Advance Math question and answers for July 12, 2023
- Q Does every linear transformation from a complex vector space toitself have an eigenvector?
- Q Show that (x-2)2 -lnx = 0, [1,2] and [e,4] have atleast one solution in the given intervals.
- Q Find the Fourier series of the following functionsf(x) = sinx+x^2+x,−2 < x < 2
- Q 1.Find all rational zeros of the polynomial, and then find theirrational zeros, if any. Whenever appropriate, use the RationalZeros Theorem, the Upper and Lower Bounds Theorem, Descartes' Ruleof Signs, the...
- Q Suppose T ∈ L(V)a) Show that V = ImT0 ⊃ ImT1 ⊃ImT2 ⊃ ...b) Show that if m ≥ 0 is such that ImTm = ImTm +1, then ImTm +...
- Q Find the solution of the given initial value problem.y(4) + 2y''' + y'' + 8y' − 12y = 12 sin t −e−t;    y(0) =7,    y'(0) = 0,    y''(0)= −1,    y'''(0) = 2
- Q find the eigenvalue and eigenfuction for the Sturm-liovillesystemy\"+ky=0y(0)=y(2pi)y'(0)=y'(2pi)
- Q Jessica bought a portfolio of five bonds for $50,000. Each ofthe bonds is a par valued 10,000 6% bond with annual coupons. Thesefive bonds mature at time t=16 through t=20....
- Q a) Prove that if X is Hausdorff, then X is T1b) Give an example of a space that is T1 , but notHausdorff. Prove that the space you give is...
- Q For each of the following relations, determine if fis• a function,• surjective, or• injective.Conclude by stating if the relation represents a bijectivefunction.For each point, state your reasoning in proper sentences.a)...
- Q Solve the following differential equations.a.) (2xy^2 +2x)dx−(4x^2 +1)dy=0b.) (3ye^(3xy) +4xy)dx+(3xe^(3xy) +2x^2)dy=0
- Q Q11: Use the Lagrange interpolating polynomial of degree threeor less and four-digit chopping arithmetic to approximate cos 0.750using the following values. Find an error bound for theapproximation.cos 0.698 = 0.7661...
- Q Use the Laplace transform to solve the given initial valueproblem.y(4) − 4y''' + 6y'' − 4y' + y = 0;y(0) = 1,y'(0) = 0,y''(0) = 0,y'''(0) = 1
- Q d^2y/dx^2 − dy/dx − 3/4 y = 0,y(0) = 1, dy/dx(0) = 0,Convert the initial value problem into a set of two coupledfirst-order initial value problemsand find the exact solution...
- Q In this project we explore how two populations develop when onepreys on the other. Clearly if there are no predators, the preypopulation will keep growing, whereas if there are no...
- Q Explain the difference between supervised and unsupervisedlearning. Provide examples.
- Q The Last Stop Boutique has a special sale of five days. Eachday, Starting Monday, the price will decrease 10% of the previousday. For Example, the original price of the product...
- Q An application of Newtonian Cooling is calculating the time ofdeath of a person. When healthy, a human body has a steadytemperature of 37â—¦C. Once a person dies, the regulatory mechanismsstop...
- Q The school population for a certain school is predicted toincrease by 80 students per year for the next 14 years. If thecurrent enrollment is 800 students, what will the enrollment...
- Q Define the following on R3:〈(a, b, c), (a′, b′, c′)〉 = 2aa′ + bb′ + 3cc′.(a) Prove that 〈 , 〉 is an inner product on R3.(b) Let B =...
- Q find the n-th order Taylor polynomial and the remainder forf(x)=ln(1+x) at 0
- Q (a) Let n be odd and ω a primitive nth root of 1 (means that itsorder is n). Show this implies that −ω is a primitive 2nth root of1. Prove...
- Q Prove that any graph where every vertex has degree at most 3 canbe colored with 4 colors.
- Q Using MATLAB:Consider the following Boundary Value Differential Equation:y''+4y=0y(0)=-2y(Ï€/4)=10Which has the exact solution: y(x)= -2cos(2x)+10sin(2x)Create a program that will allow the user to input the step size(in x), and two guesses...
- Q for each matrix A below, describe the invariant subspaces forthe induced linear operator T on F^2 that maps each v set of F^2 toT(v)=Av. (a) [4,-1;2,1], (b) [0,1;-1,0], (c) [2,3;0,2],...
