Numerade

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1-4 Find the area of the region that is bounded by the given curve and lies in the specified sector. 1. $ r=e^{-t / 4}, \pi / 2 \leqslant \theta \leqslant \pi $ 2. $ r=\cos \theta, \quad 0 \leq \theta \leq \pi / 6 $ 3. $ r=\sin \theta+\cos \theta, \quad 0 \leqslant \theta \leqslant \pi $ 4. $ r=1 / \theta, \quad \pi / 2 \leqslant \theta \leqslant 2 \pi $

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Many studies have been conducted to test the effects of marijuana use on mental abilities. In one such study, groups of light and heavy users of marijuana in college were tested for memory recall, with the results given below. Items sorted correctly by light marijuana users: 𝑛 = 64, 𝑥̅ = 53.3, 𝑠 = 3.6. Items sorted correctly by heavy marijuana users: 𝑛 = 65, 𝑥̅ = 51.3, 𝑠 = 4.5. Use a 0.01 significance level to test the claim that the population of heavy marijuana users has a lower mean than the light users. Should marijuana use be of concern to college students? a) Step 1: What is the parameter of interest? Provide notation. What is the hypothesis of interest? b) Step 2: What method would you use to test the above hypothesis (stating the name of the function used in TI-calculator will suffice)? Provide brief reasoning for your choice. c) Step 3: If using the p-value method, then provide the name and value of the test statistic. If using the CI-method, then provide the name for the type of interval and its value. d) Step 4: What do you conclude? Provide reasoning for your conclusion.

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(1 point) Let $f(r) = 3\sqrt{r} + 6\sqrt[3]{r}$. $f'(r) = \frac{3}{2\sqrt{r}} + 2r^{-2/3}$ $f'(2) = 2.320581222$ $f''(r) = $ $f''(2) = $

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Question 4 (20 Marks) 4.1 When 0.50 mol of an ideal gas is expanded isothermally and reversibly at 298 K from a volume of 10.0 L to 25.0 L, (a) What is the $\Delta S_{gas}$? (b) How much work was done? (c) What is the $\Delta S_{surr}$? (d) What is the $\Delta S_{total}$? 4.2 At 25.0 $^\circ$C the equilibrium constant for the reaction: CO(g) + H$_2$O(g) $\rightleftharpoons$ CO$_2$(g) + H$_2$(g) is 1.00 x 10$^{-5}$, and $\Delta S^\circ$ is 41.8 J K$^{-1}$ mol$^{-1}$. Calculate $\Delta G^\circ$ and $\Delta H^\circ$ at 25.0 $^\circ$C.

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Consider three identical black barrels filled with water, as shown in the diagram at right. Each barrel has a different laser beam incident on it, as represented by the EM waves in the figure. The amplitude of the wave hitting barrel 2 is double that of barrel 1 (A=2A), but the wavelength is the same. The amplitude of the wave hitting barrel 3 is the same as that hitting barrel 1, but the wavelength is half (Î»/2). a[3 points] Rank the barrels according to the rate at which they heat up. If any barrels heat up at the same rate, state so explicitly. Explain your reasoning. b[7 points] Is the number of photons hitting barrel 2 each second (N) greater than, less than, or equal to the number of photons hitting barrel 3 each second (N)? First, explain your reasoning qualitatively, then determine a specific quantitative relationship and explain your reasoning.

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For the circuit shown below, calculate: a. The total resistance b. The total current c. The power dissipated in the 20k\Omega resistor 15k\Omega 1k\Omega 3.5k\Omega 2k\Omega 20k\Omega 1k\Omega 12k\Omega 1.5k\Omega 4.5k\Omega

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c) Consider the continuous control system shown in Figure 7. Here plant, G(s), is controlled by a proportional controller, C(s). Initially C(s) = 1. Determine the sensitivity of the closed loop system to parameter b. R U C(s) G(s) C(s) = 1 G(s) = \frac{a}{(s+b+cd)} Figure 7 [8 Marks] d) Consider the continuous control system shown in Figure 8. In this system, the control signal that is applied to the plant is subject to an unwanted disturbance, D(s). D(s) R(s) U Y(s) C(s) G(s) G(s) = \frac{5}{s+5} C(s) = 2 Figure 8 As a result, the output response of the system is given by: $Y_o(s) = \frac{C(s)G(s)}{1+C(s)G(s)}R(s) + \frac{G(s)}{1+C(s)G(s)}D(s)$ [Turn over Page 7 of 11 [EEE8007] Given D = 0.2 (a DC offset) determine the output, Y, due to this disturbance only (assume R(s) = 0). [4 Marks] e) Explain how output measurement noise affects the sensitivity of closed loop control systems? What impact does this have on setting the controller gain? [4 Marks]

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The following figures appeared in the Wall Street Journal in 2013. The figures depict, respectively, the price of lumber in the U.S. and the rate of unemployment in an Oregon town where the logging and milling of lumber is a major industry. Using the terminology of real options (e.g., put, call, underlying asset, exercise price, etc.), briefly describe why the price of lumber and unemployment rate would be expected to vary inversely as generally shown in the figures. Unemployment rate for Eugene-Springfield, Ore. Framing lumber composite price* $500 per thousand board feet 400 300 200 Jan. 2013 $393 100 0 2002 '04 '06 '08 '10 '12 *Composite price is a weighted average of 15 key framing lumber prices Metropolitan Statistical Area (includes all of Lane County). Data are seasonally adjusted. Sources: Random Lengths; Oregon Employment Department The Wall Street Journal

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$9n^2 + 30nd + 25d^2 = (\underline{\hspace{1cm}} - 5d)^2$

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7. In the triangle PQR, what is the m?R? A. 20° C. 45° B. 30° D. 60°

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jerry l.