An inventory consists of a list of 115 items, each marked “available” or “unavailable.” There are 60 available items. Show that there are at least two available items in the list exactly four items apart. (Pigeonhole principle)

Q: The matrix A can be factored as A = PDP-¹ where D = - •[17]+²]· If * = 6 [3 0 -4 = [8] and P=[1₂1]…

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Q: Exercise 11.4.2 Consider R4 with the usual dot product. Let 0 = = ----- 5 Note that µ₁, ₂, and u3…

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Q: 4. We are filling water from a conic tank (with vertex down) to a cylindrical tank. The conic tank…

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Q: the Fourier series for f(x) - + 4) = f(x) for all x. 30, 0<x< 20, 2<x<

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Q: (b) S dx x³ ln(x) (c) For this part, completing the square (and showing each step in that process)…

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Q: Consider the following system. λ = dt dz dt Find the eigenvalues of the coefficient matrix A(t).…

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Q: Solve, graph, and explain the graph of the parabolas: a) y=x² +7x-9 b) u=-3x² + 4x - 20

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Q: 2. Use Frobenius (power series) techniques to find the first four nonzero terms in each of two…

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Q: Prove or disprove the statement ∀n ∈ N: ln(n + 1) ≤ 1 +1/2+ · · · +1/n≤ 1 + ln(n)

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Q: 3. In this problem we study another approach to show that certain equations have a unique solution…

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Q: 3. Solve using the Laplace transform: (a) y"+y=03(t), y(0) = 0, y'(0) = 1. (b) y"=t04(t), y(0) = 0,…

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Q: Lori is going on a vacation and doesn't want to over pack. She currently has three shirts, four…

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Q: Exercise 11.6.2 Which of the following matrices define orthogonal transformations? Which ones defin…

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Q: be the vector space of all polynomials of degree 3 or less in the variable z. Let PI(T) 2+x+1²,…

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Q: What happens to this base function and why? a(x)= x2

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Q: (²+²+²/2/2 V, where D is the By changing to spherical coordinates, calculate A = region in the first…

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A: We have Then

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Q: A particular gym maintains a gross margin of 55% on all its weight training product. in April, the…

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Q: If f(n) (0) = (n + 1)! for n = 0, 1, 2, ..., find the Maclaurin series for f. Σ( n = 0 Find its…

A: The Maclaurin series for the function  is given byTherefore,

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A: Note:  Since you have asked multiple questions, we will solve the first question for you. If you…

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Q: The solution to the second order differential equation: dx² dy + a +b=0 de is given by: y =…

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Q: A manufacturer of disk drives for notebook computers wants an MTBF of at least 50,000 hours. Recent…

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Q: The power series Σο(-1)" converges to 01 07/10 O N O eπ +e-² те O 0 72n+2 22n+2 (2n+1)!

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Q: Laplace Transform

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Q: b) L[(t² +51)U3(1)] (544 2 (5²+4)² 11

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Q: Name: CGI Problem #1 Avi got hired as a video game tester at a salary of per week. He wants to be a…

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Q: Can you explain how to find each value of f(x) within the series? For example, f(x0), f(x1),…

A: For the given problem the trigonomatric polynomial og degree 2 is given by the formula So if we find…