Advance Math question and answers for September 08, 2023
- Q For each of these lists of integers, provide a simple formulaor rule that generates the terms of an integer sequence that beginswith the given list. Assuming that your formula or...
- Q 2 Let F be a field and let R = F[x, y] be the ring ofpolynomials in two variables with coefficients in F.(a) Prove thatev(0,0) : F[x, y] ? Fp(x,...
- Q How many integer solutions are there tox1+x2+x3+x4= 100 withall of the following constraints:10 ? x1 , 0? x2 < 20 , 0 ?x3 < 40 , 10 ? x4< 50Please...
- Q Suppose you are deciding whether to buy an electric or a naturalgas hot water heater. Assume you live in California.Note: 1 therm of natural gas equals ~30 kWh of electricityNatural...
- Q True/False: If A is an invertible m x m matrix and B is an m x nmatrix, then AB and B have the same null space.(Hint: AB and B have...
- Q Course: Differential Geometry (Vector Calculus & LinearAlgebra)Provide all proofs(a) Find the formula for the distance from p to the liney=mx(b) prove that the set U={(x,y): y<mx} is an openset
- Q Problem 2-25 (Algorithmic)George Johnson recently inherited a large sum of money; he wantsto use a portion of this money to set up a trust fund for his twochildren. The trust...
- Q An eulerian walk is a sequence of vertices in a graph such thatevery edge is traversed exactly once. It differs from an euleriancircuit in that the starting and ending vertex...
- Q Solve the differential equation using the Laplacetransform. y''' + 3y''+2y' = 100e-t , y(0) =0, y'(0) = 0, y''(0) = 0
- Q What is overmatching versus undermatching? Give an example ofovermatching and undermatching (with hypothetical proportions) thatmight occur on a concurrent VI 20-sec VI 30-sec schedule (whichmeans that you must first work...
- Q What is the number of permutations of the six digits 123456 inwhich the strings 123, 234, 345, 456, 654, 543, 432, 321 don'tappear?
- Q 1) . Solve the IVP:y^''+6y^'+5y=0, y(0)=1, y^' (0)=32. Find the general solution to each of the following:a) y^''+2y^'+5y=e^2xb) y^''+2x/(x^2+1) y'=xc) y^''+4y=1/(sin?(2x)) (use variation of parameters)
- Q Consider the linear transformation T : P1 ? R^3 given by T(ax +b) = [a+b a?b 2a]a) find the null space of T and a basis for it(b) Is T...
- Q Let f : R ? R be a function.(a) Prove that f is continuous on R if and only if, for everyopen set U ? R, the preimage f ?1...
- Q find the general solutiony'''-y''-4y'+4y=5-e^x-4e^2x(UNDETERMINED COEFFICIENTS—SUPERPOSITION APPROACH)
- Q A pharmacist has fluocinolone ointment with50%fluocinolone , and the other contains15% fluocinolone. How many grams of each may be used to prepare1950 g of a 20%fluocinolone ointment?
- Q Show that any conditionally convergent series has arearrangement that diverges.
- Q How many sets of five numbers from 1 to 15 can you make in whichexactly two of the numbers are divisible by 3?
- Q Use stars and bars to solve each counting problem. You may leaveyour answers as binomial coefficients.(a) How many collections of 6 (not necessarily distinct) coinscan be made from an infinite...
- Q Homework 1.1. (a) Find the solution of the initial value problemx' = x^(3/8) , x(0)=1 , for all t, where x = x(t). (b) Find thenumerical solution on the interval...
- Q P4.4.2 Give a rigorous proof, using strong induction, that everypositive natural has at least one factorization into primenumbers.
- Q roblem 3 Find the solutions to the general cubic a x^3 +b x^2+cx +d=0 and the solutions to the general quartic a x^4+b x^3+c x^2+dx+e=0. Remember to put a space...
- Q LetV be the space of polynomials with real coefficients of degree atmost n, and let D be the differentiation operator. Find alleigenvectors of D on V.
- Q Abstract AlgebraLet G be a discrete group of isometries of R2.Prove there is a point p ? R2 whose stabilizer is trivial.
- Q Let P2 be the vector space of all polynomials ofdegree less than or equal to 2.(i) Show that {x + 1, x2 + x, x ? 1} is a basis...
