A tank contains 40 lb of salt dissolved in 500 gallons of water. A brine solution is pumped into the tank at a rate of 5 gal/min; it mixes with the solution there, and then the mixture is pumped out at a rate of 5 gal/min. Determine A(t), the amount of salt in the tank at time t, if the concentration of salt in the inflow is variable and given by cin(t)

Step-by-step explanation:

Volume of water in the Tank =500 gallons

Let A(t) be the amount of salt in the tank at time t.

Initially, the tank contains 40 lbs of salt, therefore:

A(0)=40 lbs

Rate of change of the amount of Salt in the Tank

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

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

Therefore:

We then solve the resulting differential equation by separation of variables.

Taking the integral of both sides

Recall that when t=0, A(t)=40 lbs (our initial condition)

to find the unit price, we must figure out the cost of one item (in this case one dish towel).   to do this, we divide the total price ($7.92) by the number of items bought (for this problem it is 8, because there are eight dish towels in one pack).  

$7.92/8 = $0.99

therefore, the unit price, or the price of one dish towel, is $0.99.

hope this !

step-by-step explanation:

the true ones are a b and d