Advance Math question and answers for July 03, 2023
- Q what are some factors that a manufacturer shouldconsider when determining whether to test a sample or the entirepopulation to ensure the quality of a product?
- Q y″+9y′=162sin(9t)+324cos(9t)y(0)=7y'(0)=7
- Q Let M(x, y) be \"x has sent y an e-mail message\" and T(x, y) be \"x has telephoned y, \" where the domain consists of all students inyour class. Use...
- Q A Trigonometric Polynomial of order n is a function of the form:?(?) = ?0 + ?1 cos ? + ?1 sin ? + ?3 cos(2?) + ?2sin(2?) + ⋯ +?ncos(??)...
- Q Prove that every cyclic rhombus is a square
- Q Derive a three-point formula with the highest possible order (ofh) to approximate f '(a) and f \"(a), respectively, using f(a − 2h),f(a + h), f(a + 2h).
- Q Show that the set â„2R2, equipped with operations(?1,?1)+Ëœ(?2,?2)=(?1+?2+1,?1+?2−1)(x1,y1)+~(x2,y2)=(x1+x2+1,y1+y2−1)? â‹…Ëœ (?,?)=(??+?−1,??−?+1)(1)defines a vector space over â„R.(2)Show that the vector space ?V defined in question 1 isisomorphic to â„2R2 equipped with its...
- Q T41(Robert Beezer) Consider the system of linear equationsLS(A,b), and suppose that every element of the vector of constantsb is a common multiple of the corresponding element of a certaincolumn of...
- Q 1) A radioactive substance decays at a rate proportional to theamount of the substance at present time. Initially 200 grams of athe substance was present and remain 80% of the...
- Q Let T : Rn →Rm be a linear transformation.(a) If {v1,v2,...,vk} is a linearly dependent subset of Rn,prove that {T(v1),T(v2),...,T(vk)} is a linearly dependent subsetof Rm.(b) Suppose the kernel of...
- Q 1. (a) Construct a magic Venn diagram (MVD) or order 3, i.e.,label the eight non-overlapping regions of a Venn diagram of 3generic sets A, B, C with the integers 1...
- Q discrete mathmost important is c) and e) and f) statements withnested quantifiers: variables ...please with a clear and concise explanation on how to doeach steps. So not just the answer...
- Q Based on dynamics, describe the behavior of a phase portrait ofa n-body problem.
- Q Find the directional derivative of f(x,y)=arctan(xy) at the point (-2,5) in the direction of maximum decrease.  What is the Domain and Range of f(x,y)=arctan(xy)?
- Q Use the method of Undetermined Coefficients to find a generalsolution of this system X=(x,y)^TShow the details of your work:x' = 6 y + 9 ty' = -6 x + 5Note...
- Q Show that any polynomial over C (the complex numbers) is thecharacteristic polynomial of some matrix with complex entries.Please use detail and note any theorems utilized.
- Q Let a and b be integers which are not both zero.(a) If c is an integer such that there exist integers x and ywith ax+by = c, prove that gcd(a,...
- Q Prove that 3 divides n^3 −n for all n ≥ 1.
- Q Consider the following linear optimization model.Z = 3x1+ 6x2+ 2x3st      3x1 +4x2 + x3 ≤2          x1+3x2+ 2x3 ≤ 1     X1, x2, x3 ≥0              (10) Write the optimization problem in standard form...
- Q Suppose we define a relation on the set of natural numbers asfollows. Two numbers are related iff they leave the same remainderwhen divided by 5. Is it an equivalence relation?...
- Q 1. Use the ε-δ definition of continuity to prove that (a) f(x) =x 2 is continuous at every x0. (b) f(x) = 1/x is continuous atevery x0 not equal to...
- Q 3. Given the parametric equations x = 3t /1 + t^3 and y = 3t^2/1 + t^3 . a) Show that the curve produced also satisfies theequation x^3 + y^3...
- Q Use Theorem 4.2.1 to determine which of the following sets ofvectors are subspaces of F(−∞,∞). (Justify!)(a) The set of all functions f ∈ F(−∞,∞) for which f(0) = 0.(b) The...
- Q LetD and D'be integral domains.Let c = charD and c'= charD'(a) Prove that the direct product D ×D'has unity.(b) Let a ∈D and b∈D'.Prove that (a, b) is a unit...
- Q 3) Determine the longest interval in which the given initialvalue problem is certain to have a unique twice-differentiablesolution. Do not attempt to find the solution t(t − 4)y\" + 3ty'...
