Advance Math question and answers for July 27, 2023
- Q Maximize or minimize the following functions. Be sure to checkyour second-order conditions.(a) maxQ ? = (20 ? Q)Q ? 4Q(b) maxQ ? = (12 ? Q)Q ? 2Q2(c) maxL ?...
- Q Find a general solution to the following? higher-order equation:y''''+17y''+16y=0I know you have to rewrite this question into :r4 + 17r2 +16 = 0factoring I get (r2 +1)(r2+16), facotringfurther (r+i)2(r+4i)2Am I...
- Q Solve using Laplace Transform:1) y'' - 2y' + 5y = cos(2t) - cos(2t)u4pi(t); y(0) =0, y'(0) = 0
- Q Determine the solution of a homogeneous linear first orderOrdinary Differential Equation system: (use 2 methods, substitutionmethod, and matrix method)x1'= -4x1-6x2 x2'=x1+x2With the initial values: x1 (0) = 2 ;x2 (0) =...
- Q Again considering y'' + 4y' + 3y = 0:(a) Solve the IVP y'' + 4y' + 3y = 0; y(0) = 1, y'(0) = ? where? > 0.(b) Determine the...
- Q use bisection to find the real root x = sin(x) + 1 with theinitial guesses of x l = 0 and x u = 3.perform the computation until the approximate...
- Q inbound taxation questionsTrue / False QuestionsService revenue is sourced based on the location in which suchservices are rendered.Income tax treaties can generally only result in an increase inthe amount of...
- Q 12. You plan to save for your retirement during the next 30years. To do this, he will invest 700 dollars a month in a stockaccount and 300 dollars in a...
- Q You bought 500 Forever stamps just before the price went up inJanuary of 2014 at $0.46/stamp, a $0.03 savings per stamp. If youcould have paid off a credit card charging...
- Q Let a,b be an element in the integers with a greater or equal to1. Then there exist unique q, r in the integers such that b=aq+rwhere z less than or...
- Q 1. Prove or disprove: if f : R ? R is injective and g : R ? R issurjective then f ? g : R ? R is bijective.2. Suppose...
- Q 7. Finding Roots Using the Bisection MethodWrite a function that implements the "bisection method" forfinding the roots of function. The signature of your functionshould look likedef find_root(f,a,b,n):where n is the...
- Q Find the intervals of increase and decrease, find the localmaximum and minimum values, find the intervals of concave up andconcave down, find the inflection points and sketch the graphf(deta) =...
- Q ?(Cost of? short-term bank loan?) On July? 1, 2015, theSouthwest Forging Corporation arranged for a line of credit withthe First National Bank? (FNB) of Dallas. The terms of theagreement call...
- Q Un tanque inicialmente tiene 220 galones de agua limpia, perouna solución de sal de concentración desconocida se vierte a unritmo de 6 galones por minuto. Si a la vez que...
- Q 1.) Corn is blanched in a 5 meter long steam tunnel blancher.The corn goes into the blancher 5 cm deep on a 50 cm wide belt. Therequired blanch time is...
- Q 4) In this problem, we will explore how the cardinality of asubset S ? X relates to the cardinality of a finite set X.(i) Explain why |S| ? |X| for...
- Q Problem for submission: For which positive integers k can asimple graph G = (V, E) be constructed such that: G has k vertexes,that is, |V | = k, G is...
- Q The integers satisfy a property known as mathematical induction.This is a familiar topic in high school textbooks.(a) The First Principle of Mathematical Induction is stated asfollows. Suppose S is a...
- Q Let G be an abelian group and n a fixed positive integer. Provethat the following sets are subgroups of G.(a) P(G, n) = {gn | g ? G}.(b) T(G, n)...
- Q Find the maximum off(?1,?2)=4x1+ 2?2 +?12 ? 2?14 +2?1?2 ? 3?22 using thesteepest ascent method with initial guess ?1=0 and?2=0.(a) Find the gradient vector and Hessian matrix for the functionf(?1,?2).(b)...
- 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 A company manufactures Products A, B, andC. Each product is processed in three departments: I, II,and III. The total available labor-hours per week for DepartmentsI, II, and III are 900,...
- Q (a) Let n = 2k be an even integer. Show that x = rkis an element of order 2 which commutes with every element ofDn.(b) Let n = 2k be...
- Q Show that, given any 3 integers, at least 2 of them must havethe property that their difference is even.
