Advance Math question and answers for August 25, 2023
- Q A. Prove that R and the real interval (0, 1) have thesame cardinality.
- Q The region bounded by y=(1/2)x, y=0, x=2 is rotated around thex-axis.A) find the approximation of the volume given by the rightriemann sum with n=1 using the disk method. Sketch the...
- Q Prove that any non identity element of a free group isof infinite order
- Q u=sinatsinbxShow that this function u is a solution of the partialdifferential equation u_tt = c ^ 2*u_xx and find the appropriatec.
- Q A measure of the adhesiveness of honey can be modeled asf(x.y) = -125.48 + 4.26x + 4.85y -0.05x^2 - 0.14y^2where x is the percentage of glucose and maltose and y...
- Q For the matrix A, find (if possible) a nonsingular matrix P suchthat P?1AP is diagonal. (If not possible, enter IMPOSSIBLE.) A = 2?2 3 0 3 ?2 0 ?1 2...
- Q Prove or disprove: If G = (V; E) is an undirected graph whereevery vertex has degree at least 4 and u is in V , then there areat least 64...
- Q Define the linear transformation S : Pn ?Pn and T : Pn ? Pn by S(p(x)) =p(x + 1), T(p(x)) = p'(x)(a) Find the matrix associated with S and T...
- Q Often, cruise ships conduct all on-board transactions, with theexception of gambling, on cashless basis. At the end of the cruise,guests pay one bill that covers all onboard transactions. Supposethat 60...
- Q Prove that if two non-equal letters are interchanged in a ISBNcode word the error will be detected (the word is no longer an ISBNcode word)Prove that the ISBN code can...
- Q (Elgamal encryption): given elgamal encryption ciphersystem:a)show how can we create a new legal encryption from twodifferent encryptions that we don't know their decryptionsb)how can an adversary take advantage of the...
- Q Prove true or false.For each natural number n, ((n5/5)+(n^4/2)+(n^3/3)-(n/30)) is an integer
- Q Prove the following using any method you like: Theorem. If A, B,C are sets, then (A ? B) C = (A C) ? (B C) and A ? (B C)...
- Q Find parametric equations for the line through the point(0, 2, 3)that is perpendicular to the linex = 2 + t,y = 2 ? t, z= 2tand intersects this line. (Use...
- Q 1. Let a < b. (a) Show that R[a, b] is uncountable
- Q Consider the weighted voting system?[15?: 12?, 9?, 5?, 2?].(a)Which players are critical in the coalition?{P1?, P2?, P3?}?(b)Write down all winning coalitions.(c)Find the Banzhaf power distribution of this weighted votingsystem
- Q Ineach case, find the conditions for F to be an integral factor.suggestion assume that F (Pdx + Qdy) = 0 is exact.F = x ^ a and F = x...
- Q Question2.Let A = [2 1 11 2 11 1 2 ].(a) Find the characteristic polynomial PA(?) of A and theeigenvalues of A. For convenience, as usual, enumerate theeigenvalues in decreasing...
- Q A $60,000 bond with a coupon rate of 5.00%, payablesemi-annually, is redeemable in 10.5 years. What was the purchaseprice of the bond, when the yield rate was 5.50% compoundedsemi-annually?
- Q Bob makes his first $ 600 deposit into an IRA earning 7.1%compounded annually on his 24th birthday and his last $600 depositon his 43rd birthday ?(2020 equal deposits in? all)....
- Q Block copy, and paste, the argument into the window below, anddo a proof to prove that the argument is valid. This question isworth 25 points. 1. (p ? x) • (x...
- Q How do we find singular solutions for a first order DifferentialEquation?
- Q Real Analysis:Detail the constructed definition of the Riemann Integral anddiscuss conditions for the existence of the integral.
- Q The algorithm is basically as follows. The notation is slightlydifferent from that in the website you were given, but there is nodifference in the method.Given the initial value problemdy/dx=f(x,y),y(a)= y_0Euler’s...
- Q prove or disprove: every coset of xH is a subgroup of G
- Q What aWorkbook!Math example ofeachRequirements:Three different application problems involving setting up andsolving a system of equations.BasicMixtureDistance, Rate, and TimeThree different application problems involving setting up andsolving an equation using factoring of...