- Q 7 2 -3 x1 -122 5 -3 x2 = -201 5 -6 x3 -26LU Decomposition Method?
- Q The following problem is reprinted from the November 1989Actuarial Examination on Applied Statistical Methods. Source:Society of Actuaries.Consider the following table of dataxy1112212299(a) Calculate the least squares line and the correlationcoefficient.(b)...
- Q 1) Come up with your own story to illustrate Russel’s paradoxinformally.
- Q Differential Equations (FREE, UNDAMPED MOTION)A 12-lb weight is placed upon the lower end of a coil springsuspended from the ceiling. The weight comes to rest in itsequilibrium position, thereby stretching...
- Q V=[(a b), a,b E R+] with (a1 b1)+(a2 b2)=(a1a2b1b2)and for c E R, c(a b)=(a^c b^c) is a vector space over R.Define T:R^2 to V by T[a b]= (e^a e^b)....
- Q The equation 2x1-3x2=5 defines a line in R2.a. Find the distance from the point w=(3,1) tothe line by using projection.b. Find the point on the line closest to w byusing...
- Q Let n greater than or equal to 2 and let k1,...,kn bepositive integers. Recall that Ck1,..., Ckn denote the cyclicgroups of order k1,...,kn. Prove by induction that their directproduct Ck1×Ck2×....×Ckn...
- Q How to write a self-defined function to find the inverse of amatrix by using Gaussian Jordan method in MATLAB? Thanks.
- Q Prove that Desargues' configurations satisfy the principle ofduality.
- Q Use separation of variables to find a series solution ofutt = c 2uxx subject to u(0, t) =0,ux(l, t) + u(l, t) = 0, u(x, 0) = φ(x), &ut(x, 0)...
- Q How to prove that player I can always win a Nim game in whichhte number of heaps with an odd number of coins is odd.I understand the objective, having trouble...
- Q For each of the following indexed collections of sets {Ai : i ∈I}, determine ∪i∈I Ai, ∩i∈I Ai, and whether or not the collectionis pairwise disjoint. Prove your claims.(a) I...
- Q create a table of data for two different linear functions. Thetable should use the same values of X for both functions. Based onyour table will the graph of these two...
- Q Show your understanding of the unsolved mathematical below andpresent a description of the problem.Yang-Mills Theory and the Mass Gap (mathematical physics)
- Q Find A, B, C, D, E such that the rule Af(a − 2h) + Bf(a − h) +Cf(a) + Df(a + h) + Ef(a + 2h) approximates f\"'(a) with the...
- Q Let vectors u and v form a basis in some plane, in each of thefollowing cases determine if the vectors e1 and e2 for a basis inthis plane:a)e1=u+v e2=u-v b)e1=-u+2v...
- Q Hanson Inn is a 96-room hotel located near the airport andconvention center in Louisville, Kentucky. When a convention or aspecial event is in town, Hanson increases its normal room ratesand...
- Q Current IssuesOne of the biggest issues facing this company is the rise inprices of raw materials, especially the iconic almond, which due todrought in California has seen a price rise...
- Q Write the first three non-zero terms of the Taylor series of sinx near x0 = 3Ï€/2. Sketch a plot of the curves for sin x and yourapproximation.
- Q Consider the differential equationy′(t)+9y(t)=−4cos(5t)u(t),with initial condition y(0)=4,A)Find the Laplace transform of the solutionY(s).Y(s). Write the solution as a singlefraction in s.Y(s)= ______________B) Find the partial fraction decomposition of Y(s). Enter...
- Q (a) Let M be a Cr submanifold of Rn, and let f : M → R be a Crfunction. Showthere is an open neighbourhood V of M in Rn and...
- Q Find five positive natural numbers u, v, w, x, y suchthat there is no subset with a sum divisible by 5
- Q (Discrete Math) Prove that the equation 2x² + y² = 14 has nopositive integer solutions.
- Q Find 4 examples from an outside source of a real-worldscenario that involves a sequence.Define the sequence in three differentways.Determine if the sequence is arithmetic, geometric, orneither.Discuss which representation of the...
- Q A ​$257 comma 800 mortgage for 30 years for a new home isobtained at the rate of 7.8​% compounded monthly. Find​ (a) themonthly​ payment, (b) the interest in the first...
- Q y'''-8y=e^ix by the method of variation of parameters
- Q y''-3y+2y=e^3ty(0)=1y'(0)=0laplace transformation
- Q Let X be the set of equivalence classes. So X = {[(a,b)] : a ∈Z,b ∈ N} (recall that [(a,b)] = {(c,d) ∈Z×N : (a,b) ∼ (c,d)}).We deï¬ne an addition...
