content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Cosine Approximations
Date: 12/29/97 at 16:11:56
From: phil
Subject: Cosine of 40 degrees
You derived a cubic equation for cosine of 40 degrees. Did you know
the following approximation?
cos (2x/3) = approx 0.5*(1 + cos x)
so if x = 60 degrees, cos 40 = approx 0.5*(1+0.5) = 0.75 versus
actual cos 40 = 0.76604, for ... | 5 | [
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0.04736328125,
... | 42,500 | 42500 | |
defense
Acoustic Classification Using
Independent Component Analysis
James Brock
May 17, 2006
Motivation!!
Scene Aspect Recognition
Music Database Organization
Motivation
โข Digital Media Organization
โข Online music databases categorization
โข Con... | 4 | [
0.045654296875,
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0.0228271484375,
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0.07958984375,
... | 42,501 | 42501 | |
std.math
Source: std/math.d
e
log[2]10
log[2]e
log[10]2
log[10]e
ln 2
ln 10
ฯ
ฯ / 2
ฯ / 4
1 / ฯ
2 / ฯ
2 / โฯ
โ2
โยฝ
Calculates the absolute value
For complex numbers, abs(z) = sqrt( z.re^2 + z.im^2 ) = hypot(z.re, z.im).
Complex c... | 4 | [
-0.0625,
0.0267333984375,
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0.01239013671875,
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0.01141357421875,
-0.0203857421875,
-... | 42,502 | 42502 | |
linear operator proof
October 10th 2009, 11:37 AM
guroten
linear operator proof
Let W be the space of all n X 1 column matrices over a field F. If A is an
n X n matrix over F, then A defines a linear operator L on W through left
multiplication: L(X) = AX. Prove that every linear operator on W is left mul... | 5 | [
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Doubling Pennies for a Year
Associated Topics || Dr. Math Home || Search Dr. Math
Doubling Pennies for a Year
Dat... | 5 | [
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-0.10498046... | 42,504 | 42504 | |
Logarithmic Expression
July 26th 2012, 04:06 AM
Pernello
Logarithmic Expression
How would this be simplified?
Attachment 24350
I understand what would be done if the base on the logarithm were 9 but what happens in a case like this?
Any help would be greatly appreciated.
July 26th 2012, 04:23 AM
... | 4 | [
0.0026092529296875,
0.03857421875,
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0.072265625,
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0.0654296875,
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0.123535... | 42,505 | 42505 | |
Counting square-free numbers smoothly
up vote 3 down vote favorite
Let $f:\mathbb{R}^+\to \mathbb{R}^+$ be given by
$f(t) = 1$ if $0\leq t\leq 1$
$f(t) = 1/t^2$ if $t>1$.
Question:
What is the sum $\sum_{n\; \text{squarefree}} f(n/x)$, for $x$ large?
Just by the simplest inclusion-exclusion, one can get an estima... | 4 | [
-0.087890625,
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0.083984375,
-0.06640625,
0.012... | 42,506 | 42506 | |
limit help
February 7th 2006, 09:14 PM
tnkfub
limit help
If you can help me on this id greatly appreciate it
(steps in helping me understand helps alot)
Lim ((1/x^(1/2))-(1/2))/(x-4)
x->4
February 8th 2006, 12:04 AM
ticbol
Quote:
Originally Posted by tnkfub
If you can help me on thi... | 5 | [
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NEED HELP ONCE AGAIN
Page 1 of 1 [6 Posts] View previous topic :: View next topic
Author Message
Missy Posted: Sun Jul 16, 2006 2:16 am Post subject:
science Please help I need to know how to so... | 4 | [
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-0.02... | 42,508 | 42508 | |
Homework Help
Posted by Maura on Monday, November 21, 2011 at 4:32pm.
O.k. I'm 42 trying to help my nephew with algebra and lets just say it's been awhile....
Total money $ 101.25
45 more dimes than nickels
3 times as many quarters as dimes.
How many nickels, dimes & quarters?
โข algebra - Damon, Monday, Novembe... | 4 | [
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... | 42,509 | 42509 | |
Whether a series converges or diverges.
January 20th 2008, 03:58 PM #1
Member
Joined
Sep 2007
Posts
94
Whether a series converges or diverges.
