8. [-/12 Points] DETAILS Consider an object moving in the plane whose location at time t seconds is given by the parametric equations: x(t)=4cos(nt) y(t)=2sin(nt). Assume the distance units in the plane are meters. (a) The object is moving around an ellipse with equation: =1 62 where a= and b= (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/s. (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)= m/s. (f) The vertical velocity of the object at time t=1/3 seconds is m/s.(c) The horizontal velocity of the object at time t is x ' (t)= m/s. (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)= m/s. (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)]z 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= (i) 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