Use Green's Theorem to evaluate the following integral Let² dx + (9x + 5) dy Where C is the triangle with vertices (0, 0), (9, 0), and (8, 7) (in the positive direction).

Q: E is the solid region that is above the paraboloid z = x² + y² and below the upper semi sphere x² +…

A: The solid region above the paraboloid , and below the sphere x2+y2+z2=2, and is in the 1st…

Q: 3 10 The matrix A = has an eigenvalue = -9. 3-4 Find an eigenvector for this eigenvalue. Note: You…

A: The answers are as follows: An eigen vector is [53​].  The eigen value is λ=3.Explanation:Steps and…

Q: Use Kruskal's algorithm to find a minimal spanning tree for the weighted graph shown below, and…

A: To apply Kruskal's algorithm, we first need to sort the edges of the graph by their weights in…

Q: can you please show the step by step solution. please do not skip steps. explain why you got the…

A: The answer is in the explanation.Explanation:Decrease in amortization per period: The decrease in…

Q: Question 1 The mass density of a cube is given by p = x² + y² + z² kg m³. Calculate the total mass…

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Q: can you please show the step by step solution. please do not skip steps. explain why you got the…

A: The answer is in the explanation.Explanation:10-year call scenario calculations:For the 10-year…

Q: Let F(x, y, z) =, S is the part of the paraboloid z = x² + y² - 1 that lies below the XY-plane and S…

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Q: The percent of concentration of a certain drug in the bloodstream x hours after the drug is…

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Q: Click and drag the steps that are required to prove 1k+ 2k +...+nk is O(nk + 1) to their…

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Q: Find f'(x). f(x) = (x+9)¯ -2 f'(x) = ☐

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Q: Find the orthonormal set of vectors from A = { [1, 1, 1], [1, 1, 0], [1, 0, 0] } using the…

A: The final answer are goven in steps.Explanation:Step 1:Step 2:Step 3:

Q: Determine all restricted values for : (over 0°- 360°) sec x ln (csc x) (Show steps and calculations)…

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Q: Please help me with these question. I am having trouble understanding what to do. Please tell me if…

A: The objective of the first question is to prove that for all real numbers 'a' between 0 and 1, and…

Q: Find a basis for the column space of 4 1 3 0 - -31 3 2 1 4 -1 A -3 -2 -1 - -4 2 6 -4 -2 -8 3 Basis…

A: image uploadedExplanation:Step 1: Step 2: Step 3: Step 4:

Q: (4) Consider the following LPP where all the constants c¿ are positive: maximize Σ1 (−1) ² cixi…

A: Solution given below Explanation:Step 1:

Q: Find the area below the curve f(x) = √√4-x4 2x from x = 0 to x = √√2

A: The objective of this question is to find the area under the curve of the function f(x) =…

Q: (a) Consider the general Sturm-Liouville equation with eigenvalue \ dx de (pdy) +qy+oy=0, a<x<b.…

A: The general Sturm Liouville equation  with  eigenvalue  is Corresponding to  the eigen function is…

Q: 6. Let xn = n¹/ for n = N. a. Show that xn+1 3. (See Example 3.3.6.) Conclude that (in) is…

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Q: 3) Suppose that we need information about the derivative of the data below. a) Apply forward,…

A: The data is given for the function…

Q: Arrange the given steps in the correct order to prove that 12+3+...+ Rank the options below. Assume…

A: Step-1:    For n = 1, the left hand side of the theorem is 1/(1.2) = 1/2 and the right hand side =…

Q: Suppose you want to type sequences of vowels (that is, the letters a, e, i, o and u). However, the e…

A: Given  the number of sequences of length   (i) Find (ii) Write a second-order difference equation…

Q: Find the angles between each vector in A where the set of vectors A = { [1, 1, 1], [1, 1, 0], [1, 0,…

A: Question explained below :Explanation:ANSWER :​​

Q: 4. Consider two spheres of equations x² + y²+z² = -4x-6y+4z+8 and x² + y²+z² = 4x+2y+4. Find the…

A: For simplicity taking the equation of sphere x2+y2+z2=R2Boundary of the green and red portions is…

Q: Problem 2. Cholesky factorization. a Let A = If a² <b, show that A is positive definite and find the…

A: L = [1a​0b−a2​​]Explanation:To show that a matrix A is positive definite, we need to prove that it…

