Suppose that A and B are two positive numbers and that x = In(A) and y = In(B). Write the following expressions in terms of x and y. (a) In(AB) (b) In(B’VA) (c) In В (d) In(A) In(B)

Q: Show by an example that (AB)" B™A".

A:

Q: (4) Prove in two different ways that if a is a positive r number, then (a + 1)" > a" + na"-1:

A:

Q: Find (a) ∣A∣, (b) ∣B∣, (c) AB, and (d) ∣AB∣. Then verify that ∣A∣∣B∣ = ∣AB∣.

A: Hello! Thank you for the question but as per our honor code we'll able to solve only three sub -…

Q: 2 - If A and X then - 11 5 7 А.Х —

A: From the given problem:   A=-20-115 ; X=-17   Now,   A.X=-20-115.-17

Q: d) Prove (AV (Vx) BC = (Vx)B(AV C), as long as x not free in A. (Hint: Translate first to Standard…

A: Given,  Prove (AV (Vx)BC = (Vx)b(A V C), as long as x not free in A. (Hint: Translate first…

Q: 6. Evaluate In (x - In (r-...))dr in terms of some new variable t (do not simplify).

A: Given :- ∫lnx-lnx-...dx To find the given integral in terms of some new variables t

Q: Let →u=⟨6,−4,−6⟩ and →v=⟨−5,−3,−6⟩. Compute the following:

A:

Q: (b) Let A¡ = [-i, 1] for every positive integer i. Find U A¡ and N1 Aj.

A: Given that Ai=-i,1 for every positive integer i. That is, A1=-1,1, A2=-2,1, A3=-3,1 and so on. To…

Q: I (Inx)³ nx-X

A: Let u and v be the function of x  Then∫uvdx=u∫vdx-∫(dudx∫vdx)dx

Q: Ex: evaluate 1 203 (1- 3 (1 – t)0.9 dt 0.

A: Explanation of the solution is given below...

Q: Let F = (, , 2). Calculate div (F) and curl (F). (Use symbolic notation and fractions where needed.)…

A: We have to calculate  and .

Q: Let A = (-0,0), B=(0,0) then AUB=

A:

Q: PROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 4

A: To verify the given expression is followed by matrix X .

Q: Find the argument of 1+i ал with integer a,b b write your answer as a/b for Arg (1+i) =-

A: We have to find the argument of 1+i in the form of arg(1+i)=aπb with integer a, b.

Q: 6x 3x 5y 2. 5y 6x-4 3. + 3r+8 1ly 11y

A: Given that: 6x5y-3x5y To solve, Apply  rule:  ac±bc=a±bc6x5y-3x5y=6x-3x5y=3x5y

Q: (i) (Z- Q) and specified in it using the most concise notati

A: Firstly we write elements of both sets Z and Q and then find Z–Q

Q: Evaluate the following commutators [Â, B] = ÂB – BÂ. Hint: use an arbitrary function that cancels at…

A: a x,PxPx=-ih∂∂xx,Pxφ=x,-ih∂∂xφ=-ihx∂φ∂x+ih∂∂xxφ=-ihx∂φ∂x+ih∂φ∂x+ihφ=ihφ∴x,Px=ih

Q: If x=y+qp and f=xy+qp² Express x in terms of q,p and f

A:

Q: 2 4. Express 989 = 23 43 in the form x² + xy + 5y².

A: The given number is 989. The objective is to express the given number in the form of x2+xy+5y2.

Q: Evaluate: (8t – 121 + 6)dt

A:

Q: Q1) Find the inverse of A (1 00 A=2 1 0 5 4 1

A: A=100210541

Q: Let the score on Fred’s first exam be q, the score on his second exam be s, and the score on his…

A: Score in first exam = q Score in second exam = s Score in third exam = t Total score = q + s + t…

Q: 1 0 A= 0 0 0 -1 3 2 1 7 3 1 1 -1 0 -600 3OTSO 0 1 0 2 1 B= 3/2 6 1 -1/2 3 5 -2 2 1 -6 4 1 1 0 3/8 3…

A:

Q: IfÂ=ax+ißP,, where a and B are real then (axR+1BP,x]is -hB

A:

Q: S= 1 dx xinx

A: This is a problem related to integration. Please follow the procedure given below.

Q: Show that Q[x]/⟨x 2 − 2⟩ ≅ Q[x]/⟨x 2 + 4x + 2⟩.

A:

Q: Show that * y = (y² – r*)(2² – x*)(2² – y³)

A:

Q: Suppose SCR is a set of numbers. (a) Define inf(S) and sup(S). (b) Show that inf(S) = - sup(-S). (c)…

A: Set: A well-defined collection of objects or numbers is called a set. We can write a set in two…

Q: Let 1 2 3 1 A = | 6 -2 3 and I3 =| 0 1 5 4 1 If 2. is a real number, compute 2I3 – A.

A: A = 1236-23524 I3=100010001

Q: Compute the following values, showing your work: φ(20), φ(25), φ(54) and φ(8!)

A:

Q: x(3-5х) J - (3x-1)(х-1)* # 2) Evaluate: -dx-

A:

Q: (² 4 Calculate AT Let A = Select one: O a. O b. O C. O d. (63) 5 TOT -4 0 0 -2 -3 2B. 2 (9²) -5 -2 0…

A: The matrices are given by A = 0-24-3B = 21-11 To evaluate: The value of AT-2B.

Q: HxER x2- 9х — 36 >0 х>12 or x < —3

A:

Q: Which of the following are multiplicative inverses:  (a) 5y/x and 5x/y (b) 5y and 7y (c) 7y/x and…

A: Here we have to find which of the options are multiplicative inverses.

Q: Please answer A and B.

A:

Q: (a) Show that (A B)? + |A X B2 = (AB)? %3D

A: Question a) (A.B) = AB*Cos(x°) (A*B) = AB*Sin(x°) where, x is the angle between vector A and vector…

Q: Let x, y, and z be real numbers. Prove the following a. -(-x) = x b. (-x) * (y) = -(xy) and (-x) *…

A: I have provided detailed proof for each question in the Explanation section.Explanation:Let's go…

Q: Let ged(a, b) = d then which of the following is correct @ dla (i) dlb (i) dl(ax + by) (a) only (i)…

A: gcd(a,b) = d