(b) Use Stoke's Theorem to evaluate the line integral $ (3? – 22) dr + (z² – x²) dy + (y² – x²) dz, where the curve C is the intersection of the paraboloid z = x2+y? – 1 with the plane x + y – z = 1, oriented counterclockwise viewed from above.

Q: Verify that 1, is an eigenvalue of A and that x, is a corresponding eigenvector. 2 = -11, x, = (1,…

A: To verify that given eigenvalues and eigenvectors are belongs to the given matrix A.

Q: cOS X (1+sin x)

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Q: Suppose S = {r,u, d} is a set of linearly independent vectors. If x = 2r + 2u + 2d, determine…

A: Given :  S = {r, u, d} is linearly independent set of vectors  and  x = 2r+2u+2d. To find :  We have…

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A:

Q: 1 Give one example r that makes log. (r) rational but not an integer

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Q: (a) Define ƒ : R –→ Z as follows: f(r) is the smallest integer y which is at least r. Decide whether…

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Q: 3. f(x) —D ех — cosx e* - 2 COSX |

A: Here ex-cos(x)-2=0Let f(x)=ex-cos(x)-2Here x 0 1 f(x) -2 0.178 1st iteration :Here…

Q: (10) Convert 375eight to base 10. (11) Convert 487 to base 5.

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Q: 17. Evaluate L{y"(1) + 2y'(1) + y(1)}; y'(0) = -1, y(0) = 5. Let L {y()} = {s). A) (s°+2s+ 1)Y(s) –…

A: Here we use basic laplace transform

Q: do - k· (0 – 10), dt where k is a constant. If the temperature of the body is initially 70°C and 10…

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Q: Given that log, a+log, b=3, calculate all the possible integer values of a if b is also an integer…

A:

Q: Part 2. Prove that the following are equivalent A. by Constructing a truth table 1. [p V (~ p ^q] →…

A: A) prove that the following are equivalent by constructing truth table 1) p∨~p∧q↔p∧q 2)…

Q: B. Volume of Solids of Revolution 3. Consider the figure below. Using Circular disk method, find the…

A:

Q: 1. Use a Chain rule to find aw and ar aw , if w = x², x = sin(r²s) əs %3D

A: Given w = x2x = sin(r2s)

Q: A scientist would like to clear his liquid sample of sediment by pouring it through a cone shaped…

A: Introduction: In mathematics, a differential is an expression based on a function's derivative that…

Q: Solve the following system of equations using the Gauss-Jordan elimination method. х - Зу + 7z = 15…

A:

Q: Find the series for cos⁡x/(1+sin⁡x ) by differentiating the power series of ln⁡(1+sin⁡x ). With…

A:

Q: Find the general solution of the given linear differential equations y" - y = cos x - 5 sin(2x) By:…

A: 1) By using method of undetermined coefficient ,  We have given a differential equation  ,  y'' - y…

Q: Suppose p and q are distinct prime numbers. Find the number of positive integers r < pq such that…

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Q: 18. Evaluate L (s² + 1)²

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Q: Find a 2 x 2 matrix A with integer entries where the characteristic polynomial |A – AI| is X² + 2A +…

A: Finding such a is equivalent to finding a 2 by 2 matrix with trace -2 and determinant 5. As in…

Q: How many random errors of magnitude plus of minus one would be necessary to have 35 different ways…

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Q: 7.4Find a subset of the vectors v= (1, -2, 1, -1), v2= (0, 1, 2, –1), vz= (0, 1, 2, –1) and v,= (0,…

A:

Q: Find the positive root in 4th iteration of the equation xeX-3 in the interval [1,2] using Regula…

A: We have to find the positive root in the 4th iteration of the given equation in the interval 1,2…

Q: f(x) 3D 2.4х5 — 5.5х3 + 4.2х — 2.8

A:

Q: I am confused what is the right answer this is the second time submitting this problem and have got…

A: The given numbers are first converted to Base 10 numbers and multiplied together to find the food…

Q: if 0 2 t Let f(t) 1

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Q: 19. Solve y'(1) + y(t) = sin t; y(0) = 1 by Laplace transfrom. %3D

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Q: 3. f(x) = ez* – x² – 1 (Xi = 5) ез || -

A: Here we use python to solve this problem.

Q: EXCERSICE D Show that the minimal sufficient statistic for the uniform(8,0+1). is not complete.

A: Given: Show that the minimal sufficient statistic for the uniform (θ,θ+1) is not complete

Q: Solve the equation x dy + y dx = 2x^2y dx. Select one: O a. In |x+y| = X^2 + c O b. In |xy| = x^2 +…

A:

Q: To evaluate the exact value of f(x) = x(8x49 - x)(x30 - 3) , what order of the Taylor series…

A: f(x) = x(8x49 - x) (x30 - 3)

Q: d. Give an example of a different function with exactly the same roots as f(2). g(x) =s is a new…

A: Solution

Q: 2. The height above the ground, h, in metres of a car on a Ferris Wheel as the Ferris Wheel turns…

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Q: Consider the following system of tanks. Each tank initially contains V1 = 200 gallons and V2 = 300…

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Q: 1. Consider the equation ODE dy dt y (1? – 9). %3D (a) Sketch the graph of dy as a function of y. dt…

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Q: 'ind the inverse Laplace transform of 1 H(s) : 1 2 + 4 1 -4s %3D

A:

Q: 18. Find all critical points of f(x, y) = In(x+y) +x² – y +1 and classify each critical point as a…

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Q: Consider the permutation (1 2 3 4 5 6 \3 4 5 6 1 2 7)* 1. Express as a product of disjoint cycles.…

A: Given Permutation: 12345673456127

Q: Consider the following. 3x4 - 8x + 5 = 0, [2, 3) (a) Explain how we know that the given equation…

A: Given that  3x4−8x3+5=0, 2,3

Q: Described and sketch several representative members of the family after obtaining the differential…

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Q: For the following differential equation y = x * (x + y) + 2 and the following initial condition y(7)…

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Q: If z = f(x, y), where x = 2ts and y = t2 + s², show that () - 2 + 2x + 4y %3D dsdt

A: Here given z=fx, y and x=2st, y=s2+t2

Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

A: We have to find the percentage of error at n=3

Q: A = (P(0) ^ (Vn e N.P(n) → P(n +1) - 1)) (Yn e N.P(m) В UA А. A entails B В. В entails A С. A and B…

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Q: Solve the system of differential equations 356x + 135y y' = - 936x – 355y x(0) = – 19, y(0) = 50 -…

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Q: If m rst = 164, what is m<RVT?

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Q: Determine whether the function involving the n × n matrix A is a linear transformation. T: Mn,n →…

A: Here we use basic property of matrix and linear transformation

Q: Find the inverse Laplace transform of H(s) +ed

A: