Numerade

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A recently hired chief executive officer wants to reduce future production costs to improve the company’s earnings, thereby increasing the value of the company’s stock. The plan is to invest $82,000 now and $66,000 in each of the next 5.00 years to improve productivity. By how much must annual costs decrease in years 6.00 through 12.00 to recover the investment plus a return of 14.00% per year? (Round the final answer to three decimal places.)

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A study that examined children’s use of social comparisons in an achievement task found that ________ made use of social comparisons to judge their abilities.

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QUESTION 1 a. Using an appropriate test for convergence, determine whether or not the series $\sum_{n=1}^{\infty} \frac{n^2}{(n+2)!}$ converge. Show your workings to justify your response. [4 marks] b. Evaluate: $\int_0^\infty 3e^{-2x} dx$ and state if this integral converges or diverges. [3 marks] c. Given the vectors $\vec{a} = \vec{i} - 3\vec{j} + \vec{k}$ and $\vec{b} = 2\vec{i} + \vec{j} - 2\vec{k}$, find the: i. scalar (dot) product, $\vec{a} \cdot \vec{b}$; ii. vector (cross) product, $\vec{a} \times \vec{b}$; iii. angle between the vectors, expressed in degrees, to two decimal places. [2+3+4 marks] d. A function is defined by $f(x) = \frac{3x}{1+x^2}$ Find: i. the intercepts (x and y); ii. asymptotes (vertical and/or horizontal). [2+2 marks] [Total marks 20]

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CO(g) + 2 H2(g) = CH3OH(g) \Delta H < 0 6. The synthesis of CH3OH(g) from CO(g) and H2(g) is represented by the equation above. The value of Kc for the reaction at 483 K is 14.5. Which of the following explains the effect on the equilibrium constant, Kc, when the temperature of the reaction system is increased to 650 K? A. Kc will increase because the activation energy of the forward reaction increases more than that of the reverse reaction. B. Kc will increase because there are more reactant molecules than product molecules. C. Kc will decrease because the reaction is exothermic. D. Kc is constant and will not change.

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24 4 polnts A pipelined vector arithmetic unit has a clock frequency of 800 MHz; there are 8 stages in the pipe. It is used to multiply all elements of a vector operand by a scalar value. How long does it take for the pipeline to process a vector of length 128? Edit View Insert Format Tools Table 12pt Paragraph BIU 25 2 points As an alternative to the use of the pipelined vector unit in Question 24, suppose the vector can be processed by a scalar instruction loop that takes 2.75 ns per iteration. How long would it take to process the 128-element vector in this fashion? Edit View Insert Format Tools Table 12pt Paragraph BIU 26 2 points What is the speedup factor for vector processing of this operand? [In other words, how many times as fast is it to process the vector using the pipelined vector arithmetic unit from Question 24 vs. using the scalar loop described in Question 25?] Edit View Insert Format Tools Table 12pt Paragraph BIU 27 4 points What is the smallest (shortest) vector (give the number of elements) for which using the pipelined vector unit from Question 24 would be faster than processing it as a scalar loop (as in Question 25)? Edit View Insert Format Tools Table 12pt Paragraph BIU

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Consider the following hash table operations, and a hash function of key % 10. How many list items will be compared for the search operations? Collision resolution method: linear probe. insert: 12 insert: 75 insert: 22 insert: 52 delete: 22 insert: 25 The hash table after these operations is shown below: search: 25 search: 52 search: 72 none 2,3,5 2,3,3 2,2,4 1,2,4 22// 12 52 75 25 deleted

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Task: How many processes are created if the following program is run? main(int argc, char ** argv) { forkthem(5) } void forkthem(int n) { if (n > 0) { fork(); forkthem(n-1); } }

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Question 20 (5 points) The integer: 1234 is in base 10. This number in base 5 is: 41445 41443 14414 41441

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Consider the mechanical system shown in Figure 3. If the excitation force $p(t) = P \sin \omega t$, where $P = 1$ N and $\omega = 2$ rad/s, is applied, the steady-state amplitude of $x(t)$ is found to be 0.05 m. If the forcing frequency is changed to $\omega = 10$ rad/s, the steady-state amplitude of $x(t)$ is found to be 0.02 m. Plot the steady state response $x(t)$ vs. $t$ for $\omega = 2$ rad/s and $\omega = 10$ rad/s using MATLAB. $p(t) = P \sin \omega t$ x k b Figure 3

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2. (35 pts) The giant swing at a county fair consists of a vertical central shaft with a number of horizontal arms attached at its upper end as shown in the figure. Each arm supports a seat suspended from a cable that is 5.00 m long with the upper end of the cable attached to an arm that is 3.00 m long. The mass of the person and swing together is 123 kg. A) What is the tension in the cable? B) Find the angular speed of the swing in rev/min if the cable supporting the seat makes an angle of 30.0º with the vertical. C) Would the angle the cable makes with the horizontal increase, decrease or stay the same if the angular speed increased? Explain. Pictorial Representation Mathematical Representation

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kathleen c.