A tank contains 54 gallons of a solution composed of 85% water and 15% alcohol. A second solution containing half water and half alcohol is added to the tank at the rate of 4 gallons per minutes. At the same time, the tank is being drained at the same rate. Assuming that the solution is stirred constantly, how much alcohol will be in tank after 10minutes?

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: In a factory, machine A can produce 230 fortune cookies in 5 minutes, while machine B can produce 20…

A: Unity law

Q: Suppose that you drive 50,000 miles per year and gas averages $4 per gallon. Complete parts a. and…

A:

Q: A 15-quart cooling system is checked and found to be filled with a solution that is 40% antifreeze.…

A: SOLUTION-

Q: An apple farm yields an average of 39 bushels of apples per tree when 21 trees are planted on an…

A: (1)  Given that, an apple farm yields an average of 39 bushels of apples per tree when 21 trees are…

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

A: This question is related to differetial equations, we will solve it using given information.

Q: In a mixing vat there are initially 100 litres of volatile liquid. 3 litres of fresh liquid are…

A: Solution

Q: new homeowner purchases furniture worth $10,000, which depreciates at a constant rate of 7% every 2…

A: NOTE: Refresh your page if you can't see any equations. . the initial worth is $10000 sot ake…

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 200 gal tank is half full of distilled water. At time = 0, a solution containing 1 Ib/gal of…

A: given capacity of tank =200 gal concentration =1 lb/gal rate of enter =4 gal/min rate of withdrawn…

Q: How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that…

A:

Q: An apple farm yields an average of 42 bushels of apples per tree when 20 trees are planted on an…

A:

Q: It takes an ant farm 3 days to consume of an apple. At that rate, in how many days will the ant farm…

A: An ant farm takes 3 days to consume ½ of an apple. → An ant farm consume ½ of an apple in 3 days

Q: airplane flying to the Dominican Republic has an altitude of 31,000 feet and is ascending at a…

A:

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 mixture containing 6% boric acid is to be mixed with 2 quarts of a mixture which is 15% acid in…

A: It is given that mixture containing 6% boric acid is to be mixed with 2 quarts of a mixture which is…

Q: the radiator in a car is filled with a solution of 60% antifreeze and 40% water. the manufacturer of…

A: In a 3.6 L radiator, the quantity of antifreeze is given by: In a 3.6 L radiator, the quantity of…

Q: In a city with 500,000 population, the rate of the spread of a new flu epidemic is proportional to…

A:

Q: A motor vehicle has a maximum efficiency of 32 mpg at a cruising speed of 40 mph. The efficiency…

A:

Q: n a culture of yeast, the amount of active ferment grows at a rate proportional to the amount ... If…

A: Growth given in the problem has exponential growth. If the quantity growing exponentially is denoted…

Q: In a chemical reaction a substance decomposes at a rate proportional to the amount of substance…

A:

Q: Suppose Chad has $5000 to invest. If he invests $3000 at 5% interest,  at what rate must he invest…

A: Suppose Chad has $5000 to invest. If he invests $3000 at 5% interest

Q: Two tanks, A and B, each contain 10 L of salt water. Initially, 31 g of salt are found in A, and 27…

A: Given: To explain the given statement as follows, V = 10L, u(0) = 31, v(0) = 27

Q: Under certain water​ conditions, the free chlorine​ (hypochlorous acid,​ HOCl) in a swimming pool…

A:

Q: A scuba tank holds 2.6 ㎥ of compressed air. A diver at a shallow depth uses about 0.002 ㎥ per breath…

A: Total compressed air in scuba tank = 2.6 m^3 Compressed air used per breath is 0.002 m^3 Breath…

Q: Mervin and Leela are in bumper cars. They are at opposite ends of a 100-meter track heading toward…

A:

Q: A roast turkey is taken from an oven when its temperature has reached 190 degrees Fahrenheit and is…

A: This is the problem of the Application of the Calculus.

Q: A 450 gal tank initially contains 110 gal of brine containing 52 Ib of salt. Brine containing 1lb of…

A:

Q: The city of Anville is currently home to 23000 people, and the population has been growing at a…

A:

Q: Due to the large number of human tourists and a declining food supply, the blue-footed booby…

A: a) Given that the half-life = 13.7 years So the fraction of the booby population that will remain in…

Q: A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are…

A:

Q: Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing…

A: Let at any instant t, the weight od salt in tank A is 2 and tank B is y. By using the given…

Q: The radiator car is filled with a solution of 65% antifreeze and 35% water. The manufacturer of the…

A: The capacity of the radiator is 3.9L.Let x be the amount of coolant to be drained.

Q: The city of Anville is currently home to 29000 people, and the population has been growing at a…

A:

Q: An apple farm yields an average of 38 bushels of apples per tree when 24 trees are planted on an…

A:

Q: The​ half-life of polonium is 139​ days, but your sample will not be useful to you after 91​%of the…

A:

Q: A 6-quart cooling system is checked and found to be filled with a solution that is 40% antifreeze.…

A: Given that      A 6-quart cooling system is checked and found to be filled with a solution that is…

Q: A 21-quart cooling system is checked and found to be filled with a solution that is 40% antifreeze.…

A: Given: A 21-quart cooling system is checked and found to be filled with a solution that is 40%…

Q: Sugar dissolves in water at a rate proportional to the amount still undissolved. If there were 70 kg…

A: The amount of sugar present initially is 70 kg and at the end of 4 hours only 30 kg is left. The…

Q: The population of a bacteria increases at a rate proportional to the present number of bacteria ‘P0’…

A: Given problem is : The population of a bacteria increases at a rate proportional to the present…

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: A 120-gallon tank initially contains 80 lbs. of salt dissolve in 90 gal of water. Brinemcontaining…

A: Let xt be the amount of salt in tank at time t.  The amount of salt in is given by salt in=10 The…

Q: Two machines are turned on at 8:00 A.M. If one can produce 36 items each hour and the other can…

A:

Q: A certain type of bacteria is known to grow at the rate proportional to the amount that is present.…

A:

Q: An apple farm yields an average of 41 bushels of apples per tree when 21 trees are planted on an…

A:

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

A:

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.