Use the branch and bound method to solve the following IP: max z = x₁ + 2x₂ s.t. x₁ + x₂ = 10 2x₁ + 5x₂ = 30 X1, X2= 0; X1, X2 integer

Q: Let V and V" be vector spaces over a field F and let /:VV be a linear map. Which of the following…

A: 1.   f is bijective if Ker f = 0 .This statement is False , consider the below example.…

Q: If the sequence { 2-4 an an+2 } converges to 7, then the sequence {an} converges to 9. True or…

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Q: Exercise 8.8. Let p be a prime. Prove that ZpZp has exactly p+1 subgroups of order p.

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Q: Question 4. Find L- Note: Here L-¹ stands for Inverse Laplace Transform s²-2s+2 and L−¹ s²-2s+1

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Q: The plot of the vector field F is given below. Place the following line integrals in the correct…

A: 2nd option will right.

Q: Exercise 8.6. Let G be a group. (a) Prove that G = {e} ≈ G. (b) Prove that G/{e} ≈ G. (c) Prove that…

A: 8.6 Let G be a group   (a) To Prove: G⊕e≅G (b) To Prove: G/e≅G (c) To Prove: G×e≅G

Q: Exercise 8.2. (a) Suppose G₁ = (gi) for i = 1, 2, ..., m, |G₁| <∞. Prove that ged(|G₁|, |G₁|) = 1…

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Q: Is W a subspace of the vector space? If not, state why. (Select all that apply.) W is the set of all…

A: Subspace :- If S is a non-empty subset of vector space V, and satisfying following conditions: (1) x…

Q: The binary operation ab=a+b-3ab is defined on Q. Select the correct statements. Select the correct…

A: Introduction: To demonstrate that a group of integers Since I is an abelian group, we must ensure…

Q: Find the Laplace transform of the following periodic function? 0 < t < π π < t < 2π 1- f(t) = { cos…

A: Solution:

Q: : The region D in the x, y plane defined by the inequalities 0 ≤ y ≤4, √√4y-1² ≤x≤ Isas √√16-₁², can…

A: We have use relation between cartesian and polar co ordinate system  x= r cosθ  , y = r sinθAlso…

Q: Consider the set (Z;. x), where x is multiplication mod 9. Which of the following state- ments are…

A: 1st Statement is Wrong :   an element [a] in (Zn*, ×) has an inverse if and only if gcd(a, n) = 1 .…

Q: 9. Prove that nullity(A) = nullity (AT) if and only if A is a square matrix.

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Q: Show directly from definitions that if f(x) and g(x) are real func- tions, bounded on [0,1], and so…

A: Given: fx and gx are real functions, bounded on [0, 1], and limx→0+fx=2 and limx→0+gx=3 We have to…

Q: Let h be a prime number and let k be some integer. What are the possible values of ged(h+k, h-k)?

A: We have given that ,  h be any prime number and k be some integer. We need to find possible values…

Q: Exercise 8.5. (a) Is Z₁ Z6 isomorphic to Z24? (b) Is Z3 Z7 isomorphic to Z21? (c) Is Z10 Z20…

A: 8.5 (a) Is ℤ4⊕ℤ6 is isomorphic to ℤ24? (b) Is ℤ3⊕ℤ7 is isomorphic to ℤ21? (c) Is ℤ10⊕ℤ20 is…

Q: find the missing term 689, 481, 377, 325,299,____

A: Solution:- given that  689, 481, 377, 325, 299,_____ And we want to find out missing term.…

Q: Let S be the portion of the plane 3x + 4y +z = 7 within the solid cylindrical region x² + y2 ≤ 1.…

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Q: C) Use a known series to express f(x)= sin(x²) X as a Taylor series.

A: Given function is f(x)=sin(πx4)x As, we know  sin x = x-x33!+x55!-x77!+…

Q: Let f: R2 R³ be a linear map such that ƒ(1, 2) = (1,1,2), and ƒ(2, 1) = (2,2,1). Then which…

A: We are given that f is a linear map such that f(1,2)=(1,1,2) and f(2,1)=(2,2,1)

Q: dN₁ dt dN₂ dt 5N₁ 1 N₁ 20 N₂ 17 9N₂ 1-- N₂ 20 N₁ 17 1.6- 0.6-

A: This is a question of the equlibrium of the system.

Q: Let B=[u, be a base for V=R², where = (1,2) and =(-1,1). We know that every vector in V is a linear…

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Q: Use the inverse Laplace transform to find the solution to the following initial value problem. No…

A: Introduction: If a function has a finite number of breaks and does not blow up to infinity anywhere,…

Q: Show that the image of the hyperbola x² - y² = 1 is the transiscate p² = cos24.

