3. Suppose you have a 300 gallon tank filled to the top with brine that begins with 50 lbs of saltin it. If you begin draining the well-mixed brine from the bottom of the tank at a rate of 15gallons per minute while. If you want the tank to have 10 lbs of salt in it when it gets downto 100 gallons, at what rate should you be pouring in brine with a 1 lb of salt per 10 gallonsconsistency?

Answered: Image /qna-images/answer/adec7ae0-1d81-40c0-ada9-6701fcc23d44.jpg

Answered: 3. Suppose you have a 300 gallon tank…

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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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
Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). A B Suppose: The vat contains 230 gallons of liquid, which never changes. Sugar water with a concentration of 7 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. • Sugar water with a concentration of 3 tablespoons/gallon flows through pipe B into the vat at the rate of 25 gallons/minute. The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 30 gallons/minute. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (A) Write the DE model for the time rate of change of sugar in the vat: dS dt (B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your function will have an arbitrary constant K in it. Assume that K > 0. S(t) = (C) Suppose that there are 22 tablespoons of sugar in the vat at t = 0. How many tablespoons…
(14) The coffee shop sells a coffee blend made from two coffees, one costing 5 €/ kg and the other costing 6€/kg. If the blended coffee sells for 5.60€ /kg, find how much of each coffee is used to obtain the desired blend. Assume that the weight of the blended coffee is 100 kg.
1. Suppose that a commercial truck has an efficiency of 120 – 2v m(v) miles/gallon going at speed of v miles/hour. The driver's rate is 15 dollars/hr, and gas is $3.50/gal- lon. a. Find the cost C(v) per mile to travel at speed v mph. b. Find the cheapest driving speed.
9. Imagine a medieval world. In this world a Queen wants to poison a King, who has a wine keg with 500 L of his favorite wine. The Queen gives a conspirator a liquid containing 5 g/L of poison, which must be poured slowly into the keg at a rate of 0.5 L/min. The poisoner must also remove the well-stirred mixture at the same rate, so that the keg is not suspiciously full. (a) Find a formula for the amount of poison in the keg at any time, measured from the start of the pouring by the poisoner. (b) A plot is hatched for the King to drink wine from the keg while he is on a hunt, where he will become so addled that his prey will surely kill him. The poisoner must pour for a time T, when the poison in the keg reaches a dangerous concentration of 0.005 g/L. Find T. (c) The Lord High Inquisitor of the Realm never learned about differential equations. Nonetheless, knowing the basic numbers (keg size, poison concentrations, etc.), he can produce an estimate for the time T that the poisoner was…
A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially contains 100 liters of pure water. The mixed solution is drained at 3 liters per minute. At what time will the solution contain 10% ammonia?
20. An aquarium contains 10 gallons of polluted water. A filter is attached to this aquarium which drains off the polluted water at the rate of 5 gal- lons per hour and replaces it at the same rate by pure water. How long does it take to reduce the pollution to half its initial level?

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