Advance Math question and answers for August 15, 2023
- Q On the day of their son’s birth, Mr. and Mrs. Su decided to setaside a sum ofmoney to provide for his college education. They wish to make asingle deposit in...
- Q 1. Let V and W be vector spaces over R.a) Show that if T: V ? W and S : V ? W are both lineartransformations, then the map S...
- Q This is Discrete MathWrite a small paragraph about Russell-Zermelo? (3 to 5)linesWhat is Russell-Zermelo paradox? and what is it usedfor? (least 3 lines)What is the proof of Russell-Zermelo paradox?Give at least...
- Q We define SO(3) to be the group of 3 × 3 orthogonal matriceswhose determinant is 1. This is the group of rotations inthree-space, and you can visualize each element as...
- Q Show that drastic sum and drastic product satisfy the law ofexcluded middle and the law of contradiction. [Hint: substitute thes-norm and t-norm operation for intersection and union in the twolaws,...
- Q ExerciseMinimize Z= X1 - 2X2Subject to X1- 2X2 ? 4 X1 + X2 ? 8 X1, X2 ? 0
- Q R.A.T.-Create Your Own Water Park Apply your knowledge ofpolynomial functions to create a water park, with 6 waterslides -one for under 6 years old (highest point at least 5m above...
- Q ExerciseSolve the following linear programs graphically.Maximize Z= X1 + 2X2Subject to 2X1+ X2 ? 12 X1 + X2 ? 5 -X1 + 3X2 ? 3 6X1 – X2 ? 12 X1, X2 ? 0
- Q 1. prove that if{xn} is decreasing an bounded frombelow, then {xn} is convergent.
- Q In the Dihedral Group D4, determine all left cosets and rightcosets of <pt>(the t is tau and the p is rho)
- Q Suppose that x is real number. Prove that x+1/x =2 if and onlyif x=1.Prove that there does not exist a smallest positive real number.Is the result still true if we...
- Q Prove that ?(n) < 2 n for any positive integer n. This is aquestion in Number theory
- Q Provep ? (q ? r), q ? s, r ? s ? p ? s
- Q y''+5y'+6y=sint–cos2t
- Q Let ? ? Sn be the cycle (1, 2, . . . , k) ?Sn where k ? n.(a) For ? ? Sn, prove that ???-1 = (?(1),?(2), . ....
- Q Exercise 1. Establish the following logical equivalencies wherethe domain of P(x) is non-empty and Adoes not depend upon x:i) ?x(A ? P(x)) ? A ? ?xP(x).ii) ?x(P(x) ? A) ?...
- Q Show linear dependence or independence. Show all stepsalgebraically.a. let v1= < x1, x2, ... , xn > and v2 = < y1, y2, ..., yn > be vectors in R^n...
- Q How many times is line (5) executed in the following pseudocode?Enter your answer in the box below.NOTE: Please read the pseudocode very carefully.(1) n=14n=14(2) m=16m=16(3) for i=1i=1 to n+2n+2(4) ----...
- Q A natural cubic spline S is defined by S(x) = { S0(x) = a0 +b0(x ? 1) + d0(x ? 1)3 , if 1 ? x ? 2, S1(x) =...
- Q Calculate the first three terms in the power series solutions ofthe following differential equations taken about x=0.x^2y''+sinx y'-cosx y=0
- Q Please solve all partsConsider the following IVPy? = 2t ? y + 1, y(0) = 1.Find an approximation of y(1) using(a) the Euler’s method with N = 4,(b) the Euler’s...
- Q An environmentally toxic radioactive chemical is continuallyreleased at a constant rate of 1 (mg per vol per time) at themidpoint of a canal of length L with still water. As...
- Q #1 Let H= Span{v1,v2,v3,v4}. For each of the following sets ofvectors determine whether H is a line, plane ,or R3. Justify youranswers.(a)v1= (1,2,?2),v2= (7,?7,?7),v3= (16,?12,?16),v4= (0,?3,?3)(b)v1= (2,2,2),v2= (6,6,5),v3= (?16,?16,?14),v4= (28,28,24)(c)v1=...
- Q For the following, you can either provide a vector equation forthe curve, or you can describe the curve in words with sufficientdetails.a) Describe a curve that has curvature zero.b) Describe...
- Q Formulate Newton’s method for the systemx^3 = yy^3 = xNote that this system has three real roots (?1, ?1), (0, 0) and(1, 1). By taking various initial points in the...
- Q 11.Given a row echelon form or the reduced row echelon form of anaugmented matrix of a system of equations, determine the number ofsolutions the system has.
- Q a spherical ice of initial volume 1000 cm^3 is melting at a rate2 times the surface area. when does it completely melt? volume ofthe sphere of radius is r=4/3 pir^3...
- Q The surface of a spherical conductor of radius a is kept at atemperature of u(?)=300K+50K cos(?). The temperature inside isgoverned by the Laplace equation. Find an expression for thetemperature everywhere...
