Find the amount of salt in the tank when the tank is full.

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 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: 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 600 litre tank initially contains 200 litres of water in which 10 grams of salt are dissolved.…

A: (a) A 600 litre tank initially contains 200 liters of water. 10 grams of salt are dissolved in it.…

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 100 liters of brine, with 50 kg total dissolved salt. Saltwater, with a…

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Q: If 10 pounds of salts is dissolved in a large tank in partially filled with 100 gallons of fluid.…

A: Given :   10 pounds of salts is dissolved in a large tank in partially filled with 100 gallons of…

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: 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,…

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Q: A 128 L mixing tank initially contains 74 L of brine solution with a concentration of 5 g/L. Brine…

A: Brine solution with a concentration of 8g/L flows into the tank at a rate of 7L/min.The solution is…

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

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

A: Schematic diagram of the given situation:…

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

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 400 gal tank initially contains 100 gal of brine containing 25 lb of salt. Brine containing 2 lb…

A: A real-life scenario can be described mathematically through a differential equation. By solving the…

Q: The height of a rectangular box is 10 in. Its length increases at the rate of 2 in./sec; its width…

A: Volume of rectangular box = l b hwhere, l = length of boxb= width of boxh = height of boxRate of…

Q: A tank contains 100 gal of brine made by dissolving 60 lb of salt in water. Saltwater containing 1…

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Q: A large tank is partially filled with 100 gallons of fluid in which 10 pounds of salt is dissolved.…

A:

Q: A solution containing 3g/L of a salt solution pours into a tank, initially half full of water, at a…

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 brine solution of salt flows at a constant rate of 6 L/min into a large tank that initially held…

A: given, brine solution of salt flows at a constant rate of 6 Lmin the tank initially had 100 L of…

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

A:

Q: A patient's blood is traveling at a rate of 16 mL/sec while conveying a medicine into the liver and…

A: so, initially, liver is full at t = 0, but has no medicine,  medicine rich blood comes in, mixes…

Q: A container contains 80 liters of pure water. A brine solution with 2 kg/L of salt enter at 2 L/min,…

A:

Q: A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 2 grams…

A: A tank contains 200 liters of fluid with 30 gm salt is dissolved.2 gm of salt per liter is pumped…

Q: A 100 L mixing tank initially contains 50 L of brine solution with 16 g/L concentration. Brine…

A: Let V be the volume of the tank. Thus, Vt=50+4+2-5t       =50tL where, t is the time in minutes.

Q: air containing 30% oxygen passes slowly into a 3 gallon flask initially filled with pure oxygen and…

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Q: A tank contains 40 L of solution containing 2g of substance per liter. Salt water containing 3g of…

A: Initially there is 40*2 = 80 grams Let Q be the amount of substance in the tank and dQ/dt be the…

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

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Q: A large tank initially contains 100 liters of brine in which there is dissolved 5 grams of salt.…

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Q: gallon is poured into the tank at a rate of 2 gal/min, while the well-stirred mixture leaves the…

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

A:

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 large tank is partially filled with 400 L of fluid in which 5 kg of salt is dissolved. Brine…

A: The number of kilograms of salt in the tank after 30 minutes is 133.18 kg.

Q: vulcanizing shop has a trapezoidal drum that is 5 meters long, 1.5 meter wide at the top, 1 meter…

A: Solution of the problem as follows

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 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: The radius of an air bubble is increasing at the rate of 1/2 cm/s.At what rate is the volume of the…

A:

Q: A 131 L mixing tank initially contains 58 L of brine solution with 310 g of dissolved salt. Brine…

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Q: Water flows into an empty reservoir at a rate of 2200+10t gal/hour . What is the quantity of water…

A:

Q: A tank containing 100 gallons of brine made by dissolving 40 lbs of salt in water. Pure water runs…

A: Pure water in flow rate = 5 galmin

Q: A large mixing tank currently contains 300 gallons of water, into which 8 pounds of sugar have been…

A: given: Capacity of tank = 300 gallon Amount of sugar = 8 pounds Rate of pouring of water = 20…

Q: A tank initially holds 80 gal of a brine solution containing of salt per gallon. At t=0, another…

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.