0
votes
0answers
4 views

discrete finite summation of non-linear functions

Can anyone have idea for dealing with the two following series summations ∑_(i=1)^n▒1/(a+bx_i )=c ∑_(i=1)^n▒x_i/(a+bx_i )=d I need to find the values of 'a' and 'b'; 'c' and 'd' are known. x_i is ...
0
votes
1answer
6 views

Inequtions problem - how to calculate total of sales for a determined ROI?

A company has determined that the cost of production of X cellphones is according to this formula: $$ C = 150x + x^2 + 25$$ If each cellphone is sell at 220, how many of them must be produced and ...
0
votes
0answers
5 views

Euclidean Geometry (Potential Menelaus Theorem)

I have a strong suspicion that this problem applies Menelaus's theorem, but I can't see it. I also tried algebraic manipulation (such as trying to re-write BD/DC in terms of AB or CP), but to no ...
0
votes
0answers
6 views

With 2 as smallest period of the function $f(x)$= $\tan^2[(\frac{\pi x}{n^2-5n+8})]$ + $\cot(n+m)\pi x$ ;the period m can't belong to is?

Here n $ \in N$ , m $\in Q$. Options are: A) $(-\infty, -2) \cup (-1, \infty)$ B) $(-\infty, -3) \cup (-2, \infty)$ C) $(-2,-1) \cup (-3,-2)$ D) $(-3, -5/2) \cup (-5/2, -2)$ I have an answer to ...
1
vote
2answers
30 views

Notation: $f(A)$ when $f$ is a function $f:A\to B$.

I've seen the following notation with no previous clarification: $f(A)$, when $f$ is a function $f:A\to B$. Am I correct to assume $f(A)$ should be the image of $f$? E: I'd appreciate downvoters ...
0
votes
0answers
8 views

Tangent Bundle of the open positive orthant

What is the expression for the tangent bundle of the open positive orthant $\mathbb R_+^n$? I think I know the answer, but just to be sure. Thanks
0
votes
0answers
10 views

Is my work correct? (Easy problem, confidence intervals)

The r.v. $X$ represents the time taken by a computer in company $1$ in order to perform a certain job, and $Y$ represents the same thing but for company $2$. A sample of $n_X = 12$ computers are taken ...
-1
votes
1answer
10 views

Probability question - multiple choice experiment.

Suppose a student who is about to take a multiple choice test has only learned $60\%$ of the material covered by the exam. Thus, there is a $60\%$ chance she will know the answer to the ...
0
votes
1answer
20 views

Alegebra- Function or NOT a function

if you have a relation with the domains: 0,1,2,3,4 and a range of: 3,1,2,4,2 does this mean it is not a function because there are two outputs of the number 2? Or can it only not be function if there ...
2
votes
2answers
23 views

Showing an equation has one positive root

Let $n\geq 2$ be an integer and $\beta > 0$. Consider the polynomial equation: $$p(x) = x^n + x^{n-1} - \beta = 0$$ Show the equation had exactly one positive root $p(\beta)$ Do I use the ...
1
vote
2answers
69 views

Opposite of Fermat's Last Theorem?

So Wiles' proof showed that no three positive integers $a$, $b$, and $c$ can solve the equation $a^n+b^n=c^n$ for any integer value of n greater than $2$. Now what about the opposite? What does this ...
3
votes
0answers
17 views

Help with partitions, equivalence classes, equivalence relations.

The following definitions and results are from my textbook. A partition $\mathcal{P}$ of a set $X$ is a collection of nonempty sets $X_1, X_2, \dots$ such that $X_1 \cap X_j = \emptyset$ for $i ...
-4
votes
1answer
18 views

STATISTICS AND PROBABILITY

John and Isaac shot at a target. The probability that John hit the target is 1/4 and the probability that Isaac hit the target is 3/5. If they shot together, what is the probability that; A) both John ...
1
vote
0answers
7 views

Radicial Morphism over DVR's

I would like a reference for the truth/falsity of the following statement: Suppose that $X \rightarrow Y$ is a map of $S$ schemes where $S$ is the spectrum of a DVR with generic point $\eta$ and ...
-1
votes
2answers
23 views

proof of isosceles triangle?

How do you prove this isosceles triangle? Given line AC is congruent to line BC Prove: Angle A=Angle B I've gotten to the angle bisector and SAS(side- angle- side), and I believe there is one more ...
3
votes
1answer
23 views

Borel sets: alternative characterization for metric space

For any topological space $(X,\tau)$, the Borel $\sigma$-algebra $\mathcal{B}$ is the $\sigma$-algebra generated by the open sets. In other words, it is the intersection of all $\sigma$-algebras on ...
3
votes
2answers
27 views

Trouble solving this differential equation: $x'=3(x-2)$, $x(0)=-1$.

