ompute the gcd of 11 + i and 61 in Z[i] to find x + yi such that x2 + y? = 61.

Q: Q) fınd Fourier series on [0,27] (1) ƒ(x)=r- x (2) ƒ(x)=sinx (3) ƒ(x)=cos x (4) ƒ(x)=xsin x (5)…

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

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Q: 5) Let A= (2,3) U {4} be a subset of R with the standard opology. Find Ə(A).

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Q: 17. Evaluate V|r|3 A. rr В. 2rr C. 4rr D. 3rr

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Q: 4) Simplify by combining like terms: 3x + 3x + 3x A) 3x3 B) 9x C) 9x2 D) 27x 5) Divide and simplify.

A: Simplify by combining like terms : 3x + 3x + 3x

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A: The union of set A and B is denoted by A∪B has elements both inset A and B The complement of A has…

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A: We have to draw graph of r=1-3cos(theta)

Q: x, + 2x, + 2x, + 2x, = 2 2x, + 4x, +8x, +6x, = 5 3x, + 6x, +10x, + cx, =7 %3D

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Q: Graph each function using radians. y- 4cos 20 2 O *T

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Q: 8. Show that f(x) = ½n² - ½n is O(n²)

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Q: f(x)= (1-cos x)/sinx +(sin x)/(1-cos x) find its integral

A: To find the integral  ∫1-cosxsinx+sinx1-cosxdx

Q: pand f(x) =5x as a half-range Fourier sine series in the range 0 < x <A , and sketch the function…

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Q: 1.) Find the area of the parallelogram with vectors as adjacent sides. и %3D (-2,9, —3) аnd v %3D…

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Q: If lim S(P, f, a) exists as µ(P) → 0, then fe R(a), and lim S(P, f, a) =|f da. H(p)0

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Q: what is the final answer

A: The final answer is dwdt=8t−14t2−t+4

Q: When dividing x^3+2x+4 by 3x+2 in Z11[x], the remainder is O 5 4 O 2 None of the choices о

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Q: X3 D.

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Q: Let x be a continuous random variable with PDF 3 x > 1 x4 fx (x) otherwise Find the mean and…

A: Given PDF is fX(x) = 3x4,x ≥ 10,otherwise

Q: 1375 Q1. Arrange the following fractions 3 in descending order. LCM of 2,4,8 and 12 is 24 Q2. Write…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1-Determine if W is a subspace of Mnn CEMn,W = {AEMnn: CA'C1= A}

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Q: Let e1, e2,..., en be an orthonormal list of vectors in an inner product space V over F. For any…

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Q: 2. 4 csc" xdx

A: Given ∫csc4xdx We have to evaluate the integral.

Q: ts no real number x such that x6 +x* – 2x² + 1 = 0

A: solution

Q: 3. What is (x + x) / (x² + 1)?

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Q: Find the volume of the solid that results when the region enclosed by the curves is revolved about…

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Q: Use Green's Thoerem to evaluate F dr. where F(r, y) = (-3Vx² + 2, 7 tan '(x)) and C is the triangle…

A: We have to evaluate by Green's theorem.

Q: Using Lagrange's formula, find f(1.3) 1 У 1 -1

A: The value of table for x and y x -1 0 1 2 y 1 -1 -1 1

Q: The total number of positive integer solution to the equation (x + y + z)(a + b + c + d) = 15 is

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Q: 3. Solve the equation cosh 2x + cosh x 5, giving x to three dec. places. %3D

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Q: Consider an Ultimaton game in which the disagreement payoff of each player is c> 0. Which of the…

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Q: Test MCV4U Curve Sketching Problem 1.Sketch the function fx) = x' - 6x + 9x, indicating any extrema,…

A: To find the graph of the function and indicate the point of inflection and extrima .

Q: 1-Determine if W is a subspace of Mnn CEMn, W = {A€Mn: CA°C1 = A}

A: W is a subspace of V if:  u,v∈W ⇒ u+v∈W au∈W, a  is a scalar Now, we have W=A∈Mnn : CAtC-1=A Let…

Q: Find the area. a. Inside one leaf of the three-leaved rose r cos30

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Q: Let V be a vector space, and T :V → V a linear transformation such that T(501 + 302) = 4®1 – 402 and…

A: Given  V be a vector space and T:V→V be a linear transformation such that  T5 v1→+3 v2→=4 v1→-4 v2→…

Q: Suppose that an amount of 10,000 dollars is invested at an annual interest rate of r% compounded…

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Q: (ii) Find the area of the region bounded by r - 200 cos (20).

A: To find- Find the area the region bounded by r2 = 200 cos2θ.

Q: Which option is equal to the DOT product uV of vectors 3 u = 1 4 -4 26 24 N N

A: The given vectors are: u=314 and v=22-4 Multiply the numbers component wise to find the dot product…

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Q: E Cousider a linear transformation T: R - R defimed by (a) Find the matrix A for T. (b) Find a basis…

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Q: 2-Show that the following polynomials from a basis for P2. 1- 3x + 2x?,1 + x + 4x?,1 – 7x

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Q: xx                                    −2−2                                       11…

A:

Q: р-1 Suppose p = 1 mod 4 and g is a primitive root mod p. Show a = gʻ4 satisfies a? = -1 mod p.

A: p = 1 mod 4. g is primitive root modulo p. =&gt; order (g) = p-1.  =&gt; gp-1 = 1 mod p and gn ≠ 1…

Q: Let W be the fraction of the width of the moon illuminated (as we observe it) as a function of time…

A: We have the model, W = 12+12cos2πt29.5 Where t is time in days.

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Q: 6. Evaluate the integral! ~ 0.7 c0.6 e* sin y dy dx 0.2 (i) Using the trapezoidal rule in both…

A: Given that,      ∫0.10.7∫0.20.6exsinydydx∴ ∆x=0.1=∆y⇒∫0.10.7exdx∫0.20.6sinydy xn ex exsiny 0.1…

Q: f(x, y) = (-x – 2y, x – 4y).

A: Follow the steps.

Q: Determine whether each of the P-boxes with the following permutation tables is a straight P-box, a…

A: Given P-boxes are a. 3 2 6 5 1 4b. 1 2 5 4 3c. 2 4 1

Q: Given the region R inside the circle x^2+y^2=4 and above y= sqrt(3) A) Establish that d A exists B)…

A: Double integral over the region.