wo large tanks A and B are each partially filled with 100 gallons of salt water. Initially,80 pounds of salt is dissolved in the solution in tank A, and 30pounds of salt is dissolvedin the solution in tank B. The system is closed so that the wellstirred saline solution ispumped only between tanks A and B. The saline solution in tankA travels to tank Balong a pipe at the rate of 3 gallons per minute, and the salinesolution in B travels totank A at the rate of 2 gallons per minute. Write a system of IVPs that will describe theamount of salt, x1, in tank A at timetand the amount of salt, x2in tank B at timet.

At the start, it's given that x₁ (0) = 80 lb and x₂ (0) = 30 lb.

The amounts of salt in either tank change according to

dx₁/dt = (2 gal/min) (x₂/(100 - t ) lb/gal) - (3 gal/min) (x₁/(100 + t ) lb/gal)

dx₂/dt = (3 gal/min) (x₁/(100 + t ) lb/gal) - (2 gal/min) (x₂/(100 - t ) lb/gal)

To break this down a bit, consider tank A, for instance:

• solution flows in from B at a rate of 2 gal/min

• the volume of liquid in tank B after t minutes is

100 gal + (2 gal/min - 3 gal/min) (t min) = (100 - t ) gal

because the tank starts with 100 gallons of liquid, and 2 gallons are pumped in while 3 gal are pumped out each minute

• at any time t, the solution in B contains x₂ pounds of salt

• the concentration of the solution in A is then x₂/(100 - t ) lb/gal

• multiplying this by the inflow rate tells you how much salt is moving around each minute

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step-by-step explanation:

step-by-step explanation:

we can use this expression to calculate the energy gain as a particle moves with a field or the energy loss as it moves against it. (note that it is also used to define the electron-volt, a unit of energy equal to that gained by an electron as it falls through a pd of 1 v, i.e. w = 1 ev = 1.6 10-19 c 1 v = 1.6 10-19j).in fact this expression is really nothing more than the statement that potential is the potential energy per unit charge. in this case, v= w/qis simply stating that the change in potential energy(or work done) per unit charge is equal to the change in potential (or potential difference), v.student questions: uniform electric fields2electron beamcathode+5 kvanode0 v