A tank initially contains 17 pounds of salt dissolved in 450 gallons of water. Starting at to = 0, water that contains 2/5 pounds of salt per gallon is poured into the tank at a rate of 10 gallons per minute and the mixture is drained from the tank at the exact same rate. Assume the tank is uniformly mixed at all times. Use this information to answer the following questions. a) Find a differential equation for the quantity of salt in the tank at time t > 0 b) Solve the differential equation from part (a) to find Q (t)

A tank initially contains 17 pounds of salt dissolved in 450 gallons of water. Starting at to = 0, water that contains 2/5 pounds of salt per gallon is poured into the tank at a rate of 10 gallons per minute and the mixture is drained from the tank at the exact same rate. Assume the tank is uniformly mixed at all times. Use this information to answer the following questions. a) Find a differential equation for the quantity of salt in the tank at time t > 0 b) Solve the differential equation from part (a) to find Q (t)

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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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.

Question

A tank initially contains 17 pounds of salt dissolved in 450 gallons of water. Starting at to = 0, water that contains 2/5 pounds of salt per gallon is poured into the tank at a
rate of 10 gallons per minute and the mixture is drained from the tank at the exact same rate. Assume the tank is uniformly mixed at all times. Use this information to
answer the following questions.
a) Find a differential equation for the quantity of salt in the tank at time t > 0
b) Solve the differential equation from part (a) to find Q (t)

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Please solve and explain this differential equ
Tank A initially contains 500 Litres of a brine solution with a concentration of 0.5 kg perlitre and tank B contains 500 Litres of water. Solution is pumped from tank A to tank B ata rate of 4 Litres /min and from tank B to tank A at a rate of 8 Litres /min. The tanks are keptwell stirred. Let the number of kilograms of salt in tank A be A1 after t minutes and B1in tank B.(a) Write down equations showing, respectively, the concentrations C1 and C2 inthe tanks after t minutes.(b) Write down two differential equations to show how A1 and B1 vary with time.(c) What is the relation between A1 and B1?(d) Eliminate B1 between the two equations in (b) and solve the resulting equationfor A1.(e) What is the concentration in tank A after 10 minutes?
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please show work
Assign variables and restate the following problem in terms of known and unknown derivatives (but do not solve it): How fast is the volume of a cube increasing if its side increases at a rate of 0.5 cm/s?
According to Newton's law of cooling, the temperature of a body changes at a rate proportional to the difference between the temperature of the body and the temperature of the surrounding medium. Thus, if Tm is the temperature of the medium and T = T(t) is the temperature of the body at time t, then T'= -k(T - Tm) where k is a positive constant. In this exercise, you will verify that T = Tm+ (To-Tm)e -kt is a solution to the differential equation. Here To denotes the initial temperature T(0) of the body. (a) First substitute the above expression for T into the left side of the differential equation. In other words, compute T'. Use an underscore "_" to write the subscripts on To and Im T'= (b) Next substitute the above expression for T into the right side of the differential equation. In other words, compute -k(T – Tm). - -k(T - Tm) (c) Are your answers in parts (a) and (b) equal? No Yes