Numerade

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PROBLEM 2 (50 POINTS) Determine all the polar coordinates of the points and draw them: a. $(3, \pi/4)$ c. $(3, -\pi/4)$ b. $(-3, \pi/4)$ d. $(-3, -\pi/4)$

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Life Events and Difficulties Schedule (LEDS) is a psychological measurement of the stressfulness of life events, created by Brown and Harris in 1978. The schedule is based upon an interview which discusses the contextual information around the event. True False

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A house is a good that takes up large portion of your budget allows a long time to purchase and has many substitutes. A house has likely a what demand curve, elastic or inelastic.

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Nicole Smith's yearly salary is $95,500. During the week, she worked 46 hours, and she is entitled to time-and-a-half for all hours over 40.

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The distance between the objective lens and the microscope stage is called the field of view. True False

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The protons in a nucleus are approximately $2 \times 10^{-15}$ m apart. Consider the case where the protons are a distance $d = 1.94 \times 10^{-15}$ m apart. Calculate the magnitude of the electric force (in N) between two protons at this distance.

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1.) In class, a graphic was shown that illustrated a velocity selector for molecular beam experiments or, in that instance, used to experimentally verify the Maxwell-Boltzmann distribution. A copy of that graphic is reproduced here: Gas Collimating slits Vacuum Detector Velocity selector Source Pump 900.01 Selector Deterkar a.) Consider that there is a set of disks in a given experiment. Let the distance between the disks be $d$ and the angle between the slits can be considered to be $\theta$. Calculate the rotational frequency needed in order to select molecules having the velocity, $v$. In a laboratory experiment, Argon gas was equilibrated at a given temperature, T. When emitted through a pinhole and run through the velocity selector, the following data representing the measured intensity at the detector was obtained. The distance between disks is 2 cm and the angle offset between slits is 1.5 degrees Rev/min Intensity 625 149 1250 530 1875 1012 2500 1347 3125 1501 3750 1420 4375 1201 5000 870 5625 585 6250 341 6875 181 7500 96 b.) From this data and your answer in a.), produce a plot of the normalized distribution for this system. c.) Carry out a spline fit of this system and determine maximum velocity of the gases.

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An ideal Otto cycle has a compression ratio of 8. At the beginning of the compression process, the air is at 100 kPa and 17°C, and 800 kJ/kg of heat is transferred to the air during the constant-volume beat addition process. a. Draw this Otto cycle on a R-v (pressure-specific volume) diagram. (3 points) b. Determine: i. The maximum temperature and pressure that occur during the cycle (5 points); ii. The net work output (5 points); iii. The thermal efficiency (5 points); iv. The mean effective pressure for the cycle (5 points). c. Explain how using a different gas (instead of air) would affect the thermal efficiency an Otto cycle. Assume all other operating conditions would remain the same (3 points). d. An ideal gas in a piston + cylinder is adiabatically and reversibly expanded to twice its original volume. i. What is the final temperature of this gas? (5 points) ii. Given that entropy is a state function, show that this expansion is isentropic by treating the process as a reversible isothermal process followed by a reversible isochoric process. (2 points) e. An ideal gas in a piston + cylinder is adiabatically and irreversibly expanded to twice its original volume. Assume no work is produced, i. What is the final temperature of this gas? (5 points), ii. Derive, from $W = \int P \cdot dV$ how much work was lost due to the irreversibility. (2 points)

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Question 19 3 pts Consider the frequency response of the LTI system is $H(j\omega) = \frac{1}{2} \frac{e^{-3j\omega}}{j\omega + 1}$. Find $h(t)$? None of these $\frac{1}{2}e^{-t}u(t)$ $\frac{1}{2}e^{-(t-3)}u(t-3)$ $\frac{1}{2}e^{-|t-3|}u(t)$ $\frac{1}{2}e^{-(t-3)}u(t)$

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2) (Area under a function) When we derived the area of a circle with radius $r$, we compute the indefinite integral and plug in the upper and lower boundaries in notes. Now we'd like to do in a definite integral all the way through. a) Write down the definite integral for the area of the upper half of the circle. b) To solve it, use the substitution $x = r \cos t$ then rewrite the definite integral c) Compute the integral to its completion with the definite integral

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jeffrey b.