content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Manipulating Sums
October 21st 2010, 11:59 AM #1
Hi there,
I am trying to solve the following problem. I have gotten a fair way into it, but the last steps elude me. Here is the problem:
Show that $\displaystyle\sum_{r=0}^n ^nC_r 2^r = 3^n$
So, we already know that $\displaystyle\sum_{r=0}^n ^nC_r =... | 4 | [
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-0.0390625,
0.0242919921875,
0.057373046875,
-0.11572265625,
-0.1025390625,
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0.05908203125,
0.0255126953125,
0.033447265625,
-0.03564453125,
0.007080... | 37,800 | 37800 | |
Double Integrals - Order of Integration
November 24th 2009, 10:05 AM #1
Double Integrals - Order of Integration
Find the area of A by evaluating the double integral
$\int\int_A \, dxdy$
where the region A is bounded by the curve $y=x^2-x$ and the line $y=2$
Is this correct:
$\int\int_A \, dxdy... | 4 | [
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0.06787109375,
0.0152587890625,
0.014892578125,
-0.007080078125,
-0.08984375... | 37,801 | 37801 | |
Fourier Coefficients
March 30th 2009, 06:21 PM #1
Newbie
Joined
Feb 2009
Posts
15
Fourier Coefficients
Find the Fourier coefficients of the piecewise continuousfunction
f(t) = {0 if t <= (less than or equal to) 0 or 1 if t > 0.}
I get why Ck is equal to 0. But why is Bk = 2/(k(pi)) when k is ... | 5 | [
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0.0771484375,
0.0322265625,
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0.01220703125,
-0.0556640625,
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-0.0712890625,
0.0264892578125,
-0.064453125,
... | 37,802 | 37802 | |
Curiosity about surface are
October 4th 2011, 01:03 AM #1
Curiosity about surface are
The volume of a sphere is
V = 4/3(pi)r^3
If you differentiate with respect to r you get
dV/dr = 4(pi)r^2
This is the surface area of the sphere.
How come this works so well for the sphere? It doesn't wor... | 5 | [
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0.11376953125,... | 37,803 | 37803 | |
Three group Kirman’s agent based model for financial markets | Physics of Risk
Three group Kirman’s agent based model for financial markets
As we have seen previously application of the original Kirman’s model enables reproduction of single power law spectral density [1]. While actual financial markets and sophisti... | 4 | [
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0.041259765625,
-0.090820312... | 37,804 | 37804 | |
The Schrödinger equation on a finite graph
January 2, 2011 by Qiaochu Yuan
One of the most important discoveries in the history of science is the structure of the periodic table. This structure is a consequence of how electrons cluster around atomic nuclei and is
essentially quantum-mechanical in nature. Most of it (... | 4 | [
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... | 37,805 | 37805 | |
Math Forum: Teacher2Teacher - Q&A #104
Factoring trinomials
T2T || FAQ |... | 4 | [
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0.0065612792... | 37,806 | 37806 | |
Math Forum Discussions
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Topic: Radius algorithm
Replies: 1 Last Post: Dec 8, 1996... | 4 | [
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-0.05419921875,
-0.0446777... | 37,807 | 37807 | |
Gordan's Theorem with $Ax=b$
up vote 2 down vote favorite
1
Is there a version of Gordan's Theorem in which $Ax=0$ has been replaced by $Ax=b$? That is, I want a condition (possibly including conditions on $A$) for when $Ax=b$ has a solution $x \neq 0$, for
$A \in \mathbb{R}^{m \times n}$ and $b \in \mathbb{R}_+^m \se... | 4 | [
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0.01708984375,
-0.0368652343... | 37,808 | 37808 | |
Prove that R is an equivalence relation. Determine the distinct equivalence classes.
November 17th 2013, 03:22 PM
MadSoulz
Prove that R is an equivalence relation. Determine the distinct equivalence classes.
Course: Foundations of Higher Math
A relation $R$ is defined on $\mathbb{Z}$ by x R y if $3x-7y$ is ... | 4 | [
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0.0400390625,
0.0045471... | 37,809 | 37809 | |
What is the domain of the "average operator"?
up vote 4 down vote favorite
1
I can try to define an averaging operator for functions, namely let $$A: D \subset L^\infty([0,\infty]) \to \mathbb{R}$$ by $$Af = \lim_{N\to\infty} \frac{1}{N}\int_0^N f(x)dx$$ whenever the limit
converges. My question is: is there any intui... | 4 | [
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0.040771484375,
... | 37,810 | 37810 | |
Partial derivative
November 9th 2009, 05:54 PM #1
Newbie
Joined
Oct 2008
Posts
4
Partial derivative
Find $\frac{dw}{ds}(-2,2)$ and $\frac{dw}{dt}(-2,2)$ if $w= xy -yz -5xz,$ where $x = st, y = e^{st}, z= t^2$
I'm confused since only two coordinates are given but the problem has 3 variables $x,y, z$
... | 4 | [
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-0.0732421875,
0.0... | 37,811 | 37811 | |
Distance From a Point to a Plane
Date: 03/31/98 at 16:57:06
From: Keir Larock
Subject: Distance between a point (x0,y0,z0) and the plane
ax+by+cz+d
Hi,
In my calculus class the other day, we went over the proof that the
distance from the point (x0,y0,z0) to the plane ax + by + cz = d is
|ax0 + by0 + cz0|/((a^... | 5 | [
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-0.05981445312... | 37,812 | 37812 | |
Does the function u match the differential equation
February 4th 2013, 06:17 AM #1
Junior Member
Joined
Oct 2010
Posts
29
Does the function u match the differential equation
Problem statement: If $u=\frac{1}{r}$ where $r=\sqrt{(x-a)^2+(y-b)^2+(z-c)^2}$, for $re0$ prove that $\bigtriangleup u \equiv \frac... | 5 | [
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Is it a field? set of real numbers in the form...
January 4th 2010, 11:48 PM #1
Is it a field? set of real numbers in the form...