- Q 1. Find the Legendre polynomial PL(x) for L = 3,4,5,6 where thepolynomian is the series solution for Legendre equation2. Find the other solution QL(x) for the Legendre equation for L=...
- Q 6) (a) Denote the successive intervals that arise in thebisection method by [a0,b0,[a1,b1] , [a2,b2], andso on Show that bn – an= 2-n(b0-a0)(b) The bisection method is said to have...
- Q Write up a full proof of the fact that every k-dimensionalsubspace of R^n is the intersection of (n-k) hyperplanes. Tip: Ifyou don't know how to start, begin by summarizing your...
- Q the result of a recent bc election are summarised byparty belowliberal 1,140,000Nfp 430,000green 250,000reform 180,000a. in a system of proportional representation (each party wouldreceive seats in proportikn yo fhe number of...
- Q 2examples of each1-Direct Products and Finitely Generated Abelian Groups DirectProduct2-Homomorphisms
- Q Question 2. True or false2. If [T]? is the matrix representing the linear map T in thebasis ?, then the jth column of [T]? contain the coordinates of theT(?j) in...
- Q Solve the equation CX + 5X = D respect to the matrix X.C =? ?[ -4 3 5 ] [ 2 0 6 ] [ 1 2 -3 ]D =?...
- Q Your firm designs training materials for computer trainingclasses, and you have just received a request to bid on a contractto produce a complete set of training manuals for an 8-sessionclass....
- Q What is a Bessel Differential Equation? Classify Bessel Equationwith respect to its order, linearity and homogeneity. How manyindependent solutions of Bessel Differential equation are needed toconstruct general solution?
- Q One of the luxury car manufacturers usually wants to make alimited number of automobiles in a given year and the company’s aimis to expand their profit margins in each car...
- Q Find a power series solution of this ODE:y''+x^2y'=0 ; y(0)=1 y'(0)= 2
- Q Prove verbally without referencing a Venn diagram, can use aVennn diagram to visually see it but cannot be a reference inproof.a) Let A be a set. Prove that A? A.b)...
- Q what would be some practical research scenarios in the field ofSocial Work where this type of statistical test would beappropriate.
- Q 1)A full rectangular water tank has a base of 10 ft x 15 ft and is20 ft high. What is the pressure at the bottom of the tank in a)PSI...
- Q I have no clue how to do the math here and get thevalues asked? Please help by working out theequation. Two species of algae (called Blue and Green) compete.Their dynamics can...
- Q 1. Prove the Heine-Borel Theorem (Theorem 3.35).2. Suppose f: X ? Y maps from the metric space X to the metricspace Y, and x ? X.Prove that f is continuous...
- Q Prove the following:Let V and W be vector spaces of equal (finite) dimension, andlet T: V ? W be linear. Then the following are equivalent.(a) T is one-to-one.(b) T is...
- Q You need to complete the following SWOT analysis:Math Study StrategiesStrengthsWeaknessOpportunitiesThreatsWarm Up for Math classLearn new material firstStudy BreaksLearning ResourcesGroup StudyFlash CardsReview notes after classWrite down important concepts after completing homeworkAsk...
- Q Consider the lattice of real numbers in the interval [0,1] withthe relation ?. Does this lattice have any atoms?
- Q Creative Computing sells a tablet computer called the Protab.The $780 sales price of a Protab Package includes thefollowing:One Protab computer.A 6-month limited warranty. This warranty guarantees thatCreative will cover any...
- Q y1(t) = (1+t)2 is a solution to y'' +p(t)y' + q(t)y = 0. Find a second solution that is linearlyindepentent of y1(t).
- Q Prove1. For each u ? R n there is a v ? R n such that u + v= 02. For all u, v ? R n and a ?...
- Q We have already derived the integral formulae for the mass m,the moment My about the y-axis, and the moment Mx about the x-axis,of the region R where a lamina with...
- Q Compute the quartic interpolating polynomial for the Hermiteinterpolation problemp(0) = 2, p'(0) = -9p(1) = -4, p'(1) = 4p(2) = 44with respect to the Newton basis. Compute the divideddifferences. Find...
- Q Suppose ?? (?,?)=???? +??? and ? is the line segment from point?=(2,0) to ?=(0,3).(a) Find a vector parametric equation ?? (?) for the linesegment ? so that points ? and...
