Use calculus to find the arc length of the line segment x=3t+1, y=4t, for 0≤t≤1. Check your work by finding the distance between the endpoints of the line segment. 

Air drop A plane traveling horizontally at 80 m/s over flat ground at an elevation of 3000 m releases an emergency packet. The trajectory of the packet is given by

x = 80t, y = −4.9t² + 3000, t ≥ 0

where the origin is the point on the ground directly beneath the plane at the moment of the release (see figure). Graph the trajectory of the packet and find the coordinates of the point where the packet lands.

41–44. Intersection points and area  Find all the intersection points of the following curves. Find the area of the entire region that lies within both curves

r = 3 sin θ and r = 3 cos θ

102–104. Spirals Graph the following spirals. Indicate the direction in which the spiral is generated as θ increases, where θ>0. Let a=1 and a=−1.

Spiral of Archimedes: r = aθ

80–83. Equations of circles Use the results of Exercises 78–79 to describe and graph the following circles.

r² - 8r cos(θ - π/2) = 9

37–48. Polar-to-Cartesian coordinates Convert the following equations to Cartesian coordinates. Describe the resulting curve.

r = 3 csc θ

49–52. Cartesian-to-polar coordinates Convert the following equations to polar coordinates.

y = x²