animate the particle along the x-axis.
2. Write a set of parametric equations and set the Graph Style to animate the path of the particle so that the turning points are clearly visible after the graph is finished.
3. What is the particle's position when it is furthest to the left?
4. When is the particle moving to the right?
5. When is the particle moving to the left?
6. When is the particle at rest?

A baseball is hit at an angle of 30° above the horizon with an initial velocity of 138 ft/sec and an initial height of 3.5 feet off the ground.

7. Write a set of parametric equations to model the trajectory of the ball.
8. Approximately when will the ball hit the ground? Approximately how far away from home plate will it land?
9. What is the ball's maximum height? Use a derivative to find the answer.

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