Author Question: A tank contains 200 litres of fluid in which 60 grams of salt is dissolved. A brine solution of 2 ... (Read 103 times)

elizabeth18 · **on:** May 27, 2021

Question 1

Solve the differential equation (3y + 8xy²) dx + (x + 4x²y) dy = 0 by finding an integrating factor depending on x.
◦ x³y + 2x³y² = C
◦ 3xy + 4x²y² = C
◦ x³y + 2x⁴y² = C
◦ x⁴y + 4x⁵y² = C
◦ x²y + 3x³y² = C

Question 2

A tank contains 200 litres of fluid in which 60 grams of salt is dissolved. A brine solution of 2 grams of salt per litre is pumped into the tank at a rate of 2 litres/minute. The well-stirred solution is then pumped out at the same rate.
(a) Write the differential equation in terms of Q(t) and t and write the initial condition to model this problem. (Q(t) should represent the amount of salt in the tank at time t.)
(b) Solve the equation in part (a).
(c) How much salt will be present in the tank after a long period of time?
◦

(a)

= 400 -

, Q(0) = 60

(b) Q(t) = 40 - 34 e^-t/100

(c) 40 grams

◦

(a)

= 200 -

, Q(0) = 60

(b) Q(t) = 20 - 34 e^-t/100

(c) 20 grams

◦

(a)

= 400 -

, Q(0) = 60

(b) Q(t) = 4 - 3.4 e^-t/100

(c) 4 grams

◦

(a)

= 2 -

, Q(0) = 60

(b) Q(t) = 200 - 340 e^-t/100

(c) 200 grams

◦

(a)

= 4 -

, Q(0) = 60

(b) Q(t) = 400 - 340 e^-t/100

(c) 400 grams

yuyiding · **Reply #1 on:** May 27, 2021

A FREE account is required to view all solutions!

Lorsum iprem. Lorsus sur ipci. Lorsem sur iprem. Lorsum sur ipdi, lorsem sur ipci. Lorsum sur iprium, valum sur ipci et, vala sur ipci. Lorsem sur ipci, lorsa sur iprem. Valus sur ipdi. Lorsus sur iprium nunc, valem sur iprium. Valem sur ipdi. Lorsa sur iprium. Lorsum sur iprium. Valem sur ipdi. Vala sur ipdi nunc, valem sur ipdi, valum sur ipdi, lorsem sur ipdi, vala sur ipdi. Valem sur iprem nunc, lorsa sur iprium. Valum sur ipdi et, lorsus sur ipci. Valem sur iprem. Valem sur ipci. Lorsa sur iprium. Lorsem sur ipci, valus sur iprem. Lorsem sur iprem nunc, valus sur iprium.

Answer Preview

Only 25% of students answer this correctly