Numerade

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Problem 3 (40 points) $x(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} X(j\omega)e^{j\omega t} d\omega$, and $X(j\omega) = \int_{-\infty}^{\infty} x(t)e^{-j\omega t} dt$ A causal and stable LTI system S has the frequency response $H(j\omega) = \frac{j\omega + 2}{12 - \omega^2 + j7\omega}$ a. Determine a differential equation relating the input x(t) and output y(t) of S. (10 points) b. Find the unit impulse response of the system S. (15 points) c. Compute the response y(t) of the system to the input x(t) = e???u(t), where u(t) is the unit step signal. (15 points) Problem 3 Solution

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Green M&Ms Express 0.116 6 p 6 0.192 in the form of pn { E.

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Find the sum using the formulas for the sums of powers of integers. sum_(i=1)^6 (5i-6i^(3)) Which formulas for the sums of powers of integers are needed to find the sum? (Select all that apply.) 1+2+3+4+cdots+n=(n(n+1))/(2) 1^(2)+2^(2)+3^(2)+4^(2)+cdots+n^(2)=(n(n+1)(2n+1))/(6) 1^(3)+2^(3)+3^(3)+4^(3)+cdots+n^(3)=(n^(2)(n+1)^(2))/(4) 1^(4)+2^(4)+3^(4)+4^(4)+cdots+n^(4)=(n(n+1)(2n+1)(3n^(2)+3n-1))/(30) 1^(5)+2^(5)+3^(5)+4^(5)+cdots+n^(5)=(n^(2)(n+1)^(2)(2n^(2)+2n-1))/(12) So, we have the following. sum_(i=1)^6 (5i-6i^(3))=sum_(i=1)^6 5i-sum_(i=1)^6 (,)i^(3) =5((6(6+1))/(2))-6((()^(2)(6+1)^(2))/(4)) =5(21)-6(,) = Find the sum using the formulas for the sums of powers of integers. 5i-63 Which formulas for the sums of powers of integers are needed to find the sum? (Select all that apply.) 1+2 =n+1 2 12 + 22 + 32 + 42 + ... + n2 = n(n +1)(2n +1) 13+23 +33+43+...+3=n2n+12 14 + 24 + 34 + 44 + ... + n4 = n(n + 1)(2n + 1)(3n2 + 3n - 1) 30 15 + 25 + 35 + 45 + ... + n5 = n2(n + 1)2(2n2 + 2n - 1) 12 So, we have the following. (5i - 6i3) = 5i - 66+1 6+12 =521-6

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Crane Company issued $500,000 of 5-year, 7% bonds at 98 on January 1, 2022. The bonds pay interest annually. (a1) (a2) A (b1) Prepare the journal entry to record the issuance of the bonds, assuming the bonds were issued at 103. (Credit account titles automatically indented when amount is entered. Do not indent manually.) Account Titles and Explanation Debit Credit

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Example 2. Find the volume of the solid generated by rotating the region of the $xy$-plane between the line $x = 5$, the curve $x = y^2 + 1$, and the $x$-axis, about the $x$-axis.

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1. In the plane-strain compression of a slab between two rough (frictional stress is equal to the shear yield stress, $k$) parallel plates, show that the average compression pressure $p$ is expressed by $\frac{p}{2k} = (n - \frac{1}{2})a + \frac{n + \frac{1}{2}}{4n - 1}a$ where $a = \frac{T}{W}$, for the velocity field given in the following figure.

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1. How many bits would you need to address a 32G X 32 memory if \begin{itemize} \item The memory is word-addressable(nothing else is given, what will be the default value here) \item The memory is word-addressable (word size = 16)? \item The memory is byte-addressable? \end{itemize} 2. Convert the following numbers. \begin{enumerate} \item $(3AF.8C)_{16} = (\quad)_2$ \item $(1110010001)_2 = (\quad)_{16}$ \item $(100111001.11011)_2 = (\quad)_{16}$ \end{enumerate} 3. Suppose a 512M x 32 word-addressable memory built using 128K x 8 RAM chips \begin{enumerate} \item How many RAM chips are required to build an entire memory? \item How many address bits are needed for a single RAM chip addressing? \item How many banks will this memory have? \item How many address bits are needed for the entire memory? \end{enumerate}

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Show that each of the following systems is reversible, and sketch the phase portrait. 1 $\dot{x} = y(1 - x^2)$, $\dot{y} = 1 - y^2$ 2 $\dot{x} = y$, $\dot{y} = x \cos y$

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(15 points) Stability: Consider the following list of poles and zeros: • (Three) Poles: (.5 + .5$i$), (.5 - .5$i$), (-.25) • (Two) Zeros: (2), (-1.5) (a) Plot the poles and zeros in the complex plane. (b) If the Laplace transform of the impulse response of a causal LTI system is rational and has the above poles and zeros, is it stable? What is the region of convergence for the Laplace transform of a system that is stable but perhaps not causal and has the same poles and zeros. Is the causal inverse to this system stable? (c) Answer the same questions as above for a discrete-time system, where the stated poles and zeros correspond to a rational Z-transform. Also, considering this system as a filter, approximately which frequency is amplified the most?

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stion Completion QUESTION 1 List and give examples of the ten common Executional styles for advertising. TTT Arial ?3 (12pt) Path: p QUESTION 2 List and explain the five elements that make up the retailing mix. TTT Arial ?3 (12pt) Click Save and Submit to save and submit. Click Save All Answers to save all answers.

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michelle w.