The rate of depreciation dv/dt of a machine is inversely proportional to the square of t+ 1, where Vis the value of the machine t years after it was purchased. If the initial value of the machine was $500,000, and its value decreased $100,000 in the first year, estimate its value after 4 years.

Solve for k. 4k – 10 = 8 k %3D k = ||

Due to an excessive amount of rain, the village water storage tank is filling at a rate of 6007(6+4t) litres a day (t≥ 0). The mayor is planning to evacuate the village before the water storage tank overflows, flooding the valley. The amount of water currently in the water storage tank is 17,894, 400 litres and the mayor wants to know how many days it will take for the water storage tank to be completely full. The water storage tank is a large cylinder which is 20 metres high and has a radius of 30 meters. You can assume that the villagers are not using any of the water storage water and there is no water loss through evaporation. (1) Give the volume of a cylinder. (2) What is the maximum capacity of the water storage tank in litres? (Hint: 1000 litres 1 cubic metre) = (3) Find the function that gives the number of litres in the water storage tank at time t days. (4) The village mayor wants to have the town evacuated before the water storage tank is full. At what time t would the water…

Paul's firm produces the same good as Sal's firm. The total cost of producing qp units in Paul's firm is Cp( qp ) = 8.6 qp + 1.1. The total cost of producing qs units in Sal's firm is    Cs( qs ) = 8.6 qs + 1.1. What is the efficiency loss if each person's firm produces half of a total of 523 units?