Suppose that we are interested in the amount of salt (in kg) at a certain moment in time, denoted by A(t), in a well-mixed, infinitely large tank with 400-L of water initially. Further, suppose we have set-up the experiment such that a salt solution containing 16 kg/L flows into the tank at a rate of 9 L/sec. If we allow the solution to flow out at 6 L/sec, then what is the volume of water in the tank at time t? V(t) = _____? ( (DO NOT use commas in your answer) Construct a model for the change of salt in the tank at time t. [To ensure you are marked correct, please use A to represent the amount of salt in the tank at time t not A(t)]. dA/dot=_________?

Q: A brine solution of salt flows at a constant rate of 6 L/min into a large tank that initially held…

A:

Q: Consider a large vat containing sugar water that is to be made into soft drinks (see figure below).…

A:

Q: A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held…

A: Given that,  xin =0.2×4=0.8 kg/minxout=xv×3dxdt=xin-xout            →1     V=qin-qout+Vo…

Q: 2) A tank with capacity of 500 gallons initially holds 200 gallons of salt water containing 100 lb…

A: The capacity of the tank is 500 gallons initially holds 200 gallons of salt water containing 100 lb…

Q: A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held…

A: given,Brine solution of salt flows at a constant rate of the tank initially had  of pure…

Q: A brine solution of salt flows at a constant rate of 3 L/min into a large tank that initially held…

A: Given: A brine solution of salt flows at a constant rate of 3 L/min into a large tank that initially…

Q: 1. A tank initially holds 100 gallons of brine solution containing 20 lbs. of salt. At t = 0, fresh…

A: Solution...

Q: A tank initially contains 1 gram of blue dye dissolved in 10 liters of water. Pure water will be…

A: Given Data: The amount of blue dye dissolved is: D= 1 g The amount of water in the tank is: W = 10 L…

Q: a tank holding initially 100 L of a salt Consider solution begins to flow into the tank at a…

A:

Q: A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held…

A: Given: In flow=4 L/min, Volume of tank=100L of water, Out flow=3 L/min and the concentration of salt…

Q: Suppose you have a 200-gallon tank full of fresh water. A drain is opened that removes 3 gal/sec…

A: Let the concentration of brine =x lb/gal Amount of salt entering in per minute = 2 gal1 min×x lb1…

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: Suppose a 50-gallon tank contains a volume V0 of clean water at time t = 0. At time t = 0, we begin…

A: (a) It is given that, a 50-gallon tank contains a volume V0 of clean water at time t = 0. At time t…

Q: Suppose a water tank is being pumped out at 3 L/min. The water tank starts at 10 L of clean water.…

A:

Q: A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held…

A: given,brine solution of salt flows at a constant rate of the tank initially had  of pure…

Q: a tank in which 1 gram of chlorine is initially present in 80.38 m3  of a solution of water and…

A: The solution to a differential equation of the form y'(x)+p(x)y=q(x) is given by: Here, IF is the…

Q: Abrine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held…

A: Assume the mass of the salt in the tank after t min. is  kg.The rate of change of amount of salt in…

Q: 2. A large tank initially contains 100 gallons of brine in which 10 lb of salt is dissolved.…

A: Given that, Initial volume of brine is 100 galloons. Initial amount of salt is 10 lb. Water in rate…

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.