Atank contains 120 liters of fluid in which 50 grams of salt is dissolved. brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 3 l/min; the well-mixed solution is pumped out at the same rate. find the number a(t) of grams of salt in the tank at time t.

If A(t) is the amount of salt in the tank at time t, then A(0) = 50 g and

A'(t) = (1 g/L)*(3 L/min) - (A(t)/120 g/L)*(3 L/min)

Multiply both sides by , so that the left side can be condensed as the derivative of a product:

Integrate both sides and solve for A(t).

Given that A(0) = 50 g, we have

so that the amount of salt in the tank at time t is

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6

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step-by-step explanation: