Advance Math question and answers for August 13, 2023
- Q Give a counterexample:a) Xn + Yn converges if and only if both Xn and Yn converge.b) Xn Yn converges if and only if both Xn and Yn converge.
- Q Find a particular solution to the following non homogenousequations1) y''' + y = t^3 + sin (t) + 11e^t2) y'' + y = 2tsin(t)3) y''''' - 4 y''' = e^2t...
- Q (abstract algebra)(a) Find d = (26460, 12600) and find integers m and n so that dis expressed in the form m26460 + n12600.(b) Find d = (12091, 8439) and find...
- Q Give your own example of a plane figure and itsquadrature.How does the quadrature of the triangle depend on thequadrature of the rectangle?Draw a lune like Hippocrates.’ What is the relationship...
- Q Sketch the region of continuity for f (x; y) on a set of axesand sketch the region ofcontinuity for df/dy (x. y) on a separate set of axes. ApplyPicard’s Theorem...
- Q 1.let {v=(1,2,3,5,9),v2=(3,1,2,8,9),v3=(2,-5,5,9,4)} and{u1=(0,1,1,1,2),u2=(0,2,-2,-2,0)} be basis of subspaces V and U ofR5 respectively.find a basis and the dimension of V+U and Vintersection U.2.does a matrix have a right inverse ?if so...
- Q Find the adjoint of matrix A, the determinant of matrix A, andthe determinant of the adjoint A.A= 1 1 0 22 1 1 00 2 1 11 0 2 1
- Q National governments issue debt securities known as sovereignbonds, which can be denominated in either local currency or globalreserve currencies, like the U.S. dollar or euro. First define whatthese bonds are....
- Q Consider the initial value problem given below.y'=x+4cos(xy), Y(0)=0Use the improved? Euler's method subroutine with step size h=0.3to approximate the solution to the initial value problem at pointsx= 0.0,0.3,0.6.....3.0
- Q Q- A manufacturer of outdoor clothing makes waxjackets and trousers. Each jacket requires 1 hour to make, whereaseach pair of trousers takes 40 minutes. The materials for a jacketcost $32...
- Q 2. (Solving linear systems)Consider the linear system Ax = bwith A =[14 9 14 6 -10;-11 -11 5 8 6;15 -2 -14 8 -15;14 13 11 -3-7;0 9 13 5...
- Q I am asked to find the square roots using the bisection methodfor x * x - a = 0.I was wondering how the bisection method is performed.Let's suppose a =...
- Q Solve the initial value problem dy/dx = ?(2x cos(x^2))y +6(x^2)e^(? sin(x^2)) , y(0) = ?5Solve the initial value problem dy/dt = (6t^5/(1 + t^6))y + 7(1+ t^6)^2 , y(1) =...
- Q A 100 gallon tank initially contains 10 gallons of fresh water.At t=0 a brine solution containing 1 pound of salt per gallon ispoured into the tank at the rate of...
- Q The base of a right pyramid is a regular hexagon with sides oflength 10 m. The altitude is 5 m. Find the total surface area ofthe pyramid. The area is...
- Q Boise Lumber has decided to enter the lucrative prefabricatedhousing business. Initially, it plans to offer three models:standard, deluxe, and luxury. Each house is prefabricated andpartially assembled in the factory, and...
- Q Find a subgroup G in symmetric (permutation) group Sn suchthat(1) n = 4 and G is abelian noncyclic group(2) n = 8 and G is dihedral group.
- Q Identify the following groups:(a) ?a, b: a4 = b2 = 1, bab =a3?(b) ?a, b : a3 = b2 = (ab)2 =1?(c) ?a, b, c : abc = bca =...
- Q Starting from mynewton write a function program mysymnewton thattakes as its input a symbolic function f and the ordinary variablesx0 and n. Let the program take the symbolic derivative f...
- Q Scott secured a 5-year car lease at 6.20% compounded annuallythat required him to make payments of $881.83 at the beginning ofeach month. Calculate the cost of the car if he...
- Q Let f be a function with domain the reals and range the reals.Assume that f has a local minimum at each point x in its domain.(This means that, for each...
- Q 1. Must be nicely written up AS A PROOF.a. Show that gcd(m + n, m) = gcd(m, n).b. If n | k(n + 1), show that n | k.c. Show...
- Q Which of the following sets are closed under addition?(i) The set of all vectors in R2 of theform (a,?b) where b = a.(ii) The set of all 3?×?3 matrices that...
- Q Question 1. State the prove The Density Theorem for Rational Numbers.Question 2. Prove that irrational numbers are dense in the set of real numbers.Question 3. Prove that rational numbers are...
