A tank initially contains a solution of 9 pounds of salt in 60 gallons of water. Water with 7/10 pound of saltper gallon is added to the tank at 6 gal/min, and the resulting solution leaves at the same rate. Let Q(t)denote the quantity (lbs) of salt at time t (min).(a) Write a differential equation for Q(t).Q' (t) =(b) Find the quantity Q(t) of salt in the tank at time t > 0.(c) Compute the limit.lim Q(t) =18

Given that a tank initially contains a solution of 9 pounds of salt in 60 gallons of water. Water…

Answered: A tank initially contains a solution of…

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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The consumption of tungsten (in metric tons) in a country is given approximately by p(t) = 136t² + + 1,071t+14,910, where t is time in years and t= 0 corresponds to 2010. (A) Use the four-step process to find p'(t). (B) Find the annual consumption in 2021 and the instantaneous rate of change of consumption in 2021, and write a brief verbal interpretation of these results. (A) p'(t) = C
Newton’s law of cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e., the temperature of its surroundings). We let (t) denote time, T(t) be the temperature of the object at time (t), (T0 = T(0)) (the object’s temperature at (t = 0)), and Tomg be the constant ambient temperature. Set u(t) = T(t) - Tomg and show from Newton’s law of cooling that (u) satisfies the initial value problem (*) u’(t) = ku(t), u(0) = T0 - Tomg for a constant (k). Solve the initial value problem (*), i.e., find u(t)) (expressed in terms of (k), T0, and Tomg . Find T(t).
Let y(t) represent your bank account balance, in dollars, after t years. Suppose you start with $40000 in the account. Each year the account earns 6% interest, and you withdraw $3000. Write the differential equation modeling this situation. dy dt y(0) =
A tank initially contains a solution of 6 pounds of salt in 40 gallons of water. Water with 1/2 pound of salt per gallon is added to the tank at 9 gal/min, and the resulting solution leaves at the same rate. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t). Q'(t) (b) Find the quantity Q(t) of salt in the tank at time t > 0. (c) Compute the limit. lim Q(t) = t→∞ Submit Question
Suppose that news spreads through a city of fixed size of 800000 people at a time rate proportional to the number of people who have not heard the news. (a.) Formulate a differential equation and initial condition for y(t), the number of people who have heard the news t days after it has happened. No one has heard the news at first, so y(0) the number of people who have heard the news is proportional to the number of = 0. The "time rate of increase in people who have not heard the news" translates into the differential equation dy k( |3D dt
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A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution with 1/5 pound of salt per gallon is added to the tank at 10 gal/min, and the resulting mixture is drained out at 5 gal/min. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t) which is valid up until the point at which the tank overflows. 50t+ Q' (t) = X Check your variables you might be using an incorrect one. 50+t (b) Find the quantity of salt in the tank as it's about to overflow. 38.5 X Oll ✓ @ W # 3 e t² + c C $ 4 % 5 + 6 & 7 O * 8 O 9 11 OF
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