Advance Math question and answers for August 21, 2023
- Q How to determine all the basic solutions of an optimizationproblem, and classify them as feasible or infeasible?As an example,Maximize z= 2x1 + 3x2Subject to:x1 + 3x2 <= 63x1 + 2x2...
- Q Let R be the relation on Q defined by a/b R c/d iff ad=bc. Showthat R is an equivalence relation. Describe the elements of theequivalence class of 2/3.
- Q Solve the given initial-value problem. y''' ? 2y'' + y' = 2 ?24ex + 40e5x, y(0) = 1 2 , y'(0) = 5 2 , y''(0) = ? 5 2
- Q Draw a graph having the given properties stated below, orexplain why no such graph exists: In each case assume simple graphs(no self loops and no parallel edges) a. Six vertices...
- Q Which study design is best to minimize confounders--cohort orcase-control?
- Q Is rational number divided by an irrational number equal toirrational number or rational number? for example such as ( 5 /2pi )
- Q s QUESTION 10 Car payments are determined using simple interest.If you don’t remember this formula, go back and look it up! Tofinance your vehicle purchase you have two choices. Write...
- Q Using the constructive proof of the Chinese Remainder Theorem,find the unique x(mod 100) satisfying the congruencesx ? 1(mod 25),x ? 0(mod 4).
- Q . For this problem, you may find Proposition 3.1.5 useful whichin turn implies that tan x is continuous whenever x is not an oddmultiple of ? 2 . Moreover, you...
- Q 9. Let f be continuous on [a, b]. Prove that F(x) := sup f([x,b]) is continuous on [a, b]
- Q (62). (Transient Behavior of a Mixing tank): A tank initiallyholds 80 gal of a brine solution containing 0.125 lb of salt pergallon. At t=0, another brine solution containing 1 lb...
- Q Solve by solving the dual problem.Minimizez = 30x1 +15x2 +28x3,subject to5x1+3x2+4x3?455x1+6x2+8x3?12020x1+6x2+14x3?300x1?0,x2?0,x3?0.
- Q A mass weighing 8 lb is attached to a springhanging from the ceiling, and comes to rest at its equilibriumposition. The spring constant is 4 lb/ft and thereis no damping.A....
- Q CSM Machine Shop is considering a four-year project to improveits production efficiency. Buying a new machine press for $415,000is estimated to result in $154,000 in annual pretax cost savings.The press...
- Q proof Sin(A)-Sin(B), cos(A)+cos(B) Geometrically, A and B are acuteangles
- Q Let (X,dX),(Y,dY ) be metric spaces and f: X ? Y be a continuousbijection. Prove that if (X, dX ) is compact, then f is ahomeomorphism. (Hint: it might be...
- Q I would like to know how to plot two graphs in matlab and findwhere they intercept.
- Q an investment of $54000 was made by a business club. Theinvestment was split into three parts and lasted for one year. thefirst part of the investment earned 8% interest, the...
- Q A linear transformation from R3-R4 with the V set of vectors x,where T(x)=0, is V a subspace of R3?
- Q Abstract AlgebraFor the group S4, let H be the subset of all permutations that fixthe element 4.a) show this is a subgroupb) describe an isomorphism from S3 to H
- Q Find the modulus of:(a) (3 – j4) (-5 + j12)(b) (2+?)/(4?+(1+?)^2)Express (6 – ?8)^?3 in the standard form ? + ??. Find itsconjugate.If ? + ?? = (?+?)/ (???) ,where...
- Q The legislature in a state has 59 seats. Apportion these seatsto the five counties below using Jefferson's method. CountyPopulation Seats receivedAdams 131,000Grant 350,000Colton 300,000Davis 347,000Hayes 236,000
- Q Present two cases of the Cardano’s formula
- Q Let R be a commutative ring with identity with the property thatevery ideal in R is principal. Prove that every homomorphic imageof R has the same property.
- Q An unknown radioactive element decays into non-radioactivesubstances. In 340 days the radioactivity of a sample decreases by37 percent. (a) What is the half-life of the element? (b) How longwill it...
