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Advanced-Math Questions
1. A person receives a raise of 23% it is worth $36. Calculate how many dollars...
The report should include: The procedure detailed The graph of the primary function (the function to...
Please answer below question. Let C(h,k) be the statement “ h is a student in the...
1) For each of the following state whether it is true or false. If true give...
convolve A with B where A=[4 -2 0 1 ] and B= [0 0 2 0...
Find all fo the local extrema of the function x-2cosx on the domain (0,2pi). Say which...
transform my'' +cy' +ky = kAsin((omega)t) + c(omega)Acos((omega)t) into Laplace domain. Solve for transformed variable (leave...
Suppose V is a vector space and T is a linear operator. Prove by induction that...
Let X be a set and A a σ-algebra of subsets of X. (a) A function...
Show that for all integers n>1, f_(n+1)f_(n-1)=(f_n)^2 + (-1)^n Please use detailed explanation(I am confused on...
Show that a compact subset of a Hausdorff space is closed in detail.
1/ What are some drawbacks to using SDS-PAGE to determine the molecular mass of a polypeptide?...
Find the least positive residue: If 18! is divided by 437
Linear Algebra Find the 2x2 matrix A of a linear transformation T: R^2->R^2 such that T(vi)...
Describe all of the homomorphisms from D8 to Z8(verify each is a homomorphism and prove there...
Kernels on real vectors Let x,z ∈ Rn, show the following is valid kernel: Gaussian or...
4. (a) Let n = (dkdk−1 . . . d0)b. Prove that (b + 1)|n if...
You know from class that, for any real numbers ?,?,?a,b,c such that ?<?<?a<c<b and for any...
A set of reals is totally disconnected if and only if it contains at least two...
Prove that there is an isomorphism between Lie superalgebras sl(2|1) and sl(1|2) ?
Show that the group Q^+ of positive rational numbers under multiplication is not definitely generated
prove that the lebesgue measure on R has a countable basis
obtain the green's function for the boundary value problem y''+y = f(x), y(0)=y(1)=0
Evaluate using Stokes' theorem: a) ∬ ∇ × ? ∙ ???, if F = (xy, yz,...
The desired distance for Flextronchip customers is 0.9 mm between two adjacent pins. Any deviation from...
Exercise 9.1.11 Consider the set of all vectors in R2,(x, y) such that x + y...
8. Let g be an automorphism of the group G, and fa an inner automorphism, as...
Identify a large class of groups for which the only inner automorphism is the identity mapping.
4. Prove that {(x, y) ∈ R 2 ∶ x − y ∈ Q} is an...
5. Prove or disprove the following statements: (a) Let R be a relation on the set...
1. The Fundamental Theorem of Arithmetic states: Every integer greater than or equal to 2 has...
Suppose you have a metal washer of the form {(r,θ) : 1 ≤ r ≤ 2}....
Solve the following wave equation using Fourier Series a2uxx = utt, 0 < x < pi,...
Determine if the indicated subgroup H is a normal subgroup of G. (a) Let G =...
Solve the following wave equation using Fourier Series a2uxx = utt, 0 < x < L,...
Let G be the graph obtained by erasing one edge from K5. What is the chromatic...
Solve the following wave equation using Fourier Series a2uxx = utt, 0 < x < pi,...
Solve the heat equation and find the steady state solution: uxx = ut, 0 < x...
Partition of integers What is s(k,1)?
2. Rotate the semicircle of radius 2 given by y = √(4 − x^2) about the...
Prove that the ring Z[x]/(n), where n ∈ Z, is isomorphic to Zn[x].
For question 43 find (a) the recurrence formula and (b) the general solution of the given...
Draw the cube and the octahedron as planar graphs. Show that the octahedron is the dual...
Show that f: [1, infinity) --> [2, infinity), f(x) = x+1/x is bijective and find it's...
express the f(x)=3x^2-18x+15 in the standard form. find its vertex and its x and y intercepts....
Show that the following statement holds: i) for each simple module M, we have rad M...
b) More generally, find the matrix of the linear transformation T : R3 → R3 which...
Let A and B be nonempty sets. Prove that if f is an injection, then f(A...
Use the Laplace transform to solve the given system of differential equations. 2 dx/dt + dy/dt...
Given the 2 ODE's: y" + y = 0 and y" + y = 100 What...
A couple who borrow $50,000 for 15 years at 8.4%, compounded monthly, must make monthly payments...
Give two examples each of sets that a) are denumerable b) are not denumerable c) are...
Explain how to construct the array of rational numbers as Cantor did, and why all rationales...
An investment pays 1000 in one year, 2000 at the end of the second year and...
Prove using the definition of O-notation that 2^(n+2)∈O(2^(2n)), but 2^(2n)∉O(2^(n+2)).
Prove that a simple graph with p vertices and q edges is complete (has all possible...
Prove that motions preserve angles. In other words, show that if f is a motion and...
Let f, g : [a, b] ---> R continuous such that (f(a) - g(a)) (f(b) -...
Let f ∈ Z[x] be a nonconstant polynomial with the property that all the roots (in...
Let f ∈ Z[x] be a nonconstant polynomial. Prove that the set S = {p prime:...
X^2y’’ − 5xy’ + 8y = 8x^6; y(1/2) = 0; y’ (1/2) = 0 differential equation...
John wants to buy a new sports car, and he estimates that he'll need to make...
x^2y'' − 3xy'+ 4y = 0 ; y(1)=5 y'(1)=3 differential equation using the Cauchy-Euler method
Let f, g : [a, b] ---> R continuous such that (f(a) - g(a)) (f(b) -...
Use strong induction to prove that every natural number n ≥ 2 can be written as...
Let U be the span of (1,2,3) in R^3. Describe a basis for the quotient space...
Use Mayer Vietoris to compute the reduced homology groups of the Klein bottle, K.
In the next two problems, find all Laurent series around the indicated point and state the...
Solve the given system of differential equations by systematic elimination. 2 dx/dt − 6x + dy/dt...
Show 3 | (a − b)(b − c)(c − d)(a − c)(b − d)(a − d)...
Consider the following difference equation for populations called the nonlinear logistic model ?t+1=?xt(1−xt) (a) Find the...
Factor each of 17, 53, and 19i-13 into a product of Gaussian primes. Find the gcd...
Let A m×n be a given matrix with m > n. If the time taken to...
Problem 3.2 Nature’s Treasure tree farm is trying to decide which fertilizer to use to grow...
In the first two problems, find the first four non-zero terms of the Laurent series of...
let A be a nonempty subset of R that is bounded below. Prove that inf A...
show that the relation "≈" is reflexive, symmetric, and transitive on the class of all sets.
A 128 lb weight is attached to a spring whereupon the spring is stretched 2 ft...
A steel ball weighing 128 lb is suspended from a spring, whereupon the spring is stretched...
let Xn be a sequence in a metric space X . If Xn -> x in...
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