Advance Math question and answers for August 06, 2023
- Q Prove the following:(a) Let A be a ring and B be a field. Let f : A ? B be asurjective homomorphism from A to B. Then ker(f) is a...
- Q A Ferris wheel has a radius of 10 feet and is boarded in the 6o’clock position from a platform that is 3 feet above the ground.The wheel turns counterclockwise and...
- Q Assigned Exercise IX.1. IX.1. (a) Suppose that f : [a, b] ? R iscontinuous. Define A := 1/b?a integral of f from a to b, and B :=1/b-a integral of...
- Q Give examples–a formula and an illustration–of two-dimensionalvector fields F?(x,y) with each of the following properties. Youcould do the illustrations by hand.a) The direction of F? is constant but the magnitude...
- Q 2a. Find the orthogonal projection of [9,40,-29,4] onto thesubspace of R4 spanned by [1,6,5,6] and [5,1,5,5].Answer choices: [2,14,-15,7] [-32,13,-10,7] [0,9,12,6][-5,-2,3,2] [-12,0,-9,-9] [-16,20,0,4] [27,29,29,21] [-3,1,2,7][-23,7,-3,-9] [-15,5,-15,30]2b. Find the orthogonal projection of...
- Q The Weemow Lawn Service wants to start doing snow removal inwinter when there are no lawns to maintain. Jeff and Julie Weems,who own the service, are trying to determine how...
- Q A coffeehouse sells a pound of coffee for ?$8.25. Expenses are?$3 comma 500 each? month, plus ?$3.50 for each pound of coffeesold. ?(a) Write a function? R(x) for the total...
- Q Please prove the following formally and clearly:Let X1 = 1. Define Xn+1 = sqrt(3 +Xn). Show that (Xn) is convergent and findits limit.
- Q You plan to take out a $700,000 mortgage for 30 years withmonthly payments.If you don’t have a down payment, they will offer you aninterest rate of 5.7%. If you can...
- Q Solve the following differential equation using the power series method.(1+x^2)y''-y'+y=0
- Q A stock expects to pay a dividend of $3.72 per share next year.The dividend is expected to grow at 25 percent per year for threeyears followed by a constant dividend...
- Q A cohort study was undertaken to examine the association betweenhigh lipid level and coronary heart disease (CHD). Participantswere classified as having either a high lipid level (exposed) or alow or...
- Q (3) Consider the linear map ? : R2 ? R2 which sends (1, 0) ??(?3, 5) and (0, 1) ?? (4, ?1).(a) What is the matrix of the transformation? What...
- Q Linear algebra confusion: We haven't learned about rank andsuch:For the following I am looking for examples or checking to see whysomething is impossible.a.) What does it mean when we have...
- Q 2.LetT:R3?R3suchthatT(?1,1,—1?)=?2,1,0]andT(?0,1,1?)=?1,1,1?.(a) Find T(? 5,3-7?).(b) Can you find T (?1,0,0?) from the information given in part(a)? Explain.(c) Suppose you are now told that T(?1,0,0?) = ?4,2,0?. Find the(standard) matrix of T...
- Q Let H be the subset of all skew-symmetric matrices inM3x3a.) prove that H is a subspace of M3x3 by checkingall three conditions in the definition of subspace.b.) Find a basis...
- Q (8) TRUE/FALSE: Circle either T or F. No justification isneeded.(a) (T : F) Each line in R n is a one-dimensional subspace of Rn .(b) (T : F) The determinant...
- Q Use the Cauchy Criterion to prove the Bolzano–WeierstrassTheorem, and find the point in the argument where the ArchimedeanProperty is implictly required. This establishes the final link inthe equivalence of the...
- Q Recall that a standard 52-card deck has four suits, ?, ?, ?, and?, each of which has13cards, one each of the following kinds, A, K,Q, J,10,9,8,7,6,5,4,3,and2. A hand of seven...
- Q Let A be an n × n matrix which is not 0 but A2 = 0.Let I be the identity matrix.a)Show that A is not diagonalizable.b)Show that A is not...
- Q Find the infinite series solution about x = 0 for the followingDE, using Bessel's, Legrende's, or Frobenius method equations.3x^2y" + 2xy' + x^2y = 0Find the first 4 non-zero terms...
- Q Use ‘Reduction of Order’ to find a second solution y2 to thegiven ODEs:(a) y??+2y?+y=0, y1 =xe?x(b) y??+9y=0, y1 =sin3x(c) x2y??+2xy??6y=0, y1 =x2(d) xy?? +y? =0, y1 =lnx
- Q Let W be the set of P4 consisting if all polynomialssatisfying the conditions p(-2)=0.a.) prove that W is a subspace of P4 by checking all3 conditions in the definition of...
