Exam 10: Parametric Equations, Polar Coordinates, and Vectors

Suppose the two particles travel along the space curves and .A collision will occur at the point of intersection P if both particles are at P at the same time.Find the point of collision. ​

Find an equation of the tangent line at a point on the curve , . ​

How fast is the particle moving at time ? Round your answer to three decimal places.

​The velocity vector of a particle in the xy-plane is for all real t​.If the position of the particle at is ,then the position vector of the particle is ​

Use the given acceleration function and initial conditions to find the position at time . ​ ​

​A particle moves in the xy-plane so that its acceleration vector for time is .If the velocity vector at is ,then how fast is the particle moving when ? ​

Give the velocity vector of at time .Round your answer to three decimal places.

Evaluate the limit given below. ​ ​

The graph below is most likely the graph of which of the following equations? ​ ​

Determine the maximum height of a projectile fired at a height of 6 feet above the ground with an initial velocity of 700 feet per second and at an angle of above the horizontal.Use the model for projectile motion,assuming there is no air resistance.Round your answer to three decimal places. ​

Find a vector-valued function,using the given parameter,to represent the intersection of the surfaces given below. Surfaces Parameter

Write an integral that represents the area of the shaded region for as shown in the figure.Do not evaluate the integral. ​ ​

Find a vector-valued function,using the given parameter,to represent the intersection of the surfaces given below. Surfaces Parameter

A baseball player at second base throws a ball 87 feet to the player at first base.The ball is thrown 5 feet above the ground with an initial velocity of 50 miles per hour and at an angle of above the horizontal.At which height does the player at first base catch the ball? Round your answer to three decimal places. ​

Determine the t intervals on which the curve , is concave downward or concave upward. ​

Sketch the curve represented by the parametric equations . ​

Find the vector v whose initial and terminal points are given below. ​ (5)5,2.1), (9.5,6.1) ​

Find a set of parametric equations for the rectangular equation . ​

Find the length of the curve over the interval .Round your answer to two decimal places. ​

Sketch the curve represented by the vector-valued function and give the orientation of the curve. ​