2. Prove: "The size of every bipartite graph of order n is at most ". Provide an 4 illustration and explanation to substantiate the proof.

Q: The graph of the function f(x) is (the horizontal axis is x.) Given the differential equation æ'(t) ...

A: Given the graph is 

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A: Rational Numbers: All the numbers which can be written in the form of pq. Here, p and q are integers...

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Q: cos(kr)e¬lz dx, Hint: consider cases for k and I.

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Q: (d) dim ker(A) = dim ker(B). Combine (b) and (c) to show that if A and B are similar matrices, then ...

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Q: 2. Let f : (0, ] → R such that f(z) = r². • Show that f(x) < z. • Show that f has no fixed point on ...

A: Since you have asked multiple questions, we can solve first question for you. If you want other ques...

Q: Given the following Case 2 rational function, 1 f(x) = х- 2 X +4 Simplify the right side of the func...

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Q: For the following Venn diagram, determine the set Bnc. k 10 a 4 11 9 A 15 d 7. 14 6. B. 8 1 12 13 3 ...

A: The intersection of A and B is the set of all those elements which belong to both A and B.  A ∩ B =...

Q: Note : m=0 1. The height of a ball thrown by a child is given by the following formula: x+(4+m) x - ...

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Q: 6 If PL=114, RN=84, and OR= 153, find LM. Round answer to the nearest hundredth. M 88.32 B 69 ©62.59...

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Q: Problem 4: Define f: [0, 1] R by f(x) = 2x if x is irrational and f(x) =-1 if x is rational. Careful...

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Q: Suppose f is a function that satisfies f(2) = 20 and f(2n) +nf(2) = f(2n + 2) for all positive integ...

A: It is given that, f(2)=20      ...(1) and  f(2n)+nf(2)=f(2n+2)     ...(2)   Here 'n' must be a posit...

Q: Using the definition of the derivative 1. find S'(2) if f(x)=x 2. find f" if 2x

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

Q: Identify the law of logic used in the following simplification step: raovqvr vs)=r

A: The main objective is to identify the the law of logic which is used in simplification.

Q: Find z when In z = e – nj

A: Complex number

Q: 4 8. A = -3 -5

A: Solution

Q: Determine whether the series converges. Σ V2k – 1 O The series converges. O The series diverges.

A: Solution: ∑k=1∞12k-13 Definition: If there exists N ≥k so that for all n≥N,f(n)=an is positive, cont...

Q: How many days are there are there in 157 weeks

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Q: 7. Recall the following statement from class: If A and B are similar matrices, then A and B have the...

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Q: Solve the equation for x, give EXACT answers,

A: the given equation is 5+2lnx=4 subtract 4 from both sides 5+2lnx-5=4-52lnx=-1  

Q: (x1 - 2x2- X3 = 2 a3 = -4, Findb3 2a1 2a2 2a3 bị a a1 a2 az b2 a2 %3D et b b2 b3 IC3 + 3b3 C2+3b2 C ...

A: Given, a1b1c1a2b2c2a3b3c3=-4 We have to find  2a32a22a1b3-a3b2-a2b1-a1c3+3b3c2+3b2c1+3b1    

Q: Use any method to determine whether the series converge. 21 (a) ). VR + 1 This series >

A: Since you have asked multiple questions, we can solve first question for you. If you want other ques...

Q: 38 Divided by 3

A: A fraction is a number in the form xy (where x and y are both integers and y≠0). In the above number...

Q: 1. Compute the Lị norm of the following vector: v = Compute the L, norm of the same vector.

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Q: (a) Show that the curvature of a'smooth curve r(t) = f(t)i+g(t)j defined by twice-differentiable fun...

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as...

Q: t the following functions : allest maximum value to ximum value. f(x) = -5a? – 11 5x²

A: In this question, the concept of maxima and minima is applied. Maxima and Minima The extrema of a fu...

Q: If 19(B)| = 128 %3D then |B| = %3D

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Q: diverges, I f it Determine whether the seauence Converges or limit. +(nn) 100 l00 l007+n an= n.+Sn +...

A: We have to check the given sequence is convergent or divergent.

Q: i Let f(x) : r3 and c= 0.01. Find an interval (a, b) containing c such that f(x) > 0 for all x E (a,...

A: Given that f(x) = x3, this is a polynomial function and that's why it is continuous everywhere on th...

Q: Proof by Induction 1 Prove by induction that 1 + 2-3 1 + n(n +1) for all integers n >1. 1.2 n+1

A: We can solve this by induction

Q: A matrix A and an echelon form of A are shown below. Find a basis for Col A and a basis for Nul A. 3...

A: Remark: A basis for the column space ( the space that spanned by the column vectors) of a matrix A i...

Q: F+9 V2x-(4+F) 4. Let f(x) h(x) = Vx + (k +3 + F) and g(x) . Answer VBx -(F+5) 8+K the followings: a....

A: The main objective is to solve all sub parts for F=0 and K =2.

Q: prove that S" erf (x) dx =0

A: To prove the below equation. ∫−aaerfxdx=0

Q: Determine validity using euler circles. No cat is easy to please. All persons who are easy to pleas...

A: Eulers circle is a dramatical representation which tells about the set and its relation. It helps to...

Q: 2. Let p be an odd prime not equal to 5. Prove that either p² – 1 or p? +1 is divisible by 10. 3. Pr...

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Q: Consider the 6 × 8 matrix 3 0 0 0 0 1 2 1 0 0 0 0 1 0 0 -3 4 -7 -9 A = 0 0 0 0 0 0 0 0 0 1 8 1 and l...

A: The main objective is to answer the sub parts by using given matrix which is in reduced row echelon ...

Q: Ms Lewis wishes to have her roast duck ready to serve when she returns home at 6:30 PM. If she allow...

A: Ms. Lewis wants to serve the roasted duck at 6:30 PM.It takes 2 hours and 45 minutes to roast the du...

Q: A matrix A and an echelon form of A are shown below. Find a basis for Col A and a basis for Nul A. 1...

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Q: 2. Solve the diophantine equation x = y'.

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Q: mation to th- correct to thre

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Q: 4. Solve the differential equation by the method of undetermined coefficients. (Section 4.4) у" - 16...

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Q: A bar is insulated at end x =0, and open to the ambient temperature at end x =2L. There is a heat so...

A: The solution to the above question is in the images below.

Q: 3. Suppose that the characteristic polynomial of a square matrix A is fA(^) = –X³ + 3A (a) What is t...

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three subp...

Q: dz

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Q: The variables on a date base have a strong correlation.  What of the following correlations coeffici...

A: The relationship between two variables is generally considered strong when their r value is larger t...

Q: cosh z = cosh 6 has two sets of solutions: 6 + 2nri and a + 2nri where n is an integer. What is the ...

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Q: Q.3 Solve the heat equation: U, =U U (0,1) = 0, U(2,1) = 0, U(x,0) = 3sin 2x - 3sin 3x

A: The given problem is to solve the given heat equation with given initial conditions and boundary con...

Q: QUESTION 2 Suppose that z depends on variables a and b. and a and b depend on variables s and. Find ...

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Q: 7 Express in partial fraction form, hence find the summation of the series, r(r+ 1)(r + 2) 7 Σ r(r+ ...

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