DON'T USE CHATGPT 13. Find the centroid and the moments of inertia Ix, ly and Iz of the tetrahedron whose vertices are the points (0, 0, 0), (1, 0, 0), (0, 1, 0) and (0, 0, 1).

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A: The solution is given as

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Q: λι = From smallest to largest, the eigenvalues are ₁ <₂<3 where 2₂ 3 23 = Find the eigenvalues and…

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Q: 1. 2. 3. 1. Cv (~Dv-X) 2. ~C 3. X 1. AD B 2. B 3. ~AD (~Cv B) 1. AD D 2. ~Dv (~B~~~~A) 3. ~A 4. ~B…

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Q: D. Consider R³ with the metric i. Verify that d is really a metric. ii. State and prove the…

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Q: Exercise 11.7.1 For each of the following symmetric matrices, find the eigenvalues, an orthonormal…

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Q: Lm 0-29- 28 17 +26 0-251 024 012? олга соня! о-го 19 6118 6-17 онь FCH3) 980 420 зеч зго 288 L(m)…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. 4s 4s² + 1.

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Q: Evaluate the given integral along the indicated contour C. So 6z dz, where C is z(t) = 3t³ + i(2t4 -…

A: We have Then

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Q: 4) Let the composition of two functions f(x) = sin(x) - 2x² + 1 and g(x) = eº be h = fog. At a point…

A: f(x) = sin(x) - 2x2 + 1g(x) = e0 = 1 h(x) = ()(x)= f(g(x))= sin(g(x)) - 2(g(x))2 + 1= sin(1) - 2(1)2…

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

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Q: 2. Prove that the union of two disjoint sets, where one is countably infinite and the other is…

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Q: Find the general solution of the given system. dx dt dy dt = 3x + 4y = 8x + 7y (x(t), y(t)) = |

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Q: You are given Calculate a31 8₂ 1 8+t fort≥0

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Q: i) Consider maximising the function f(x, y) = 2x + 3y subject to the simultaneous constraints x…

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Q: Problem 3 Find an invertible matrix U such that UA = R is the REEF of A, for [2 1 -1 0] A = 3 -1 2 1…

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