A mixing tank contains 80 gallons of pure water solution. When the mixing system is turned on, a saltwater solution with 2 Ib/gal of salt enters at a rate of 5 gal/min. The well stirred solution leaves the mixing tank at a rate of 3 gal/min. Determine the formula for the amount of salt in the mixing tank at any time. a) Draw a diagram of the mixing tank labeling the given parameters of the problem. b) Determine the differential equation and the initial conditions. c) Determine the formula for the amount of salt in the mixing tank at any time.

Q: A tank initially holds 40 gallons of a brine solution containing lb of salt per gallon. At t = 0,…

A: We will form differential equation for amount of salt in the tank and then solve it to get amount…

Q: Use the method of comparing the coefficients to find a particular solution for the differential…

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Q: A tank contains 60 kg of salt and 2000 L of water. Pure water enters a tank at the rate 12 L/min.…

A: Given that a tank contains 60 kg of salts and 2000 L of water. Pure water enters a tank at the rate…

Q: a) A maintenance staff member of the company has found that water tank is affected by some bacteria…

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Q: Find the general solution for the given equation: y’’ + y = csc x

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Q: A system of pulleys will be needed to assemble the cable tower on site. A differential equation…

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Q: 6- y" + 4y = cot(t)

A: Given:        y''+4y=cott        4yt+d2dt2yt=cott The differential has the form        y''+py'+qy=s…

Q: Solve the problem. A tank initially contains 100 gal of brine in which 40 lb of salt are dissolved.…

A: Step:-1 Let x be the quantity of salt in lb, dissolved in brine at time t. Now, Given that initially…

Q: 2. Solve the first order equation by using integrating factors. y' - 3y = e-2x

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Q: Solve the following initial value problem: DE: y' = -ty? and Initial value: y(0) = 9. Then write the…

A: See the attachment

Q: Solve the following differential equations : 1. xdy + ( 4y - )dx = 0 when x = 1, y = 1 y

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Q: A 2500-gallon tank initially contains 500 gallons of water with 6 pounds of salt dissolved in it.…

A: Let the amount of salt in tank at a time t is yt.   Given information capacity of tank = 2500 gallon…

Q: 3) For an ideal gas, the pressure is related to temperature and volume by the formula 8.31T V . If…

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Q: Two cylindrical water tanks are vertically connected to each other. Initially, the top and bottom…

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Q: A body weighing 24 lb stretches a vertical spring 1 foot beyond its natural length. The spring is…

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Q: Feren Ea (x°+y) dy xy

A: Given differential equation is not homogeneous. See the attachment

Q: Use the method of comparing the coefficients to find a particular solution for the differential…

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Q: The ideal gas law crates that the preccure [p], temperature [T], & volume [v] of a confined gas are…

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Q: A tank initially contains 17 pounds of salt dissolved in 450 gallons of water. Starting at to = 0,…

A: According to the given information, For part (a) Tank initially contains 17 pounds of salt that is…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.