Use Stokes' Theorem to evaluate ( r(t) curl (F) · ds). F(x,y,z) = 2x + 2yj + zk S is the hemisphere x² + y² + z² = 36 y ≥ 0 is oriented in the direction of the postive y - aixs 5 cos (t) + 5 sin(t)j + 6 tk = 0 ≤ t ≤ 2π

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Q: Q14. Suppose A and B are defined as follows. A = B = 1 4 -3 || -5 -2 3 5 -5 1 -6 Compute c22 in the…

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Q: (4) Compute 3180 mod 13 without using a calculator.

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Q: Which of the following graphs have Euler circuits? K R I S H M L A: Has Euler circuit. N U T C: Has…

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Q: 3. Let A = 1 -2 (d) Let b = -2 -2 -2 2 (a) Find a basis of S = N(A). (b) Find a basis of the…

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Q: 5. F(z) = 10z² z²-6z+25

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Q: 3. Find a Laurent series for the given function centered at the given point z, that converges in the…

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Q: 6) Given the data 0.90 1.42 1.30 1.50 1.61 1.31 1.35 1.47 1.95 1.66 1.96 1.47 1.92 1.35 1.05 1.85…

A: Given: The data of 25 observations is given.To find: a) Mean              b) Median              c)…

Q: 4. Solve the initial value problem: x - 4y = x¹ ex,y(1) = 0.

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Q: Let S be the solid obtained by rotating the region bounded by C1: y = x2 − 6x + 9 = (x − 3)2 and C2:…

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Q: Calculate f f(x, y, z) dS For Is f(x, y, z) ds = x² + y² = 4, 0≤ z ≤ 9; f(x, y, z) = e-²

A: We have to calculate the integral ∬Sfx, y, zdS. For x2+y2=4, 0≤z≤9; fx, y, z=e-z.

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Q: 0 C) Check if function f(z) = zz satisfies Cauchy-Riemann condition and write this function…

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Q: You have complex numbers Z₁ = e³-14, z2 = √√3+2i, 23 = = 3-1/2/³ 1. Write Z₁ in classical form z = x…

A: z1=e3-iπ4z2=3+2iz3=35-i32

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Q: 7. What is the last digit of 21000?

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Q: (a) For parts (i) and (ii) below, suppose that A is a 4 x 4 matrix with eigenvalues 6,-2, 1 and 3.…

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Q: Exercise 7.2.7 Suppose A is an nxn matrix and let V be an eigenvector such that AV = V. Also suppose…

A: Given that A is an n×n matrix and let V be an eigenvector such that AV=λV. The characteristic…

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Q: 4. Suppose that a positive integer is written in decimal notation as n = akak-1 a2a1ao where 0 <a;…

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Q: QUESTION 7 Provide an appropriate response. Evaluate dy and Ay for y = f(x) = 20 + 15x²-x³, x = 2,…

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Q: A. In your own words, what is Newton's method used for? B. Use Newton's method with 3 iterations to…

A: An equation sin(x) = x - 1 is given with an initial value x0=1. The aim is to find the roots of the…