Evaluate the integral S [(2te 61? ) it (3 61) ; + (8) k ] at. 0 [[(2te 61? ) it (3e 61) ; + (8) k at = ( ) i+ (); + ( ) k 0 (Type exact answers.)The position of a particle in the xy-plane at time t is r(t) = (t +5) i+ (t + 1) j. Find an equation in x and y whose graph is the path of the particle. Then find the particle's velocity and acceleration vectors at t = 3. ST . . . The equation for the path of the particle is y = The velocity vector at t = 3 is v = ()i+(i. (Simplify your answers.) The acceleration vector at t = 3 is a = ()i+ji (Simplify your answers.)An athlete puts a 16-lb shot at an angle of 45 to the horizontal from 6.5 ft above the ground at an initial speed of 45 fu/sec. How long after launch and how far from the athlete does the shot land? The shot remains in the air for seconds. (Round to two decimal places as needed.) The shot travels |feet. (Round to two decimal places as needed.)