please, write the necesery steps clearly, thank you. diidertial equation question #5 (1) What is the order of the following differential equation? y? + 6x*y" = sinº (2) Solve 16r2 -0. (3) Suppose Tank A initially has 30 gallons of water containing 55 ounces of dissolved salt, and Tank B initially has 20 gallons of water containing 26 ounces of dissolved salt. Water from an external source with a salt concentration of 1 ounce per gallon flows into Tank A...
(1 point) A tank holds 250 gallons of water than contains 50 pounds of dissolved salt. Pure water is flowing into the tank at the rate of 1/2 gal/min while the solution flows out of the tank at the rate of 4 gal/min. (a) Write down a differential equation describing this situation. Use y for the amount of salt in the tank dy 4y/250-3.5t) dt (b) Write this equation in the correct form for using the method of separation of...
(1 point) A tank holds 280 gallons of water than contains 35 pounds of dissolved salt. Pure water is flowing into the tank at the rate of 1/2 gal/min while the solution flows out of the tank at the rate of 2 gal/min. (a) Write down a differential equation describing this situation. Use y for the amount of salt in the tank. dy dt = (b) Write this equation in the correct form for using the method of separation of...
6 that is continuous on the entire Note that F(x) = J-6 V44 +6 dt. So assume f(e) = V 24 + 6 real line. Use the Second Fundamental Theorem of Calculus, which states that, if f is continuous on an open interval I containing a, then for every x in the interval, d f(x). f(t) dt = dx Step 2 In this problem, F(x) = Live* +6 dt. Therefore, F'(x) = f(t) dt = f(x) = V Submit Skip...
2. A tank contains 100 gallons of pure water. Beginning at t O, a salt water solution containing 0.2 pounds of salt per gallon is pumped into the tank at a rate of 3 gallons per minute. At the same time, a drain is opened at the bottom of the tank which allows the mixture to leave the tank at a rate 3 gallons per minute. Assume the solution is kept perfectly mixed. (a) What will be concentration of salt...
1. A large mixing tank currently contains 100 gallons of water into which 5 pounds of sugar have been mixed. A tap will open pouring 10 gallons per minute of water into the tank at the same time sugar is poured into the tank at a rate of 1 pound per minute. Find the concentration (pounds per gallon) of sugar in the tank after 12 minutes. Is that a greater concentration than at the beginning? In which of the molecules...
1.(4 pts) A rectangular tank, shown in Figure A, is 4 ft long, 2 ft wide, and 3 ft high. Initially there is 4 fts of water in the tank and water starts flowing into the tank at the time t Let V (t) denote the volume of the water in the tank at the time t. The graph of V', the derivative of V, o ft3 is given in figure B, where t is in minutes, and V'in min...
PLZ HELP answer all of them plz what value of à are the functions F)- and )- A linearly dependen Match the following direction field with the appropriate diff contains 60 gallons of pure water. Brine (a water-salt mixture) containing 1 pound of salt per gallon flows into the tank at the rate of 2 gal/min, and the mixture (which is assumed to boe perfectly mixed) flows out of the tank at the rate of 3 gal/min; thus the tank...
13. A 600 gallon capacity tank initially contains 50 pounds of salt dissolved in 100 gallons of water. Water containing 2 pounds of salt per gallon enters the tank at a rate of 6 gallons per minute (assume the salt is evenly distributed throughout the water in the tank). Water is drained from the tank at a rate 4 gallons per minute. How many pounds (rounded to 1 decimal place) of salt will be in the tank when the tank...
2. A tank contains 100 gallons of pure water. Beginning at t O, a salt water solution containing 0.2 pounds of salt per gallon is pumped into the tank at a rate of 3 gallons per minute. At the same time, a drain is opened at the bottom of the tank which allows the mixture to leave the tank at a rate 3 gallons per minute. Assume the solution is kept perfectly mixed. (a) What will be concentration of salt...