Let ut satisfy the recursion with u = 3. = Ut+1 (4ut + 1) mod 5 = Number and uz , 22: = Number Then u1 In order to map ut to the interval [0, 1) we would divide by Number = Number

Q: Write a proof that proves the Union Un an element of natural numbers (-1/n, 2-1/n)=(-1, 2). Also…

A: The given interval is (-1/n,2-1/n) where natural number n belongs to positive integers. So that we…

Q: obtain 2- transform for the flow ing xCt) = tCt- 2T)

A: We have to use z transform table.

Q: Let u = (5,5,0) and v= = (5,5,5√√2). Compute |uxv|. Then sketch u, v, and uxv. |uxv= (Simplify your…

A: I have explained everything with in the solution. Please go through that.

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: prove that :: 2) (1+i) (1-1)² = 64

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Q: For 1 De

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Q: 1. Expand and simplify. /10K] a) (5m – 8)(3m –- 2) b) (5x – 3)² c) (x + 4)(x – 5) + 3(4x – 5)(x –…

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Q: Prove that √1+i√3+√1-i√3 = √6

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Q: Let f and g be permutations. Show that the order of h=fgf^−1 is the same as the order of g.

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Q: If the first seven terms in row 9 of pascal's triangle is given by: 1 9 36 84 126 126 84 a)…

A: the first seven terms in row 9 of pascal's triangle is given by:   1     9     36     84     126…

Q: Prove the following using a direct proof.  If a,b, and c are integers such that b is a multiple of…

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Q: y QI:: Let X₁, X₂ ~ N(0,1) 1) X1-X₂ X₁ + X2 2) (x1+x²)2 X₁-X2 what dist of 2X² 3) x² + x²

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Q: Use the substitution u = √x+9 to evaluate =(√x +9) * +c ² / (√x +9) ²¹ +C 1 / (√x +9) ²+ + C =(√x+9)…

A: By using substitution u=x+9 to evaluate ∫x+93x dx.

Q: [2 4 21 A = l1 3 1 1 1 B = -2 -1 [2 4 D = 4 C = 1 3 21 -1 %3D 2

A: Given A = 242131B = -1111-2-1C = 242131D = 1-1-1-121 Clearly  C = AD = -B

Q: 16. Find the set of real values of x for which:/3 - 2x/S/x + 4/. N.Find the set of values of x for…

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Q: for ne J, x is a (1-x)(1+x+x²+.. + x^²) = 1=x^²+₁ variable, prove that

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Q: how did the y' and 2y' apearred out of no where in line 7

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Q: Prove that 13n13 + 11n" is always divisible by 24.

A: Consider the given expression.

Q: 28) 28) -4 < xs -2 A) (-4, -2) B) (-4, -2] C) [-4, -2) D) [-4, -2]

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Q: 2. Show that if a]b then a'|b² for all integers a and b (Symbols V, 3, A, V, V,A,→,-)

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Q: Queshon 6) Compute the arthogonal projection of 8 onto the Line L through -S] and the origin. -6 LS.

A: We have to find the orthogonal projection of v on the line through P and the origin.

Q: If a =(2,3,-1) ,(1,6,0) ,(2,1,3) prove that Aa^-1 =A^-1A=I Please show all the step

A: Given matrix is, A=23-1160213

Q: 23) Expand: 2r(x² +1)-(x² + 5x - x - A) x² - x² - 3x - 7 B) x* + 2x² - 3x -7 C) x² +x² - 3x +7 D) x*…

A: The given expression is2xx2+1-x3+5x-x4-7 expand the given expression and then simplify to obtain the…

Q: Prove that {4a + 126 : a, b E Z} = {4c: c € Z}.

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Q: = solve (y² + 2y² + ay +18) dx. (5x³y²-x²y + 17x²) dy

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Q: Using strong PMI, show that every natural number is a sum of powers of 2. For example, 11 = 23 +2¹…

A: Using strong PMI, we have to show show that every natural number is a sum of powers of 2.

Q: a) b) Negate and simplify the following statement in symbolic form. *xx.y [((x>0)^(y <0))-(xy <0)]…

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: 11) Find x if ST=x+3 and SU=2x/

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Q: 3 4 Evaluate [, S* 2dydx

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Q: 5 М — 11 Find formulas for the entries of M", wheren is a positive integer. M" =

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Q: expressions. @-岩。) 3b 9. 2a 2х -3 Зх-2 4. 4x 3 6. 긁-꽃 + 13 7 X-3 2x 3x 8. 5х-20 x2-16 x2- 3x +2 3x-3…

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Q: If gcd( m, 91) = gcd( n,91) = 1 then show that 91|m³7 – n37 %3D

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Q: Use substitution method to prove step-by-step that (PAQ)^(P = –(Q^R))^(S = R) = ¬S.

A: We are asked to prove the following using the substitution method, P∧Q∧P⇒~Q∧R∧S⇒R⇒~S We will show…