Reference no: EM13970894
Question 1:
Consider the pair of differential equations
dx/dt= 1-y,
dy/dt= x^2 - y^2.
(a) Find all the equilibrium points of these equations.
(b) Classify each equilibrium point of this non-linear system as far as Possible by considering the Jacobian matrix.
Question 2:
Consider the pair of differential equations
dx/dt=(x^2 - 1)(y + 2),
dy/dt= x(y^2 - 1).
(a) Find all the equilibrium points of these equations.
(b) Using Maxima, or otherwise, plot the phase portrait of these equations.
(c) Briefly describe the phase path that goes through the origin.
Question 3:
Consider the pair of differential equations
dx/dt=(1 - 2x/π)cos y +(1 - 2y/π)sin x, dy/dt= sin x + cos y.
(a) Show that (π, 1/2π) is an equilibrium point of these equations.
(b) Classify this equilibrium point of this non-linear system as far as possible by considering the Jacobian matrix.
|
What is the net present value of this project
: You are analyzing a project with a 30-year lifetime, with the following characteristics: The project will require an initial investment of $20 million and additional investment of $5 million in year 10 and $5 million in year 20. What is the net prese..
|
|
What level of pretax operating profit
: Sara Inc is considering a five-year project to improve its production efficiency. The new machine has an initial investment of $480,000. The salvage value at the end of the project will be $80,961. The machine also requires an initial investment in s..
|
|
Should the company buy and install the vending machine
: You have been asked by the president of your company to evaluate the proposed acquisition of a new vending machine. The machine’s basic price is $100,000 and it will cost another $20,000 to modify it for special use by your firm. What is the operatin..
|
|
Financial distress different from agency benefit of leverage
: What are agency costs, and how are agency costs of financial distress different from agency benefits of leverage? Explain their impact on calculating the value of a firm with financial distress.
|
|
Find all the equilibrium points of these equations
: Find all the equilibrium points of these equations - classify each equilibrium point of this non-linear system as far as Possible by considering the Jacobian matrix.
|
|
Gross pay for that week
: Determine his gross pay for that week if the company uses the one-half average rate method.
|
|
Dividend payment process and open-market repurchase process
: What are the dividend payment process and the open-market repurchase process? In your answer, be sure to explain the effects they have in a perfect world.
|
|
Present value and rate of return of project
: If Solitaire undertake the project, what is the net present value and rate of return of the project for Solitaire?
|
|
Consider when making the cash flow estimates
: For what reasons would a firm use a financial model in projecting future cash flows from an investment, and what are the primary factors to consider when making the cash flow estimates?
|