Q: Given ▼ = 3 ỉ + 2] + 6k and a = −1 ỉ + 2] + 3k, please determine the radius of curvature at the…

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Q: Calculate the area enclosed by the curve - y(t) = (6 cost = cos(6t), 6 sint - sin(6t)), t: 0→2π. A…

A: Given, a curve It is required to find the area enclosed by the above curve.Area under a Parametric…

Q: The vector u = i- j + 2k is positioned at a point P in space with coordinates: (x, y, z) = (2,1,3).…

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Q: Let M be a 3 x3 matrix with eigenvalues ₁ = -2, A2 = 0.25 A3 = 1.6 with corresponding eigenvectors 0…

A: c1=-5, c2=-14,c3=-4Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Recalling that the (i, j)-entry of the matrix CCT is given by Σ 1<k<m Ci,k Cj,k, explain what the…

A: i answered the question in the explanation block. if you have any doubts you can ask me in…

Q: Locate the centroid of the quarter elliptical area shown below y y = x 1/2 I ¦0.6 m - y = x 3/2 ¦…

A: We have to find the centroid of the elliptical area.

Q: Let W denote the subspace of R5 consisting of all vectors having coor- dinates that sum to zero. The…

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Q: Suppose that a distribution of 500 items has mean 115 and standard deviation 44. Find the​ z-score…

A: We know z-score = (data points- mean) / standard deviationhere data points = 500mean = 115standard…

Q: roject the vector b onto the line through a. Compute the error e = b - p. Che at e is perpendicular…

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Q: Let k be the k-th coordinate functional corresponding to the natural basis of 1, that is k(x)=x(k)…

A: We have to show that φk is linear, we need to demonstrate that it satisfies the properties of…

Q: Find f'(x). f(x)=(4+ Inx) 8

A: Derivative - The derivative of a function represents the rate of change.

Q: Find bases for the column space, the row space, and the null space of matrix A. You should verify…

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Q: 52 5 4-1 1 0 41 1 1 20 -1 6 The null space for the matrix 44 is spanned by the vector

A: The final answer given in steps.Explanation:Step 1:Step 2:Step 3:Step 4:

Q: 8.4.4. For what numbers n is K 1,n a penny graph? graph theory question 8.4.4. For what numbers n is…

A: The objective of the question is to determine for which values of 'n' the graph K1,n is a penny…

Q: Let F(x, y, z) =, E is the unit ball x² + y² + z² ≤ 1. Verify the Divergence Theorem by evaluating…

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Q: Arrange the steps in the correct order to prove that 21 divides 4n+1+52n-1 whenever n is a positive…

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Q: Find g'(x) if g(x) = 6xe2x

A: Given a function: .It is required to find the derivative of the given function with respect to…

Q: Suppose UCC is a domain, f, g = O(U). If |ƒ(z)|2 + |g(z)|² = 1 for all ZEU, show that ƒ and g are…

A: The solution to the problem is in the segment below.Explanation:To show that f(z) and g(z) are…

Q: 522 Construct a matrix whose column space contains 2 and contains 0 -1 and whose nullspace 2

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Q: Ex 4. Let h(x) = x²/3 (2-x). i) Find the open intervals on which h(x) is increasing and decreasing.…

A: We will find the increasing and decreasing interval. Then we will find extreme value.

Q: If two functions each have a branch point at z0, does their product necessarily have a branch point…

A: Given, two functions, say  and , each having a branch point at .It is required to determine…

Q: Find a basis for the eigenspace of the eigenvalue λ = 3 for the matrix A = 4 2 3 -1 1 -3 2 4 9

A: We will find the basis for the eigenspace of the given eigenvalue.

Q: 3. Solve the following system using LU-decomposition: 2x1 +8x=-2 21-22-2

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Q: 5-8 Find the area of the surface generated by revolving the given curve about the y-axis. 7. x =…

A: Given,  , -2y2We have to find the area of the surface generated by revolving the given curve about…

Q: Q1) Solve and plot the following system of ordinary differential equations: x'(t) = x(t)-2y(t) +…

A: Consider the given system of differential equation:The initial conditions are .We need to plot the…

Q: The graph of a degree four polynomial function, f, is shown below. W (a) Determine the zero(s) of f.…

A: The graph represents a function of degree four polynomial.Note: According to the guidelines we are…