Numerade

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1. (20 pts) Review the Euler's formula for complex numbers by solving several exercises below. (a) Write 1+2i, 3+3i, 4-6i, -5 using complex exponential form. (b) Write $3exp(\frac{\pi}{4}i)$, $10exp(\frac{\pi}{2}i)$, $2exp(\pi i)$ as $a+bi$ form. (c) Solve $x^3=1$, $x^4=16$ including complex number solutions. (d) Manually sketch $f(t)=2exp((\frac{\pi}{4})jt)$ (sketch all three Re vs t, Im vs t, and 3D plot; clearly show a couple of periods)

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Suppose the law of diminishing marginal utility holds for coffee. As a person drinks more coffee during the day, the total utility he or she receives will: Group of answer choices increase faster and faster. fall steadily. remain constant. rise, but at slower and slower rates.

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Suppose you save $18,000 per year at an interest rate of i = 5.219% compounded annually. How much will you have after 35 years?

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Question 1 of 8 1 Points Consider the following equations: (1) \frac{1}{2}x + y - 3z = 5 (2) x + 2y - z = \sqrt{3} (3) \frac{1}{2}x + 3y - z = 0 (4) 3x - \sqrt{y} + 5z = 9 Which of the above equations are linear equations in $x$, $y$ and $z$? A. None of them. B. (1) only. C. (2) only. D. (1) and (2) only. E. (1), (2) and (4) only. Reset Selection

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Problem2 (10 points) The switch in the following circuit has been closed for a long time before it is opened at $t = 0$. Find $i_L(t)$, $i_o(t)$ and $v_o(t)$ for $t \ge 0$.

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Question 8 The function $f(x, y) = -x^2 + 8x - 6y + y^2 - 4$ has a local \\ (maximum / minimum / saddle point) at the critical point, where $x = $ \\ and $y = $

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4. You are an engineer designing the suspension of an ATV. You want to ensure that the vehicle doesn't \"bottom out\" even when landing from being airborne. A first order approximation describing the vertical acceleration of the suspension upon impact is $a(s) = 9.8(1 - 9.0s)$ in units of m/s², where the initial vertical velocity during impact is $v_0 = 1.5$ m/s with the spring initially uncompressed, $s_0 = 0$. a) What is the vertical velocity of the ATV chassis after the spring is compressed 0.2 m? b) What is the maximum distance the spring gets compressed? (Hint: Find the velocity as a function of position, s. The max. distance occurs at the turnaround point.)

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1. On how to use the analysis or synthesis equations to calculate the Fourier transform of signal $x(t)$ or the inverse Fourier transform of $X(j\omega)$. (a) $x(t) = e^{-2|t-1|}$ (b) $x(t) = \frac{d}{dt}\{u(-2 - t) + u(t - 2)\}$ (c) $x(t) = 1 + cos(6\pi t + \frac{\pi}{8})$ (Note that this is a periodic signal) (d) $X(j\omega)$ is complex where $|X(j\omega)| = 2\{u(\omega + 3) - u(\omega - 3)\}$ $\angle X(j\omega) = -\frac{3}{2}\omega + \pi$

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Using the Comprehensive Annual Financial Report obtained for Exercise 1–1, answer the following questions. Exercise 2-1 Part f f. From the governmental fund statements, take one major fund (other than the General Fund) and prove, using the 10 percent and 5 percent criteria described in this chapter, that the fund is required to be reported as a major fund.

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To critically analyses and investigate the importance of information system security and its application to the modern business?

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