Given the following figure and information, solve for the following: A. The working matrix of the system of differential equations;

Consider the two tanks shown in the figure below. Assume that tank A contains 50 gallons of water in which 25 pounds of salt is dissolved. Suppose tank B contains 50 gallons of pure water. Liquid is pumped into and out of the tanks as indicated in the figure; the mixture exchanged between the two tanks and the liquid pumped out of tank B are assumed to be well stirred. We wish to construct a mathematical model that describes the number of pounds x₁(t) and x₂(t) of salt in tanks A and B, respectively, at time t. dx₁ dt dx₂ dt mixture 4 gal/min This system is described by the system of equations 1 50 2 2 25 2 dx₁ dt dx2 dt = = pure water 3 gal/min = 2 25 2 110 25 A + 1 1 mixture 1 gal/min B with initial conditions x₁(0) = 25, x₂(0) = 0 (see (3) and the surrounding discussion on mixtures on page 107). What is the system of differential equations if, instead of pure water, a brine solution containing 4 pounds of salt per gallon is pumped into tank A? mixture 3 gal/min

You learnt from chemistry and ECH 3023 that hydrogen sulfide may be reacted with sulfur dioxide in a sulfur recovery raector in accordance with the equation: a H2 S + b SO2 → c S + d H2O Find the smallest positive integer values of the stoichiometric coefficients a, b, c and d by setting up a set of linear system of equations from the atomic balances and solving the linear system using Gauss elimination and back substitution. Show the details of your work.

Find the corresponding compartment diagram for the following system of differential equations. bxp - 0.4x1 + 0.1×2 dt dx2 - 0.1x2 dt ..... Find the value of the coefficients in the diagram to the right. a = |, b = C = |, d = ax1 (Type integers or decimals.) bx, |dx2 cx