Recall solving the linear system dx 1 - dt 50 dx , dt 50 * 1 75 dx 3 dt 75 25 using elimination techniques. Recall this linear system is a mathematical model for the number of pounds of salt x, (t), x2 (t), and X3(t) in the connected mixing tanks A, B, and C shown in the figure. pure water 4 gal/min A B C 200 gal 150 gal 100 gal mixture mixture mixture 4 gal/min 4 gal/min 4 gal/min (a) Use the eigenvalue method of this section to solve the system subject to x (0) = 20, x, (0) = 15, x, (0) = 10. x, (t ) = X 2 ( t ) = X3(t) = (b) What are lim x (t), lim x, (t), and lim x3(t)? t-+0 t - + 0 t-+ 20 lim x (t) = t -+ 00 lim x,(t) = t -+ 00 lim X3(t) = t-+ 00 Interpret this result. This means eventually tank A will contain ---Select--- , tank B will contain ---Select--- , and tank C will contain ---Select