Advance Math question and answers for July 05, 2023
- Q Equilibrium solutions of non linear ODEsdx/dt = cot(x) & dx/dt=sin(x)Using linear stability characterise the E.S.
- Q Let f: Q8 to D8 be a homomorphism from the quaternion Q8 to thedihedral group D8 of order 8. Suppose that f (i) = rs and f( j) =r^2.(a) Find...
- Q Using Excel, Mathcad, or any similar program, create a 256-pointzero-mean random noise sample i(x).(a) Calculate mean and variance of i(x).(b) Calculate autocorrelation function C(Δ) for i(x). Describe howyou did this...
- Q After3 months ofendurance training John (who you may remember from Applied Essay 3is not very fit; initialVO2max of 35.0mL·kg-1·min-1) couldnot believe how much further he could run without having to...
- Q Adaptive bilateral filter (ABF) is used for sharpnessenhancement and noise removal. The ABF sharpens an image byincreasing the slope of the edges without producing overshoot orundershoot. It is an approach...
- Q The port operations staff in Izmir Port tries to make loadingschedule of a ship that will arrive on Monday. There are 6container yards in the port. The containers first must...
- Q what does it mean for a set to be well ordered, countable andcompact?
- Q How do you use mathmatical induction to show that thecoefficient of x^2 in the expansion of (1+x+x^2+...x^n)^n is(1+2+...n).
- Q prove that a compact set is closed using the Heine - Boreltheorem
- Q Provide an example1) A nested sequence of closed, nonempty sets whose intersectionis empty.2) A set A that is not compact and an open set B such that A ∪ B...
- Q Did any of your previous assignments involve math calculationsfor premium and or salary analysis and adjustments? Please providedetailed example(s).
- Q suppose that for every pair of disjoint closed sets A and B of Xthere exist a countinous function f:X-> {0,1} such that f(A)={0}and f(B)={1}. show one point set is closed...
- Q at time t=0, a particle is located at thepoint(4,8,7). it travels in a straight line to the point (7,1,6),has speed 7 at (4,8,7) and constant acceleration 3i-7j-k. Find anequation for...
- Q Apply the KKT conditions to determine whether or not thesolution XT = (1,1,1) is optimal for the following problem:minimize 2X1 + X2^3 + X3^2subject to2X1^2 + 2X2^2 + X3^2 >=4X1,...
- Q Calculate the SVD of matrix A =22-11by hand and find the rank 1 approximation of A
- Q What is the lower bound on a bivariate CDF with uniform binarymarginals? What is the upper bound on a bivariate CDF with uniformbinary marginals? What do these bounds mean? What...
- Q canyou explain optimization problems and the best way to solve them.also if you can explain related rates and the best atrategy. thankyou!
- Q 4. Sampling Without ReplacementWe have n−2 beer bottlesb1,…,bn−2 and 2 cider bottlesc1 and c2 . Consider a uniformly randompermutation π1,…,πn of these nbottles (so that each of the n! permutations...
- Q Let X be a set and A a σ-algebra of subsets of X. (a) What doesit mean for a function f : X → R to be measurable? [2%] (b)...
- Q let n belongs to N and let a, b belong to Z. prove that a iscongruent to b, mod n, if and only if a and b have the sameremainder...
- Q Is it possible to have 60 coins, all of which are pennies, dimesor quarters, with a total worth $3. List all possibilities.Please fully explain each step.
- Q prove that L^∞ is complete
- Q proof: L t^(n+1)*f(t)=(-1)^(n+1)*(d^(n+1)/ds^(n+1))*F(s)
- Q Solve the following wave equation using Fourier Seriesa2uxx = utt, 0 < x < pi,t > 0, u(0,t) = 0 = u(pi,t), u(x,0) = sinx, ut(x,0) =pi - x
- Q Solve the following heat equation using Fourier Seriesuxx = ut, 0 < x < 1, t > 0,ux(0,t) = 0 = ux(1,t), u(x,0) = 1 -x2
- Q Solve the following heat equation using Fourier Seriesuxx = ut, 0 < x < 1, t > 0,u(0,t) = 0 = u(1,t), u(x,0) = x/2
- Q Poof ifa) A is nonsingularb) N(A) = {0}c) rank(A) = n
- Q (5) Taking into account identical letters, how many ways arethere to arrange the word CALLITRICHIDAE?(5) Taking into account identical letters, how many ways arethere to arrange the word CALLITRICHIDAE that...