- Q Calculate the present value of the annuity. (round your answer tothe nearest cent.)$1800 monthly at 6.1% for 30 years.Determine the payment to amortize the debt. (round your answerto the nearest...
- Q Determine the payment to amortize the debt. (round your answer tothe nearest cent.)Quartey payments on $15,500 at 3.5% for 6 years.Find the unpaid balance on the debt. (Round your answer...
- Q Question 1. State the prove The Density Theorem for Rational Numbers.Question 2. Prove that irrational numbers are dense in the set of real numbers.Question 3. Prove that rational numbers are...
- Q Briefly describe the main similarities and differences betweenthe threshold phenomena for the stochastic general epidemic modeland the deterministic general epidemic model.(Topic: Epidemics)Pls explain in a simple way to understand. Thxs
- Q Write a MATLAB code to obtain the following. Keep yourcode commented whenever required. Copy your source code and commandwidow outcomes and screen shots of any plots in yoursolution.Develop three functions...
- Q Determine whether or not W is a subspace of V. Justify youranswer.W = {p(x) ? P(R)|p(1) = ?p(?1)}, V =P(R)
- Q There are 12 students in a party. Five of them are girls. In howmany ways can these 12 students be arranged in a row if (i) thereare no restrictions? (ii)...
- Q Find the power series solution for the equation y'' + (sinx)y =x; y(0) = 0; y'(0) = 1Provide the recurrence relation for the coefficients and deriveat least 3 non-zero terms...
- Q A mass of 50 g stretches a spring 3.828125 cm. If the mass isset in motion from its equilibrium position with a downwardvelocity of 10 cm/s, and if there is...
- Q Quad Enterprises is considering a new 3-year expansion projectthat requires an initial fixed asset investment of $3.0 million.The fixed asset falls into the 3-year MACRS class (MACRS Table) andwill have...
- Q Notes 2.7 Using CRT notation, show what is going on for all thecombinations you considered in Notes 2.6. Explain why gcd(s + t,35) sometimes gave you a factor, and it...
- Q A person buying a personal computer system is offered a choiceof three models of the basic unit, four models of keyboard, andthree models of printer. How many distinct systems can...
- Q 1. Find the 100th and the nth term for each of the followingsequences.a. 50,90,130,...b. 1,4,16,...c. 7, 74,77,710,...d. 197+7x327, 197+8x327,197+9x327,...2. Find the first five terms in sequences with the following nthterms.a....
- Q Problem 4-23 (Algorithmic)EZ-Windows, Inc., manufactures replacement windows for the homeremodeling business. In January, the company produced 15,000windows and ended the month with 9,500 windows in inventory.EZ-Windows’ management team would like...
- Q Can you explain how kernels related with uniqueness, whileimages related with consistent?
- Q Differential Geometry3. Evaluate the 1-form f = x2 dx - y2 dzon the vector fields V = xU1 + yU2 + zU3, W = xy (U1 - U3) + yz...
- Q Describe a setting where you could use exponential functions tomake investment decisions.What kind of information could exponential functions tell youthat would be valuable?
- Q Use the Newton’s method to find the root for ex+1 = 2+ x, over [?2, 2]. Can you find a way to numerically determinewhether the convergence is roughly quadratic using...
- Q Prove: There are infinitely many primes of the form 6n ? 1 (n isan integer).
- Q Suppose that we have access to an unlimited number of 5 and 11cent stamps. Prove, using simple induction, that we can use thesestamps to make any amount of postage that...
- Q Find a particular solution to y??+4y?+4y=(e^?2x)/x^4 usingvariation of parametersyp= ?
- Q Let a,b be any relatively prime positive numbers. (The case b =1 is allowed). We have the rational number a/b. Without appealingto anything but Euclid’s lemma (no use of ?(p,...
- Q Use laplace Transform in solving the ff.:After cooking for 45 minutes, when a cake is removedfrom an oven its temperature is measured at 300°F. 3 minutes laterits temperature is 200°F....
- Q In this project you are given the task of estimating the number of trees that will maximize the fruit production per acre of a local orchard. By researching other orchards,...
- Q Formulate the situation as a system of linear equations. Be sureto state clearly the meaning of each variable. Solve using theGauss-Jordan method. State your final answer in terms of theoriginal...
- Q Prove that {??+?:?,???} is dense in ? if and onlyif r is an irrational number.
- Q Find the first four nonzero terms in a power series expansionabout x0 for a general solution to the given differential equationwith the given value for x0.(x^2-8x)y''+5y=0, x0=4
- Q 2. (Improved Euler’s Method ) Second, work out the first threesteps by hand. Then approximate y(2) for each of the initial valueproblems using Improved Euler’s method, first with a step...
