in a graph What is a k-coloring ? And give examples

Q: a non-planar graph that is not homeomorphic to K5or K3,3.

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Q: Compute the trigonometric functions of the complex numbers cos(5+ j8) tanh( 0 – j8)

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Q: The line of best fit to the data (2, 2), (0, 1), (1, 2) is y = 1/x + 7. The least squares error is…

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Q: برهن على صحة التكاملات التالية : fx²J, (x) dx = x²3, (X) + x1(x)-[Jux) dx J, [x*J₁ (x) dx = x* J,…

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Q: ) Solve by using Laplace transform the partial differential equation a²y 8² 9. dt2 Ox² y(0,t)= 0,…

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Q: TASK 2: Prove that if G is a group and a, b = G, then (1) o(a¹ba) = o(b) o(ab) = o(ba)

A: These two results follow by proving G is abelian. We present the detailed solution in the next step.…

Q: Consider the sequence of functions {fn}nen, where nx fn(z) = Va € [1, 10]. 1+ nx' (a) Find the…

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Q: Summary of what is Mathematics in modern world about

A: Mathematics is the science that deals with the logic of shape, quantity and arrangement. Math is all…

Q: 7/ Find the optimal solution of the following (T.P) by using Least-Cost method. 6 40 50 70 90 90 100…

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Q: Q2/ The region bounded by the curve y = x² and the line y = 3x, in the first quadrant is revolved…

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Q: Show that the following equation is exact and solve it: (2y sin x cos x - y + 2y² exy²) dx - (x -…

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Q: Use Laplace transform to solve the partial differential equation: d²u du du(x,0) = , t> 0, 0<x<1,…

A: Solution

Q: Use Laplace transform to solve the partial differential equation: o'y dy = ox² dt +xt where y(x,0) =…

A: Solution

Q: For each of the following, find the number of shortest lattice paths from (3, 3) to (15, 15) which:…

A: Introduction: A lattice is a pattern composed of repeating points. A square lattice in two…

Q: Ex. 15. Transform Bessel's equation d²ydy + x². dx² +x+(x²-n²)y=0 by substitution x=- : 1102 at 2 dx…

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Q: Hiwo- solve the hyperblic partial differential equation numericaly where d²u d²u dx² = with initial…

A: Given  ∂2u∂x2=∂2u∂t2 The wave equation is ∂2u∂t2=c2∂2u∂x2 So c2=1 The difference for the given…

Q: Question 4: Plot the function y 3x³-26x+10, and its first and second derivatives, for all in the…

A: y=3x3-26x+10 -2≤x≤4

Q: u)n(p+u°О

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Q: GROUP holds four properties simultaneously: i) Closure, ii) Associative, iii) Identity element; and…

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Q: Let I (a, b) be a bounded open interval and f: 1 2 be a monotone increasing function on I. (i) If f…

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Q: Use the Crank-Nicolson method with h = 0.1 and k = 0.01 to approximate the solution to the problem…

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Q: Solve the following system of equations by Gauss-Jordan in terms of k, then find the values of k for…

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Q: Evaluate So ·∙log 1+ax 1-ax (: ( dx x√√1-x²

A: A very good problem. This problem illustrates the power of differentiating under the integral sign.…

Q: Convert point (-8,8,-7) from Cartesian coordinates to cylindrical coordinates. Hint: r² = x² + y²…

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Q: In a day, Julia can produce 12 bushels of wheat or 4 pounds of meat while Carlos can produce 10…

A: For the given question, we can simplify the problem by making a table,   Wheat O.C. (Wheat) Meat…

Q: A + ՏԵ + - 2 1}}=?

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Q: Please answer II only. THANKS!

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Q: Let A be a 7 × 4 matrix with independent columns, and let b = null(AT). How many least squares…

A: Introduction: The least squares technique is a sort of mathematical regression evaluation that…

Q: Use Laplace transform to solve the partial differential equation: d'y dy ox² ôt -+xt where y(x,0) =…

A: Introduction: Like other transforms, the Laplace transform converts one signal into another using a…

Q: If the function of is odd function (i.e. f(-x) = - f cx)) then, the Fourier transform of f(x) is…

A: Introduction: The Fourier Transform may be used to deal with preliminary boundary cost problems at…

Q: 1.a) Apply the Trapezoid and Corrected Trapezoid Rule, with h=, to approximate the integral ₁³e-2x²…

A: 1. a) Consider the given integral, I=∫13e-2x2dx, with h=18. The trapezoid rule states that,…

Q: 1. One algorithm for polynomial evaluation is the straight term-by-term evaluation which follows the…

A: Let's assume the polynomial to be of the form  P(x)=a1x5-a2x4+a3x3-a4x2+a5x-a6 If we take into…

Q: ide a detailed solution. Us

A: Given,       f(x)=xe-x-sin2x

Q: (a) Consider the feasible region in R² shown below (the red shaded region). 10 x+y=8 x+y=2 -3x - y =…

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Q: Let What is the rank of AT A? Answer: A 3 0 0 0 0 0 5 11 −4 0 3 6 5 2 0 0 3 6 2 0 0 0 8 0 0 00 0 0

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Q: 7) Solve the system x=(6₁ -24 x 12 subject to the initial condition x(0)=(:).

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Q: Use Laplace transform to solve the partial differential equation: o²y_by -+xt where y(x,0) = 0,…

A: Solution

Q: Given: f(x, y) = xy + 8; R is bounded by y = x7.5 and y = 7.5x Question: What is the average…

A: The region bounded by  y = x7.5   and  y = 7.5x is shown

Q: @ Fs [ f ² (x)] = √ √ √ # Pfco) - P² Fs {f(x)] proof: How.

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Q: By using Laplace transform to solve y + y = sinht with y (0) = -1, what would the particular…

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Q: Use Laplace transform to solve the partial differential equation: dy dy +xt where y(x,0)= 0,…

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Q: ax xe 1-e-bx let a, b 0 define f: x- show that r+∞ S f(x) dx = +∞ n=0 (a+nb)²

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Q: Q2/ Find ow/or if w = (x+y+z)³, x=r-s, y = cos(rs), z = sin(r + s) at the point (r, s) = (0,1)

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Q: 10. Prove that T/2 75/2. sin e cos (cos a cosec 0) de 10 T 2 (1-cos a).

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Q: 6. Let f(n)= o(n)/n. (a) Show that if p is prime, then f(p) = f(p). (b) Find all n such that f(n) =…

A: Introduction: Euler's Totient function is a mathematical multiplicative function that counts the…

Q: 1. Find the adjacency matrix of each graph Matrix A= [?] 1/2 Matrix B= [? ] V/₂

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Q: Use Laplace transform to solve the partial differential equation: d'y dy +xt where y(x,0) = 0,…

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Q: If Sue eats 1/8 of a large cake, and Bill eats 2/4 of a small cake, who eats more cake?

A: Let large cake = 1 pound       Small cake = 1/2 pound Sue eats 1/8 of large cake. Bill eats 2/4 of a…

Q: show that, 8 = 1², when € IR³ we have x 1x)=870

A: Please five the answer in next step.

Q: You have 14 presents to give to your 3 kids. How many ways can this be done if: a. The presents are…

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