A light ray strikes the perfectly smooth boundary between two different materials. The index of refraction of the material before the boundary is lower than that of the material after the boundary. On the basis of this information, the light ray will be

a. partially transmitted in a direction deviating more from the normal and partially reflected.

b. partially transmitted in a direction deviating less from the normal and partially reflected.

c. partially transmitted exactly in the same direction and partially reflected.

d. totally transmitted exactly in the original direction, without any reflection.

e. totally reflected in the first material, without any forward transmission.

A certain material has an index of refraction of 5/4. That means that in this material, as compared to a vacuum, light

a. travels at the same speed but has (4/5) of the frequency it would have in a vacuum.

b. travels with a speed (5/4) c and the frequency is the same it would be in a vacuum.

c. travels at the same speed but has (5/4) of the frequency it would have in a vacuum.

d. travels with a speed (4/5) c and has (4/5) the frequency it would have in a vacuum.

e. travels with a speed (4/5) c and the frequency is the same it would be in a vacuum.

Consider the following wave equation for u(t, x) with boundary and initial conditions defined for 0 ≤ x ≤ 2 and t ≥ 0.

∂ 2u ∂t2 = 0.01 ∂ 2u ∂x2 (0 ≤ x ≤ 2, t ≥ 0) (1)

∂u ∂x(t, 0) = 0 and ∂u ∂x(t, 2) = 0 (2)

u(0, x) = f(x) = x if 0 ≤ x ≤ 1 1 if 1 ≤ x ≤ 2.

(a) Compute the coefficients a0, a1, a2, . . . of the Fourier cosine series of f(x) in the interval 0 ≤ x ≤ 2. For your calculation, recall that sin(πn) = 0 for all integers n.

(b) Find all the possible values of λ, µ ≥ 0 such that the function v(t, x) = cos(λx) cos(µt) solves the wave equation (1) and the boundary condition (2).

(c) Use the superposition principle, the Fourier series coefficeints a0, a1, . . . from part (a) and the functions v(t, x) from part (b) to write down an expression for the solution u(t, x) of the boundary and initial condition problem (1)–(3).

Critical Thinking

The global marketplace has witnessed an increased pressure from customers and competitors in manufacturing as well as service sector (Basu, 2001; George, 2002). Due to the rapidly changing global marketplace only those companies will be able to survive that will deliver products of good quality at cheaper rate and to achieve their goal companies try to improve performance by focusing on cost cutting, increasing productivity levels, quality and guaranteeing deliveries in order to satisfy customers (Raouf, 1994).

Increased global competition leads the industry to increasing efficiency by means of economies of scale and internal specialization so as to meet market conditions in terms of flexibility, delivery performance and quality (Yamashina, 1995). The changes in the present competitive business environment are characterized by profound competition on the supply side and keen indecisive in customer requirements on the demand side. These changes have left their distinctive marks on the different aspect of the manufacturing organizations (Gomes et al., 2006). With this increasing global economy, cost effective manufacturing has become a requirement to remain competitive.

To meet all the challenges organizations try to introduce different manufacturing and supply techniques. Management of organizations devotes its efforts to reduce the manufacturing costs and to improve the quality of product. To achieve this goal, different manufacturing and supply techniques have been employed. The last quarter of the 20th century witnessed the adoption of world-class, lean and integrated manufacturing strategies that have drastically changed the way manufacturing firm’s leads to improvement of manufacturing performance (Fullerton and McWatters, 2002).

1. Assess the reasons for using lean thinking (suitable examples), what are the benefits from Suppliers to end users?

2. Due to COVID 19 emergency do you think agile supply chain is the right concept in this kind of situation? Give reason with example.

The Answer should be within 1- 2 pages. for each question

The Answer must follow the outline points below:

• Lean Thinking and JIT Concept
• Agile Supply chain
• Their Main functions
• Reasons with suitable Examples
• Reference

write one paragraph for each answer

What are possible consequences if found violating the Academic Integrity code?

What are things that people can do to help spread a culture of professional integrity?

Identify and discuss 2 weaknesses that anyone can have that relate to ethical decision-making and academic/professional integrity.

Question 2 List and describe the components of a research report and provide a brief overview of each component? Refer to Week 11 Lecture slides and recordings, as well the internet for further information. (Must provide 2 references, there should be at least one academic reference and one non-academic). (at least 400 words).

that have you learned about yourself as a learner and student in transitioning to this environment? Comment on your most significant accomplishments (academic and personal); some of the difficult challenges (academic and personal) you have faced and how you dealt with them? What advice would you offer to an incoming first year student ?

An educational researcher wishes to know if there is a difference in academic performance for college freshmen that live on campus and those that commute. Data was collected from 267 students. Can we conclude that freshman housing location and academic performance are related? Location Average Below Average Above Average Total On campus 89 29 27 145 Off campus 36 43 43 122 Total 125 72 70 267 Copy Data Step 2 of 8 : Find the expected value for the number of students that live on campus and have academic performance that is average. Round your answer to one decimal place.

Let x = inf E. Prove that x is an element of the boundary of E. Here R is regarded as a metric space with d(p,q) = |q−p| for p,q ∈R

Use the method of Undetermined Coefficients to find the solution of the boundary value problem x^2 y '' + y' + 2y = 6x +2 y(1) = 0 y(2) = 1