5. Use element proof to show that for any sets A and B, if A ≤ B then A U B = B. 6. Construct an algebraic proof for the given statement. For all sets A, and B, (AUB) - B = A - B.

Q: 18. Apply the method of reduction of order to find a second solution of the given differential…

A:

Q: Determine the Fourier integral representation of the following: f(t) = {6, 0 < t < 1 elsewhere A. B.…

A:

Q: Let fn(x) = nxe-n, for x = [0, 1]. (a) Show that for each x € [0, 1] we have fn(x) converges to 0.…

A:

Q: 23. Apply the method of reduction of order to find a second solution of the given differential…

A:

Q: The average height of water in a harbour is 5 m. At low tide, the water height is 3 m. The tide…

A:

Q: Find the solution of the given differential equation using the method of undetermined coefficients.…

A:

Q: Solve the following LPP using Two Phase Method. Max P = 4x1 + 7x2 Subject to 2x1 + x2 > 2 x1 + 3x2 ≥…

A: Given LPP is max P=4x1+7x2subject to2x1+3x2≥2x1+3x2≥3x1+x2≤4x1, x2≥0 Phase 1: The given problem is…

Q: Solve the following: (Show all details) III. Find the determinants of the following matrices using…

A: 1. Consider matrix A=90-7-32-1241 Now,  R3↔R1Factor=-1 A=241-32-190-7

Q: Given the following periodic function, f(t), find the Fourier series coefficient, ao, where a = =…

A:

Q: 10-1

A:

Q: (x + y) dx + (3x + 3y − 4) dy = 0 -

A:

Q: Consider the following. C: counterclockwise around the circle  x2 + y2 = 49  from  (7, 0) to (−7, 0)…

A: Given,   C: Counterclockwise around the circle            x2+y2=49       from (-7, 0), and (7, 0).…

Q: Find the general solution of the system of equations x': ( 2 0 Eigenvalues=₁^₂=2, ^3=2 Eigenvectors…

A: given system of differential equation x'=11121-10-11x which is of the form x'=Ax where A=11121-10-11…

Q: Determine the forces in members BC, BE, and BF. The triangles are isosceles. The forces are positive…

A: Suppose, AG=AF=BF=EC=x In triangle AGA', AA'AG=sin63°AA'=AGsin63°AA'=xsin63° and,…

Q: Use the Laplace transform to solve the given initial-value problem. y' +4y=e-4t, y(0) = 2 y(t) = 4t…

A:

Q: Find the solution of the given initial value problem. y(4) +22y"" + 183y" +682y' +962y = 0; y(0) =…

A:

Q: If a 20-meter flagpole casts a shadow that is 40 meters long, how long is the shadow cast by a tree…

A:

Q: Question 3 This is similar to the previous problem, but you will double the number of trapezoids…

A: We have to find the solution.

Q: Find the general solution in terms of real functions. From the roots of the characteristic equation,…

A: Below given clear explanation

Q: Use the method of variation of parameters to find a particular solution of the differential equation…

A:

Q: Find a unit normal vector to the surface x² + 3y +z³ = 147 at the point (5, − 1, 5). O O O 1 √2,636…

A:

Q: = 11. Consider the matrix equation X5 : I2, where I2 is the 2 × 2 identity matrix. Over each of the…

A:

Q: ✓ )² + y² = 4 In polar coordinates we have x² + y² = 2² and x = rcos(8), so the boundary circle…

A:

Q: - Solve the initial value problem 25y" − 40y' + 16y = 0, y(0) = 2, y'(0) = 3. Choose one Decreasing…

A:

Q: (5x+24 (2x + 8 A) Let g(x)=x² x<-3 -3<x<4 x ≥ 4 a) lim g(x), lim g(x) x-3 x→0 evaluate the following…

A:

Q: (a) For all n N and a # 0, show that ak an k=1 (b) For a sequence (xn) in R, suppose that there…

A:

Q: Find a differential equation whose general solution is 6t y = c₁et + c₂e -3t = 0

A: We find a differential equation whose general solution is y=c1e6t+c2e-3t.

Q: . Find the solution of the given differential equation using the method of undetermined…

A:

Q: 7. Given 8 = 56.78°, u = (-3, 2, -1), v = (2, 3, 4) and ||w|| = √17, find ||lu|| a) b) u. W

A:

Q: 6. Evaluate the following real integrals by residue theorem 3 •S= B Sin H соz mx (x²+9²)(x²7b²) .dx…

A:

Q: h of the following statements correctly describes the waveform corresponding to this frequency…

A: we have to define the given graph.

Q: Manually use Newton-Raphson iterative technique with 6 iterations to find a root of vr(t) in the…

A: Given function is v(t)=0.250t4+0.166t3-0.500t2 In interval [0.3; 0.7] Here v(0.3)=-0.0385&lt;0…

Q: x = 7u + 2v y = 7v -0.5 y 8 1.5 (0,0) 2 1.0 (2,7) 0.5 R (0, 1) S (0,0) (7,0) 4 0.5 (1,0) 1.0 6 1.5 u…

A:

Q: 6. Evaluate the following real integrals by residue theorem 3 & •S= Sin H соз mx ~ (x²+a ²) (x²+ b²)…

A:

Q: ABCDV is a solid glass pyramid. The base of the pyramid is a square of side 3.2 cm. The vertical…

A: Since you have asked a question with multiple subparts, we will solve the first three sub parts for…

Q: Identify the type of solution for each problem and solve for the general solution. Choose the most…

A:

Q: Explain why the function f(x) = 2 ln x − x attains an absolute maximum and absolute minimum on [1,…

A: Here first we have to find the critical points of the function on given interval by solving f'(x)=0…

Q: 17. Given 2x+4 — 2x+3 = 1, find x.

A:

Q: (a) Find the general solution in terms of real functions. (b) From the roots of the characteristic…

A:

Q: uppose two circles intersect at A and B. Let P be point on one circle, let PA intersect the second…

A: We have show that the length of CD is independent of the location of P from given picture.

Q: 13. In finding a smooth piecewise parametrization of path C, A. the direction of the sub-paths must…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: . Consider the following problem max 10 (1-s)√kdt s.a. k= s√k k(0) 1, k(10) libre, s(t) = [0, 1], Vt…

A: As per the question we are given a constrained optimization (maximization) problem. And we have to…

Q: The matrix below shows when communication exists between people in the group Alex, Beth, Chen and…

A:

Q: Suppose T: M2,2→P3 is a linear transformation. Let A, B, and C be the matrices given below, and…

A: Suppose T:M2,2→P3 is a linear transformation. Let A, B and C be the matrices given below, and…

Q: Explain the solution to prove the questions validity

A:

Q: Z-1 Let f(z) = 23C with R>2, and I = If(z)| ≤ be the upper half circle |z| = R in the…

A: Given function is fz=z−12z3+3 and CR be the upper half circle z=R in the counter clock wise…

Q: A solid consists of a pyramid with a slant height of 39 cmn attached to a cuboid with absquare base…

A: Given: A solid consists of a pyramid with a slant height of 39 cm attached to a cuboid with a square…

Q: Example 40 Each of the following four matrix equations represents a system of simultaneous linear…

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

Q: 14- Establish the identity €iksemps = Sim Skp - бір бкт by showing that each side of the equation is…

A:

Q: dx Q3: : Find the area of the region D bounded by y = x, y = √x, y = 1 and y = 2. Using double…

A: 3. Given region D is bounded by y=x,  y=x,  y=1, and y=2   To Use: double integral to find the area…