Hi,
problem:
Let $Q(\sqrt{2})$ be the set of all real numbers of the form
$\alpha+\beta\sqrt{2}$, where $\alpha\;and\;\beta$ are rational.
(a) Is $Q(\sqrt{2})$ a fiel... | 5 | [
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Distribution of primes in smooth moduli
From Polymath1Wiki
(Difference between revisions)
Teorth Teorth
( (
Talk ... | 4 | [
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Planes and parametric equation
October 10th 2012, 06:09 AM #1
Junior Member
Joined
Sep 2012
From
sweden
Posts
61
Planes and parametric equation
Hello everybody
We have four planes:
x + y + z = 0
2x - y + z= 1
x + y - 2z = 2
x - 2y + 2z = 1
And we know that they have a li... | 5 | [
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Trace = Sum of eigen values - proof?
October 18th 2008, 06:04 PM #1
Newbie
Joined
Oct 2008
Posts
2
Trace = Sum of eigen values - proof?
Hi,
I recently learnt that trace (sum of diagonal elements) of a matrix is equal to the sum of its eigen values. I was wondering why this holds true. Could anyone e... | 5 | [
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0... | 37,817 | 37817 | |
Derivative of Log Function
October 31st 2009, 06:57 PM
dark-ryder341
Derivative of Log Function
Hey guys,
I'm really having some difficulty understanding how to find the derivative of log functions - I keep trying these homework questions and getting most of them wrong and I'm really starting to get
ann... | 5 | [
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0.1416015625,
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0.026733... | 37,818 | 37818 | |
Area, Volume of a Cone
Associated Topics || Dr. Math Home || Search Dr. Math
Area, Volume of a Cone
Date: 6/4/96 ... | 4 | [
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The Backpropagation Algorithm
Next: Issues in ANN Learning Up: Artificial Neural Nets Previous: Multilayer Nets, Sigmoid Units
1. Propagates inputs forward in the usual way, i.e.
□ All outputs are computed using sigmoid thresholding of the inner product of the corresponding weight and input vectors.
... | 4 | [
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A question about the construction of Francia flip
up vote 3 down vote favorite
3
Here is the construction.
Start with $U$ a normal variety of dimension 3 with a unique singular point locally isomorphic to the quotient of $(x, y, z) \to (-x, -y, -z)$. Also assume we have a small contraction which contracts
a smooth ra... | 5 | [
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M
Lab 4 -- MANOVA on SPSS
A Multivariate Analysis of Variance (MANOVA) is often used as a multivariate analog of the ANOVA, but when there are multiple dependent variables. (Note that an ANOVA can handle multiple independent
variab... | 4 | [
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Another "mixed partials" question
September 27th 2011, 02:47 PM
s3a
Another "mixed partials" question
The question and my work are both attached as PDF files.
Basically, in my work I only found the partial derivatives to be different and therefore did not proceed because of this but apparently this is wrong... | 5 | [
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0.00411987304687... | 37,823 | 37823 | |
Quick probability question
November 5th 2009, 11:59 AM #1
Newbie
Joined
Nov 2009
Posts
1
Quick probability question
Hello everyone,
I'm finishing up some of my stat HW right now and I have hit a wall. There are two questions that are on the tip of my tongue and I can't answer them! It's maddening!
... | 4 | [
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-0.1... | 37,824 | 37824 | |
Matrix problem, please help!
January 14th 2010, 05:19 AM #1
Newbie
Joined
Aug 2009
Posts
21
I have the following problem:
I have 2 3x3 matrices, on called M and the other N^-1 (this one has a few unknown numbers, k). I am asked to find the following:
(MN)^-1. Now we have NOT learned how to do th... | 5 | [
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0.053466796875,
-0.... | 37,825 | 37825 | |
Proof of a Theorem in the paper "Construction of bundles on P^n" by Horrocks
up vote 3 down vote favorite
1
I am trying to understand Horrocks's construction of vector bundles. However I have been stuck on the proof the first theorem in the paper.
In the paper, a trivial bundle is a direct sum of Hopf bundles $\mathc... | 4 | [
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... | 37,826 | 37826 | |
Characteristic functions
May 2nd 2010, 04:27 PM #1
Member
Joined
Jan 2010
Posts
104
Characteristic functions
Given that E(e^(itx)) (the characteristic function of a Cauchy rv)=e^(-abs(t)), use this fact to find the pdf for X bar for all n.
I have no idea how to do this, and it was on the test. I got... | 5 | [
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-0.052978515625,
-0.05126... | 37,827 | 37827 | |
Implicit Differentiation Problem
February 23rd 2006, 02:04 PM #1
Newbie
Joined
Dec 2005
Posts
14
Implicit Differentiation Problem
Consider the curve given by X^2+4y^2=7+3xy
a) show that dy/dx=3y-2x/8y-3x
b) show that there is a point P with x-cooridnate 3 at which the line tangent to the curve at... | 5 | [
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-0.034912109375,
-0.04... | 37,828 | 37828 | |
Question regarding a Lemma on axiom of choice
January 2nd 2012, 03:59 AM #1
Newbie
Joined
Jan 2012
Posts
7
Hello all,
I am currently reading a book on set theory "Joy of Sets" by Keith Delvin. In page 58 he proves a lemma which is stepping stone for proving that axiom of choice(AC) and 'Every set ca... | 5 | [
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-0.0859375,
-0.006896972... | 37,829 | 37829 | |
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Here's the question you clicked on:
kirk.freedman Group Title
Simplify (sqrt x... | 4 | [
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0.022216796875,
-0.015869140625,
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0.01904296875,
-0.0493164062... | 37,830 | 37830 | |
The Marlins and their Hitting Streak: What are the Odds?
