A tank originally contains 100 gal of fresh water, Then water containing ib of salt per gallon is poured into the tank at a rate of 2 galimin, and the mixture is allowed to leave at the same rate. After 10 min the process is stopped, and fresh water is poured into the tank at a rate of I gal/min, with the mixture again leaving at the same rate. Find the amount of salt in the tank at the end of an additional 10 min. Round your answer to two decimal places.

Q: A 250 mg per L solution of drug is adminstered intravenously at a rate of 50 ml. per hr to a patient…

A: 1st we will make differential equation for amount of drug in the body and then solve it to get exact…

Q: A 12 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A: A 12 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4ft/s.

Q: A container initially contains 15 L of water in which there is 30 g of salt dissolved. A solution…

A:

Q: Two capacitors with capacitance of 6 μF and 4 μF are connected in series across a 100 V dc source.…

A: Question- Two capacitors with capacitance of 6 μF and   4 μF are connected in series across a 100 V…

Q: Consider a tank with volume 100 liters containing a salt solution. Suppose a solution with 2…

A:

Q: A 10-foot ladder leans against the side of a building. If the top of the ladder begins to slide down…

A:

Q: A 3 lb bucket containing 20 lb of water is hanging at the end of a 20 ft rope that weighs 4 oz/ft.…

A: Given that, a 3 lb bucket containing 20 lb of water is hanging at the end of a 20 ft rope that…

Q: A tank contains 200 gallons of fresh water. Brine containing 2 lbs/gal of salt enters the tank at 4…

A:

Q: A tank initially contains 200 L of fresh water. Brine containing 2.5 N/L of dissolved salt runs into…

A: Let "s" represents the quantity of salt in the tank. dSdt=(8×2.5)-8S200dSdt+0.04S=20   and S(0)=0…

Q: A candy company wants to produce 25 kilograms of a special 35% fat content chocolate to conform with…

A: Given: A candy company wants to produce 25 kilograms of a special 35% fat content chocolate.To…

Q: A tank with a capacity of 5000 kg of water is initially half full. Twenty kilogram per minute is…

A: Given that the capacity of the tank is 5000 kg. Let Q be the quantity of water in the tank after t…

Q: A truck travelling southwards at 40kph and a car traveling eastward at a rate of 60kph ar headed for…

A:

Q: 18. A kite string is paid out at a constant rate of 3 ft/s. If the wind carries the kite…

A:

Q: A van is 5 km due north of a pus at 2:00 PM. if the van is traveling northward at the rate of 60 kph…

A: The rate at which the distance between bus and van is changing is solved below

Q: A bucket that weighs 4 lb and a rope of negligible weightare used to draw water from a well that is…

A:

Q: A 25-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 5…

A:

Q: er 10 meters long is leaning against the wall. If the bottom of the ladder is being pushed…

A: Consider the provided information, Let AB be a ladder, where given that AB = 10 m.Because, OAB is a…

Q: A container that has 5 L of water with 1 kg salt dissolved is to be filled by pure water at a rate…

A: Solve by making differential equation

Q: A tank contains 400 liters of brine. Twelve (12) liters of brine, each containing 2.50 N of…

A: Given: 400 litres of brine are kept in a tank. The tank receives 12 litres of brine each minute,…

Q: There is a large mixing tank that initially holds 120 gallons of brine (water in which salt has been…

A:

Q: A tank contains 80 galloons (gal) of pure water. A brine solution with 2 lb/gal of salt enters at 2…

A: Given that, A tank contains 80 galloons (gal) of pure water. A brine solution with 2 lb/gal of salt…

Q: A ladder 20 ft. long leans against a vertical wall. If the top slides downward at the rate of 2…

A:

Q: 6. A 25-ft ladder is leaning against a wall. If we push the ladder toward the wall at a rate of 1…

A:

Q: Worker A is a loader and worker B is an unloader. Worker A can load a truck in 10mins, while worker…

A: The time taken by worker A to load the truck is = 10 min  The time taken by the worker B to unload…

Q: A tank contains 400 liters of brine. Twelve (12) liters of brine, each containing 2.5 N of dissolved…

A: If volume of any liquid is inside the container and some amount of liquid is entering and leaving…

Q: A tank with a capacity of 400 gal originally contains 150 gal of water with 25 lb of salt in…

A:

Q: A tank contains 4000 liters (L) of a solution consisting of 120 kg of salt dissolved in water. Pure…

A: Here, ri = 4, ci = 0, r0 = 5, The differential equation is There is no inflow of salt, thus the…

Q: A 75 kg box is pushed off of a 120 m tall building with an initial horizontal speed of 15 m/s. How…

A: We have to first sketch the given situation.

