Discrete Math: Q1: a) Find 8 + 32 + 126 + … + 8192.       b) Find 5 + 15 + 45 + · · · + 5·3^20        c) Find 1 − 2/3 + 4/9 − · · · + 2^30 / 3^30 .

Q: Find the B-matrix for the transformation xAx, where B = {b₁,b₂}. -5 -1 2 A = [*] -0 -0 b₁ = b₂ 5 The…

A: Given that the matrices  A=-5-15-1  , b1=-1-1  , b2=21   .

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Q: 7.) Find the area of the region bounded by the graphs of the equation given below. 2 y = (x - 2)²…

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Q: 1. Solve the difference equations and analyze the time paths Yt+22yt+1 + 2y = 1, Yo = 3, V₁ = 4

A: We solve the differential equation and then find the time of path

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Q: 1. Find the derivative of each function. Simplify where possible, using standard notations and only…

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Q: Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise (6x…

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Q: 1 a T What is the chromatic number of the above graph? 4 List the vertices in groups with the same…

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Q: Find the chromatic index of each graph? 2 2 4 3

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Q: Derive a formula for the numerical second derivative (f"(x)) such that your final answer includes…

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Q: Arguing geometrically, find all eigenvectors and eigenvalues of the linear transformation: Scaling…

A: Linear transformation :Scaling by 5 in ℝ3

Q: ) Determine the sign property of the quadratic form Q: R2R given by Q(x, y) = x² + 4xy + y², by (i)…

A: Since you have posted multiple questions so as per guidelines we will the question b for you .To get…

Q: Let the matrix in c². 31 -5 5 Select all that apply. A. =-4+2i; v = c. A=4+2i; v = E. A=2+4i; v = G.…

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Q: Discuss and describe exponential order a. Define and draw graphs to illustrate, etc. Give an example…

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Q: 4. Determine the exact equation of the tangent line to the function y = 3-4 cos at x = IT

A: According to the given data, find the tangent line of a function.

Q: Let G be a connected graph having the following adjacency matrix: Find the order of G. 00 00 86 4 5…

A: Let G be a connected graph having the following adjacency matrix:   0 1  0 0  1  0   1 1  2  1  0

Q: Solve (-2)/(x-1)=(x-8)/(x+1) by cross multiplying. Select the solution (s).

A: (-2)/(x-1) = (x-8)/(x+1)

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Q: 11. Let A -3 = [36]. Find its eigenvalues. 2

A: The matrix is: A=-3621. To Do:We have to find the eigenvalues of the given matrix.

Q: Find an open connected set GCC and two continuous functions f and g defined on G such that f2(z) =…

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Q: What about b,

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Q: Find the area of the part of z = 12-x² - y² between z = 3 and z = 8. =

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Q: For the following function, find dA in terms of x 7m y = 2x¹ 10m dA = (8x³) dr dA = (7-2x¹) dr dA =…

A: We have been given a curve y=2x4. To Do:We have to find dA in terms of x.

Q: ALEKS LTI 1.3 = H Unit 3 Homework 5.2 Question 1 of 10 (1 point) | Question Attempt: 1 of Unlimited…

A: I have explained everything with in the solution .please go through that

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Q: 5. Write a how-many-groups word problem for 5 + 1 = ? and solve your problem with the aid of a math…

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Q: 1. At a local supermarket, Jhudiel bought 3 kilograms of red peppers and 5 kilograms of green…

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Q: Find the inverse of the 45 x 45 matrix 1 23 0 0 1 2 0 1 ⠀⠀⠀ 000 000 ⠀⠀⠀ 44 45 43 44 42 43 1 0 ⠀ 2 1…

A: Find the inverse of the given matrix:

Q: Which number line represents the solution of m+ 3 < 10? A C. O A B OD 5 6 7 8 9 10 11 12 13 14 15 +…

A: The inequality :m+3&lt;10

Q: Quation-1) Investigate the convergence of T Provide reasons! dx -1 + Inx

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Q: Let hn denote the number of ways that a 1×n rectangle can be tiled with red, blue, green, and yellow…

A: Let hndenote the number of ways that a 1×n rectangle can be tiled with red, blue, green, and yellow…

Q: Let S be the surface parametrized by r (u, v) 0 ≤ ≤ 27. What shape is S? a sphere part of a sphere…

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Q: Use the functions f(x) = 2x + 5 and g(x) = 3x² to calculate each operation and simplify, if…

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Q: 5. It is given that two linearly independent solutions of x²y + xy + - y=0, x>0 are -1/2 sina and…

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Q: Evaluate the definite integral. Show all work. You may check your answer by using your So x² dx…

A: The given integral is ∫01x2x3+2dx. We have to solve this integral.

Q: We know that (-1)"42n = 1 − t² + t²¹ - t6 + t8 - n=0 which converges to 1 1+1² **** for t values in…

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Q: A certain experiment produces the data (3,7.5), (4,5.4), and (5,-0.4). Describe the model that…

A: A certain experiment produces the data (3,7.5), (4,5.4), and (5,-0.4). We have to describe the model…

Q: For what values of b does the following set of vectors form a basis? 3 3 {·B·} 12 5 -5 11

A: The given vectors are, 145,3b-5,31211. A set of vectors forms a basis if the matrix is linearly…

Q: ے /sz+25+5)

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Q: could you solve c?

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Q: (T 1) (core) Is the following linear transformation injective? Surjective? (Justify both with full…

A: A given transformation T is injective if kernel(T) = {0} (vector)    Here, T(x, y, z) = (x + 3y, y -…

Q: Prove that: (A) = {1,2,3,6,7,8) and (BC) (AG) = {2,3,6,7). Show each step in your proof.

A: AUB=elements in A or elements in B. A intersection B= common elements in A and B. A©=All the…

Q: 13 3] Let A== -10 Find two different diagonal matrices D and the corresponding matrix S such that A…

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Q: Arguing geometrically, find all eigenvectors and eigenvalues of the linear transformation below.…

A: Find the eigen value and eigen vector of the given linear transformation:Find an eigen basis and…

Q: . Find the inverse Laplace transform L¹. L' s² +6s+9 (s-1)(s-2)(s+4) f

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Q: A particle starts at point (-4, 0), moves along the x-axis to (4, 0), and then travels along…

A: Given that F(x ,y) = xi+(x3+3xy2) j The  work done  on the particle by force field is…

Q: Find the area of the region bounded by the graphs of the given equations. Write the exact answer. Do…

A: Introduction:The area between two curves can be determined by computing the difference between the…