- Q 1) find the solution t the non-homogenous DEy''-16y=3e5x , y(0)=1 , y'(0)=22)find the solution to the DE using cauchy-euler methodx2y''+7xy'+9y=0 , y(1)=2 , y'(1)=33)find the solution to the DE using...
- Q Suppose y1 = -6e3t - 6t2 andy2 = 4e-2t - 6t2 are bothsolutions of a certain nonhomogeneous equation: y'' + by' + cy =g(t).a. Is y = 12e3t - 4e-2t...
- Q x*y' '+y'-x*y=01> use Frobenious series solution to solve the ODE.
- Q Find the eigenvalues ?n and eigenfunctionsyn(x) for the given boundary-value problem. (Give youranswers in terms of k, making sure that each value ofk corresponds to two unique eigenvalues.)y'' + ?y...
- Q (a) Can the sum of 12345 odd pos-itive integers be 12345678 ? Prove or disprove.(b) Prove that for every possible re-arrangement (b1, b2, . . . ,b999) of thenumbers (1,...
- Q A two-lane tunnel opening in the shape of a semi-ellipsehas a height of 16 feet and a width of 32 feet.a) Determine an equation that represents the tunnelopening.b) Explain with...
- Q (a) a sequence {an} that is not monotone (noreventually monotone) but diverges to ?(b) a divergent sequence {an} such that{an/33} converges(c) two divergent sequences {an} and {bn}such that {an +...
- Q Let H = {A?GL(2,R)|(detA)2= 1}. Prove that H / GL(2,R).
- Q Question 10: (1 point)We want to solve the differential equationdy/dx=[x(e^(7x+y^5)]/y4a) This differential equation is separable andcan be writen.?N(y)dy=?M(x)dx ,whereM(x)= __________andN(y)= __________b) To compute the integral ?N(y)dy, you need touse the...
- Q Write the multiplication table for D8. Find the order of eachelement D8.
- Q Let G be a bipartite graph with 107 left vertices and 20 rightvertices. Two vertices u, v are called twins if the set ofneighbors of u equals the set of...
- Q Billy Bob is the sole proprietor of Billy Bob's Smokers and is afabricator of competition-level, wood-fired smokers. Billy Bob isintroducing a home-grade version of his smoker and has a contractwith...
- Q . Let ? : R ? S be a ring homomorphism of R onto S.Prove the following:J ? S is an ideal of S if and only if ? ^?1...
- Q What is the main difference between Deterministic Models andStochastic Models? Provide two examples for each type ofmodels.
- Q For f: N x N -> N defined by f(m,n) =2m-1(2n-1)a) Prove: f is 1-to-1b) Prove: f is ontoc) Prove {1, 2} x N is countable
- Q Due October 25. Let R denote the set of complex numbers of theform a + b ? 3i, with a, b ? Z. Define N : R ? Z?0, by...
- Q 2. Consider functions f : {1, 2, 3, 4, 5, 6} ? {1, 2, 3, 4, 5,6, 7, 8, 9, 10}.(a) How many of these functions are strictly increasing (i.e.f(1)...
- Q Convert the complex number to polar form rcis?.(a) For z=?1+ithe modulus of zis r=, and the principal argument is ? =.(b) For z=?33???3ithe modulus of zis r=, and the principal...
- Q For each part below, find a binary relation on the set S ={1,2,3,4} that satisfies the given combination of propertiesa) reflexive, symmetric, and transitiveb) not reflexive, but symmetric and transitivec)...
- Q Explain if the set below is a vector space given standardoperations.The set of all even functions defined on R with addition and scalarmultiplication defined as follows:1.) (f+g)(x) = f(x) +...
- Q There are n types of coupons. We collect coupons one-by-one.Each coupon collected is of type i with probability pi P , andindependent of other coupons. Assume that n i=1 pi...
- Q 1) Solve each of the following differential equations.a)16y"-8y'+y=0b) (d^4y)/(dx^4)-13((d^2y)/(dx^2))+36y=02) use Variation of Parameters to solve y"+16y=(1/3)csc4t3) use undetermined coefficients to solvey"-5y'+4y=3e^(3t)-5e^(2t) with y'(0)=-1 and y(0)=14) Explain why the product (A+B)(A-B)...
- Q f(x) = ((x ? 1)^2) e^xHow easy would it be to apply the Bisection Method compared toNewton's method and modified Newton's method to the function f(x)?Explain.
- Q Consider a tank containing at time t = 0, 100 gallonsof brine. Assume that water containing 1/4 lb of salt per gallon isentering the tank at a rate of 3...
- Q Suppose U is a subspace of a finite dimensional vector space V.Prove there exists an operator T on V such that the null space of Tis U.
