A sewage disposal plant has a big concrete holding tank of 100,000-gal capacity. It is % full of liquid to start with and contains 60,000 Ib of organic material in suspension. Water runs into the holding tank at the rate of 20,000 gal/hr and the solution leaves at the rate of 15,000 gal/hr. How much organic material is in the tank at the end of 3 hours?

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

A:

Q: How many liters of each 20% (v/v) alcohol and 80% (v/v) alcohol must be mixed to yield 20 liters of…

A: We are given two percentages of alcohol that are 20% and 80%. We have to produce 20 liters of 50%…

Q: A 200-gal tank is half full of distilled water. At time t=0, a solution containing 0.5 Ib/gal of…

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Q: Consider a reservoir with a volume of 8 billion cubic feet (ft^3) and an initial pollutant…

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Q: Elena has a washing machine with a 20 gallon capacity. She always uses a 20 gram measure of soap for…

A: Let x(t) be the amount of a substance at time t. The concentration of the substance can be modeled…

Q: Water is pumped from a tank at constant rate, and no more water enters the tank. If the tank…

A: To solve the following problem and find the amount of water left at 6:10pm.

Q: A tank contains 300 gal of water and 100 gal of pollutants. Fresh water is pumped into the tank at…

A: Fresh water is pumped into the tank at the rate of 2 gal/min, and the well stirred mixtureleaves at…

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 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: 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: Initially a tank holds 100 gal of a brine solution containing 4 lb of salt. At t = 0, brine…

A: We will find out the required time.

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A: Given, the half-life palladium-100 is 4 days. Here, we use the radioactive decay model, given as…

Q: A 100-gallon tank contains 50 gallons of water. Brine, containing 2 lbs of salt per gallon, flows…

A: Given that, A 100-gallon tank contains 50 gallons of water. Brine, containing 2 lbs of salt per…

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced…

A: Given :Half life of Palladium-100= 4 days

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

A:

Q: The cost of installing insulation in a particular two-bedroom home is $2400. Present monthly heating…

A: Given: The cost of installing insulation in a particular two-bedroom home is $2400. Present monthly…

Q: How long will it take 1,000 mL to infuse if the flow rate is 125mL/h?

A:

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: A Styrofoam cooler contains ice at 0° C. The cooler is left outside where the temperature is 30.° C.…

A: Given data: The cooler contains ice at 0°C, i.e. 273K The outside temperature is 30°C, i.e. 30+273K,…

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: An automobile uses gasoline at a rate of 12 kilometres per litre and has a 65 litre tank. How far…

A:

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

A: Form the first order differential equation and solve using separation of variables.

Q: A clinical laboratory technician determines that a minimum of 75 mL of working reagent is needed for…

A: Given, reagent =75mL Mixture = 4x75 =300mL

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 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: The cost of installing insulation in a particular two-bedroom home is $2400. Present monthly heating…

A: It is given that present heating cost per month is $200. As the heating cost reduced after…

Q: How many mL of solution will be infused in 4 hours if the flow rate is 20mL/h?

A:

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

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Q: A storage area has space for 20,000 parts. Currently 15,000 parts are stored there. How many percent…

A: We have to find capacity used.

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: A bunch of hooligans dump 164 pounds of  pizza boxes into a lake. If the pizza boxes dissipates at a…

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Q: Tank A contains 402 litres of brine holding 123 N of dissolved salt, and tank B contains 402 litres…

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Q: The side of a cube is increasing at a rate 7m/8, then the rate at which the m³/s. volume of the cube…

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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: The side of a cube is increasing at a rate 9m/s, then the rate at which the volume of the cube…

A: The function f(t) is a rule that associates or fixes a number to the particular point t. The…

Q: A 200-gal tank is half full of distilled water.At time t = 0, a solution containing 0.5 lb / gal of…

A:

Q: A nurse gives 1,100 mL of an intravenous (IV) solution over a period of 9 h. It is given first at a…

A: Suppose, the time taken at a rate of 140 mL/h is x and the time taken at a rate of 100 mL/h is y.…

Q: How much water should be evaporated from 40% v/v alcohol in order to prepare 3000 ml of 60% ( v/v)…

A:

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A:

Q: We have a mixing tank that contains 100 gallons of water into which 5 pounds of sugar have been…

A: According to question. Initial amount of water in tank= 100gallons Initial amount of sugar = 5 pound

Q: How long will it take to purge a 15ft section of 6in pipe with a flow rate of 35cfh

A: Given information Length of the section L=15 ft=15×12=180 in Hence, L=180 in Diameter of the pipe is…

Q: One mole of gas expands isothermically to double its volume. If the gas temperature is 340 k what…

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Q: Water is drained from a pool at a rate of R(t) = 50e-0.08t gallons per hour. If the drain is left…

A: 625 gal. water drains from the pool.

Q: In a room containing of air 20,000 m3 of air, 600 m3 of fresh air flows in per minute, and the…

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

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Q: Assume that you are attending a patient receiving intravenous medication. The doctor orders 24 mls…

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Q: Elena has a washing machine with a 20 gallon capacity. She always uses a 20 gram measure of soap for…

A: To determine the time taken to correct the error of adding extra soap to the water, we have to…

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.