Two 100L tanks are connected in line. Saline is pumped into the first tank at a rate of 5L/min at a concentration of 2kg/L. Tank 1 is initially filled with pure water, and has an overflow drain which flows into Tank 2. Tank 2 initially contains 10kg of salt dissolved in 20L of solution, and has a drain with outflow at 5L/min. Let y(t) denote the amount of salt in Tank 1. Let x(t) denote the amount of salt in Tank 2. Determine the (two) differential equations describing the rates of change of y(t) and x(t). 5 L/min Tank 1 y(t) 100 L 5 L/min →→→ Tank 2 x(t) 100 L 5 L/min

3. A large tank with the capacity of 500 gallons is fully filled with pure water. Brine containing 2 pounds of salt per gallons is pumped into the tank at a rate of 5 gal/min. Find the amount A(t) pounds of salt in the tank at timer minutes, if the well-mixed solution is pumped out (a) with the same rate as the entering one; and (b) with the rate of 10 gal/min. In case (a), how much salt is in the tank after a long time? In case (b), what is the concentration of the solution in the tank by the time it is empty? (c) Let everything be the same except that, initially, the tank is filled with 250 gallons of pure water, while the well-stirred solution is pumped out with the flow rate of 2.5 gal/min. Find (t). What is the concentration of the solution in the tank by the time it is fully filled? Hint: (a) The volume of the solution in the tank at time (b) The volume of the solution in the tank at time minutes is V(t)= 500 gallons minutes is V(t)=500-5r gallons (c) The volume of the solution…

5. Suppose that the rate of water flows into an initially empty tank is a -0.5t m³ per minute at time t (in minutes). The volume of the tank is 25 m³ and suppose that the tank is fully filled when the flow rate becomes 0. Find the value of a.

A tank initially have 100 L with 50 g of dissolved salt. brine is pumped into the tank at a rate of 2 L/min carrying 2 grams of salt per liter. The well-stirred mixture is pumped out of the tank at a rate of 3 L/min. Find the concentration of the solution after 1 hour.

4. A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held 100 L of pure water. The solution inside the tank is kept well stirred and flows out of the tank at a rate of 3 L/min. If the concentration of salt in the brine entering the tank is 0.2 kg/L, deter- mine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.1 kg/L?

It is desired to divert 5.1 m3/s water from a pool whose water surface elevation is 45m, to an adjacent pond whose water surface elevation is 42 m by means of a short concrete culvert 8 m long and with both ends submerged. What size of culvert shown below is needed assuming C=0.58?

A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held 100 L of pure water. The solution inside the tank is kept well stirred and flows out of the tank at a rate of 3 Limin. If the concentration of salt in the brine entering the tank is 0.4 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.2 kgt? Determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.2 kg/L.? The concentration of salt in the tank reach 0.2 kgl. aftern (Round to two decimal places as needed.) minutes. Came

24) Over the years, a farmer has collected data on the average volume of the oranges in his erop in cubic inches based on the number of sunny days in the 120-day growing season. The equation of the line of best- fit is volume=4 +0.08(number of sunny days ). Find t the volume residual for an average orange volume of 9 cubic inches in a season with 23 sunny days. 25) A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 104 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h =-16t? + 104t +7. a) How long will it take the rocket to reach its maximum height? b) What is the maximum height? 26) The average traffic signal in a small town is 22 feet from the ground, with a standard deviation of 2 inches. The traffic signal by the bank is 22 feet, 8 inches from the ground. What is the z-score of the traffic signal's height? Is the traffic signal's height…

A 500-gallon tank contains a 0.5 lb/gal salt solution with a volume of 200 gal. Then the tank is fed with a saline solution with a concentration of 1 lb/gal at a flow rate of 3 gal/min. This saline solution is stirred in a tank and has a tank outflow rate of 2 gal/min. Determine the model for the exit product concentration as a function of time and determine the value of the exit product concentration (in lb/gal) at 3.8 minutes.

1. Use the Linear Approximation to estimate Δf for f(x)=3/(2+x^2) when a=2 and Δx=−1/2. (Use decimal notation. Give your answer to five decimal places.) 2.Compute the error (Use decimal notation. Give your answer to four decimal places.) 3.Compute the percentage error. (Use decimal notation. Give your answer to two decimal places.)