What is the process of obtaining a Fourier series solution for the heat equation with Dirichlet boundary conditions and an arbitrary initial condition.

A sheet of metal of 2 m ´ 2 m and 1.5 mm thickness is being tested in a wind tunnel.

a. Calculate the critical velocity, in m/s, at which the boundary layer will remain laminar.

b. For an upstream velocity of 35 m/s, what percentage of the metal sheet surface will have a laminar boundary layer.

c. For each of the previous cases (all laminar B.L and mixed laminar/turbulent B.L), calculate the drag force on the plate, in N. Use Table 9.3 to calculate the appropriate drag coefficients.

Using the models and theories of either (1) market structure, conduct and performance, (2) game theory or (3) the boundary of the firm, perform a microeconomic analysis of one appropriate economic issue or phenomenon of your choice. Clearly explain your chosen question, method and conclusions. Comment on the link between market structure and performance for your chosen issue. what are some issues or phenomenoms i could discuss for (1) market structure, conduct and performance, (2) game theory or (3) the boundary of the firm. Thank you

Macarthurs, a manufacturer of ropes used in abseiling, wished to determine if the production of their ropes was performing according to their specifications. All ropes being manufactured were required to have an average breaking strength of 228.5 kilograms and a standard deviation of 27.3 kilograms. They planned to test the breaking strength of their ropes using a random sample of forty ropes and were prepared to accept a Type I error probability of 0.01.

1. State the direction of the alternative hypothesis for the test. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.

2. State, in absolute terms, the critical value as found in the tables in the textbook.

3. Determine the lower boundary of the region of non-rejection in terms of the sample mean used in testing the claim (to two decimal places). If there is no (theoretical) lower boundary, type lt in the box.

4. Determine the upper boundary of the region of non-rejection in terms of the sample mean used in testing the claim (to two decimal places). If there is no (theoretical) upper boundary, type gt in the box.

5. If the average breaking strength found from the sample is 234.9 kilograms, is the null hypothesis rejected for this test? Type yes or no.

6. Disregarding your answer for 5, if the null hypothesis was rejected, would it appear that the new fibre has affected the breaking strength of the rope at the 5% level of significance? Type yes or no. Blank 6

For each of the following, fill in the blanks with "Less than", "Greater than", or "Equal to"

*) A gas flows through a one-inlet, one-exit control volume operating at steady state with no internal irreversibilities, Qcv = 0. Heat transfer at a rate Qcv takes place only at a location on the boundary where the temperature is Tb. The specific entropy of the gas at the exit is _____ than the specific entropy of the gas at the inlet.

*) A gas flows through a one-inlet, one-exit control volume operating at steady state with no internal irreversiblities, Qcv < 0. Heat transfer at a rate Qcv takes place only at a location on the boundary where the temperature is Tb. The specific entropy of the gas at the exit is _____ than the specific entropy of the gas at the inlet.

* ) A gas flows through a one-inlet, one-exit control volume operating at steady state with no internal irreversibilities, Qcv > 0. Heat transfer at a rate Qcv takes place only at a location on the boundary where the temperature is Tb. The specific entropy of the gas at the exit is _____ than the specific entropy of the gas at the inlet.

*) A gas flows through a one-inlet, one-exit control volume operating at steady state with internal irreversibilities present, Qcv >= 0. Heat transfer at a rate Qcv takes place only at a location on the boundary where the temperature is Tb. The specific entropy of the gas at the exit is _____ than the specific entropy of the gas at the inlet.

The Australian Medical Association believed that the Health Minister's recent statement claiming that 75% of doctors supported the reforms to Medicare was incorrect. It thought that the actual support for the reforms was lower than this. The Association's President suggested the best way to test this was to survey 150 members, selected through a random sample, on the issue. She indicated that the Association would be prepared to accept a Type I error probability of 0.05.

1. State the direction of the alternative hypothesis for the test. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.

2. State, in absolute terms, the critical value as found in the tables in the textbook.

3. Determine the lower boundary of the region of non-rejection in terms of the sample proportion of respondents (as a % to two decimal places) in favour of the reforms. If there is no (theoretical) lower boundary, type lt in the box.

4. Determine the upper boundary of the region of non-rejection in terms of the sample proportion of respondents (as a % to two decimal places) in favour of the reforms. If there is no (theoretical) upper boundary, type gt in the box.

5. If 102 of the survey participants indicated support for the reforms, is the null hypothesis rejected for this test? Type yes or no.

6. Disregarding your answer for 5, if the null hypothesis was rejected, could the Association claim that the Health Minister's assertion is incorrect at the 5% level of significance?

The Australian Medical Association believed that the Health Minister's recent statement claiming that 75% of doctors supported the reforms to Medicare was incorrect. It thought that the actual support for the reforms was lower than this. The Association's President suggested the best way to test this was to survey 150 members, selected through a random sample, on the issue. She indicated that the Association would be prepared to accept a Type I error probability of 0.05.

1. State the direction of the alternative hypothesis for the test. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.

2. State, in absolute terms, the critical value as found in the tables in the textbook.

3. Determine the lower boundary of the region of non-rejection in terms of the sample proportion of respondents (as a % to two decimal places) in favour of the reforms. If there is no (theoretical) lower boundary, type lt in the box.

4. Determine the upper boundary of the region of non-rejection in terms of the sample proportion of respondents (as a % to two decimal places) in favour of the reforms. If there is no (theoretical) upper boundary, type gt in the box.

5. If 102 of the survey participants indicated support for the reforms, is the null hypothesis rejected for this test? Type yes or no.

6. Disregarding your answer for 5, if the null hypothesis was rejected, could the Association claim that the Health Minister's assertion is incorrect at the 5% level of significance?

The National Association of Realtors estimates that 23% of all homes purchased in 2004 were considered investment properties. If a sample of 800 homes sold in 2004 is obtained what is the probability that at most 175 homes are going to be used as investment property? Round to four decimal places, if necessary.

The consumer Price Index for the different years are as follows.

2003 10.75

2004 89.25

2005 83.34

2006 56.25

1) Calculate Inflation rate for 2003, 2004, and 2005.

2) What kind of fiscal policy will you use to fight against inflation. Explain it briefly.