Find eigenvalue (?) and eigenfunction and evaluate orthogonality from the given boundary value problem. ?2?′′ + ??′ + ?? = 0, ?(1) = 0, ?(5) = 0. Hint: Use Cauchy-Euler Equation, (textbook pp141-143).

3. Suppose a beam of particles of mass m and kinetic energy E is incident from the left on a potential well given by:

U(x) = ?U₀ (for 0 < x < L where U₀ > 0)

U(x) = 0 ( otherwise )

(a) What is the Schrodinger Wave Equation (S.W.E.) for the region x < 0 ? (Hint: include both incident and reflected waves)

(b) What is the S.W.E. for the region x > L ? (Hint: this will only be a transmitted wave)

(c) What is the S.W.E. for the region 0 < x < L ? (Hint: in general there are two terms)

(d) What are the four boundary value equations for this case?

(e) Starting from the boundary value equations, derive the Transmission Probability (T) for this case.

When you use a numerical method like the finite element method, you divide a large body into an equivalent system of smaller bodies called elements. This is done because using an analytical method on the larger body may require a solution to a boundary value partial differential equation; a task that might be difficult or impossible to solve. The question: why does dividing a large object into smaller objects help at all? If you divide a rectangle into tiny rectangles and ask each of those tiny rectangles the same question that you were asking the large rectangle (which would require the solution to a boundary value differential equation), what good have you done? Please explain.

For the elastic body defined in Question 1 (below), define the boundary conditions in terms of displacement, assuming the boundary surface at the point in question has direction cosines with respect to x and y and z equal to l=0.8 and m=0.6 and n=0 . Consider the case when the change in volume is negligible.

Are all the compatibility equations satisfied for the Plane Stress conditions? If not, which equations are not satisfied? Explain the case for the Plane Strain conditions?

Question 1:

Write down the equilibrium equations for a three-dimensional isotropic material in terms of displacements. Assume that the material modulus of elasticity, Poisson ratio and density are, and that the body forces are due to the material weigh and the constant gravitational accelerations applied in z-direction.

Prob. 4-68 A piston–cylinder device contains 2.2 kg of nitrogen initially at 100 kPa and 25C. The nitrogen is now compressed slowly in a polytropic process during which PV^1.3 = constant until the volume is reduced by one-half. Determine the work done and the heat transfer for this process.

4–69    Reconsider Prob. 4–68. Using EES (or other) software,plot the process described in the problem on a P-V diagram, and investigate the effect of the poly- tropic exponent n on the boundary work and heat transfer. Let the polytropic exponent vary from 1.0 to 1.4. Plot the boundary work and the heat transfer versus the polytropic exponent, and discuss the results.

A piston-cylinder device initially has a volume of 1.5 m3 containing steam at 300 kPa absolute and 150 oC. It is then heated so it expands at constant pressure until it reaches a temperature of 400 oC.

Draw a diagram of the device showing system boundary and flows of energy. What boundary work is done by the cylinder, in kJ, during the expansion? State your assumptions.

1. What is the mass of steam in the piston-cylinder?

2. How much heat is added to the cylinder, in kJ, during the expansion? State your assumptions.

3. Assuming there are no irreversibilities during the expansion; S.GEN=0, does the entropy of the steam decrease, remain constant, or increase during the expansion? Explain your answer.

Compute and Interpret Liquidity, Solvency and Coverage Ratios
Balance sheets and income statements for Lockheed Martin Corporation follow. Refer to these financial statements to answer the requirements.

1. Compute Lockheed Martin's quick ratio for 2005 and 2004. (Round your answers to two decimal places.)

2005 quick ratio = Answer

2004 quick ratio = Answer

2. Compute total debt-to-equity ratios for 2005 and 2004. (Round your answers to two decimal places.)

2005 total debt-to-equity = Answer

2004 total debt-to-equity = Answer

3.  Compute cash from operations to total debt ratio, and free operating cash flow to total debt ratios. (Round your answers to two decimal places.)

2005 cash from operations to total debt = Answer

2004 cash from operations to total debt = Answer

2005 free operating cash flow to total debt = Answer

2004 free operating cash flow to total debt = Answer

Austin Clemens is writing a report for his high school environmental science class about the city’s climate. To impress his teacher, Austin would like to show evidence that the population mean daily low temperature during the five-year period from 1998–2002 is less than the population mean daily low temperature during the five-year period from 2013–2017. He researches the claim using a website that records all of the weather data observed at a local airport. After conducting the research, Austin assumes that the population standard deviation is 10.48∘F for 1998–2002 and 11.29∘F for 2013–2017. Due to the large amount of data in each five-year period, Austin randomly selects the daily low temperatures for each group. The sample statistics are shown in the table below. Let μ1 be the population mean daily low temperature during the five-year period from 1998–2002 and μ2 be the population mean daily low temperature during the five-year period from 2013–2017. The p-value rounded to three decimal places is 0.192, the significance level is α=0.10, the null hypothesis is H0:μ1−μ2=0, and the alternative hypothesis is Ha:μ1−μ2<0.

1998–2002 2013–2017 x

x=44.31∘F x2=46.02

n=59 n=63

Which of the following statements are accurate for this hypothesis test to evaluate the claim that the difference between the population mean daily low temperature during the five-year period from 1998–2002 and the population mean daily low temperature during the five-year period from 2013-2017 is less than zero? Select all that apply:

A)Reject the null hypothesis that the true difference between the population mean daily low temperature during the five-year period from 1998–2002 and the population mean daily low temperature during the five-year period from 2013-2017 is equal to zero.

B)Fail to reject the null hypothesis that the true difference between the population mean daily low temperature during the five-year period from 1998–2002 and the population mean daily low temperature during the five-year period from 2013-2017 is equal to zero.

C)Based on the results of the hypothesis test, there is not enough evidence at the α=0.10 level of significance to suggest that the true difference between the population mean daily low temperature during the five-year period from 1998–2002 and the population mean daily low temperature during the five-year period from 2013-2017 is less than zero.

D)Based on the results of the hypothesis test, there is enough evidence at the α=0.10 level of significance to suggest that the true difference between the population mean daily low temperature during the five-year period from 1998–2002 and the population mean daily low temperature during the five-year period from 2013-2017 is less than zero.

Compare the results of good vs poor capital budgeting decisions on an organization, be specific on the long term impact to the organization and describe characteristics included in the definition of capital budgeting.

Provide an example of a capital budgeting project for a church

What landmarks distinguished European Christendom in the so-called “Age of Faith” and what role did the Roman Catholic Church play in the rise of medieval European culture? Focus on three landmarks and discuss them elaborately.