- Q Evaluate the integral of f(x) below between x=1.5 and x=5.3using Gauss-Legendre formulas for 2, 3, and 4 points.Compare with analytical integration, calculate the % error ofthe numerical method.f(x)=4+8x−21x2 +16x3 −5x4+7x5
- Q Let T be an operator on a finite-dimensional complex vectorspace V, and suppose that dim Null T = 3, dimNullT2 =6. Prove thatT does not have a square root; i.e....
- Q  Consider n numbers x1, x2, . . . , xn laid out on a circle and some value α. Consider the requirement that every number equals α times the sum...
- Q Give a proof for the standard rule of differentiation, the ChainRule. To do this, use the following information:10.1.3 Suppose that the function f is differentiable at c, Then,if f′(c) >...
- Q 1. Identify each of the following statements as true of falseand explain your reasoning in full sentences. The domain ofdiscourse is the integers.(a) ∃x∀y(y > x)(b) ∀y∃x(y > x)(c) ∃x(x...
- Q Give an orthogonal basis for R3 that contains the vector[1,2,2]T,
- Q Locate the results of a recent survey that show at least twovariables in a newspaper, magazine, or internet article. Outlinethe survey data so that your peers can understand the variables...
- Q In Exercises 5–37, solve the given differential equations byLaplace transforms. The function is subject to the givenconditions.13. 4y″ + 4y′ + 5y = 0, y(0) = 1, y′(0) = -1/217....
- Q Compute, by Euler’s method, an approximate solution to thefollowing initial value problem for h = 1/8 : y’ = t − y , y(0) = 2; y(t) = 3e^(−t) +...
- Q The Alternate Interior Theorem states that if two lines cut by atransversal line have a pair of congruent alternate interiorangles, then they must be parallel. Prove this theorem in NeutralGeometry...
- Q Summarize seperable equations, integrating factor, exactequations, and auxiliary equation in your own words and whatmathematical skills are needed in each technique. Please nohandwriting unless I can read it please.
- Q “We must differentiate our mindset first and our lessonssecond.†(Dweck, 2012). What does this saying mean to you? In yourown words, what is the difference between differentiation andtracking?
- Q Use the Laplace transform to solve the following initial valueproblem:?″+6?′+58?=?(?−4)?(0)=0,?′(0)=0(Notation: write u(t-c) forthe Heaviside step function ??(?)uc(t) with step at ?=?t=c.)
- Q 3. Before you sit three chests – one made of wood, one of stone,and one of steel. You know that one of the chests contains a greattreasure, while the other...
- Q consider f(x) = ln(x) use polynomial degree of 5!!!a) Approximate f(0.9) and f(1.1)b) Use Taylor remainder to find an error formula for Taylorpolynomial.Give error bounds for each of the two...
- Q The pottery shop opened a new branch this year. The followingfigures show the sales volume and advertising expenses.Sales LY $900,000Sales TY $1,050,000Sales plan for next year $975,000Advertising costs LY $28,500Advertising...
- Q Jane wants to auction off an item, but does not know where to goto find bidders. David offers to find bidders for her, but willcharge her $10 per bidder he...
- Q The owner of a major league baseball team is considering movinghis team from its current city in the upper Midwest to a city inthe Southeast that offers a larger television...
- Q hey hey! mechanical engineering student who is VERY confused andhas absolutely no idea what any of this means but really wants toknow. could you please help me! this is the...
- Q Find the green's function then find the solutiony\"+4y=xy(0)=0, y'(1)=0
- Q Let R be a relation on a set that is reflexive and symmetric butnot transitive? Let R(x) = {y : x R y}. [Note that R(x) is the sameas x...
- Q How many ordered quadruples (x1, x2, x3, x4) of positiveintegers satisfy the conditions x1 < x2 < x3 < x4 < 15and xi+1 − xi ≥ i for each i...
- Q The following table shows the number of fifth and sixth gradeteachers in a school district and the number of students in each ofthose grades. The number of teachers for each...
- Q Find all of the symmetries of each of the following figures inE2 (Euclid Plane). Describe each symmetry precisely,e.g., explain which line you are reflecting over, what point youare rotating about,...
- Q 6) Solve the ff IPV: U(X,0) =f(X)b1) 2Ut + (X+1)2UX = 0b2) Ut + Xt^2UX=0b3) Â Â Ut + U^2UX=0
- Q You need a new computer. You are considering either leasing orputting the purchase on your credit card.The terms of the lease agreement are $250 down and a monthlypayment of $100...
