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Advanced-Math Questions
1. Use mathematical induction to show that, ∀n ≥ 3, 2n2 + 1 ≥ 5n 2....
1. Use the classification theorem for finite abelian groups (Theorem 6.6) to classify all finite modules...
Fit a curve for the following data. Fit a curve for the following data. x 1...
Find the asymptotic notation for cos3x, tan4x, cot5x, sec6x and csc7x each as O(|x|^n) for some...
Solve 5x^2 y'' + 15xy'+ 50y = 0.
Prove that 1/(2n) ≤ [1 · 3 · 5 · ··· · (2n − 1)]/(2 ·...
Given that x = 1/2 is a root of 2x3 - 9x2 + kx - 13...
What steps would we take to find: Let S z = az+b/( cz+d) and T z...
in investment firm recommends that a client invest in bonds rated AAA, A and B the...
Investment Condition 1 None 2 Only if 1 3 Only if 1 4 Must if 1...
For PDEs, when should i know wether i should use Seperation of variables or Laplace transform...
Prove that for every x ∈ R \ Q, the set Ax = {qx | q...
1a. Using the e − δ definition of continuity, show that the absolute value function f(x)...
List these functions so that each function is big-O of the next function in the list:...
Represent f(x) = { 1 if 0<x<1 or 0 if x>1} in the form f(x) =...
We are given a sequence of numbers: 1, 3, 5, 7, 9, . . . and...
The force of interest delta(t) is given by ln(1.5) for all non-negative t. Find the accumulation...
Consider the differential equation t 2 y" + 3ty' + y = 0, t > 0....
A. Find unit vector u1 perpendicular to u. Find unit vector w1 in the direction of...
Prove that 1 · 1! + 2 · 2! + ··· + n · n! =...
Prove that for positive integers a and b, gcd(a,b)lcm(a,b) = ab. There are nice proofs that...
A local dental practice decides to run a Groupon campaign. The campaign offered $360 worth of...
Let P be the set of all people, dead or alive. Consider the function f: P\longrightarrow...
Show that integral from 0 to infinity of ( cos wx + wsin wx)/(1+w2 ) =...
Find an orthogonal matrix P such that a change of variables, x = Py, where x...
consider y"+2y'+y=0 (a) verify that y1=e^(-x) is a solution (b) solve the initial value problem y"+2y'+y=0,...
Solve the system of linear equations: x-2y+3z=4 2x+y-4z=3 -3x+4y-z=-2 2. Determine whether the lines x+y=1 and 5x+y=3...
Decide if each of the following statements are true or false. If a statement is true,...
How many ways can you choose 3 numbers randomly out of 1,2,3,4.... 9, 10 and the...
Let S be the universal set, where: S = { 1 , 2 , 3 ,...
Show the following polynomials are irreducible. All answers should be justified. If you find that the...
You find the following corporate bond quotes. To calculate the number of years until maturity, assume...
(x^2-4)dy/dx+xy-x^3+4x=0. y(3)=7
Elise and her friend Eloi developed an online car repair training course and sell it for...
If A · B = A · C, does it mean that B = C? Now,...
Write a python program to determine the smallest number in a sequence and illustrate it with...
Develop a basic model in Extendsim that represents Lanchester's Ancient Warfare model. Use the following linear...
Use this fact: A positive integer n ≥ 3 is constructive if it is possible to...
A dam which is v = 21 meters tall has an outflow gate. The gate, height...
y''+y'-20y=xe^3x+e^4x Find the general solution.
Consider a horizontal spring-mass vibration system without damping, where the mass is 2 kg, the spring...
Need to use Multivariable Calculus to solve the question. Basic projectile motion algebra equations cannot be...
find all solutions to x^2+y^2=2z^2
Check that K ( T ) is always a subspace of V .(Topological data Analysis)
If an n × n matrix A has all the n eigenvalues λ1, λ2, ..., λn,...
Find the parametrize for the vector field that goes through a point P at t=0 1)...
A proof of the Triangle Inequality for vectors (let v and w be vectors in R^n,...
Suppose that A is a 6 x 6 matrix that can be written as a product...
5+5-90+900
Consider ODE y''' - 4y" + 13y' = 2te^(2t) sin3t 1.) Solve corresponding homogeneous ODE 2.)...
2. Given the vectors ? = (−2,1,2) and ? = (1, − 3, 1), find: a)...
Find the area of one stretcher course of 16 blocks if the blocks are 8 5/6...
Using Matlab 1. Give the flowchart for finding the root of the function f(x) = [tanh(x-2)]...
Draw a graph for the function using information from the function and its first and second...
Question 2: Let A = 2 −2 4 3 −2 5 −3 3 −4...
5. Convert each of the following binary numbers into base 10. Show your work. (a) 0011...
Determine the global extrema of the multivariable quadratic function: f(x,y)=ax2+2bxy+cy2
The three following coordinate vectors are given in unitary coordinates (in [m]): a = (5; 0;...
Determine all homomorphic images of Z12.
2. Show that each of the following functions is O(x^2 ). Clearly state your C and...
Please give the postfix form of the arithmetic expression (a*b + 2*c)/(2 - 3*d) + c
In GF(24), derive the multiplicative inverse of x2 modulo (x4+x+1).
Furniture Store Credit Card Disclosure Statement: On approved furniture store credit card purchases—based on your credit...
Briefly describe the main properties of Galois Field?
If your were going to predict population using the logistic growth equation, what would be the...
4. You are building a new walking track in Providence, above the city. The company that...
Abstract Algebra: Prove that F5[X]/(X3 + X + 1) is a field with 125 elements and...
Water is being pumped into a leaky inverted conical tank at a rate of 10 m3/h....
See four problems attached. These will ask you to think about GCDs and prime factorizations, and...
Please provide a proof that if G be sequentially compact, f(G) will also be sequentially compact....
Let F be a field and let f(x) be an element of F[x] be an an...
Abstract Algebra: Prove that the polynomial f(X) = X4 + X + 1 is irreducible on...
Consider the function f defined on R by f(x) = ?0 if x ≤ 0, f(x)...
Show that the pair of equations A = 1/2 ( B × r) , B =...
B1. Consider the initial value problem given by y 0 (t) = sin2 (y) ln(t +...
Determine which of the vector fields is conservative (ie gradient vector fields). If the vector field...
1. (a) Determine whether or not F is a conservative vector field. If it is, find...
a) Find a function that is continuous on the interval (3,6), but not uniformly continuous on...
2. Perform 2 iterations of Newton’s method on f(x,y)=x^4+4x^2*y+4y^2+2x+2y starting at(1,1).
Calculate the line integral I C <y,z,x> where C is the curve of intersection of the...
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