- Q When Maria Acosta bought a car212years ago,she borrowed $13,000 for 48 months at 7.8% compounded monthly. Hermonthly payments are $316.15, but she'd like to pay off the loanearly. How much...
- Q 1) a) Prove that the union of two countable sets iscountable.b) Prove that the union of a finite collection of countable setsis countable.
- Q 7. Let n ∈ N with n > 1 and let P be the set of polynomialswith coefficients in R.(a) We define a relation, T, on P as follows: Let...
- Q Solve y''-y'-2y=e^t using variation of parameters.
- Q Find solutions to the following difference equations:• xn+2 − 4xn = 27n 2 , x0 = 1, x1 = 3• xn+1 − 4xn + 3xn−1 = 36n 2 , x0...
- Q Orthogonally diagonalize the matrix by finding an orthogonalmatrix Q and a diagonal matrix D such that QTAQ = D. (Enter eachmatrix in the form [[row 1], [row 2], ...], where...
- Q Find the general solution and solve the IVPy''+y'-y=0, y(0)=2, y'(0)=0
- Q determine the range and domain of the following: the function kdefined by k(x)= square root x-3
- Q 20. Give the values of x for which x > 500 lg x.Note: lg is log base 2 (not ln).
- Q Find the solution of the initial-value problem. y'' + y = 3 + 5sin(x), y(0) = 5, y'(0) = 8
- Q For an arbitrary ring R, prove that a) If I is an ideal of R,then I[ x] forms an ideal of the polynomial ring R[ x]. b) If R andR'...
- Q Question: Linda has 5 weeks to prepare for herCSCA67 final. Her friend has volunteered to help her for either15min or 30min every day until the test but not for more...
- Q If you had a routine for computing all of the eigenvalues of anonsymmetric matrix, how could you use it to compute the roots ofany polynomial?
- Q Prove that L = {a + b √ 5i | a, b ∈ Q} is a field containing theroots of x2 + 5. Moreover, prove that if Q ⊆ K...
- Q (a) Devise and then describe a method to systematically list allrational numbers between 0 and 1.(b) Using your answer to part (a), show that the set ofrationals between 0 and...
- Q For the Fibonacci sequence, prove the formulau2n+1 = un un+2 +(-1)n
- Q Consider the following differential equation:x2y\"-2xy'+(x2+2)y=0Given that y1=x cos x is a solution, find a secondlinearly independent solution to the differential equation.Write the general solution.
- Q Scenario1Mr. Abbas seesa book displayed in a shelf of a book shop with a price tag of Rs.85. Mr. Abbas tenders Rs. 85 on the counter and asked for the...
- Q NEW NUMBERSChris Froome is a purchasing agent for a firm that sellcomponents for high performance bicycles. One of the most popularcomponents is the TDF bicycle frame which has an annual...
- Q Does every hyperbolic triangle have an inscribed circle?Circumscribed circle?
- Q Solve the following differential equation using the power seriesmethod.(1+x^2)y''-y'+y=0
- Q 5. y′′ + xy′ = 0, x0 = 0 Series Solution Method. solve the givendifferential equation by means of a power series about the givenpoint x0. Find the recurrence relation;...
- Q Calculate the Y values corresponding to the X values givenbelow.  Find the critical values for Xfor the given polynomial by finding the X values among those givenwhere the first derivative, dy/dx...
- Q Three digits are randomly chosen from {1,2,3,4,5,6,7} withoutreplacement.a) What is the probability the number formed is 123 or 567?b) What is the probability the number formed has first digit1?c) What...
