Advance Math question and answers for September 07, 2023
- Q According to Zeller's Formula, the day of the week can becalculated by:f=k+(13m?1)/5+D+D/4+C/4?2Cwhere:•k is the day of the month.•m is the month number designated in a special way: March is 1,April...
- Q Consider the set of real numbers S=[-1,0)U{1/n:n=1,2,3,...}.Give the explicit set for each of theThe complement of S,The closure of S,The boundary points of S,The limit points of S,The isolated points...
- Q There are two career fairs held at a Catholic ChicagoUniversity.Career FairAttendeesHiredNot HiredFall1000150Spring600120Fill in the not-hired counts for each fair.Do the samples meet the Success-Failure Conditions?What are the proportions of hired...
- Q Show many ways can you tile a 3xn checkboard with a 2x1 tile?Create a recursive relation and show how to derive thenumber of ways.
- Q . Let x, y ? R {0}. Prove that if x < x^(?1) < y <y^(?1) then x < ?1.
- Q Find a particular solution, Yp, of the non-homogenous DE y" +3y' + 2y = 1/1+ex
- Q forevery bounded, closed and convex subset K of Y, there exists aretract from Y onto Kprove the lemma
- Q Solve the initial value problemdy/dx + H(x)y = e5x ; y(0) = 2whereH(x) = ?1 0 ? x ? 31 3 < x
- Q Find all possible orders of elements in the group Z4 × Z5 × Z10.For each possible order, give an example of an element of thatorder, and prove that no other...
- Q (Discrete Math) A routing transit number (RTN) is a bank codethat appears in the bottom of checks. The most common form of anRTN has nine digits, where the last digit...
- Q Let G be a group, and let a ? G be a fixed element. Define afunction ? : G ? G by ?(x) = ax?1a?1.Prove that ? is an isomorphism...
- Q List below is the number of cars serviced per day at XYZMechanics in June 2014.101289101113151411129141511121391413101213151314Required:Array the dataCalculate the meanCalculate the modeCalculate the median
- Q ExampleExplanation• The original number was 101 in binary which is equivalent to 5 indecimal.• The answer after shifting to the right is 2 in decimal.• That means by shifting one...
- Q 2. The official currency of the Kingdom of Mathemagiclandistanis Shrute-bucks. Shrute-bucks bills come in denominations of 3 and5.a.) What is the smallest amount of Shrute-bucks, n that can bemade using...
- Q Find the solution of the given initial value problem.ty?+2y=sin(t), y(?/2)=7, t>0Enclose arguments of functions, numerators, and denominators inparentheses. For example, sin(2x) or (a?b)/(1+n).
- Q Prove and apply the fundamental theorem of calculus in findingthe value of specific Riemann integrals of functions. This is for aclass in real analysis. Right now, I just need a...
- Q 1. Prove``The left and right cosets partition G into equal sizedchunks." (Cor 5.11 and 5.13 in your book). You have to show the ~is an equivalence relation, you can't just...
- Q Determine which of the following pairs of functions y1 and y2form a fundamental set of solutions to the differential equation:x^2*y'' - 4xy' + 6y = 0 on the interval (0,...
- Q Let S ? R and let G be an arbitrary isometry of R . Prove thatthe symmetry group of G(S) is isomorphic to the symmetry group ofS. Hint: If F...
- Q Write your own R-function for the linear regression using qr()function. You must not use solve() function. The input of yourfunction would be a design matrix X and a response vector...
- Q Determine the eigenvalues and eigenfunctions of the followingoperator (assume ?(x) ? 1): L(u) = u''?2u x ? (?1,1) with periodicboundary conditions u(?1) = u(1), u'(?1) = u'(1). Box your ?nalanswer
- Q Granite Housing Association Granite Housing Association (GHA), acharitable organisation, is a Registered Social Landlord (RSL). Itsoperations are part funded by the Government. GHA is based in theSouth East of England...
- Q Find the values of ? (eigenvalues) for which the given problemhas a nontrivial solution. Also determine the correspondingnontrivial solutions? (eigenfunctions).y''+2?y=0; 0<x<?, y(0)=0, y'(?)=0
- Q Define a relation ~ on Z x Z such that (a,b) ~ (c,d) preciselywhen a + b = c + d.Let R = {[(a,b)] : (a,b) in Z x Z}...
