Using the relation z=x+iy = rcosθ + irsinθ=re^iθ . Derive z^n = r^n(cosθ + isinθ)^n = r^n(cosnθ + isinnθ).

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Q: . Find a stable age distribution vector for a population with age transition matrix 4 [1] 16

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Q: 10. For the curve r =4, 0 ==, 0≤ø≤² osøs a. Sketch the curve b. Calculate the length of the curve. 2

A: Explanation:Spherical coordinates represent a point P in space by ordered triples (r,θ,ϕ) in which r…

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Q: 3. Write the dual for each of the following primal problems: (a) Maximize z = -5x₁ + 2x₂ subject to…

A: (a) Primal:Maximize  z=−5x1+2x2Subject to  −x1+x2≤−2  2x1+3x2≤5           x1,x2≥0Here primal have…

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Q: rove the following equation for all n ∈ N by mathematical induction method: 12 + 32 + ... + (2n −…

A: To Prove the following equation for all n ∈ N by mathematical induction method:

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A: Let  be the number of refrigerators must ship to warehouse A and warehouse B.Since Warehouse A holds…

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Q: If supX∈S ||X||p 1, then S is uniformly integrable.

A: Given: sup for some .Objective: To show that  is uniformly integrable.

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Q: 272 Sketch sin for n = 1 and n = 2 over the intervals 0 to a andand. Using even and odd arguments,…

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Q: d Consider the equation i(t) + x² [′ i(x) dx = e(t), t≥ 0, with the initial condition i(0) = 0. II.…

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Q: Consider the matrix A and vector b given below: ^= [ A 3 -1 -1 1 -1 3 2 -8 b Is b in the span of the…

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Q: Describe the elementary row operation that corresponds to the elementary matrix 1 000 0 100 -3 0 1 0…

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Q: (a) Show that x* is a global minimizer of g x* Pg= { € R" :x= =prox (x)}.

A: To show that: is a global minimizer of

Q: Let A = 10-6 11 0 3-4 and b= -1 Denote the columns of A by a₁, a2, a3, and let W= Span (a₁, az, a3).…

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Q: Use the following table. Zeros of Jo. Ji, Yo, and Y₁ Jo(x) Ji(x) 0.0000 3.8317 7.0156 2.4048 5.5201…

A: Give the zeros of the polynomial  are  .To evaluate  such that  .

Q: (1-xy)-2dx+[y2+x2(1-xy)-2]dy=0 when x=2, y=1

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Q: 11. a. Is 3 € {1,2,3}? d. Is {3} € {1,{2}, {3}}? e. Is 1 € {1}? h. Is {2} € {{1},2}? į. Is {1} =…

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Q: 1. Let RE SO (3), a unit vector u denote the axis-angle satisfying: R = 1+ sin 0 [u]x + (1 - cos…

A: Let , a unit vector u denote the angle-axis satisfying:To find:a) The determinant of .b) In epipolar…

Q: = [#1, #2, #3]T 2. Let T = 2x2 - 6x32 2 221 +2 ≤8 271 +372 +13 < 5 #1 -

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Q: Solve the integral equation for F(x), 8 (1, S F(x) sin ax dx = 2, .0, 0 ≤a < 1 1<a < 2 a ≥2…

A: Problem 1:To find:The function Problem 2:To find:Inverse  transformation.Concept used:The integral…

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Q: In​ 2015, there were approximately 4,022,000 births in a country. Find the birth rate in births per…

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Q: Describe the elementary row operation that corresponds to the elementary matrix 1 0 0 0 0 100 -3 0 0…

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Q: Exercise 1.6. Give two situations where "zero" and "nothing" mean the same thing, and two situations…

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Q: PART 2. Identify the 5 errors on the given truth table. Explain the reason that they are wrong. (p…

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Q: Read Example 3 (p. 739). Explain how the geometric meaning of the cross product  helps solve this…

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Q: Let f H²H² have the form f(x, y) = (x, g(x, y)). Determine the conditions on g(x, y) which imply…

A: Let such that .To find:The conditions on  which imply that f preserves the hyperbolic area.Give a…

Q: what is Z in rectangular coordinates (A+jB)?

A: To simplify the expression and calculate Z in rectangular coordinates (A+jB), let's break down the…

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Q: Verify that (x)= 1-ce 5x dy- where c is an arbitrary constant, is a one-parameter family of…

A: Given  To Verify:  , where c is an arbitrary constant, is a one-parameter family of solution to…

Q: Identify a basis for the following subspace: -a a-b 2b 3a W = A B D (9) 2 3 1 ( 1 ER 0-3 1 © [ ] C…

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Q: 6 -1 -2 -3 0 2 0 1-2 nations of the columns of A. . W is the • Is b € W? . In one line (with minimal…

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Q: So " 1 (x - 5)²/3 dx.

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Q: Find a basis for the column space of B = 1 0 -1 6 0 10-3 0 0 1 00 00

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