- Q Problem 17.5. Consider the function ?(0,1) : R ? R (this is thecharacteristic of Definition 14.4). Find: (a) ?(0,1)((0,1)); (b)?(0,1)((?1,3)); (c) and (in general) ?(0,1)((a,b)), where a,b ? Rand a...
- Q G is solvable if and only if G/Z(G) is solvable
- Q 5. Of the 9-letter passwords formed by rearranging the lettersAAAABBCCC (4 A’s, 2 B’s, and 3 C’s), I select one at random.Determine the following probabilities.(a) Prob (my word is a...
- Q Parametrize the osculating circle to the parabola y =x2 at x = -1
- Q What is a feasible solution of an LP? how can wedefine it in terms of Mathematical proof.
- Q Please describe how you have prepared for your intended major,including your readiness to succeed in your upper-division coursesonce you enroll at the university.I'm major at Math
- Q Investigate the following theorems(h) For sets A, B and C we havei. A(B ? C) = (AB) ? (AC),ii. A(B ? C) = (AB) ? (AC),iii. A ?= B if...
- Q Let A be an infinite set and let B ? A be a subset. Prove:(a) Assume A has a denumerable subset, show that A is equivalentto a proper subset of...
- Q 1. A company that makes cell phones has the following coststructure. The have fixed costs of $145 000 per period andmanufacturing costs of $15.16 per cell phone. Advertising isexpected to...
- Q 1. Explain how to convert positive integers from base 3 to base10 and vice versa. Include examples.2. Explain how to convert fractions from base 3 to base 10 andvice versa....
- Q Below is a proof of Theorem 4.1.1 (b): For the zero vector ?0 inany vector space V and k ? R, k?0 = ?0.Justify for each of the eight steps...
- Q In questions below determine whether each of the following setsis countable or uncountable.For those that are countably infinite exhibit a one-to-onecorrespondence between the set of positive integers andthat set.1) The...
- Q A polynomial in Z[x] is said to be primitive if the greatestcommon divisor of its coefficients is 1. Prove the product of twoprimitive polynomials is primitive. [Hint: Use proof bycontradiction.]
- Q A company operates a solar installation in the desert in WesternAustralia. It is reviewing its operating practices with a view tomaking them more efficient. a) The solar installation generates electric...
- Q Prove that Z/nZ is a group under the binary operator "+" forevery n in positive Z, where Z is the set of integers.
- 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 that every product of three glide reflection isa reflection or a glide reflection.
- Q Determine if the following statements are true or false:1. There is exactly one two-digit number (in the range from 10through 99} that is congruent to 1 modulo 3, to 3...
- Q a. 1 1 cos(x)cos(y) = -cos(x-y) + -cos(x + y) 1 lsin(x)sin(y) = -cos(x-y)--cos(x+ y) 1 l sin(x)cos(y) =—sin(x-y)+-sin(x + y) A DSB-FC (double sideband-full carrier) signal s(t) isgiven by,...
- Q PROOF; COMPLEX ANALYSISShow that the sequence {z_n} = {z_1, z_2, ...} is said to convergeto the complex number w if and only if the sequence of realand imaginary parts of...
- Q Please show all steps!!!!1. Let Q1=y(1.1),Q2=y(1.2),Q3=y(1.3), where y=y(x) solves y??+(?3.75)y?+(3.125)y= 0, y(0) = 1.5, y?(0) =?0.6252. Let Q1=y(1.1),Q2=y(1.2),Q3=y(1.3), where y=y(x) solves y??+(?3.75)y?+(3.125)y= 114e?3.5x, y(0) = 5.5, y?(0) =?14.625.3. Let Q1=y(1.1),Q2=y(1.2),Q3=y(1.3),...
- Q step by step solution, pleaseIf -13 < a < -2 and 1 < b < 9. Which of thefollowing could be equal to the product of ‘a’ and ‘b’. Indicateall...
- Q x2uxx --2xyuxy -- 3y2uyy = 0 u(x,1) = x, uy(x,1) = 1
- Q 1. Simplify each of the following sets as much as possible.a) ((? ? ??)? ? (? ???))?b) (? ? ?+)? ? ??2. Determine the cardinality of eachset:a) ((? ? ?) ?...
- Q Explain how the rank of a matrix and existence and uniqueness ofsolutions of “Systems of Linear Equations” are related.Explain how Eigenfunctions”, “Eigenvalues” and “Orthogonality”terms and concepts are defined in Matrix...
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