A: Introduction: An hyperbola is another significant conic section. It has Cartesian as well as polar…

Q: Consider the system T1 = T2 = The eigenvectors are dx dt where x is a 2 x 1 vector. a) Find the…

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Q: Find an equation of the plane. The plane through the origin and the points (2, -1, 5) and (9, 3, 2)

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Q: Apply Power Series to find the general solution of x" + x = 0.

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Q: Which of the following expressions are not valid? Why? (a) [ f* 1(x, y) dy dz [T (c) [[1(x, y) dy de…

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Q: 1. Consider the curve C = C₁ UC2, where C₁ is the line segment from (0, 1.1) to (1,1,0) and C2₂ is…

A: Given: The given curve is C=C1∪C2, where C1 is the line segment from 0,1,1 to 1,1,0 and C2 is the…

Q: Suppose T:R4 R³ is the transformation given below. Determine whether I is one-to-one and/or onto. If…

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Q: The series (k+1)* k=1_p*k! IS a) Converges absolutely b) Conditionally convergent c) Diverges d)…

A: The given series  ∑k=1∞k+1kpkk! is ; a) Converges absolutely b) Conditionally convergent c) Diverges…

Q: Find what "d" equals. Use the above formula to find the distance from the point to the given line.…

A: Introduction: The shortest distance between two points is along a line, and it is the amount of…

Q: Consider the following linear transformation. T(x, y) = (-2x, 2y) Find the standard matrix A for the…

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Q: 1. Calculate the uncertainty of the result of: Show working. (10.1 ± 0.7) (22.6 ± 0.1) x (13.2 ±…

A: We have to calculate uncertainty. Firstly we solve without uncertainty,2ndly we solve uncertainty…

Q: =) Find the remainder of 9045142161 on division by 247 using Euler's Theorem. [Hint: 247 = 13 x 19.]

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Q: 5. (a) Solve the cauchy problem given by x²ux + xyuy + xu = Xx-y where (x, y) + (0,0) if u(x, xln x)…

A: Given x2ux+xyuy+xu=x-y where x,y≠0,0 if ux,xlnx=-lnx, x&gt;0

Q: Find the matrix product ABC by grouping the factors as (AB)C and grouping the factors as A(BC). Show…

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Q: Find the eccentricity e and distance d from the pole to the directrix. I dentify the cenic and…

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Q: Number of voters 5 1st choice C 2nd choice 3rd choice 4th choice 5th choice اداه اوایان Points for…

A: The candidate points are given according to their places on each ballot. Give 1 for last place, 2…

Q: κα Σ (20 + 1) sin2 δι l=0 = = κα κα Elsin de + Σ ( + 1) sin? δι l=0 l=0 ka 1 Σε (sin? δε + sin?…

A: As per the question we are given a partial sum involving sin function and we have to show the given…

Q: Find the matrix A' for T relative to the basis B'. A' = T: R² R², T(x, y) = (x + y, 3y), B' = {(-4,…

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

Q: 1. Consider the curve C = C₁ UC₂, where C₁ is the line segment from (0, 1, 1) to (1,1,0) and C₂ is…

A: Here we have given that the force is, F→x,y,z=ez-y,x-z2,y3 and the curve C=C1∪C2. where C1 is the…

Q: Find n(A) for each of the following sets A: A. {4,5,6,7....15} B. {xI x is a letter in the word…

A: The given sets are  A = {4,5,6,7,8.......15} B = {x| x is a latter in the word Titanic } And we are…

Q: Consider the initial value problem X₁ x(t) = dx 01 dt = (a) Find the eigenvalues and eigenvectors…

A: The main objective is to solve the given IVP.

Q: Which of the following is/are  non-Eulerian graph? a. Graphs B C D ONLY b. Graphs B C D E c.…

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Q: Fourier cosine integral (a) representations : =x² + a² if 0a.

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Q: 2. Use the method of Lagrange multipliers to show that for x, y ≥ 0, we have z"+"> (²+)" 2

A: Introduction: For minimizing a multi-variable function under some certain constraint or constraints,…

Q: The function f is defined as follows: f: R² R² with f(x, y) = (2x, x+y) Which statement is correct?…

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Q: Define a set X by • 4 EX If a E X, then -x-12 € X - x² € X Prove that every element of X is…

A: A Well defined collectipn of object is called set. Define a set X X = { 4, -16 } 4 belongs to X -4…

Q: For each of the following vectors spaces over a field F, provide a basis and compute the resulting…

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