Express the complex number z = 4+2j, in the polar form z = r(cos0+ jsine), where - < 0 ≤T. Express your answers correct to three decimal places. Enter r: Enter 0:

Q: If (G, *) is a group such that (a * b)−¹ = a¯¹ * b-¹, for all a, b € G, then G is -1 a/an Select…

A: The correct option is PART B (abelian group) We are given that (a*b)-1 = a-1 * b-1, We have to prove…

Q: Define f(n) = +¹-(-1)" for all n € Z. Thus, f: Z → Z. Which is correct? Select one: O a. O b. O c. f…

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Q: Given the statement P(n) for integers n > 0. If you can't prove the base case, for which values of n…

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Q: A rectangular electric burner plate of the region 1 ≤ x ≤ 3,-≤ x ≤ is heated so that the temperature…

A: Given: It is given that a rectangular burner plate of the region 1≤x≤3, -π4≤x≤π4, is heated so that…

Q: R B > The graph of y = 2* is shown in black (K). Match each equation with a graph above. 2³+1 22-1 G…

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Q: II. Solve the system of equations 2x - y = 3 (3x + 2y = 1

A: The given system of equations are: 2x-y=3                . . . i3x+2y=1              . . . ii We…

Q: A. The radius of convergence of 1(-1)43kk(x-4). B. 0 C. 00 D. 3 series solution about z = -2

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Q: Let (Q be the set of negative rational numbers and () is the arithmetic multiplication. Then (Q,) is…

A: False. Since the set of negative rational numbers are not closed under the algebraic multiplication,…

Q: Let = 5√2-5√/2i 8 Write z in polar form. Then find z24 and write it in the form x + yi. Draw the…

A: Polar form of any complex number z=x+iy z=r cosθ+i sinθ Where r=x2+y2   and    θ=tan-1yx

Q: Consider the term In(N!). Compare this exact value with the more accurate Stirling approximation,…

A: The given term is lnN!. We have to compare this exact value with the more accurate Stirling…

Q: Why is 1% = e ?

A: To Prove: 1♾️= e

Q: Answer by computing and showing the computation 4 -------- 2 b= 5 C = 6 1. Let: a = 3 1 find: 3 a…

A: We have to solve given vector questions.

Q: Prove that if n, a and b are positive integers such that nlab, and ged(n, a) 1, then n|b. (You may…

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Q: Solve the following edo of ricatti dy dx = y² + xy + 2x - 4, 3/₁ = -2

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Q: 10. The equivalent form of Using unit step functions is A. u(t-2) (sin(t) - 3) +3 D. 3u(t-2)-…

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Q: It can be shown that for arbitrary b, 8(bx): 8(x) You can assume these results for this part of the…

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Q: (c) A triathlon competition consist of three events, running, swiming and cycling. The winner,…

A: To solve this, we use the following relation: Time=DistanceSpeed Let x, y, and z be the lengths of…

Q: Q1: Determine whether the sequence a(n) = n*sin(1/2n) converges or diverges. If it converges, find…

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Q: Compute the periodic rate and interest in the first period for a $2,000 loan with 8.5% APR for the…

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Q: 5. Find the solution of the owing constrained maximizatio problems (assum y ≥ 0). (a) maxx,y {f(x,…

A: We find maximum value

Q: Find the fourier Transform for the signal Given Ye Sinh (H)

A: Given: Signal, y=sinhtTo find: Fourier transform of the given signal.

Q: If a, ß and y are the roots of the equation, x³ - x - 1 = 1 + a 1+ B + 1 - α - 1- B + 0, then 1 + y…

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Q: Find the eigenvalues and eigenvectors associated with the matrix A = = (²₁³) Determine the…

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Q: Consider the following true fact: For all n, m € Z \ {0}, if ged(n, m) = 1 then there are a, b € Z…

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Q: Solve the initial value problem for t> -1 with y(0) = 8. Put the problem in standard form. Then find…

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Q: A cold metal bar at -10°C is submerged in a pool maintained at a temperature of 50°C. After 55…

A: Answer given below.

