On the interval 0

On the interval O S 0 S 2r, the graphs of the polar curves r = 3 and r = 2 + 2 cos(0) intersect when e = '7/3 and 0 = 5r/3. (a) Let R be the region enclosed within both r = 3 and r = 2 + 2 cos(0). Find the area of the region R. (Round your answer to four decimal places.) -.6851 x (b) A particle moving along the curve r = 2 + 2 cos(0) has position (x(t), y(t)) at time t, where 0 O when t = O. The particle moves along the Curve such that dr/dt = dr/d0. Find the value of dr/dt at 0 = Jt/3 Interpret your answer in terms of the motion of the particle. The particle is moving towards B the origin of the polar coordinate system. (c) For the particle described in part (b), dx/dt = dx/d0. Find the value of dx/dt at 0 = n/3. dx dt Interpret your answer in terms of the motion of the particle. The particle is moving to the left Need on the rectangular coordinate system.