in Research related to
MATHEMATICAL/ANALYTICAL Perspective of Inquiry

• What are the economical issues involved?
• Which economic theories or approaches best explain the issue?
• What are the statistical facts related to the issue?
• Which statistical processes used to study the issue provide for the best explanation or understanding of the issue?

Create a table that computes the money in an account for three years under the following investment scheme: the account starts at $500, each month 0.75% is added in interest and then $100 is added in new principal. Compute the total principal invested, the total amount in the account, and the total interest after three years of investing.

Solve the initial value problem:

y''' - 12y'' + 48y' - 72y = 0 ; y(0) = 1, y'(0) = 0, y''(0) = 0

Solve two different first order differential equations (one linear and one non-linear) both analytically and numerically and compare the results in tabular and graphical forms. Include at least two different numerical solution techniques for each differential equation analyzed.

a) In a collection of 900 coins, one is counterfeit and weighs either more or less than the genuine coins. Find a good lower bound on the number of balance scale weighings needed to identify the fake coin and determine whether it is too heavy or too light. Assume the balance scale has three states: tilted left, tilted right, or balanced.

b)In a collection of 10 coins, 2 coins are counterfeit and weigh less than the genuine coins. Find a good lower bound on the number of balance scale weighings needed to identify all the fake coins. (Assume the balance scale has three states: tilted left, tilted right, or balanced. )

c)Consider the problem of identifying a counterfeit coin with a balance scale. Suppose, as we did in Example 5.18, that 1 coin out of a set of 10 is fake, but this time suppose that the fake coin could be eithertoo heavy or too light, and it must be determined which is the case. What does Theorem 5.1 say about the minimum number of weighings in this case?

d)Suppose that one coin in a set of fourteen coins is fake, and that the fake coin is lighter than the other coins.

Use Theorem 5.1 to find a lower bound on the number of balance-scale weighings needed to identify the fake.

Discuss the application of Fibonacci numbers in music.

Need some detailed explanation in like 200 words.Thank you.

Exercise 3 A test for the variance can be done based on the following rejection rules: Case (a) Case (b) Case (c) H0 : σ 2 ≤ σ 2 0 (or σ 2 = σ 2 0 ) H0 : σ 2 ≥ σ 2 0 (or σ 2 = σ 2 0 ) H0 : σ 2 = σ 2 0 H1 : σ 2 > σ2 0 H1 : σ 2 < σ2 0 H1 : σ 2 6= σ 2 0 Reject if (n − 1)S 2 σ 2 0 > χ2 n−1,α (n − 1)S 2 σ 2 0 < χ2 n−1,1−α (n − 1)S 2 σ 2 0 < χ2 n−1,1−α/2 or (n − 1)S 2 σ 2 0 > χ2 n−1,α/2 Use this test to solve the following problem: A pharmaceutical company is concerned about the variability of the content of the active ingredient in a new allergy medication they plan to submit for approval to the FDA. Even though certain level of variability is not a problem, if there is evidence that the standard deviation of the content exceeds 0.1mg, the FDA would not approve the new medication. The pharmaceutical company’s managers want to make sure that the new medication will get the approval before submitting it because, otherwise, the reputation of the company would be seriously damaged and, therefore, conduct a test at the 1% significance level to try to prove that, at this level of significance, they can prove that the variability is below the standards required by the FDA. (a) Propose a null and an alternative hypothesis to test the safety of the medication (note that the test is written for the variance and not for the standard deviation!). (b) The company takes a sample of 100 pills and measures the content of the active ingredient in all of them, obtaining a standard deviation of 0.085mg. Is this enough evidence at the 1% significance level to say that the variability is below the FDA requirements? (c) Find and interpret the p-value of this test. Should the company submit the medication?

A good starting point is to explore the life of Pythagoras and his contribution to the world of mathematics, and one part of his life or his discoveries. supported with a detailed example.

Is it possible to have one region whose volume can be described in BOTH cylindrical and spherical coordinates using triple integrals that have only constant bounds (i.e., no variables in any of the bounds)? If yes, provide an example of such a region. If no, explain why not.

Please Answer 1-3 for me

1. Solve the system of linear equations using the Gauss-Jordan elimination method.

(x₁, x₂, x₃) = ( )

2. Formulate a system of equations for the situation below and solve.

For the opening night at the Opera House, a total of 1000 tickets were sold. Front orchestra seats cost $90 apiece, rear orchestra seats cost $70 apiece, and front balcony seats cost $50 apiece. The combined number of tickets sold for the front orchestra and rear orchestra exceeded twice the number of front balcony tickets sold by 400. The total receipts for the performance were $70,800. Determine how many tickets of each type were sold.

3.

Formulate a system of equations for the situation below and solve.

Joan and Rick spent 3 weeks (21 nights) touring four cities on the East Coast—Boston, New York, Philadelphia, and Washington. They paid $220, $440, $180, and $200 per day for lodging in each city, respectively, and their total hotel bill came to $6,360. The number of days they spent in New York was the same as the total number of days they spent in Boston and Washington, and the couple spent 3 times as many days in New York as they did in Philadelphia. How many days did Joan and Rick stay in each city?

Suppose that your air conditioner fails on Sunday at midnight (t0 = 0),
and you cannot afford to have it repaired until payday at the end of
the month. Assume that the outside temperature varies according to
the function

A(t) = 80 5 cos(π/12)-5√3sin(π/12t)

and that your inside temperature, u(t) obeys Newton’s law of cooling
and is governed by the differential equation
du/dt= -0.2(u-A(t))

(a) If your indoor temperature when the air conditioner failed was
70◦F , determine the dynamics of temperature inside your apart-
ment over time. i.e. find a particular solution to the initial value
problem.
(b) What will the temperature inside the apartment be, 24 hours after
the break down?
(c) In the long run (t → ∞), what is the maximum and minimum
temperature you can anticipate inside your apartment?

Complex Numbers: What's the difference between Log(z), log(z) and ln(z)?

where z is a complex number, z = x + iy

A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from rest from a point 5 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s2 for the acceleration due to gravity.)

(c) Deduce that the Horton graph (p. 240) is nonhamiltonian.

Assume no time lags. Political turmoil in the us leads to a none period adverse spending shock in 2018. The repercussions are felt globally causing exchange rate in developing countries to strong depreciate. The prices of imported goods in the us would fall except for the imposition of tariffs so the us economy experiences a one period adverse supply shock also felt in 2018. Call the initial pre shock point a and call the after shock point B. I should see points a and b I both graphs on the left ( both labelled carefully). Illustrate the shock described using the AE/PC model without time lags. ( Use the AE PC graph similarly to the textbooks). For your analysis, chose as a starting point, and economy operating at potential GDP and at its inflation target. Describe the appropriate feds response by following if it is following non accommodative monetary policy. The response should start with point b as earlier shown. Introduce point c to show the intervention ( in 2018 ) and point d to indicate the final outcome of the intervention.

Shock ( two graphs)                                                                        RESPOSE                                        

( SPACE)                                                                                       

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                y*                                                                                      y*

(SPACE)

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