Find the solution of the differential equation x'=3(x-2) given initial value condition of x(0)=-1 Here's my attempt. x'=3(x-2) dx/dt = 3(x-2) dx/x-2 = 3dt int dx/x-2 = int 3dt+c ln|x-2| = 3 + C ...
2
votes
1answer
30 views

Minimum value of $\cos x+\cos y+\cos(x-y)$

What is the minimum value of $$ \cos x+\cos y+\cos(x-y). $$ Here $x,y$ are arbitrary real numbers. Mathematica gives (with NMinimize) $-3/2$. But I don't know if this is correct and if so, how to ...
0
votes
1answer
16 views

Finding the adherent points of $A=\left\{\left(1/n,1/m\right)|n,m\in\mathbb{N}\right\}$

The obvious adherent point is $(0,0),$ then I thought about fixing a point for each component and finding the adherent points on each line, but it leaves a mess. Doing it "my way" would lead to find ...
1
vote
1answer
17 views

Trying to construct a specific function

I am trying to construct a function $f$ with the following property: $\mathbf{N}$ is the set of natural numbers without 0. Show that $\forall \epsilon>0: \forall a,b \in \mathbf{N}: a < b: ...
0
votes
1answer
27 views

Is it possible to follow another way to perform this calculation steps?

So, I have an four numbers. There is they are: Number 1 is 40008260280899465341031700284668165694305281399205262735419849961365494809955 Number 2 is ...
-1
votes
1answer
12 views

How far is the bottom of the ladder from the house?

A 13 foot ladder is leaning against a house. The distance from the bottom of the ladder to the house is 7 feet less than the distance from the top of the ladder to the ground. How far is the bottom ...
1
vote
2answers
19 views

Question about product topology notation

Instead of using the general form, I will use a simpler one such as $\mathbb{R} \times \mathbb{R}$ (which is $\mathbb{R}^2$ of course). Now the notation says that the open sets are the union of the ...
-1
votes
0answers
7 views

Zoom level leaflet map to google map in meters.

I looked at both maps and made a ruff estimate of the zoom level of the leaflet map and how many meters it represent on the google map. 8 = 338477m 12 = 20484m I ...
1
vote
0answers
14 views

Field of formal Laurent series over $F$.

Let $F$ be a field and let $K$ be the set of all functions $f\in F^\mathbb{Z}$ satisfying the condition that there exists an integer (perhaps negative) $n_f$ such that $f(i)=0$ for all $i<n_f$. ...
0
votes
1answer
14 views

Generating Random Variates from CDF

Suppose I am given a CDF of a distribution, given by $F(x) \propto x + x^2 + x^4 + x^7$. How do I generate a random variable from this distribution?
0
votes
1answer
14 views

Problem with injective functions on an explanation of the Birthday problem

The Wikipedia article on the Birthday problem gives an "abstract proof" of the problem, in which the birthday function $$ b:\mathcal{S} \mapsto \mathcal{B} $$ where $\mathcal{S}$ is the set of ...
0
votes
3answers
27 views

Why is the limit of this graph not 4.3?

I just took an online exam as part of a Precalculus course, and one of the problems on my test was as follows: Estimate $\lim \limits_{x \to 2} f(x)$ from the graph below. The available ...
1
vote
2answers
25 views

Log function solve for x

The function is defined by $y=f(x)=3e^{{1\over3}x+1}$ Solve for x in terms of y My answer: $x={ln({y\over3})-1\over3}$ Is this the correct way to go about this question?
0
votes
0answers
28 views

Balancing chemical equations using linear algebraic methods

I know there are already plenty of questions on this site regarding this topic but I am having difficulty with a particular chemical equation. I am trying to balance the following: $$ { C }_{ 2 }{ H ...
1
vote
0answers
20 views

Lagrangian in Navier-Stokes equations (steady incompresible)

First: Stokes problem (abstract analysis). Let $X$ and $M$ Hilbert spaces and $a:X\times X\longrightarrow\mathbb{R}$ and $b:X\times M\longrightarrow\mathbb{R}$ bilinear and bounded operators. We ...
0
votes
1answer
19 views

Equality of mixed partial/total derivative

I have $F = F(x_1(t),x_2(t),\dotsc,t)$, where $x_1,x_2,...$ are (unknown) functions of $t$. Everything is continuous, differentiable, etc. Is it possibly, necessarily, or never true that ...
0
votes
1answer
15 views

Divergence theorem and applying cylindrical coordinates

This time my question is based on this example Divergence theorem I wanted to change the solution proposed by Omnomnomnom to cylindrical coordinates. $$ \iiint_R \nabla \cdot F(x,y,z)\,dz\,dy\,dx = ...
-1
votes
2answers
45 views

Is $S_5$ isomorphic with the direct product $A_5 \times Z_2$?

