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Advanced-Math Questions
Q.3 (Applications of Linear Second Order ODE): Consider the ‘equation of motion’ given by ODE d2x...
The integer 145 has the curious property that 145 = 1! + 4! + 5!It is...
Counting theory: Find how many 4-digit positive integers are there with no repeating digits (e.g.: 5823)...
Prove the statement true or use a counter-example to explain why it is false. Let a,...
Set up the linear system for the clamped cubic spline S that interpolates the data f(0)...
Let G1 and G2 be isomorphic groups. Prove that if G1 has a subgroup of order...
Let G1 and G2 be isomorphic groups. Prove each of the following. -- If G1 is...
For 1 and 2 find the compound amount on the given original principal at the compound...
Given the following data f(0) = 1.00000, f(0.25) = 1.64872, f(0.5) = 2.71828, and f(0.75) =...
How to represent sphere's surface with 2 dimensional vector? What would be the base?
Use power series to approximate 1/(1+x^10) then calculate integral .
Give an example of a non-invertible function f:ℝ→ℝf:R→Rff fails one of the conditions for being a...
Write each vector as a linear combination of the vectors in S. (Use s1 and s2,...
Consider the differential equation y′′+ 9y′= 0.( a) Let u=y′=dy/dt. Rewrite the differential equation as a...
dx/dt = 1 - (b+1) x + a x^2 y dy/dt = bx - a x^2...
Sketch the region in the xy-plane defined by the inequalities x − 7y2 ≥ 0, 1...
Let H be a subgroup of a group G. Let ∼H and ρH be the equivalence...
Let G = 〈(1 2 3 4 5 6), (1 6)(2 5)(3 4)〉. Let H1 :=...
an open tank with a 200L capacity is half filled with pure water. a salt solution...
Show that if G is a subgroup of Sn and |G| is odd, then G is...
Modify Prim’s algorithm so that it finds a maximum spanning tree
If S=(v1,v2,v3,v4) is a linearly independent sequence of vectors in Rn then A) n = 4...
US Robotics Inc. has a current capital structure of 30% debt and 70% equity. Its current...
Reflect on the concept of polynomial and rational functions. What concepts (only the names) did you...
Problem 4-11 (Algorithmic) Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project....
Last year I planted 40 watermelon plants in my garden. On average each plant produced 260...
The inverse-demand curve for oil in the Middle East is given by P = 20 –...
1.find the equation of the ellipse with center (0,0), focus at (4,0), vertices at (7,0) and...
1) Prove: Any real number is an accumulation point of the set of rational number. 2)...
Let G be a group of order 4. Prove that either G is cyclic or it...
Prove Euler’s theorem: if n and a are positive integers with gcd(a,n)=1, then aφ(n)≡1 modn, where...
Relations and Functions Usual symbols for the above are; Relations: R1, R2, S, T, etc Functions:...
The paraboloid z = 5 − x − x2 − 2y2 intersects the plane x =...
(Lagrange Multipliers with Three Variables) Find the global minimum value of f(x,y,z)=(x^2/4)+y^2 +(z^2/9) subject to x...
A 50-gallon tank initially contains 10 gallons of fresh water. At t = 0, a brine...
Let A be a (n × n) matrix. Show that A and AT have the same...
The Enormous State University History Department offers three courses—Ancient, Medieval, and Modern History—and the chairperson is...
Consider the vector space M2x2 with the usual addition and scalar multiplication. Let it be the...
What mathematicians were instrumental in developing the epsilon-delta definition of a limit? In your own words,...
Give the order of the element in the factor group a) 7 + <3> in Z15...
Let Z be the set of integers. Define ~ to be a relation on Z by...
Using the Newton’s second law model for a vibrating spring with damping and no forcing, 〖my〗^''+by^'+ky=0,...
In R^3 consider the following two bases B= { v1=(2,2,-3), v2=(2,2,0), v3=(1,2,4)} and B' = {...
Consider the vector: u1=(1,1,1), u2= (2,-1,1), u3=(3,0,2), u4=(6,0,4) a)Plot the dimension and a basis for W=...
Give a proof base on the proof of the Determinant of a Vandermonde matrix that the...
A solid is described along with its density function. Find the center of mass of the...
Write down a homogeneous second-order linear differential equation with constant coefficients whose solutions are: a. e^-xcos(x)...
1, Solve cos(x)=0.17cos(x)=0.17 on 0≤x<2π0≤x<2π There are two solutions, A and B, with A < B...
Let G be a group and let a ∈ G. The set CG(a) = {x ∈...
The graph of the tilted ellipse is x^2 - xy + y^2 - x - y...
Determine the relationship between the number of heptagons (7-sided polygons) and pentagons in a polyhedron made...
Find all values of c ∈ C such that the linear transformation T ∈ L(C^3) given...
The matrix [−1320−69] has eigenvalues λ1=−1 and λ2=−3. Find eigenvectors corresponding to these eigenvalues. v⃗ 1=...
Find a general term (as a function of the variable n) for the sequence{?1,?2,?3,?4,…}={45,1625,64125,256625,…}{a1,a2,a3,a4,…}={45,1625,64125,256625,…}. Find a...
Glenn has made contributions of $250 at the end of every three months into an RRSP...
Solve the differential equation by variation of parameters. y'' + 3y' + 2y = 1 /...
A mass of 100 g stretches a spring 5 cm. If the mass is set in...
You are in charge of scheduling the baseball games for your town’s Little League. There are...
This is for Differential Equations. I was sick last week and missed class so I do...
let G be a connected graph such that the graph formed by removing vertex x from...
Use Sylow Theorems: Show that every group of order 144 is not simple.
Prove that (n − 1)^3 + n^ 3 + (n + 1)^3 is divisible by 9...
Use polynomial fitting to find the formula for the nth term of the sequence (an)n≥0 which...
How do you recognize in which situations the idea of strong induction might be useful?
consider 1/n. Find all the values of n for which 1/n has a decimal representation with...
For map g:(x,y) --> ( e^x cos y, e^x sin y), find the image of g....
IN MATLAB: Write a function file that takes a vector as an input and returns another...
Extend the function f(a,b) = (sin a - sin b)/ (a-b) so that it is on...
The psychology club is having a self-proclaimed psychic come to their campus fund-raising event to demonstrate...
Exclusive OR the two Hexadecimal numbers and give the result in Hexadecimal (hint: Change the two...
Let{Ai :i∈I} be a collection of sets indexed by a set I. (a) Prove that if...
Let V be an n-dimensional vector space and W a vector space that is isomorphic to...
Find the first two positive solutions to the system of 3 congruence equations x ≡ 3...
Prove that a bipartite simple graph with n vertices must have at most n2/4 edges. (Here’s...
Two years ago your orange orchard contained 50 trees and the yield per tree was 75...
Let S and T be nonempty subsets of R with the following property: s ≤ t...
Define a right angle given whichever of the undefined terms below you need: point, line, incidence...
Sketch the phase portrait of y” - y’ - 6y = 0, y(0) = 2, y’(0)...
A plan for an executive traveler’s club has been developed by an airline on the premise...
Find the first four nonzero terms in a power series expansion about x = 0 for...
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