Advance Math question and answers for July 23, 2023
- Q a) Your initial belief about stock A is that its future pricecannot be predicted on the basis of existing public information. Aninsider comes forward claiming that the price will fall....
- Q (9) (a) If f(t) = x1e −kt cos(ωt) +x2e −kt sin(ωt), then f'(t) has the same formwith coefficients y1, y2.(i) Find the matrix A such that y = Ax.(ii) Find...
- Q a) Verify that the indicial equation of Bessel's equation oforder p is (r-p)(r+p)=0b) Suppose that p is not an integer. Carry out the computationto obtain the solutions y1 and y2...
- Q On the island of Knights and Knaves we have three people A, Band C. (The island must be known for its inhabitants’ very shortnames.) A says: We are all knaves....
- Q y\"+y=cos(9t/10)1. general solution of corresponding homongenous equation2. particular solution3.solution of initial value problem with initial conditionsy(0)=y'(0)=04. sketch solution in part 3
- Q Question 1. The math department needs a printer in the computerroom of the second floor of MSB, and the department is planning thepurchase and maintenance schedule of the printer for...
- Q 4. Suppose that the price per unit of input K is 1 euro, theprice per unit of input C is 12 euros and the price per unit ofinput L is...
- Q Carlos takes a glass of cold water from the refrigerator and puts it on a table. The day is sunnyand the temperature is 30 °C. Once outside the refrigerator, the...
- Q 1. (15pts)A standard 52-card deck consists of 13 cards from each of 4 suits(spades, hearts, diamonds, clubs). What is the probability that a5-card poker hand drawn from a standard 52-card...
- Q Type a proposition involving p, q, r and s that is true justwhen at least two of the propositional variables are true. Forexample, your proposition would be true in any...
- Q 2. In the proof of Gauss’ Lemma, I stated that each of the terms|a|, |2a|, …, |(p-1)a/2| are distinct modulo p. Prove this bycontradiction. [Hint: As in college algebra, there...
- Q Advanced Calculus 1Problem 1 If the function f : D → R is uniformly continuous andα is any number, show that the function αf : D → R also isuniformly...
- Q Show that two m×n matrices are equivalent if and only if theyhave the same invariant factors, i.e. (by Problem 4), if and onlyif they have the same Smith normal form.
- Q Consider the second-order boundary value problemy′′ +(2x^2 +3)y′ −y =6x, 0≤x ≤1, (4)y(0) = 1, y(1) = 0.(a) Rewrite the second-order equation (4) as a system of twofirst-order equationsinvolving variables...
- Q Boris and Natasha agree to play thefollowing game. They will flip a (fair) coin 5 times in a row. Theywill compute S = (number of heads H – number of...
- Q 3. For the inhomogeneous differential equation x ′′ + 2x ′ + 10x= 100 cos(4t),(a) Describe a system for which this differential equation wouldbe an appropriate model.(b) Find the general...
- Q Find Laplace transform of50x''+ 100x' + 60x = 0, x'(0)=0, x(0)=0
- Q Part I On a certain university campus there isan infestation of Norway rats. It is estimated that the number ofrats on campus will follow a logistic model of the formP(t)=50001+Be−ktP(t)=50001+Be−kt.A)...
- Q Assume that the matrix A is row equivalent to B. Without​calculations, list rank A and dim Nul Upper A. Then find bases forCol​ A, Row​ A, and Nul A.A=[1,1,-2,0,1,-3;1,2,-3,0,0,-6;1,-1,0,0,1,7;1,4,-4,1,13,-11;1,4,-5,0,3,-32]B=[1,1,-2,0,1,-3;0,1,-1,0,-1,-3;0,0,1,1,15,1;0,0,0,0,1,-2;0,0,0,0,0,1]
- Q A screening test is applied to a population of 1,000 in whichthe prevalence of the disease in question is 10%. The sensitivityof this test is 96% and the specificity is...
- Q Let gcd(a, p) = 1 with p a prime. Show that if a has at leastone square root, then a has exactly 2 roots. [hint: look atgenerators or use x^2...
- Q Consider the group G = {1, −1, i, −i, j, −j, k, −k} undermultiplication. Herei2= j2= k2= ijk = −1. determine which of the following sets is asubgroupof G. If...
- Q (Lot sizing) The demand for a product is known to be dt units inperiods t = 1,...,n. If we produce the product in period t, weincur a machine setup cost...
- Q A circus clown is to be fired from a cannon at an angle of 60degress to the horizontalwith an initial        speed of 60 ft/sec. The clown issupposed to hit...
- Q Think of a scenario where you'd want to know if the graph thatrepresents that scenario has an Euler Path, Euler Circuit orneither?