Is $S_5$ isomorphic with the direct product $A_5 \times Z_2$? How i can check it?
0
votes
0answers
21 views

Real integral done by complex methods [duplicate]

$\int_{-\infty}^{\infty} \frac{cosx}{x^2+25} dx $ = $ \frac{\pi}{5e^5}$ Any ideas?
1
vote
0answers
11 views

Help with order of quantifiers

I have to say if the following are true or false and why. Can someone check to see if I understand how orders of quantifiers affect the meaning? For every integer x, there exists an integer y such ...
3
votes
1answer
22 views

Was this arithmetic Möbius/Mangoldt function ever used for something?

Let $n=\prod_k p_k^{c_k}$, with $p_k \in \mathbb P$ and $$ A(n)=\sum_{d|n} \mu(d)\Lambda(d), $$ with the $\mu$ Möbius function, which has values in {−1, 0, 1} depending on the factorization of n ...
0
votes
0answers
8 views

Koszul sign convention and symmetric group action on the graded n-th tensor product

Let $V_\bullet = (V_k)_{k \in \mathbb{Z}}$ and $W_\bullet = (W_k)_{k \in \mathbb{Z}}$ be two graded vector spaces on 0 caracteristic field. We define the tensor product of $V_\bullet$ by $W_\bullet$ ...
1
vote
2answers
22 views

Smallest convex polyhedron containing integer points of a cylinder

A cylinder has height $6$ and radius $3$. The centers of the two bases are $(0,0,0)$ and $(0,0,6)$. Find the volume of the smallest convex polyhedron that encloses every lattice point inside the ...
2
votes
1answer
36 views

Shortest Path in a maze

There is a maze, which is nothing but made of 2 parallel polylines, which looks like a zig zag road. We have to find the shortest path between the entrance and exit. Any ideas on how to proceed? Does ...
3
votes
5answers
63 views

What is $\limsup_{n\to\infty} \frac{p_{n+1}}{p_n}$?

Let $(p_n)_{n\in\mathbb N}$ be the strictly increasing sequence of all primes. I'm wondering what $$S:=\limsup_{n\to\infty} \frac{p_{n+1}}{p_n}$$ is. Is the result already known? By Bertrand's ...
0
votes
1answer
10 views

Making a basis from the Column Space of a Matrix in MatLab

Starting with matrix A whose entries are all zeros or ones, I want to make a new matrix B whose columns form a basis for the column space of A. I know that rref puts A in Gauss Jordan form and the ...
3
votes
4answers
31 views

Into how many equivalences classes does $R$ partition $\mathbb{Z}$?

Let $R= \{ (a,b) \in\mathbb{Z}\times\mathbb{Z} \mid a^2\equiv b^2 \bmod 7\}$. Into how many equivalences classes does $R$ partition $\mathbb{Z}$? My best guess is that there are $7$ equivalence ...
-9
votes
1answer
69 views

Help me out please with Algebra? [on hold]

OK. Listen, guys, maybe this question is unorthodox, and "it may be unclear to tell what I am asking" and "this is not a real question" and, obviously this question is "too broad". But please, let ...
0
votes
0answers
5 views

Infinite sets of rvs equal in distribution

Assume $\{\mathcal{L}(X_{k})\}_{k\in I}=\{\mathcal{L}(Y_{k})\}_{k\in I}$ for all finite $I\subset \mathbb{N}$ i.e. equal in all finite dimensional distributions. Then I want to show that ...
0
votes
2answers
18 views

Show that the projection map $p: \mathbb{R}^2 \to \mathbb{R}$, where $p(x,y) = x$, is open

I have to take an open set in $\mathbb{R}^2$ and show that it maps to an open set in $\mathbb{R}$. So let $A \times B$ be an open set in $\mathbb{R}^2$. I have to show that $A$ is an open set. By ...
4
votes
4answers
48 views

How do you factor $\frac{2x^2-x-1}{x^2-9} \cdot \frac{x+3}{2x+1}=$?

\begin{align} & \frac{2x^2-x-1}{x^2-9} \cdot \frac{x+3}{2x+1}= \frac{2x^2-x-1}{(x-3)(x+3)} \cdot \frac{x+3}{2x+1} \\[10pt] = {} & \frac{2x^2-x-1}{(x-3)} \cdot \frac{1}{2x+1}= ...
0
votes
1answer
20 views

Show that if $f$ is analytic on a domain $D$, and if $|f|$ is constant, then $f$ is constant.

If $f(z)=0$ for some $z\in D$ then since $0$ is a constant, $f'(z)=0$ on $D$. Also since $f$ is analytic, then by theorem $f(z)$ is constant. Here is where I get stock! If $f(z)\not=0$. I want to ...
1
vote
0answers
28 views

Find the man who will survive till the last

I got the in Arthur Engel's book:Problem-Solving Strategies in the Number Theory section(p-$137$ & prob-$166$) If you are condemned to die in Sikinia, you are put into Death Row until the last ...
3
votes
1answer
42 views

What does the notation $11\mid a^2$ mean?

What does the notation $11\mid a^2$ mean as used in this answer: http://math.stackexchange.com/a/948251/13230 I am trying to understand the proof that $\sqrt{11}$ is an irrational number, but am ...

15 30 50 per page