Let S be a nonempty subset of Z and let R be a relation defined on S by xRy if 3 | (x + 2y).  If S = {−7, −6, −2, 0, 1, 4, 5, 7}, then what are the distinct equivalence classes in this case? Please show how you find them

Q: Ellen estimates that she drives approximately 1,000 miles per month and gasoline costs on average…

A: Given that Ellen drives approximately 1000 miles per month. In a year, it is 12000 miles.The cost of…

Q: Find the characteristic polynomial and the eigenvalues of the matrix. -7 -7 1 - 1 The characteristic…

A:

Q: Let z(x, y) = x³y where x = t³ & y = tº. dz dx dy by first finding & and using the chain rule. dt dt…

A:

Q: Find fourier series 0 f(x) = {x² ≤ x ≤ 0. 0 ≤x≤ TT.

A:

Q: #3: The following vectors form an orthogonal basis for Rª. V₁ = (1,-1,2,-1), V₂ = (-2,2,3, 2) V3…

A:

Q: 4.) In how many ways can two dozen identical robots be assigned to four assembly lines with: (a) at…

A: To the first line we can assign 3 or 4 or 5 or ....... robits and the same for the remaining 3 lines…

Q: Let W be the plane with the equation 3x-y+ 7 = 0. Find the standard matrix P for the orthogonal…

A:

Q: Consider the following data: Year Deaths Answer Number of Deaths in the U.S. by Drug Overdose 2002…

A:

Q: P.V. So 6.⁰⁰ xa dx = x² - 1 J 2 sin(лα) xa 1 + 2x cosp + x² α = 0, −π <¢ <л, ¢ ‡0 dx = -[1 -…

A: As per the question we are given two improper integrals, which we have to evaluate using residue…

Q: Chain Rule (One independent variable) Let x(x, y) = xe²y where x - dz Calculate by first finding dt…

A:

Q: Let R be the relation on Z defined by xRy if x² = y² (mod 5). Prove that R is an equivalence…

A: We recall the definition

Q: A new school building was recently built in the area. The entire cost of the project was…

A:

Q: 5. Suppose that a function f: R → R is a uniform limit of a sequence of polynomials on R. Prove that…

A:

Q: Problems: The inferior limit of a bounded sequence (an) ∞ n=1 is lim infn an = supn inf m≥n an Show…

A:

Q: Write a logarithmic equation corresponding to the graph shown. Use f(x) = log4(x)as the parent…

A:

Q: a) Calculate 6x² (1-y) 0<x<1 0<y<1 0 otherwise b) Evaluate £xv (x, y) = {6x*(1-y) E(XY)=ffxy.f(x,…

A:

Q: The order of the Galois group G(K, F) is equal to [K:F].

A: The given statement is true only when K is a finite Galois extension of F. Then the order of the…

Q: 1a. Σ₁ dim V₁, (A) = 4. i=1 [Answer: J is diagonal (5 cases).] [Answer: diag[J₂(X1), J1 (A2), J1…

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

Q: In (Z,+) determine ({2,4,5}), the subgroup generated by the set {2,4,5). (As always, please provide…

A: In  , we have to determine , the subgroup generated by the set .We know thatDefinition : Given a…

Q: [1 2] Find an orthonormal basis for the column space of 4 1 02

A: The given matrix .The aim is to find the orthonormal basis of the column space of the matrix.

Q: a) Σ=3 (inn 1(Inn), b) Σ=1(−1)" (3) c) Σ=1(n+1)

A:

Q: (a) Let A € Mmxn (F) and let Are be the reduced echelon form of A. Prove that Ax = 0 if and only if…

A:

Q: 1. Use a double integral and trigonometric substitution, together with the formula 1 1 [cos²u du…

A:

Q: Can you explain the simplex method to me with a simple exercise, please?

A:

Q: Let A be a nonempty set and R be a relation on A such that domain(R) = A. Prove that if R is…

A:

Q: Suppose that [a, b] R is a closed and bounded interval, and let {G:a E A} (where A is any index set)…

A:

Q: Give dim H and the E-coordinate map.

A: Given that  is a vector space contained all  lower triangular matrices.           and   is a…

Q: At the National Baseball Batting Contest, the organizers have set up game booths for the…

A: The probability of Richard successfully hitting all the pitches is

Q: To be honest I still dont get it, I'm still confused on how we get the number sets, please elaborate…

A:

Q: 17. Find -1 A) (4x²-10)² + C B) ln(4x² - 10) + C J 8x dx (4x² - 10) C) 4x4 - 10² + C D) 8x(4x² −10)²…

A:

Q: G Let be a locally compact group and let hip in (G) be supported in the subsets A and B of ,…

A: In harmonic analysis and abstract algebra, the concept of convolution is central when dealing with…

Q: 3. Let V denote the vector space of all functions f: R→ R, equipped with addition +: V x V → V…

A:

Q: ) How many ways can Mary split up 12 hamburgers and 16 hot dogs among 4 kids (R, P, C, and J) in a…

A:

Q: Determine co(S) in the cases shown in Figs. (c) and (d). (In (d), S consists of the four dots.) a 2

A: We know that, Convex hull is the smallest convex set that contains it. It is denoted by Co(S).In…

Q: Determine constants a, b, c, d that will produce a quadrature formula 1 [ ƒ(x)dx = af(−1) + bƒ(1) +…

A:

Q: Exercise 9.2.4 (a) Write A = 1 3 00 as a linear combination of 0 1 0 (49) 83 69- [(88) [ 1 1 0 1 (b)…

A: Solution:[9.2.4](a)

Q: An inventory consists of a list of 80 items, each marked "available" or "unavailable". There are 50…

A: To show that there are at least two unavailable items that are either three or six items apart in…

Q: 50m 25m Zom LEX шос,

A: The given problem is to find the volume of the given solid figure with given dimensions.

Q: ·Sª 4. xa 0 (x² + 1)² dx = л(1 - α) 4 сos(αл/2)* -1 < a <3, a ‡ 1

A:

Q: 2. 5.0⁰ xa-1 x +1 dx I sin(лα)' 0 < a <1

A:

Q: Let A = {a, b, c, d} and let R = {(a, a), (a, b), (a, c), (a, d), (b, b), (b, c), (b, d), (c, c),…

A: The objective of the question is to determine which properties - reflexive, symmetric, and…

Q: 12. Consider the continuous function y = f(x), such that ƒ(x) is not a piecewise continuous…

A: is a continuous function  such that  is not piecewise continuous function and  on the interval

Q: Can you explain the simplex method to me with a more difficult exercise, please?

A:

Q: Mr. and Mrs. Wagner are getting ready to drive across the US from Philadelphia, PA to Los Angeles,…

A:

Q: Let z(x, y) = x³y where x = t³ & y = tº. 8 Calculate dx dt dy dt dz dx dy by first finding & and…

A: We have

Q: Let V be an inner product space over the field of real numbers with the inner product defined as (u,…

A:

Q: Exercise 9.3.19 Show that the sets S= = {[i], [6]} same subspace of M2,2. and T = {[11], [-1-1]}…

A:

Q: Vectors A and B are shown. What is the magnitude of a vector Cif C = A - B? 40 60 50 O a. 10 O b. 78…

A: Squaring on both sides, Given, And, angle between  is

Q: Find the eigenvalues of the triangular or diagonal matrix. (Enter your answers as a comma-separated…

A: Let the given triangular matrix be Find the eigenvalues corresponding to the given matrix.

Q: The following questions concern the classification of second order PDEs. For each question,…

A: