Suppose the rate at which water is flowing into a tank is given by the function, (see image) (a) How much water flows into the tank between t = 1 and t = 3 seconds. (b) Suppose that the tank is full after the water flows into the tank for t = 46 seconds. If there was initially 1000 litres of water in the tank, how much water does the tank hold?

4.1: 10) A circle is inside a square.The radius of the circle is decreasing at a rate of 1 meter per minute and the sides of the square are decreasing at a rate of 3 meters per minute. When the radius is 6 meters, and the sides are 20 meters, then how fast is the AREA outside the circle but inside the square changing? The rate of change of the area enclosed between the circle and the square is  ?   square meters per minute.

Page 6 of 7 7. [4] The total accumulated costs C(t) and revenues R(t) (in thousands of dollars), respectively, for a photocopy machine satisfy: . a) b) C'(t) = 2t² and 22 R' (t) = 5t² e-t³ Find the useful life of the machine, to the nearest year. Find the total profit accumulated during the useful life of the machine.

18. A company makes $1000 on the first 100 widgets sold. The rate of change for profit is given by the function: P'(x)=√x. What is the total profit if 200 widgets are sold?