Numerade

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For the bar problem shown, determine the displacement (node 1, 2 and 3) and stress (element 1 and 2). Here the bar is fixed at node 1, width and thickness of the bar 2 in and 0.125 in respectively and E = 10.4×106 psi. i. Solve this problem using Exact/Analytical Method. ii. Solve this problem using Finite Element Formulation (Hand Calculation) iii. Compare your solution using the above two methods. 5.0 in. 5.0 in. Element-1 Element-2 1000 lb $u_1$ 1000 lb $u_2$ $u_3$ The stiffness matrix for any Element is given by $[K]^{(i)} = \begin{bmatrix} k_i & -k_i \\ -k_i & k_i \end{bmatrix}$ $k_i = \frac{A_i E_i}{L_i}$

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(a) II III D E C F 2,2,8 III II E F C D -4,-4,-4 6,4,0 10,-2,8 0,0,0 Put the given game in strategic form. 4,4,4 (b) Underline best responses to find all pure strategy NE and list them here: (c) Change a single outcome so that B weakly (but not strongly) dominates A for player I.

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23-28 Find a formula for the inverse of the function. 23. f(x) = (4x-1)/(2x+3)

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infuse 250 mL NS drop factor: 15 gtt/mL Infusion rate: 60 gtt/min How many hours will it take to infuse?

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The equation E = mc2 illustrates that Question 4 options: travelling at the speed of light converts matter into energy rest mass and energy are equivalent energy can be converted into mass matter can be converted into energy both b and d

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xercise 4.1 Calculate the indicated terms and sum of the following A.P (a) $ a_{12} $ and $ S_{8} $ of $ 6,10,14, \ldots $ (b) $ \mathrm{a}_{36} $ and $ \mathrm{S}_{26} $ of $ 45,12,39 \ldots $

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Ka for acetic acid is 1.74 x10??; Kb for ammonia is 1.76 x10?? Q1) What is the percent ionization of a 0.0383 M solution of CH?COOH? % ionization = Q2) What is the percent ionization of a 0.0632 M solution of NH?? % ionization = Q3) What is the pH of a buffer solution containing 0.100 M of CH?COOH and 0.300 M of CH?COONa? pH = Q4) What is the pH of a buffer if 0.100 mole of CH?COOH and 0.150 mole of CH?COOK are dissolved in 50 mL of deionized water? pH = Q5) What is the pH of the solution if the buffer in question 4 has 0.00500 mole of solid NaOH added to it? pH = /5

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Metronidazole IV is available in a concentration of 0.5 g/100 mL of solution. How many milligrams of metronidazole does each milliliter of solution contain? Provide the answer as a whole number.

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Evaluate the integral $ \int \frac{\cos x}{1 + \sin^2 x} dx $ Select the correct answer. $ -\tan^{-1}(\sin x) + C $ $ -\tan(\sin^{-1} x) + C $ $ \tan^{-1}(\frac{\sin x}{1}) + C $ $ \cot^{-1}(\frac{\sin x}{1}) + C $

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10. Consider a firm that uses 2 inputs and has the production function $f(x_1, x_2) = 12x_1^{1/3}x_2^{1/2}$. Let the firm face the input prices $(p_1, p_2)$ and the output price $q$. Find the input combination for maximizing the firm's profit. 11. A student is preparing for exams in two subjects. She estimates that the grades she will obtain in each subject as a function of amount of time spent working on them are: $g_1 =$ $20 + 20(t_1^{1/2})$ and $g_2 = -80 + 3t_2$, where $g_1$ and $g_2$ are grades in each subject and $t_1$ and $t_2$ are the number of hours per week spent in studying the subjects. She wishes to maximize her grade average $(g_1 + g_2)/2$. She can not spend in total more than 60 hours studying in the week. Formulate the problem as a constrained optimization problem and find the optimal values of $t_1$, $t_2$ and the Lagrange multiplier. Interpret the Lagrange multiplier. 12. Maximize $Y = x_1^{0.25}x_2^{0.75}$, subject to $100 - 2x_1 - 4x_2 = 0$. Check the relevant second order sufficiency condition.

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lourdes l.