- Q Use the procedures developed in this chapter to find the generalsolution of the differential equation.x2y'' ? 6xy' + 10y = ?2x4 +3x2
- Q Prove that Z_5 with addition and multiplication mod 5 is afield.
- Q 5). Let f : [a,b] to R be bounded and f(x) > a > 0, forall x in [a,b]. Show that if f is Riemann integrable on [a,b] then1/f :...
- Q Q3. A)I. Put the following sentences into their Clausal Elements:Eg. John / danced / yesterday. S V Ai. Seeing is believing.ii. I wish you good luck.iii. What he said at...
- Q a spherical vessel with a diameter of 2cm when empty,has a mass of 2.00g. what is the greatest volume of water that canbe placed in the vessel and still have...
- Q 3.5.4 ([Ber14, Ex. 3.6.14]). Let T : V ? W and S : W ? U belinear maps, with V finite dimensional.(a) If S is injective, then Ker ST =...
- Q 3) Prove that the cardinality of the open unit interval, (0,1),is equal to the cardinality of the open unit cube:{(x,y,z) E R^3|0<x<1, 0<y<1,0<Z<1}.[Hint: Model your argument on Cantor's proof for...
- Q Find the root of the function f(x) = 8 - 4.5 ( x- sin x ) in the interval [2,3]. Exhibit anumerical solution using Newton method.
- Q Solve the nonhomogeneous heat equation:ut-kuxx=sinx, 0<x<pi, t>0u(0,t)=u(pi,t)=0, t>0u(x,0)=0, 0<x<pi
- Q Let Vand W be vector spaces over F, and let B( V, W) be the setof all bilinear forms f: V x W ~ F. Show that B( V, W)...
- Q Construct a TM that computes the function: f(x) = 2x. (firstgive a brief outline, then show how it works for x=11 (in unarysystem, not eleven) using instantaneous description.
- Q Block copy, and paste, the argument into the window below, anddo a proof to prove that the argument is valid.1. (p ? x) • (x ? ~q)2. p • n3. ...
- Q A company makes four types of gourmet chocolate bars.Chocolate Bar I contains 5 grams of nuts, 5 grams of biscuit, 10grams of caramel, and 100 grams of chocolate, and...
- Q Find the eigenvalues and eigenvectors of the following matrix.Justify if its diagonaliazble or not.1 2 0-3 2 3-1 2 2
- Q Block copy, and paste, the argument into the window below, anddo a proof to prove that the argument is valid.1. (p ? z) • (q • ~z)2. (~p • q) ...
- Q Prove or disprove: two consecutive rotations about two differentaxis are commutative. That is, is RuRv = RvRu? (Hint: Forsimplicity, you can assume that the axis u is the x-axis and...
- Q 1. As you are solving a related rates problem that is asking forthe rate of change of an angle, you come up with the followingequation that relates the given variables....
- Q Consider the following LP. Use revised simplex formula toanswer the questions.Max Z = -x1 +2x3 +3x4subject tox1 -x2+2x3 ?84x1 +2x2 +7x3 +9x4 ? 30 2x1 +3x3 +7x4 ? 20 3x1...
- Q For the function f(x)4tan(2x), find the following:What is the period of fT=B. List all x-intercepts of f in the interval [-?,?]c. List all the equations of the vertical asymptotes in...
- Q 1. Darla purchased a new car during a special sales promotion bythe manufacturer. She secured a loan from the manufacturer in theamount of $24,000 at a rate of 4.5%/year compounded...
- Q 7. Construct a LOAN AMORTIZATION schedule for a 3 year 5% loanof $100, 000.Please show your calculations clearly and include calculatedanswers in the table below.(Please only do this question if...
- Q On R2, consider the function f(x, y) = ( .5y,.5sinx). Show that f is a strict contraction on R2. Isthe Banach contraction principle applicable here? If so, how manyfixed points...
- Q Derive Kelvin Stokes' theorem using differential equations
- Q y"+y=-1 , y(0)=0 , y(Pi/2)=0please repeat the answer by details (by properties of greenfunction only)and the answer will be : sin(x)+cos(x)-1
- Q Write 10 - 15 applications of each.( note: formulas and diagrams are not required justapplications)1- Numerical differentiations2-Numerical integration3- Composite Numerical integration.
