Let R = Z[i] = {a + bi : a, b € Z; i² = −1} and let M = {a + bi € R : 3|a; 3|b}. Show that R/Mis a field.

Q: Find the general solution to the homogeneous differential equation tion can be written in the form s…

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A: Given differential equation x2-1y''-6xy'+12y=0-----(1)

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Q: A square matrix is half-magic if the sum of the numbers in each row and column is the same. Find a…

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Q: Find the general solution to the homogeneous differential equation tion can be written in the form s…

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Q: 3. Let R-Z18. Determine the units and zero divisors of R giving the explicit unit or zero divisor…

A: We know that  no of units in ring Zn = phi(n), and  no of zero divisor of Zn = n - phi(n) -1

Q: 52-4 OC. There is no solution. 7-7z There are (Type whole numbers.) z), where 2 is any 3. A theater…

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Q: Take the Laplace transform of the following initial value problem and solve for Y(s) = L{y(t)}: y" +…

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Q: For the function f(x)=1/16x​, construct and simplify the difference quotient f(x+h)−f(x)/h.

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Q: Let f,g: A B be functions. These functions induce functions f*, 9+ P(A) → P(B) and f*,g* : P(B) →…

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Q: B) Evaluate the following limit or show that it does not exist: 7xy lim (x,y)→(0,0) 3x² + 5y²

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Q: For each of the following two LP models, respond to the following questions using graphic tools and…

A: (1) The constrain which are binding the solution is  3x+4y≤242x+y≤10x≥1y≤5y≥0 (2) The redundant…

Q: Consider the periodic function f(t) defined as follows: - 2t f(t) = 2 e for 0≤ t < 2, and f(t+2) =…

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Q: In the number 467xy2 you are asked to find the values for x and y. You know that this number is…

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Q: 5) Find the center of mass of the triangular region with vertices (0, 0), (4,0) and (4,1), if p(x,…

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Q: If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability that all 4 cards are…

A: Option-1: Total number of diamond in a deck of 52 cards is 13. The probability of drawing 1 diamond…

Q: Determine whether or not the following set of vectors span R3 ,Show steps clearly {(1, 1, 2), (1,…

A: Note:1. Suppose v1, v2, v3 are vectors in ℝ3 then then set v1, v2, v3 is said to be a spanning set…

Q: Let a, b, c E Z and n E N. Assume a = b (mod n). Prove that a + c = b + c (mod n).

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Q: How many integers in between 1 and 3000, inclusive are divisible by either 5 or 7?

A: Let A and B are two sets such that then number of elements in A and B are obtained as…

Q: Given f(x, y, z) = 9y and E = {(x, y, z) | 1 ≤ x² + z² ≤ 25, 0 ≤ y ≤ 5 − x² − z² }, convert the…

A: Triple integrals conversion of cylindrical coordinates

Q: If

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Q: 8 Two line segments AB and CD, have endpoints at A(-5, 11), B(3, 5). C(9. 3). and D (2. 10). Which…

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Q: (b) Do you think it is possible to change any other numbers in the first three rows of A such that…

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Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. A…

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Q: Use the Euler method to numerically approximate x(1.5) for the IVP *+5x+6x=0, x(0)=1, x(0)=2 use a…

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Q: Q #2 Please complete the blanks on the Unit Circles in Diagrams I-II. Diagram I Angle 8 (x,y)=( (cos…

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Q: Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: y" +9y= =…

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Q: Rather than use the standard definitions of addition and scalar multiplication in R3, let these two…

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Q: During 2010, the sales of vinyl records were 114% of the previous year’s sales. Sales were 2.8…

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Q: 7. Consider Bessel's differential equation of order zero given by 2d²f df +x + μ²x²f = 0, dr² da…

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Q: Find the following matrix product, if it exists. -6-1 -7 4 O A. 9 5-3 0 1 8-2 Select the correct…

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Q: a) Determine the domain of the function and write it in interval notation b) Determine the…

A: We know that, if we draw the graph of an odd function then it has rotational symmetry with respect…

Q: 1. Describe (24). What is p(24)?

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Q: Let f(x) = 424-82² + 12 Input the interval(s) on which f is increasing. Input the interval(s) on…

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Q: c) Use Euler's method to obtain a four-decimal approximation for y(1) by using h = 0.25, and…

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Q: 4. Consider the vector space M of 2 x 3 matrices. (a) Define the subset SC M a 0 b-c S = -{(a = a…

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Q: O a b c d a a b (d) b C С d d a (There are two different ways to complete this one: find both)

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Q: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

A: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

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Q: A pair of parametric equations is given. x = e²t, y = et (a) Sketch the curve represented by the…

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