Problem 2.9. Let 9 be a root of an irreducible polynomial p E Q[r]. Prove that if 0 € C, then deg (p) = 2h for some n E N.

Q: 3. fy dy + 10g = e + dt +7 -2t

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Q: A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away…

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Q: which sketch is a cross-section in the y-direction (L to the x-axis)? Why?

A: Given: Let us determine the cross-section in the y-direction perpendicular to the x-axis.…

Q: 1 Given the vector field F=rcos$ ar+- 2 cos 0 4 r cos + 1-2 None of the choices 2 cos o r 2 cos o…

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Q: Given a differential equation of y’=ln(x+1) and y(0)=1. Find the value of y when x=1 using Euler’s…

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Q: Find the first approximate root of the equation 2x^3-2x-5=0 up to 4 decimal places using Xn=1.5…

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Q: Q2: (A) Choose the correct answer for each of the following: 1. The cancellation law holds in a. any…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Ex. Locate the centroid X of the shaded area shown. 1m 1m X

A: Calculate the area A of common region between the curves y2=x that is y=x and y=x2.

Q: Let D be the region bounded by the lines y = x, x = 3 and the curve y = (a) Sketch the region of…

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Q: Find the interest on 28, 700 at 7.3 % from August 15 , 2018 , to March 10 , 2020 , using the…

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Q: 1. Compute u + v and u-2v where u = -5 and v = T 2

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Section 4.3 In Exercises 1 and 2, compute the solution of the given IVP. d²y 1. +9y2 cos(3t), y(0) =…

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Q: (6). If V (km/hr) and R(kg/ton) are related by a relation of type R = a + bV2, find by the method of…

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Q: | Example 8.12. Use the Trapezoidal rule to estimate the integral exª dx taking the number 10…

A: The given problem is to estimate the given following integral using Trapezoidal method with n=10…

Q: Solve the following simultaneous DE using Laplace transforms. 1. dx dy 2 + dt dt 5et dy dt 3 da - 5…

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Q: Find the solution. dy sin x x +2y = y(2) = 1 dx , X A y = (4 + sin 2 + cosx²)/x² (B) cy= (3 cos 2x -…

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Q: The estimate of an integral of f(x) dx is given as 1860.9 using 1-segment trapezoidal rule. Given:…

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Q: 5 By separation of variables, Solve the followin PDES :- du dt d2u dx2 @ o U (0₂t) =(4,t) = G u(x,0)…

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Q: Please answer with complete solution. Let A be the curve containing of the line segment from (0, 0)…

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Q: e terminal side on the unit -:-)

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Q: F. Change the Cartesian integral to polar coordinate dy dx 171-77 حول من كان إلى يولير ار -1 0

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Q: Consider the curve C which is the intersection of the surfaces shown in the attached figure.

A: To evaluate the below integral. ∫Cx−y−2zds

Q: (Hint: Use trigonometric substitution to evaluate the formulated double integral.) 3. 3] Set-up the…

A: The given problem is to set up the double integral in polar coordinates that gives the volume of…

Q: dx 1 + x method. Hence find the value of log 2. Example 8.18. Evaluate f . correct to three decimal…

A: Problem can be solved using Romberg's Method.

Q: (B) Find the zero-divisors of Z6.

A: Here we have to find zero divisors of Z6 .

Q: 8. Given the parallelogram ABCD below, with E and F the midpoints of sides AB and CD, AF||EC, and BP…

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Q: III 1. dt2 fip +6- dt and the gen +8y=2e-3t am to nor 2. d'y dt2 fip +4 +13y=et dt 3. +10y = e

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 1. Let A be an m X n real matrix with full column rank. Show that the Gram matrix AT A associated…

A: As per the policy, we are allowed to answer only one question at a time. So, I am answering the…

Q: 2. Find the elementary row operation that transforms the first matrix into the second, and then find…

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Q: What if the jelly bean machine gives 3 jelly beans to the first customer who put in a coin, 4 to the…

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Q: 5 UA_n is open where A_n=(n-1,n). ΟΝ OS O A 6

A: Q5. Since the arbitrary union of open sets is open,the given statement is Always true

Q: 3. Use Laplace transforms to solve y+3y=1351 24 y(0) = 6

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Q: (2x - y)dx + (4x + y - 6)dy = 0

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Q: Let f and g be functions which are differentiable on R. For each of the following statements,…

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Q: Let B = {B-[3]} and = {[14]-8} B' 3 Suppose that A = is the matrix representation of a linear…

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Q: ANSWER THE FF. IF THEY ARE ALWAYS TRUE, SOMETIMES TRUE OR NEVER TRUE 1. If x is in S, then x may be…

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Q: 2. (a) Find the unique polynomial of degree 2 or less such that f(0) = 1, f(1) = 3, f(3) = 55 using…

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Q: erential equations 1. y - xy = 0; M(1,1). 2. y4y² = 1; M(1,0). 3. y 4. yy' - ry³ = 0; M(1,1). 1=1/4

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Q: Six second-order equations and four y(t)-graphs are given below. For each y(t)-graph, determine the…

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Q: For integers m, n, p, q E Z, n, q0, use this and the field axioms (a) Prove m + P 9 mq+np and m. 2…

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Q: Consider the given differential equation: + = cos x - sinx, y(0) = 1, h = 0.25, at what value of x…

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Q: Use LU decomposition method to solve the system of equation. (Show your solution) X1 + x2 + x3 = 1…

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Q: Example 8.17. A solid of revolution is formed by rotating about the x-axis, the area between the…

A: Simpson rule for integral  ∫abfxdx≈Δx3​fx0​+4fx1​+2fx2​+4fx3​+2fx4​+⋯+2fxn-2​+4fxn-1​+fxn​   where…

Q: eff curl(F). ds. F(x, y, z) = x² sin(z)i + y²j + xyk, S is the part of the paraboloid z = 9 - x² -…

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Q: (e) Calculate the length of AC in metres. (d) Show that the length of BC is 19.1 metres correct to 3…

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Q: (a) Find the solution set of the homogeneous linear system below. x + y + 2z = 0 -y-3z + w=0 3x + y…

A: as per the guidelines, I am answering first question only. Kindly repost and  ask to answer other…

Q: 3 By direct partial integration, Solve the following PDES 8- 82u axdy = CBX COSY x cosy, x 2…

A: We have ∂2u∂x∂y=cosx cosy The initial conditions are ∂∂xux,π=x, uπ,y=2 cosy Integrate ∂2u∂x∂y=cosx…

Q: Let f and g be functions which are differentiable on R. For each of the following statements,…

A: (a) The given statement is: "If f'x=g'x for all x, then f0=g0" The statement is false. Take the…

Q: Let D be the region in the xy-plane bounded by y = x and y = x², and C be the associated boundary…

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Q: 4. (a) Compute the general solution for: +4- +3y=e-¹/2 dt² dt (b) Compute the solution with y(0) =…

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