Consider an object moving in the plane whose location at time t seconds is given by the parametric equations: x(t)=5cos(at) y(t)=3sin(at). Assume the distance units in the plane are meters. (a) The object is moving around an ellipse with equation: + ==1 where a= 5 and b= 3 (b) The location of the object at time t=1/3 seconds is (2.5 2.598 (c) The horizontal velocity of the object at time t is x' (t)=-5π sin(n) (d) The horizontal velocity of the object at time t=1/3 seconds is (e) The vertical velocity of the object at time t is y' (t) = 3π cos(πt) m/s. m/s. m/s. (f) The vertical velocity of the object at time t=1/3 seconds is 4.712 m/s. (g) The slope of the tangent line at time t=1/3 seconds is -0.347 (h) Recall, the speed of the object at time t is given by the equation: s(t)=√√ [x '(t)]² + [y' (t)]² m/s. The speed of the object at time t=1/3 seconds is (i) The first time when the horizontal and vertical velocities are equal is time t= 0.828 (j) Let Q be the position of the object at the time you found in part (i). The slope of the tangent line to the ellipse at Q is