- Q The Bradley family owns 410 acres offarmland in North Carolina on which they grow corn and tobacco.Each acre of corn costs $105 to plant, cultivate, and harvest; eachacre of tobacco...
- Q A liquid culture of infectious bacteria was accidentally dumpedinto a river 900 m upstream of the intake pipe for the municipalwater plant; 10^(11) organisms are introduced into the river whichhas...
- Q Let (xn) be a sequence with positive terms. (a) Provethe following: lim inf xn+1/ xn ≤ lim infn√ xn ≤ lim sup n√xn ≤lim sup xn+1/ xn .(b) Give example...
- Q 1. If f(x) = ln(x/4)-(a) Compute Taylor series for f at c = 4-(b) Use Taylor series truncated after n-th term to compute f(8/3)for n = 1,.....5-(c) Compare the values...
- Q Euler’s Methodand Introduction to MATLAB•Start MATLAB•Inline Commands: You can type commands directly into the command window: Type andexpression and then hit enter to evaluate the expression. Forexample:>> 2+2If you want...
- Q I need an in-depth explanation for quaterniongeometry in game developing?
- Q 1.Calculate the commutator C of Dn2.Calculate the commutator C of Sn where n=3,4(use the fact that if H is a normal subgroup of G, thenG/H is abelian if and only...
- Q Let E be the set of all positive integers. Define m tobe an \"even prime\" if m is even but not factorable into two evennumbers. Prove that some elements of...
- Q (5) In each part below, find a basis for R4 that contains thegiven set, or explain why that is not possible: (a){(1,1,0,0),(1,0,1,0),(0,1,1,0)} (b){(1,−1,0,0),(1,0,−1,0),(0,1,−1,0)} (c){(1,1,0,0),(1,−1,0,0),(0,1,−1,0),(0,0,1,−1)} (d){(1,1,1,1),(1,2,3,4),(1,4,9,16),(1,8,27,64),(1,16,81,256)}
- Q 3.Let A = D + 1, B = D − 3, C = D + x, where D = dx. Calculate thedifferential operators AB, BC, CA and their effect on...
- Q Consider the equation t^2 -y\"-t(t+2)y'+(t+2)y=2t^3,(t>0). Given that y1(t)=t3, y2(t)=te^t are the two fundamentalsolutions of the corresponding homogeneous equation, find thegeneral solution of the nonhomogeneous equation.
- Q The merry-go-round rotates counterclockwise with a constantangular speed u. The distance between the horse on themerry-go-round and the rotational center is r.(a) Find the position of the horse x and...
- Q We are working on functions of complex variables in calculus(Chpt. 17.4 in Advanced Engineering Mathematics), and our profposed us the following question:\"Find the function w = u + iv =...
- Q  a) Use Fermat’s little theorem to compute 52003 mod 7,52003 mod 11, and 52003 mod 13.b) Use your results from part (a) and the Chinese remaindertheorem to find 52003 mod...
- Q Use the data from problem 12 BELOW. If the lead time for placingan order is 5 days, and Technology Corporation holds a safety stockequal to a 30-day supply of chips,...
- Q Express sin 6θ as a polynomial in sin θ and cos θ.
- Q Let F be a vector field. Find the flux of F through the givensurface. Assume the surface S is oriented upward. F = eyi + exj +24yk; S that portion...
- Q Please solve the recurrence relation by finding the explicitformula of each problem. Show all work, thanks!A. ck = 6ck-1 -9ck-2    k≥2,  c0 =1, c1=3B. dk = 2dk-1 +k                    k≥1,  d0...
- Q The​ input-output matrix for a simplified economy with just foursectors​ (natural resources,​ manufacturing, trade and​ services,and personal​ consumption) is given below. Suppose the demand​ (inmillions of​ dollars) matrix is matrix...
- Q Solve the following differential equations using Taylor seriescentered at 0. It’s enough to find the recurrence relation and thefirst 3 terms of the series.(a) y''− 2y' + y = 0(b)...
- Q Let C(R) be the vector space of continuous functions from R to Rwith the usual addition and scalar multiplication. Determine if Wis a subspace of C(R). Show algebraically and explain...
- Q A real estate developer wishes to study the relationship betweenthe size of home a client will purchase (in square feet) and othervariables. Possible independent variables include the familyincome, family size,...
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