This question from the final exam They don't give information.

(6] (20 pts) A car is traveling at 50 mph due south at a point 1/2 mile north of an intersection. Another car is traveling at 40 mph due west at a point 1/4 mile east of the same intersection. At what rate is the distance between the two cars changing? [7] (20 pts) An offshore oil well is leaking oil onto the ocean surface, forming a circular oil slick about 0.005 meter thick. If the radius of the slick is r meters, then the volume of the oil spilled is 0.005mr2 cubic meters. Suppose the oil is leaking at a constant rate of 20 cubic meters per hour. Find the rate at which the radius of the oil slick is increasing at a time when the radius of the oil slick is 50 meters. [8] (20 pts) A certain airline requires that carry-on luggage be such that the sum of the three dimensions is at most 120 centimeters. Use calculus to find the dimension of the square-ended rectangular package of greatest volume that meets this requirement. A closed rectangular box with a square base and volume 12 cubic feet is to be constructed using two different types of materials. The top is made of metal costing $2 per square foot, and the remaining sides and the base are made of wood costing $1 per square foot. Find the dimensions of the box that minimizes the cost of construction. 10)(20pts) A bacteria culture starts with 500 bacteria and grows at a rate proportional to its size. After 3 hours there are 8000 bacteria. Find an expression for the population after t hours. Find the number of bacteria after 4 hours. 1/) (20 pts) A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area? 2 (4 points) A bacterial culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420. Find an expression for the population size after t hours and compute when the population will reach 10, 000. 13) () Two cars start moving from the same point. One travels south at 60 miles per hour and the other travels east at 25 miles per hour. At what rate is the distance between the cars increasing 2 hours later? ly)A rectangular box with an open top is to have volume 10 cubic feet. The length of the base is to be twice the width. Material for the base costs $10 per square foot and for the sides costs $6 per square foot. Find the dimensions of the cheapest such container