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Problem 2 A metal composite shaft $AB$ with length $L$ consists of a steel rod with radius $r$, the outer surface of which is bonded to the inner surface of an aluminum tube, whose outer radius $r_o$ is equal to $1.5r$. The shaft has the geometry and cross section shown below. One end $(B)$ of the shaft is fixed onto a rigid wall while the other end $(A)$ is subjected to an external torque $T_A$. Take $G_{st} = 78$ GPa for the steel rod and $G_{Al} = 28$ GPa for the aluminum tube. (a) Find the angle of twist at $A$ ($\phi_A$) due to $T_A$. (b) Find the maximum shear stress in the steel rod. (c) Find the maximum shear stress in the aluminum tube. (d) If the allowable angle of twist is $(\phi_A)_{allow} = 2 \times 10^{-3}$ rad, determine the maximum length the shaft can have when subjected to the torque $T_A$ at the free end. Take $L = 1.2$ m, $r = 24$ mm, $T_A = 360$ N-m, $\phi_{A,allow} = 2 \times 10^{-3}$ rad.

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What is the default access specifier in a class? O Private O Public O Local O Global

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use the method of lagrange multipliers to find the extreme values of f(x,y)=x+y subject to the given constraint x^2-xy+y^2=1

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Bell provides $500 of services to customers on account with terms 3/10, n/30. The Service Revenue account is credited for $500. If the customer pays within 10 days, Bell will record which of the following? Debit Service Revenue $500 Credit Cash $500 Credit Sales Discount $50 Debit Sales Discount $15

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An economy can described as C=100+((2)/(3))(Y-T) I=800-((50)/(3))r ((M)/(P))^(d)=0.5Y-50r G=500 T=600 M=1200 P=1 a. (4 points) Solve- for IS and LM curve and solve for the equilibrium income and interest rate for this economy. b. (4 points) If tax increased to 720 , solve for the new equilibrium. c. (4 points) What is the tax multiplier for this economy? According to the tax multiplier (if we ignore the changes in the money market), what is the new income level? You compare the results in part b) and c), explain the differences in the income level. d. (4 points) With the tax increase, in order to keep the income to the original level, the central bank should increase or decrease the money supply and by how much? e. (4 points) Assume the economy is at the equilibrium level of Part a) (money supply is M=1200 ), there is cost push shock makes the price level increase P=3, calculate the new short run equilibrium income and interest rate. Assume in an economy the Philips curve is pi =Epi -0.5(u-0.05). a. (5 points) Assume Epi =pi _(-1). The economy was at its natural level of unemployment initially. However, the economy has a relatively high level 1An economy can described as C=100+ Y-T I=800 =0.5Y-50r G=500 T=600 M1200 P=1 and interest rate for this economy b. 4 points If tax increased to 720,solve for the new equilibrium. c.4 points What is the tax multiplier for this economy According to the tax multiplier (if we ignore the changes in the money market,what is the new differences in the income level. income level? You compare the results in part b and c, explain the d.4 points With the tax increase, in order to keep the income to the original how much? level, the central bank should increase or decrease the money supply and by e.4 pointsAssume the economy is at the equilibrium level of Part a(money P-3,calculate the new short run equilibrium income and interest rate. supply is M-1200,there is cost push shock makes the price level increase 2Assume in an cconomy the Philips curve is n=En-0.5u-0.05 a.5 points Assume En=n-.The cconomy was at its natural level of unemployment initially.However,the economy has a relatively high level

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We assume that a person's chances of getting married (in some small time interval At) is proportional to the fraction of people who are already married by that age; this can be considered peer pressure [1] 1. We first assume that the rate of change of m(t) is proportional to the number of interactions (the fraction of) people married (for a first time) by age t have with (the fraction of) people of age t who have not yet married. (a) Using our notation above, what fraction of people are married by age t? What fraction are unmarried at age t? How many interactions are there between these groups of people? (b) Write and solve a differential equation modeling the situation with these assumptions. (c) What is the long-term behavior of this solution? Does this make sense for the scenario? Hint: Based on the situation, is the proportionality constant positive or negative? Why? (d) This differential equation is autonomous. i. Find the equilibrium point(s). ii. Analyze the stability of the equilibrium point(s). (e) Your general solution to Problem 1b should have two unknown constants in it; the propor- tionality constant and another constant that arose when solving the first-order differential equation. Choose three different combinations of values for these constants. Plot the solution with these values plugged in. i. Do these graphs support your answers from Problem 1c and 1d? ii. What do you notice about solution at t = 0? Does this make sense? (f) One criticism of this model is that it assumes people experience that peer pressure to the same degree at every age. Come up with at least two other criticisms.

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Assume that the following data relative to Oniole Company for 2025 is available: Net Income $2,830,590 Transactions in Common Shares Change Cumulative Jan. 1, 2025, Beginning number 690,000 Mar. 1, 2025, Purchase of treasury shares (50,400) 639,600 June 1, 2025, Stock split 2-1 639,600 1,279,200 Nov. 1, 2025, Issuance of shares 246,000 1,525,200 6% Cumulative Convertible Preferred Stock Sold at par, convertible into 210,000 shares of common (adjusted for split). $1,050,000 Stock Options Exercisable at the option price of $25 per share. Average market price in 2025, $30 (market price and option price adjusted for split). 96,000 shares (a) Compute the basic earnings per share for 2025. (Round answer to 2 decimal places, e.g. 52.75.) Basic earnings per share $

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Chapter 3 - Cam/ 4. A cam rotating with a uniform speed about a fixed centre O moves a lever PQ which is pivoted at Q as illustrated below. The base radius of the cam is 25 mm. The nose of the cam is an arc of a circle of radius 10 mm with a centre E, the distance OE being 30 mm. The flanks are straight lines tangential to the base and nose circle. The lever carries a roller at P of radius 20 mm. The length PQ is 160 mm. The centre of gravity of the lever including the roller is at point G, 100 mm from Q. The mass moment of inertia of the lever ($I$) is 0.136 $kgm^2$. The lever moves through equal angles above and below the horizontal position and the path of P may be approximated to a vertical straight line passing though O. The lever rests on the cam only by its own weight and has a mass of 10 kg. Find the greatest speed of the camshaft at which the roller will always be in contact with the cam. For this speed of camshaft find; (a) At which point maximum downward acceleration occurs. (b) The angular acceleration of the lever when the roller is just leaving its lowest position. (c) The angular acceleration of the lever when the roller is just about to leave the straight flank on the cam on the upward stroke.

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What is a negative spring back effect? Write down the possible ways you can prevent it.

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What effect does incomplete adduction of the vocal folds have on the acoustic-perceptual quality of an individual's voice?

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victor manuel d.