2)(a) When an object falls from rest at t = 0 through a resisting liquid. the rate of changedvof its velocity at time t is given by= -k(v – 600), where k is a positive constant.dt%3D(i) Show that v = 600 + Pe¬kt is a solution to the differential equation for someconstant P.(ii) If the velocity of the object at t = 3s is 25 ms-1, find P and k.(iii) Find the velocity of the object at t = 10s. Give your answer correct to onedecimal place.(iv) What is the limiting value of v as t – x?

We need to solve given differential equation and use the solution to answer other part

Answered: (a) When an object falls from rest at 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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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
The initial concentration of phosphorous (C) in a waste water pond is 107 ppm, as against the acceptable limit of 6.75x10 ppm. The concentration (C) will reduce as fresh water enters the pond. The differential equation that governs the concentration, C as a function of time (in weeks) is given by. dc +0.06 C = 0, C (0) =107 ppm dt Using Euler's method and a step size of 3.5 weeks, Calculate (.) The concentration of the phosphorus after 7 weeks. (H.) Exact concentration after 7 weeks (l.) Relative absolute error
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
At t=0, a 600 liter tank initially contains 50 grams of salt dissolved in 300 liters of water. Then, water that contains 2 grams of salt per liter is poured into the tank at a rate of 5 liters per minute. The solution in the tank is constantly stirred so the salt concentration is uniform at any given time t. Water leaves the tank at a rate of 2 liters per minute. Determine when the tank will overflow and create a differential equation to determine how much salt will be in the tank after 1 hour.
2. (10%) Consider a tank filled with water with a draining tap at the bottom. The water level in the tank is a function of the time, h(t). It has been observed that the rate of change of h with respect to time is proportional to the square root of the water level h at a given time. Write the differential equation for the water level h(t) at a given time t. h(t) Тар exit
<< A bank account that earns 5% interest compounded continuously has an initial balance of zero. Money is deposited into the account at a constant rate of $20 per year. The differential equation (DE) that describes the rate of change of the balance B is: dB dt Where f(B) = 5B + 20 O A. O B. = f(B), D. 0.05B + 20 Oc0.05B - 20 20B +0.05 984 K NO

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