Advance Math question and answers for July 28, 2023
- Q If x and y are arbitrary real numbers such that x < y, prove that there exists at least one rational number r satisfying x < r < y, and...
- Q An integer n is called even if n = 2m for some integer m, and odd if n + 1 is even. Prove the following statements:(a) An integer cannot be...
- Q Given integers a, b, c,g.c.d.(a, b, c) = 1 if and only if g.c.d.(a, b) = 1 and g.c.d.(a, c) = 1
- Q What is the vertex of y=2x²+6x+4 ? Give details explaination
- Q Let G be finite with |G| > 1. If Aut(G) acts transitively on G ? {e} then G ?= (Z/(p))n for some prime p.
- Q Solve using Gaussian elimination with partial pivoting and 4 digit arithematic
- Q How many (group) homomorphisms are there from Z20 onto (surjective to) Z8. How many are there to Z8?
- Q Find the equation of the plane through the point (1,1,1) which is perpendicular to the line of intersection of the two planes x?y?3z=?1 and x?3y+z= 2.
- Q Prove the formulas given in this table for the derivatives of the functions cosh, tanh, csch, sech, and coth. Which of the following are proven correctly? (Select all that apply.)(square...
- Q We want to construct a box whose base length is three times the base width. The material used to build the top and bottom cost $10/ft2 and the material to...
- Q Find two linearly independent solution of y"+7xy=0. of the formy1=1+a3x^3+a6x^6+....y2=x+b4x^4+b7x^7+....Enter the first few co-efficientsa3=a6=b4=b7=
- Q A population of squirrels living in a forest with a carrying capacity of 2600.(assume logistics growth with constant k=0.9yr)(a)find a formula for the squirrels population p(t) assuming an initial population...
- Q Find the Maclaurin Series of the following functions:(a) f(x)= Ln(3+x)(b) f(x)= cos(3x)(c) f(x) = x^(2)(e^(-x))
- Q Let Rx denote the group of nonzero real numbers undermultiplication and let R+ denote the group of positivereal numbers under multiplication. Let H be the subgroup {1, ?1} ofRx. Prove...
- Q For each of the following degree sequences, determine if theexists a graph whose degree sequence is the one specified. In eachcase, either draw a graph or explain why no such...
- Q Question: Find ?A for the following matrix A=[12 -3 8 ; 8 1 8 ;-3 3 1] then check if ?A ?A=A
- Q Prove that the product of a finite number of compact spaces iscompact.
- Q a) Let S ? R, assuming that f : S ? R is a continuous function,if theimage set {f(x); x ? S} is unbounded prove that S is unbounded.b) Let...
- Q A painter wants to know the amount of paint needed to paint onlythe walls and the interior side of the door in a room. The chosenpaint covers 100 square feet...
- Q A hardware store will run an advertising campaign using radioand newspaper. Every dollar spent on radio advertising will reach60 people in the "Under $35,000" market, and 60 people in the...
- Q How to proof:Matrix A have a size of m×n, and the rank is r. How can werigorous proof that the dimension of column space are always equalto the dimensional of...
- Q Using the function f(x)=ln(1+x)a. Find the 8 degree taylor polynomial centered at 0 andsimplify.b. using your 8th degree taylor polynomial and taylorsinequality, find the magnitude of the maximum possible error...
- Q Use your knowledge of second-order systems forced by asinusoidal function to solve (a) y '''' + y ?? = sin x.Hint: Try to integrate twice immediately. Extra hint: Yoursolution should...
- Q Show that g(x) = 1/2sin(x-1) has a unique fixed point on theinterval [-1,1]Estimate the number of iterations required to achieve 10^-2accuracy
- Q A company needs to purchase several new machines to meet itsfuture production needs. It can purchase three different types ofmachines A,B,andC. Each machine A costs $80,000 and requires 2,000square feet...
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