- Q In 2006?, there were 11,300 students at college? A, with aprojected enrollment increase of 800 students per year. In thesame? year, there were 30,900 students at college? B, with aprojected...
- Q f(x)=0 if x?0, f(x)=x^a if x>0For what a is f continuous at x = 0For what a is f differentiable at x = 0For what a is f twice differentiable...
- Q Find a particular solution to the non-homogeneous differentialequation:(a) y'' ? 4y = 4t^2(b) y '' ? 4y = sin(2t)(c) y '' + 4y = sin(2t)(d) y '' + y =...
- Q USING BISECTION METHOD, FIND THE ROOT OF 0.5e^x - 5x + 2 = 0 ONTHE INTERVAL [ 0 , 1 ] UP TO 3 DECIMAL PLACES.USE NEWTON'S METHOD TO APPROXIMATE...
- Q y??+12y?+35y=8cos(8t+0) y(0) = 14; y'(0) = 3find the particular, complimentary, and total solution.I have found the complimentary to be. C1e^-5t + C2e^-7tI'm having trouble finding the particular, so I can't...
- Q Looking at the first 2z integers 1, 2, . . . , 2z. Choose z + 1of them. Then demonstrate that there is at least one pair ofintegers from the...
- Q Let A = {a, b, c, d} and B = {b, d, e}. Write out all of theelements of the following sets.(a) B ? ?(b) A ? B(c) (A ?...
- Q A group of six friends play some games of ping-pong with theseresults: Amy beats Bob Bob beats Carl Frank beats Bob Amy beatsElise Carl beats Dave Elise beats Carl Elise...
- Q Decide, with justification, on the truth of the followingpropositions, both when the Universe of discourse is the set of allpositive integers, and when the Universe of discourse is the set...
- Q dy/dx + y/x x3y2
- Q Let {an} and {bn} be bounded sequences.Prove that limit superior {an+bn} ? limitsuperior {an} + limit superior{bn}
- Q (10pt) Let V and W be a vector space over R. Show that V × Wtogether with (v0,w0)+(v1,w1)=(v0 +v1,w0 +w1) for v0,v1 ?V, w0,w1?Wand?·(v,w)=(?·v,?·w) for ??R, v?V, w?W is a...
- Q Use the remaining balance method for all parts of thisquestion.Your company bought metal fabrication equipment that cost$350,000 using a bank loan with the following terms: 7% APR,compounded semi annually, monthly...
- Q On the interval [-1,1], consider interpolating Runge’s functionf(x) = 1/ (1 + 25x^2) By Pn(x), use computer to graph:(c) Take 11 equally spaced nodes in [-1,1], starting at –1,ending at...
- Q Let X = NN endowed with the product topology. For x ?X denote x by (x1, x2, x3, . ..).(a) Decide if the function given by d : X ×...
- Q A certain bookstore chain has two stores, one in San Franciscoand one in Los Angeles. It stocks three kinds of book: hardcover,softcover, and plastic (for infants). At the beginning of...
- Q 1. (Covering part 1 of the lecture slides)Consider the subset A of natural numbers, defined by A={ allnatural numbers n : n is congruent to 1 (mod 3) }First consider...
- Q 2. Let A = {1,2,3,4}. Let F be the set of all functions from Ato A. Recall that IA ? F is the identity function on A given byIA(x) =...
- Q Let Dn be the set of positive integers that divide evenly inton. List the elements of each of the sets D6,D16, D12, and D30
- Q Suppose a miniature golf player sinks a hole-in-one once forevery game (10 holes) out of 18 attempts at the game.Part A: Design a simulation.1. Design and conduct a simulation to...
- Q Let f(x,y) = 3x3 + 3x2 y ? y3 ?15x.a) Find and classify the critical points of f. Use any methodtaught during the course (the second-derivative test or completingthe square).b)...
- Q Answer for a and be should be answered independently.Let (X,d) be a metric space, anda) let A ? X. Let U be the set of isolated points of A. Provethat...
- Q A machine in a factory has an error rate of 10 partsper 100. The machine normally runs 24 hours a day and produces 30parts per hour. Yesterday the machine was...
- Q Let F be a field, and recall the notion of the characteristic ofa ring; the characteristic of a field is either 0 or a primeinteger.Show that F has characteristic 0...
