Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 65, Problem 46AR

Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified.
A circular aluminum casting 2.63 inches thick has a 22.08-inch diameter. The aluminum used for the casting weighs 168.5 pounds per cubic foot. Find the weight of the casting. Round the answer to the nearest pound.

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4. Assume that a risk-free money market account is added to the market described in Q3. The continuously compounded rate of return on the money market account is log (1.1). (i) For each given μ, use Lagrange multipliers to determine the proportions (as a function of μ) of wealth invested in the three assets available for the minimum variance portfolio with expected return μ. (ii) Determine the market portfolio in this market and calculate its Sharp ratio.
3. A market consists of two risky assets with rates of return R₁ and R2 and no risk-free asset. From market data the following have been estimated: ER₁ = 0.25, ER2 = 0.05, Var R₁ = 0.01, Var R2 = 0.04 and the correlation between R1 and R2 is p = -0.75. (i) Given that an investor is targeting a total expected return of μ = 0.2. What portfolio weights should they choose to meet this goal with minimum portfolio variance? Correct all your calculations up to 4 decimal points. (ii) Determine the global minimum-variance portfolio and the expected return and variance of return of this portfolio (4 d.p.). (iii) Sketch the minimum-variance frontier in the μ-σ² plane and indicate the efficient frontier. (iv) Without further calculation, explain how the minimum variance of the investor's portfolio return will change if the two risky assets were independent.
2. A landlord is about to write a rental contract for a tenant which lasts T months. The landlord first decides the length T > 0 (need not be an integer) of the contract, the tenant then signs it and pays an initial handling fee of £100 before moving in. The landlord collects the total amount of rent erT at the end of the contract at a continuously compounded rate r> 0, but the contract stipulates that the tenant may leave before T, in which case the landlord only collects the total rent up until the tenant's departure time 7. Assume that 7 is exponentially distributed with rate > 0, λ‡r. (i) Calculate the expected total payment EW the landlord will receive in terms of T. (ii) Assume that the landlord has logarithmic utility U(w) = log(w - 100) and decides that the rental rate r should depend on the contract length T by r(T) = λ √T 1 For each given λ, what T (as a function of X) should the landlord choose so as to maximise their expected utility? Justify your answer. Hint. It might be…

Chapter 65 Solutions

Mathematics For Machine Technology

Ch. 65 - The following Exercises 7 through 19 involve...Ch. 65 - The following Exercises 7 through 19 involve...Ch. 65 - The following Exercises 7 through 19 involve...Ch. 65 - The following Exercises 7 through 19 involve...Ch. 65 - The following Exercises 7 through 19 involve...Ch. 65 - The following Exercises 7 through 19 involve...Ch. 65 - The following Exercises 7 through 19 involve...Ch. 65 - The following Exercises 7 through 19 involve...Ch. 65 - The following Exercises 7 through 19 involve...Ch. 65 - The cross section of a dovetail slide is shown....Ch. 65 - Compute the area of the pattern shown. Round the...Ch. 65 - The following Exercises 22 through 27 involve...Ch. 65 - The following Exercises 22 through 27 involve...Ch. 65 - The following Exercises 22 through 27 involve...Ch. 65 - The following Exercises 22 through 27 involve...Ch. 65 - The following Exercises 22 through 27 involve...Ch. 65 - The following Exercises 22 through 27 involve...Ch. 65 - Find the area of each of the segments ACB for...Ch. 65 - Prob. 29ARCh. 65 - Find the area of each of the segments ACB for...Ch. 65 - Find the area of the shaded segment shown. Round...Ch. 65 - A circular plate with a 15.00-inch radius is cut...Ch. 65 - Compute the cross-sectional area of the grooved...Ch. 65 - Find the area of the pattern shown. Round the...Ch. 65 - Prob. 35ARCh. 65 - Express each volume in Exercises 35 through 40 as...Ch. 65 - Prob. 37ARCh. 65 - Express each volume in Exercises 35 through 40 as...Ch. 65 - Express each volume in Exercises 35 through 40 as...Ch. 65 - Express each volume in Exercises 35 through 40 as...Ch. 65 - Solve these prism and cylinder exercises. Where...Ch. 65 - Solve these prism and cylinder exercises. Where...Ch. 65 - Solve these prism and cylinder exercises. Where...Ch. 65 - Solve these prism and cylinder exercises. Where...Ch. 65 - Prob. 45ARCh. 65 - Solve these prism and cylinder exercises. Where...Ch. 65 - Prob. 47ARCh. 65 - Solve these prism and cylinder exercises. Where...Ch. 65 - Prob. 49ARCh. 65 - Solve these prism and cylinder exercises. Where...Ch. 65 - Prob. 51ARCh. 65 - Prob. 52ARCh. 65 - Prob. 53ARCh. 65 - Solve these prism and cylinder exercises. Where...Ch. 65 - Solve these prism and cylinder exercises. Where...Ch. 65 - Prob. 56ARCh. 65 - Solve these prism and cylinder exercises. Where...Ch. 65 - Solve these prism and cylinder exercises. Where...Ch. 65 - Solve these prism and cylinder exercises. Where...Ch. 65 - Prob. 60ARCh. 65 - Prob. 61ARCh. 65 - Diameter 9.050 centimeters; Volume Round the...Ch. 65 - Prob. 63ARCh. 65 - Volume = 42.98 cubic inches; Diameter = Round the...Ch. 65 - Volume = 775 cubic centimeters; Diameter = Round...Ch. 65 - The side view of a steel roundhead (hemisphere)...Ch. 65 - Prob. 67ARCh. 65 - A hollow glass sphere has an outside circumference...Ch. 65 - Prob. 69ARCh. 65 - Compute the number of cubic centimeters of iron...
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