- Q Newton's law of cooling states that the temperature of an objectchanges at a rate proportional to the difference between itstemperature and that of its surroundings. Suppose that thetemperature of a...
- Q 5. For each piecewise linear function, graph the function andfind: ? ? ? ? ? 2 lim x f x ? ? ? ? ? 2 lim x f x...
- Q Problem 1 [20 pts]: An experiment consists of tossing acoin 6 times. Let X be the random variable that is the number ofheads in the outcome. Find the mean and...
- Q Let A =0110(a) Calculate the matrix exponential e^(At). (Hint: It mighthelp to write down the power series expansions for the hyperbolicfunctionscosh(t) =(e^t + e^(?t))/2and sinh(t) =(e^t ?e^(?t))/2and then try to...
- Q Let set E be defined as E={???? +? | [?]?R2}, where ?? is thenatural exponential?function, please show E is a vector space by checking all the 10axioms. (Notice: you may...
- Q Bonus Problem:Find the number of spanning trees in Km,n.Note: I need how to get the right formula-not just oh this isthe formula you need.
- Q Cucina Corp. signed a new installment note on January 1, 2018,and deposited the proceeds of $51,000 in its bank account. The notehas a 3-year term, compounds 6 percent interest annually,...
- Q Forthe differential equation (2 -x^4)y" + (2*x -4)y' + (2*x^2)y=0.Compute the recursion formula for the coefficients of the powerseries solution centered at x(0)=0 and use it to compute the firstthree...
- Q write a procedure that implements the Pollard rho factorizationmethod in Mathematica.
- Q (1) In each part, decide whether or not the described relationis an equivalence relation.Explain your answers.(a)Ais the set of all residents of the United States. Therelation?onAgiven by:x?yifx, yare in the...
- Q May I know the how to solve this question?Consider the two functions f(x) = ?|x| ? 1 and g(x) = 1/(x2 ? 1)defined on the maximal set of real numbers...
- Q show thar up to isomorphism there are two abelian groups of order200that have exactly 7 subgroups of order 2
- Q 2.) Use the method of Lagrange multipliers to find themaximum and minimum values of the function ?(?, ?) = ??^2 ? 2??^2given the constraint ?^2 + ?^2 = 2 along...
- Q Question 1. Go to random.org. This website is a random numbergenerator. Use it to generate three numbers a, b, c between -10 and10. Now let your a, b and c...
- Q Problem 13.6. (a) How many different relations are on X = {1, 2,3}.(b) How many different equivalence relations are on this set?
- Q Find the smallest n ? N such that 2(n + 5)^2 < n^3 and callit n^0?Show that 2(n + 5)^2 < n^3 for all n ? n^0.
- Q True or False and support your decision1.) if Ax=0 has only one trivial solution, then Ax=0 has a uniquesolution.2.)The linear system given by Ax=0 consisting of 3equations and 4 unknowns...
- Q Find at least the first four nonzero terms in a powerseriesexpansion about x = 0 for a general solution to thegivendifferential equation: Include a general formula for thecoefficients (recurrence formula)....
- Q Q1:What is the Big M method, and when do we use it?Q2: What is the simplex method and when do we use itQ3: What is the shortest path tree, and...
- Q Check that the following differential equation is not exact.Find an integrating factor that makes it exact and solve it.ydx + (3 + 3x-y) dy = 0__Solve the initial value problem:(cos...
- Q Let ? (n) denote the number of positive divisors of n and ?(n)denote the sum of the positive divisors of n (as in the notes).(a) Evaluate ? (1500) and ?(8!).(b)...
- Q Show that x^8 ? 2 ( mod 13) has no solutions.
- Q Consider the initial value problemmx??+cx?+kx=F(t), x(0)=0, x?(0)=0modeling the motion of a spring-mass-dashpot system initially atrest and subjected to an applied force F(t), where the unit offorce is the Newton (N). Assume that...
- Q Write a formal proof to prove the following conjecture to betrue or false.If the statement is true, write a formal proof of it. If thestatement is false, provide a counterexample...
- Q Solve the initial value problem below using the method ofLaplace transforms.y'' - 4y' + 8y = 5e^ty(0) = 1y'(0) = 3
- Q Formulate the definitions of linear dependence and independenceof a set of k vector functions f1(x),... , fk(x) continuous on an intervalI.
