QUESTION

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# (1 point) A tank contains 90 kg of salt and 1000L of water. Water containing 0.6kg/L of salt enters the tank at the rate 15 L/min. The solution is mixed and drains from the tank at the rate 3 L/min. A(t) is the amount of salt in the tank at time t measured in kilograms. b) A differential equation for the amount of salt in the tank is _______________=0. (Use t,A, A', A'', for your variables, not A(t), and move everything to the left hand side.) c) The integrating factor is ____________d) A(t) = ____________ (kg)e) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.) concentration = _______________ (kg.L)(1 point) A tank contains $90 \mathrm{~kg}$ of salt and $1000 \mathrm{~L}$ of water. Water containing $0.6 \frac{\mathrm{kg}}{\mathrm{L}}$ of salt enters the tank at the rate $15 \frac{\mathrm{L}}{\mathrm{min}}$. The solution is mixed and drains from the tank at the rate $3 \frac{\mathrm{L}}{\mathrm{min}}$. $\mathrm{A}(\mathrm{t})$ is the amount of salt in the tank at time $\mathrm{t}$ measured in kilograms. (a) $\mathrm{A}(0)=$ 90 $(\mathrm{kg})$ (b) A differential equation for the amount of salt in the tank is $A^{\prime}+3 /(1000+12 t) A-8 \quad=0$. (Use $t, A, A^{\prime}, A^{\prime \prime}$, for your variables, not $A(t)$, and move everything to the left hand side.) (c) The integrating factor is (d) $A(t)=$ $(\mathrm{kg})$ (e) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.) concentration $=$ $\frac{\mathrm{kg}}{\mathrm{L}}$  