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Advanced-Math Questions
prove by induction that n(n+1)(n+2) is divisible by 6 for n=1,2...
Find y as a function of x if y‴−13y″+36y′=24ex y(0)=19, y′(0)=30, y″(0)=13 y(x)=
Find a particular solution to the differential equation −16y″+8y′−1y =−2t2+2t+2e-3t yp=
Real Topology: let A={1/n : n is natural} be a subset of the real numbers. Is...
a) A pot holds 16 cups of broth. Every hour, 4 cups of the broth is...
Each natural number greater than 1 is either a prime number or is a product of...
Discreet Math: Prove or disprove each statement a) For any real number x, the floor of...
Charles and James are both math professors. One day Charles and James have the following conversation:...
Find all primitive Pythagorean Triples that contain the number 12
Important Instructions: (1) λ is typed as lambda. (2) Use hyperbolic trig functions cosh(x) and sinh(x)...
Real Analysis I Prove the following exercises (show all your work)- Exercise 1.1.1: Prove part (iii)...
Prove that for every integer n, 30 | n iff 5 | n and 6 |...
y= 95.808 e^-1E-04x y = 50 please show steps. Also is e^-1E-04x the same as e...
Prove the following(please write neatly and explain): The Cayley graph Γ(G, S) is connected if and...
1. Can a sequence attain its limit; that is, can the limit of a sequence be...
Given the following pairs of lines, determine whether they are parallel, intersecting or skew, if they...
When will change-of-basis matrix be equal to identity matrix?
Two solutions to the differential equation y00 + 2y0 + y = 0 are y1(t) =...
Consider the initial value problem dy dx = 1−2x 2y , y(0) = − √2 (a)...
Which of the following subsets of R form a field (justify) { a + b cube...
Prove the union of a finite collection of countable sets is countable.
Write down the Cayley table for the multiplication in U(9). Explain your answer.
How many ways are there to roll ten different 6-sided die so that all six faces...
A circle has radius 2 and center (0, 0). A point P begins at (2, 0)...
Use a proof by cases to show that: min(a, min(b,c)) = min(min(a,b),c), whenever a, b, and...
In a group of 5 people, what is the probability that at least two were born...
Let ?? be the path with ? edges and ?? (?) be the characteristic polynomial of...
22. Consider the general S-I-R model for a measles-like illness: S′ = −aSI, I′= aSI−bI, R′...
Give a complete residue system modulo 17 consisting entirely of integers congruent to two modulo 5.
let A = {1/n : n element N} show that every point of A is a...
Indicate whether the argument form is valid (V), or invalid (I). Show your work. ~p ∨...
4. Let f(x) = 14xex+1 + 30ex+1 −7x3 −43x2 −95x−75. (a) Apply Newton’s method to find...
Determine if {(1, 3, −4, 2),(2, 2, −4, 0),(1, −3, 2, 4)} is linearly independent or...
A tank contains 40 lb of salt dissolved in 400 gallons of water. A brine solution...
A tank contains 120 liters of fluid in which 50 grams of salt is dissolved. Brine...
Find the inverse function of f(x)= 1+2cos(x) and then find the domain and the range of...
In October 2005, a family's gasoline consumption is 30 gallons per month and is increasing at...
15) show that a graph with at most two odd length circuits can be 3 colored.
as I show that P(A) and 2^A are numerically equivalent
On a hot Saturday morning while people are working inside, the air conditioner keeps the temperature...
use lagrange multipliers to locate the maximum of f(x,y,z) = 2x^2 - 2y + z^2 subject...
7) (1 − x2)y'' − 2xy' + 2y = 0; y(0) = 0, y'(0) = 3...
If H is a normal subgroup of G and |H| = 2, prove that H is...
Prove whether or not the intersection and union of two uncountable sets must be uncountable
Compute the total and annual return on the following investment. Three years after paying $3300 for...
Consider the equation x-1- a = 0 , (1) where a > 0 is a given...
At the bean farm, the automatic seedling planter creates rows 30 in. apart and places seedlings...
You have a job with a gross pay of $63,000. Using the website 2018-2019 Federal Tax...
Find a basis for each of the following vector spaces and find its dimension (justify): (a)...
The weekly demand function for x units of a product sold by only one firm is...
Suppose A is an orthogonal matrix. Show that |λ| = 1 for all eigen- values λ....
A stereo system is being installed in a room with a rectangular floor measuring 15 feet...
Please describe in one or two sentences what an orthogonal projection is. Also, do the same...
Show that the origin is a spiral point of the system x' = -y - x(sqrt(x2...
Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the recursion...
Let f be a function of two variables that has continuous partial derivatives and consider the...
Let x = {x} and y ={y} represent bounded sequences of real numbers, z = x...
How many ways can we pick three distinct integers from {1,2, ...,15} such that their sum...
Prove that for all n ∈ Z, there exists a k ∈ Z such that n^3...
Let γ : [c, d] −→ R 3 be a C 1 path and φ :...
Compute three iterations of Newton Raphson method to find the root of the following equations i....
** Linear Programming ** Max Z = 6x1 + 10x2+9x3 + 20x4 constraint 4x1 + 9x2...
Please do both: a. Suppose that A ∈ Mn is non-singular. Prove that if λ ∈...
Suppose that you follow a population over time. When you plot your data on a semilog...
Let X be an object that has exactly three symmetries, so its symmetry group Sym(X) has...
Consider the following initial value problems and solve by hand. y' = 2x-3y+1 y(1)...
y''''+16y= cos x by the method of variation of parameters
QUESTION 1 Given a normal distribution with μ = 50 and σ = 4, what is...
In number theory, Wilson’s theorem states that a natural number n > 1 is prime if...
Solve Differential equation by variation of parameters method. y"-5y'+6y=e^x
A body falls from rest against a resistance that is proportional to the speed at any...
Linear algebra Find a transformation matrix A for P^2 -> P^3 then show its onto
Q1 Electric cars of the same type have ranges, X, that are normally distributed with a...
Let x1, x2, ..., xk be linearly independent vectors in R n and let A be...
Let V be a vector space and let U1, U2 be two subspaces of V ....
Hi I am trying some proofs and I am stuck on this one. It says to...
3. (a) (2 marks) Consider R 3 over R. Show that the vectors (1, 2, 3)...
Show that if f is an arithmetic function that is invertible for the Dirichlet convolution and...
Let A = {0, 3, 6, 9, 12}, B = {−2, 0, 2, 4, 6, 8,...
Given that A, B, and C are sets, determine if each statement below is true or...
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