Example 6.13. Prove that ge + 8 1+ 4 (i) A (ii) 1 + 8°µ? = | 1+ : 2+A 1 1+ 4 (iii) u = 2V(1+ A)

Q: A Living a pom is 7:2m fog and 15 m wide. what ire gresesd wald 7 be of a joale plan qucun p a feale…

A: The given length of the room is 7.2 m. The given width of the room is 4.5 m. We need to find the…

Q: 2. Three different types of computers need varying amounts of four different types of integrated…

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Q: If there are 4 roads from Town A to Town B and 6 roads from Town B to Town C, in how many ways can…

A: Solution:  It is given that there are 4 roads from town A to town B and 6 roads from town B to town…

Q: 1. Solve by D operator method dx2 d?y 20+y = x²e3x. dy dx

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Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: Describe the graph of the equation. r = - 181 + (1 – 12)j + t k O It is a parabola in the plane x =…

A: We need to describe the graph of the parametric equation r=-18 i+(1-t2)j+t k.

Q: Find the vertex set, edge set, and edge endpoint table of the digraph G. e1 V2 V1 e5 e6 ez e7 e4 e8

A: Given a graph with edges and vertices as shown above. To find the vertex set, edge set and edge end…

Q: For each of the following, factor the matrix A into a product QDQ" where Q is orthogonal and D is…

A: This is a problem of linear transformation.

Q: 1940 1950 1960 1970 1980 1990 132,165 151, 326 179, 323 203,302 226,542 249,633 e population in year…

A: Sol

Q: 3. 2х, X2 = 2 4. 4x, + х х, — Зх, + х; 3 —2 -x, + x2 - 3xz x – 7x 3x1

A: Q3 asked and answered.

Q: 36 – x² – y² and S2 be the Let Si be the hemisphere with Cartesian equation z = 6 – upper nappe of…

A: The solution is below.

Q: product = (detA)(detB) an Inner Product? Prove or give a counter-example ning which specific…

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Q: In Exercises 1- 4, apply the Jacobi method to the given system of linear equations, using the…

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Q: ди k = N k > 0

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Q: Solve, 9 7 0 3 0 5 - 9 1 3 -8 5 3 -7 5 7 6 2 6 4 0 1 -1 9

A: We have to solve    753-7862  6101-19×-8 9 7   5 0 3   4 0 5-9 1 3.

Q: sin° (ec) cos" (eF) dc COS

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Q: In deciding whether two graphs are isomorphic or not, one can employ the use of a brute force…

A: Sol

Q: What is the transitive closure of the following graph? a

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Q: Describe the graph of the equation. r = 2 cos t i - 9 sin t j + k O An ellipse in the plane z = 1,…

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Q: Suppose the function g is defined by g(x) = { e-1/x x > 0 0, x 0, g(k) (x) Pk(x) e-1/x, for some…

A: Sol

Q: The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for…

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Q: if x = 2 ; for the if x + 2 uous at x = 2 the valu

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Q: Determine two linearly independent power series solutions centered at x = 0. y" +2x²y'+2xy = 0

A: We determine two linearly independent power series solutions of the given differential equation…

Q: Find T(t) and N(t) at the given point. r(t) = (t2 – 3)i + tj; t = 3 T(3) N(3)

A: Given r(t) = (t2-3)i + tj ; t = 3

Q: Find the 3rd degree interpolating polynomial by Newton's backward formula X f(X) Af(X;) A²f(X;)…

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Q: Draw a tree on 6 vertices where all but one vertex has degree 1.

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Q: z)dr where C is given by r(t) = (sint, cost, sint), 0<t< 2n. %3D

A: Sol

Q: Find the perimeter and area of a trapezoid PQRS if QR = 8ft, P = 45°, S = 10 35°, and with an…

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Q: Draw a bipartite graph with a vertex partition into the two sets {v1, v2, V3, V4} and {v5, v6, v7}…

A: This is a problem of graph theory.

Q: Solve by D operator method dx2 d'y 20 dx +y = x2e3*.

A: We have to find the solution of given differential equations.

Q: * The given matices , verify directly thart (RS)* -5*R* and (E) - p*i* 3 i . R= 3i %3D 1

A: The given matrices are: R=123i4, S=3i70, To prove: (RS)*=S*R*.

Q: Determine the equation of the circle graphed below.

A: We have to find the equation of given circle.

Q: 2. Using the given pairs of x and f(x), construct a an appropriate table (difference or divided…

A: We have to find f(5) and the equation of the polynomial that will fit the given points.

Q: Find an equation of the plane. the plane that passes through (8, 0, -1) and contains the line x = 5…

A: The equation of plane through a point and contains a line

Q: rlog 2 Vex – 1 dx -2 S, x8Vx2 – 1 dx x² x8 dx (a? Loc2)7

A: Sol

Q: 6. Use Laplace transforms to solve the initial value problem, 4t, 0<t<1 y' +2y = f(t), y(0) = 0,…

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Q: Trees Draw a tree on 6 vertices where all but one vertex has degree 1.

A: Given: We have to draw a tree diagram with 6 vertices with 5 vertices of degree 1.

Q: Let 2 -2 and y = Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of…

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Q: Consider the polar curves C2 : r = 4 cos 0 and C3 : r = 4 sin 0. (a) Determine the slope of the…

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Q: 4) Find the eigenvalues and eigenvectors of the given matrix A = =

A: We have given a matrix , A = 5-29-6 First we will find Eigenvalues of matrix. For that , consider ,…

Q: Let a (> 1) be an irrational number. Show that the kth convergent of the simple continued fraction…

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Q: 3. Prove that a flat surface of revolution is part of a plane, cone, or cylinder.

A: prove that a flat surface of revolution is part of plane or cone or cylinder. solution a flat…

Q: he curve y = X fc (vî (yi

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Q: Example 3.37. Solve the equations 2x2 + 3xy + y? = 3, 4x² + 2xy +y = 30 correct to three decimal…

A: Here, We need to use the newton-raphson method. x0 = -3 y0 = 2

Q: John sells decorated eggs on Easter. Each egg costs him $2, and John can sell the decorated eggs for…

A: Given: The cost price of the egg=$2 Selling price=$5 Salvage price=0 Mean=80 standard deviation=12.

Q: Euler Paths and Circuits Use the theorems for Euler paths and circuits to determine if the graphs…

A: The Euler paths or circuits of the given graphs are determined by using theorems as shown below.…

Q: 3. 2х, — х, = 2 3x, + x3 х; 3 — 2 -X, + x, - 3xz | ||

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Q: Reduce the quadratic form x2+y²-9xy into a canonical form of the matrix.

A: The given equation is x2+y2-9xy. The standard equation is ax2+by2+cz2+2fyz+2gzx+2hxy. The…

Q: Solve by D operator method d²y - 2y +y = x²e 3x dy dx2

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Q: For any element z e Z,, let z denote 1 + , so that 2 is 0 when r is 1 and a is 1 when r is zero. Let…

A: We are given the following information. For any element x∈ℤ2, let x¯ denote 1+x, so that x¯ is 0…