#8. Uses Stokes's Theorem to evaluate ff curl F n ds where S is the paraboloid z = x² + y², z≤ 9 and C is the boundary curve x² + y² = 9,z = 9. Here F = (2y, 6z,3x).

Q: Q.2 Solve the following set of equations using the inverse of the coefficient matrix: 8x2+2xy=-7 2xy…

A: Here we have to solve the set of equations by finding the inverse of the coefficient matrix.

Q: The matrix A= 2 0 -1 4 1 -5 07 0 has eigenvalue A₁ = 1 with eigenvector ₁ = A2 = 2 of multiplicity 2…

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Q: Let D be the region shown in the figure that lies inside the square with vertices (±3, 0) and (0,…

A: We have to find ∫C2Fdr Using Greens Theorem.

Q: 1) Suppose T is a linear transformation of TH=2-3x + x² and T[3] =1-x² T[2¹] and T Determine. R² to…

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Q: Let ƒ: R → R³ be defined by f(x) = = a. f(x + y) f(x) + f(y): + Does f(x + y) = f(x) + f(y) for all…

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Q: 4. Consider the binomial (a + b)^n and calculate what is asked below. a) Use De Moivre's theorem to…

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Q: Let f: R → R be defined by f(x) = (x, 2x², -6x). Is ja linear transformation? a. f(x + y) = f(x) +…

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Q: Consider the initial value problem given below. dx dt = 3+tsin (tx), x(0) = 0 Use the improved…

A: Consider the initial value problem given below.= 3 + tsin(tx),   x(0) = 0We have to use the improved…

Q: Consider the matrix B= 10 0 a 4 1 4 say for which values of alpha matrix B does not admit inverse

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Q: Prove or disprove that [x/2] = [(x+1)/2] for all real numbers x . Prove or disprove that [x/2] =…

A: We disprove by giving a counter example

Q: Solve by using formulas. (Round your answer to the nearest cent.) Ordinary Annuity Annuity Payment…

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Q: Consider the following matrix A and column vectors K₁, K2, and K3. 4 5 5 5 4 5 5 4 A = K₁ = -5 1 er…

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Q: For the system of differential equation ' = A, with coefficient matrix given by, 1 1 A) (4) -3 "…

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Q: 2. Given the following functions f(t), use the formulas to find the Laplace transform a) f(t)=4t²-5…

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Q: at most 2. Find a basis {p(x), q(x)} for the vector space {f(x) = P₂[x] | f'(-8) = f(1)} where P₂[x]…

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Q: Find the maximum value of f(x1, x2, x3) = 6x₁ + 7x₂ + 2x3 subject to the following constraints. S x₁…

A: subjected to constrain

Q: 3 1. Consider a function f(x) = x³ + x² - 4x 4. (a) Compute the minimum number of iterations…

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Q: Consider the ordered bases B=( a. Find the transition matrix from C to B. TB = b. Find the…

A: Given Information:To find:a)The transition matrix from C to B.b) Coordinate vector  when c) The…

Q: Find all the roots of the given function. Use preliminary analysis and graphing to find good initial…

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Q: Let P, denote the vector space of polynomials in the variable æ of degree n or less with real…

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Q: The set B = {- (2 + 2x²), (6+4x+6x²), 18 + 8x + 16x²} is a basis for P₂. Find the coordinates of…

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Q: Let D be the region between the circles C₁ and C₂ centered at the origin of radius 1 and 4,…

A: Let C be the positively oriented, smooth, and simple closed curve in a plane, and D be the region…

Q: Let f(x) = 3 + cos (5 a) where 0 < x < 2π. Next we do a Fourier series expansion of f(x). The…

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Q: 1. (1) Show by hand¹ that 2 is a primitive root mod 19. (ii) Find² a complete set of primitive roots…

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Q: Three boats are out at sea: Boat A, Boat B, and Boat C. The crew of Boat A can see both Boat B and…

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Q: SHOW THIS PROBLESM IS INFEASIBLE: ???????? 3?1−2?2 ??????? ?? ?1+?2≤2 −2?1−2?2≤−10 ?1,?2≥0

A: The objective of this question is to demonstrate that the given linear programming problem is…

Q: Following a change of variable, the quadratic Q = 5x² − 12x₁x2 + 0x² can be expressed with no…

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Q: B. Show directly from definitions that if sn and to are sequences so that limm- Sn = -8 and limn -…

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Q: Use the simplex method to solve the linear programming problem.Convert linear equations by using…

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Q: The set B={[−1010],[00−11],[0002]} is a basis of the space of upper-triangular 2×2 matrices. Find…

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Q: Find the Fourier series for extended to a 2π-periodic function. ao N + an cos(nt) + bn sin(nt) = ∞ ∞…

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Q: lowing values. ㅏ t) = 2t e 20et 35et x(0) = + 18- -t e [] eAt 3 4e2t-e-t 4e2t - 4e-t - e

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Q: Express the function as the sum of a power series by first using partial fractions. (Give your power…

A: Express the function as the sum of a power series by first using partial fractions. (Give your power…

Q: Write the general solution of the ODEs by finding two power series solutions about the ordinary…

A: The differential equationTo find the series solution about x=0, ordinary points.

Q: Numerical analysis Find the fixed point iteration of f(x)=x^2-2

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Q: Evaluate the following integral So x(ax³)¹ Where a = 0.55 and b = 0.78 Give your answer to the…

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Q: Solve the initial value problem for initial values 2 0 y' = ( 1₂9₁ ) y, у, 1 1 a) y(0) = ( −¹₁),…

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Q: Solve the following differential equations with initial conditions by applying the Laplace transform…

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Q: Which of the following transformations are linear? Select all of the linear transformations. There…

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Q: There is a vector field F = (4y, 5x, z) and a scalar field g(x,y,z) = yz(x+4y+z). (a) Provide the…

A: For vector field FF and scalor field g we have to solve a), b), c).

Q: when values of theta are small approximations are sometimes used for trig functions sin theta, cos…

A: 1. Sine Function (sin(θ)):Approximation: Small angle approximation  for small angles in…

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = y" + y = f(t), y(0) = 0,…

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Q: TB Consider the ordered bases B = [M]B = -3 4 (8 96382)- 0 0 -2 -3 1 0 4 2 c=3² 39.6 * 3) ) for the…

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Q: (b) Consider the function f(x) = cos(2x) - sin(x). Compute the root of the function using Newton's…

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Q: The displacement of an object is given by b Sº t³ − 6t+ / dt Eveluate s for a = 1.74 and b = 7 S =

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Q: dx, dt = 2x₁ + x₂ +u dx₂ = -2x₁ + u dt Z = 3x₁

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Q: =ider some specific examples of the influence of e heated plate. The differential equation is Eq.…

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Q: Let 3 A = -1 -1 3 -1 -1 3 (a) Find a matrix P that orthogonally diagonalizes A. (b) Find B = P-¹AP…

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Q: 1. Given that Pn(x) flrol+flro, z1](z-ro) + a₂(x-xo)(x-T₁) +as(x − To) (x − x₁)(x − x₂) + ......+ an…

A: Let  be the values of  corresponding to the arguments . Then from the definition of dividend…

Q: TB = matrices. a. Find the transition matrix from C to B. MB = Consider the ordered bases B = == )…

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