1. We have a large tank initially containing 1, 200 gallons of pure water. Webegin adding an ethanol-water mix at a rate of 5 gallons per minute. Thisethanol-water mix being added is 70 percent ethanol. At the same time, themixture in the tank is drained at a rate of 5 gallons per minute. Throughoutthis entire process, the mixture in the tank is thoroughly and uniformly mixed.Let y(t) be the number of gallons of pure ethanol in the tank t minutes afterwe started adding the ethanol-water mix.(a) Find the differential equation which describes this scenario (for y(t)). Youmust explain in your own words and logically derive the equation.(b) Using the differential equation just obtained, solve for y(t).(c) Approximately how many gallons of ethanol are in the tank at i. t =30? ii. t = 70? iii. t = 1200?(d) When will the mixture in the tank be 75% ethanol?

As per the rule we are authorized to answer only 3 subparts So, providing the answer for the first…

Answered: We have a large tank initially…

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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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).
Weekly sales of a new brand of sneakers are given by: S(t) = 200 − 150e−t/10 pairs sold per week, where t is the number of weeks since the introduction of the brand. Estimate S(5) and dS/dt | t=5 and interpret your answers.
A tank contains 120 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 3 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t. A(t) = 9
A tank contains 1,000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min. Let y(t) be the amount of salt (in kg) in the tank after t minutes. (a) Find the rate of change of amount of salt in the tank after t minutes. dy dt kg min How much salt is in the tank when t = 0? y(0) How much salt (in kg) is in the tank after t minutes? y = = kg (b) How much salt (in kg) is in the tank after 50 minutes? (Round the answer to one decimal place.) y(50) = kg
The population of Normal, Illinois grows proportionally to its population at time t. At an initial population of 2100, it grows at a rate of 8% over 10 years. What is the value of the proportionality constant?
Water containing 0.5 lb/gal of salt enters a tank at a rate of 2 gal/min and leaves the tank at a rate of 3 gal/min. Suppose the tank initially contains 300 gallons of water and 60 lb of salt. (a) Set up an ODE for the amount of salt in the tank, x(t). b)solve it c)Sketch an accurate solution for x(t). Don't omit details.
A tank contains 150 liters of fluid in which 20 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 3 Limin; the wall-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t. A(t) = 9
dC The rate of change in the concentration of a drug with respect to time in a user's blood is given by = - kC + D(t), where D(t) is dosage at time t and k is the rate that the drug leaves the bloodstream. Complete dt parts (a) and (b) below. t (a) Solve this linear equation to show that, if C(0) = 0, then C(t) = e -kt ,ky D(y)dy. dC dy Begin by writing the differential equation, = - kC + D(t), in the form dt + P(x)y = Q(x). dx dC + %3D dt
SOLVE STEP BY STEP IN DIGITAL FORMAT PLEASE Through the point P(-2,-7) tangents are drawn to the ellipse 2x² + y² + 2x-3y - 2 = 0; determine the equations of the tangents and the points of tangency +

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