Before anyone gets too worked up over this 14-game streak by the Marlins of 10 or more hits, let's remember that the last team to do it -- the 1937 St. Louis Browns -- finished with the
worst record in the majors that season: 46-108. You're correct ... | 4 | [
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... | 37,831 | 37831 | |
Integration
December 11th 2010, 09:40 AM #1
Junior Member
Joined
Oct 2010
Posts
28
Hi,
I am still bad in integration, I do not know which way to choose, integration by part or substination.
integration x^2cos(x)
So I shoul do like this
integration x^2cos(x)=x^2 (-sinx)-integration2x (-sinx... | 5 | [
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||x-y||+||y-z||=||x-z|| iff y= ax + (1-a)z
September 22nd 2009, 02:39 AM #1
Newbie
Joined
Sep 2009
Posts
7
Dear mathematician,
I need to show that:
||x-y||+||y-z||=||x-z||
if and only if
y= ax + (1-a)z with 0<=a<=1
In other words, if x,y and z are on the same line, that relation b... | 5 | [
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hard time with graph problems
June 11th 2007, 05:53 PM #1
Newbie
Joined
Jun 2007
Posts
24
hard time with graph problems
Identify the exponential function of the form
f (x) = a(2 x ) + b whose
graph is shown in the figure.
a. f (x) = 3(2 x )
b.
f (x) = 2(2 x ) − 4
d. ... | 4 | [
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counting inverses of finite group
June 21st 2011, 09:22 AM #1
Member
Joined
Oct 2010
From
Mumbai, India
Posts
203
counting inverses of finite group
Hi
I am using Charles Pinter's book on abstract algebra . I have to prove that
for any finite group G, if we define the set
$S=\{x\in G : x... | 4 | [
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Minimum Investment and Number of Assets Portfolio Cardinality Constraints
October 19, 2011
By systematicinvestor
The Minimum Investment and Number of Assets Portfolio Cardinality Constraints are practical constraints that are not easily incorporated in the standard mean-variance optimization framework. To help
us im... | 4 | [
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-0.060546875... | 37,836 | 37836 | |
Newton's Cooling
January 15th 2006, 06:11 AM
jacs
Newton's Cooling
Hi, I have tried this many times and just can't seem to figure it out.
A body, initially at room temperature 20C, is heated so that its temperature would rise by 5C/min if no cooling took place. Cooling does occur in accordance with Newton's... | 5 | [
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SU(2) spin 1/2 functions
April 27th 2006, 06:28 AM #1
SU(2) spin 1/2 functions
It's been a while since I posted a Physics question for y'all to ponder so here's another one.
One of the deficiencies in learning Physics is that no one seems to want to explicitly write down SU(2) invariant functions for spin 1/... | 4 | [
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0.1... | 37,838 | 37838 | |
A tricky equation of the first order
March 7th 2011, 10:29 AM #1
Newbie
Joined
Mar 2011
From
Karlskrona, Sweden
Posts
7
A tricky equation of the first order
My teacher gave me a "bonus" assignment the other day, and I've been racking my brain trying to solve it. Here it is:
$xy'(ln(\frac{x}{y}) ... | 5 | [
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Real Analysis - Sequences 3
d.) Assuming this sequence is in the metric space $(M,d)$, if $\{b_n\}$ converges, then it is bounded. ( $\exists x_0\in M, R\in\mathbb{R}$ such that $d(x_0,b_n)<R~\forall n$) So $d(a_n,x_0)-R<d
(a_n,b_n)~\forall n$. (Triangle Inequality) But since $\{a_n\}$ is unbounded, so is $d(a_n,x_0)$,... | 4 | [
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0... | 37,840 | 37840 | |
Integral equation
From Encyclopedia of Mathematics
2010 Mathematics Subject Classification: Primary: 45-XX [MSN][ZBL]
An equation containing the unknown function under the integral sign. Integral equations can be divided into two main classes: linear and non-linear integral equations (cf. also Linear integral
equati... | 4 | [
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Temperature and Pressure Gradient in Ideal Gas
Introduction
Consider a narrow horizontal tube. The curved surface made with perfect insulator. The flat faces made with perfect heat conductor. One end of the tube is maintained at 100 oC and the other end is
maintained at 0 oC. Once the steady state is attained, heat... | 5 | [
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Sir Isaac Newton – Book 1: Of The Motion of Bodies: Section 1: Of the method of first and last ratios of quantities, by the help whereof we demonstrate the propositions that follow
SECTION I
Of the method of first and last ratios of quantities, by the help whereof we demonstrate the propositions that follow
LEMMA I
Q... | 4 | [
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0.03... | 37,843 | 37843 | |
[SOLVED] Surface integrals and flux
September 24th 2008, 10:15 AM #1
[SOLVED] Surface integrals and flux
1)
$S: x^2 + 4y^2 = 4$, $0 \leq z \leq 1$. Calculate the flux of the vector field $\overline{A}(x,y,z) = \left(\frac{-6x}{x^2+y^2},\frac{-6y}{x^2+y^2}, z+1\right)$ out through the z-axis.
2)
$S: z... | 5 | [
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-0.06494140625,
-0.060... | 37,844 | 37844 | |
antiderivative of 7^cost sint dt
∫(from 0 to pi/2) 7^cost sint dt
i know that it is a^u du
but sin needs to be negative so I tried this:
-∫(from 0 to pi/2) 7^cost (-sint) dt
then made u=cost and du= -sint
so: ∫ 7^u du= 7^u/ ln7= 7^cost /ln7
and when i plug in pi/2 i get 1/ln7
but the ans... | 5 | [
0.0007171630859375,
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0.109375,
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... | 37,845 | 37845 | |
Building a scale by diagonalization and transfinite induction
up vote 2 down vote favorite
I'm asking a question following the reading of Set Theory from Jech (page 126).
For the record, a $\kappa$-sequence of functions $\langle f_\alpha : \alpha < \kappa\rangle$ is called a $\kappa$-scale if $f_\beta < f_\alpha$ whe... | 4 | [
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-0.0079345703125,
-0.048... | 37,846 | 37846 | |
equation of plane tangent
March 11th 2011, 04:51 AM
maximus101
equation of plane tangent
Let S be the surface parameterised by
$r(u,v):=(e^ucosv,u,e^usinv), <br /> u\in\Re, v\in[0,2\pi]$
(i) Find the equation of the plane tangent to S at r(u,v).
