A 100 gallon tank initially contains 100 gallons of sugar water at a concentration of 0.25 pounds of sugar per gallon suppose that sugar is added to the tank at a rate of p pounds per minute that sugar water is removed at a rate of 1 gallon per minute and that water in the tank is kept well mixed. What value of P should we pick so that that when 5 gallons of sugar solution is left in the tank the concentration is .5lbs of sugar/gallon?

At the start, the tank contains

(0.25 lb/gal) * (100 gal) = 25 lb

of sugar. Let be the amount of sugar in the tank at time . Then .

Sugar is added to the tank at a rate of P lb/min, and removed at a rate of

and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

Separate variables, integrate, and solve for S.

Use the initial value to solve for C :

The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

has passed. At this time, we want the tank to contain

(0.5 lb/gal) * (5 gal) = 2.5 lb

of sugar, so we pick P such that

3; 9 is 8 to -4

step-by-step explanation:

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.