Exam 10: Parametric Equations, Polar Coordinates, and Vectors

The quarterback of a football team releases a pass at a height of 6 feet above the playing field,and the football is caught by a receiver 42 yards directly downfield at a height of 3 feet.The pass is released at an angle of with the horizontal.Find the maximum height of the football.Round your answer to one decimal place. ​

Find the area of the surface formed by revolving about the polar axis the following curve over the given interval. ​ ​

The area inside the polar curve is ...(round your answer to three decimal places) ​ ​ ​

Find . ​ ​

Find an equation of the hyperbola with vertices and asymptotes . ​

Find the area of one petal of . ​

Find the arc length of the curve on the given interval. ​

​A plane curve has parametric equations and .An expression for the rate of the slope of tangent to the path of the curve is ​

Find the area of the surface generated by revolving the curve , about the y-axis on the interval .Round your answer to two decimal places. ​

Use the properties of the derivative to find given the following vector-valued functions. ​ ​ ​ ​

Use the result,"the set of parametric equations for the circle is " to find a set of parametric equations for the circle with a center and radius 5. ​

A particle moves in the xy​-plane for values of time t​ in the interval according to the parametric equations and ​ .For what value(s)of t in this interval is the line tangent to the path of the particle vertical? ​

Find the second derivative of the parametric equations , .Round your answer to two decimal places,if necessary. ​

Sketch the curve represented by the parametric equations . ​

Find and if possible,and find the slope and concavity (if possible)at the point corresponding to . ​ ​

Given and ,find . ​

Find a set of parametric equations for the rectangular equation that satisfies the condition at the point . ​

The path of a projectile is modeled by the parametric equations and where x and y are measured in feet.Use the integration capabilities of a graphing utility to approximate the arc length of the path.Round your answer to one decimal place. ​

Find the domain of the vector-valued function given below. ​ ​ ​ Where​ ​

Suppose a plane is flying in the direction 302° (relative to the west).Its speed with respect to the air is 600 kilometers per hour.The wind at the plane's altitude is from the southwest at 80 kilometers per hour (see figure).What is its speed with respect to the ground? Round your answer to one decimal place. ​ ​