(ii) At what points is the tangent plane to S parallel ... | 4 | [
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0.041748046875,
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-0.056396484375,
-0.059326171875,
-0.07666015... | 37,847 | 37847 | |
Smallest integer not divisible by integers in a finite set
up vote 7 down vote favorite
Hello all, if $a_1,a_2, \ldots a_t$ are $t$ integers $\geq 2$, the set $G(a_1,a_2, \ldots a_t)=\lbrace N \geq 1 |$ In any sequence of $N$ consecutive integers there is at least one not divisible by
any of $a_1,a_2, \ldots a_t\rbrac... | 5 | [
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0.091796875,
-0.021... | 37,848 | 37848 | |
Sum of reciprocals of squares of integers congruent to 1 mod 3 ?
up vote 2 down vote favorite
What is the value of $$\sum_{i=0}^\infty \frac{1}{(3i+1)^2} ?$$
Methods for other $a\pmod p$ would be helpful, i.e., the value of $$\sum_{i=0}^\infty \frac{1}{(pi+a)^2} .$$
Thanks in advance Herman :+)
nt.number-theory
... | 4 | [
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-0.002868652... | 37,849 | 37849 | |
Rational Expressions
March 2nd 2009, 04:15 PM #1
Newbie
Joined
Aug 2008
From
San Ramon, CA
Posts
17
Rational Expressions
$\frac {y^2}{y^2-9} + \frac {9-6y}{y^2-9}$
$\frac {3x}{x^2-4} + \frac {5x}{x^2+x-2} - \frac {3}{x^2-4x+4}$
Complex Fraction: $\frac {x+2}{x-2}- \frac {x-2}{x+2} over \fra... | 4 | [
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0.03857421875,
-0.0703... | 37,850 | 37850 | |
Poincare's Universe: simple Calculus question
April 29th 2010, 04:36 PM #1
Newbie
Joined
Apr 2010
Posts
4
Poincare's Universe: simple Calculus question
I have been reading "Prelude to Mathematics" by W.W. Sawyer. In it he describes Poincare's hypothetical universe.
This universe is contained in the ... | 5 | [
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-... | 37,851 | 37851 | |
Special values of L-functions as periods
up vote 21 down vote favorite
9
If $M$ is a pure motive over $\mathbb{Q}$, one cas define its $L$-function $L(M,s)$ which conjecturaly is a meromorphic function over $\mathbb{C}$ with finitely many poles. For example, when $M=\
mathbb{Q}$ is the trivial motive, $L(\mathbb{Q},s)... | 5 | [
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... | 37,852 | 37852 | |
Solving Trigonometry
November 20th 2011, 08:20 PM
BlackOut14
Solving Trigonometry
1) When a pendulum 0.5m long swings back and forth, its angular displacement Ɵ from rest position, in radians is given by Ɵ=1/4sin((pi/2)t), where t is the time, in seconds. At what time(s)
during the first 4 s is the pendulum ... | 4 | [
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-0.028564453125,
0.050048828125,
0.06982421875,
0.00... | 37,853 | 37853 | |
Work Out Percentages - PowerPoint
SATs Mathematics Preparation
Number, Algebra and Shape and Space
Questions
Levels 3 - 6 in Yellow
Levels 7 - 8 in Red
Reading Scales
• Remember to check what one
mark on the scale is –
• If there are 5... | 4 | [
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0.10546875,
0.0087890625,
-0.004669189453125,
-0.01574707... | 37,854 | 37854 | |
deductive geometry (2)
October 30th 2009, 02:52 AM #1
Senior Member
Joined
Jan 2009
Posts
381
deductive geometry (2)
Vertices B and C of the triangle ABC lie on the circumference of a circle . AB and AC cut the circumference of the circle at X and Y respectively . Show that angle CBX +angle CYZ =180
... | 4 | [
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0.0791015625,
0.0218505859375,
0.0030670166015625,
-0.0027008056640625,
0.0196533203125,
0.01104736328125,
0.037109375,
0.010498046875,
0.01116943359375,
0.044677734375,
-0.0888671875,
0.08349609375,
0.027099609375,
0.04150390625,
0.0213623046875,
-0.046875,
0.0022... | 37,855 | 37855 | |
a dilogarithm identity: known or new?
up vote 4 down vote favorite
2
I was playing around with dilogarithms and numerically found the following dilogarithm identity:
$$\text{Li}_2\left(\frac{2 m}{m^2+m-\sqrt{((m-3) m+1) \left(m^2+m+1\right)}-1}\right)$$ $$-\text{Li}_2\left(\frac{m^2+m-\sqrt{((m-3) m+1) \left(m^2+m+1\... | 5 | [
-0.08349609375,
-0.057861328125,
-0.0189208984375,
0.044921875,
0.005523681640625,
-0.0203857421875,
-0.048828125,
0.035888671875,
0.010009765625,
-0.0419921875,
0.0546875,
-0.0296630859375,
0.010986328125,
0.0027923583984375,
-0.035400390625,
0.06689453125,
0.041259765625,
0.04296... | 37,856 | 37856 | |
GMAT question
March 26th 2011, 10:43 AM #1
Newbie
Joined
Mar 2011
Posts
3
GMAT question
I put this one under the high school level because it really shouldn't be that hard, but it has me stumped. Any advice?
Question: what is the value of m in the following expression?
(1/5)^m * (1/4)^18 = 1/(2... | 4 | [
0.0250244140625,
0.043212890625,
0.01416015625,
0.03466796875,
-0.016357421875,
-0.06787109375,
0.00982666015625,
0.0361328125,
-0.03662109375,
0.049072265625,
0.004180908203125,
-0.08251953125,
0.07373046875,
0.0869140625,
-0.016845703125,
0.193359375,
-0.02392578125,
0.0532226562... | 37,857 | 37857 | |
Differential equation check?
May 19th 2009, 06:25 AM
dankelly07
Differential equation check?
COuld someone check this out for me and see if If done this right..
