A sewage disposal plant has a big concrete holding tank of 100,000-gal capacity. It is 3⁄4 full of liquid to start with and contains 60,000 lb 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: 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: How much 15% solder must be added to 25% solder to produce 30.0 g of 18% solder? In a race, car 1…

A: For part 1 of question   let amount of solder be x so according to the statement  15% of x + 25% of…

Q: At 1:00 p.m.., oil begins leaking from a tank at a rate of (4 + 0.75t) gallons per hour. , answer…

A: At 1:00 p.m.., oil begins leaking from a tank at a rate of (4 + 0.75t) gallons per hour. , Let time…

Q: (c) Bags are filled with bird food at a rate of 420 grams per second. How many 20 kg bags can be…

A: Given : Rate 420 gram per second               No of 20 kg bags filled in 4 hours =?

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

A: Given that the size of the tank is 200 gallon. Half of it is full, that means 200/2=100 gallon is…

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: 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 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: The mass of a cube in grams is M=x^3+0.1x^4, where is the length of one side in centimeters. If the…

A:

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

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

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Q: A tank contains 10m^3 of free water, brine having a concentration of 15kgsalt/m^3 is sent into the…

A:

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

A: Let s be the side of the cube in meter and V be the volume of the cube and t be the time in…

Q: A chain lying on the ground is 10 m long and its mass is 60 kg. How much work (in J) is required to…

A:

Q: At 9 p.m., a cylinder containing 240 liters of brine in which 12kg of salt is dissolved. Brine…

A: We will find how much salt in the cylinder is by 9.30

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

A:

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

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Q: A tank with a capacity of 400 gal originally contains 150 gal of water with 25 lb of salt in…

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: 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 deep-dish apple pie, whose internal temperature was 220°F when removed from the oven, was set out…

A: Given: Apple pie's internal temperature=220oF After 15 minutes later pie's internal temperature…

Q: with 2.60 moles of oxygen at 39.3 degrees Celcius?

A:

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…

A:

Q: A worker uses 450 inches of steel wire to make 300 springs of the same size. At this rate how many…

A: Let he needs ' x ' inches for making 1 spring.

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

A: Form the differential equation of first order and solve to get the answer.

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: 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: Into a 100 - gal tank initially filled with brine containing 50 lb of salt flow 3 gal/min of brine…

A: Into a 100-gal tank initially filled with brine containing 50 lb of salt flow 3 gal/min of brine…

Q: How long (in hours) would it take to fill a city water tank that has an inside diameter of 120 feet…

A:

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

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

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

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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: 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: A vessel with 500 gallons of beer contains 4% alcohol (by volume). Beer with 7% alcohol is pumped…

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

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: The radius of a sphere decreases at a rate of 5 m/s. when the radius is 7 m, then the rate at which…

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Q: A truck with a mass of 1500 kg is decelerated at a rate of 5m/s2 . How much force did this require?

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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: 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…

Q: The width of a rectangle is increasing at a rate of 2cm/sec, while the length increases at 3cm/sec.…

A: Suppose that the length of rectangle is “l” and width is “w”   So according to the question, dwdt=2…

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.