- Q Use the Gauss–Jordan method todetermine whether each of the following linear systems has nosolution, a unique solution, or an infinite number of solutions.Indicate the solutions (if any exist).i. x1+ x2 +x4=...
- Q let R = Z x Z. P be the prime ideal {0} x Z and S = R - P. Provethat S^-1R is isomorphic to Q.
- Q A biologist must make a medium to grow a type of bacteria. Thepercentage of salt in the medium is given by S=0.01(x^2)(y^2)z ,where S is the percentage expressed as a...
- Q Assume the reader understands derivatives, and knows thedefinition of instantaneous velocity (dx/dt), and knows how tocalculate integrals but is struggling to understand them. Usestudents’ prior knowledge to provide an explanation...
- Q Let A be a commutative ring and F a field. Show that A is analgebra over F if and only if A contains (an isomorphic copy of) Fas a subring.
- Q Consider the following function ?(?) = ?^ 4+ 2? ^3 + 8?^ 2+ 5?With the initial guesses of ?1 = ?2, ?2 = ?1, and ?3 = 1, find theminimum...
- Q Let R and S be equivalence relations on a set X. Which of thefollowing are necessarily equivalence relations?(1)R ? S(2)R S .Please show me the proof. Thanks!
- Q An element a in a field F is called a primitiventh root of unity if n is the smallest positiveinteger such that an=1. For example, i is a primitive4th root...
- Q A study was conducted to determine whether a new drug,nomasbesos, was effective in preventing the swollen spleen thatoften occurs when a person has a mononucleosis (mono) infection.Individuals with mono were...
- Q Suppose a water tower in an earthquake acts as a mass-springsystem. Assume that the container on top is full and the water doesnot move around. The container then acts as...
- Q Use MATLAB to figure out the following problem, if youdo not know how to use MATLAB then please do not answer. Coding isrequired for the exercise.For f(x) = arctan(x), find...
- Q Find a basis and the dimension of the subspace:V = {(x1, x2, x3,x4)| 2x1 = x2 + x3,x2 ? 2x4 = 0}
- Q Formulate the following problem using the following steps.a. Define the decision variables.b. Specify the objective function.c. Specify the constraints and simplify them so that the lefthand side of each constraint...
- Q Solve the following initial value problem: tdy/dt+5y=5t withy(1)=8.Put the problem in standard form.Then find the integrating factor, ?(t)=and finally find y(t)=
- Q E) Another pair are called missers. They are supposed to roll 3& 7 more often than fair dice Below is the data from 16rolls.{ 10, 3, 5, 7, 3, 7,...
- Q The simplex algorithm is to continue in this manner, alwaysperforming basis exchanges which improve the objective function,until no more exchanges are possible. We conclude with an example:Buzz Buzz Buzz Coffee...
- Q For each n ? N, let f_n(x) = a_nx + b_n where a_n,b_n aresequences of real numbers. Prove that if f_n ? f on [0,1] where fis a function on...
- Q Q: Find the power series solution centered at the ordinary pointx = 0 for each equation.((x^2) + 1) y''-6y=0
- Q Request to solve the second order differential equation by rangeRange kutta 4th order method 8d^2y/dx^2-x^2+2y^2=0 with initialconditions y(0)=1 and dy/dx(0)=0 compute y at 1 (NumericalMethod)
- Q For each of the subspaces ? and ? of ?4 (?) defined below, findbases for ? + ? and ? ? ?, and verify that dim[?] + dim[? ] =...
- Q June Watson is contributing ?$3,500 each year to a Roth IRA. TheIRA earns 3.3% per year. How much will she have at the end of35?years?
- Q Ex 3. Consider the following definitions:Definition: Let a and b be integers. A linear combination of aand b is an expression of the form ax + by, where x and...
- Q Solve the following differential equations:1. x"(t)+ x(t)=6sin(2t) ; x(0)=3, x'(0)=12.y"(t)- y(t)=4cos(t) ; y(0)+0 , y'(0)=1
- Q QUESTION 3 USE LINGO OR MANUAL LP) Chemco produces threeproducts: A, B, and C. They can sell up to 30 pounds of eachproduct at the following prices (per pound): product...
- Q There are 4 mathematicians m1;m2;m3;m4 and 4 computer scientistsc1; c2; c3; c4. mi and ci are enemies for each i = 1; 2; 3; 4 (i.e.m1 and c1 are enemies,...
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