Q: 3. Find the values of x and y that solve the system of equations (assume x ≥ 0 and (a) xy = 4 and…

A: We have to find the values of x and y that solve the system of equations (assume x≥0 ) a xy=4 and…

Q: (470) Find the matrix A if A 1

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Q: A Norman window has the shape of a rectangle with a semicircle on top, as shown below. h A Norman…

A: Outer perimeter 90 ft

Q: (t-7)y' + (t-1)y = Int+t-¹, y(-2) = 4 Find the interval in which the solution of the initial value…

A: From the Existence Theorem : An ODE of the form y'+P(t)y=Q(t) has a solution in an interval, where…

Q: For each series, determine whether it converges absolutely, converges conditionally, or diverges. ∞…

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Q: 2. Determine the equation of: a. The cubic function with zeroes 1, -2, -5 and y-intercept 10. b. The…

A: (a) Let fx=ax3+bx2+cx+d The function  has zero at 1,-2,-5 and y- intercept at 10 that f0=10…

Q: Consider the differential equation (2x-xy) dx - 2dy=0 with the initial condition y = 1 when x = 1.…

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Q: 30(2te¹ +5) The number of members of a newly founded club is given by M(t) = et members per month,…

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Q: For the following graph G, let X denote the set of vertices in G that have even distances from…

A: (a) We first determine and note down the distances of the all the vertices from z.      dist(z, z) =…

Q: (Section 5.3) i. Show that the vectors v₁ = (1, 2, 3, 4), №₂ = (0, 1, 0, −1), and v3 = (1,3,3,3)…

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Q: The union of any two subgroups of a group G is a subgroup of G. TRUE FALSE

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Q: Manually apply the Hungarian algorithm to solve the assignment problem having the following cost…

A: The given cost table is   1 2 3 4 A 4 1 0 1 B 1 3 4 0 C 3 2 1 3 D 2 2 3 0 Solve…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT Determine {f(t)} for: a) f(x) = 3x3 - 10x+8 b) f(t)= e-4x

A: a).  Given f(x) = 3x3 - 10x + 8 As Lf(t) = ∫0∞e-stf(t)dt So here Lf(t) = ∫0∞(3t3-10t+8)e-stdt…

Q: When Jose just moved into the town and wanted to set up an internet connection using AT&T, he was…

A: Total payment p=$200 Rate of interestr=1%  monthly Total periode n=4

Q: Find the eigenvalues and the corresponding eigenvectors for the matrix. -6 5 A 3

A: A=-4-635

Q: Let a₁5 -6 5 -25 and b= 5. For what value(s) of his b in the plane spanned by a, and a₂? The…

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Q: By calculating the Finite Differences, determine a. Which type of polynomial function best models…

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Q: A couple pays $600 at the end of each 6 months for 5 years into an ordinary annuity paying 6%…

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Q: Exercise 1.4.8: Solve x²+1 y² + xy = 3, with y(0) = 0.

A: The answer provided below has been developed in a clear step by step manner.

Q: Let F = Z₂ and let f(x) = x³ + x + 1 € F[x]. Suppose thataisa zero of f(x) in some extension of F.…

A: F(a) is the smallest field containing F and a. Since f(a) = a^3 + a + 1 = 0 in some extension of F,…

Q: can you write it?

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Q: Question 7. Give an example of a set A, for which A^[1,4] = A^N and A \ Z ‡ Ø.

A: Answer given below.

Q: 3) The solution of, y(1) - 1 is. B. y²=²+1 A. r² = y² +1 C. y² = 2x² +1 D. ²-²=0.

A: Given: The differential equation dydx=xy , y1=1. To Find: Solution of the given differential…

Q: Find the general solution of the given differential equation. dy dx y(x) = + y = ( 1 ) ² x + ce x ~…

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