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Q: 2 Let A be a fixed nonempty subset of set X and I= {Bc X | A Z B}. Show that (X,I) %3D is a matroid.

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Q: Exercises &-Find the Chromatic for indeX of each graph and dual graph and Face graph

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Q: sin(r )dt = i

A: We have to evaluate ∫04sin(t2)dt using calculator.

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A: Here we can use the fact that  D+an+1 annihilates xne-axD2+b2n annihilates xnsinbx

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A: Introduction: In mathematics, a function is an expression, rule, or law that specifies a…

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Q: Evaluate the line integral / -ydx + xdy along the curve C : y? = 6x from (6,6) to (0,0). NOTE: Enter…

A: We have to find the line integral ∫C-ydx+xdy along the curve C: y2=6x from (6,6) to (0,0).

Q: lse the definition of Laplace ransforms to find the Loplace cansform of: o st<z hCf) = も22

A: Laplace transform of the function

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Q: For which of the following does there exist a graph having the given properties? Select one: a full…

A: To determine: The graph that exists: (a.) A full binary tree with all 31 terminal vertices at level…

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Q: No graphing utilities. Solve the system using Gauss or Gauss-Jordan elimination method. You must…

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Q: Determine the fitst three nonzero terms in the Taylor polynomial approximation for the given initial…

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Q: Determine the vector field of F. F(x, y) = 8i – 4j 1 1

A: We have given vector F=8i-4j. We have find the vector field.

Q: Find the residue of the following functions: z3 i. f(z) : at z = 1,2,3. (z-1)(z-2)(z-3) 1 2 ii. f(z)…

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Q: 2.f (t) = cosh wt sin wt

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Q: Find the characteristic polynomial and the eigenvalues of the matrix. [:] - 3 - 1 ... The…

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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: If A = yz(^2) i - 3xz(^2) j + 2xyz k , B = 3x i + 4z j - xy k and ∅= xyz , find (a) Ax (∇∅), (b)…

A: Since you posted a question with multiple sub-parts, we will solve first three sub-parts for you. To…

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: Determine whether the function is a linear transformation. T: R2 → R2, T(x, y) = (x, 4)

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Q: Q1. Decide which of the following functions are linear transformation? (i). T : R² → R² defined as,…

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Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

A: Introduction: When we apply force 'F' to a block, the body accelerates or speeds up or down…

Q: a = (5, - 1) and b = (-2, –2). Represent à + b using the head to tail method.

A: This is the problem of vector analysis.

Q: Question 1. Given a metric space . (a) If x, y E X and p(x, y) 0, prove that x = = y. (b) Prove…

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Q: Find the Fourier sine and cosine transform of f (x), if х, 0 2

A: Fourier Cosine transform and Fourier sine transform

Q: a. Find the area of the parallelogram formed by u and v. b. Find the volume of the tetrahedron whose…

A: As per the company rule, we are supposed to solve the first three subparts of a multi-parts problem.…

Q: Suppose a definite integral has lower and upper bounds as follows. 7.006 < < 7.018 If the midpoint…

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Q: r the given data, determine the following.

A: Given, x 100 169 144 32 175 y 80 118 112 32 162

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Q: Use Green's Theorem to evaluate the line integral. | (x - 4y) dx + (x + y) dy C: boundary of the…

A: The given integral is ∫Cx-4y dx+ x+y dy,  where C is the region bounded by x2+y2=1 and  x2+y2=16 To…

Q: What is the chromatic number of a full m-ary tree of height h? Select one: O a. 2 O b. 1 C. h O d. m…

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Q: Solve the following system of linear equations х1 + 2 * ӕ2 + 3 * *з x1 – 3 * x2 + 3 * x3 60 10 || -…

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

A: Here we use python to solve this problem.

Q: Prove that u = e-* sin 2y is harmonic. Find a function vsu f(z) = u + iv is analytic. Also express…

A: The function u=e-xsin2y is harmonic if ∂2u∂x2+∂2u∂y2=0 therefore  ∂u∂x=∂∂xe-xsin2y=-e-xsin2y…

Q: (b) Show that any nonzero element of the ring QIV2 = {a + bv2 | a, b e Q} is invertible, that is,…

A: b)  We have given that ,  ℚ2 = a + b2 / a , b ∈ ℚ We need to show that , for any non-zero element of…

Q: It is estimated that z months from now, the number (in thousands) of out-of-state cars on a ferry…

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

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Q: Let f, g:R R defined by if x 1 (x2 and g(x) = 3x + 2. %3D Find f-1 and g-1.

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Q: Solve the equation (r + sin x - cos x) dr + r(sin x + cos x) dx = 0. %3D Select one: O a. r^2 + r…

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Q: 210 -1 0 1 1 31 Let A = 2.1 Find the eigenvalues of A. 2.2Find bases for the eigenspaces of A.

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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: Real Cheap Car Rental Agency operates agencies in two cities, city 1 and city 2. The fractions of…

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Q: Let U={a,b,c,d,e,f,g,h,k}, A={a,b,c,g}, B={d,e,f,g}, C={a,c,f} and D={f,h,k} 1. Compute: a.) A U B…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

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Q: (5xy --- 6x(2^

A: Given,        F=(5xy-6x2)i+(2y-4x)j and   y=x3 from the point (1, 1) to (2, 8).

Q: 2. Find the cerntroid of the area bounded by the curve y= 2x + 1 x+y =7 and x= 8

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Q: (a) V16x"y 16 (b) Vóx(V6 + (245 - 3) (c)

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Q: Find approximate value of the following integral by using the Simpson method for n = 6. S° 10 sin…

A: I have rounded the final answer upto four decimal places.

Q: (B) = 10 and n(A N B) = 4, what is n(A u

A: n(A U B)=12