A tank contains 4,000 L of brine with 18 kg of dissolved salt. Pure water enters the tank at a rate of 40 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. a. How much salt is in the tank after t minutes?
b. How much salt is in the tank after 30 minutes? (Round your answer to one decimal place.

In this exercise we have to use the integral to calculate the salt concentration:

(a)

(b)

Knowing that the volume of brine in the tank = 4000L, the initial Amount of salt, A(0)=18 kg. The rate of change in the amount of salt in the tank at any time t is represented by the equation:

Rate In = (concentration of salt in inflow)(input rate of brine). Since pure water enters the tank, concentration of salt in inflow =0.

Rate In = 0

Rate Out=(concentration of salt in outflow)(output rate of brine)

Therefore:

This is a linear D.E. which we can then solve for A(t). Integrating Factor:   . Multiplying all through by the Integrating Factor:  

Taking integral of both sides:

Recall our initial condition:

Therefore, the amount of salt in the tank after t minutes is:

(b)When t=30 mins

The amount of salt in the tank after 30 minutes is 13.3kg.

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(a)

(b)13.3 kg

Step-by-step explanation:

The volume of brine in the tank = 4000L

Initial Amount of salt, A(0)=18 kg

The rate of change in the amount of salt in the tank at any time t is represented by the equation:

Rate In = (concentration of salt in inflow)(input rate of brine)

Since pure water enters the tank, concentration of salt in inflow =0

Rate In = 0

Rate Out=(concentration of salt in outflow)(output rate of brine)

Therefore:

This is a linear D.E. which we can then solve for A(t).

Integrating Factor:

Multiplying all through by the I.F.

Taking integral of both sides

Recall our initial condition

A(0)=18 kg

Therefore, the amount of salt in the tank after t minutes is:

(b)When t=30 mins

The amount of salt in the tank after 30 minutes is 13.3kg

20

step-by-step explanation:

v = 1/3 a^2h

step-by-step explanation:

if the height is 57.7cm and the height of the slant edge is 18.2cm, then the volume is 1/3 a^2h.