A large tank is filled to capacity with 700 gallons of pure water. Brine containing 3 pounds of salt per gallon is pumped into the tank at a rate of 7 gal/min. The well-mixed solution is pumped out at the same rate. Find the number A(t) of pounds of salt in the tank at time t.

Therefore

Step-by-step explanation:

Given that, a large tank contains 700 gallons of pure water.

At a time t , A(t)is the amount of salt in the tank .

The differential equation of rate of change of salt is

First we find and

=(concentration of salt ).(input rate of brine)

     =(3 lb/gal).(7 gal/ min )

     =21 lb/min

Since the rate of solution which is pumped out is same rate of pumped in..

= (the concentration of salt in the tank).(output rate)

      lb/min

    lb/min

Therefore,

 ....(1)

Here and Q = 21

The integrating factor of the differential equation is

=

Multiply the integrating factor the both sides of ODE of (1)

Integrating bot sides

 [c is an arbitrary constant]

At the initial time, the tank contains 700 gallons of pure water.

It means A(0)=0

Putting A=0 ,t=0

Therefore

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi