Let n e Z. Prove that n² + 4 is divisible by 8 if and only if 3n + 6 is divisible by 12. (Hint: the statements n | m, 3k e Z: m = nk, m = 0 (mod n) are all equivalent)

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Q: Solve for y in terms of x for the foltowing

A: e(ln2)y=12lne(ln2)y=ln12yln2=-ln2y=-1  

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Q: e theolem Let f be acontinyous fanchion o interior Tand citfble on ay - Point XEI then O f )<o VxeIt...

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Q: II. Perform the following conversions 1. FADE base 16 to base 8 2. 1110011100 base 2 to base 5

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Q: Leminia A novmad spuce F has astricty conven norm if and only 1R the tringle inequality is strić on ...

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A: Introduction: The rate of change of a function is the derivative of the function. It is obvious that...

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Q: Find a value a > 0 so that the graph of the exponential function f(x) = a" contains the point (3,1/2...

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Q: Determine if g is differentiable at r = 0 if 2 cos r, if -1<r<0 9(r) = %3D if r2 0. r+cos r

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Q: Suppose that the tringle inequality is strict llel veetor s that means para V Qe R on non get 11 x+y...

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Q: 2. Consider a square ABCD and an equilateral triangle BCE in its exterior. Let F be the midpoint of ...

A: Given figure is Since ABCD is a square and ∆BCE is equilateral . So DC=CE

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Q: X1 + X2 – X3 = –-3 6x1 + 2x2 + 2x3 = 2 -3x, + 4x, + x3 =1 %3D

A: Given system is  x1+x2-x3=-36x1+2x2+2x3=2-3x1+4x2+x3=1 1: Simple Gauss elimination: We can write it ...

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Q: 10 Find lim x12s 3. X->- X -25 2 lim Jx +3 - 2 メ→」 O lim Sitx - -x 3. 1-X 2 X

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Q: For the following questions (11.i– 11.iii), a) Find the intervals of increase or decrease. b) Find t...

A: Let us consider the function f(x) The critical point is obtained by taking first derivative if the f...

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Q: Problem (1): Show that there is only one automorphism, the identity function, of Q.

A: Since you have posted a multiple  question according to guildlines I will solve first   question fo...

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Q: (a) Find the determinant of the matrix A = where z E R. (Hint: Use row reduction and factor the dete...

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Q: a² sin(2y – 52) =1+ycos(6zx) 4.xsin(2y – 5z)+ sin(2zx)6zy O A. cos(2y – 52)(-5)a² + sin(3zy)6xz 4.xs...

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Q: Let T = ((14)(23567)), the cyclic subgroup generated by (14)(23567) in S7. (a) Determine all subgrou...

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Q: SANTIQUEVATET AADT-this are data that are countable and can be 3 MIRRPAY ATDA- data that gather to t...

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