Suppose A and B are both countably infinite sets. Show that the union of A and B is also countably infinite by displaying a one-to- one, onto function f: N→ (AUB).

Q: The Bernoulli's form of the differential equation x³ydx + (3x¹ − y³ )dy = 0 is

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Q: Suppose that z = x³y²2, where both x and y are changing with time. At a certain instant when x = 1…

A: The product rule of differentiation states that ddtfg=fdgdt+gdfdt. The power rule of differentiation…

Q: A simplified version of input-output analysis of a national economy has the following input-output…

A: Let A be the given matrix A=0.2450.1020.0510.0990.2910.2790.4330.3720.011 Let X=AMH where H= 1 unit…

Q: SOLVE FOR THE LAPLACE TRANSFORM OF THE GIVEN EQUATION. Jell 2. f(t) = cosh wt sin wt

A: The function cosh(ωt) can be rewritten as eωt+e-ωt2. Thus, ft=cosh(ωt)sin(ωt) can be rewritten as…

Q: An observer is located at 60 degrees North latitude and wants to know the highest something with a…

A: Given,Latitude of the observer=60 degrees (North)Declination= -20 degrees  To find: Maximum altitude…

Q: Problem 5 Let A = {m+n√2: m, n e Z}. Prove A is countable.

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Q: Let the set H be the union of the line segments from (1, 1) to (1,3), from (1, 2) to (2, 2), and…

A: Given that H be the union of the line segments from A1,1 to B1,3,from C1,2 to D2,2, and from D2,2 to…

Q: Suppose that the point P can be placed anywhere on the line segment AB in order to change the angle…

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Q: Consider the system of equations: (a +1)x+ (2c-4)z = 2 -2by +z = 0 (-a - 1)x+ (1 - c)z = 1 Determine…

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Q: LA Find lim ujs (Ад 10ex csch x

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Q: Determine the Laplace Transform of the following functions. Show your detailed solutions. 3.…

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Q: 9. Which figure comes next in the series? 000 do A ● o ● 6 ● 103 B C ● 9 ●●● D

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Q: - Find the laplace transform of the 1VP: y''' — 4y = et + t, y = y'(0) = y"(0) = 0 Find the lanlace…

A: Laplace transform of the given differential equation

Q: TL (s+ π)²· 2 L-¹ {

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Q: Use Green's Theorem to evaluate the line integral. J. 2xy dx + (x + y) dy C: boundary of the region…

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Q: 50 Evaluate Σ j=1 1 j+1

A: Series and it's value

Q: Let x ∈ R ^n and r > 0. Is the set B(x, r) = {y ∈ R^ n : ||y − x|| ≤ r} a closed set in R ^n? Y/N

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Q: 1 defined on R {0}. Find the points of relative extrema of f and the and those on which f is…

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Q: 4c) Given the following 2₁= Beis (-30°) and 22= Scis 60 sur Gols Z3 = 2√3 - 21. Find 2,² x 72

A: Given  z1=3cis-30°z2=5cis60°z3=23-2i We will find z12×z2

Q: 3. Let What is (CA) U B? (a) {x € Z] x % 4 = 2} \ {10} (b) {x€N | x % 4 = 2} \ {10} (c) {x€N |…

A: Using the way in which the sets are defined we solve the problem. The typeset solution in latex is…

Q: Maximize the function p = -x+y over the following constraints: a) x+y>=4, x>=0, y>=0, -x+2y<=2,…

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Q: a. Show that if a, b, c, de Zwith a +b√2 = c+d√2, then a = c and b=d. You may use, without proof,…

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Q: y Consider the surface of equation z = X+Y² What is the equation for the tangent line to S at the…

A: This is a problem of vector calculus.

Q: In Exercises 1-4, apply the Jacobi method to the given system of linear equations, using the initial…

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Q: Compute the eigenvalues of matrix A and its inverse -3 1 -1 4 2 A = [23] and A-¹ | If A has…

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Q: 10. (a) Suppose f≥0 is continuous on [a, b] and [² f = 0. Prove that f = 0. rb (b) Suppose f: [a, b]…

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Q: 7x + 5y 3z = 16 3x - 5y + 2z = -8 5x + 3y - 7z = 0

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Q: Let a = e and consider the set U₁8 = {1, a, a²,..., a¹7}. Give the elements of U18 (as powers of a)…

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Q: 4:²+4 if zi Let f(2)= 8i if z = i (a) Calculate limf(z) using properties of limits. (b) Use the e-6…

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Q: Solve for y" (2): y" - y = 0, y(0) = 12, y'(0) =

A: Differential equation and it's solution

Q: 9. In order to have P1 million in a fund at the end of 15 years, how much must be deposited in the…

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Q: 4. For the linear canonical system x' = Jx, x € R², determine the nature of the origin as a fixed…

A: Given canonical system x'= Jx  Case-1:-  det &gt;0 if both Eigen value positive:- The product of the…

Q: 5. The Bernoulli's form of the differential equation xdy-[y + xy ³ (1 + ln x)]dx = 0 is In

A: Bernoulli's differential equation.

Q: A large company with offices in four cities must distribute 146 new color printers to the four…

A: Total employee = 2628 Standard divisor (S. D.) for 146 printers = 2628/146 = 18 Standard divisor (S.…

Q: Suppose that you decide to purchase a home and you secure a 30-year, $335,000 loan at an annual…

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Q: Find T(t) and N(t) at the given point. r(t) = 4 cos(t)i + 4 sin(t)j; t = ( N()=[ T انت 713 ㅠ

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Q: 5. Determine whether these biconditionals are true or false. a.) 1 + 1 = 3 if and only if monkeys…

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Q: 5. Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (1, 0, 0) to…

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Q: Bige Estimates Find a Bige estimate for the functions using an estimation target. a) f(n) = 6n² +…

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Q: Gauss sediel method and jacobi method is the same?

A: We have to see how gauss Jacobi is different with gauss sediel method .

Q: Hom worke: Consider the ring (Z [√3], +,.), Let A={ a+b√3:a, be Z₂} Is A subring of Z[√3]?

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Q: 1 and y= Questions (a) and (b) in this problem refer to the vectors u = 2 (a) Find the orthogonal…

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Q: 7. Use Green's Theorem to evaluate the integral f x²y dx - xy²dy where C: is the circle x² + y² = 4…

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Q: Determine whether the statement is true or false. If C is a smooth curve in the xy-plane and f(x, y)…

A: We have to determine whether the statement is true or false.

Q: 2. A public school teacher receiving a monthly salary of P26,494 with mandatory annual deductions of…

A: Given: Let us consider a public school teacher earning P26,494 per month is required to pay P34,185…

Q: C) USE PIVOTAL ELEMENT METHOD FIRST APPLICATION: (EXPAND ABOUT COLUMN 2, REF. ELEMENT = a32) SECOND…

A: As per the question we are given a 5×5 matrix A and we have to find its determinant by : Expanding…

Q: Find the work done by the three-dimensional inverse-square field 1 F(r) = r on a particle that moves…

A: Solution :-

Q: 2x 8+ 9+ 64x 3+ 3 1

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Q: A "bead" is formed by removing a cylinder of radius r from the center of a sphere of radius R (see…

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Q: Suppose that the point P can be placed anywhere on the line segment AB in order to change the angle,…

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