Advance Math question and answers for July 05, 2023
- Q NUMBER THEORY1.Use the Euclidian algorithm to calculate the GCD of 1160718174and 316258250.2.Use Fermat’s Little Theorem to solve forx^86 ≡ 6 (mod 29).
- Q Solve this problem with the revised simplex method:Maximize           Z= 5X1 + 3X2 + 2X3Subject to           4X1+ 5X2 + 2X3 + X4 ≤ 20                           3X1 + 4X2 - X3 + X4 ≤30                          X1, X2, X3,...
- Q Determine the number of DISTINCT colorings of the four faces ofa tetrahedron, where each face is a color from the set { orange,purple, black} - Frobenius Orbit counting
- Q Prove that if f is a bounded function on a bounded interval[a,b] and f is continuous except at finitely many points in [a,b],then f is integrable on [a,b]. Hint: Use...
- Q y′ = t, y(0) = 1, solution: y(t) = 1+t2/2y′ = 2(t + 1)y, y(0) = 1, solution: y(t) = et2+2ty′ = 5t4y, y(0) = 1, solution: y(t) = et5y′...
- Q i)prove that a cylindrical co-ordinate system isorthogonal.                                    iii) Express the velocity v and acceleration of a particle incylindricalco-ordinates.                                                  iii) find the square of the element of arc length in cylindricalco-ordinates and determine...
- Q Consider a mass-spring system with an iron ball (weight 16 poundforce) that stretches 8/9 ft with undamped motion. The spring isinitially displaced 6 inches upwards from its equilibrium positionand given...
- Q Hello!Is someone able to solve the integral of the followingfunction?f(x) = x sin(pix/2)/(x^4+4).The boundaries are -inf to +inf.Thank you!
- Q Use the branch and bound method to find the optimal solution tothe following integer programming problem: maximize 7x1 + 3x2subject to: 2 x1 + x2 < 9 3 x1 +...
- Q P11.7A (LO 4)On April 2, 2021, Pharma Company entered into a contract tosupply medication to Laxall Drug Stores, FOB shipping point, terms2/30, n/45. The selling price of the medication is...
- Q Amass weighing 32 pounds stretches a spring 16 feet. The mass isinitially released from rest from a point 2 feet below theequilibrium position, and the subsequent motion takes place in...
- Q Problem 4 (Sets defined inductively) [30 marks] Consider the setS of strings over the alphabet {a, b} defined inductively asfollows: • Base case: the empty word λ and the word...
- Q Use the Gram-Schmidt process to transform the following vectorsinto an orthonormal basis of R4:u1=?(0 2 1 0)?, u2=(?1 −1 0 0) ,u3=?(1 2 0 −1?), u4=?(1 0 01?)can you do...
- Q Suppose A and B are closed subsets of R. Show that A ∩ B and A ∪B are closed.
- Q An oil company produces gasoline from five inputs. The cost,density, viscosity, and sulfur content, and the number of barrelsavailable of each input are listed in the file PO4_78.xlsx.Gasoline sells for...
- Q Abstract Algebra and Galois TheoryShow how to one can deduce the Fundamental Theorem of Galoistheory from the Artin's lemma.
- Q Assume that ψ : [a, b] → R is continuously differentiable. Acritical point ofψ is an x such that ψ'(x) = 0. A critical value is a number y suchthat...
- Q y′ = t, y(0) = 1, solution: y(t) = 1+t2/2y′ = 2(t + 1)y, y(0) = 1, solution: y(t) = et2+2ty′ = 5t4y, y(0) = 1, solution: y(t) = et5y′...
- Q 1. For each matrix A below compute the characteristic polynomialχA(t) and do a direct matrix computation to verify that χA(A) =0.(4 3-1 1)   (2 1 -1 0 3 0...
- Q (3) Use the Hungarian Method to find the minimum possible costfor assigning the following jobs to the following four workers. Thethree jobs are new flooring, a new roof, and a...
- Q Recall that a 5-bit string is a bit strings of length5, and a bit string of weight 3, say, is one with exactly three1’s.a. How many 5-bit strings are there?b....
- Q Assume that you are breaking a stick into 3 pieces by uniformlyand independently selecting two break points ? and ?. If we denotethe event that these pieces form a triangle...
- Q Adam is loaning $5000 to Bert for a period of 2 years. SupposeBert will repay the loan with a $5000 balloon payment at the end ofthe 2 years and will...
- Q IfR is a P.I.D. then an R-module Q is injective if and only if rQ=Qfor every nonzero r in R.
- Q volumes of revolutiona.) Sketch the region in the first and fourth quadrants bounded bythe graphs of f(x)=x^4-4x^2 and g(x)=4-x^2, and find the area.b.) find the volume of the solid generated...
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