Atank holds 300 gallons of water and 100 pounds of salt. a saline solution with concentration 1 lb salt/gal is added at a rate of 4 gal/min. simultaneously, the tank is emptying at a rate of 1 gal/min. find the specific solution q(t) for the quantity of salt in the tank at a given time t.

The amount of salt in the tank changes with rate according to

which is a linear ODE in . Multiplying both sides by gives

so that the left side condenses into the derivative of a product,

Integrate both sides and solve for to get

Given that , we find

and we get the particular solution

your answer would be b

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240