Numerade

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Silicon combines with oxygen in a _______ mass ratio to form silicon dioxide, SiO2.

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The theory that individuals, groups, and peoples are subject to the same Darwinian laws of natural selection as plants and animals is called: A

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Urban growth occurred in the nineteenth century because? towns and cities were becoming increasingly planned and managed transport systems were not provided, so it was easier to live in the city commuters started moving out of villages and into cities industrial capitalism led to a shift of population from rural to urban areas Axiom 3

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one kind of battery used in watched contains mercury (II). If 2.5 g Hg (I) is uzed and a current if 1.5 x 10^-3 amps flows continuously, how many hours will the battery last? the mercury(II) oxide reduced to mercury by ghr folliwing reaction:HgO(s) + H2O(l) +2e -----> Hg(l) + 2OH^- (aq)

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16. Transfer the data from the single coin toss in Table 1 to Table 6 below and calculate $\chi^2$ value. Next indicate the degrees of freedom and the range of P values associated with the $\chi^2$ value you have calculated, and conclude whether or not the data are a satisfactory approximation of the expected ratio. 17. Table 6: Calculation of $\chi^2$ on data from single coin toss (Table 1) Results O E O - E $(O - E)^2$ $(O - E)^2$/E Heads 10 15 -5 25 1.67 1.6667 Tails 20 15 5 25 1.67 1.6667 Totals 30 30 0 0 $\chi^2 = 3.34$ 3.3334

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the side chain or R group. This is the part of the amino acid that differs from one amino acid to another and gives each amino acid its unique properties.

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Problem 1: $g(t) = c_1 \cos(\omega_1 t + \theta_1) + c_2 \cos(\omega_2 t + \theta_2)$ where $\omega_1 = \omega_2$. Show that the power is $\frac{1}{2} [c_1^2 + c_2^2 + 2c_1 c_2 \cos(\theta_1 - \theta_2)]$

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26. The number of arbitrary constants in a particular solution of a fourth order differential equation is a) 1 b) 0 c) 4 d) 3 27. The function $y = 3 \cos x$ is a solution of the function $y'' - 3y' = 0$. a) True b) False 28. The number of arbitrary constants in a general solution of a second order differential equation is a) 1 b) 0 c) 2 d) 3 29. $x(t) = -5e^{3t}$ is a solution to $\ddot{x} - 5\dot{x} + 6x = 0$. a) True b) False 30. $x(t) = 3 \cos t - 5 \sin t$ is not a solution to $\ddot{x} + x = 0$. a) True b) False

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Write a C++ function that accepts a number and a character as parameters. If the character is 'A', return the square root of the number. If the character is 'B', return the 4th power of the number (num$^4$). If the character is neither, return -1. In main, read in a number and a character, call the function and print the returned value. You may assume the number will always be positive, and you do not have to account for floating-point precision. You may use the iostream and cmath libraries. Sample Run 1: Enter a number: 3 Enter a character: B The result is 81 Sample Run 2: Enter a number: 20 Enter a character: A The result is 4.4721 Sample Run 3: Enter a number: 2.5 Enter a character: X The result is -1 Edit Insert Format Tools Table

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r +e Gc(s) G(s) y Figure 1: Feedback Control System Problem 1. (10 points) Consider the feedback control system in Figure 1, where 20 G(s) = \frac{20}{(s+1)(s+20)} Using lead-lag design in the frequency domain, determine the parameters K > 0, N ? N, a_i > 1, \tau_i > 0, i = 1,2, of the cascade compensator G_c(s) = \frac{K}{s} \frac{1 + \tau_1 s}{1 + \alpha_1 \tau_1 s} \frac{1 + \alpha_2 \tau_2 s}{1 + \tau_2 s} such that the following specifications are satisfied: • The closed-loop system has a 10% steady-state error with respect to a ramp input. • The percent overshoot to a step reference input is less or equal than 10%. • The crossover frequency of F(j?) = G_c(j?)G(j?) satisfies ?_c ? 0.5 rad/s. • The gain margin satisfies G_m ? 25 dB.

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lisa p.