I'm worried incase I went wrong somewhere...
$<br /> \begin{gathered}<br /> 4\frac{{d^2 y}}<br /> {{dx^2 }} + 8\frac{{dy}}<br /> {{dx}} + 3y = ... | 5 | [
-0.06396484375,
-0.00970458984375,
-0.020751953125,
-0.0264892578125,
-0.0037994384765625,
0.00408935546875,
-0.01519775390625,
0.0120849609375,
0.0191650390625,
-0.021240234375,
0.1025390625,
-0.09765625,
-0.0223388671875,
0.044189453125,
0.03466796875,
0.010498046875,
-0.0659179687... | 37,858 | 37858 | |
Computing Competing Probabilities
How do we deal with games having more points? For this we use recursion. Suppose again that both teams shoot only three point shots under "loser-takes-out." Let probAwin(Aposs, x, y) mean "the
probability that A wins when A has possession, A has x points to win, and B has y points to w... | 5 | [
-0.027587890625,
-0.028076171875,
-0.052490234375,
-0.12060546875,
-0.0045166015625,
0.044677734375,
0.1318359375,
-0.016357421875,
0.1328125,
0.0712890625,
-0.02001953125,
-0.0242919921875,
0.07373046875,
0.0439453125,
0.12890625,
0.06396484375,
-0.026123046875,
-0.03564453125,
... | 37,859 | 37859 | |
11. Math module - Fraction and Percentege
MEP Practice Book SA11
11 Fractions and
Percentages
11.1 Fractions, Decimals and Percentages
1. Express each of the following percentages as a fraction in its lowest terms.
(a) ... | 4 | [
0.01092529296875,
0.08642578125,
0.000331878662109375,
-0.064453125,
-0.0033721923828125,
-0.0155029296875,
0.031982421875,
0.0869140625,
-0.076171875,
0.0556640625,
0.00604248046875,
-0.0693359375,
0.049072265625,
0.072265625,
0.01165771484375,
0.0634765625,
0.049560546875,
0.1035... | 37,860 | 37860 | |
Set theory/ Cardinal Help
February 14th 2010, 12:32 PM #1
Newbie
Joined
Feb 2010
Posts
4
Set theory/ Cardinal Help
If f : A-B is the given function, the graph f is the subset of AcrossB consisting of all (a,f(a)).
1. Prove that a-(a,f(a)) is a one-to-one map of A onto the graph of f.
2. Let D a... | 5 | [
0.05859375,
0.08984375,
0.057373046875,
-0.10302734375,
-0.00531005859375,
0.0439453125,
0.07080078125,
0.07080078125,
-0.02197265625,
0.01708984375,
-0.05517578125,
-0.03271484375,
0.042236328125,
-0.07470703125,
0.051513671875,
0.00433349609375,
0.0181884765625,
-0.09521484375,
... | 37,861 | 37861 | |
23: Calculus
Chapter 23: Calculus
This chapter covers J operators for differentiation and integration. It covers
• The conjunction d. which differentiates and integrates analytically, that is, it transforms expressions denoting functions into expressions denoting functions.
• The conjunction D. which differenti... | 5 | [
-0.039306640625,
-0.00634765625,
0.01397705078125,
-0.016357421875,
-0.0712890625,
-0.0294189453125,
-0.0302734375,
-0.0206298828125,
0.0281982421875,
0.0177001953125,
0.0198974609375,
0.052734375,
0.0030059814453125,
0.0279541015625,
0.044677734375,
-0.029541015625,
-0.05224609375,
... | 37,862 | 37862 | |
Please help with these function problems!
November 8th 2006, 06:52 PM #1
Newbie
Joined
Oct 2006
Posts
24
Please help with these function problems!
Hey guys any help I could get on these few questions would be amazing. Thanks!
1) Find the average rate of change of the function f(x)=e^x - e^(-x) as x ... | 5 | [
-0.01495361328125,
-0.00115203857421875,
0.0306396484375,
-0.0255126953125,
-0.005157470703125,
-0.059814453125,
-0.0286865234375,
0.0703125,
-0.04345703125,
0.08203125,
0.06640625,
-0.0546875,
0.050048828125,
-0.038330078125,
-0.00665283203125,
-0.055419921875,
-0.11669921875,
-0.... | 37,863 | 37863 | |
Expressing a Fraction as a Decimal
Associated Topics || Dr. Math Home || Search Dr. Math
Expressing a Fraction as a Decimal
... | 4 | [
0.00286865234375,
0.06201171875,
0.02685546875,
0.04296875,
-0.055419921875,
0.0179443359375,
-0.0380859375,
0.054443359375,
0.048583984375,
0.016357421875,
-0.03466796875,
-0.1044921875,
-0.0142822265625,
0.07666015625,
0.04150390625,
-0.04296875,
-0.03759765625,
0.080078125,
-0... | 37,864 | 37864 | |
[SOLVED] Method of differences problems
February 11th 2009, 02:29 AM #1
MHF Contributor
Joined
Sep 2008
From
West Malaysia
Posts
1,261
[SOLVED] Method of differences problems
If $f(r)=\frac{1}{r^2}$ , simpify f(r)-f(r+1) . Hence , find the sum of the first n terms of the series
$<br /> \frac{3}{... | 5 | [
-0.02783203125,
0.052490234375,
0.01483154296875,
0.041748046875,
-0.009765625,
0.0169677734375,
-0.13671875,
0.054443359375,
-0.01318359375,
0.00360107421875,
-0.08984375,
-0.07177734375,
-0.0189208984375,
0.015869140625,
-0.052490234375,
-0.08447265625,
0.040771484375,
-0.0400390... | 37,865 | 37865 | |
go
Bogobogosort
Introduction
Bogobogosort is a sorting algorithm based on the popular bogosort algorithm.
Algorithm Description
To understand bogobogosort, it is necessary to first have an understanding of the finer points of bogosort.
