Let p, q, and r be prime natural numbers with p # q and n= p2q. Then, all the subfields of GF(r") are a) GF(r4) for d=1, p, and q. b) GF(rd) for d = 1,p,q and pq. c) GF(r") for d = 1,p,q.pq,p² and p'q. d) GF(r4) for d = 1,p.p².q.r.pq.pr.qr.pqr, and p q. O a) O b) O c) d)

Q: Compute (-1AT + 2B) C, where A = (-14T +2B) C = 9 7 4 -3 7 -5 " B = -5 9 -4 6 7 3 and C= 6 3 () -3 7…

A: To find (-1AT+2B)C

Q: Let p, q, and r be real numbers such that p + q +r = 26 and '/p + lq + '/, = 31. What is the value…

A:

Q: Determine the positive real numbers x and y such that • x + y = 4 and 2.n2 + y² is small as…

A:

Q: Show that Sn is solvable when n ≤ 4.

A: We see that S1  is the trivial group {e} and it is solvable.   We see that , |S2| = 2 so it is…

Q: Recall the property that (a, b) = 1 if and only if ax + by = 1 for some integer x, y. Use this…

A:

Q: Show that PLEU FUG) = P(E) + P(F) + "P(G) - PLENF) - P(ENG) - P(FNG) + P(ENENG)

A: There are three events. These are E, F, G. The objective is to show that,

Q: r A continous random variable x has p.d.f.,then f(x) >;0 a O It; f(x)==0 f(x) >==0 f(x) >=1 .b O .CO…

A: fx is probably density function that must be positive.

Q: Suppose s and t are distinct natural numbers. Show that lcm(s, t) + lcm(s+1, t+1) > 2st/(sqr(|s −…

A: Given: s and t are distinct natural numbersTo prove: lcm(s, t)+lcm(s+1, t+1)>2sts-t

Q: How, Form P.D.E. from: a (3) Ucx,y) = (x²+a)lytb)

A:

Q: Reducir: 2-3 + (– 3)–2 – + (2012)° а) 3/8 d) 1/2 b) 9/8 c) 2/5 e) 3/7

A:

Q: If n = 12 m (me N), prove that "C₂ (2+√√3)² "Co- - + "C4 (2+√√3)4 "C6 (2+√3)6 ·+···=(−1)| 2√2 1+√3 n

A:

Q: f6) = 5-31 5+3x Q11. Let %3D

A: Given: To Find:

Q: Suppose X~N(19, 2.5).  Find P(X = 17)

A: Given X~N(19, 2.5)

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: Let a > 0 be a real number and I = [" LL* rdzdrd0. Then I = 2па 4па па None of these

A:

Q: 8. flx) =3=x*, glx)=x² 4 d) Domain A domain Domain

A: A function is like a machine that takes an input and gives an output. In mathematical terms, a…

Q: Factory full, if possible. a) 40a b5-85a?b"

A:

Q: 7. I) Find, if possible, AB ond BA A= 3212/ 2.

A:

Q: а) За — 5 <7х + 7 -6 –5 –4–3 -2 – 1 1 2 4 5 3

A:

Q: E. On the right: a. r*ak + r*(-ak) = r*(ak + (-ak)) b. r*(ak + (-ak)) = r*0 c. r*0 = 0 F. So, r*(aj…

A: the last three lines also proves b and c too.

Q: Find the values of z2n = 5- i, n will be taken from the set (2, 3, 4, 5} while w is the argument…

A: In the given question we have to find the value of z2n=5-i,n∈{2,3,4,5}.in the given we use the…

Q: For 1 De

A:

Q: verify that (A + B) + C = A + (B + C)

A: Now,

Q: verify that (A + B)C = AC + BC

A: To verify that (A+B) C = AC + BC.

Q: To show B(m,n)=+x²² -dx (1+x)"¹"

A:

Q: 7) The perimeter of a square is 16x²-12y Find an expression for the length of each side. ( [atnioq…

A:

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

A:

Q: be the sets B1={u1=(-3,0,-3),u2=(-3,2,-1),u3=(1,6,-1)} B2{v1=(-6,-6,0), v2=(-2,-6,4),v3=(-2,-3,7)}…

A:

Q: ) List all the possible rational zeros of flx) = 2r - 5x + 2x + 6 A) 2, ±3, 26 * 21, 2, 23 ±1, C)…

A: Topic = Algebra

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

A:

Q: 1. Determine whether or not the expressions below are wff (well-formed formulae). Explain your…

A:

Q: 5) For each + ive integer i, where i is equal to three, then find the union and intersection of…

A: 5 Given that Ai=x∈R|−1i&lt;x&lt;1i=−1i,1i. a We have to find the A1∪A2∪A3 and A1∩A2∩A3. Here,…

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: ) = Zzz 2(러)(2-3) Find XCK) is X(2)

A: