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Advanced-Math Questions
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...
sketch the graph f(x)6^x+5 describe how the graph can be obtained from the graph of basic...
Determine whether or not each of the following signals is periodic. If a signal is periodic...
(abstract alg) Let G be a cyclic group with more than two elements: a) Prove that...
A. What is the y-coordinate of the point on the unit circle generated by a central...
Let A be square matrix prove that A^2 = I if and only if rank(I+A)+rank(I-A)=n
Prove using Mean Value Theorem that if f' is bounded then f is bounded too.
Use a comparison test to prove the following (here M1 and M2 are constants) if ak...
i want full example of finite differene method with numbers and solution by using one of...
Is the span of the rows of a matrix the same as the span of the...
Let A and B be 3x3 matricies, with det A = 9 and deb B =...
Find the (a) center, (b) foci, and (c) asymptotes of the hyperbola. 6.) 6x^2-y^2-48x+6y-9=0
polar form write in exponential form: 9. 4 +3i 11. -6.3 13.1+i
solve the given DE equation y''-4y'+20y= (x+1)e^2x cos x + 2x^2 e^2x sinx
Show that if a, b, c are real numbers such that b > (1/3)a^2 , then...
Hi! I ve got troubles to evaluate the integral with boundaries -inf to inf of the...
What are some real life applications of slope fields and examples of the applications?
4) Allison started an RRSP on March 1, 2011, with a deposit of $2470.00. She added...
Determine wether the given function has any local or absolute extreme values, and find those values...
A tank contains 100 kg of salt and 1000 L of water. Pure water enters a...
Assume that (X, dX) and (Y, dY ) are complete spaces, and give X × Y...
The company “Le chocolat d ́elicieux” has you solve an LP problem, the ob- jective being...
You are offered a $2,800,000 retirement package to be given in $100,000 payments at the end...
Prove that a 15 x 8 board cannot be covered by 2 L-tetrominoes and 28 skew...
given the differential equation y'+y=x^2+2x, compute the value of the solution y(x) at x=1 given the...
If we let N stand for the set of all natural numbers, then we write 6N...
fixed point iteration method solve x^2+3x-18
PLEASE EXPLAIN ANSWER You are making Ginger Sweet Potato Salad. The recipe calls for 6 lbs....
PLEASE EXPAIN ANSWER You purchase 6 heads of Bibb lettuce. Each head weighs on average 6...
2. For each 3*3 matrix and each eigenvalue below construct a basis for the eigenspace Eλ. A=...
Use Gaussian elimination to solve the following system of linear equations. 2x1 -2x2 -x3 +6x4 -2x5=1...
Find the general solution of the given higher order differential equation y^(4) + 4y^(3) − 4y^(2)...
a) How many non-negative integer solutions are there to the following equation? ?1+?2+⋯+?10=5 b) How many...
A man set out at noon to walk from Appleminster to Boneyham, and a friend of...
An urn initially contains 3 tags, of which 1 is red, 1 are green and 1...
Three pastures with grass of identical height, density, and growth rate are of size are 3...
a) Let f : [a, b] −→ R and g : [a, b] −→ R be...
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