- Q What is an equilibrium solution? I am in an ElementaryDifferential Equations course. The problem is dy/dx = e^y-1; (0,0)and (1,1) and wants the equilibrium solutions. Been a few yearssince I've...
- Q Problem 7.3. Let f (x, y) = x6 + 3xy + y2 + y4.(a) Show that f remains unchanged if you replace x by ?x and y by?y. Hence,if (x,...
- Q For the wheel W9 find the minimal coloring. Show thatthe coloring is sufficently large by enumnerating it. Explain whyit may not be colored with fewer.
- Q Ken played golf yesterday and shot 107. Considering that henormally shoots in the low 80’s or high 70’s, this round of golfreally frustrated him. It was so frustrating that he...
- Q Problem 7-19 (Algo) A cafeteria serving line has a coffee urnfrom which customers serve themselves. Arrivals at the urn follow aPoisson distribution at the rate of 2.5 per minute. In...
- Q 1) Give parametrizations of the following circles with theindicated centers C(a, b) and radius R, and any other indicatedproperties.a) C(1, 1), R = 2, traversed once counter clockwise.b) C(1, 1),...
- Q Let V = { S, A, B, a, b, ?} and T = { a, b }, Find thelanguages generated by the grammar G = ( V, T, S, P...
- Q The solution to the Initial value problemx??+2x?+17x=2cos(6t),x(0)=0,x?(0)=0 is the sum of the steadyperiodic solution xsp and the transient solution xtr. Find both xspand xtr.
- Q Consider the mathematical system with the single element {1}under the operation of multiplication. Answer and explain thefollowing:a) Is the system closed?b) Does the system have anidentity element?c) Does 1 have an inverse?d) Doesthe associative...
- Q The selling prices of all stocks listed on the CDNX stockexchange are known to be normally distributed with a mean of $20and a standard deviation of $4. (a) What percentage...
- Q Hessian Matrix Determinant and Convex/ConcaveI have a function which has a Hessian Matrix of:-2000-1610010-4Can anyone explain why this is neither a positive nor a negativedefinite?And could you please explain 2*2...
- Q Suppose we had defined some bijection f : N ? Q +.(a) Discuss how you could use f to prove that Q ? is countablyinfinite. That is, define a new...
- Q Use Warshall’s algorithm to find the transitive closure of therelation R={(1,1),(1,3),(1,4),(2,4),(2,5),(3,1),(4,4),(5,3)}
- Q prove that positive operators have unique positive squareroot
- Q use Simpson's 3/8th Rule on the first 3 segments, and multipleapplication of Simpson's 1/3rd Rule on the rest of thesegments.?(?)=400?5?900?4+675?3?200?2+25?+0.2a = 0.12b = 1.56n = 7
- Q Let Q1=y(1.1), Q2=y(1.2), Q3=y(1.3), where y=y(x) solves...1) y'''+2y''-5y'- 6y=4x^2 where y(0)=1, y'(0)=2, y''(0)=32) y'''- 6y''+11y'- 6y=6e^(4x) where y(0)=4, y'(0)=10,y''(0)=303) y''- 6y'+9y=4e^(3x) ln(x) where y(1)=, y'(1)=2Please show all steps and thank...
- Q (a) Seek power series solutions of the given differentialequation about the given point x0;find the recurrence relation.(b) Find the first four terms in each of two solutions y1 and y2(unless...
- Q Discrete mathSummarize all the theorem regarding to graph theory.e.g.) A connected graph has a Euler circuit iif every vertex is of even degree.
- Q solve for matrix BLet I be Identity matrix(I-2B)-1=1-33-22-53-89
- Q Idont understand why we graph polar coordinates in the complextplane, if x = rcos(theta) and y =rsin(theta) why cant we justconvert all polar vectors to x and y? In my...
- Q Let R be the relation on Z+× Z+ such that (a, b) R (c, d) if andonly if ad=bc. (a) Show that R is an equivalence relation. (b) Whatis the...
- Q letG be a simple graph. show that the relation R on the set ofvertices of G such that URV if and only if there is an edgeassociated with (u,v) is...
- Q Solve the system using an eigenvalue/eigenvector approach and plotboth x(t) and y(t) over a 60 minute time interval.dx/dt= 8y/200-8x/100dy/dt=8x/100-8y/100inital conditions: x=0, y=100, t=0
- Q what is the principal on a $10,000 loan at a rate of7% number of compounding per year is 12 term in years is 18 monthswhat is the payment and the...
- Q Prove the following statements by using the definition ofconvergence for sequences ofreal numbers.a) If {cn} is a sequence of real numbers and {cn} converges to 1then {1/(cn+1)} converges to 1/2b)...