Bogosort can be described as follows:
1. Check if your list of number is sort... | 4 | [
0.032958984375,
0.0025177001953125,
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0.08642578125,
-0.0228271484375,
-0.0062255859375,
-0.12109375,
-0.042724609375,
0.005096435546... | 37,866 | 37866 | |
Introducing 'propagate'
Introducing ‘propagate’
With this post, I want to introduce the new ‘propagate’ package on CRAN.
It has one single purpose: propagation of uncertainties (“error propagation”). There is already one package on CRAN available for this task, named ‘metRology’ (http://cran.r-project.org/web/packages... | 5 | [
-0.08154296875,
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0.0286865234375,
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0.0888671875,
-0.016845703125,
-0.0223388671875,
-0.039306640625,
0.03271484375,
0... | 37,867 | 37867 | |
Centre of gravity of a right angled triangle?! is this right?
June 3rd 2009, 03:55 AM #1
Newbie
Joined
May 2009
Posts
17
Centre of gravity of a right angled triangle?! is this right?
If I have a triangle with the coodinates A(0,0) B (30,0) and C (30,40)
Is the centre of gravity 1/3 of the base and 1... | 4 | [
-0.0157470703125,
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0.0247802734375,
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0.0888671875,
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0.0224609375,
0.0157470703125,
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0.09130859375,
0.09521484375,
0.11279296875,
-0.0634765625,
0.0390625,
... | 37,868 | 37868 | |
Basic identity proving
April 5th 2009, 01:10 PM #1
Newbie
Joined
Apr 2009
Posts
1
Basic identity proving
Hi,
I just started with trig and trig proofs are like really hard for me, I just can't seem to understand them. This is the first question in my workbook..
$\frac{\cot \theta -1}{\tan \theta... | 4 | [
-0.1279296875,
0.0167236328125,
0.046875,
0.039306640625,
0.015869140625,
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0.08154296875,
-0.01324462890625,
0.07666015625,
0.0284423828125,
0.057861328125,
-0.09326171875,
0.0101318359375,
0.04541015625,
0.01165771484375,
-0.0108642578125,
-0.037841796875,
0.04101562... | 37,869 | 37869 | |
Joseph-Louis Lagrange
Back to the front page
... | 4 | [
-0.0400390625,
0.058837890625,
0.0272216796875,
0.0036773681640625,
-0.06982421875,
0.0023956298828125,
-0.006591796875,
0.11181640625,
-0.041748046875,
0.0390625,
0.0230712890625,
-0.002593994140625,
0.01409912109375,
-0.0191650390625,
-0.042724609375,
0.0272216796875,
-0.0495605468... | 37,870 | 37870 | |
Vector Arithmetic for Physics Help
By
Stan Gibilisco
— McGraw-Hill Professional
Updated on Apr 25, 2014
Introduction
A vector has two independently variable properties: magnitude and direction. Vectors are used commonly in physics to represent phenomena such as force, velocity, and acceleration. In contrast, real... | 4 | [
-0.013671875,
-0.043701171875,
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0.08203125,
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-0.06689453125,
... | 37,871 | 37871 | |
How many well orderings of $\aleph_0$ are there?
up vote 8 down vote favorite
1
What is known about the set of well orderings of $\aleph_0$ in set theory without choice? I do not mean the set of countable well-order types, but the set of all subsets of $\aleph_0$ which (relative
to a pairing function) code well orderi... | 5 | [
0.0155029296875,
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0.059814453125,
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0.04345703125,
0.040771484375,
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0.043701171875,
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0.0230712890625,
-0.0069580078125,
-0... | 37,872 | 37872 | |
Power Series Representation
June 3rd 2013, 04:24 PM #1
Power Series Representation
I need help finding the power series representation of ln(root(4-x^2)).
I have gathered that I pull out the root 4, so I'll have ln(2)+something, but I'm not sure where to go from there.
I know that ln(1-x) is -x^k/k, but... | 5 | [
0.08935546875,
-0.0634765625,
-0.026611328125,
0.045654296875,
-0.0296630859375,
-0.09228515625,
-0.05126953125,
0.0106201171875,
0.103515625,
0.04052734375,
-0.015625,
-0.00390625,
-0.0380859375,
0.02001953125,
-0.07275390625,
0.09423828125,
0.0126953125,
-0.041015625,
-0.016967... | 37,873 | 37873 | |
Need help for Proving Quadratic Equations
August 27th 2009, 10:51 PM #1
Junior Member
Joined
Aug 2009
Posts
62
Hello people,
How do i prove these?
1) If a, b and c are real, show that the roots of the following equations are real:
(i) (b+c)x^2 - (a + b + c)x + a = 0
(ii) (a + b)(x^2 + 5... | 4 | [
-0.1123046875,
-0.00811767578125,
0.029296875,
0.004638671875,
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0.0546875,
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0.0137939453125,
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0.01611328125,
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0.0177001953125,
0.05615234375,
-0.030029296875,
0.0216064453125,
-0.0213623046875,
-0... | 37,874 | 37874 | |
Radical Equations Dimensions Problem
September 20th 2009, 03:03 PM #16
$(\sqrt{x+1} + 2)^2 = (\sqrt{3x+1})^2$
$(x+1) + 4\sqrt{x+1} + 4 = 3x+1$
combine like terms on the left side ...
$4\sqrt{x+1} + x + 5 = 3x + 1$
$4\sqrt{x+1} = 2x - 4$
divide all terms by 2 ...
$2\sqrt{x+1} = x - 2$
... | 4 | [
-0.0194091796875,
-0.0284423828125,
0.037109375,
0.10107421875,
-0.0034637451171875,
0.00060272216796875,
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0.0191650390625,
0.0869140625,
-0.061279296875,
0.061767578125,
0.00848388671875,
0.0233154296875,
0.103515625,
-0.06591796875,
0.0233154296875,
-0.048828125,
0... | 37,875 | 37875 | |
More Triangles
April 30th 2007, 05:58 PM #1
Please help me solve this!
Prove: If an isoceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle.