- Q y''+4y=u?(t)?u3?(t) ; y(0)=0,y'(0)=0a.Sketch the graph of the forcing function on an appropriateinterval.b.Find the solution of the given initial value problem.c.Plot the graph of the solution.d.Explain how the graphs of the...
- Q 1. Use the definition of convexity to prove that the functionf(x) = x2 - 4x + 8 is convex. Isthis function strictly convex?2. Use the definition of convexity to prove...
- Q All necessary steps much show for these problems, please.Use the Euclidean algorithm to find gcd(12345, 54321).Write gcd(2420, 70) as a linear combination of 2420 and 70. Thework to obtain the...
- Q The number of words defined on pages randomly selected from adictionary are given below. Find the range and standard deviationfor the set of numbers.72 52 68 51 78 43 45...
- Q Find the Fourier Series for the function defined over -5 < x< 5f(x) = -2 when -5<x<0 and f(x) = 3 when 0<x<5You can use either the real or complex...
- Q Let y = mx where m = tan(37) is the slope. That is 37degrees.a. Find the Matrix that projects vectors onto this line. Find alleigenvaluesand Eigenvectors.b. Find the Matrix that...
- Q Identify the Fourier series for the half-wave rectified sinefunction with period 2?. This is the function that is sin(x) whensin(x) is positive, and zero when sin(x) is negative
- Q y"´-9y"+26y´-24y=1 y(0)=y´(0)=y"(0)=1
- Q Order reductionGenerate the general solution for eachof the given equations if y_1 is known to be a solution.1. y``-4y'+4y=0, y1=e^2x2. y''+2y'+y=0, y1=xe^-x3.x^2y''-xy'+2y=0, y1=xsin(lnx)
- Q The numerical aspect of statistics can be described as "numberswith social context." What does this mean to you?
- Q please explain step by step. see if the given matrix A isdiagonalizable, if so, give a diagonal matrix similar to A as wellas a matrix P so that P?¹AP is...
- Q Part 4:Discuss in one paragraph which aspects of your roller coasterwould realistically make sense in the real world and which aspectswould not. Make sure you refer to graphs you used...
- Q Calculate the integral from (-infinty) to (+ infinity) of [x^2 /(x^4 + 4)[ dx
- Q Use the method of variation of parameters to find a particularsolution of the given differential equation and then find thegeneral solution of the ODE.y'' + y = tan(t)
- Q You and your classmates are boarding a lifeboat from a shipsinking in the middle of the ocean. You each are guaranteed a seat.Unfortunately, there are 10 others seeking a seat,...
- Q Find the solution of the following problems. Before doing theseproblems, you might want to review Exercise 3** on page 63:d.) xy" + y' = x, where y(1) = 1m and...
- Q V and W are finite dimensional inner product spaces,T: V?W is alinear map1A: Give an example of a map T from R2 to itself (with the usualinner product) such that?Tv,v?=...
- Q Lett= 20389208 mod 4 and M= t+25a. Find integers a and b such that 0<a<M, 0<b<Mand ab= 0 (mod M)b. Find integers a and b such that 0<a<M, 0<b<Mand ab=...
- Q Show that the connected sum of two compact surfaces is a compactsurface.
- Q 2. Let D be a relation on the natural numbers N de?ned by D ={(m,n) : m | n} (i.e., D(m,n) is true when n is divisible by m. Forthis...
- Q Determine whether the equation is exact. If it is exact, findthe solution. If it is not, enter NS.(8x^2?2xy+5)dx+(8y^2?x^2+8)dy=0
- Q In practice, an LFSR sequence would not be used as keystreamfor a stream cipher, due to the linear complexity. Answer thefollowing questions about linear complexity.What is the linear complexity of...
- Q The nine entries of a 3×3 grid are filled with ?1, 0, or 1.Prove that among the eight resulting sums (three columns, threerows, or two diagonals) there will always be...
- Q Explain the process for modeling a linear spring in a staticsystem using F = k*s
- Q A 6 lb weight is placed upon the lower end of a coil springsuspended from a fixed beam. The weight comes to rest in itsequilibrium position, thereby stretching the spring...
- Q Question 16:What is the general solution of the following homogeneoussecond-order differential equation?Non-integers are expressed to one decimal place.d^2y/dx^2 ? 11.y = 9(a)y = Ae -3.3.x + Be 3.3.x + 0.82(b)y...
- Q prove that a group of order 9 is abelian
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