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9. A tank contains 20 pounds of salt dissolved in 50 gallons of water. Three gallons of brine containing 2 lb of dissolved salt per gallon run into the tank every minute. The contents of the tank are continually stirred, and the mixture runs out of the tank at a rate of 2 gal/min. a) Create a 3 x 4 table. The top row should consist of a blank box followed by the headings Initial, Rate In, and Rate Out. Below the blank box in the top-left corner, write Salt ($) and Water (W). Fill in the remaining boxes using the information provided above. b) Express the rate of change of the amount of salt S as a differential equation. c) Find the amount of salt in the tank at any time t. d) How much salt is in the tank at the end of one hour? 10. According to Toricelli's Law, the rate of liquid flow from an orifice is equal to dV/dt = -4.8Agvh where h is the height (in feet] of the liquid above the orifice, A, is the area of the orifice, V is the volume of the liquid, and t represents elapsed time (in seconds]. If a cylindrical tank with height 9 ft and base radius 4 ft is filled with a liquid that is draining through a small circular hole (radius 1 in.) in its base, how many minutes does it take for the tank to empty? a) Draw the tank. Include its measurements. b) Use the fact that the hole has a radius of 1 inch to solve for A, in square feet. c) Find an expression for dV/dt from the formula for the volume of a cylinder. d) Find an expression for dV/dt from Toricelli's law. e) Set these two dV/dt expressions equal to each other. Solve for h in terms of t. g) Plug in the initial values to solve for C. h) Figure out what value of t causes h to equal zero and convert to minutes