Let G be a graph with n ≥ 3 vertices that has a clique of size n − 2 but no cliques of size n − 1. Prove that G has two distinct independent sets of size 2. Show your work and complete proof.

Q: Let E be the 3 x 3 matrix that corresponds to the row operation R3 = R3+3R₁. (a) Find E-¹. (b) Find…

A:

Q: from A to B. B 2 z dx + 2ydy + 2xz dz A Let M = z², N = 2y, and P = 2xz. Apply the Test for…

A: Integral

Q: f(x) = √²+36

A: A function is concave (or concave downward) on an interval (a, b) if f"(x)<0 for all x in (a,…

Q: Please help me with the questions below. In a tidal river, the time between high tide and low tide…

A: Given information:The time between high tide and low tide is .Depth at high tide is , and at low…

Q: Given the three basic functions: /(x) = sin x f(x) = log* f(x) = 2^* Determine how and which of the…

A:

Q: Evaluate 5⁰⁰ x dx. -∞ x sin 2x x²+3 0

A:

Q: Q6: ) Suppose (X, 7) is aftopological space, and p a point not in X. Let Q = {UU {p}, UET, and X-U…

A: Let's go through the two parts of the question:a) To show that T=Q∪T is a topology on Y=X∪{p}, need…

Q: on ) Consider the topology r = {GCR:0€ Gor G=0} o R. Is [0, 1) compact in (R, 7)? Explain why.

A: Given, topology  on defined by, Consider the open cover of  in Since, is open set in  for every…

Q: The limit is equal to 0 ∞ -3 O 3 lim x→0 St³+27 dt X

A:

Q: In Problems 7, 8, 9, and 10 the independent variable x is missing in the given differential…

A:

Q: Swell Productions is sponsoring an outdoor conclave for owners of collectible and classic Fords. The…

A: Given information:Swell Productions is sponsoring an outdoor conclave for owners of collectible and…

Q: that the amounts of time (in minutes) required for assembling the frames, installing the wheels, and…

A: Given information:Time required for assembling frames, installing wheels, and decorating for…

Q: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

Q: Find the Jordan decomposition of the following matrix 000 0

A:

Q: #8. Uses Stokes's Theorem to evaluate ff curl F n ds where S is the paraboloid z = x² + y², z≤ 9 and…

A:

Q: Given that g(x) + 7x sin(g(x)) = 35x² + 24x − 35 and g( ² ) = 0, find g'( ² ). g ( ½¾7 ) =

A:

Q: I can't follow any of the writing.  Some of it is dim, and some doesn't make sense: In the problem,…

A: One must not assume f(c)= 0.But If one assumes that , then the claim "" is true.

Q: can both parts be written on paper please, if you can only do one then let it be part

A:

Q: Q(x₁, x2, x3) = x² + x² + x² + 4x₁x2 − 2x13 subject to x1+x2+x3 = 0 and -x₁+x2+x3 = 0, Q(x, y, z) =…

A: To determine the definiteness of the quadratic forms subject to the given constraints, we can use…

Q: Note that you must answer all parts of this problem to receive any credit. [41] 21 H [₁]. Is w a…

A:

Q: Suppose a subspace is spanned by the set of vectors shown. Find a basis for the subspace, using the…

A:

Q: Given the three basic functions: /(x) = sin x f(x) = log* f(x) = 2^* Determine how and which of the…

A:

Q: 2 Arc Length (#integration, #composition) We have seen that integrals can be used to compute the…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Which of the following functions from Z → R are partial functions, rather than total functions?…

A:

Q: A company periodically produces a part that is a basic component of an assembled product. Each fixed…

A:

Q: 5. The average number of students per computer in public schools is given in the table. Year 1 is…

A:

Q: P.) Consider the topology 7 = {GCR:0 EG or G=0} or on R. Is [0, 1) compact in (R, 7)? Explain why.

A: Given, topology  on defined by, Consider the open cover of  in (Since,  is open set in  for every…

Q: Determine how and which of the functions above should be added, multiplied, divided or composed to…

A: f(x)=sinx,f(x)=logx and f(x)=2xdetermine  how and which of the functions should be added,…

Q: Problem: G Let's verify that gravity is conservative (F is just a force field) and then find the…

A:

Q: Using contour integration, evaluate the following integral •2πT 1 4+3 cos 0 de

A:

Q: 1. is this given problem belowe com be considered as lineau programmning? If not, convert or Find an…

A: The objective of the question is to determine whether the given problem can be considered as a…

Q: Find a basis of the given subspace by deleting linearly dependent vectors. -19 {[][]} 10 S = span of…

A:

Q: Use the limit comparison test to determine whether (a) Choose a series bn with terms of the form bn…

A: Given sqence is Here

Q: per month, where t is time in months and S(t) is the number of computers sold each month. 2 3 S'(t)…

A:

Q: Problem: For the following ODE, find the general solution, y = y + y using methods from Chapter 8…

A:

Q: x"(t) + 2x(t) − y'(t) = 2t +5 x' (t) − x(t) + y' (t) + y(t) = −2t −1 when : x(0) = 3, x'(0) = 0,…

A: “Since you have posted multiple questions, we will provide the solution only to the firstquestion as…

Q: Let I:= [a, b] and let f: I -> R be a continuous wetion such that f(x) >0 for each x iN I. Prove…

A:

Q: GIVEN: A E M(3,3), a € R. -1) -6 0 2 -4 -2 (a + 6)) Find all values of a so that A¹ does not exist…

A:

Q: The system of first order differential equations 3/₁ = − 4y1 + 5y2 +1 y2 = 5y1 - 4y2 + 1 where y₁…

A: Given system of first order differential equations is y'1 = - 4y1 + 5y2 + 1y'2 = 5y1 - 4y2 + 1With…

Q: Let I:= [a,b] and let f: I - IR be a continuous functioN ON I such that for each X IN I there exists…

A:

Q: A2. Use Bordered Hessians to determine the sign properties (definiteness) of the following con-…

A: To determine the definiteness of the quadratic forms subject to the given constraints, we can use…

Q: J cos(y + x) dA, Problem 6. Use a change of variables to evaluate where P is the parallelogram…

A:

Q: Follow the steps below to solve the given differential equation using series methods. Assuming the…

A: By using  , we will find the series solution of the given differential equation.

Q: Determine the potential function for the region inside. a rectangular trough of in finite length…

A: The potential function V(x,y) satisfies the Laplace equation,Vxx+Vyy=0,      0≤x≤b , 0≤y≤aFrom the…

Q: Let A = {1, 3, 5, 6, 7, 9, 10, 12} and B = {1, 2, 3, 5, 7, 8, 9, 11, 12}. Consider the following…

A: Given a function f: A -> B , we have to determine whether it is injection, surjection,…

Q: Let q be demand for product A and suppose that QAQA (PA-PB), so that q, is the quantity of A…

A:

Q: Graph the curve described by the following function, indicating the positive orientation. r(t) = 7e…

A: We will find out all the components of the vector r(t) from the initial t=0 and final tGiven…

Q: (10) t=3 mo A t=4 mo B t=1 mo (30) (20) (40) D F t=3 mo C E t-3 mo t=3 mo (50

A:

Q: -9 Using only a simple calculator, find the values of k such that det(M) = 0, where M = 1 your…

A:

Q: You are reviewing data collected on TV sales in three different branches of your electrical retailer…

A: We have three sites, each with their own data on 'Data Collection Time' and 'TV Sales'.Specifically…