- Q Suppose ? is a finite-dimensional with dim ? > 1 and ? ??(?). Prove that {?(?)|? ? ?[?]} ? ?(?).
- Q according to the US census bureau, the population of the USseniors65 and older, in the year 2004 was approximately 36,300,000people. In the year 2010, it was 40,267,984 people. the seniorpopulation...
- Q The probability destiny function is where statistics andprobability come together. While there are several different kindsof discrete probability functions (or PDF's), three in particularare most commonly used. These are the...
- Q Consider the group Z/24Z.(a) Find the subgroups ?21? and ?10?.(b) Find all generators for the subgroup ?21? ? ?10?.(c) In general, what is a generator for ?a? ? ?b? in...
- Q Calculate the first three terms in the power series solutions ofthe following differential equations taken about x=0.x^2y''+xy'+(x^2-1/9)y=0
- Q (1) Suppose that V is a vector space and that S = {u,v} is a setof two vectors in V. Let w=u+v, let x=u+2v, and letT ={w,x} (sothatT is another...
- Q A regular hexagonal foundation 3 in. deep is being poured for ahexagonal building. If the distance across the flats of thefoundation is 27 ?ft, how many cubic yards of concrete...
- Q Determine the convergence or divergence if each integral byusing a comparison function. Show work using the steps below:A. Indicate the comparison function you are using.B. Indicate if your comparison function...
- Q Given the surface x= (3 (y-1)^2)+ (2 (z+ 3)^2)+ 7. Find anequation of the tangent plane at the point(12,2,2) in fourways:a) By using the surface as given,x=h(y,z)b) By writing the...
- Q The results of a blinded study assessing the use of plasmaD-dimer levels for diagnosing deep venous thrombosis (DVT) inpatients hospitalized for stroke rehabilitation reported increasedaccuracy over the standard procedure involving...
- Q The Eleatics say that there is no such thing as the void, butthe Atomists say that there must be a void. Explain thereasoning behind both sides of this disagreement.
- Q Determine whether each statement is true or false, and prove ordisprove, as appropriate.(a) (?x?R)(?y?R)[xy=1].(?x?R)(?y?R)[xy=1].(b) (?x?R)(?y?R)[xy=1].(?x?R)(?y?R)[xy=1].(c) (?x?R)(?y?R)[xy>0].(?x?R)(?y?R)[xy>0].(d) (?x?R)(?y?R)[xy>0].(?x?R)(?y?R)[xy>0].(e) (?x?R)(?y?R)(?z?R)[xy=xz].(?x?R)(?y?R)(?z?R)[xy=xz].(f) (?y?R)(?x?R)(?z?R)[xy=xz].(?y?R)(?x?R)(?z?R)[xy=xz].(g) (?x?Q)(?y?Z)[xy?Z].(?x?Q)(?y?Z)[xy?Z].(h) (?x?Z+)(?y?Z+)[y?x].(?x?Z+)(?y?Z+)[y?x].(i) (?y?Z+)(?x?Z+)[y?x].(?y?Z+)(?x?Z+)[y?x].(j)(?x,y?Z)[x<y?(?z?Z)[x<z<y]].(?x,y?Z)[x<y?(?z?Z)[x<z<y]].(k)(?x,y?Q)[x<y?(?z?Q)[x<z<y]].(?x,y?Q)[x<y?(?z?Q)[x<z<y]].
- Q Write a code to approximate the derivative of a function f(x) using forward finite difference quotient f( x...
- Q A manufacturer of an external hard disc provided the informationthat when the price per external hard disk is RM89, then 1 millionhard disc will sell. When the price of each...
- Q James Bond, Q, and M have agreed to meet at a pub after work fordrinks. Bond cannot remember if they agreed to meet at the “Fannyon the Hill” or at...
- Q How would you go about finding which of the following PDEs canbe separated into ODEs by assuming a product of unknown functionsx,y, and z?1) aUxy+bU=02) x^2Uxx+yUyy=03) Uxx+3Uxy+7Uy=04)Uxx+Uyy+Ux+Uy=0
- Q Find the general solution of the differential equationy??+9y=13sec2(3t), 0<t<?/6.Use C1, C2,... for the constants of integration. Enter an exactanswer. Enter ln|a| as ln(|a|), and do not simplify.y(t)=
- Q Consider the differential equation y' = -18 + 11x -x2.(a) Find the equilibria (i.e. constant solutions).(b) By analyzing the sign of dy/dt around the equilibria,determine whether each equilibrium solution is...
- Q 3.5. Each of the following measurements is a rounded value. Wehave no way of knowing the exact value that was rounded to obtainthese rounded values. For each, i) state the...
- Q A? third-order homogeneous linear equation and three linearlyindependent solutions are given below. Find a particular solutionsatisfying the given initial conditions.y(3)+2y''-y'-2y=0; y(0)=1, y'(0)=2, y''(0)=0,y1=ex , y2=e-x,y3=e-2xFind the particular solution.
