# All Questions

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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 $i<n_f$. ...
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### 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?
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### 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 ...
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### 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 ...
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### 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?
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### 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?
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### Real integral done by complex methods [duplicate]

$\int_{-\infty}^{\infty} \frac{cosx}{x^2+25} dx$ = $\frac{\pi}{5e^5}$ Any ideas?
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### 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 ...
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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 ...
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### 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 $W_\bullet$ ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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}= ...
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### 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 ...
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 ...
### 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 ...