Determine the starting position of a 15 kg block in order to have it travel 8 meters up a 30 degree ramp with a constant force applied of 8N. Assume Us and Uk both equal 0.30.

Part 1: calculate acceleration of the box up the ramp then determine velocity needed at the bottom of the ramp for the box to travel up 8m with 80N force applied.

Part 2: calculate initial position of the box needed to achieve velocity at the bottom of the ramp calulate in part 1.

Part 3: Predict whether or not the box will slide down after stopping at 8m up the ramp.

Purchase-Related Transactions Using Perpetual Inventory System The following selected transactions were completed by Capers Company during October of the current year:

Oct. 1. Purchased merchandise from UK Imports Co., $13,082, terms FOB destination, n/30.

3. Purchased merchandise from Hoagie Co., $10,150, terms FOB shipping point, 2/10, n/eom. Prepaid freight of $210 was added to the invoice.

4. Purchased merchandise from Taco Co., $13,150, terms FOB destination, 2/10, n/30.

6. Issued debit memo to Taco Co. for $4,250 of merchandise returned from purchase on October 4.

13. Paid Hoagie Co. for invoice of October 3.

14. Paid Taco Co. for invoice of October 4, less debit memo of October 6 and discount.

19. Purchased merchandise from Veggie Co., $26,110, terms FOB shipping point, n/eom.

19. Paid freight of $425 on October 19 purchase from Veggie Co.

20. Purchased merchandise from Caesar Salad Co., $22,900, terms FOB destination, 1/10, n/30.

30. Paid Caesar Salad Co. for invoice of October 20.

31. Paid UK Imports Co. for invoice of October 1.

31. Paid Veggie Co. for invoice of October 19.

Journalize the entries to record the transactions of Capers Company for October.

For a compound transaction, if an amount box does not require an entry, leave it blank.

Gobin plc is a furniture manufacturer in the located in Scotland and trading on the London Stock Exchange. The firm has a beta of 1.2. The historical rate of return on the FTSE All-Share index (i.e., the market portfolio) is 14% and the risk-free rate of return in the United Kingdom is currently at 6%. Managers at Gobin plc are planning to issue corporate bonds with a rate of 7.20%. The market value of the bonds is £250 million and the bonds will be issued at par. Gobin’s stock, of which 25 million shares are outstanding, sells for £30 per share. The UK corporate tax rate is 10%.

(a) Calculate (i) Gobin’s cost of equity, and (ii) after-tax weighted average cost of capital (WACC)

(b) Managers at Gobin plc must decide whether or not to purchase additional capital equipment. The cost of the equipment is £9 million to be paid upfront (today). The expected after-tax cash flows from the new equipment are £3 million a year for the first 4 years, £0.5 million in the fifth year, £0 million in the sixth year and £0.1 million a year for the 10 years that follow (i.e., from year 7 to year 16). The salvage value of this equipment is zero. Assume that all after-tax cash flows occur at the end of the year. You are required to (i) demonstrate by calculation, whether Gobin plc should purchase the new equipment, and (ii) briefly explain how an increase in the UK corporate tax rate from 10% to 30% might impact on the suitability of the project.

1. Given below are a set of foreign exchange quotes for several currencies against the Australian dollar as of August 5, 2020.

Australian Dollar Exchange Rates

(a) A friend of yours is totally confused by these rates. She is planning to visit Thailand next month and wishes to purchase 10,000,000 Baht. How many Australian dollars does she require, assuming she is able to use the above quotes?

(b) What are the direct quotes for the following currencies with respect to the Australian dollar?

(i) UK pound

(ii) Chinese Renminbi

(iii) Indian rupee

(iv) Malaysian ringgit

(v) South African rand

(c) Create a table showing the bid and ask quotes of each of the following currency pairs:

(i) GBP/CHF

(ii) PHP/THB

(iii) HKD/MYR

(iv) JPY/INR

(v) RMB/ZAR

(d) On August 5, 2020, you received 100,000 ZAR. Using the rates in the above chart how many AUD will you receive upon selling this?