- Q BCDsubtraction of 759-380show work please.
- Q Battle Creek Cereal Company has four main products: CornFlakes, Frosted Flakes, Bran Flakes and Strawberry Flakes. Theaverage daily demand for the products is:Corn Flakes: 1,250 CSFrosted Flakes: 1,430 CSBran Flakes:...
- Q prove that every integer greater than 2 can be broken into sumof multiples of 2 and 3
- Q Calculate the first three terms in the power series solutions ofthe following differential equations taken about x=0.x^2y''+sinx y'-cosx y=0
- Q Exercise 1. Write an algorithm (pseudocode) to read a set ofsales data items from standard input and calculate and output theirtotal and their average. Prompt user to enter number of...
- Q Consider equation: mx”+cx’+kx=F0cos(omega t) Find the transientmotion and steady periodic oscillations of a damped mass and springsystem with m=1; c=2; and k=26 under the influence of an externalforce F(t)=82cos(4t) with...
- Q find the general solution2xy^3+e^x+(3x^2y^2+siny)y'=0xy'=6y+12x^4y^(2/3)(2x+1)y'+y=(2x+1)^(3/2)
- Q Prove that a subspace of R is compact if and only if it is closed and bounded.
- Q Give an example of integers a, b, m such that a 2 ? b 2 (mod m),but a 6? b (mod m)
- Q Describe the elements of the M’Naughten insanity test andcompare it to the elements of the Substantial Capacity Test underthe MPC and what tests were combined to form the SubstantialCapacity test.
- Q Choose the general slicing method, the disk/washer method, orthe shell method to find the volume of the following solids.The region bounded by the curves y=x+1, y=12/x, and y=1 isrevolved about...
- Q 1) In this problem, you may use the fact (which we will prove inChapter 6) that an integer n is not divisible by 3 if and only ifthere exists an...
- Q Let X be a subset of R^n. Prove that the following areequivalent:1) X is open in R^n with the Euclidean metricd(x,y) = sqrt((x1 - y1)^2+(x2 - y2)^2+...+(xn - yn)^2)2) X...
- Q Let F3={cos?(t),sin?(t),cos?(3t),sin?(3t)} andT3={cos3(t),cos2(t)sin(t),cos(t)sin2(t),sin3(t)}. Use the powerreduction formulas and the triple angle identities to show thefollowing:Show T3?Span(F3).Show F3?Span(T3).
- Q Kiana has a rectangular back yard that is 50 feet wide and 60feet deep. She plans to construct a pool area and a patio area asshown in Figure 1. She...
- Q Report about (Applications of Differential Equations in Heat Exchanger System)
- Q Question 1If "P v Q" is false, then what can you say about the truthvalue of P?A.P is trueB.P is false.C.P can be true or false.Question 2If ( P v...
- Q Find det(A) and determine if Ax=b has a solution? If yes, is itunique. You do not need to find X. B is any order-n vector.A =Row1 = (-4,9,-4,1)Row2 = (2,3,0,-4)Row3...
- Q Determine the quantity of grout needed for the wall in problem6-1 if 18 cubic feet of grout is required per 100 square feet ofblock. (Problem 6-1) Determine the number of...
- Q Problem 3 1. Choose either the Halton or the Sobol sequence ofquasi-random numbers. Brie?y describe how they are constructed.2. Illustrate graphically the di?erence between pseudo-randomnumbers and quasi-random numbers.3. Repeat step...
- Q An airline has 50 airplanes in Los Angeles, 16 airplanes in St.Louis, and 8 airplanes in Dallas. During an eight-hour period, 20%of the planes in Los Angeles fly to St....
- Q Write the equation in general form.8x2 + 7 = x2 ?8x + 8Write the equation in general form.(y + 1)(y + 3) = 8Solve the equation by factoring. (Enter your...
- Q PerformancemetricsBuffalo BBQ Restaurantis trying to become more efficient in training its chefs. It isexperimenting with two training programs aimed at this objective.Both programs have basic and advanced training modules. Therestaurant...
- Q 1. Find all solutions to the following linear congruences usingFermat’s Little Theorem or Euler’s Theorem to help you. Show allyour steps.(a) 3462x ? 6 173 (mod 59)(b) 27145x ? 1...
- Q Let T : P3(R) ? P4(R) be defined by T(f(x)) = 5f?(x)-? f(t)dt(integral from 0 to x)1. Show that T is a linear transformation.2.Find dim (P3(R)) and dim (P4(R)).3.Find rank(T)....
- Q D^2 (D + 1)y(t)= (D^2 +2)f(t)a.) Find the characteristic polynomial, characteristic equation,characteristic roots, and characteristic modes of the system.b.) Find y_o(t), the zero-input component of response y(t) fort>=0, if the...
- Q If K is finite and F is an algebraic closuer of K, then theGalois group Aut F over K is abelian. Every element of Aut F over Khas infinite order.
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