Consider an object moving in the plane whose location at time & seconds is given by the parametric equations: x(t)=5cos(nt) y(t)=3sin(nt). Assume the distance units in the plane are meters. (a) The object is moving around an ellipse with equation: =1 62 where a=] xa and b= X (b) The location of the object at time t=1/3 seconds is (c) The horizontal velocity of the object at time t is x ' (t)= m/5. (d) The horizontal velocity of the object at time t= 1/3 seconds is m/s. (e) The vertical velocity of the object at time t is y ' (t)= n/5. (f) The vertical velocity of the object at time t=1/3 seconds is m/s. (g) The slope of the tangent line at time t=1/3 seconds is (h) Recall, the speed of the object at time t is given by the equation: s(t)=v [x '(t)] + [y ' (t)]? m/s