- Q How many ±1-sequences of length n are there?For example, (1, −1,−1, 1) is not a happy sequence, because although 1 ≥ 0 and 1 − 1 ≥0,the sum 1−1−1 is...
- Q Problem 2.55. Consider the dihedral group D3 introduced inProblem 2.21. To give us a common starting point, let’s assume thetriangle and hole are positioned so that one of the tips...
- Q a) Suppose that A = AT can be row reduced without rowswaps. If E is an elementary matrix such that EA has zero as asecond entry in the first column,...
- Q Explain why an FMEA online excel template is much easier to findthan a Tolerance analysis (TA) online excel template?
- Q How to proof that the 2-partition problem can be transformed to3-partition problem and the time complexity of thetransformation(i.e. the 2-partition problem can be solved by using analgorithm that solves the...
- Q Use systematic elimination to solve the system??/?? + ??/?? = −? + ? + 3??/?? = −4? − 3? − 1
- Q Specify part U (x, y) and VA. Write the function f (z) = ? ^ ? in its real and imaginarypart. And write the function q (z) = ln? in...
- Q 1) Use the simplex method to solve the linear programmingproblem. Maximize P = 6x + 5y subject to 3x + 4y ≤ 34 x + y ≤ 10 3x+ y...
- Q Which of the following vectors does not belong to span{ (2,0,3),(3,0,2) } ?a) (5,0,5)b) (1,0,-1)c) (3,2,0)d) (0,0,5)
- Q Let G be a finite group and p be a prime number.Suppose that prdivides the order of G. Show that G has a proper subgroup of orderpr.
- Q Prove the following more general version of the ChineseRemainder Theorem: Theorem. Let m1, . . . , mN ∈ N, and let M =lcm(m1, . . . , mN )...
- Q . Let U be a non-empty set. For A and B subsets of U, define therelation A R B if an only if A is a proper subest of B....
- Q Solve these first-order Differential Equations using anintegrating factor.1. dy/dx+2xy=02. dy/dx-y=53. dy/dx+y=x4. (x)dy/dx+(x+1)y=3/x5. (x^2)dy/dx=e^x-2xy
- Q A new type of fueling truck is under consideration for anairport on a resort island. The company has been testing onealternative and feel it has the potential to significantly reducefueling...
- Q solve the initial values:if Y(3)-4Y\"+20Y'=51e^3xY\"(0)=41, Y'(0)= 11. Y(0)= 7 > solution is Y(x)= e^3x+2 e^2xsin(4x)+6so, what is the solution for:Y(3)-8Y\"+17Y'=12e^3xY\"(0)=26, Y'(0)= 7. Y(0)= 6Y(x)=???
- Q Consider the initial-value problem y' = 2x − 3y + 1, y(1) = 7.The analytic solution is y(x) = 1/9 + 2/3 x + (56/9) e^(−3(x −1)).(a) Find a formula...
- Q Given the following numbers: (i) 123456; (ii) 546777; (iii)456734561883. Solve the following questions for each of thenumbers.(a) Identify the check digit.(b) Does the number satisfy the checksum?(c) For the numbers...
- Q Find the first four terms in eachportion of the series solution around x0 =0 for the following differentialequation. x2 y//- 5x y/ + 6y = 0
- Q (1) Show that the set { 1 m + 1 n : m, n ∈ N} is countable.(2) Show that the set {a + b √ 2 : a, b...
- Q Partial Differential Equations(a) Find the general solution to the given partial differentialequation and (b) use it to find the solution satisfying the giveninitial data.Exercise 1. 2∂u ∂x − ∂u ∂y...
- Q a) If you add the terms ax^2+bxy+cy^2 to the function L(x,y) = 1- 0.5y, how would this affect the derivatives of L(x,y) at(0,0)?b) What a, b and c you would...
- Q For this activity, select a recurring quantity from your OWNlife for which you have monthly records at least 2 years (including24 observation in dataset at least). This might be the...
- Q Find the best weights (w0...w4) of the highest possible orderfinite difference formula of the form f'(x) ~ w0*f(x) + w1*f(x+h) +w2*f(x+2h) + w3*f(x+3h) + w4*f(x+4h) and use Taylor series topredict...
- Q 7. Let m be a fixed positive integer.(a) Prove that no two among the integers 0, 1, 2, . . . , m − 1are congruent to each other modulo...
- Q Let Σ ⊆ P rop(A). Show thatΣ|− p iff Σ ∪ {¬p} isunsatisfifiable.
- Q The following is a payoff table giving costs for varioussituations. What decision would an optimist make?State 1State 2State 3Alternative 1453783Alternative 2165972Alternative 3236591Alternative 4443355
- Q Using concepts from funding models, how can they refocus itsactivities to generate funds to continue the work of theorganization?
