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Q: (a) Verify that Q(√3 ) is a subfield of R. (b) Show that Q(√3 ) is isomorphic to the quotient Q[x] /…

A: We shall use the following result.  Subfield test: Let F be a field and let K be a subset of F with…

Q: 1) Calculate the Fourier Series of the given function on the given interval and state the first and…

A: The Fourier Series of a function "f(x)" is defined by; f(x)≈a02+∑n=1∞ancosnπx2+bnsinnπx2  where…

Q: 2xyzx − xzy - 2yz = 2x²y cos(x + y²)

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Q: Remaining Time: 4 hours, 44 minutes, 03 seconds. Qu Browse Local Files Status: QUESTION 13 A state…

A: I have explained everything with in the solution .please go through that.

Q: Consider the problem of finding the point (s) on the plane 8x + 3y + 5z - 120

A: We have an plane 8x+3y+5z=120 we have to find a point on the plane which closest to the (0,0,0) Here…

Q: Use appropriate formulas from geometry to evaluate the integral √/9 - ²dx. Write the exact answer.…

A: The given definite integral ∫-309-x2dx. We have to find the value of the integral using geometry.

Q: what is the mean distance of these numbers 36,26,30,28

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Q: If N and M are normal subgroup of G, then NM is also a normal subgroup of G.

A: N and M are normal subgroups of G. To Prove: NM is also a normal subgroup of G.

Q: 个 {......., 0, 1, 1, 3, 3, 1, 2, 0,........} 个 b. {......., 0, 1, 1, 3, 3, 1, 2, 0,........} 个 C.…

A: A discrete time signal is a type of signal that is represented by a sequence of values that are only…

Q: Evaluate foe-² dr. I

A: This is a improper integral.we will solve this by the following way. For finding the answer, here we…

Q: Task: Do the indicated task individually. Apply the concepts you gained in this lesson in doing this…

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Q: 8) A scientist places 7.35 grams of a radioactive element in a dish. The half-life of the element is…

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Q: Write an expression for the operation described below. 4 times a

A: Write an expression for the operation described below. 4 times a

Q: ■ Prove that the function x) = { win = ²+ = = 0 x X 0, x f(x) satisfies the intermediate value…

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Q: Prove by induction that Σ²₁(5² + 4) = (5″+¹ + 16n − 5) -

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Q: Suppose f(x) = x + x² + x³ for every real number . True or false: The function f is strictly…

A: We are given        f(x) = x + x2 + x3  Differentiating w.r.t x, we get        f'(x) = 1 + 2x + 3x2…

Q: Problem 7.2 Find the GS of xy" - (x + 1)y' + y = x² ex

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Q: Minimize c = x+y+z+ w subject to 5x y + w z 9,000 Z+W≤ 4,000 S 200 0, y ≥ 0, z ≥ 0, w ≥ 0. 4200 X X…

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Q: 2. Consider the surface defined by 1² + 2xy + y² + 2²- 25 Let F(x, y, z) = 1² + 2xy + y² + 2². (a)…

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Q: 1. Consider the graph G below. G

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Q: 8) Find an upper bound on the integral where I is |z| = 2 CCW fra dz

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Q: A discrete-time a. b. C. d. signal x(n) = {.…....0, 2, 1, 3, 3, 1, 1, 0,.....), determine x(n − 3) ↑…

A: correct answer is option a.     for explanation see attached image in  step 2

Q: EXAMPLE 9 Solving a Homogeneous System of Linear Equations Solve the system of linear equations. x₁…

A: The given problem is to solve the given system of linear equations. Given system of linear equations…

Q: Sketch the function f(x) = following the 12-step algorithm of curve sketching. Ensure you state all…

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Q: The vector O True False 0 is a solution of the homogeneous system 3 1 -2 -12 10 | -4 8 70 0 0

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Q: Solve the initial value problem. dy dx + 5y - 7e4X = 0, y(0) = 10

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Q: 5 3x Use four rectangles to estimate the area between the graph of the function f(x) = and the…

A: Function, fx=53x, x-axis.Interval : 1, 5

Q: Verify that the following are formulas of sentential logic and identify the main connective. Part…

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

Q: To factor 3x^(2)-10x+3 by grouping, find two numbers whose product is

A: Consider the quadratic form ax2 + bx + c,   where a, b, c are constants…

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Q: State and prove Littlewood's Third Principle

A: Littlewood's Third Principle, or the law of iterated logarithm, can be understood intuitively as…

Q: Evaluate the integral by changing to spherical coordinates. 100 - x² 200- x² - y² 10 1. To 100000 3…

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Q: 1. Factor each of the following polynomials completely into irreducible polynomials: a) x² + 1 in…

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Q: Find the work done by F = 3xy³i+ 8x²y²j in moving a particle once counterclockwise around the curve…

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Q: 1. Answer the following for A = -3 -5 -3 3 3 1 a. Determine the characteristic polynomial of A and…

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Q: A B D Which of the following is true? To be in reduced row echelon form, all the entries must be 0.…

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Q: If I let f be continuously differentiable on R^2, how do I prove that gradf = (fx,fy)?

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Q: Find a particular solution to the differential equation using the Method of Undetermined…

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Q: 2. Is -3 an eigenvector of A = 3 -4 2 79 -5 1? If so, find the eigenvalue. 44

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Q: 3. If 7,7 € R", which of the following is a necessary condition to the equality ||7|| = ||||?

A: Equality, x→=y→x→, y→∈ℝn"As per the guidelines, only the first question will be answered. Kindly…

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Q: One tedious bit about elliptic curves is that each point has both an x- and a y-coordinate to keep…

A: (a) For the elliptic curve, there are two square roots of x3+Ax+b. These are b,p-b. The values of…

Q: Evaluate the logical expressions with x = y = 1, and w = z = 0. Evaluate the following expression xy…

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Q: Use the simplex method to solve the linear programming problem. Maximize z = 5x₁ + 2x₂ + x3 subject…

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Q: Suppose f: R → R is defined by the property that f(x) = x + x² + x³ for every real number x, and g:…

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Q: 3. Answer the following for A = a. Determine if u = 1 A -1 13 3 -3 -5 -3 3 3 1 1 -B₁ and v = are…

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Q: a. Compute the outward flux across the quarter circle C: r(t)= (14 cos t, 14 sint) for Osts ¹2 The…

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Q: let method for 1 order ean. L= Dx-Dy Solve L²d using characteristic

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Q: Evaluate the line integral along the given curve. f(3xz+yz) ds, y: line segment from (1, 2, 3) to…

A: The given curve γ is a line segment from the point 1, 2, 3 to the point 3, 5, 7 in the three…