On a certain day, the rate, in kilograms per hour, at which unmolded plastic arrives at...

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On a certain day, the rate, in kilograms per hour, at which unmolded plastic arrives at a LEGO molding plant is modeled by P(t) = 500 + 50 cos(), where t is measured in hours and 0 < t < 10. At the beginning of the workday (t = 0), the plant has 1000 kilograms of unmolded plastic. During hours of operation, 0 < t < 10, the plant molds the plastic at a constant rate of 500 kilograms per hour. 46. Find PI(6). Using correct units, interpret your answer in the context of the problem. 47. Is the amount of unmolded plastic at the plant increasing or or decreasing at time t = 6 hours? Show the work that leads to your answer. 48. At what time t in hours is the maximum amount of unmolded plastic at the plant during the hours of operation on this workday? Assume that the amount of unmolded plastic at the beginning and end of the workday is less than the maximum amount sometime during the workday. Justify your answer. On a certain day, the rate, in kilograms per hour, at which unmolded plastic arrives at a LEGO molding plant is modeled by P(t) = 500 + 50 cos(), where t is measured in hours and 0 < t < 10. At the beginning of the workday (t = 0), the plant has 1000 kilograms of unmolded plastic. During hours of operation, 0 < t < 10, the plant molds the plastic at a constant rate of 500 kilograms per hour. 46. Find PI(6). Using correct units, interpret your answer in the context of the problem. 47. Is the amount of unmolded plastic at the plant increasing or or decreasing at time t = 6 hours? Show the work that leads to your answer. 48. At what time t in hours is the maximum amount of unmolded plastic at the plant during the hours of operation on this workday? Assume that the amount of unmolded plastic at the beginning and end of the workday is less than the maximum amount sometime during the workday. Justify your answer.