- Q Evaluate the polynomial y= x^3- 5x^2+ 6x + 0.55 at x=.137. Use3-digit arithmetic with rounding. Evaluate the percent relativeerror. (b) Repeat (a) but express y asy= ((x- 5)x +6)x +...
- Q 1) A 10-milliliter graduate weighs 42.745 grams. When 6milliliters of distilled water are measured in it, the combinedweight of graduate and water is 48.465 grams. By definition, 6milliliters of water...
- Q This problem is an example of over-damped harmonic motion.A mass m=4kg is attached to both a spring with spring constantk=72N/m and a dash-pot with damping constant c=36Nâ‹…s/mThe ball is started...
- Q Describe a problem that can be solved by using theshortest-route model. Give a detailed mathematical example.
- Q Explain what it means for an assignment model to be balanced.Give detailed mathematical examples.
- Q In a job shop operation, four jobs may be performed on any offour machines. The hours required for each job on each machine arepresented in the following table. The plant...
- Q Now that we have seen Euler in action, let's return to examiningthe content of the M-File Euler.m. We have already explained thefirst line, where we defined the parameters our function...
- Q Show all workA ball is projected upward from the top of a 90 foot building ata velocity of 64 feet per second. The ball's height above theground below the building...
- Q consider f(x) = ln(x)a) Approximate f(0.9) and f(1.1)b) Use Taylor remainder to find an error formula for Taylorpolynomial.Give error bounds for each of the two approximations in (a).Which of the...
- Q Determine the solution of the following initial boundary-valueproblem using the method of separation of VariablesUxx=4Utt 0<x<Pi t>0U(x,0)=sinx 0<=x<PiUt(x,0)=x 0<=x<PiU(0,t)=0 t>=0U(pi,t)=0 t>=0
- Q Find the biggest “*prime gap†(see definition) from the primenumbers between 1 and 1,000,000.*Prime gap = the difference between two consecutive primes.The exercise can be completed manually or with a...
- Q 1.) A sheet of paper is cut into 6 same-size parts. Each of theparts is then cut into 6 ​same-size parts and so on.a. After the 8th cut, how many...
- Q 1. (20 pts) For each of the following statements, please circleT (True) or F (False). You do not need to justify your answer. (a)T or F? Any eigenvector of a...
- Q Determine if the following set forms a subspace in R^2.The set is (x1,x2)^t ,in other words the column vector [x1,x2].Can you go through each axiom and show your work?, I...
- Q (The “conjugation rewrite lemmaâ€.) Let σ and Ï„ bepermutations.(a) Show that if σ maps x to y then στ maps Ï„(x) toÏ„(y).(b) Suppose that σ is a product of disjoint...
- Q Derive the variation of parameters formula for the solution ofthe initial value problem for a non-homogeneous, linear system offirst order, ordinary differential equations in terms of afundamental matrix of solutions...
- Q Solve the given system of differential equations by systematicelimination.(D − 1)x+(D2 + 1)y=1(D2 − 1)x+(D + 1)y=2(x(t), y(t)) =
- Q Let f and g be two functions whose ï¬rst and second orderderivative functions are continuous, all deï¬ned on R. Whatassumptions on f and g guarantee that the composite function f...
- Q 1.  Inventory ManagementWilliams & Sons last year reported sales of $145 million,cost of goods sold (COGS) of $120 and an inventory turnover ratioof 5. The company is now adopting a new...
- Q Consider a rocket that burns steadily. The higher pressure inthe combustion chamber, the faster the propellant burns. Why isthis? The relationship is such that the higher the pressure, thecloser the...
- Q Give an example of proof by construction.For example, prove that for every well-formed formula f inpropositional logic, an equivalent WFF exists in disjunctive normalform (DNF).HINT: Every WFF is equivalent to...
- Q In the 3-month period November 1, 2014, through January 31,2015, Hess Corp. (HES) stock decreased from $80 to $64 per share,and Exxon Mobil (XOM) stock decreased from $96 to $80...
- Q A recent college graduate buys a new car by borrowing $22,000 at8.4%, compounded monthly, for 4 years. She decides to pay $552instead of the monthly payment required by the loan.(a)...
- Q Design a spreadsheet to calculate the class’s grades. Considerthe following requirements:Each project will be graded from 0 to 10.the contribution of each grade to the final grade are ( 7...
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