Problem 5. Suppose the rabbit population r and the wolf population w are governed bydrdtdwdt(a) Is this system stable, neutrally stable, or unstable?(b) If initially r = 30 and w = 30, what are the populations at time t?(c) After a long time, what is the proportion of rabbits to wolves?= 6r-2w= 2r+w.

Answered: Image /qna-images/answer/430026b7-36df-40ea-850a-86a065dfdb23.jpg

Answered: Problem 5. Suppose the rabbit…

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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6. For the competing species population model dx dt dy = 2x (1 - -/-) - ху = 3y (1-1)-2xy dt studied in this section, we showed that the equilibrium point (1, 1) is a saddle. (a) Find the linearized system near each of the other equilibrium points. (b) Classify each equilibrium point (as either a source, a sink, a saddle, ...). (c) Sketch the phase portrait of each linearized system. (d) Give a brief description of the phase portrait near each equilibrium point of the nonlinear system.
Can anyone here solve this question? At least 2 parts if not all but please correctly and handwritten
A new town was incorporated in 1960. The size of the town's population was recorded every 5 years after 1960. Using the variables x, for number of years since 1960, and y, for the size of the population, three models were created to predict the population from the number of years since 1960.
Exercise 1. A student is asked to prove If m is even and n is odd, then m² +n² is odd. The student provides the following proof: Proof. If m is even and n is odd, then m² + n² is odd. Since m is even, m = = 2k for any integer k. Since n is odd, n = 2k + 1. Note that m² + n² = (2k)² + (2k + 1)² = 8k² + 4k +1 So m² + n² is odd because it is an even number plus 1. (a) Identify the errors in the proof above. There are multiple errors. Explain each error. Your explanation should be written to the student who made the error and should try to help the student understand why what they wrote is incorrect. (b) In addition to errors, provide suggestions to improve the student's proof writing. That is, explain what parts of the proof are unclear or unjustified. Explain how such parts of the proof prevent some students from fully following the ment made. (c) Finally, provide a correct proof of the theorem above.
2 Problem 2. Sketch a proof of these formulas for linear regression, described on the following page. P;(x1, y1) y = mx + b P2(x2, y2) w = (mx + b – y)² + ... + (mxr, + b – (1) (See the accompanying figure.) Show that the values of m and b that do this are (E»)(E») - »>»» (E.) - »>«? т (2) b= Σχ (3) - m
P1: The output y(t) of a causal linear time invariant system is related to the input x(t) by the equation džy(t) +3 0.5 dt2 dy(t) +4y(t) = x(t), dt (a) Find the frequency response H(ju) = Yjw of this system. (b) Find the impulse response, h(t). (c) What is the response of this system h(t) to a new input to the system x(t) = e-tu(t)? (d) What is the response of this system h(t) to a new input to the system x(t) = e-(t-2)u(t - 2)?
Two numbers are greater than 10 but less than 40. Their GCF is 17. What are the two numbers?
2. Factory A produces a solution of 40% concentration of chemical Y at a rate of 7 kg/min, while factory B produces a solution of 20% concentration of chemical Y at a rate of 4 kg/min. Both solutions are fed into a mixer containing 60 kg of a 25% concentration solution of chemical Y. The mixture leaves the mixer at a rate of 10 kg/min. Assuming uniform mixing, what will be the concentration of chemical Y in the final solution after 20 minutes?2)
E9.2 Lotka-Volterra Model. The following Lotka-Volterra equations are a Kolmogorov- type model of predator-prey relationships for interacting populations, e.g. hosts and parasites, yeasts and sugars, sharks and surfers. x₁ = P₁x₁ - P2X1X2 X₁ (0) = x10 x₂ = P3x2 + P1P4X1X2 X₂(0) = x20 (9.11) Parameters p₁ to p4 are constant death and birth rates; x₁ is the host population, x₂ is the par- asite population, and the product x₁x2 represents the "getting-together" of the two species. a) Find the equilibrium steady state solutions for these equations, [xeye]¹ = x₂ in terms of the parameters.
1. Which of the following models are linear in their parameters? (a) y = 0₁ +0₂e-2u +03e-3u 0, sin(2iu). (b) y = (c) y 0₁ (d) y = e-u +0203u. (e) y = 0₁u₁ + 02u2 +03u1₂. 2. Write down the regression matrix X for those models from Problem 1 which are linear in their parameters.
(a) A family of 25 lions and lioness are released into a game preserve in Africa. Initially, the population of this group of wild animals grows at a rate of approximately 30% per annum (year). The game preserve has a limited food supplies, because of this reason the preserve is believed to support only 40 lions and lioness. The population model of the lions and lioness is given by: dQ 0.3 dt 40 Find the population of lions and lioness, Q for time 0
Problem 2. # 7.2.7 Heart disease patients often experience spasms of the coronary arteries. Be- cause biological amines may play a role in these spasms, a research team measured amine levels in coronary arteries that were obtained postmortem from patients who had died of heart discase and also from a control group of patients who had died from other causes. The following table summarizes the concentration of the amine serotonin (NG/GM). Use a t-test to compare the means at the 5% significance level. Control 12 Heart Disease 3840 5310 SE 850 640

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