Numerade

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1. Sebuah benda tegar seragam dua dimensi dengan densitas $ \sigma $ dan luas total $ A $ terdiri dari sebuah persegi panjang dengan panjang sisinya $ 2 a $ dan $ 2 b $, sebuah setengah lingkaran dengan jari-jari $ a $ dan sebuah segitiga dengan panjang alas $ 2 a $ dan tinggi $ 2 b $ seperti yang ditunjukkan oleh gambar. Tentukan Titik pusat massa benda tegar terhadap titik $ O $ (cari terlebih dahulu titik pusat massa masing-masing bagian dengan memanfaatkan sifat simetri dan menggunakan teknik integrasi). 2. Dengan menggunakan teorema sumbu sejajar, tentukan momen inersia bola pejal homogen yang di dalamnya dibuat rongga berbentuk bola seperti yang ditunjukkan oleh gambar. Misalkan bahwa massa total bola pejal sebelum dibuat rongga adalah $ M $.

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3. Describe how lagging strand of DNA synthesis occur? (5 points)

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For young children already exhibiting serious risk factors, delaying intervention until adolescence will likely make it more difficult to overcome risks. By adolescence, children's attitudes and behaviors are well established and not easily changed. True False

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What is reverse osmosis (RO), and how does it differ from regular osmosis? Explain the basic principles behind the process of reverse osmosis. What are the primary components of a typical reverse osmosis system? How does RO effectively remove impurities from water? Describe the role of a semipermeable membrane in reverse osmosis. What factors influence the efficiency of a reverse osmosis membrane?

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The internal loadings at a section of the beam consist of an axial force of 500 N, a shear force of 800 N, and the moment components of 30 N$\times$m and 40 N$\times$m. Determine the principal stress at point A. Also, calculate the maximum in-plane shear stress at this point A. Use the Mohr's circle.

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Theorem 3.3 A monotonic sequence is convergent if and only if it is bounded. 3.2 Exercises 1. (a) We need to show that for any $\epsilon > 0$ there must be some value $N$ such that $\left| \frac{n}{n+1} - 1 \right| < \epsilon$ for every $n > N$. That is, $\frac{1}{n+1} < \epsilon \implies \frac{1}{\epsilon} < n+1$ which holds for any $n > (1/\epsilon) - 1$. Thus we can satisfy the condition $\left| \frac{n}{(n+1)} - 1 \right| < \epsilon$ for any $n > N$ by choosing $N$ to be the next integer greater than the number $(1/\epsilon) - 1.$

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Question 25 (1 point) Margo is the owner of a food truck that specializes in traditional Italian cuisine. Having entered the food truck business only three months ago, Margo has noticed that there are two other food trucks in the city also specializing in Italian cuisine. Margo would like to target price-sensitive customers, stimulate trial of her products, and encourage consumers to purchase from her food truck instead of her competitors. Which type of promotion best addresses Margo's objectives? 1) specialty advertising 2) premiums 3) coupons 4) contest

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Problem 2 (20 points): For the half-wave rectifier with a free-wheeling diode has resistance is 10 ?, the source with $V_m$ is 100 V at 60 Hz. The average output voltage across the resistor. Determine: (a) The absorbed power by the load with inductance L is 50 mH. (b) The value of L such that the amplitude of the first ac current term in the Fourier series is less than 10% of the dc current. Note that the function of the output voltage is expressed by Fourier series as, $\frac{V_m}{\pi} + \frac{V_m}{2}sin(\omega_0 t) - \sum_{n=2,4,6...}^{\infty} \frac{2V_m}{(n^2 - 1)\pi}cos(n\omega_0 t)$

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7. MATLAB Fresnel equation analysis (submit your code and your plots, all as a pdf) a. Using MATLAB or Octave, plot the Fresnel reflection and transmission coefficients $r_{\perp}, r_{\parallel}, t_{\perp}, t_{\parallel}$ vs. incident angle $\theta$, for internal and external incidence. (Don't plot imaginary amplitude ratios for internal incidence transmission.) Let the interface be air on an N-BK7 glass with $n_{air} = 1.00$, $n_{glass} = 1.517$. You should have two figures, one for internal and one for external, with four plots in each figure. b. Use MATLAB to find Brewster's angle for internal and external incidence in the above example. Explain the polarization of the reflected and transmitted rays at Brewster's angle. c. Use MATLAB to find the critical angle. d. Repeat these plots when glass is replaced by diamond, $n = 2.42$. Comment on the qualitative or quantitative differences between them.

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Problem2: Design a second-order analog low pass Sallen-Key equal-component filter with a Butterworth response. Set $f_{-3dB} = 1KHZ$. a) Draw schematic (Show calculation of capacitor and resistor values) b) Compute the transfer function $H(s) = \frac{V_{OUT}}{V_{IN}}$

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pedro g.