1. Find the general solution of the system: -6 2 X = -3

Q: Solve the given differential equation. All solutions should be found. (10y + 2x°y) dx – (9xy³ + æ°)…

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Q: If 1 d] 1 d] a a det b 1 -5, and det b 2 5, e [c 1 f 3 f then a 3 d] det |b 3 and 3 f] d] det b -3 a…

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Q: Prove that a circle in H projects to a Euclidean circle in D. Conclude that not all triangles in…

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Q: Set up and simplify (but do not evaluate) : 3x ds, where C is the arc of the circle r2 + y² = 4 from…

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Q: 20 Use a power series to represent the function f(x) centered at a = 0. = 15x4 +4 Provide your…

A: We have to find the power series of f(x) centered at x=0.

Q: QUESTION 4 By using the method variation of parameters, find the general solution of the…

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Q: Match the vector field with its graph. F(x, y) = yi 華

A: give vector field F(x, y)=yi

Q: Find the angle a between the vectors [] 5 and -1 a = 48.37 2.

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Q: a. Use long division to divide 4x3+9x-12 by 2x-1 b. Write your answer in quotient form.

A: We have to perform the long division

Q: x' + y = 0 y' + x = 0 x(0) = 0, y(0) = 1.

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Q: 1. The area B is given by = {(r, y, -) € R* | + <1,: =-, y? { (x, y, z) E R² | 1, 2 = r² – y² В…

A: Given that B=x,y,z∈ℝ3 | x24+y29≤1, z=x2-y2 and the vector field assign for Stokes's integral theorem…

Q: Faith is decorating the outside of a box in the shape of a right rectangular prism. The figure below…

A: The surface area of a solid object is a measure of the total area that the surface of the object…

Q: 2. Find the volume of the solid generated by revolving the region under the curve f (x) = x² + 1…

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Q: Consider the polar curves C2:r=4 cos e and C3 :r = 4 sin 0. (a) Determine the slope of the tangent…

A: We will find point of intersection. Derive slope of tangent for.polar curve and then substitute…

Q: Let T: R2 R2 be a linear trasformation such that T (x1, 22) T (x) = (3, 1). (x1 +x2, 2x1 + 3x2).…

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Q: In a particular Insurance Life Office, employees Smith, Jones, Williamson and Brown have 'A' levels,…

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: ACBinf fCx) şinf R Cx). X6 A XE13

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Q: Identify the correct truth table that represents the compound proposition (p -g)v(-p-r)* P-r (p-…

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Q: Suppose f(x) is positive, continuous, and f'(x) < 0 for all z in [ – 8, 4], and / f(x)dx = 76 and…

A: Given that fx is positive, continuous and f'x≤0 for all x in −8,4 and ∫−84fxdx=76 and ∫−14fxdx=21.…

Q: xact length of the portion of the curve shown in blue, and find the e

A: Introduction: The arc length of the polar curve r=r(θ) is given by the formula, L=∫abr2+drdθ2dθ…

Q: Draw a graph on six vertices with degree sequence (3, 3, 5, 5, 5, 5); does there exist a simple…

A: In graph theory, the degree  of a vertex of a graph is the number of edges that are incident to the…

Q: Let P. Q. R be true, false true, respectively. Which of the following is true? * PA ΡAQAR PA~Q ^~R O…

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Q: - Use the Cauchy-Schwarz inequality to prove that for all real values of a, b, and 0, (a cos e + b…

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Q: (b) у" — 4у'+ Зу %3D Зе2х + 4е* + 2e3х

A: Given differential equation: y''-4y'+3y=3e2x+4ex+2e3xTo find: General solution of the differential…

Q: Use Gauss-Jordan row reduction to solve the given system of equations. (If there is no solution,…

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Q: Use Induction to prove that 22n+1 + 32n+1 is divisible by 5 for all n > 0.

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Q: Using LaGrange Multipliers, solve the following problem. It is desired to build a rectangular box…

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Q: Solve the system of equations E below in R3. x + 2y + 5z = 2 (Σ ) : 3x + y + 4z = 1 2.x – 7y + z = 5

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Q: In this problem, y c, cos(4x) + c, sin(4x) Is a two-parameter family of solutions of the…

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Q: Find the area of the shaded region. The image is not to scale. y=F y=- Consider c=64. Enter the…

A: Given that,An area is covered by the equationsy=x, x=C, y=-1CxWe have, C=64Substituting C=64, we…

Q: R.1. Let N represent the set of positive integers. Define f :N→N by ƒ(n)=n² +1. Is fa one- to-one…

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Q: L3x3 + M (subspace sum). sym 3×3 !! L3x3 O M (direct sum). sym 3×3 !! express A E M3x3 as A = L+U…

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Q: Ryevin was racing in a bike marathon. He was 3/8 of the way across a narrow bridge when he heard the…

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Q: 7.2) Consider the production function Y = 24KL find (i)- (1) (1) (ii)

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Q: Find the area of the region inside: r 8 sin 0 but outside: r = 1

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Q: x + x + 1, where E 1, 2]. The Consider the function f(x) domain of the inverse function f'(x) is O…

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Q: be sec of SIze an B SiZe HOW mons funce ions f:A B are there chas for every beB, there eleme n Es…

A: Given that the size of set A is  8 and size of set B is 4. Now to be total number of functions f:A→B…

Q: x-ビ ere S70 and --xe g 00ー

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Q: Let C be the parametric curve defined by Sx(t) = t2 – t – 2, |v(t) = t* – º +t. Determine if C is…

A: Substitute x=-2 in the given equation xt=t2-t-2 and simplify to calculate the value of t.…

Q: he statement "All of us are OK and all of them are losers." is an example of* O negation )…

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Q: - 1 - 1 dx ?

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Q: u, = and u, = Find (T]B- Verify that Formula (8) holds for every vector x in R2.

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Q: s (x) In (1t x2) 74.8

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Q: What is the 109th term of the arithmetic sequence (963, 936, 909, 882, .)?

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Q: a bc If det de f = -4 g hi -- a - 8g 6b - 48h c - 8i then det бе g 6h i

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Q: Question 7. Using induction prove that 13 + 23 +... + n³ = + u)u for n > 1.

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Q: what is a perfect matching? And give examples

A: A matching graph is a subgraph of a graph in which there are no edges adjacent to each other. That…

Q: 2) Show that the digital line topology on Z is not Hausdorff.

A: Given that Digital line topology on ℤ, we have to prove that it not Hausdorff Therefore, Let a space…

Q: differential equations: Y' = ay + bx   X' = cy Where a, b, and C are constants. 1 ) Use the two…

A: Sol

Q: In a CCS block of 45 students: 32 enrolled in DISCTRU; 23 enrolled in COMPRO2; 18 enrolled in…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…