- Q TV Circuit has 30 large-screen televisions in a warehouse inErie and 60 large-screen televisions in a warehouse in Pittsburgh.Thirty-five are needed in a store in Blairsville, and 40 are neededin...
- Q For m, n in Z, define m ~ n if m (mod 7) = n (mod 7).a. Show that -341 ~ 3194; that is to say 341 is related to...
- Q Let G and H be groups. Define the direct productG X H = {(x,y) | x ∈ G and y ∈H }Prove that G X H itself is a group.
- Q b belongs to N. Prove that if {7m, m belong to Z} is not belongsto {ab, a is integer}, then b =1
- Q find a particular solution toy\"-2y'+y=-12.5e^t
- Q Consider the Sturm-Liouville problemX′′(x) + λX(x) = 0 subject toX′(0) = 0, X(l) = 0.Are the boundary conditions symmetric?Do these boundary conditions yield negative eigenvalues?Determine the eigenvalues and eigenfunctions, Xn(x)....
- Q Use the method of Frobenius to obtain two linearly independentseries solutions about x = 0. Form the general solution on(0,inf).2x^2y'' - xy' + (x^2 + 1)y = 0
- Q 6.3.8. Problem. Let f : A → B be a continuous bijectionbetween subsets of R.(a) Show by example that f need not be a homeomorphism.(b) Show that if A is...
- Q A population of animals oscillates annually from a low of 1300 on January 1st to a high of 2200 on July 1st. and back to a low of 1300 on...
- Q Prove that an abelian group G of order 2000 is the directproduct PxQ where P is the Sylow-2 subgroup of G, and Q the Sylow-5subgroup of G. (So order of...
- Q A department contains 10 part-time employees and 15 full-timeemployees. In how many ways can a committee be formed with 6members if it must have more full-time employees than part-timeemployees?
- Q Â a) Check e^5x, xe^5x for independence using Wronskianb) solve y\" + 5y' + 6y = 0c) convert the above equation to a system and solve itd) Solve x^2y''-2xy'-4y= 0 by...
- Q Use Lisp to achieve an informed search(8-queen): 8 queensrandomly placed on a board and returns a list that consists of thesame queens in locations that they don't threaten each other.Requirement...
- Q Without using the Tutte-Berge formula, prove that every cubicgraph with at most two bridges contains a perfect matching.
- Q For each given integer n, determine if n is a sum of twosquares. (You do not have to find the squares.)(a)n= 19(b)n= 45(c)n= 99(d)n= 999(e)n=1000
- Q Let ?∈ℕ, and assume √? is irrational. Show thatâ„š(√?)={?+?√?∶?,?∈ℚ} is a field (show that there is multiplicativecommutativity and multiplicative inverse). What would change if â„šwas replaced with â„.
- Q I have n books with n different titles. I want to put them onthe shelves in my library. How many different ways are there toarrange them on one shelf? On...
- Q Daryl Kearns saved $240,000 during the 25 years that he workedfor a major corporation. Now he has retired at the age of 50 andhas begun to draw a comfortable pension...
- Q Find the infinite series solution about x = 0 for the followingdifferential equation x2y\"+ 4xy' + (2+x)y = 0,without using ksubstitution and using Bessel's, Legrende's, or frobeniusequations.
- Q Â Solving Differential Equations using Laplace Transforma) y\" - y' -2y = 0y(0) = 1, y'(0) = 0answer: y = 1/3e^2t + 2/3e^-tb) y\" + y = sin2ty(0) = 2, y'(0)...
- Q 2. Guyana forestry Commission wishes to carry out a survey tocharacterize Acai berry palms within Guyana.(a) Identify the target population.(b) Suggest and justify an appropriate sampling technique(c) Suggest and justify...
- Q Suppose that m is a fixed positive integer. Show that theinitial value problemy' = y2m/(2m+1) , y(0) = 0has infinitely many continuously differentiable solutions. Whydoes this not contradict Picard’s Theorem?
- Q The demand for roses was estimated using quarterly figures forthe period 1971 (3rd quarter) to 1975 (2nd quarter). Two modelswere estimated and the following results were obtained:Y = Quantity of...
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