Show that Z[√-2] is a Euclidean Domain with respect to the norm N defined by N(a+b√-2)=a² +2b². (Modify the proof for Z[i] in lecture 17, example 5)

Q: nows not only that 5 + 2 is 7, +2 or 2 + 5. 0 +1, 10 + 2, 10 + 3, ..., 10 + 10. The doubles 1 + 1, 2…

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Q: you deposit $4000 in an account that pays 7% interest compounded semiannually. After 3 years,…

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Q: 22. If r(t) = (e2, e-21, te 2¹), find T(0), r"(0), and r'(t) r"(t). .

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Q: Angle and axis of rotation. Find the angle and axis of rotation for [T] and T-¹. [T] = 0.866 -0.5 04…

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Q: dy dx = y² y² - 1 x² - 1 ´‚y(2) = 2

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Q: 0-2 1 -2 0 0 0 duced echelon form of the augmented matrix [A b] i 1 (a) Express the general solution…

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Q: D. If the original inequality of interest were instead 0 < |x − 2| < 3, exactly one real number must…

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Q: Write the following complex numbers in Cartesian from. Simplify as much as possible. (2 – 3i)(3+5i)…

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Q: What is the maximum profit Jesaki Inc. can expect from widget sales? Round to the nearest dollar.…

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Q: This extreme value problem has a solution with both a maximum value and a minimum value. Use…

A: We have to solve given Questions.

Q: The function u(x, t) = exp(-x²) is a solution of the heat equation 4rt au au² 30-3422 at ax² Use…

A: Given the solution ux,t=14πtexp-x24t of the heat equation ∂u∂t=∂2u∂x2.

Q: Solve the problem. 8) Use a graphing calculator to predict what income the company should expect in…

A: Let the model function is fx=a+bx The normal equation are given by, ∑yi=na+b∑xi∑xiyi=a∑xi+b∑xi2

Q: 4. [Core content] Tomaslav has learned the following facts well: All the sums of whole numbers that…

A: Given: In this problem, some facts are given, 1) All the sums of whole numbers that add to 10 or…

Q: A potato is launched vertically upward with an initial velocity of 170 feet per second from a potato…

A: Solution: (a) s = -16t2 + 170t + 66        Velocity is given by,           v = ds/dt = 170 - 32t…

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Q: Using separation of variables, solve the differential equation, Use C to represent the arbitrary…

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Q: Calculus 1. Abby has developed an app that focuses on connecting potential renters with owners of…

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Q: = 0 has solutions that generate a vector subspace V. The system of equations Ax i. Solve the system,…

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Q: You'll enjoy your physics class if and only if you understand the mathematics, or you won't be able…

A: Symbol representation for propositional statement  or ∨             and ∧…

Q: 1. Describe and sketch the following sets of points defined by the following conditions. a. x² + (y…

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Q: Are there any nonconstant polynomials in Z[x] that have multiplicativeinverses? Explain your answer.

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Q: Find the solution for the DE. y'+(y/x)=y^2

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Q: Determine which of the polynomials below is (are) irreducibleover Q.

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: (d) A sequentially compact subset of R2 that contains the point (2, 2).

A: We have to find a sequentially compact subset of ℝ2 that contains the point 2,2

Q: Let f : A → B be a function. Prove that for any B1, B2, ⊂ B, f -1(B1) ∪ f -1(B2) ⊂ f -1(B1 ∪ B2)

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Q: 1. At a certain university 523 of the seniors are history majors or math majors (or both). There are…

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Q: We need to produce 2000 chocolate bars. Each one contains 160mg of thc and 75 MG of cbd.we are using…

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Q: Estimate the value of f' (50)

A: We know that  y = f'(a) represents the slope of the tangent to f(x) at x = a.

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Q: 1. A function is performed and then a 2nd function is performed on the result of the first function.…

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Q: 3. Let Y= {1, 2, 3} be a finite set, and X its power set. Define a feature map embedding it into…

A: Given: In this problem, the given details are Here, let's consider the set Y=1,2,3 be a finite set…

Q: dy exy- dx = e-y +e-2x-.

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Q: Suppose that a group of order 8 has exactly five elements of order 2.Identify the group.

A: Abstract Algebra, Dihedral group

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Q: 5. Simplify the expression using a Pythagorean identity: 6. Simplify the expression using a…

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Q: Approximate the critical numbers of the function on the open interval shown in the graph. Determine…

A: We can see that the function is defined in the open interval (-1,1). The function has critical…

Q: Step 1 Solution: 2a +1=b² = 2a = b2 - 1 = (b - 1) (b => both (b - 1), form 2k for som i.e, b-1= 2m,…

A: This can be achieved by solving upper two equations in the solution.

Q: 1. Suppose A is a 3x3 matrix. Suppose det A = 12 which are necessarily true ? a) AX-B has an…

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Q: 1.50 0.75 4.50 PLAN 0.75 200 FIG.2 2. a. Length of 1 rib of the gable roof b. Surface area of the…

A: (A) gable roof length =0.75+4.504             =0.75+1.125             =1.875 length of 1 rib of…

Q: Find the first derivatives. 1. f(1) = (1² + 1)5 2. f(P) = P³ + 3. v(1) = 41² +11V1 + 1 4. g(y) =…

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Q: -12 = 1 22

A: Given complex function e-iz=12i ∴e-iz=12i⇒e-iz=-i2⇒e-iz+2nπ=-i2⇒-iz+2nπ=ln-i2⇒iz=2nπ-ln-i2…

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Q: Differential equations Undetermined coefficients 1. +12y = 4 dy dt 2. + 2xy = x³ dy dx

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Q: Solve the linear programming problem by the method of corners. Minimize C = 7x + 6y      subject to…

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Q: f(x) = 3x² + 2; df = dx 6x

A: f(x) is said to be a solution to the differential equation if f(x) satisfies the differential…

Q: Consider the groups Z[i] = {a + bi | a, b = Z, i² = -1} and Z (both under +), and the function o:…

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Q: The initial guesses for the root are assumed to be x0=3 and x1=2, for these initial values, f (x0)…

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Q: Define T:R³ R³ by T → Then we can write T(7) - D-[ Az where A- I1 - 23 11 + 312 - 13 12 +213

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Q: Construct a truth table for the given statement. q~p

A: Truth table: The truth table is a tabular view of all combinations of values for the inputs and…