A tank contains 1060 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank atthe rate 2 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate.(a) How much sugar is in the tank at the begining?y(0)(kg)=(b) Find the amount of sugar after t minutes.y(t)=(kg)(c) As t becomes large, what value is y(t) approaching? In other words, calculate the following limit.lim y(t) =(kg)t→∞0Question Help: Video

Answered: A tank contains 1060 L of pure water.…

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 tank contains 2100 L of pure water. Solution that contains 0.01 kg of sugar per liter enters the tank at the rate 4 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate. (a) How much sugar is in the tank at the begining? y(0) = (kg) (b) Find the amount of sugar after t minutes. y(t) = (kg) (c) As t becomes large, what value is y(t) approaching? In other words, calculate the following limit. lim y(t) = (kg) 00+7
f(x) = (0, 5/3) %3D Vx + 9 f "(0) Enter a mathematical expression. 5.
SCIENCE: Environmental Sustainability. A factory is polluting a lake so that the rate of pollutants entering the 3 lake after t months isN' (t) 280 t7, where N (t)is the total number of pounds of pollutants in the lake after t months? How many pounds of pollutants enter the lake in 16 months. An environmental board recommends that the factory begin the clean-up procedure after 50,000 lb of pollutants have entered the lake. As the head of this factory, after what month will the recommended schedule clean-up to follow this mandate. you may use a graphing application to justify your answer. ***
A large tank is filled to capacity with 400 gallons of pure water. Brine containing 3 pounds of salt per gallon is pumped into the tank at a rate of 4 gal/min. The well-mixed solution is pumped out at the same rate. Find the number A(t) of pounds of salt in the tank at time t. A(t) = Ib
The deck of a bridge is suspended 285 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by y = 285 − 16t2. (a) Find the average velocity (in ft/s) of the pebble for the time period beginning when t = 2 and lasting the following amount of time. (i) 0.1 seconds (ii)0.05 seconds (iii)0.01 seconds (b) Estimate the instantaneous velocity (in ft/s) of the pebble after 2 seconds.
A tank contains 350 liters of fluid in which 20 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 5 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
cot(n2) = 0 iff %3D TE =+ kn.
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 3,000 L of brine with 12 kg of dissolved salt. Pure water enters the tank at a rate of 30 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. (a) How much salt is in the tank after t minutes? y = kg (b) How much salt is in the tank after 20 minutes? (Round your answer to one decimal place.) y =
Looking for the steps on how to solve it using: y=p(1-r)^t
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 7070 kg of salt and 10001000 L of water. A solution of a concentration 0.035 kg of salt per liter enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the same rate.(a) What is the concentration of our solution in the tank initially?(b) Find the amount of salt in the tank after 2.5 hours.(c) Find the concentration of salt in the solution in the tank as time approaches infinity.

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