Q: A 400-gal tank initially contains 100 gal of brine containing 50 lb of salt. Brine containing 1 lb…

A:

Q: A freshly brewed cup of coffee is set on the counter and has a temperature of 200° Fahrenheit. After…

A: Let us assume that hot coffee is poured at time t=0 Given:   Initial temperature at  t=0, T=200°F…

Q: A tank contains 1000 liters (L) of a solution consisting of 170 kg of salt dissolved in water. Pure…

A: The rate of change of a quantity with respect to time is the differential of that quantity. In a…

Q: A van is 5km due north of a bus at 2:00PM. If the van is traveling northward at the rate of 60 kph…

A:

Q: Tank A contains 499 litres of brine holding 192 N of dissolved salt, and tank B contains 499 litres…

A:

Q: trouble which detains it an hour, after which it proceeds at three-fifths of its original rate and…

A:

Q: A tank contains 80 gallons of pure water. A brine solution with 2lb/gal of salt enters at 2 gal/min,…

A: Given: r1=2 galsmin., r2=2 galsmin.,  c1=2 lbsgal,, v0=80 gallons, x0=0

Q: If the tank is completely full, how much is overflowing if 530 GPM is being taken off the bott

A: Given: Let the rate of filling be Qin = 1250 GPM  the rate of draining be Qdrain = 530 GPM Because…

Q: Two large tanks, each holding 24 liters of a brine solution, are interconnected by pipes as shown in…

A: Let x(t) and y(t) be the mass of salt in tanks T1 and T2 respectively. Fresh water follows into tank…

Q: A 1000-kg car traveling at 35 m/s takes 3 m to stop under full braking. The same car under similar…

A: We have given  initial velocity u=35m/s, final velocity v=0  and taking time t=3m=180 s we know that…

Q: A tank contains 100 L of water. A salt solution containing 2 kg of salt per liter flow in at the…

A:

Q: The sides of the square are increasing at a rate of 3 cm per second . When the sides are 5cm long ,…

A:

Q: A tank contains 1,000 gallons of brine in which 500 lbs of salt are dissolved. Fresh water runs into…

A: Given:-amount of brine in the tank=1000 gallonssalt are dissolved in brine=500 lbsrate of fresh…

Q: A 14 ft ladder is leaning against a wall. If the top of the ladder slides down the wall at a rate of…

A: Definition used -                Related rate -  These are the problems in which we know one of…

Q: A 100 gallon tank is filled with brine containing 60 pounds of dissolved salt. Water runs into the…

A: Form the differential equation of first order and solve to get the answer.

Q: 1. Air is being pumped into a spherical balloon at a rate of 4 cm3/min. How fast is the radius of…

A: 1. Given:   The rate at which air is pumped into the spherical balloon = 4 cm3/min   Diameter of the…

Q: A tank contains 400 gallons of fluid in which 50 lb. of salt is dissolved. Brine containing 2 Ib/gal…

A: Given that : A tank contains 400 gallons of fluid in which 50 lb of salt is dissolved.

Q: A 150 mg per L solution of drug is administered intravenously at a rate of 30 mL per hr to a patient…

A: Given that: A 150 mg per L solution of drug is administered intravenously at a rate of 30 mL per hr…

Q: A tank contains 1000 liters (L) of a solution consisting of 195 kg of salt dissolved in water. Pure…

A: Solution is given below:

Q: A 80 foot ladder leaning against a wall is being pushed so that the bottom of the ladder is sliding…

A: Here dydt=6feet/secondx=48 feety=64feet

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.