Evaluate the line integral along the given counterclockwise oriented curve: yds where C is the half-circle x² + y² = 3 in the second quadrant. You need to parametrize the circle as r(t) first.

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Q: (a) For any sets A, B and C, prove that if AC BUC and AnC= Ø, then ACB.

A: Since you have posted multiple questions according to guidelines we can solve only first question.…

Q: Let A = 0 1 -1 1 -1 2 a) Find the QDQ™ factorization (spectral decomposition) of A. || √6 √6 INIC 1…

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Q: For which value of a the system of ODES y₁ = sinh(y₁) + a tanh(y2), y2 = -2 cos(y₁) +2e³+ + tanh…

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Q: Lemma 14.11 Let Sn = integer n. n k=1 = 1+ 1 1 n · + -, where n € N. Then S2 ≥1+ for every positive…

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Q: 1. Which of the following is TRUE for a differential equation?

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Q: Suppose A E M(R). Write A = (a₁ | |ax). a. A vector x ER is in the null space of A if (select all…

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Q: Let W be the set of all vectors Find a basis of W. X x + y with x and y real.

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Q: Y₁' = 3Y₁ + 1/₂ ل3 Y/₂ = 2y + 2y₂

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Q: 5. A firm sells two products. The demand functions for two products are: q1 = 120-4p1 - p2 q2 =…

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Q: Let f(x, y, z) = xy +e+yz and Vf is continuous on any curve C starting at Fundamental theorem of…

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Q: a) Which of the following systems of ODEs is autonomous and dynamical? OII OIII, where 1: y₁' = 3y₁,…

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Q: 53. lim √√3x = 0. - x-3-

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Q: For the following system to be consistent, 721 + 6x2 + 123 8 2x1 +502 + kx3 3x₁4x2 | we must have k…

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Q: Study the stability of the origin and plot some solutions for: x' = -2 1 X

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Q: Suppose the functions F: R→R and G: R→R are defined by these formulas: F(x) = x² + x and G(x) = 3x…

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Q: Group blood testing During World War II it was necessary to administer blood tests to large numbers…

A: Given that y=N(1−qx+1x) with q=0.99 and N=1000.We need to find the integer value of x that minimizes…

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Q: Show that [1 1 0 0 1 1 0 001 1 0 det⠀⠀⠀⠀ ⠀⠀⠀⠀ 000 0 100 0 001 00 00 ⠀ ⠀| = 1+ (−1)n+1. ⠀⠀ 1 1 0 1

A: Consider the given matrix .We need to prove that the determinant of  is , where  is order of matrix.

Q: Find the surface area of the surface (r, 0) = r cos 01 - n0ĵ+r²k, 0≤r≤ 2, 0≤0 ≤ 2π. sin

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Q: SevdA in the order drdy where R is bounded by y = x + 3, 14. Write the iterated integral for y=-x+3,…

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Q: Determine the first order partial derivatives indicated below: b) f(x, y) = ln(4x² +5y³) respect x…

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Q: The row reduced echelon form of an augmented matrix related to the system Ax = b where A is a 3 X 3…

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Q: Let R be a ring, and let ICR be an ideal. Prove that R/I is commutative if and only if xy - yx € I…

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Q: the se f(x,y)=yx +xe* +y" cosx mixed der

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Q: P = Let D = A = If possible, find an invertible matrix P so that D = P-¹AP is a diagonal matrix. If…

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Q: Let V = R³ and S be the set of all vectors (x, y, z) in V such that x = r-3s, y = 2r + s an z = s,…

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Q: Usando a definição, verifique que f²dz = −1+i, em que C é o quadrado com vértices em z = 0, z = 1, z…

A: Let  then                        also                         -------- (1)

Q: We showed that Σ 1/n2 converges to some value A that is at most 2. Show that A is between 1.5 and…

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Q: The row reduced echelon form of 3 X 4 matrix A with columns c1, c2, c3 and c4 1001 is given by 0 1 0…

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Q: Compute the integrals (where n € Z), simplifying as much as possible: dx (a) Lat J. 1+x¹ 9 n> 1; (b)…

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Q: Jo F-dr where F(x, y, z) = xi+yj + 6(x² + y²)k and C is the boundary of the part of the paraboloid…

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Q: d. What is the optimal solution and what is the objective function value at the optimal solution?…

A: The optimal solution is:

Q: Šv ل ذل - (+۱) dz

A: (c)  Let the given integral is                                            ----------- (1)…

Q: Find the prime factorization of \\( 33^{3} \\cdot 39 \\cdot 49^{14} \\)

A: We just have to write them into product of primes

Q: 3. Solve the following system. x + 2y W y + w 2y W - +1++ 2 = 1 0 0 2 + 2z = - Z =

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Q: Prove that (a) For all integers m and n, n + m and n - m are either both odd or both even.

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Q: If the system has infinitely many solutions, then

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Q: Let F(x, y, z)= xyi+yzj+k and a smooth curve C given by the line segment from Answer format: a, b, c…

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