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The amounts x₁ (t) and x₂(t) of salt in two brine tanks satisfy the differential equations below, where k₁ = r/V₁ for i = 1, 2. The volumes are V₁ = 20 (gal) and V₂ = 10 (gal).
First solve for x₁ (t) and x₂(t) assuming that r = 10 (gal/min), x₁ (0) = 25 (lb), and x₂ (0) = 0. Then find the maximum amount of salt ever in tank 2. Finally, construct a figure showing the graphs of x₁ (t) and x₂ (t).
dx₁/dt = -K₁X₁, dx₂/dt =K₁X₁-K₂X₂
X₁ (t) =
X₂(t) =

Sagot :

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