Express In in terms of In x, In y, and In z. O - In x + 2In y – In z O In x - 2 In y + 2 In z O Inx - 2 In y + In z O 2 In x + 2 In y + In z

Q: 1 For any integer k, 3|(2k² + 1) if and only if 3 k

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Q: 17. Express 4xi + 5yi + 6xi? + 2yi“ in simplest a + bi form.

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Q: Determine L-1) 9s – 8 (? – 2sJ*

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Q: Find all n ∈ Z for which 3x^2 + 2nx + 12 is irreducible over Q.

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Q: Given a positive integer n, let a2,n–1 a2,n a3,n-2 a3,n-1 a3,n An = аn-1,2 аn-1,n-2 аn-1,п-1 @n-1,п…

A: Given: Here the given positive integer n, Let An = 00...00a1,n00...0a2,…

Q: Let a = (17 3)(5 94 2) and B = (2 3)(7 4)(5 1 8) be elements of S10. Then, a²B- is O (1 4)(27 539 8)…

A: Given permutations: α=(1 7 3)(5 9 4 2), β=(2 3)(7 4)(5 1 8). To find: α2β-1.

Q: O 8x² √4-x+ 3 O 8√4-x+ 2(4-x) √4-x 3 *-*-*) J+ +0

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Q: 2. What is the general term of 1, 3, 6, 10, 15? O 2n – 1 n^2 – 1 (n^2+1)/n O (n(n+1))/2

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Q: 5. Let, a1 = 1, a2 = 2, b1 = 0, b2 = 1, for n ≥ 3, an = 2an-1+ bn-1 for n ≥ 2 bn = bn-1 + an-1…

A: Given Let, a1 = 1, a2 = 2, b1 = 0, b2 = 1, for n ≥ 3, an = 2an-1+ bn-1 for n ≥ 2 bn = bn-1 + an-1…

Q: Find the sum of 73 ㅈ5 11.3 3.5 ㅗ ㅈ - + ㅈㄱ 15.7 + n-1_2n+1 ㅈ (1)h 12n-1 (2n+1)

A: We can solve as follows

Q: Find the difference between the sum of the first 11 terms of {an} and the sum of the first 11 terms…

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Q: Show hat + £ +} + - - +$ is out entges

A: Given The given statement is that 1+12+13+· · ·+1n is not an integer.

Q: If In x +In(x-3)=In(6x), then X=

A: The equation is given as ln x+ln x-3=ln 6x

Q: 5. Identify the mistake(s) in the following "proof": Theorem: The sum of any two positive integers…

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Q: A cosets of of 212 are اخترأحد الخیارات + 2, +1,.1 O + 1,.2 O + 4, + 1, .3 + 4, + 2, + 1 , .4 O

A: Cosets Definition: Let G be a group and let H is a nonempty subset of G. A left coset of H in G is a…

Q: Prae that x4 -5x +3 is ineducible ouer Q

A: Given polynomial is f(x)= x^4 -5x^3 +3

Q: Determine the quotient 3x- 1)6x + x + 8x + 9x- 4 O A. 2x + 3x2 - 2x + 4 O B 2x + 4x² + x-4 O C 2x +…

A: We can find the quotient as below.

Q: (W/) Express In x in terms of In x, In y, and In z. - In y + 1. In z 2 2 In x + 1 2 In x- In y + In…

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Q: 21. How many positive integers x are there such that 3x has 3 digits and 4x has four digits?

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Q: 2 [[t+²2] ² Evaluate Lt+ :

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Q: Show that among any 4 n−1 people, there are either some n of them who mutually know each other, or…

A: Pigeonhole Principle  :  Simple form Theorem 1  :  If n + 1 objects are put into n boxes, then at…

Q: 9. The inverse of an element a of Z under the operation * defined as a*b = a + b - 1 is_ A. a -2…

A: Given ;a*b=a+b-1

Q: (3) VL1, L2 ((L1 L₂ L₁*)* = (L2 U L₁)*). O True

A: True.  this statement generally

Q: compute AB

A: Given,A=314-201122 and B=102-3112-41

Q: hen Let here a11 = , 923 = , 912 = " A = A-¹ a31 = = 1 1 all a21 a31 8 8 -8 , a13 = a12 a22 a32 " 0…

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Q: Express In x V in terms of in x, In y, and In z. 2mx-글 my-글 nz 2 Inx + 글 Iny-글 mz znx+my+nz In y 2nx…

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Q: Char(3ZOZ4) is اختر احدى الدجابات O 3 O 12 O 4 O o

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Q: Ifx+y+z= 1 and x, y, z are positive, then show that ( 1)² ( 1)² ( 1)² 100

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Q: 15. Use a 30-60-90 triangle to find the tangent of 60°. 2 /60° 1 30% √3

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Q: 1. Simplify 7V8-V18. O 17/2 O 7V8 - 3V2 O 7V8-V18 O 11/2

A: NOTE: Refresh your page if you can't see any equations. .

Q: 10. By Binomial Theorem (2a – b)* =16a* – 32a’b+24a*b? – 8ab³ +b* | a. TRUE. b. FALSE.

A: We know the binomial therom expansion

Q: (-5) + 4 – 1+ 4- (-21) * (-7)) ova

A: Simplification