- Q Compare and explain “random error of a regression” with“residuals of regression.”
- Q As a spring is heated, its spring “constant” decreases in value.Suppose a spring is heated so that the spring “constant” at time tis k(t) = 6 ? t. If the...
- Q a) Suppose f:[a, b] ? R is continuous on [a, b] anddifferentiable on (a, b) and f ' < -1 on (a, b). Prove that f isstrictly decreasing on [a,...
- Q (i) There are two non-isomorphic groups of order 4: C4 andC2xC2. Let C3 be a cyclic group of order 3. For each group G oforder 4, determine all possible homomorphisms...
- Q Let T be a linear operator on a finite-dimensional complexvector space V . Prove that T is diagonalizable if and only if forevery ? ? C, we have N(T ?...
- Q 4.2.1. Problem. Suppose that (xn) and (yn) are sequences ofreal numbers, that xn ? a and yn ? b, and that c ? R. For the casewhere a and b...
- Q Explain the basic concepts ordinary and partial 2differential equations (ODEs,PDEs), order general and particularsolutions initial value problems (IVPs)Give examples ?
- Q Problem 7.6A. Unmatched Elegance GiftShop sells cards, supplies, and various holiday greeting cards.Sales to retail customers are subject to an 8 percent sales tax.The firm sells it merchandise for cash;...
- Q Prove the following stronger variant of Proposition 7.4. SupposeC is collection of connected subsets of a metric space X and B ? C.Show, if for each A ? C, A...
- Q y'=2t-y Given: y(0)= -1 and h=0.1 estimate y(0.4) using (AB4)adam bashforth and (AM4) adam moulton using RK4 method
- Q Determine whether the following statement about graph theory istrue or false.(1) If a graph with m vertices is connected, then there must beat least m-1 edges.(2) If a graph with...
- Q LetG be a finite group and H a subgroup of G. Let a be an element of Gand aH = {ah : h is an element of H} be a...
- Q In this quiz, use the following touchdown data for TomBrady:YearPassing yards, yTouchdowns, t2000602001284318200237642820033620232004369228200541102620063529242007480650200876020094398282010390036201152353920124827342013434325201441093320154770362016355428201745773220182748172 (a) Find the correlation coefficient, accurate to foursignificant figures, between the number of touchdowns, t, and thenumber...
- Q 1. Calculate the future value of an investment worth $2800that pays 1.5% simple interest rate after 4 years.2. Derek invested $1000. What would that money grow to in 18months at...
- Q Please justify and prove each statement (Use explicitly the fouraxioms)a) Prove that a finite positive linear combination of metrics isa metric (Use explicitly the four axioms). If it is infinite,...
- Q There are 8 Broadway musicals and they offer a specialthree-night package (Friday, Saturday, Sunday nights) where one canorder one ticket that is good for three different musicals onsuccessive nights (a...
- Q Ashley has earmarked at most $210,000 for investment in threemutual funds: x dollars in a money market fund, y dollars in aninternational equity fund, and z dollars in a growth-and-incomefund....
- Q A laguerre equation is any differential equation of the formxy"+(1-x)y'+ny=0 where n is an integer. Solve the Laguerre equationwith n = 1, that is solve xy"+(x-1)y'+y=0 about the singlular pointx=0.
- Q 1. Prove or Disprove: If n is a nonnegative integer, then 5 |(2*4n + 3*9n)
- Q Find all primitive roots:(a) modulo 25, or show that there are none(b) modulo 34, or show that there are none(c) Assuming that 2 is a primitive root modulo 67, find...
- Q How many poker hands (of 5 total cards) are dealt such thatthe first three cards havethe same rank, but the total hand does not contain anotherpair and is not a...
- Q Would a logistic regression analysis reveal the keys toimproving customer retention?Examine the enclosed results of logistic regression of Retainedon Esent and on Eclickrate, and then discuss the results and makerecommendations...
- Q Prove or disprove whether the function f: Z x Z -> Z x Zgiven by f(x,y) = (2x+y, 3x-6y) is injective, surjective orboth.
- Q 10? + 50? + 20? + 10? = 1005? + 15? + 75? ? 25? = 20025a ? 15? ? 5? = 30010? + 20? ? 30? + 100? =...
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