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2. Figure 2 shows a stepped shaft ABCD fixed at A and loaded with a linearly distributed torque between B and C that varies from zero at B up to 2500 N mm/mm at C and a uniformly distributed torque of 2500 N mm/mm between C and D. AB is a tubular shaft of 100 mm outer diameter and 80 mm inner diameter whilst BCD is a solid circular shaft of 80 mm diameter. (a) Calculate the distribution of internal torques and stresses within the whole shaft. and draw the torsion graphs (b) Find the angular deflection of D relative to A. The material's shear modulus is 76.92 GPa. Ignore localised effects due to the support and the coupling at B. (20 marks) A 0 Nmm/mm 2500 Nmm/mm 2000 mm B 1500 mm D 1000 mm Figure 2 2500 Nmm/mm

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[1] Solve the following initial value problem: x^(')(t)=3x(t) 4y(t)-2z(t),x(0)=10 y^(')(t)=2x(t) y(t)-4z(t),y(0)=-2 z^(')(t)=x(t) 2y(t),z(0)=3 Find a fundamental matrix.

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Assume the market for oranges is perfectly competitive and the market equilibrium price for pound of oranges is $3.00. Thomas is an individual orange grower with a short-run total cost of TC = Q + 0.025Q2 and a marginal cost of: MC = 1 + 0.05Q. How many pounds of oranges should Thomas harvest if he wants to maximize profits? A. 3 B. 40 C. 80 D. 120

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There are two consecutive integers, each greater than 3, that are both primes. Select one: True False

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Is there any way that Ashley's treatment can be justified? My subject is Bioethics

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Question 1 (2 points) Select the best statement pertaining to a behavioral model of depression: It is caused due to stressful events or lack of reinforcers in the environment. It is caused due to an individual not receiving unconditional positive support. It is caused due to cultural tendencies and groupthink. It is caused due to depletion or low levels of serotonin.

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Differentiate and apply normalization processing. Given a relation R={A,B,C,D} Answer the following 2 questions (parts A and B) with the given a set of FDs: 1. Identify candidate keys 2. State the strongest normal form that R satisfies (e.g., 1NF, 2NF, 3NF or BCNF) 1. FDs: A ? B B ? C C ? D 2. FDs: AB ? C AB ? D B ? C C ? D

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Problem 2 Two point charges are located at positions ±l on the x axis. (a) Find $E_x(x)$ at points close to the origin on the x axis. (b) Find $E_y(y)$ at points close to the origin on the y axis. Hint: Make suitable approximations with $x \ll l$ and $y \ll l$. Problem 3 (see Problem 2.5 on p. 65) (a) One ring with radius $r$ has a uniformly distributed to- tal charge $+Q$. The ring lies in the x-y plane with its cen- ter at the origin. Find the electric field at all points on the z axis. At which point(s) is the electric field at a maxi- mun? (b) Two rings with radius $r$ have uniformly distributed charges $+Q$ and $-Q$. The rings are parallel and located a distance $h$ apart, as shown in Figure 2. Let $z$ be the vertical coordinate, with $z=0$ taken to be at the center of the lower ring. Express the electric field at a point $P(z)$ located on the z axis in between the two rings. Problem 4 (see Examples 2.3, 2.4, 2.5 in the book)

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Given these coordinate points, is this triangle acute, obtuse, or right? (2, 3), (1, 1), (7, 4)

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only answer number 7 please 6. For the following questions, assume that you can earn 3.0% interest per year in a risk-free savings account for up to 10 years. You can also borrow any amount of funds at 3.0% interest per year for up to 10 years. For parts a-c, choose the better option. (a)1 Receive $10,000 today.2 Receive $10,500 two years from today (b)(1 Receive $5,000 five years from today.2 Receive $4,850 four years from today (c) (1) Receive $10,000 at the end of each year for the next ten years.(2) Receive $75,000 today d How much would you need to receive today to change your decision in part c? 7. Suppose the US Treasury rates are the same as in question above. a What is the current market price of a one-year US Treasury bond that promises $1,000 one year from today? b) Suppose you are offered an alternative investment that requires an initial investment of $960.00 today and pays $1,000.00 with certainty one year from today. Should you take the investment? Explain how you could make an arbitrage profit without spending any of your own money. (c) Suppose you are offered an alternative investment that requires an initial investment of $985.00 today and pays $1,000.00 with certainty one year from today. Should you take the investment Explain how you could make an arbitrage profit without spending any of your own money.

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