Calculated the requested distance. 1. The distance from the point S(7, 2, 1) to the line: x = -6 + 1t, y = -7 + 2t, z = -7 + 2t.

Q: (a) Set up a double integral for calculating the flux of the vector field F(x, y, z) = xi+yj through…

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Q: ) Let Pn be the vector space of all polynomials of degree n or less in the variable x. Let D: P3 →…

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Q: Use the definite integral to find the area between the x-axis and f(x) over the indicated interval.…

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Q: Let Pn be the vector space of all polynomials of degree n or less in the variable x. Let D : P3 → P₂…

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Q: Let Find a basis for the kernel of A (or, equivalently, for the linear transformation T(z) = Ar). A…

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Q: 2. The first order differential equation 2ydx = (3y - 2x)dy is a. Non-exact and Non- Homogenous c.…

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Q: g) x" +0.4x + 2x = 1 - H(t-5), x(0)=0, x'(0) = 0.

A: Since both are different. So as per our guideline, we are supposed to solve only first question.…

Q: A rancher has 800 feet of fencing to put around a rectangular field and then subdivide the field…

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Q: Use Stokes' theorem to write a line integral that is equal to the surface integral c curl F. ds,…

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Q: Let n be an element in Z. Prove that 5|n^2 if and only if 5|n.

A: If n be an element in Z. We have to prove that 5|n^2 if and only if 5|n.

Q: 1) Make a change of variable so that the following series begins with k = 5. n i=2 (−1)²+1 (i-1)²

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Q: subject to: Max z 4x12x2 + x3 2x1 x3 = 5 x2 + 3x3 3x1 + x₂ ≤ 6 X1, X2, X3 20 - -7

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Q: B. Fun Subspaces Consider the following 3 x 4 matrix A and its Reduced Row Echelon form, denoted U.…

A: It is given that A=120101201201 and U=10-4101200000 is its Reduced Row Echelon form. 1. The…

Q: 3) For the argument given below, a valid conclusion can be drawn (however the valid conclusion is…

A: The given arguments are, No birds except ostriches are 9 feet tall. There are no birds in this…

Q: e² dV where E is enclosed by the paraboloid z = 5 + x² + y², the cylinder Evaluate x² + y² = 5, and…

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Q: (c) ry"+y = 36x

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Q: A = Find the matrix A of the linear transformation T(f(t)) = 8ƒ' (t) +3f(t) from P₂ to P₂ with…

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Q: b a C c and d b and c b and d d and f e and f a and b c and f f d e elect all pairs of vertices…

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Q: Let A = -61 -33 P = 110 60 a) Is matrix A diagonalizable? b) If A is diagonalizable, find a matrix P…

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Q: Use the phase-plane method to show that the solution to the nonlinear second-order differential…

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Q: you have wrong 3rd derivarive and 4th as well

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Q: The function f from R to R is defined as f (x) = x²(x − 1), determine (a) whether f is one to one.…

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Q: A positive integer N is said to be a congruent number if it is the area of a right triangle with…

A: Given : A Positive Integer Is Said To Be Congruent, If It Is The Area Of A Right Triangle With Sides…

Q: Suppose that P2(x) = a +bx+ca² is the second degree Taylor polynomial for the function f about x =…

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Q: Polar (Trigonometric) Form of Complex Numbers. Write the complex number in polar (trigonometric)…

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Q: Evaluate the surface integral. [6 ( ² + x²y) ds S is the part of the cylinder y2 + z² = 9 that lies…

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Q: Determine whether the function f: ZxZ → Z is onto if a) f(m, n) = m+n. b) f(m, n) = m² +n². c) f(m,…

A: We know that a function f:X→Y is said to be onto if every element of set Y has a preimage in set X.…

Q: Show that (u, v) = (4u + 6, u − v, 7u + v) parametrizes the plane 2x − y − z = 12. Then: (a)…

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Q: (a) Choose a series C lim = lim -100 bm 11-00 b with terms of the form b₁ = 1. 1 and apply the limit…

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Q: Q2D. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f} E = {[a, b},…

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Q: Find the general solution (D²+3D+2)y=12x² A B C y=c₁₂e-²x+c₁₂e-21+ 18x − 6x² - y=c₁e¯²x+c₂e¹+21−18x…

A: The given differential equation is D2+3D+2y=12x2 Our aim is to find the general solution of the…

Q: Find the flux of the vector field F across the surface S in the indicated direction. 2 F = 3x²j-z²k;…

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Q: A function f : N × N → N is defined by f (m, n) = 2ᵐ−¹(2n − 1). (a) Prove that f is one to one and…

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Q: Solve the system of linear equations using matrices. 6x - y -28 - 5z 4x + 2y = 10 5x + 6z = -23…

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Q: The left end of a rod of length I is held at temperature 0, and the right end is insulated. The…

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Q: Let G be a group. a) Define the center Z(G) b) Show that Z(G) is a subgroup of G c) Show that Z(G)…

A: WE HAVE GROUP G  THEN WE HAVE TO DEFINE CENTRE OF G AND SHOW THAT IT IS SUBGROUP AND NORMAL SUBGROUP…

Q: Calculate ffs f(x, y, z) do For Sfs f(x, y, z) do = x² + y² = 16, 0≤z≤ 9; f(x, y, z) = e

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Q: 15. Determine whether the function f: Zx Z → Z is onto if a) f(m, n) = m + n. b) f(m, n) = m² + n².…

A: Solution given below.

Q: Find the solution of the Differential Equation (D³ - 3D²+4) y = 40cos2x+6

A: D3-3D2+4y=40cos2x+6

Q: Let W be the subspace of R³ spanned by the vectors Find the matrix A of the orthogonal projection…

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Q: Sketch the image of A JKL under the similarity transformation composed of a size transformation…

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

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Q: Find eigenvalues and eigenvectors for the matrix The smaller eigenvalue The larger eigenvalue has an…

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Q: (x²+4)y + 3xy: = Use trigonometric substitution for the indefinite integral of the integrating…

A: As per our company guideline we are supposed to answer only first qs, kindly post remaining qs in…

Q: Consider the Boundary-Initial Value problem where bn = and 8²u u 0 0 8.x² It u(6, 1) = 0, t>0 u(0,…

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Q: 4. Solve the two-point boundary-value problem Jy" + 2y' + 10x = 0, [y(0) = 1, y(1)=2 for y() and y()…

A: Given : The equations  y'' + 2y' + 10x = 0,y0 = 1,    y1 = 2   To solve : The two-point…

Q: Find the auxiliary roots (D4-2D³-7D²+ 8D+12) y=0 A) -2, 1, 2, 3 B) -2,-1, 2, 3 C none of the choices…

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Q: Use the ratio test to find the radius of convergence of the power series R= (If the radius is…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: f(n) (0) Write the first six terms of the Maclaurin series f(x) = E=0 n! Write the first six terms…

A: For writing first six terms of the following series we will put n=0,1,2,3,4,5 As follows