- Q A consumer electronics company is planning to introduce a newdevice. After careful consideration of costs, (e.g., there is afixed cost of $5 million for developing the item), theprojected state of the...
- Q 1. A survey of 500 high school students was taken to determinetheir favorite chocolate candy. Of the 500 students surveyed, 64like Snickers, 125 like Twix, 141 like Reese's Peanut Butter...
- Q (a) What is the maximum degree of a vertex in a simple graphwith n vertices?(b) What is the maximum number of edges in a simple graph ofn vertices?(c) Given a...
- Q Given the function f(x,y)=2x^3 + 6xy^2 - 3y^2 - 150x. Find thelocal minimums, maximums and saddle points of f(x,y).
- Q Show that if G is a group of order np where p is prime and 1< n < p, then G is not simple.(Please do not use Sylow theorem)
- Q Belden, Inc. acquires 30 percent of the outstanding votingshares of Sheffield, Inc. on January 1, 2017, for $306,000, whichgives Belden the ability to significantly influence Sheffield.Sheffield has a net book...
- Q x' = -3x + 2y,y' = -10x + 5y +2e^t/cos 2tSolve the system by variation of parameters
- Q Make the program(such as matlab) for solving the linearsystemAx = busing the Naive-Gaussian elimination & also the Gaussianelimination with partial pivoting.
- Q (a) Patty Stacey deposits $2200 at the end of each of 5 years inan IRA. If she leaves the money that has accumulated in the IRAaccount for 25 additional years,...
- Q Let S = {x : x 3 < 1}.(a) Find supS(b) Is S bounded?Thank you!
- Q Show that every sequence contains a monotone subsequence andexplain how this furnished a new proof of the Bolzano-WeierstrassTheorem.
- Q Use the simplex method to solve the following linear programmingproblems. Clearly indicate all the steps, theentering and departing rows and columns and rows, the pivotand the row operations used. An...
- Q What are theeigenvalues and eigenvectors of a diagonal matrix? Justifyyour answer (explain)These questions followthe exercises in Chapter 4 of the book, Scientic Computing: AnIntroduction, by Michael Heath. They study some...
- Q solve using MATLAB.Title: Numerical differentiations.Use Richardson extrapolation to estimate the firstderivative of y =cos x at x = ?/4using step sizesof h1 = ?/3and h2 = ?/6. Employcentered differences of O(h2) for theinitial estimates.solve using MATLAB.
- Q x^2*y''+x*y'+(x^2-1)y=0 what is the solution by using Frobeniusmethod
- Q Consider the following initial value problem: ?? ? 2?? = ?? ? 2?+ 3 ?? ?(0) = 61. Write the equation in the form ?? ?? = ?(?? + ??...
- Q (PDE)Find the series soln to Ut=Uxx on -2<x<2, T>0with Dirichlet boundary { U(t,-2)=0=U(t, 2)initial condition { U(0,x) = { x, IxI <1
- Q Use the method of steepest ascent to approximate the optimalsolution to the following problem: max? z=-(x1-2)^2-x1-(x2)^2 .Begin at the point(2.5,1.5)(p.s. The answer already exists on the Chegg.Study website isincorrect)
- Q x' = -6x - 3y + te^2ty' = 4x + yFind the general solution using undetermined coeffiecients
- Q 1.Use Newton's method to find all solutions of the equationcorrect to six decimal places. (Enter your answers as acomma-separated list.)ln(x) = 1/(x-3)2. Use Newton's method to find all solutions of...
- Q x' = -6x - 3y + te^2ty' = 4x + yFind the general solution using undetermined coeffiecients
- Q Hey.Given C = {z | z = z(t) = 10*e^(it), 0 <= t <= 2 pi}.How do I solve the following two integrals. Is there a way to do itwith...
- Q Recall the following theorem, phrased in terms of least upperbounds.Theorem (The Least Upper Bound Property of R). Every nonemptysubset of R thathas an upper bound has a least upper bound.A...
- Q The Verbrugge Publishing Company’s 2019 balance sheet and incomestatement are as follows (in millions of dollars):Balance SheetCurrent assets Net fixed assetsTotal assetsIncome StatementNet sales Operating expense$300 200$500Current liabilities?Advance payments by...
- Q Determine whether each of these proposed definitions isa valid recursive definition of a function f from the setof nonnegative integers to the set of integers. If f is welldefined, find...
- Q Let V be a finite dimensional vector space over R. If S is a setof elements in V such that Span(S) = V ,what is the relationship between S and...
- Q 2. The following data represent Salary, years of experience, andrank (A, B, or C). Salary is the dependent variable. For class andthe interaction effect between class and years of experience,...
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