Problem 3. For the graphs below, determine the minium number of colors nccessary to color them. Give an appropriate coloring (use numbers 1, 2, 3.... for colors) and prove that there is no coloring with fewer colors. (Hint: identify subgraphs for which the number of colors is easy to determine.)

Q: using calculus Find the center of mass of the region bounded by the following functions. (a) y = 0,…

A: The region bounded by the curves, a) y=0, x=0, y=ln x and x=e. b) y=2x and y=x c) y=sin x, y=cos x,…

Q: Consider the system: x+2y+3z=6 2x + 5y +3z=7 x + 8z = 14 a. Write the system as a matrix equation in…

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Q: uu, + x-y x + y uu, = x² + y² x + y

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Q: B. Using MODULO OPERATOR, where k = 7 6. Rene Descartes 7. Mathematics in the Modern World 8. Rise…

A: To encrypt: The given messages by shift cipher using Modulo Operator, where k=7. (6.) Rene Descartes…

Q: 8.23 Show that the expression for the variance of a random variable can be expressed in terms of the…

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Q: Expand f(x) = cos 0 < x < π, in 3. a Fourier sine series. In addition, indicate when the Fourier…

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Q: 3- Find the charge q(t) on the capacitor of the series LRC circuit, when: L = 0.25, R = 10, C =…

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Q: 9. The number of particles emitted from a source of radioactivity during a specified period is a…

A: Probability is the occurrence of an event. Probability is defined by the ratio of a number of…

Q: The principal represents an amount of money deposited in a savings account subject to compound…

A: Given: Principal amount (P) = $8000; Rate percentage (r) = 8% semiannually; Compounded Time t = 2…

Q: [1 2. (a) Find the eigenvalues and eigenvectors of B = (b) Explain why the matrix A cannot be…

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Q: The principal P is borrowed and the​ loan's future value A at time t is given. Determine the​ loan's…

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Q: intercepts f(x)=x√g-x² relative minimum relative maximum O (x, y) = (x, y) = -6 (x, y). (x, y) =…

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Q: fy y³dx - x³dy, where C is the boundary of the region between the circles x² + y² = C Evaluate 2 and…

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Q: (+*+ ² + 2) = (0)4 -

A: Inverse Laplace transform of a function Fs is a piecewise continuous function ft with the following…

Q: Solve the following linear program using the simplex method: 7x₁ + 8x2 4x1 + x2 ≤ 100 (a) (b) (c)…

A: Given: (a) maximize: 7x1+8x2subject to:4x1+x2≤100x1+x2≤80x1≤40x1 and x2≥0 (b) minimize:…

Q: 2. [Falkner Section 11 Exercise 17 - modified] Let f: [1, ∞) → R xx-1. (a) Show that Rng(ƒ) ≤ [0,…

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Q: The graph of a function is given. Graph the inverse function.

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Q: Each week, of people who wear home-made masks switch to store-bought masks, while the other stick…

A: To find the matrix P and D for the given distribution matrix.

Q: Prove that S = {e²kk € Z is a subgroup of G.

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Q: You are putting 10% down on a car that cost $24,350. How much are you putting down?

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Q: Each of the following problems can be solved by finding either the chromatic number of a graph or…

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Q: [Green's Theorem] Practice using Green's Theorem by calculating the following line integrals; we can…

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Q: A population of birds and insects is modelled by the equations dx/dt = 0.4x (1 - .000005x) - .002xy…

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Q: Find the characteristic equation det(A - XI) = 0 for the matrix A Hint: You equation should equal 56…

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Q: K A committee of 4 students is to be selected from 11 students in a fraternity. a. In how many ways…

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Q: Evaluate the flux integral [F•dS = [[F•ñdS where F(x,y,z) = ( − y,x, 3z) and S S the portion of the…

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Q: Suppose you roll a special 46-sided die. What is the probability that the number rolled is a "1" OR…

A: Given that ,you roll a special 46-sided die.

Q: Compute the "best fit" plane containing the following points: (4, 0, -2) (2, 1, -3) (-3, 1, 4)…

A: To find the best fit plane that for the points 4,0,-2,2,1,-3,-3,1,4,-2.9,0.9,4.1To find the normal…

Q: Find the volume of the given solid. Under the surface z = 1 + x²y² and above the region enclosed by…

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Q: A population increases according to P(t) = 280(1.07) where t is the time in years since 2000 (a)…

A: Given population function pt=2801.07t  where t is the time in years since 2000.

Q: → ·L.F. ♬ · dr where F(x, y, z) = (1.75yz cos(xyz), 1.75xz cos(xyz), 1.75xy cos(xyz)) and C с…

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Q: Consider the Cobb-Douglas model for a certain manufacturing plant, W = 60H0.610.4 where W is the…

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Q: Solve the difference equation 16yk+2 +8yk+1+Yk = 6 - 5k, Yo = 2, Y₁ = 3

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Q: Given -2 -5 1 3 80 3 -5 1 5 11 -19 7 1 7 -13 4 -3 (a) Find orthonormal basis for the column space. 1

A: “Since you have asked multiple questions, we will solve the first question for you.If you want any…

Q: Does the function 5 3-x f(x)= have a vertical asymptote at x = 3? Why or why not? (Completing a…

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Q: The numbers of domestic and international flights for three airlines for the year 2012 are given in…

A: To find the probability for the domestic flight operated by B.

Q: Use Newton's method to approximate a root of the equation e = 4 + x correct to eight decimal places.…

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Q: At the beginning of 2007, the population of a certain state was 55.4% rural and 44.6% urban. Based…

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Q: If the birth rate of a population is b(t) = 2000e0.021t people per year and the death rate is d(t)=…

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Q: In a game of cornhole, Sarah tossed a beanbag and it landed at the edge of the hole. The hole can be…

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Q: 14. Solve for x. X4-9x² =0. * O A. {0, 2, -3} B. {0, -2, -3) C{0, 3, -3} D. {0, 3, -2)

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Q: The principal represents an amount of money deposited in a savings account subject to compound…

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Q: Compute the flux of the vector field (x², - xy5), out of the rectangle with vertices (0,0), (3,0),…

A: Given the vector field x2, -xy5, out of the rectangle with vertices (0, 0), (3, 0), (3, 2) and (0,…

Q: second and thrid answer are incorrect

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Q: [25 -14] 42-24 Find a matrix S, a diagonal matrix D and S-1 such that A = SDS-¹ Let A = S = D= S-1

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Q: 4. Consider the linear transformation Qm: R² → R² that reflects a vector over the line y = mx. [H].…

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Q: 4. A bead of mass 0.1kg is bound to a linear track which connects the points (1,2,3) and (-1,2,4).…

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Q: A Leslie matrix is given below. [2.8 3 0.4 0 0 0 3 2 0 0 0.5 0 0 0.7 0 (a) There are (b) age groups…

A: Given: Leslie matrix as ,  2.83320.400000.500000.70To do:  (a) There are __ age groups of…

Q: 1 Find the eigenvalues and eigenbases of the matrix A = 0 0 -21 0 0 0 4

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Q: Use the method of partial fractions to find the inverse transforms of the functions: 2. F(S) = Find…

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