What is the chromatic number of the following graph? (Section 4.4) Alt text: A graph with 4 vertices and edges connecting 3 of them to form a triangle with one additional vertex on the outside of the triangle connected by a single edge. O 2 3 4

Q: 6. Consider the vector field F(x, y, z) e²7 +(x³ + e²) j+ye² k. Find a potential function G(x, y, z)…

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Q: ind an SVD of the indicated matrix. (Enter each matrix in the form [[row 1], [row 2], ...]J, where…

A: To find the SVD.

Q: The following pairs of simple graphs are non-isomorphic. For each pair, give a precise reason why it…

A: Two graphs are called isomorphic if they have a)Equal number of vertices and edges. b)Same degree…

Q: Lety 12 and V₂ Find the distance from y to the subspace W of Rª spanned by v, and v₂. given that the…

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Q: 1. Consider H= (i) and K= (-1) the subgroups of Q, the quaternion group. 1) Explain why H is normal…

A: Basic theory regarding normal subgroups from algebra will be used

Q: The business manager of a company that produces in-ground outdoor spas determines that the cost (in…

A: Average Rate of Change: The formula to calculate the average rate of change of a function f from x1…

Q: Pi

A: Given two graphs. The objective is to prove they are not isomorphic.

Q: Problem 2: Solve the following recurrence equations: a) tn to t₁ = Show your work (all steps: the…

A: We have to find general solution of the given recurrence relation

Q: 5. (CLO3) Prove that (n+3) = ("+²) + (+¹) + () for every positive integer n.

A: We need to prove        n+3C2 = n+2C2 + n+1C1 + nC0    We know, for any positive integer n and k…

Q: Creat a function and sketch with the given features. Two vertical asymptotes at x=3 and x= -4, with…

A: Consider f(x)=(x-1)(x-3)(x+4). This function has two vertical asymptotes at x=3 and x=-4 because the…

Q: 4. Prove the following. a. Let a, b, c € Z with a, b = 0. Prove that if a lc and bc, and ged(a,b)…

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Q: Find the value of the given exponential for the indicated values of the variable. 10t/2 (a) 10/2=…

A: 10t/2   , for t=-2 10-2/2 = 10-1=1/10= 0.110t/2   , for t=-2   10-2/2 = 10-1=1/10= 0.1

Q: 2. Derive the formula for the volume of a cube with side length s V = $³ using the slicing method.

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Q: Let y = and V₂ Find the distance from y to the subspace W of R¹ spanned by v, and v₂. given that the…

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Q: 1.- f_11ine initial valu . Find the general solution to the following differential equation, y" - 4y…

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Q: Give the first stage of elementary matrices for the Given Matrix A. All zeros are established from…

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Q: You have inherited $10,000 just prior to a presidential election and you wish to invest it in solar…

A: On setting the equation, we get…

Q: Solve the following exponential equation. Express the solution set in terms of natural logarithms or…

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Q: prove: for any two sets X and Y, #(X x Y) = #(X) • #(Y)

A: To prove it equals the product of the cardinality of both the sets.

Q: Problem 11. Let Prove that f(x) = Σ k=1 cos(kx) k2 π/2 | Σ f(x)dr = Σ Ο k=0 (-1) k (2k + 1)³*

A: fx=∑k=1∞coskxk2

Q: Element X decays radioactively with a half life of 11 minutes. If there are 370 grams of Element X,…

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Q: 1 13. Find a QR factorization of A = 4 -2 -45

A: We are asked to solve question number 13 only. So we shall solve only that part.

Q: Let F = I curlF. S Use Stokes' Theorem to evaluate curlF.ds, where S is the hemisphere x² + y² + z²…

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Q: What value of μ makes the above system inconsistent?

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Q: Given the force field F, find the work required to move an object on the given orientated curve. F =…

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Q: Suppose F(x, y) = x² + y²j and C is the line segment segment from point P = (-3,-4) to Q = (-3, 1).…

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Q: y' + y = sint t

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Q: Let f(x)=x3-e-x,  x0=0.5 a. Find the Taylor Polynomial, T2(x), of degree at most 2 for f(x)…

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Q: For set S, the notation S' denotes the complement of S. Which set below has the following Venn…

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Q: Identify the y coordinate of the centroid of the shaded area in terms of r₁ r2, and a. a x

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Q: 1, A simple digraph with 4 vertices with in-degrees 0, 1, 2, 2 and out-degrees 0, 1, 1, 3. Is it…

A: A simple digraph with 4 vertices with in-degrees 0, 1, 2, 2 and out-degrees 0, 1, 1, 3. Is it…

Q: f(x) = + [(-1)¹+1] n² + 1 n=1 Write the Fourier Sine expansion of sin(nx). -.7uxx = f(x) 0 0 u(0,t)…

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Q: Given the series: Σ4 (3) does this series converge or diverge? converges diverges If the series…

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Q: Find (2x + 5y)dA where Ris the parallelogram with vertices (0,0), (-5,4), (-2,-1), and (-7,3). Use…

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Q: I encrypted the following with affine cipher c=(7p+11)mod 26 PTATPPTORSSDATP What does it say in…

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Q: Let F = xyi + xyj + xyzk. Find div(F).

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Q: Coffee at temperature 180°F is cooling in a room with constant temperat 75°F. If it takes for the…

A: Initial temperature of Coffee T0 = 180° F  Temperature of surrounding room Ts= 75°F  Temperature…

Q: and question d

A: As per the  question we have to find the constant force of interest that will give rise to the…

Q: Find solution to initial value problem

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Q: y" - 2y' = e³t+cost +6

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Q: the answer of the qustion is correct ? because i think there's a mistake thank you

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Q: A periodic function is defined by < 0, f(t) = { ²²1, 0≤t<1, 2t, -t, f(t+2) = f(t). Let F(t) be the…

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Q: Q 1 The region D above lies between the graphs of y = −5 − (x − 1)² and y = −9+ = (x + 1)³. It can…

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Q: In each of Problems 5 and 6, let po(t) = 0 and use the method of successive approximations to solve…

A: (a) Given differential equation is y' = t y + 1 ,  y(0)=0 .  Take integral from 0 to t , we get  ∫0t…

Q: Solve the following initial value problem. -2 6 dy = ( − ² -1 ) y, -Y dt -2 = (-²) Y, Y(0) =

A: Here we first solve the system using matrix method then use the given initial condition to find the…

Q: Let n E Z. Then 3|(5n² + 1), if and only if 3 X n.

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Q: Describe a method for getting a fair and unbiased simple random sample of 12 people if you have a…

A: Number of people=200We need to describe a method for obtaining a fair and unbiased simple random…

Q: Draw a Venn diagram and shade the given set AU (BNC)

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Q: Question #2. (a) Change the following rectangular coordinates to spherical coordinates (p, 0, 0) (1,…

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Q: 2 If x² - y² = 9, and xy = 3, what is the value of x + y

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