Please write out any formulas usedFor example, for a, why do I add pi/3(2)^2 instead of integrating the whole thing, thanks!

30. [0/5 Points] DETAILS PREVIOUS ANSWERS LARHSCALC1 9.AP.011. On the interval 0 S 0 S 2x, the graphs of the polar curves r = 3 and r = 2 + 2 cos(0) intersect when 0 = x/3 and 0 = 5x/3. (a) Let R be the region enclosed within both r = 3 and r = 2 + 2 cos(@). Find the area of the region R. (Round your answer to four decimal places.) 13.0163 X (b) A particle moving along the curve r = 2+ 2 cos(0) has position (x(t), y(t)) at time t, where 0 = 0 when t = 0. The particle moves along the curve such that dr/dt = dr/d0. Find the value of dr/dt at 0 = 1/3. dr dt Interpret your answer in terms of the motion of the particle. The particle is moving ---Select--- @ 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 = 1/3. dx dt Interpret your answer in terms of the motion of the particle. The particle is moving to the (---Select--- @ on the rectangular coordinate system. Need Help? Read It Submit