Let A = {m € Z/m = 4k +8} where k = Z, and let B = {n € Zn = 2r + 2} where r = Z. Show |A| = |B|.

Q: Prove that Question 22 0 D={[% &]iªbER} a,b a b2a is a subspace of M2.2

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A: By stokes theorem                            ∫∫s ∇×F→ ds =∮F.→ dr→  we have evaluation of Line…

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Q: Calculate ffs f(x, y, z) do For Sfs f(x, y, z) do = x² + y² = 16, 0≤z≤ 9; f(x, y, z) = e

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Q: (1) (2) (3) Differential Equation dy sin(x + y + 2) dx x²y" xy' + e* = 0 dx dt. = = √3 - cos x DV IV…

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Q: Use Stokes's theorem to evaluate fF.dR or ff(V x F) ndo, whichever appears easier: F = xyi-yzj +…

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A: Fx=e-x+1

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Q: (d) How many functions f: A→ A are there so that fRIA? Explain.

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Q: Given a vector field F= (-y,x,0), compute the following results: (You should use any integral…

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Q: 3 Use induction to prove: for any integer n ≥ 1, 3 evenly divides n³ + 2n.

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Q: 23. F(s) = 5s² + 34s + 53 (s+3)²(s+1)

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Q: 4/5 divided 1/4

A: 4/5 divided 1/4

Q: DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then the integral f(t) =…

A: Given function is f(t) = te8t

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Q: (2) Σ3 n=1 (b) Σ n=1 (0) Σ n=1 (e) (−1)n-¹ n (n + 2)3 n-1 n-1 η2 + 2n en n!√n (1) Σ n=1 f In(n)

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A: Kindly refer to Step 2 for the solution.

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A: The given equation is, y=f(x)=ax4+bx3+cx2+dx+e. To Find: Values of a,b,c,d,e If slope is -24 at x=3…

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Q: Determine the solution of the following differential equations: (D²-1) y=- (Use MRO and MVP) 1 e2x+

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Q: 3 10 4 1. Carl bought 7 gallons of gas last week. Today, he has 2 gallons left. How much gas did he…

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Q: In Problems 21-30, determine L-¹{F}. 6s²-13s +2 21. F(s) = s(S-1) (s-6) s+11 22. F(s) = = 23. F(s) =…

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Q: The population of a certain city was 16000, then 5 years later the pouplation was 28000. Part 1…

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Q: (a) Set up a double integral for calculating the flux of the vector field F(x, y, z) = xi+yj through…

A: Solution:-

Q: 1. Use Dijkstra's algorithm to find the shortest path length between the vertices a and z in each of…

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Q: Suppose Alice and Bob want to communicate using a Elliptic Curve Diffie-Hellman scheme. They choose…

A: Given:  Suppose Alice and Bob want to communicate using a Elliptic Curve Diffie-Hellmanscheme. They…

Q: Consider r¹7 in Q[r]. (a) Find the splitting field E of over Q. (b) Compute [E : Q].

A: Given: x7-7 in ℚxTo find: a) Splitting field E of  x7-7 in ℚx              b) E:Q

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Q: Define the linear transformation T: R³ → R¹ by T() = A. Find a vector whose image under T is b. 2=…

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Q: Juanita was involved in an auto accident in which she was at fault. Her own car sustained $1,249…

A: Given that Juanita was involved in an auto accident in which she was at fault.  Her own car…