- Q Find the Fourier coefficients of the following signal.x(t) = 5 + 2sin(w0.t) + cos(2.w0.t) - 3sin(2.w0.t)
- Q (1 point)Suppose thatR1={(2,2), (2,3), (2,4), (3,2), (3,3), (3,4)},R1={(2,2), (2,3),(2,4), (3,2), (3,3), (3,4)},R2={(1,1), (1,2), (2,1), (2,2), (3,3), (4,4)},R2={(1,1), (1,2),(2,1), (2,2), (3,3), (4,4)},R3={(2,4), (4,2)}R3={(2,4), (4,2)} ,R4={(1,2), (2,3), (3,4)}R4={(1,2), (2,3), (3,4)},R5={(1,1), (2,2), (3,3),...
- Q Decide, with justification, if the following set properties aretrue for any sets A, B, and C.1. A∪(B∩C)⊆A.2. A∪(B∩C)⊆B.3. A ∩ B ⊆ A4. B ⊆ A ∪ B5. A ⊆...
- Q How do we construct the Ito's Integral(also called thestochastic integral), and what are the properties of theintegral?
- Q Consider the permutation Ï = (1, 2, 6)(3, 4, 5) in S10. How manyconjugates does Ï has in S10? Hence determine the order of CÏ(S10),the centralizer of Ï in S10....
- Q find the particular solution for:y'' - 4y' - 12y = e2x(-3x2 + 4x + 5)(hint: try y= ue2x then use: u= Ax2 + Bx + C)
- Q Since {1, 2, . . . , 6} is the set of all possible outcomes of athrow with a regular die, the set of all possible outcomes of athrow with...
- Q Now assume that the harvesting is not done at a constant rate,but rather at rates that vary at different times of the year. Thiscan be modeled by ??/?? = .25?...
- Q Is the given set of vectors a vector subspace (Give reasons)? Ifyour answer is yes, determine the dimension and find a basis. Allvectors in R5 with v1 + 3v2 -...
- Q Let Xn be the Markov chain with states S = {1, 2, 3, 4} andtransition matrix.1/32/3002/301/301/31/301/301/32/30a.) Let X0 = 3 and let T3 be the first time that the Markovchain...
- Q for the system equation of x' = Ax  if CoefficientsMatrix A be ? = [ 5 −5 −5 −1 4 2 3 −5 −3 ] , find the basicmatrix
- Q Consider the vector functions ?(?) and ?(?), where ?(?) = 〈? sin ?, ? cos ? , ?^2〉, ?(?) = 〈1, −1, 1〉, and ?′(?) = 〈1, 0, −1〉.Define ?(?)...
- Q Gaus-Jordan Elimination:A glass of skim milk supplies 0.1 mg of iron, 8.5 g of protein,and 1 g of carbohydrates. A quarter pound of lean red meat provides3.4 mg of iron,...
- Q Consider the following real 3rd order polynomialf (x)= x^3− 5.5 x^2− 5x+ 37.5A) Use the bisection method to determine one of the roots,employing initial guesses of xl = - 10,...
- Q Find the 0-divisors of the following rings. (a) Z2 × Z4(b) Z91(c) Z167
- Q Solve the linear programming problem by the method ofcorners.Find the minimum and maximum of P = 4x +2y subject to3x+5y≥203x+y≤16−2x+y≤1x ≥ 0, y ≥ 0.The minimum is P =  at (x,...
- Q Lay out the design for two between-subjects experiments: a) anexperiment involving an experimental group and a control group, andb) a factorial design with three independent variables that havethree, and two...
- Q Consider the relation R defined on the set Z as follows: ∀m, n ∈Z, (m, n) ∈ R if and only if m + n = 2k for some integer...
- Q 5. Suppose we are given both an undirected graph G with weightededges anda minimum spanning tree T of G .(a) Describe an algorithm to update the minimum spanning tree whentheweight...
- Q Let f : R → S and g : S → T be ring homomorphisms.(a) Prove that g ◦ f : R → T is also a ring homomorphism.(b) If...
- Q Problem 10.a. Construct of partition of N with exactly 4 elements anddescribe the equivalence relation defined by your partition.Remember the elements of a partition are sets.b. Construct of partition of...
- Q a) ln(x2 + y2)calculate the Laplacian ∇2 of the scalar field usingboth cartesian and cylindrical coordinatesystemsb) (x2 + y2 +z2)-1/2calculate the Laplacian ∇2 of the scalar field usingboth cartesian and...
- Q PROVE THAT COS Z,SIN Z,cosh Z and sinh z are entirefunction
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