Given: Triangle ABC is isosceles; Line CD is the altitude to base Line AB
To Prove: Line CD bisects Angle ACB... | 4 | [
-0.07568359375,
0.12890625,
0.0306396484375,
-0.0086669921875,
-0.05078125,
0.01373291015625,
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0.08154296875,
0.0262451171875,
0.05615234375,
0.022705078125,
-0.09765625,
0.03271484375,
-0.0057373046875,
0.055908203125,
0.04931640625,
-0.044189453125,
0.0224609375,
... | 37,876 | 37876 | |
Amortization - LOGS!! Help
September 12th 2008, 01:02 AM #1
Newbie
Joined
Sep 2008
Posts
1
Amortization - LOGS!! Help
I'm actually working on an amortization problem.
I am trying to solve for n. I have all of the other values.
In order to do this I end up using logs (i think...)
A/P/r = (... | 4 | [
-0.048583984375,
0.053466796875,
-0.0361328125,
0.047119140625,
0.02880859375,
-0.08740234375,
0.06201171875,
-0.0152587890625,
0.050537109375,
0.058837890625,
-0.03515625,
0.030517578125,
-0.02978515625,
0.138671875,
0.025634765625,
0.006439208984375,
-0.08251953125,
0.00988769531... | 37,877 | 37877 | |
Functions: Newton's Quotient
July 27th 2010, 12:04 PM #1
Newbie
Joined
Jul 2010
Posts
1
Functions: Newton's Quotient
I'm doing some math over the summer for fun. I have a very weak background in math, but have come around and thoroughly enjoy it. Can someone explain what is going on with this problem inv... | 5 | [
-0.1044921875,
-0.004852294921875,
0.0289306640625,
-0.051513671875,
0.0419921875,
0.04541015625,
-0.11328125,
-0.0146484375,
0.028076171875,
0.02685546875,
0.1201171875,
-0.0927734375,
0.026123046875,
0.0013885498046875,
-0.007354736328125,
0.08154296875,
-0.0238037109375,
-0.0429... | 37,878 | 37878 | |
prove that a^2sin(B-C) =
prove that: $a^{2}sin\left(B-C\right) = \left(b^{2} - c^{2}\right)sinA$ where $a,b,c$ are sides of triangle and $A,B,C$ are the corresponding angles
I'll use the sine and cosine rules. $a^2\sin(B-C)=a^2(\sin B\cos C-\sin C\cos B)=$ $=a^2\left(\frac{b}{2R}\cdot\frac{a^2+b^2-c^2}{2ab}-\frac{c}{2... | 4 | [
-0.05810546875,
0.040771484375,
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0.019287109375,
0.04345703125,
0.0174560546875,
-0.0281982421875,
-0.044921875,
-0.052978515625,
0.06494140625,
0.02880859375,
0.0361328125,
0.033203125,
0.030029296875... | 37,879 | 37879 | |
Solve the following...I keep getting strange answers
May 26th 2012, 02:22 AM
fcabanski
Solve the following...I keep getting strange answers
$x + \frac{7-2x}{x-2}<= \frac{5x+7}{x-2}$
Solve and express solution as a graph and in interval or set notation.
The solutions are x=0 or x=9. (That's given.)
... | 4 | [
-0.043701171875,
-0.002655029296875,
0.08447265625,
0.01025390625,
0.03466796875,
0.00701904296875,
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0.1005859375,
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0.037109375,
-0.08056640625,
0.007293701171875,
0.0888671875,
0.05126953125,
-0.0263671875,
0.0023345947265625,
-0.11... | 37,880 | 37880 | |
Questions regarding solving an ODE
January 22nd 2011, 07:11 AM #1
Newbie
Joined
Jan 2011
Posts
6
Questions regarding solving an ODE
Is it possible to use Euler's method to numerically approximate the solution of this system of ODEs:
dx/dt = -y + x(p - x^2 - y^2)
dy/dt = x + y(p - x^2 - y^2)
... | 4 | [
-0.056884765625,
-0.033447265625,
0.055419921875,
0.0361328125,
0.003173828125,
-0.052978515625,
0.0013275146484375,
0.021484375,
-0.06689453125,
-0.039794921875,
0.0478515625,
0.09130859375,
-0.04638671875,
0.03662109375,
0.019775390625,
-0.040283203125,
-0.049072265625,
-0.061767... | 37,881 | 37881 | |
Proof or disproof the following
April 2nd 2011, 05:35 AM
gordo151091
Proof or disproof the following
I have been asigned this problem in class.
$C\subseteq A \Rightarrow (A \cup B) \cap C \subseteq A$
Can you aid me in how should i start. I thought of puting it in terms of propositional logic, then pro... | 4 | [
-0.01611328125,
0.0107421875,
0.042236328125,
0.01165771484375,
-0.01025390625,
0.07080078125,
0.0361328125,
0.0419921875,
-0.04248046875,
0.06689453125,
-0.06494140625,
-0.07470703125,
0.0262451171875,
0.050537109375,
0.06298828125,
0.039306640625,
-0.007415771484375,
-0.027221679... | 37,882 | 37882 | |
Formula for Calculating original quantities from a price
September 16th 2010, 01:02 AM #1
Newbie
Joined
Sep 2010
Posts
3
Formula for Calculating original quantities from a price
Hi I need a formula to solve the following problem, unfortunately my maths is pretty basic.
Item A = 0.23 per unit up to a... | 4 | [
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... | 37,883 | 37883 | |
Working with expressions.
March 11th 2011, 09:44 AM #1
Newbie
Joined
Feb 2011
Posts
24
Working with expressions.
Please, if anyone could solve and explain to me the process of solving these two problems I would be extremely grateful. (It's not about the result, I really need to know HOW to do this, so If... | 4 | [
-0.031494140625,
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-0.022216796875,
0.057373046875,
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0.043701171875,
0.06689453125,
0.11279296875,
-0.016357421875,
-0.0375... | 37,884 | 37884 | |
formal power series convergence
up vote 22 down vote favorite
15
I have spent some time using gp-pari. There is, of course, a formal power series solution to $ f(f(x)) = \sin x.$ It is displayed, below, identified by the symbol $g$ because I am not entirely sure
whether it is a function of anything. On the other hand,... | 5 | [
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0.01495361328125,
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-0.0732421875,
0.07470703125... | 37,885 | 37885 | |
algebra equations
March 13th 2008, 12:41 PM
miramontes
algebra equations
Hi
I need help on these problems, these are practice problems for my final because the questions will be similar to these but I need help with these.
