Example 4 :- For the system shown in figure, Find the amount of salt in tank at any time (t). H.W Qin 50 gal/min Cin=(1+ cos t) lb/gal V=1000 gal h Cin= 200 lb/gal Qin = 50 gal/min

Q: Laplace transform L{k(t)} = -5{L(t2e-4t)}+L{sin(3t)}

A: We need to find the Laplace transform of the above.                       L{k(t)} =…

Q: Tank A initially holds 100 gallons of brine that contains 100 lbs of salt while tan B holds 100…

A: This is a problem of modeling differential equations.

Q: 2) A tank with capacity of 500 gallons initially holds 200 gallons of salt water containing 100 lb…

A: The capacity of the tank is 500 gallons initially holds 200 gallons of salt water containing 100 lb…

Q: A tank contains 90 kg of salt and 1000 L of water. A solution of a concentration 0.045 kg of salt…

A:

Q: Expenditure of a family on 3 times are in the ratio of 2:5:3. The prices of these commodities rise…

A:

Q: 7. (4Dª – 4D³ – 23D2 + 12D + 36)y =0 8. (18D3 – 33D² + 20D – 4)y = 0

A:

Q: 5. A ladder of length 4v3 metres is resting on a wall. The wall makes a 60-degree angle with the…

A:

Q: 24. If Total Cost = 5Q² – 20Q + 8 what is the cost of one more unit when current level of output =…

A: Given that Total cost=5Q2−20Q+8 We have to find the cost of one more unit when current level output…

Q: A brine solution of salt flows at a constant rate of 5 L/min into a large tank that initially held…

A: Given that, A brine solution of salt flows at constant rate of 5L/min, initial volume is 100L, and…

Q: 3. A cake is removed from an oven and its temperature is measured at 300°F. After 5 minutes, its…

A: A cake is removed from an oven and its temperature is measured at 300° F. After 5 minutes, its…

Q: temperature of the body and that of the surrounding air. If a body in air at 25°C will cool from…

A: From the Newton's law of cooling dT/dt = k(Tt – Ts) Where, Tt = Temperature of the body at time t…

Q: solve using variation of parameters: x''-6x'+9x=e^(3t)/t^2

A: The order of the differential equation is the highest order derivative present in the equation. The…

Q: Number 6

A: 6The velocity of a car is given by : v(t)=t2+2t here, v(t) is measured in ft/sec and t is measured…

Q: Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has…

A:

Q: A tank initially has 100 gallons of brine containing 5 lbs of salt. The mixture is kept well-mixed.…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.