A 100,000 liter tank of pure water wasaccidentally mixed with a 7000 liters of saltwith a concentration of 90k kilos. To solve thisproblem, they continuously pour fresh waterinto the tank at a rate of 50 liters per minuteand release the salt solution at the same rate.Find:a.The differential equation on this problem.b.The amount of salt after 3 days.c.Number of minutes at half of the originalsalt content.

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Answered: A 100,000 liter tank of pure water was…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A water tank has 142 gallons of water, At first, in t=0, a solution with 1/6 lb/gal of a chemical solvent flows inside the tank at a rate of 5 gal/min. The mixture then leaves the tank at the same rate. What is an equation that tells the amount of water with solvent at any instant “t” inside the tank
A 100 gallon tank initially contains 10 gallons of fresh water. At t = 0 a brine solution containing 1 pound of salt per gallon is poured into the tank at the rate of 4 gal/min., while the well-stirred mixture leaves the tank at the rate of 0.5 gal/min. Find the amount of salt in the tank at the moment of overflow. Enter answer as numerical decimal correct to two decimal places. pounds.
Problem: A vessel contains 1,00 Liters of brine with 15 kg of dissolved salt. Pure water enters the vessel at 10 liters per minute. The solution is kept thoroughly mixed and drains from the vessel at the same rate. How much salt is in the tank after t minutes?
please answer
While the rate at which ethanol can be produced is important, the total quantity of ethanol that can be produced from a given crop is also important. Use the information listed below to calculate the theoretical yield of ethanol from a 1 hectare plot of corn and a 1 hectare plot of sugarcane in the U.S. (1 hectare = 2 football fields). Show your calculations. Corn Yield: 138 bushels of seed per hectare 1 bushel seed = 2.8 gallons ethanol Sugarcane Yield: 89 tons sugarcane per hectare 1 ton sugarcane = 19.5 gallons ethanol
Set up an I.V.P. and solve using the following: Suppose a large mixing tank initially holds 500 liters of pure water. A brine solution is pumped into the tank at a rate of 3 L/min with a concentration of 0.2 kilograms of salt per liter. If the well-stirred solution is pumped out at the same rate, find the number of kilograms of salt in the tank at time t, A(t).
The air in a room 15 ft by 12 ft by 12 ft is 4% carbon monoxide. Starting at t = 0, fresh air containing no carbon monoxide is blown into the room at a rate of 300 ft³/min. If air in the room flows out through a vent at the same rate, when will the air in the room be 0.01% carbon monoxide? The air in the room will be 0.01% carbon monoxide after (Round to two decimal places as needed.) minutes.
A tank initially contains 50 gal. of fresh water. Brine (water in which a certain number of pounds of salt have been dissolved), containing 2 lb/gal of salt, flows into the tank at the rate of 2 gal/min and the mixture kept uniform by stirring runs out at the same rate. How long will it take to increase from 40 lbs. to 80 lbs.?
At 7 pm on a Wednesday evening. Mr Huxley's water tank was full. The capacity of the tank was 3 000 litres. Unfortunately, the tap on the tank was leaking in such a way that the change in volume at any time (r) hours was proportional to the volume (V) of the tank. This means that AP =-kV . dt Show that V= Ve is a solution of this equation. Given that the volume of the tank after 3 hours is 1900 litres, show that k = 0.1523 correct to 4 decimal places. (iii) By the time Mr Huxley discovered that the tank was leaking, there were only 250 litres of water remaining. At what time and on which day did Mr Huxley discover the leak (Answer correct to the nearest minute)?
A tank contains 200 gal of liquid. Initially, the tank contains pure water. At time t = 0, brine containing 3 lb/gal of salt begins to pour into the tank at a rate of 2 gal/min, and the well-stirred mixture is allowed to drain away at the same rate. How many minutes must elapse before there are 100 lb of salt in the tank?
A radioactive material decays at a rate which is proportional to the amount of radioactivity remaining. If the amount of radioactivity remaining is denoted by N at the time t, form an equation which represents this statement. If the half-life (the time taken for half the radioactivity to decay) is 10 years, how long will it take for ¾ of the radioactivity to decay?
Solve the given problem below in picture.

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