For n > 0, let F(n) be the number of strings of length n over an alphabet of size k. Derive a recurrence relation for this function, and then prove that F(n) = k^n using the method of generating functions.

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A: The Gray Code, also known as reflected binary code, is a series of binary number systems. The…

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A: Mass of solid of region D with density function δx,y,z M=∫∫∫Dδx,y,zdV To find z co ordinate we need…

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A: The given equation is sin2θ=6cos2θ. The trigonometry formula is sinθcosθ=tanθ. The value of tan-16…

Q: Solve the differential equation using Laplace Transform method. y’’ - 4y’ + 9y = t, y(0)=0, y’(0)=1

A: The given initial value problem is                                                 y''-4y'+9y=t,…

Q: Solve for the inverse laplace transform of the following functions

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 8. Write the vector (5,6,0) as a linear combination of the vectors (-1,2,0), (3,1,2), (4,–1,0) and…

A: We have to write the vector (5, 6, 0) as a linear combination of the vectors (-1, 2, 0) , (3, 1, 2),…

Q: 4. Expand the following functions into Taylor series at the point indicated and find their radius of…

A: We have to find the Taylor series at the given point.

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Q: n! Investigar la convergencia o divergencia de la serie E n=D1 O Converge por el criterio de la…

A: Given series is ∑n=1∞n!en

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Q: Let 2 (-1)** 'ak be a convergent alternating series with terms that are nonincreasing in magnitude.…

A: We have to find the upper bound for  error.

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Q: re inches of print. The margins at the ach 1- inches wide. d be the dimensions of print so The…

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Q: Prove that If p is prime, p divides k^2 + m^2 and p divides m^2 + x^2, then p divides k^2 + x^2

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Q: For the data (1, 9), (2 ,28), (3, 65), (4, 126), (5, 217) the highest order will be the fourth order…

A: Please post the multiple multiple question separately. Here I answered !st question as per our…

Q: Find the exponential generating function F(x) for the numbers fn of forests on vertex set [n] having…

A: Given below clear explanation

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A: Given matrix is A = 3-2004-3240

Q: a) ] Let W = span{(1, 1, 0), (1, 0, 1), (2, 1, 1), (0, 1,-1)}. i. Is (9,0,9) in W? Justify your…

A: Please post the multiple question separately. Here I answered 1st question as per out policy.

Q: PROBLEM B dx + 9x = 12 WHERE : x(0) = 1 dt

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Q: 2) Write an equation for the curve shown below. Explain what kind of graph it is and what elements…

A: Given Graph is graph of rose curve

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Q: Question or the function given below, write Newton's formula as x+1 F (X,) for solving f(x) 3D0. f)…

A: Given f(x) = -x2 + 2x + 9

Q: (4) $5.11, Suppose X is a subspace of an inner-product space V. Show that X is a subpace of V.

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Q: 3-n (a) - 3n n=1

A: According to guidelines we solve one question.thanku

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Q: An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round…

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Q: 10. On a typographic map, the contour lines show changes in elevation of the land. You and a friend…

A: We will use given contour diagram and corresponding scales to find all relevant data .

Q: 16. Integrate f(x, y, z) = x + Vy – z? over the path from (0, 0, 0) to (1, 1, 1) (see accompanying…

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Q: 3. Let a = b = Find the Span(a, b)? (3)

A: Given a = 23 , b = 04

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Q: Reverse the order of integration and integrate J e* dy dx. (If you can't figure out how to reverse…

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Q: Given: 2a  + 5b + 3c = 2 3a + b - 2c = 3 -a + 2b + c = 1 Instruction: Identify the coefficient…

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Q: a) Write the following statement in symbolic forms (i) If either Pakistan government acts against…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Find Components of the Acceleration For the curve defined by T(t) = (e-t cos(t), e' sin(t)) |3D find…

A: To find- For the curve defined by r→t = e-tcost, et sint, find the unit tangent vector, unit normal…

Q: What times 0.1 equals 11

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Q: 3. a. If f(x) = cos? 0 – 2 sin 8,0 < e < 2n, find where f is increasing, decreasing, intervals of…

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Q: ) Confim by multiplication that x is an eigenvector of A, and find the eigenvalue, b) Detemine the…

A: a) it is given that ;   A = 5-113  and  x = 11.  We have to find the eigen value of A corresponding…

Q: Find the eigenvalues and eigenvectors of: (3 and state whether the matrix is singular or…

A: Hope you like it

Q: The population of one state increases at a rate numerically equal to the cube root of the…

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Q: Let T: R3 → R3 be a linear transformation such that T(1, o, 0) = (4, –1, 2), T(0, 1, 0) = (1, 3,…

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Q: The following logarithmic table is given. f(X)=log(X) 4.0 0.6020599913 1 4.5 0.6532125138 2 5.0…

A: The interpolation polynomial's Lagrange form demonstrates the linear nature of polynomial…

Q: Given the power series expression 00 2 3 A x" + 2 2A x" n = 1 n = 3 1. Force the first power series…

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Q: 8 Two six-sided dice is rolled. What is the probability that the sum of the two dice is AT LEAST 6?…

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Q: 1. Suppose x is an eigenvector of A corresponding to an eigenvalue 1. Show that x is an eigenvector…

A: 1) Let , x be an eigen vector of A corresponding to eigenvalue λ. Thus , we will have ,  A - λIx =…

Q: 1. Solve the initial-boundary value problem ди 2 a?u 0 0 3 dx2 u(0, t) = u (4, t) = 0 t>0 u(x, 0) =…

A: We solve the given problem by method of saperation of variable.  In this method we consider the…