A 200-gal tank is half full of distilled water. At time t=0, a solution containing 0.5 Ib/gal of concentrate enters the tank at the rate 5 gal/min, and the well-stirred mixture is withdrawn at the rate of 3 gal/min. a) At what time will the tank be full? b) At the time the tank is full, how many pounds of concentrate will it contain?

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 1500 gallon tank initially contains 600 gallons of water with 5 lbs of salt dissolved in it. Water…

A:

Q: A solution containing at 2 lb of salt per gal is poured at 3 gal per min into a 300-gal tank that…

A:

Q: 4. A 105 kg male needs to work at a MET level of 8 to reach his target heart rate. If he exercises…

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

A:

Q: If the work required to stretch a spring 5 feet beyond its natural length is 15 foot-pounds, how…

A: first, we need to find the spring constant  W=∫0a fxdx here we have W=15 and a=5 feet 15=∫05 fxdx…

Q: A 600 gallon brine tank is to be cleared by piping in pure water at 1 gal/min. , and allowing the…

A: Let S be pounds of salt in tank at time t, so: or Rewritting the equation above we get:…

Q: The side of a cube increases at the rate of 5 m/sec. The rate at which the volume of the cube…

A: let side of cube is x then rate at which side increase is 5 m/secie.  dxdt=5 m/sec

Q: dv If the volume of the cube increases at the rate of 15 m / sec, then the value of is dt dv dV a) =…

A: Find the value value of rate of increase of volume of a cube

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: Two cars, one going east with the speed of 45 mph while the second car heading south at 70 mph, are…

A:

Q: A tank is initially filled with 1000 gal. of salt solution containing 500 H of salt. Fresh water…

A: Let At the amount of salt at the time t Then the rate of change of the amount of salt dAdt=0lbL.10…

Q: A 1200 gallon tank initially contains 500 gallons of water with 4 lbs of salt dissolved in it. Water…

A:

Q: A system of storm severs in a coastal city is designed to capture water runoff during heavy rains…

A:

Q: 15. A flow rate of 32 microdrops per minute on a gravity system is equivalent to how many…

A:

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

A:

Q: A 200g-tank holds 100 gallons of fresh water upon first. At t = 0, a 5 gal/min salt solution…

A: Given initial quantity of freshwater in the 200-gallon tank = 100 gallons At t=0, salt solution is…

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

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: Suppose that for the tank in Exercise 23 the pump breaks down after 4.7 X 10° J of work has been…

A:

Q: The side of a cube decreases at a rate of 9 m/sec Find the rate at which the volume changes, when…

A:

Q: The sides of a triangle measuring 40 m, 32 m, and 16 m increase at the rates of 2 m/s, 5 m/s and 3…

A: Area of triangle: If x, y and z are sides of triangle then area A of triangle is given by A = s(s -…

Q: The volume of a cube decreases at the rate of 74 m³/ sec. The rate at which the side of the cube…

A:

Q: Consider two brine tanks connected as shown in the figure below. Tank 1 contains x(t) pounds of salt…

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

A:

Q: Water is poured at a rate of 10 cubic meters per minute into a conical tank 6 meters across the top…

A:

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 side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

A:

Q: The side of a cube decreases at a rate of 9 m/sec. Find the rate at which the volume changes, when…

A: To find the rate of change of volume

Q: A cylindrical tank has 40 gallons of salt solution containing 2 lb dissolved salt per gallon, i.e. 2…

A:

Q: A cube is expanding in such a way that the length of its diagonal is increasing at a rate of 5…

A: Let y be the diagonal, x be the length of an edge and V be the volume of the cube at any time t.…

Q: The kinetic energy K of a mass is proportional to the square of its velocity y. If K = 12,960 joules…

A: To determine the kinetic energy.

Q: At a constant pressure, what temperature must be reached to increase the volume of a 100mL samples…

A:

Q: A tank contains 1000 liters (L) of a solution consisting of 100 kg of salt dissolved in water. Pure…

A: Consider, is the Rate of pure water is pumped into the tank is equal to 5 L/s. Formula used,

Q: If the volume of the cube increases at the rate of 15 m' I se dy dy b) a -15 m / sec dt a) = 15 m² /…

A: Option D is correct.  15 m^3 changing per second.

Q: an ice cube is shrinking uniformly at a rate of 8 cubic inches per hour. when the cube has a volume…

A: We are given the rate of change of volume of ice cube is shrinking uniformly at a rate of 8 cubic…

Q: A 50-gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 1b…

A:

Q: The side of a cube decreases at a rate of 10 m/sec. Find the rate at which the volume changes, when…

A: Differentiate volume of cube wrt t

Q: A tank initially holds 10 gal of fresh water. At t = 0, a brine solution containing ¼pounds of salt…

A: Given that , Initially fresh water in tank = 10 gal At t=0 , the solution containing 14 pounds of…

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 stream containing 80 grams per liter of a dye is pumped into a mixing tank with 400 liters of…

A: The answer is 32kg

Q: A 50 gallons tank initially contains 10 gal of fresh water. At t = 0, a brine solution  containing 1…

A: It is given that a 50 gallon tank initially contains 10 gallon fresh water. A brine solution with 1…

Q: The radius of a sphere decreases at a rate of 4 m/s. when the radius is 7 m, then the rate at which…

A:

Q: A tank initially holding 80 gals of fuid with 40 lbs of salt has two sources of fluid being pumped…

A:

Q: In 30 minutes, a thousand eight hundred tank of water empties from the bottom.The amount of water…

A: Proceed as shown below

Q: A 60-gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 Ib…

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.