Please, Answer all parts( a,b,c,d) in Question 1 and step by step. Also, by word document or by keyboard

1. Given below are a set of foreign exchange quotes for several currencies against the Australian dollar as of August 5, 2020.

Australian Dollar Exchange Rates

(a) A friend of yours is totally confused by these rates. She is planning to visit Thailand next month and wishes to purchase 10,000,000 Baht. How many Australian dollars does she require, assuming she is able to use the above quotes?

(b) What are the direct quotes for the following currencies with respect to the Australian dollar?

(i) UK pound

(ii) Chinese Renminbi

(iii) Indian rupee

(iv) Malaysian ringgit

(v) South African rand

(c) Create a table showing the bid and ask quotes of each of the following currency pairs:

(i) GBP/CHF

(ii) PHP/THB

(iii) HKD/MYR

(iv) JPY/INR

(v) RMB/ZAR

(d) On August 5, 2020, you received 100,000 ZAR. Using the rates in the above chart how many AUD will you receive upon selling this?

An environmentally toxic radioactive chemical is continually released at a constant rate of 1 (mg per vol per time) at the midpoint of a canal of length L with still water. As it diffuses through the canal with diffusion constant D = 1, it decays at rate λ (per unit time) The ends of the canal are connected to large bodies of toxic-free water. Set up the model equations and the boundary conditions. Find the steady-state concentration and sketch its spatial profile for different values of L and λ.

[Hint: Break the problem up into two parts, on each side of the source. At the source the concentration must be continuous, and in a small interval about the source, the ‘flux in’ minus the ‘flux out’ equals one.]

Consider the following means and sample sizes for two independent samples (with the samples being denoted by the subscripts "_X" and "_Y"): M_X = 6.286, M_Y= 1.973, n_X= 16, n_Y= 16. If the standard error (s_Difference) is 2.256, what is the the upper boundary of the corresponding 95% confidence interval? Please use a typical null hypothesis that predicts no differences between the two populations when computing your answer. When calculating your answer, please ensure that you subtract the mean for group Y from the mean for group X (i.e., M_X - M_Y).  Please also retain three decimal places for all steps (if relevant) and provide three decimal places when reporting your answer.

Consider the 1D wave equation d^2u/dt^2 = c^2( d^2u/dx^2) with the following boundary conditions: u(0, t) = ux (L, t) = 0 . (a) Use separation of variables technique to calculate the eigenvalues, eigenfunctions and general solution. (b) Now, assume L = π and c = 1. With initial conditions u(x, 0) = 0 and ut(x, 0) = 1, calculate the solution for u(x, t). (c) With initial conditions u(x, 0) = sin(x/2) and ut(x, 0) = 2 sin(x/2) − 3 sin(5x/2) calculate the solution for u(x, t).

Using MATLAB:

Consider the following Boundary Value Differential Equation:

y''+4y=0

y(0)=-2

y(π/4)=10

Which has the exact solution: y(x)= -2cos(2x)+10sin(2x)

Create a program that will allow the user to input the step size (in x), and two guesses for y'(0). The program will then use the Euler method along with the shooting method to solve this problem. The program should give the true error at y(π/8). Run your code with step sizes of π/400 and π/4000 and compare the errors. Chose any guesses for y'(0) that are reasonable. Also list the two errors you calculated.

QUESTION 4 You are the owner-manager of a chain of coffee shops in Singapore, brewing and selling the latest types of expresso drink inhouse but buying all necessary factors from the market. Your 50 or so shops located around the city can seat around 20 patrons each and currently only sell caffeinated drinks. At this stage of growing your business you are considering vertical and horizontal integration. Using the theory of the optimal boundary of the firm, discuss the make-or-buy decision as well as the scope for horizontal integration and diversification of your business. What stages of the vertical chain should you consider conducting inhouse? What other horizontal markets may you integrate into?