c) By using De Moivre's theorem, find (3/5 – 3i) in the standard form.

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A: Here, we are given the solid S inside the sphere ρ=6 cos(ϕ) and below the cone ϕ=π4. Now, we will…

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A: According to guidelines I solve first 3 subparts so kindly request you to repost the remaining…

Q: Usng polor Codirte to Sad ared bourded by ブニリ ブ=ス

A: Here we use basic polar coordinates to find this.

Q: B. Evaluate the following хе xe-4xdx 5.

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Q: Suppose that T(0) = a and T(1) = b are some constants. Define the running pairwise average as, for n…

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Q: O Find valume bounded by %3D

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Q: (iii) If u = 461 + 362 and [u]c = then the value of r is and the value of S is (iv) If V = 3c1 + 2c2…

A: Given that  b1 = 10c1 +3c2,  b2 =27c1 +8c2 c1 =-8b1 +3b2,   c2=27b1 -10b2

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Q: Use polar coordinates to evaluate sin (2² + y²)³ dA, where R is the region enclosed by the curves…

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Q: Solve: (dy/dx)? + (y– 1– (x/y)) dy/dx – x/y(y-1) = 0 |

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Q: xi = 2x1 – 5x2 x2 = 4x1 – 2x2 X1 (0) %3D 2, х2(0) — 3 2х1

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Q: Consider the following two ordered bases of R?: {{1, –1), (-2, 3)}, {(-1, –2), (1, 3)}. B a. Find…

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Q: Q4) Find plane area inside the polar function r = 2 and outside polar function r = 2 cos (-0) in…

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Q: 1 1 1 1 4 1 1 You are given that the eigenvalues of A = 1 are 1 4 1 1 1 1 4 7, 3, 3, 3, counting the…

A: The given matrix is                                     A=4111141111411114 and the eigenvalues of…

Q: * Required Upload file Solve t d²N -2t- NP + 2N =t In t di? dt 1 Add file Back Submit Never submit…

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Q: 2x –1 1 , show that y"+ y' + xy +1 c) If y =-

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Q: k 0 0 0 1 0 If A = 0 0 1 then det (A) =

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Q: Write each complex number in complex polar notation: (4.053 + 2.042 ) - ( 4.482 + 4.681 i %3D

A: As per Bartleby guidelines we're supported to answer only one question when two or more different…

Q: Q1) Evaluate the integral dy dx using polar coordinate

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Q: uppose that we use Euler's method to approximate the solution to the differential equation dy dx…

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Q: Let f(x) = sin(x). Suppose that h and k are two functions such that W (x) = cos(x), k'(x) = f(x +…

A: Let us solve the differentiation and integration based problem in the next steps.

Q: x³ – 2x? – 5 = 0, [1,4]

A: Reframe the function and find the term for x.

Q: Let V = R? and let H be the subset of V of all points on the line -3x + 4y = -12. Is H a subspace of…

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

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Q: O Prove that Q(Vationalnumber bers)is negrigibleset

A: This follows easily from the definition of a negligible set. We recall the definition and present…

Q: Suppose an urn contains 10 marbles: 4 are white and 6 are black. We will draw marbles randomly,…

A: First four are whack which means they are white and one of the first 5 drawn marbles.

Q: Solve. y" + 16y = u6(t). y(0) = y'(0) = 0 S f(t) for t 6 The solution can be written as y(t) Find…

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Q: Let f(r) = . (a). Find the average value of f on [0, e]. Use six decimal places. (b). Use Newton's…

A: Given that fx=xex2 (A) To determine the average value of f(x) on [0,e]. (B) To estimate all points…

Q: (-1)"n" sin" (4) 2n n=1 CS Samed with Camacarner

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Q: Q2) Solve the D.E dy + (xy-xy2)dx 0 %3D

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Q: Given: a, = In(n+1) – In(n) for n E N Determine if the following is convergent or divergent. (a)…

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Q: 2.Find the number of 6-letter words that use letters from {A,B,C,D,E}   in which no 5 consecutive…

A: We can solve this using permutation and  combination

Q: • Determine and draw the graph of the following equation in R3 : - 2² = 1 4 9 Also show the traces

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Q: 3)Solve D-E リラ=メジ (ans.jole) .

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Q: ーツ

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Q: a) Given f(x) =- 3Vx + 2 Find f'(x) using the definition of derivative.

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Q: 2. dz dz dy

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Q: Let y = Lal: Let L be the line spanned by u. and u %3D Write y as the sum of two orthogonal vectors,…

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Q: Solve: (dy/dx)? + (y- 1– (x/y)) dy/dx <- x/y(y– 1 ) = 0

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Q: 3-x Q1) Evaluate the integral * dy dx using polar coordinate

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Q: Let S be the solid inside the sphere p = 6cos@and below the cone Ø = 1/4 Find the volume of the…

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Q: (-1)^x2" (2n)! for all x €R. cos x = Let f(x) = cos(v). Determine the power series representation…

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Q: Consider the system of equations #--(1--) da dt *= (1 ---). dy dt 3 taking (2, y) > 0. (a) Write an…

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Q: Match the following improper integral with the improper integral below in which you can compare…

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Q: +x (-1)" Given cos(x) = (-1)". n=0 (2n)! -x2n for all x E R, %3D 1. Express the integral cos x dx as…

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Q: Find area inside out Side r=2c0s6 ra I

A: Given polar equations are r=2cosθ and r=1 Consider first polar equation r=2cosθ Multiply with r on…

Q: . Let f : [0, 1] R be defined by |-1, z = ; >50 f(x) = {0 |<a < }; 1, 21 (a) Show that f € R([0,…

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Q: -3 Are the vectors -3 -8 linearly independent? -4 and linearly dependent If they are linearly…

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Q: R? R? 12- y? 12 + y? if (z, y) # (0,0) (r, y) + if (1, y) = (0,0) • The function f is it continuous…

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