A50 gallon tank initially contains 10 gallons of fresh water. at t = 0 a brine solution containing 1 pound of salt per gallon is poured into the tank at the rate of 4 gal/min., while the well-stirred mixture leaves the tank at the rate of 0.5 gal/min. find the amount of salt in the tank at the moment of overflow..

The flow of salt in the tank is an illustration of rates.

The amount of salt in the tank at the moment of overflow is 3 gallons.

The given parameters are:

--- the size of the tank

--- the initial content of the tank

So, the volume function is:

Substitute 50 for V

Subtract 10 from both sides

Divide both sides by 4

---- this means that, the tank will overflow after 10 seconds

The differential equation that models the amount of salt in the tank is:

This gives

Integrate, and solve for x

At x(0) = 0, we have:

Multiply through by 10

So, we have:

Recall that: the time of overflow is

So, we have:

Hence, the amount of salt in the tank at the moment of overflow is 3 gallons.

Read more about rates at:

link

  n=   0.0000 - 0.3750 i  

  n=   0.0000 + 0.3750 i

step-by-step explanation:

one of these should be correct

cut 138 centimeters off

step-by-step explanation:

250-112 = 138