Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and curve C. F= (xy+ 3y²)i+(x-3y)

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A: We have given a vector field ,  Fx , y , z = sinx i + cosy j + z2 k f1x , y , z = sinx  , f2x , y ,…

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A: Alternating seriese where error estimation theorem is used

Q: 3 , evaluate the improper integral dr. x2 + x – 2 Does it converge or diverge? Justify your claim.

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Q: Evaluate (2х — у) dx + (х + 3у) dy. C: x-axis from x = 0 to x = 5

A: We can solve this using given information

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A: Consider the given data points, 0,3, 1,-2, 2,5 and 3,4 Make the table of Newton interpolating…

Q: (27>1>0) (()=47 -t, (0<t<2x)

A: Definition: The Laplace transformation of ft is given by Lft=Fs=∫0∞e-stftdt Given  ft=4π2-t2,…

Q: If A = (a, b) and B= (b, c), find: (i) (AUB) (ii) (AnB)' (ii) A'UB

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Q: Let T: R3 → R3 be a linear transformation such that T(1, 0, 0) = (2, 4, –1), T(0, 1, 0) = (1, -2,…

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Q: 5. Let V = R³ and let (-, ) be the standard dot prod- uct. (a) Calculate (3e, + 2e, – €3, 2e2 +…

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Q: Let y = and u= 3 Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to…

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Q: 1. Interval, 0 < x < 2; function, f(x) 0 < x < 1, 1 < x < 2. = 2 – x, 4 1 ANS. f(x) 1 +* E 2 cos – 1…

A: Fourier Cosine series expansion of the function

Q: 2. Consider the subset a b S = 0 1 c : a, b, c € Z3 3 C SL3(Z3). 0 0 1 (a) Show that S is a subgroup…

A: Given :  S = 1ab01c001 : a, b, c ∈ℤ3⊂ SL3ℤ3 To prove :  (a) S is a subgroup of SL3ℤ3.…

Q: [1 10 100 1000 do [227.04 1 15 225 3375 a 362.78 1 20 400 8000 | a2 517.35 1 22.5 506.25 11391 a,…

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Q: Obtain the general solution to the equation. dx y + 6x = 2y dy

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Use series to estimate the integral's value with an error of magnitude less than 10-3. 0.29 dp- ...…

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Q: 6. Given a figure below, point A and 8 are called a. collinear b. coplanar c non-collinear d.…

A: Since you have asked multiple question here, we will solve the first one for you. To get the…

Q: 12. Teachers' Salaries in North Dakota The average teacher's salary in North Dakota is $37,764.…

A: Th probability distribution function of a normal distribution is given by the equation;…

Q: Soluing liner diff erential equations dy COSX

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Q: Find the area between the innér and outer loops of the limaçon r = 2 – 4 sin 0.

A: Solution :-

Q: find the surface area obtained by rotating the circle (x – 4)2 + y? =1 about the y-axis. %3D

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Q: f(1) = u (1) sin(t)

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Q: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

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Q: Consider the second order linear homogeneous differential equation: y – 4y/+4y = 0, y(0) = 3 and…

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Q: A prestigious hospital has acquired new equipment to be used in laser operations. It classifies its…

A: We have to find a number of major operations to maximize the revenues.

Q: [(s-2)²+b²1 (s-b)2 i. F(s) = In j. F(4) = ln[1+] 2bs s²+2b2

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Q: 2 Jo x2+4 n = 6

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Q: 1. Solve the following systems of equations by matrix method (solving the eigenvalue problem). In…

A: First we will find out the eigenvalues and associated eigenvectors of the coefficient matrix.

Q: 7. solve the following differential equation. (16y - xy) dx +x dy = 0

A: To solve the given differential equation.

Q: 4. Use the lazy c method to show that 1 1 n° log2 (n) + 3n° +n² log, (n) – 2n + e O(n° log,(n).

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Q: et +e- find the length of the curve h(x) = from r = 0 to z = In 2.

A: The standard formula for arclength will be used in solving this problem. The typeset solution is…

Q: 10. Teachers' Salaries in Connecticut The average teacher's salary in Connecticut (ranked first…

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Q: Q1.O Determuine type and stablity of critical point. y = 24, t4z 2

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Q: use the divergence theorem to compute: F(x,y,z)=x2i+y2j+z2k; for the boundary of the solid region…

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Q: as instructed, to find à second sO Y2(X). 9y"- 24y' + 16y = 0; Y1=e4x/3

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Q: 7- x"(t) – 2x'(t) = 6 – 4t x(0) = 2 , x'(0) = 0 nat

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Q: Solve the given initial value problem. y"'" - 12y" + 52y' – 96y = 0; y(0) = 1, y'(0) = 0, y"(0) = 0…

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Q: Question 3 For the points A(8,12), B(8,8) C(12,8), and D(13,15), determine i) The equation of the…

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Q: Taking Joint H. Ź Fx=0 FHo Cos 45- Fan Cos67.5 Ho +130-6 563 cOszas:0 67.5 45° :: FHo Cos 45-Fan…

A: A system of equation is a set of equation with common variables in them. The solution of such an…

Q: All dinosaurs are extinct No irrational numbers are integers Some exercises have answers All COBOL…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: 8. Which of the following is a factor of x+3x² - 4x – 12? a) X -6 b) х-4 c) x-3 d) х-2 9. When…

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Q: test the convergence and divergnce 2. マ+32+1

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Q: Find a value of θ in the interval ​[0°​,90°​] that satisfies the given statement.   cos θ=0.76018172

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Q: 3. Express (j-3)° in rectangular form.

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

Q: Evaluate: i'

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Q: Find the maximum value of := 3x + 2y Objecetive function subject to the following constraints. x20 y…

A: Feasible region: In a linear programming problem, a feasible region is the set of all points which…

Q: 2. Suppose X is a continuous random variable with 0 sXS 2. Which, if any, of the following functions…

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Q: Given the linear system below: 25 a + 15b - 5c = 5 15a + 18b = -3 -5a + 11c = 6 a. Use Cholesky…

A: In part (a) we will use the chelosky Method in which Coefficient Matrics A can be Factorised by…

Q: y'- 4y + 2x = 0, x = 2 and x-axis

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Q: d the Laplace Transform of thes the Laplace Trans Ferm ITS-1+(ns+1)e² (0<t<27) Ans. F(s) 1- 1 = (1)f…

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