Calculus and Vectors

25. A commuter train carries 2000 passengers daily. The cost to ride the train i1s $7 per person. Market research shows that 40 fewer passengers would ride the train for each $0.10 increase in fare and 40 more people would ride the train for each $0.10 decease to fare. The capacity of the train is 2600 passengers and if the train carries less than 1600 passengers, then it means the cost to run the train will be greater than the revenue. What fare should the railway charge to get the largest possible revenue? 26. The speed of a plane is 420 km/hr and its heading is 140. A wind of 40km/hr is blowing on a bearing of 040. Determine the plane's resultant velocity relative to the ground. Include a diagram. ' 27. Calculate the area of the parallelogram whose adjacent sides are a=[-6>5-4]& E = [-2,2,4]. 28. Differentiate and SIMPLIFY the following functions: ) f() = o cos?(4x-5) b) f(X) = (x6)*(7x +3)