I am lost.
Any help would be greatly appreciated (Speechless)(Thinking)(Cryi... | 4 | [
0.01177978515625,
0.0654296875,
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0.005462646484375,
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... | 37,886 | 37886 | |
Ratio of consecutive divisors and average
up vote 3 down vote favorite
Let $2\leq d_1 < d_2,...,d_l < n$ be all the proper nontrivial divisors of $n$. I like to understand how much these divisors deviates from each other. Here are two questions in this regard:
(1) What is the maximum of the set $\{d_i/d_{i-1}: 1\leq... | 4 | [
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0.00897216796875,
0.024169921875,
0.01300048828125,
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0.055419921875,
... | 37,887 | 37887 | |
A Haskell monad for infinite search in finite time
I show how monads in Haskell can be used to structure infinite search algorithms, and indeed get them for free. This is a follow-up to my blog post Seemingly impossible functional programs. In the
two papers Infinite sets that admit fast exhaustive search (LICS07) and... | 4 | [
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0.025146484375,
0.019775390625,
-0.0054931640625,
0.0659... | 37,888 | 37888 | |
Multiplicativity of the Phi Function.
January 3rd 2006, 02:40 PM #1
Global Moderator
Joined
Nov 2005
From
New York City
Posts
10,616
Thanks
9
Multiplicativity of the Phi Function.
It is a classic and fundamental result that the $\phi$function is multiplicative. Meaning,
$\phi (nm)=\phi (n)\ph... | 4 | [
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0.020751953125,
-0.00160217... | 37,889 | 37889 | |
The idea behind Green's theorem
When $\dlc$ is an oriented simple closed curve, the integral \begin{align*} \dlint \end{align*} represents the circulation of $\dlvf$ around $\dlc$. If $\dlvf$ were the velocity field of water flow,
for example, this integral would indicate how much the water tends to circulate around th... | 4 | [
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0.061767578125,
-... | 37,890 | 37890 | |
derivates
February 13th 2006, 12:12 PM
lilheadbaby1
derivates
Find the derivate of p(x)= (3x)^1/2
using the alternative formula for the derivate
f ' (x)= lim f(z)-f(x)/z-x
z>x
my answer was 1/2(3x)^1/2
but its wrong
February 13th 2006, 01:48 PM
CaptainBlack
Quote:
Originally Pos... | 5 | [
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0.06640625,
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-0.054443359375,
-0.027954101... | 37,891 | 37891 | |
Which Turing machines accept the language of trivial words in a finitely presented group?
up vote 10 down vote favorite
3
Let $G$ be a finitely presented group with generators $g_1, g_1^{-1},\ldots, g_n, g_n^{-1}$. Let $L(G)$ be the language of all those words in $g_1, \ldots, g_n$ which represent the trivial element ... | 5 | [
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-0.00653076171875,
-0.017... | 37,892 | 37892 | |
Help with finance calculator
October 19th 2011, 08:52 AM #1
Newbie
Joined
Sep 2009
Posts
17
Help with finance calculator
Poor Dog, Inc. borrowed $135,000 from the bank today. They must repay this money over the next six years by making monthly payments of $2,215.10. What is the interest rate on the loan?... | 4 | [
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Interpreting the Garnir relations in terms of the Yang-Baxter equation
up vote 6 down vote favorite
4
One possible construction of the Specht modules goes as follows.
Given a partition $\lambda$ of $n$, we can write down Young's seminormal form for the representation of $S_n$ corresponding to $\lambda$. Writing a bas... | 4 | [
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0.0... | 37,894 | 37894 | |
Two exercises about real numbers
April 16th 2012, 11:50 AM #1
Junior Member
Joined
Jun 2009
Posts
58
Two exercises about real numbers
Hello!!
Could you please help me with these two exercises
1.- Let $a,b,c$ be real positive numbers and $abc = 1$
Prove that: $\displaystyle\frac{a}{(a+1)(b+1... | 5 | [
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0.041015625,
-0.0018615722656... | 37,895 | 37895 | |
Area between curve and x axis
August 3rd 2006, 10:09 AM #1
Newbie
Joined
Jul 2006
Posts
15
Area between curve and x axis
If y = √ 4 - x^2 then the area of the region limited by this curve y and the x axis is
a) ¶
b) 2¶
Calculate the correct result.
bret80
If y = √ 4 - x^2 then the ... | 5 | [
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0.0419921875,
0.0400390625,
-0.09375,
-0.09033... | 37,896 | 37896 | |
Maximum and bound for a multivariate function
December 18th 2008, 04:45 AM #1
Maximum and bound for a multivariate function
Hi there guys, I'm having alot of trouble verifying the following:
Verify that the maximum of
$\displaystyle x(1-x)y(1-y)w(1-w)(1-(1-xy)w)^{-1}$
occurs for $x=y$, and then tha... | 5 | [
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0.026123046875,
-0.1660... | 37,897 | 37897 | |
Annuities
Finance > Annuities
Annuities
An annuity is a series of equal payments over a specified time frame. For example, a cash payment of C made at the end of each year for four years at annual interest rate i is shown in the following
time line:
This time line is for an ordinary annuity, in which the cash paymen... | 4 | [
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-0.0791015625,
0... | 37,898 | 37898 | |
improper integral
February 8th 2013, 07:07 AM
happymatthematics
improper integral
Hello.
Attachment 26906
I don't know how to solve the above improper integral.
I tried to get rid of dy, but turn out to be Attachment 26907
which is even more difficult to me.
I don't know how to get rid of x... | 5 | [
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-0.0844726... | 37,899 | 37899 |