The following decision algorithm, A, is proposed for the perfect square problem: Compute x^2 for integer x starting at x = 1 until x2 either equals or exceeds n. n is accepted in the former case and rejected otherwise. Based on A, what is the complexity class of the perfect square problem? Show your reasoning. (b) What is Heron's algorithm for finding the square root of a number?

Q: Which of the following is equal to 64x2 - 36? 4 (4x- 3) (4x + 3) (4x +3) (4x – 3)

A: Given :          64x2-36

Q: Given the following LP: Min   4x1 + 6x2 s.t     2x1    +  2x2   ≥  3,         x1  +     3x2     ≥…

A: Solution 1: First we find the dual problem of the given linear programing problem. Then we find the…

Q: min z = 4x, - x2 s.t. 2x1 + x2 < 8 X2 < 5 X - x25 4 X1, X2 2 0

A:

Q: You are running algorithm with squared complexity on data with 100 elements and it takes 10 seconds.…

A:

Q: Use the simplex algorithm to solve the following LP: max z = x₁ + x₂ + x3 X2 X1 s.t. x₁ + 2x₂ + 2x3…

A:

Q: 1. Use the Euclidean algorithm to find integers x and y such that 2640x + 2110y = 10.

A:

Q: Which of the following is a factor of P(x) = x3 - 3x2 - 3x +9 c) (x + 3) %3D a)(x - 3) b) (x – 2) d)…

A:

Q: In Fermat's Factorization method, why does n = ab can be transformed to ?

A: Fermat’s Factorization method is based on the representation of an odd integer as the difference of…

Q: Q2:Write an Algorithm to evaluate the following equations: X4 + 2! x2 x6 X8 + 6! 1.Cos(X) = 1 – -- -…

A:

Q: (7) Recall that vp(n) denotes the highest power of the prime p that divides the nonzero integer n.…

A: Given that denotes the highest power of the prime p that divides the nonzero integer n.First we have…

Q: 7.1 Solve the following problem, using the stated method/ Los die volgende probleem op deur gebruik…

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: 4. The conventional algorithm for evaluating a polynomial anx" + an-1x¹ +... + a1x + ao at x = c can…

A: Algorithm Polynomial (c, ao, a1,...,an: real numbers) power = 1; y = a0 ; for i = 1 to n power =…

Q: Consider the following LP: min 5x1 + 4x2 s.t. x1 + x2 ≥ 1 2x1 − x2 ≥ 1 3x2 ≤ 2 x1, x2 ≥ 0. a. Write…

A: Consider the following LP: min 5x1 + 4x2 s.t. x1 + x2 ≥ 1 2x1 − x2 ≥ 1 3x2 ≤ 2 x1, x2 ≥ 0. a. Write…

Q: Create a box-grid with 10 rows and 9 columns (eg. using google Sheets) and, starting from the upper…

A: We will use basic knowledge of number theory to answer this question in google sheets.

Q: Problem 2. The following algorithm which is used to evaluate a polynomial anx" + an-1x" -1 ++ a₁x +…

A: Given polynomial is  p(x) = 120° + 3x - 5.x2 + 7x – 8  (a) Point C=1     Compare it with standard…

Q: A building has 13 smaller units of identical dimensions of rectangular shape and 5 larger units…

A: Given that,1. A building has 13 identical rectangular units and 5 identical square units. 2. Square…

Q: A certain computer algorithm executes twice as many operations when it is run with an input of size…

A:

Q: K = (perfect squares of integers} under addition? Is it closed or not

A: K is the perfect square of integerNow we find whether it is closed or not.

Q: The entries of A are aij. Assuming that zeros don't appear, what is(a) the first pivot?(b) the…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: How to solve this problem with the dual simplex algorithm: max 60x1 + 30x2 + 20x3 subject to 8x1 +…

A:

Q: 6. a. Apply Newton's method to the equation r²- a = 0 to derive the following square-root algorithm:…

A:

Q: Illustrate the Euclidean algorithm by using it to compute gcd(40, 134) and find a solution to…

A: The objective of this question is to find the greatest common divisor (gcd) of 40 and 134 using the…

Q: Use the Division Algorithm to prove that (a) The square of any integer is either of the form 3k or…

A:

Q: Let w(n) and A(n) denote respectively, the worst case and average case running time of an algorithm…

A: Since average case running time is always lesser than the worst case running time , So A(n) is…

Q: max z = -3x1 -x2 st x1 +x2 +x3 2 12 4x1 -x2 +x3 6 Xị 20 Vi

A:

Q: Consider the problem of maximizing the function -x? f(x)=- +3x 10 where x is allowed to vary between…

A: Given that, f(x)= 3x-(x²/10) Here, f is a polynomial function in x. So, f is continuously…

Q: (13),0 - (159), using excess-3 codes with 9's complement method.

A:

Q: How would I use the Extended Euclidean Algorithm to express this gcd as a linear combination? I…

A: I will use Euclidean algorithm to express 7 as linear combination of 14 and 203.

Q: min z = -3x + 8x2 4x1 + 2x2 < 12 2x1 + 3x2 < 6 s.t. X1, X2 2 0)

A:

Q: The following algorithm which is used to evaluate a polynomial anz" +an-12¹−¹+...+₁²+ªo at r = c is…

A: Given that: anxn+an-1xn-1+⋯+a1x+a0 at x=c is expressed in pseudocode as follows: Polynomial…

Q: Suppose that we use the bisection algorithm to approximate r = √20 which the greatest zero of the…

A:

Q: Solve the following LP using two-phase simple max z = 3x1 +2x2 st x1 +2x2 212 x1 +x2 <5

A: Two-phase simplex Algorithm: The so-called two-phase approach separates the procedure into two…

Q: 4. The "divide and average" method, an old-time mthod for approximating the square root of any…

A:

Q: Consider the following mathematical model: Max z = X1 – X2 + 3X3 S.T X1 + X2 = 10 X1, X2, X3 >= 0 a)…

A: As per the question we are given a linear programming problem and we have to :Solve it using simplex…

Q: Make this nonlinear problem to a BINARY INTEGER PROBLEM.   Max z = x2y + 3x3yw     subject to…

A: As per the question we are given a nonlinear optimization problem which we have to convert into a…

Q: II. Use Euclidean Algorithm to obtain x and y satisfying the equation of (50 364, 26 601) = 50 364x…

A: Calculating GCD(50364,26601) gives: 26601 = 0*50364 + 26601 50364 = 1*26601 + 23763 26601 = 1*23763…

Q: Use the simplex algorithm to solve the following problem (Use tableaus) max z = x, – 2x2 + x3 s.t.…

A: