3. Prove by contradiction, that if x and y are odd integers, then there is no integers z such that x² + y² = z². (Hint: If x and y are odd, then z is even.) 3

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A: Given set is A = x : x∈N and x2 + 1 = 10

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Q: -6 w Find an equation for the graph above. N 3+ g(u) 2- 1 -1 N -3- ·~ m +48 q

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Q: 3) How many arrangements are there of the letters in the word Neutrogena?

A: Sol

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Q: Rewrite the following initial value problems for a non homogeneous 4th order differential equations…

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Q: Apply Residue theorem to find the value of the integral siniz² (z+1)²(z-2)' C:lz + 11 = 3.

A: We have to apply the Residue theorem to find the value of the following integral : ∫C sin πz2z+12z-2…

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Q: Solve the given initial value problem. x'(t) = x(t) = □ 20 -9 3 8 |x(t),x(0) = 귀

A: Solution of initial value theorem

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Q: By power series method, Solve the following ODES 2 X -2x² - 2x Ans: y = c₂x² e²^² + 2x xý…

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Q: Let 0 < a < 1 be a real number. Define a₁ = 1+a, Prove that Vn € N, 1 ≤n, an+1 = 1<an< 1 - an + a, -…

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Q: Use de Moivre's Theorem to test the correctness of the following trigonometric identity: 3 sin 20…

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Q: 2 Solve the following ODES by Inverse Operator meth. 2 (D²³² +1) y = ce²³s X

A: Introduction: Ordinary differential equations are differential equations in which the dependent…

Q: Let A be a SPD matrix of order n. Show that (a) aii+ajj ≥2ajj ,1 ≤i, j≤n. (b) ajªjjaj≥0 ,1 ≤i, j≤n.

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Q: Question No : 2 of 26 If "p" and "q" are propositions, "p" is true and "q" is false, then p→q is_

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Q: Consider the system of equations 10 -5 - (20 -10)x X 20 -10 x' = (a) Use a graphing utility to graph…

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Q: 15- " + ý +4y=2 sinh t y". Hint: sinh t = (et - e-t)/2

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Q: Solve the following ODES by Inverse Operator method (- Al- (D²-2D +1) y = xe sinx xr ******* -^)

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Q: Question No: 5 of 26 An argument is valid if the conclusion is true when all the premises are.…

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Q: M 2 • (B²+1) y = cos x Ans: y = C₁ C3 x + C₂ sinx + = - =— cos2x spome

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Q: 3.7.4. Let M be a finite-dimensional subspace of a normed space X. Suppose that n E M and an →y € X,…

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A: Given equation is Ld2qdt2+Rdqdt+1Cq=Et Substituting the values given 0.001d2qdt2+100dqdt+11q=9

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Q: 1. Calculate by the Power Series Method the value of y as general solution (term-by-term from n = 0…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: By power series method, Solve the following ODES & xý - (x+2) y = - 2x² - 2x Ans: y=c₂x²³e²+2 x хе

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Q: Suppose that the damping effect of the system is changed (b-10). How will this affect the response…

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Q: Evaluate & 2 4² - [6 ÷ (-2)]³+ [€ 2) 5 (-2)7 = (2)"] = Hilroy

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Q: 1. Let {w₁, W2, W3} be an orthonormal basis for V. Given that v = between v and w₁ is 0 = 60° and…

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Q: Question No : 18 of 26 Let a, a, a,,a, be an arithmetic sequence, then sum of the terms of sequence…

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Q: 2- Find the first fundamental form of the cylinder r(u, v) = acosvi + asinvj + uk

A: Given : r u ,v =a cosv i+ a sinv j + u k TO find first fundamental form of the cylinder

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