Numerade

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9.5 Solving Trigonometric Equations Graphical For the following exercises, algebraically determine all solutions of the trigonometric equation exactly, then verify the results by graphing the equation and finding the zeros. 66. $ 6 \sin ^{2} x-5 \sin x+1=0 $ 67. $ 8 \cos ^{2} x-2 \cos x-1=0 $ 68. $ 100 \tan ^{2} x+20 \tan x-3=0 $ 69. $ 2 \cos ^{2} x-\cos x+15=0 $ 70. $ 20 \sin ^{2} x-27 \sin x+7=0 $ 71. $ 2 \tan ^{2} x+7 \tan x+6=0 $ 72. $ 130 \tan ^{2} x+69 \tan x-130=0 $

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First is the use of solitary confinement. The Crime Bill of 2018 was a major overhaul in criminal justice in Massachusetts. This bill has limited the use of "Restrictive Housing." The argument is that solitary confinement is cruel and unusual punishment and violates the 8th amendment. Since the passage of this bill, the DOC has modified its procedures in an effort to reduce solitary confinement. Do you believe solitary confinement violates the 8th amendment? In what situations are solitary confinement appropriate? in criminal justice

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The displacement h(t) in centimeters of a mass suspended by a spring is modeled by the function h(t) = 4 sin(8πt), where t is measured in seconds. Find the amplitude, period, and frequency of this displacement.

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5. Solve the PDE 3u, + 4uy = 0, together with the auxiliary condition that u(0, y) = 2sin y.

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17. Price, cost of bushel $30 26 22 18 14 10 6 2 0 1 2 3 4 5 6 7 MC ATC Figure: Revenues, Costs, and Profits for Tomato Producers Quantity of tomatoes (bushels) (Figure: Revenues, Costs, and Profits for Tomato Producers) Look at the figure Revenues, Costs, and Profits for Tomato Producers. The market for tomatoes is perfectly competitive, and an individual tomato farmer faces the cost curves shown in the figure. The market price of a bushel of tomatoes is $18. At the profit-maximizing quantity of output in the figure, the farmer's total revenue is _____, total cost is _____, and profit is _____ a. $90; $14; $76 b. $30; $42; -$12 c. $48; $56; -$8 d. $90; $70; $20

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If you have been given money now and want to convert it to an equivalent uniform payment series (same amount of money each year) over 10 years, what factor would you use to convert your present-day amount of money to this equivalent 10-year uniform series? (Use the table below to help if you wish). Use a 5% discount rate. Please round the value to the nearest 4 decimal places. Which one is the correct answer? A) 7.722 B) 12.578 C) 0.1295 D) 0.2310 5% Compound Interest Factors 5% Single Payment Compound Present Amount Worth Factor Factor Find F Find P Given P Given F F/P P/F 1.050 0.9524 1.102 0.9070 1.158 0.8638 1.216 0.8227 1.276 0.7835 1.340 0.7462 1.407 0.7107 1.477 0.6768 1.551 0.6446 1.629 0.6139 1.710 0.5847 1.796 0.5568 1.886 0.5303 1.980 0.5051 2.079 0.4810 2.183 0.4581 2.292 0.4363 2.407 0.4155 2.527 0.3957 2.653 0.3769 2.786 0.3589 2.925 0.3419 3.072 0.3256 3.225 0.3101 3.386 0.2953 Uniform Payment Series Arithmetic Gradient Sinking Fund' Factor Find A Given F A/F 1.0000 0.4878 0.3172 0.2320 0.1810 0.1470 0.1228 0.1047 0.0907 0.0795 0.0628 0.0510 0.0463 Capital Recovery Factor Find A Given P A/P 1.0500 0.5378 0.3672 0.2820 0.2310 0.1970 0.1728 0.1547 0.1407 0.1295 0.1204 0.1128 0.1065 0.1010 0.0963 0.0923 0.0887 0.0855 0.0827 0.0802 0.0780 0.0760 0.0741 0.0725 0.0710 Connnond Amount Factor Find F Given A F/A 1.000 2.050 3.152 4.310 5.526 6.802 8.142 9.549 11.027 12.578 14.207 15.917 17.713 19.599 21.579 23.657 25.840 28.132 30.539 33.066 35.719 38.505 41.430 44.502 47.727 Present Worth Factor Find P Given A P/A 0.952 1.859 2.723 3.546 4.329 5.076 5.786 6.463 7.108 7.722 8.306 8.863 Gradient Uniform Series Find A Given G A/G 0 0.488 0.967 1.439 1.902 2.358 2.805 3.244 3.676 4.099 4.514 4.922 5.321 5.713 6.097 6.474 6.842 7.203 7.557 7.903 8.242 8.573 8.897 9.214 9.524 Gradient Present Worth Given G P/G 0 0.907 2.635 5.103 8.237 11.968 16.232 20.970 26.127 31.652 37.499 43.624 49.988 56.553 63.288 70.159 77.140 84.204 91.327 98.488 105.667 112.846 120.008 127.140 134.227 n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 n 1 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 9.899 10.380 10.838 11.274 11.690 12.085 12.462 12.821 13.163 13.489 13.799 14.094 0.0387 0.0355 0.0327 0.0302 0.0280 0.0260 0.0241 0.0225 0.0210

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If you have a table/array with 18 records/lines, how many nodes of the sorted index binary tree must be visited examined on average to find an index of some record for a given key value?

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3) Greg's utility function is given by the following: U = U(x1, x2) = 20x1^{2/3}x2^{1/3}; Calculate the demand functions for both products.

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Problem 5: MATLAB Solver and Simulation Revisit the crank-rocker Class I Grashoff mechanism from the in-class example, with link lengths and vector loop equations given below. In HW 4, you solved the system of linear equations in Matlab using Newton's method, and simulated the linkage for one full revolution of the crank. Now use the Jacobian again to solve the velocity and acceleration of joints 3 and 4 and plot them versus crank angle. Note that in order to do the analysis, you will need to choose some velocity and acceleration for the crank. $ \vec{r}_2 + \vec{r}_3 - \vec{r}_4 - \vec{r}_1 = \vec{0} $, $r_1 = 4$, $r_2 = 1$, $r_3 = 3.5$, $r_4 = 2$ i: $r_2 \cos \theta_2 + r_3 \cos \theta_3 - r_4 \cos \theta_4 - r_1 \cos \theta_1 = 0$ j: $r_2 \sin \theta_2 + r_3 \sin \theta_3 - r_4 \sin \theta_4 - r_1 \sin \theta_1 = 0$

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gcd(a, m) = gcd(a, n) = 1 implies \\ $a^{gcd(m, n)} - 1 = gcd(a^n - 1, a^m - 1)$ \\ verify $a^{gcd(m, n)} - 1$ is common divisor of both $a^m - 1$ and \\ $a^n - 1$

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