List some examples explaining how quadratic equations are used in business.

For each of the following polynomials, determine the number of the roots that are in the LHP, in the RHP, and on the jw-axis.

i. s³ + s + 2 = 0

ii. s⁴ - 4s³ + 7s² - 8s + 10 = 0

** When solving for LHP, RHP, & jw-axis, can you explain what differentiates these different categories? (i.e. I understand that the RHP you need to look for a sign switch but do not understand the LHP and jw-axis) Thank you!

Solve x'' + x' -6x = 5e^tsint using variation of parameters.

Q1: Let x = [ x(t) y(t) ] and consider the system of ODEs

x' = [5/2, 3; −3/4 ,−1/2] x.

(1)

1.1 Solve the initial value problem subject to x(0) = 1, y(0) = 1.

Answer digital signatures question. assume Alice has the RSA key (eA, dA, nA) and Bob has the RSA key(eB, dB, nB), where eA, eB, nA, and nB are public, dA is known only to Alice, and dB is known only to Bob.

(a) Describe how Alice could use her RSA key to sign a public message m, and explain why this approach satisfies the objective of non repudiation.

(b) Describe how Alice could encrypt and send a secret message to Bob in such a way that only he could read it, and he would be convinced the message came from Alice.

Linear programming.

Solve the following two (2) Linear programming problems (#1 and #2) and then answer question 3:

1.. Solve the following LP problem graphically:

Maximize profit =            X + 10Y

Subject to:                        4X + 3Y < /= 36
                                           2X +4Y < / = 40
                                           Y > / = 3
                                           X, Y > / = 0

2. Considering the following LP problem and answer the questions, Part a and Part b:

Maximize profit =            30X₁ + 10X₂

Subject to:                        3X₁ + X₂ < /= 300
                                           X₁ +X₂ < / = 200
                                           X₁ < / = 100
                                           X₂ > / = 50
                                           X₁ – X₂ < / = 0
                                           X₁, X₂ > / = 0

a. Solve graphically
b. Is there more than one optimal solution? Explain

3. How many feasible solutions are there in a LP program/problem? Which ones do we need to examine to find the optimal solution?

Give an example of application of differential equation in software engineering.Explain with an example question.

The uplink portion is divided into four 2.5-MHz channels (FD). In each of these channels 32 users are accommodated through equal-duration time-slots in a TDMA fashion. Assume that the average spectral efficiency for each user is the same, SE = 1.6 b/s/Hz, and that all the users run the same application.

i) What is the total number of users that can be accommodated in an orthogonal manner?

ii) Find the rate of the application.

iii) If SE is calculated through the Shannon’s formula, what should be the SNR in dB?

Could someone assist me in setting up an annotated outline for the below listed assignment?

For this task, you will prepare an annotated outline comparing the different types of sampling techniques that you read about in the Jackson and Trochim et al. readings for this week.

Headings for the outline should be divided between probability and nonprobability sampling. Each sampling technique should be described, including when it is best to use the particular method, identify the question type for the particular technique, identify the best method to apply to each technique, and list the type of quantitative design that best fits with the sampling technique.

The following are True or False statements. If True, give a simple justification. If False, justify, or better, give a counterexample.

1. (R,discrete) is a complete metric space.
2. (Q,discrete) is a compact metric space.
3. Every continuous function from R to R maps an interval to an interval.

4. The set {(x,y,z) : x² −y³ + sin(xy) < 2} is open in R³

How do you find the complementary solution of a nonhomogeneous differential equation? Could someone give me a general rule or few rules to find the complementary solution based on the appearance of the given equation or the roots of the given equation? Thanks

Using the appropriate method, find the volume generated by revolving the plane
bounded by y − 3 = x^2, y= √x , and x = 0 about y = −3.

How do you make decisions that are expected to generate income?

At different stages of your life, you will evaluate investment options based on the expected cash flows that they are likely to produce – a process that hopefully will help you to make informed decisions. Think about the various way you might invest money to generate income in the future, and how you will make these types of decisions. For this assignment, suppose that you have been given $10,000 with the requirement that you "invest" it in one of the 3 different options below. Research the expected return and associated risk for each of the following:

• Pay down your student loan or credit card debt. Although this is not technically an investment, it is effectively the same as earning a "risk-free" rate of interest. Alternatively, you can keep the cash in a riskless (FDIC insured) bank account. Current rates are available on a number of different sites such as Bankrate.com.
• Invest in any stock(s) of your choice. Research the company on Yahoo Finance or other financial site, and get statistics regarding the expected risk and return for this investment. Be very specific about why you selected this company.
• Invest in a real estate rental property. Research property prices, rents, and expenses for residential income properties or get basic information from a property management site such as Mashvisor or Roofstock. Note that a "cap rate" or "cash-on-cash" return is like a dividend yield for a stock, and is calculated as net operating income (rental income less expenses) divided by the price.

There are no wrong answers, but you must justify your opinions using the concepts that you have learned in this course. Be sure to include all factors used in making your evaluations, and be specific about your conclusions. To receive full credit, your answers must be well thought out and well-written.

Answer ALL 4 questions below:

1. Before making any calculations, which option appeals to you the most?
2. What methods would you use to evaluate these options? Compare each option in terms of current yield, potential for appreciation, and estimate an approximate long-term total return.
3. Which option offers the best potential return given its level of risk? Which one would you choose given your level of risk aversion? Explain in detail.
4. What sort of capital investments do you think you might make in the future? What other investments (such as owning your own company or investing in a start-up) would you consider? Why? Are there any factors in addition to monetary gain that you would consider?

1. [25 marks] Consider the following model: maximize 40x1 +50x2 subject to: x1 +2x2 ≤ 40 4x1 +3x2 ≤ 120 x1, x2 ≥ 0 The optimal solution, determined by the two binding constraints, is x1 = 24, x2 = 8, OFV∗ = 1,360.

Now consider a more general objective function, c1x1 + c2x2. Perform a sensitivity analysis to determine when the current solution remains optimal in the following cases:

(i) both c1 and c2 may vary;

(ii) c2 = 50, c1 may vary;

(iii) c1 = 40, c2 may vary

Suppose the RHS of the second constraint increases by an amount ∆b. (It is now 120 + ∆b.) Solve the two equations for x1 and x2 in terms of ∆b, and hence determine its shadow price.