(a) (b) (c) (d) If P and Q are odd positive integers, we have mn ( ² ) ( ² ) = (m²). m Ⓒ) (@) = (₂) (F) () = () whenever m = n (mod P). a²m P = () whenever (a, P) = 1.

Q: 4. For n E N, n ≥ 2, find a formula for İ(¹-) j=2 and prove that your formula is correct. Note: This…

A:

Q: a. If p=√q=ra and pqr = 1, show that, x + y + z = 0.

A:

Q: Assume xo = x2 – 2h, *1 = 12 – h, a3 = x2 + h, 24 = x2 + 2h Use the undetermined coefficients method…

A: To solving the system we use the Gaussian Eliminating and back substitute method

Q: 6 (iv) (v) (8) 5

A:

Q: 4. The function A(t) = 2000(1.)' represents the growth of algae in a pound after time t (in hours).…

A:

Q: (d) (x² + 2x + 1)q(x) = 1 (mod x³ + x² + 1) over Z3

A:

Q: (a)(√2-i)-i(1 – √√2i) = −2i; (Ⓒ) (3, 1)(3, −1) (3, 1) = (2, 1). (c 5' 10 Show that (a) Re(iz) = - Im…

A: Few Complex number expressions and equations are given.

Q: HW Prove that: £x [XJv (x)] = - X √√ +1 (X)

A:

Q: Let f(x)=2x-3,g(x)-5x, and h(x)=x2 what is the sinpliest fornm of h(x)*g(f(x))

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

Q: , 7/4 /213, 33 b) Solve e In(9) + 21 = 41 for æ. a) Write In(- -) in the form a lIn(7) + bln(3)…

A:

Q: 7. (a) Find the square root 14+4√6.

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

Q: 21. Given the functions f(x) each: a.) (fog)(x), = 1 x + 5 and g(x) √2-x, find the following b.)…

A:

Q: 6. Simplify the rational expressions (a) st = ut 24 w %3D (zw)

A: As per bartleby guidelines for more than one question asked only first is to be answered please…

Q: (2) The real part of Syy (@) and the real part of Syx (@) are even functions of o, i.e., Re[Sy (@)]…

A:

Q: Show that: n n > (xi – x)2 > x? – n(x)2 | i=1 i=1

A:

Q: What is y' of y= 7√x 3√x ? A B C D 21√³ (In 7 + ln 3) (In 4) 21√x √x 21√ In 10 2√x 3 In ( - ) 21 V ²…

A: We have to find the point on paraboa y=-x2+4 whose tangent line is parallel with y=3x+5Parallel line…

Q: 2 ln (1+√√y) = 2 ln (1+√√x) + In C n{(1 + √y)²} = ln {C(1 + √@)²}

A: Given that 2 log 1+y=2log1+x+log C Here we need to explain the next steps.

Q: LAR널)] = Y(S) = [올 +2 Yi(s) = Y,(s) = (S+4)×2 블 +8S+20 N/A ( 52 ) ³²+ + 4 . √2 + 5 - S14 (S+4) e (5²…

A: To show:-

Q: 7 (4) - [9(& · Ã) –÷(¥9)]

A: In vector calculus, gradient and divergence are very significant. The operator ∇→ is used to express…

Q: prove that theta(2m) = theta(m) when m is odd and theta(2m) = 2 theta(m) when m is even

A: We can start by using the definition of theta notation to prove these statements. Recall that theta…

Q: Consider the Legendre polynomials of degree n Ph(x) = Σ (1)m 0<m</ where n is a nonnegative integer…

A:

Q: a rational number y=10.01 b) Assume an integer, b=2 from 111 to 9 I assume from the range (0, ³/25).…

A: Given, X~Uniformx-32, x+32

Q: Integrate the function. √√36-x² dx O 18 sin O sin ¹ (-2) + x√/ 36 - x² + C +C 2 O 36x √√36-x²…

A:

Q: 14 - If P(x) = 1/10, x = 10, then E(X) is: a) Zero b) -1 C) 6/8 d) 311 1

A: The formula of expected value is: E(X) = X*P(X) Given: X=10 P(X) =1/10

Q: Find limn→∞ Zn, where zn = 2n + 2 n + 2n 2n +1 -i.

A:

Q: Find the root (3 – 3i)2 - + V18[cos(r/8) + isin(x/8)] O +V18[cos(x/8) – isin(t/8)] +3 V2[cos(1/4) –…

A:

Q: Prove that (0.01)(100sin2π(5000)t)2 is equal to 0.5+0.5cos2π(10000)t

A:

Q: Suppose that Pr[A]=8/13, Pr[A|B]=5/7, and Pr[B|A]=5/8. Find Pr[A′|B′]

A:

Q: „¸ 1) and ♂ = (1, 1, 2). Find || ☎ – proj♂¯||. d) 2√3 3 (e) None of these

A:

Q: Which of the following is/are equal to 13 dr 1+æ4 You may find the following formula useful B(m +…

A: Use improper integral

Q: 9. A person on an assembly line produces P items per day after t days of training, 400 where P(t)=…

A:

Q: Q2) n(x) = x-1 , k(x) = (x – 1)/2, mx) = (x + 8)¯1 (x + 8)-1 Find a formula for ( m onok).

A: See answer below.

Q: @ Suppose that f(n) = corn, g(n)= e. Using numerical affronimation find I (0-8), 9²(0) for the…

A: