(15 points)Consider the two-step method for solving the initial value problem y'(t) = fit, Y(0), Y(0) = yo:

,, , 1 ,., , 3 ,., Yn+1 = + Yn-1) + h n+ 1 Yni -1 4-1ktn)Yn) + Triktn-1, Yn-1)) • (3)

[a] (7 points) Show that (3) is a second-order method and find the leading term in the local truncation error. Decide whether the method is convergent. [b] (8 points) Use Matlab to solve numerically the initial value problem

y'(t) = -y(t) + sin(10 t), y(0) = 1 , t E [0,1]

using the method (3). You may use the Matlab codes provided in class as model. Use for Y1 the value obtained by applying one step of the forward Euler method. Verify that the predicted convergence order of your method is correct by solving the equation numerically using h = 1/10,1/20,1/40,1/80, recording the maximal error (you need to find the analytic solution of the initial value problem), and verifying that the max-errors decay at the predicted rate. Check the predicted convergence rate using the exact errors computed by Matlab (not hand recorded 2-digit approximations). Report max-errors and rates in a table. Include in your submission the Matlab code, and a graph with all approximations plotted together with the exact solution. Also include a graph of the absolute values of the errors on a separate figure.

Attachments:

E9550D1E-7EEC….jpeg

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A. QUESTIONS1. What is internal control? Why is internal control important in organization?2. What are the four basic purposes of internal control? Give an example of each one?B. EXERCISE1. The California State University (CSU) system is the largest four-year higher educationsystem in the United States. In 2004, all twenty-three CSU campuses adopted PeopleSoft,an enterprise resource planning system, for managing finances, personnel records andother important functions. The project was referred to as the Common ManagementSystem (CMS). Considering Brown’s taxonomy of risk, identify five risks the CSU and itsmanagement took by making the PeopleSoft decision.2. The following is a question in which one is expected to evaluate internal controls.The Art Appreciation Society operates a museum for the benefit and enjoyment of the community.During hours when the museum is open to the public, two clerks who are positioned at theentrance collect a $5 admission fee from each nonmember patron. Members of the ArtAppreciation Society are permitted to enter free of charge upon presentation of their membershipcards.At the end of each day one of the clerks delivers the proceeds to the treasurer. The treasurercounts the cash in the presence of the clerk and places it in a safe. Each Friday afternoon thetreasurer and one of the clerks deliver all cash held in the safe to the bank, and receive anauthenticated deposit slip which provides the basis for the weekly entry in the cash receipts journal.The Board of Directors of the Art Appreciation Society has identified a need to improve their systemof internal control over cash admission fees.The Board had determined that the cost of installing turnstiles, sales booths, or otherwise alteringthe physical layout of the museum will greatly exceed any benefits that may be derived. However,the Board has agreed that the sale of admission tickets must be an integral part of its improvementefforts.Smith has been asked by the Board of Directors of the Art Appreciation Society to review theinternal control over cash admission fees and provide suggestions for improvement.RequiredIndicate weaknesses in the existing system of internal control over cash admission fees, which Smithshould identify, and recommend one improvement for each of the weaknesses identified.

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Based on your selected topic, evaluate the following:
o Find the best point estimate of the population mean.
o Construct a 95% confidence interval for the population mean. Assume that your data is normally distributed and σ is unknown. (The symbol should state that the population standard deviation is unknown. Construct a 95% confidence interval for the population mean. Assume that your data is normally distributed and ÃÆ’ is unknown. The symbol should state that population standard deviation is unknown.
• Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations. 
o Write a statement that correctly interprets the confidence interval in context of your selected topic. 
3. Based on your selected topic, evaluate the following:
o Find the best point estimate of the population mean.
o Construct a 99% confidence interval for the population mean. Assume that your data is normally distributed and σ is unknown.
• Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations. 
o Write a statement that correctly interprets the confidence interval in context of your selected topic. 
4. Compare and contrast your findings for the 95% and 99% confidence interval.
o Did you notice any changes in your interval estimate? Explain.
o What conclusion(s) can be drawn about your interval estimates when the confidence level is increased? Explain.

DATA:Age Data Option Checkup:
Mean 61.81666667
Median 61.5
Mode 69
Standard Deviation 8.924337
Range 41
Midrange 55.5

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SUR 340 – Flight Planning

The project area outlined is found in the file entitled Planning_map.pdf. It is a 7.5 minute quad

sheet, so the scale is 1:24,000 or 1” = 2000’.

The client wants a topographic map of this project area with a 2-foot contour interval (2-ft CI).

You will be using a standard 6-inch mapping camera with a 9-inch format, and a softcopy

workstation, so use a C-factor of 1500.

Compute the photo scale, 1:__________ or 1” = __________ feet.

Compute the flight height above mean terrain = __________ feet. (Some call this the flight

height or FH.)

Since the aircraft is not equipped with a GPS navigational and camera triggering system you

need to plan for 30% sidelap. This will result in a planned neat model that is less than 7 inches

in height on the photo.

Neat model height = __________ inches on the photo.

Distance between flight lines = __________ feet on the ground.

Fill an 8.5 x 11 inch transparency (or piece of paper) with a neat model overlay for the photo

scale and map scale you are using, and label it with the photo and map scales and the sidelap.

Also draw the flight lines for these neat models. The photo centers are wherever a flight line

crosses a neat model edge.

An example of a flight planning (neat model) overlay is found in the file entitled

“Example_overlay.pdf.

Use your overlay to determine the flight lines, and draw the flight lines and photo centers on the

planning map.

Estimate the average terrain of the mapping area, and compute the flight altitude above sea level

for the fly over, FA = __________feet ASL.

Mark the flight altitude on the planning map.

Submit the planning map, your answers on this page, and a copy of your flight planning overlay

in the Project 4 Flight Planning Drop Box.

Note: In practice, the planning map would not be adequate for the flight mission. All of

the flight information would be transferred to an original topo quad sheet and given to the flight

crew. If the camera trigger is controlled by GPS, the flight planning would be done

on a computer, so just follow their instructions.

Attachments:

Example-Overl….pdf

Topo-Map.pdf

Planning-Map.pdf

Project-4-Fli….pdf

Use-Example.pdf

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