Question 1

(a) Show that the Euler-Lagrange equation for the functional \[ S[y]=\int_{0}^{\frac{\pi}{2}}\left(y^{\prime 2}-y^{2}+4 y e^{-x}\right) d x, \quad y(0)=0, y(\pi / 2)=1, \] is \[ y^{\prime \prime}+y=2 e^{-x} . \] (b) Show that the stationary function is given by \[ y=e^{-x}-\cos x+\left(1-e^{-\pi / 2}\right) \sin x . \]

Question 2:

(a) Use the first integral of the Euler-Lagrange equation to show that the functional \[ S[y]=\int_{0}^{1} \frac{y^{4}}{y^{5}} d x, \quad y(0)=1, y(1)=\frac{1}{16}, \] has two real-valued stationary paths, given by \[ y(x)=(x+1)^{-4} \text { and } y(x)=(3 x-1)^{-4} . \] (b) Find the value of the functional on each stationary path.

Refer to the case “Blue Ocean Leadership: How to Achieve High Impact at Low Cost”, and answer the following questions: 1. Revise your time/effort ratings and the order of the acts and activities according to the results of the Leadership Grid and transfer the data to the To-Be Leadership Canvas.

Not less than 250 words 1.A company has a choice of four different modes of foreign market entry. Briefly describe each of these modes, and explain when each would be the best option. 2.Define the term global brand. How are global brands important?

7-Eleven Malaysia Holding Berhad's annual report for the fiscal year ending 2021 is available at https://www.7eleven.com.my/financial-reports. (At least two years of comparable financial statements are required.) a) Assess 7-Eleven’s financial position for year 2020 and 2021 according to i) liquidity position, and how the liquidity position has changed over time from 2020 to 2021. (6 marks) ii) asset management position, and how its asset management efficiency has changed over time. (6 marks) iii) debt management position, and how its debt management has changed over time. (6 marks) iv) profitability ratios, and how its profitability position has changed over time. (6 marks) v) market value ratios, and how its valuation has changed over time. (6 marks) b) Calculate 7-Eleven’s ROE as well as the industry average ROE, using the DuPont equation. From this analysis, how does 7-Eleven’s financial position. (10 marks) c) Write your opinion on what you think would happen to its ratios if the company initiated cost-cutting measures that allowed it to hold lower levels of inventory and substantially decreased the cost of goods sold. No calculations are necessary. Think about which ratios would be affected by changes in these two accounts. (10 marks)

Globalization has created many opportunities for organizations. There are many advantages and ways to create value through outsourcing portions of one's global supply chain. For each opportunity, there are also many ways for the project to run into problems. In your initial post, address the following: Identify one example of an organization that created value for itself through outsourcing part of its supply chain. Provide a link to one resource. Identify the benefit that occurred. How did this benefit help the organization create value? Who was the value created for—the organization, or the customer? In your replies to at least two peers, discuss potential risks of outsourcing for the examples they provided—for example, risks to supplier quality or stability, intellectual property, or reputation. The following questions may help develop your responses: Can you provide an example of an organization that started outsourcing the supply chain and then stopped? What risks did the organization face that caused them to stop the project? Can you provide an example of an organization that outsourced similarly and faced reputational damage due to the project?

In this week’s reading, you learned about one-to-one and many-to-many relationships. While the concepts may seem beneficial, there are some drawbacks. For this discussion, you need to evaluate the pros and cons of each and make a recommendation regarding the usefulness of using these concepts in the JCC RDBMs .

Research and write about Cloud and compare two cloud providers Popular Cloud providers are - 1. Google - GCP (Google Cloud Platform) 2. Amazon - AWS (Amazon Web Services) 3. Microsoft - Azure you can take any 2 from the above 3 ad compare