4. Let the function g be given by Oniseven 9(n) n =1 (mod 4). n =3 (mod 4) 1 %3D 1

Q: Compute the following. 4! 6! ]*

A: Answer - First we need to understand what is factorial before solving this question  n!…

Q: Prove this claim: For every positive integer d and every integer n, the following equation is…

A: Using division algorithm we solve this problem. The steps are given bellow.

Q: 3. Find integers x, y € [0,51] such that (a) 23x= 1(mod52) (b) 23y = 4(mod52)

A:

Q: e the exact value of the function for the given x-value without using a calculator. ( ) f(x) = f(x)…

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Q: 5. (a) If r23 = 0, prove that R₁ (23) = (23) = 712 + 7³1 01-23 = (1 - 12 - 13). 07.

A:

Q: 1' 1 3 (e) Show that 5 k=1 k k+2

A: I am attaching image so that you understand each and every step.

Q: Determine the values of X1 and X2 after 2 iterations. Assume that A= .05 by golden section of the…

A: given function is, F(x)=4x       , 0≤x≤24-x      , 2≤x≤4

Q: 6. Show that, for integer s, S. s! | x25+lexp(-ax²)dx =: 2a +1

A: Note: Given proof statement has a little mistake, I have proof the actual result. First i have…

Q: 2.24 Derive the simplest sum-of-products expression for the function f(x₁, x2, x3, x4) X₁ X3 X4 +…

A: we have to derive the simplest sum-of-products expression for the functionFor the given function,…

Q: 3s²+2s+27, +9) (s²+1) =²+62s+92

A:

Q: If k = (11.03.-9.12,3.15,-1.01) in R4 then k| = %3D %3D

A: Given  k = 11.03, -9.12, 3.15, -1.01t in R4. We have to find the value of k1.

Q: c. x[n] = e and d[n-5]

A: As per the question we have two discrete signals : e-n² and  δ[n-5] And we have to find the…

Q: Alireza will take IE 4301 next semester and attend EVERY class in person. He will wear a mask to the…

A: Solution

Q: 4. Let f(x) = r3 +x² – 3x – 1. It is known that f(2) = 0(mod 5). (i). Find a solution to f(r) =…

A: The given function is fx=x3+x2-3x-1. It is known that f2≡0 mod 5. (i) Find a solution to fx≡0 mod…

Q: If -5n-2, then f(3) is 04 O 55

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Q: anel g(x)= |- Vã , Fino × =(Xつ f え a- fog and gof b- thei range and domain of fo9 3 9of.

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Q: 5. Let f(x) = 2x² + x + 4. It is known that f(1) = 0(mod 7). (i). Find a solution to f(x) = 0(mod…

A:

Q: In A, values of k for which det(A)=D0 are * k-4 0 0. A = k 3'k-1 O k=4, k=-3 , k=-2 O k=-4, k=-3,…

A: The given matrix is - A = k-4000k203k-1 We have to find the value of k for which the det(A) is equal…

Q: 40E (mod 3) W = 1 入 人 7 11 2 4 To solve this problem should use the function on the oyou value. scme…

A:

Q: A container contains 35 green tokens, 5 blue tokens, and 3 red tokens. Two tokens are randomly…

A: There are total (35+5)=40 non-red tokens and 3 red tokens in the container.  And total (35+5+3)=43…

Q: 3. Let h: Z→ Z be the function h(r) = = x mod 4. Find h-¹(0), h-¹({0, 1, 2, 3}), and h-¹(4). Explain…

A: In this question we can easily observe that that output of the function is the remainder when any…

Q: Give a recursive definition with initial condition(s). a) The function f(n) = 5", n = 0, 1, 2, ....…

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Q: Prove that T S. Prove that S £ T.

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Q: Find SU U. 10 9. *+6 x+10 S

A: We have to find length of secent US.

Q: If k = (0.0003,-0.0012, 0.0015,-0.0014) in R4 then -5.2||||=0.0062

A:

Q: s) Let f(x) 1 and g(x) 4 + 6. - х — 6 Then (fo g)(x) = (go f)(x) =

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Q: 2 Let xk = E(k+1)(k+2) for all k e N and define S, = Ek=1 ®k• (a) Evaluate Sn as a function of n.

A:

Q: 1. Suppose that for a certain life , S, (x) = 1- . Find 100 (i) Find the prob. that a person aged 25…

A: Given : The survival function for a certain life is : SXx=1-x1002

Q: Show that (an) is increasing

A:

Q: Show that — ф+1 n=0 ||

A: Given φ is the golden ration satisfying 1φ=φ-1. To prove ∑n=0∞1φn=φ+1 It is known that φ=1+52.

Q: Prove that. 2/nJn-(n+2)Jne2 + (n+yjJney --- 3. end hence deduce that. 1xJn - (nti)Jnas -…

A:

Q: Please can i have a written stepby step working. also for this question to not be shown to others

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Q: if p is a prime, what is 10/p as a function of p?

A: We have to tell  What is 10/p as a function of p   It is given that p is prime

Q: (d) If each fn has fewer than M discontinuities (where M ∈ N is fixed), thenf has fewer than M…

A: To Show: If each fn has fewer than M discontinuities (where M ∈ N is fixed), then f has fewer than M…

Q: 3. (i). Suppose f (x) is a polynomial with integer coefficients such that f(2) = 0(mod 5) f(4) =…

A: Given that  (a) f(2)≡0(mod 5)f(4)≡0(mod 9) We have to find a polynomial such that f(x)≡0(mod 45)…

Q: 5(x+1) =x+1 if x = 1. O True O False

A: By solving this equation we get,

Q: The number e can be defined by e= (1/n!), where n!=n(n-1)-2-1 for n 0 and 0!= 1. Compute the…

A: For the solution of the problem follow the next steps.