Calculate the line integral of F(x, y, z) = (e², ex-y, e) over the closed path ABCA, where A = (4,0,0), B = (0,8,0), C = (0,0, 12). (Use symbolic notation and fractions where needed.) Incorrect . dr = 220 +916+4e12-11 +2

Sand is being dumped from a hopper railcar at a rate of 40 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other (both are growing larger as more sand is dumped). How fast is the base diameter increasing when the base is 18 feet long? Round your answer to three decimal places. ft/min

Bracket Manufacturing uses a Kanban system for a component. Daily demand is 1,100 units. Each container has a combined waiting and processing time of 0.65 days. If the container size is 100 and the alpha value (a) is 12%, how many Kanban card sets should be authorized? Round your answer up to the whole number. Kanban card set(s) What is the maximum authorized inventory? Use the rounded value from the previous question. Round your answer to the nearest whole number. unit(s)

Evaluate the integral