- Q please give examples of four row equivalent matrices which are allin row echelon forms (not necessarly reduced row echelon)
- Q Using the bisection method: Make a program to use this method using thefollowing three functions and use it to find the root of thisfunction f (x) = x * x...
- Q Statistics Analysis question! BUS310In a one-way ANOVA test, we conclude there are differencesacross population means if thea. between variation is small relative to the withinvariationb. between variation is large relative to...
- Q Amy and Lester are the owners of The Hardware Store on mainstreet in a large town. Without consulting Amy, Lester hires anaccountant to prepare a formal Balance Sheet, Income Statement,...
- Q Given the prime factors p and? q, the encryption exponent? e,and the ciphertext? C, apply the RSA algorithm to find ?(a) thedecryption exponent d and ?(b) the plaintext message M.pqeC1751965I...
- Q Abstract AlgebraLet n ? 2. Show that Sn is generated by each of thefollowing sets.(a) S1 = {(1, 2), (1, 2, 3), (1, 2, 3, 4), ..., (1,2, 3,..., n)}(b)...
- Q Prove Theorem 29.9 (Cantor). There are countably many algebraicnumbers.In this project, you will prove this theorem.
- Q Let W denote the set of English words. For u,v ? W, declare u ? v providedthat u, v have the same length and u,v have the same first letter...
- Q Determine whether the equation is exact. If it is exact, FINDTHE SOLUTION. If not write NOT EXACT.A) (y/x + 12x) + (lnx - 3)y' = 0 x>0Solve the given initial...
- Q A, B and C be sets.(a) Suppose that A ? B and B ? C. Does this mean that A ? C?Prove your answer. Hint: to prove that A ?...
- Q Let a be an element of a finite group G. The order of a is theleast power k such that ak = e.Find the orders of following elements in S5a....
- Q Consider the systems of equations?3x1 +9x2 +4x3 ?5x4 ?4x5 = 5?3x1 +9x2 +3x3 ?6x4 ?3x5 = 3x1 ?3x2 ?x3 +2x4 +x5 = ?1(a) Write this as a matrix equation Ax...
- Q **Using Matlab**Make the program for Jacobi iteration method and compare solutionsobtaned by two algorithms, Jacobi-iteration method and Gaussianelimination.
- Q Let ?1=(1,0,1,0) ?2=(0,?1,1,?1) ?3=(1,1,1,1) be linearlyindependent vectors in ?4.a. Apply the Gram-Schmidt algorithm to orthonormalise the vectors{?1,?2,?3} of vectors {?1,?2,?3}.b. Find a vector ?4 such that {?1,?2,?3,?4} is an orthonormal...
- Q Determine the truth value of the following statements if theuniverse of discourse of each variable is the set of realnumbers. 1. ?x(x2=?1)?x(x2=?1) 2. ?x?y?0(xy=1)?x?y?0(xy=1) 3. ?x?y(x2=y)?x?y(x2=y) 4. ?x?y(x+y?y+x)?x?y(x+y?y+x) 5. ?x?y(xy=0)?x?y(xy=0) 6. ?x?y(x=y2)?x?y(x=y2) 7. ?x?y?z(z=x+y2)?x?y?z(z=x+y2) 8. ?x?0?y(xy=1)?x?0?y(xy=1) 9. ?x(x2=2)?x(x2=2) 10. ?x?y(x+y=1)?x?y(x+y=1) 11.?x?y((x+2y=2)?(2x+4y=5))?x?y((x+2y=2)?(2x+4y=5)) 12....
- Q Find the solution of the initial value problem:y'' + 4y' + 20y = -3sin(2x), y(0) = y'(0) = 0
- Q pts) In a round-robin tennis tournament of players, everyplayer plays against every otherplayer exactly once and there is no draw. We call a player x adominator if for every other...
- Q Question 1A) Show that the functions y1(t) = 1 + t 2 ; y2(t) = 1 ? t 2 arelinearly independent directly from the definition of linearindependence.B)Find three functions y1(t),...
- Q Compute the center Z of SL2(Z/p)
- Q Let A and B be groups, and consider the product group G=A xB.(a) Prove that N={(ea,b) E A x B| b E B} is asubgroup.(b) Prove that N is isomorphic...
- Q Why is Gauss Elimination faster than solving a system of linearequations by using the inverse of a Matrix? (I know it hassomething to do with there being less operation with...
- Q Find a basis and the dimension of W. Show algebraically how youfound your answer.a. W = {(x1, x2, x3, x4) ? R^4 | x2 = x3 and x1 + x4...
- Q Show that the product of two Hausdorff spaces is Hausdorff.
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