Common information for 6 and 7

Andrew borrows 360,000 at i=.05. He repays this loan by paying off only the interest due at the end of each year to the lender and depositing a level amount Y at the end of each year into a sinking fund account offering 8% APY so as to accumulate the full balance of the loan amount in the sinking fund at the end of 20 years.

What value Y must he deposit into the SF account at the end of every year?

Question 3 A A A Carbon-14 (C14) decays by a nuclear process to form carbon-12 (C12). The rate of decay of C14 is directly proportional to the quantity of C14 present. The half-life of C14 (time taken for the mass of C14 to halve, eg 1.0kg to 0.5kg) is 5730 years. If you start with a 883 gram block of pure C14, what mass of C14 remains after 2922 years? Provide your answer to TWO decimal places, using the normal convention. Pad with zeros if necessary. Mass of C14 at 2922 years (g) =

Let u(x, y) = x^3 + kxy^2 + y. (a) Determine the value of k such that u is an harmonic function. (b) Find the harmonic conjugate v of u. (c) Obtain the expression of f = u + iv in terms of z = x + iy

I'm using 2005 NFL stats to come up with a multiple linear regression analysis models with the winning percentage being the dependent variable. My question would be, what are the most significant variables that are used in deciding an NFL team's capacity to win? Passing yards, rushing game, defense or field goals are some of my independent variables. But I’m considering adding the defensive stats to the regression. How do I complete the introduction and model subtopics for my presentation?

1. Introduction

A. Topic: Select a topic of research in an area of applied science in which you are interested. Make sure to get instructor approval before proceeding. Use research literature to provide an introductory summary of the topic that establishes your interest and expertise within the area of study.

B. Research Question: Formulate an analytical, researchable question based on your topic. The scope of your research question should be reasonable given the time constraints of the course.

C. Information: Gather and summarize applicable data, research, or other information that you intend to use in the creation and analysis of your model. For example, you might first consider principles or data sets to inform the creation and analysis of your model.

D. Assessment: Assess the appropriateness of the information you gathered. How will the information help you create an effective mathematical model to address your research question? Are there any underlying assumptions or limitations in the information you gathered?

II. Model

A. Selection: Select a model type to create. Defend your selection, comparing it to other types of models. In other words, why did you choose your model type? Does the model type you chose, have any limitations? What comparative tests can you perform to support your model choice? Use research to support your model type selection.

B. Creation: Create the model using the information you gathered. Remember to be cognizant of the research question and to use appropriate mathematical tools, technology, theoretical underpinnings, and/or data, if applicable.

C. Process: Explain the process you used to build your model. Include your reasoning for specific choices and decisions you made while building your model. Use research to support your choices.

D. Tools: What tools and techniques did you use to create your model? Why are these tools and techniques appropriate for the information you gathered, and the model type you selected? Be sure to provide support for your choices.

E. Analysis: Analyze the results of your model to determine whether the model fits the research question and information you gathered. How well do the model results fit the question and information? Consider including computational tests or graphical displays to support your argument.

F. Limitations: What limitations does your model have? Use algorithmic, tabular, and graphical displays to articulate the limitations of your model.

G. Approach: Explain the approach that you took to answer your research question. Be sure to fully explain the process and steps you used to achieve your results. H. Applicability: Articulate the purpose for your model. How applicable is the model to the research question? How does the model help you answer your research question? How well does it align to the research

Problem 4. Let P be the orthogonal projection associated with a closed subspace S in a Hilbert space H, that is P is a linear operator such that

P(f) = f if f ∈ S and P(f) = 0 if f ∈ S^⊥.

(a) Show that P² = P and P^∗ = P.

(b) Conversely, if P is any bounded operator satisfying P² = P and P^∗ = P, prove that P is the orthogonal projection for some closed subspace of H.

(c) Using P prove that if S is a closed subspace of a separable Hilbert space, then S is also a separable Hilbert space.

Q3

(a) Briefly describe the extended Euclidean plane, and explain how it satisfies the axioms of projective geometry.

(b) Describe the Real Projective Plane RP2, explaining what points and lines in RP2 correspond to in R 3 with respect to an ‘all-seeing eye’ at the origin.

(c) Prove that the Cross-Ratio is preserved by every projective transformation

Brian is selling balloons in 8 different colours: red, pink, yellow, blue, green, purple, black and silver.

How many different selections of 16 helium balloons can be purchased if the shop has at least 16 balloons of each colour in stock?

How many different selections of 16 helium balloons can be purchased if you buy at least 3 red balloons and at least 5 yellow balloons, and the shop has at least 16 balloons of each colour in stock?

How many different selections of 16 helium balloons can be purchased if the shop has only 7 pink balloons in stock and only 5 blue balloons in stock, but at least 16 balloons of each other colour in stock?

We see data displayed in graphs and charts on a regular basis. Because we live in a world dominated by visual information, it is not surprising that writers, advertisers, and journalists use data visualisations such as charts, graphs, and other graphics to help readers understand complex information more easily. However, it is not uncommon for published graphs to be designed to be eye-catching, shocking, or fun to look at, rather than informative and understandable.

You can find a plethora of questionable graphs and charts on Kaiser Fung’s Junk Charts blog. Fung is an expert on data analytics and visualisations, and has authored several books on the topic. As inspiration for your small group discussion post, search through the Junk Charts archives to explore some of the ways data visualisation can become misleading.

Discuss your evaluation of any published graph or chart you find particularly interesting, effective, misleading, or difficult to understand. In your discussion, focus on answering some of the following questions:

• Does the graph represent the data accurately?
• Does the graph meet best-practice criteria?
• Does the graph speak to the target audience?
• Is the graph in any way misleading, intentionally or unintentionally?

Post the graph or chart you have chosen to share with your small group as a screenshot, image, or as a link to the website from which you found it, along with an evaluation of the graph or chart.

(D^(2)+2D+5)^(2)(D-3)^(3)y=xe^(3x)-5e^(x)sin(2x)

Find the homogeneous solution.

Find a particular solution.

Finding of coefficients is not necessary.

Solve the IVP using Laplace transforms

x' + y'=e^t

-x''+3x' +y =0

x(0)=0, x'(0)=1, y(0)=0

Determine whether each of the following statements is True or False. If True, write a proof. If False, exhibit a counterexample.

1) If m, n are arbitrary positive integers, then any system of form

x ≡ a (mod m)

x ≡ b (mod n)

has a solution.

2) If m, n are arbitrary positive integers and the system

x ≡ a (mod m)

x ≡ b (mod n)

has a solution, then the solution is unique modulo mn. Modern Abstract Algebra

modern algebra

Explain how an Abacus works doing addition and subtraction arithmetic.

Cylinders left to right, “100” then “20” then “5” then “1”. The “100” has a quantity of 5 tokens. The “20” has a quantity of 4 tokens. The “5” has a quantity of 3 tokens.   The “1” has a quantity of 4 tokens.

Prove or disprove the following statements:

a) If both x² and x³ are rational, then so is x.

b) If both x² and x³ are irrational, then so is x.

c) If both x+y and xy are rational, then so are x and y.