A particle is moving along a curve such that its speed at time t is (x (t), y (t)) , where x (t) = cos ? (2t) and y (1) = 1 - + + 5. Both x and y are measured in feet per second. 46. (a) Find the speed of the particle at time / = 2 Find the time t when the vertical acceleration of the particle changes from down to up. 47. (b) Find the distance traveled by the particle from time / = 1 seconds and t = 3 seconds. 48. (c) Given that the particle's position in the y direction is 4 feet at time t = 2 seconds, find the equation for the position of the particle in the y direction and call it Y(t) . 49. (d) Find the acceleration vector at time t = 1 seconds. A plant worker is monitoring the amount of a certain chemical solution entering an empty, cylindrical tank. The tanks has a diameter of 6 meters. The rate at which the solution enters the tank is modeled by C (t) = 20 + 6 cos (0.21) where C is measured in kilograms (kg), t is measure in hours and 0 St = 10 After 4 hours, the worker falls asleep and the tank springs a leak. After the leak is sprung, the solution leaves the tank at a constant rate of 15 kilograms per hour. 50. (a) How many kilograms of solution are in the tank right before the leak is sprung? 51. (b) Is the amount of solution in the tank increasing or decreasing at time t = 7 hours? 52. (c) If C(t) also models the rate at which the volume of solution in the tank is changing , at what rate is the height of solution in the tank rising at time t = 2 hours? 53. (d) Let Q (t) represent the net rate at which chemicals are added the tank. Is Q (t) continuous at time t = 4 hours? Justify your