- Q Write a poem related to Calculus 2 content that students coverin that class!
- Q Find the solution to the heat equation in 3 dimensions on thehalf space z>0, with homogeneous Neumann boundary conditions atz=0.
- Q Assuming we have a case of influenza. Suppose the total cost ofproviding viraflu is $100 and the total cost of providingsupportive care is $10. Suppose further that viraflu will result...
- Q Recall the following definition: For X a topological space, andfor A ? X, we define the closure of A as cl(A) = ?{B ? X : B isclosed in X...
- Q . A routing transit number (RTN) is a bank code that appears inthe bottom of checks. The most common form of an RTN has ninedigits, where the last digit is...
- Q Using the method of recursion, compute y[n] for n = 0 to 20,when x[n]=u[n] and y[-1]=2:?[? + 1] ? 0.8?[?] = ?[?]Find a closed-form expression for your result.
- Q Use strong induction to show that everypositive integer, n, can be written as a sum of powers of two:20, 21, 22, 23,.....
- Q What are elliptic and hyperbolic geometries? Why were theydeveloped? Provide references
- Q 6.14 Let f = {(x, y) ?R2 : y = x5 + 4x3 + x +1}.Prove that (a) f is onto. (b) f is 1-1.Prove that g = {(x, y)...
- Q given the initial simplex tableau (Matrix):x y s1 s2 p6 9 1 0 0 3005 4 0 1 0 180-3 -4 0 0 1 0Show the matrices produced by each pivot
- Q We say that an infinite sequence a0,a1,a2,a3,… of realnumbers has the limit L if for every strictly positive number ?,there is a natural number n such that all the elementsan,an+1,an+2,…...
- Q Consider the root of function f(x) = x 3 ? 2x ? 5.The function can be rearranged in the form x = g(x) in thefollowing three ways: (a) x =...
- Q Use Newton's method to find all solutions of the equationcorrect to eight decimal places. Start by drawing a graph to findinitial approximations. (Enter your answers as a comma-separatedlist.)?2x7 ? 4x4...
- Q Recall that a?Z/nZ is called a primitive root modulon, if theorder of a in Z/nZ is equal to ?(n). We have seen in class that, ifp is a prime, then...
- Q 1. For 25 randomly selected students, (a) how many ways do all the 25 students have differentbirthday?b) find the probability that at least two students have the samebirthday.c) find the...
- Q Structural Induction on WFF For a formula ? ? WFF we let `(?)denote the number of symbols in ? that are left brackets ‘(’, letv(?) the number of variable symbols,...
- Q show that lR is not compact!
- Q Find the eigenvalues?nand eigenfunctionsyn(x)for the given boundary-value problem. (Give your answers interms of n, making sure that each value of ncorresponds to a unique eigenvalue.)x2y'' +xy' + ?y =0, y(1) =0, y'(e)...
- Q Write a program that asks the user for a file name.The file contains a series of scores(integers), each written ona separateline.The program should read the contents of the file into...
- Q diff eqWhat, if anything, do the theorems of this chapter allow you toconclude about the existence and uniqueness of solutions to thefollowing initial value problems.y??+ty??t^2y=0; y(0)=0,y?(0)=0
- Q Using definitions of dot product and cross product, show thatdot product and cross product are distributive (a) If the threevectors are coplanar. (b) in general.also,Is the cross product of two...
- Q How doesthe linear factorization of f(x), thatis,f(x)=an(x?c1)(x?c2)?(x?cn),show that apolynomial equation of degree n hasnroots?Why must everypolynomial equation with real coefficients of degree 3 have atleast one real root?If you aregiven...
- Q Exercise 4.8. For each of the following, state whether it istrue or false. Iftrue, prove. If false, provide a counterexample.(i) LetX beasetfromRn. ThesetX isclosedifandonlyifX isconvex.(ii) Let X and Y be...
- Q Suppose the joint probability distribution of X and Y is givenby the following table.Y=>3 6 9 X1 0.2 0.2 02 0.2 0 0.23 0 0.1 0.1The table entries represent the...
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