Use Euler's Theorem to find a number a between 0 and 9 such that a is congruent to 7 1000 modulo 10. (Note that this is the same as the last digit of the decimal expansion of 7 1000.)

Q: solve the operation of 01.79⊕02.E1⊕03.17⊕01.4D

A:

Q: Determine the big-Theta (0) of the following function: 3 +x² + x + 1 f(x):

A: Given function f(x) = x9 + x6 + x3 + x2 + x + 1 / x3 + 1 Given polynomial will have complex root,…

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Q: Explain how the Pigeonhole Principle can be used to show that among any 31 integers, at least four…

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Q: 1. Given A= (1001), , B=(1101), , find the following results %3D %3D

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Q: Q3 A: Simplify the following Boolean functions, using Karnaugh maps: F (x, y, z) = Σ (0,1,4,5)

A: Given F(x,y,z) = ∑(0,1,4,5)

Q: 10)Find the complement of the F= wx + yz ; the prove that F. F' = 0, and F+ F' = 1

A: the solution is an given below :

Q: Let F=xy'+xz'+z. Use Boolean algebra to prove that F=xtx

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Q: Explain CHINESE REMAINDER THEOREM with example x = 2( mod 3) x = 3 (mod 5) x = 2(mod 7).

A: Step 1  The answer is given in the below step

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Q: For aib integers aro evaluale the following: and bro

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Q: 2. For the sequence: -40, -20, 0, ... a. Find the 40th term b. Find the sum of the first 40 terms

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Q: Find the quotients and remainders for the following division problems modulo 2. Q. 1110101112 ÷…

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Q: Q/ USING TALOR SERIES FIND HE FIVETERMS FOR FUNCTION: F(X) = COS(X) AT a = T\4

A: Finding Taylor series.

Q: Find the solution of the following operation for hexadecimal numbers F26/A

A: Answer: Given Hexa-decimal numbers: (F26)16/ (A)16 Step by Step solution:

Q: The purpose of this exercise is to compute an approximation of the integral -:- 00 e-x dx -00 using…

A: clc;clear all;f=@(x) exp(-x.^2);x=-10:0.1:10; plot(x,f(x),'linewidth',2)xlabel('x')ylabel('f(x)')

Q: Q1: prove using algebraic method that ABC + ĀBC + ABC + ABC = C

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Q: 4. To find sum as Y of the following series excluding prime numbers in the series. n(n-1)x² п(п-1)x^…

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Q: Plot the graph of the given trigonometric function, f(t) = sin°(t) - cos²(t) + 2*t*sin(t). %3D…

A: Write a MATLAB program to plot the graph of the given trigonometric function, f(t) = sin3(t) -…

Q: Q1: For these Value Obtain U and V and evaluate W when Z= V5 – 2i Q2: If Z1= 4i-3 22= 3i Z1+Z2 Find…

A:

Q: - integer k, pr

A: given - for any integer k, prove that gcd(2k+3, 5k+7)=1

Q: Find the approximate root of the function f (z) = DOF <0.0001 cos(4x)- x sin a, xo 7 using…

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Q: Write down the cardinal polynomials in the Lagrange interpolation polynomial for the points x…

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Q: 3. Use the Hermite polynomial that agrees with the data xo = 1.2, x1 1.5, x2 1.8, f (xo) = 0.542, ƒ…

A: The value of table for x, f(x) and f′(x) x y=f(x) y'=f'(x) 1.2 0.542 -0.441 1.5 0.463 -0.467…

Q: Using Fermat's theorem, find 3201 mod 11.

A: Lets see the solution.

Q: 1) The truth table of function fis given below left. Please complete its k-map in the right. XI X2…

A: Given the truth table of the function f we have to complete it's K-map in the right.

Q: Show by contraposition that for any real number x if -5<xS4 then x2+x- 20 <0

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Q: The number 72 is to be represented as the sum of two positive parts, such that the product of one of…

A: - We need to highlight the numbers according to the facts asked.   - Maximum number findings is used…

Q: Find the quotients and remainders for the following division problems modulo 2. 1. a) 111010112 ÷…

A: Introduction Of Binary Number In a computer system, binary numbers are a base-2 model in which…

Q: Prove the following: X’ ∩ Y’ = (X ∪ Y)’

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Q: If an is an even number, show that a2 = 0 (mod 4), and if an is an odd number, show that a2 = 1 (mod…

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Q: 4. Show the process of using Booth's algorithm to calculate 15 x 12:

A:

Q: 1. Find the root of x² – e2* = 0 using: a. Bisection method between [0, 1] b. Simple Fixed-Point…

A: The Answer start from step-2.

Q: Use & for •, v for V, > for Ɔ, and = for = %3D What can you derive by applying De Morgan's (DM) to…

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Q: 1. Simplify the following expression to products-of-sums: xyz + yz + xy

A:

Q: 1. F= A'B'C'D' + ABC + ACD + ABD

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Q: K. Compute the volume of a cylinder, when its height and diameter is given. The volume V for a right…

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Q: Solve the following equation for x and y where xy – 2i + x + 2xyi – 5 = = – 3i -

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Q: (c) Find the sum-of-products expansion of the following Boolean function: f(a,b,c) = a(b+ €) + ab +…

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Q: of for each equation fi = 0(Ji+1) in the sequence above. log n 100n 2"

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Q: Find the quotients and remainders for the following division problems modulo 2. Q. 10111112 ÷ 111012

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Q: Given AB + AB = C, find AC + AC. %3D

A: Let's understand step by step :   Given  (AB)' + A'B = C   Now use this relation to find out given…