A 20 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of 0.6 m/min The solution is kept thoroughly mixed and drains from the tank at a rate of 1.2 m/min How much salt is in the tank when it is half full1?

Q: A sewage disposal plant has a big concrete holding tank of 100,000-gal capacity. It is 3⁄4 full of…

A: Let V(t) be the volume of liquid in the tank at time t. Let Vo be the initial volume of liquid in…

Q: . A tank contains 1,500 liters of water and 20 kg. of dissolved salt. Fresh water is entering the…

A: Using mixing problem formula we find the general amount of salt at any time t minutes and then…

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: A tank contains 100 L of pure water. Brine that contains 0.1 kg of salt per liter enters the tank at…

A: Let y(t) = the amount of salt in the tank in kg. So the concentration at time t minute is then…

Q: A 1500 gallons tank initially contains 600 gallons of water with 5 Ibs of salt dissolved in it.…

A: Please ensure that the concentration of entering water is 2t lbs/gal. ( It is not clear from the…

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 tank contains 1000 liters of brine with 15 kg of dissolved salt. Pure water enters the tank at a…

A: Let x represents the amount of salt after t minutes. Given that, the initial amount of salt is 15…

Q: A robotic machine fills containers with an acid solution at the rate of 90 + 2t milliliters (mL) per…

A:

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 tank contains 60L of water contaminated with Mercury at a concentration of 0.03 mg/L. Clean water…

A: Here we need to find and then solve the differential equation for the concentration of mercury using…

Q: A tank contains 1000L of brine with 16kg of dissolved salt. Pure water enters the tank at a rate of…

A: Given: A tank contains 1000L of brine with 16kg of dissolved salt. The pure water enters the tank at…

Q: A tank contains 100 liters of brine, with 50 kg total dissolved salt. Saltwater, with a…

A:

Q: is pumped into the tank at the rate of 5 L/s and the well-stilled mixture fl me rate. How long will…

A: Please refer to the image below

Q: The volume of a cube decreases at a rate of 10 m3/s. Find the rate at which the side of the cube…

A: We have to find rate  of change of side of cube .dV/dt  is negative beacuse it is…

Q: A 20 m tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: In this question, we find the amount of solt when the takl half full. given that  Initial amount of…

Q: a tank initialy holds 80 gal. of a brine solution containing 1/8 lb of salt per gallon. at t=0,…

A:

Q: • A tank contains 968 L of brine with 15kg of dissolved salt. Pure water enters the tank at a rate…

A: Solution : We have given that a tank contains 968 L of brine with 15kg of dissolved salt. Pure…

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

A:

Q: A tank contains 100 gal of brine made by dissolving 80 lb of salt in water. Pure water runs into the…

A: Many real-life problems can be modeled using differential equations. This is one of the significant…

Q: A bacteria population starts with 400 bacteria and grows at a rate of r(t)= 450.268 e ^1.12567t per…

A:

Q: A tank contains 100 liters of brine, with 50 kg total dissolved salt. Saltwater, with a…

A:

Q: A robotic machine fills containers with an acid solution at the rate of 80 + 4t milliliters (mL) per…

A: Solution ) given function = 80 + 4t When t=0 or when no solution put into a container f(0) = 80 +…

Q: A robotic machine fills containers with an acid solution at the rate of 90 + 6t milliliters (mL) per…

A:

Q: A tank contains 5001 of a solution consisting of 30 kg of salt dissolved in water. Pure water umped…

A:

Q: A robotic machine fills containers with an acid solution at the rate of 90 + 3t milliliters (mL) per…

A:

Q: A large tank holds (400) gallons of brine solution with (50) pounds Q5: of salt. A concentration of…

A:

Q: A tank contains 150 L of pure water. Brine that contains 0.2 kg of salt per liter enters the tank at…

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 20 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: A tank initially contains 50 gal. of fresh water. Brine (water in which a certain number of pounds…

A:

Q: A tank contains 100 gallons of pure water. A brine solution with 2 Ib/gal of salt enters at 3…

A:

Q: A tank contains 1,500 liters of water and 20 kg. of dissolved salt. Fresh water is entering the tank…

A:

Q: An IV Piggyback of lincomycin containing 5 gms of drug in 175 mL is to be infused over a 1 hour…

A:

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

A:

Q: In a water bottling process, one-liter bottles are filled through a system that provides filtered…

A:

Q: continuous IV is infusing at 40 mL/h.  How many milliliters will infuse in 30 minutes?

A: 1 hour is equal to 60 minutes.

Q: A tank contains 100 liters of brine, with 50 kg total dissolved salt. Saltwater, with a…

A:

Q: A tank initially contains 100 gallons of brine whose salt concentration is 3 lb/gal. Freshwater is…

A: We will make a differential equation for amount of salt and then will solve it to get amount of salt…

Q: A 2 lbs of salt was dissolved completely into 100 gallons of pure water. After an hour, a brine…

A: AS PER BARTLEBY GUIDELINES, EXPERTS ARE ALLOWED TO SOLVE ONLY ONE QUESTION WHEN MULTIPLE QUESTIONS…

Q: A swarm of bees is spreading from an original region of 1 square mile. The region the swarm occupies…

A: Given that the original region of 1 square mile.  After 1 year area will be 2(1)=2=21 square miles…

Q: how long will it take $800 to triple if it is invested at an annual intrest rate of 5.3%

A: P=$800 , R=5.3%

Q: A 400-gal tank initially contains 100 gal of brine containing 75 lb of salt. Brine containing 2 Ib…

A: The solution of above question is written below.

Q: The surface area of a balloon that is being filled with helium increases at a rate of 5 square feet…

A:

Q: A tank contains 70 gallons of pure water. A brine solution with 2 lbs / gal of salt enters at 2.25…

A: We convert this problem into a differential equation then solve the differentials equation.

Q: · A tank contains 968 L of brine with 15kg of dissolved salt. Pure water enters the tank at a rate…

A:

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 tank contains 200 liters of fresh water. Brine containing 2.5 N/L of dissolved salt runs into the…

A:

Q: A 30 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: Volume of the tank is 30 m3 The tank is full of brine with 40 kg of dissolved salt. Pure water…

Q: A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially…

A: Given: A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially…

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.