Find the general solution of the given system. da = 2x+y + 2z dt dy dt dz dt 3x + 6z -4x - 3z

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Q: -8 6 -12 -4 Determine the remainder when -8x³-6x²+1x-24 is divided by 2x+3.

A: Here we use Long division method.

Q: In Exercises 1-4, determine if the vectors are linearly independent. Justify each answer. 7 000 1 2…

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A: Part - 1 : Given vector-valued function is                                      rt = 5i +5j +3k +…

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Q: 8. (sta) b s²+6² 10. e-sD 11. 9. s+a (s+a)²+6² where a and n are constants. where b is a constant.…

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Q: a) Verify that the functions y₁ "1 y + 4y = 0. cos(2x) and y₂ = sin(2x) are solutions to this…

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Q: 1. If the probability density function is given by f(x)= kx² (1-x¹) = 0 Find (1) k, (11) (1) 0≤x≤1…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Given Data: Let us consider the given data, rt=cosπti-lntj+t-10k ; t0=11.

Q: linearly independent or linearly dependent? a) f(0) = 10 cos 38 and 9(8) = 40 cos³0-30 cos B b) P(x)…

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Q: Based on Discrete Mathematics, Please answer the following question without handwriting Define…

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Q: Find the equation of the circle which touches both the axes and the straight line 4x+3y=6 in the…

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Q: log Exercise 1. The series En5-4108 (nary) 1=2 A diverges to -∞o if a > { C diverges if and only if…

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Q: 2.Take the derivatives of the following functions. Do not simplify. a. f(x) 10x4 f'(x) f'(x)…

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Q: Let a, b > 0 be real numbers. Consider the helix a(t) = (a cost, a sint, bt), te R. (a) Find the…

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Q: Show that 4 is in the linear span of -3 1 t1 E- = by finding t₁, t2, t2 such that 0 0-0-0-0 = = t₁…

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Q: If z is a root complex of p(z) e R[z] then z is a root of p(z).

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Q: Write an equation that is a necessary constraint so that the matrix equation Aă – ☎ has a solution.…

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Q: Convert 189410 to Octal.

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Q: Show that the initial-value problem dy 0 ≤ t ≤ 1, dt 1+t is well posed on D = {(t, y)], 0 ≤ t ≤ 1,-∞…

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Q: 4. Let f [a, b] → R be Riemann integrable and non-negative (i.e. f(x) ≥ 0 for all x € [a, b]). cb…

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Q: Let S be a set of distinct symbols. Show that the relation defined onW(S) in this chapter is an…

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Q: (e) What other factors besides price should be considered before changing your purchasing…

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Q: Let M = = Mu= + + 24 4x + 2y Mv = (4:+2w = = (x, y), v = (z, w). Find the followi X X 4x + 4y 4 + 4w…

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Q: Find the solutions/ all point of intersection of the given graphs. You may use any technology for…

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Q: Is the following set of vectors linearly independent? 2 3 {Q.BB} 9 3 6 8 256

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Q: LA identify the increasing interval(s) of the graph above. O (-1.5, 1) U (7, infinity) O (-infinity,…

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Q: Find the first three iterations (by hand) obtained by the Power method (with Aitken's 4² procedure)…

A: Given Data: A matrix A=-134-2 with an initial matrix x0=1-1 We have to Find four iterations using…

Q: 2. Let S = span{V₁, V2, V3}. Check whether the vector u € St. (a) v₁ = [1, 0, 0, 0], v2 = [0, 3, 0,…

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Q: 24. z = —2x3 — 3y4 + 6xy2 + - - 1 16

A: The given function z=-2x3-3y4+6xy2+116. We have to find the relative minimum value of the function.

Q: Let n = 2k with k ≥ 2. (a) Prove that pk is an element of order 2 which commutes with all elements…

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Q: . Find, for the matrix B, the eigenvalues and their corresponding eigenvectors B =[-₂-¹3]

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Q: Consider the triple integral S S SM dv where M = {(x, y, z) | x² + y² + z² ≤ 4, z ≥ 0, and x² + y² ≤…

A: The given region is M=x,y,z| x2+y2+z2≤4, z≥0, x2+y2≤1. To SETUP: integrals for the volume of the…