a) Let R be a thin plate of uniform density that covers the given region: 1x + 1, if x 1: o y: x24andy2 21 Ex + 1, if x 33- 0 Once nd the K-coordinate of the centroid without integrating, explain your answer (10 marks). Then nd the xcoordinate and v-ooordinate of the centroid by evaluating the proper integrals (20 marks}. 13) Velocity of a car moving along a coordinate line at time t is given as follows: Ht : 2 _ 1? cos 2 Find the car's position at time t and at time t = 10 given it was at position 2 at time t = [l (25 marks)