Solve these problems

The diagram shows a conical section fabricated from pyroceram. It is of circular cross section with the diameter D = ax, where a = 0.25. The small end is at x, = 50 mm and the large end at x2 = 250 mm. The end temperatures are 7, = 400 K and 72 = 600 K, while the lateral surface is well insulated. 1. Derive an expression for the temperature distribution 7(x) in symbolic form, assuming one-dimensional conditions. Sketch the temperature distribution. 2. Calculate the heat rate q, through the cone.To get started in a new telecommuting position with AB Hammond Engineers, Jane took out a $1000 loan at i = 10% per year for 4 years to buy home office equipment. From the lender's perspective, the investment in this young engineer is expected to produce an equivalent net cash flow of $315.47 for each of 4 years. A = $1000(4/P,10%,4) = $315.47 This represents a 10% per year rate of return on the unrecovered balance. Compute the amount of the unrecovered investment for each of the 4 years using (a) the rate of return on the unre- covered balance (the correct basis) and (b) the return on the initial $1000 investment. (c) Ex- plain why all of the initial $1000 amount is not recovered by the final payment in part (b).7.1 Under what circumstances would the rate of return be (a) - 100%%, and (b) infinite? 7.2 A shrewd investor loaned $1,000,000 to a start-up company at 10%% per year interest for 3 years, but the terms of the agreement were such that interest would be charged on the principal rather than on the unpaid balance. How much extra interest did the company pay? 7.3 What is the nominal rate of return per year on an investment that increases in value by 8%% every 3 months? 7.4 Assume you borrow $307000 at 10%% per year in- terest and you agree to repay the loan in five equal annual payments. What is the amount of the unre- covered balance immediately after you make the third payment? 7.5 International Potash got a $50 million loan amor- tired over a 10-year period at 10%% per year inter- est. The loan agreement stipulates that the loan will be repaid in 10 equal annual payments with interest charged on the principal amount of the loan (not on the unrecovered balanoch. (a) What is the amount of each payment? (b) What is the total amount of interest paid? How does the total interest paid compare with the principal of the loan?\f\f\f