I am given the series n^2/(n^3 + 1) and I don't know how to put the Riemann sum symbol in front of it (assume its there). My guess is that the series diverges bec... | 5 | [
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Math Forum Discussions
Math Forum
Ask Dr. Math
Discussions
Internet Newsletter
MathTools
Teacher2Teacher
Teacher Exchange
Workshops
Search All of the Math Forum:
Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.
Math Forum ยป Discussions ยป sci.math.* ยป sci.math.independ... | 4 | [
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find horizontal tangent plane
October 11th 2009, 08:01 PM #1
Senior Member
Joined
Jun 2009
Posts
251
find horizontal tangent plane
the surface $6x^2+3y^2+3z^2-6yz-2y-2z=0$ has one horizontal tangent plane. Find its equation and give the point where it is tangent.
Hint(?) there is no piont on the surf... | 4 | [
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-0.0815429... | 42,512 | 42512 | |
Math Forum Discussions
arithmetic
Posts: 106
From: venezuela
Registered: 1/23/06
Re: cube root of a given number
Posted: Jul 23, 2007 9:53 AM
On 22 jul, 20:38, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
wrote:
> On 22 Jul, 23:47, arithmonic <djes...@gmail.com> wrote:
>
>
>
>
>
> > On 22 jul, 07:29, "sttscitr...@... | 5 | [
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0.0078125,
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... | 42,513 | 42513 | |
Bonds
Introduction to Investment Analysis
Valuation of Bonds
What are Bonds?
โข Bonds are a form of long-term debt (Will mature in one year or less)
that usually is secured by property, usually with an original maturity
of twenty to thirty years. A... | 5 | [
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-0.04711914062... | 42,514 | 42514 | |
New Framework for Analyzing Volatility Risk and Volatility Risk
A New Framework for Analyzing
Volatility Risk and Volatility Risk Premium
in Each Option Contract
Liuren Wu, Baruch College
Joint work with Pete... | 4 | [
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... | 42,515 | 42515 | |
Solving a 8 set Venn diagram
April 5th 2012, 09:02 AM #1
Newbie
Joined
Apr 2012
From
Australia
Posts
3
Solving a 8 set Venn diagram
Hi everyone I'm new and i'm just looking for help in doing a Venn diagram I've been set. I'm doing a bachelor of computer science and I have no idea how this relates to ... | 4 | [
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0.020751953125,
-0.10937... | 42,516 | 42516 | |
Volume 43,
Volume 43, Issue 11, November 2002
โข QUANTUM MECHANICS (GENERAL AND NONRELATIVISTIC)
โข
โ
View Description Hide Description
The fundamental elements of the variable separation theory are revisited, including the Eisenhart and Robertson theorems, KalninsโMiller theory... | 4 | [
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Grothendieck's question on the Brauer group for groups
up vote 16 down vote favorite
8
Let $G$ be a group, and let $M(G)=H^2(G,\mathbb{C}^*)$ be the Schur multiplier of $G$. There is a group $Br(G)$ of complex projective representations of $G$ modulo those that can be lifted to linear
representations. Projective repre... | 4 | [
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0.0126953125,
0.0033721923828125,
0.01007080... | 42,518 | 42518 | |
Is there a closed form for this hypergeometric expression?
up vote 3 down vote favorite
I am trying to compute the number of distinct ways a $4n$ $\times$ $4n$ chessboard can be colored black and white, with exactly half the squares black and half the squares white. By distinct, I mean
not equivalent by rotation or re... | 4 | [
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0.... | 42,519 | 42519 | |
Percentage question but I don't get it!!
October 30th 2008, 03:19 AM #1
Newbie
Joined
Oct 2008
Posts
5
Percentage question but I don't get it!!
Ranjit started work in 2003.
In 2004 he moved to a different job and his pay decreased by 15%
At the end of each of the years 2004 and 2005 he was given ... | 4 | [
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Effective Field Theory in the Early Universe
Effective Field Theory in the
Early Universe
Inflation, Axions and Baryogenesis
(Collaborations with A. Anisimov, T. Banks, M. Berkooz, M. Graesser,
T. Volansky)
... | 4 | [
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0.0791015625,
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0.01611328125,
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0.09765625,
-0.02783203125,
... | 42,521 | 42521 | |
Math Forum Discussions
Math Forum
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Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.
Topic: Mapping a sphere to a plane
Replies: 8 Last Post: ... | 4 | [
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... | 42,522 | 42522 | |
Find the area enclosed by the three curves: y=`1/x` , y=x, y=`(1/4)x` , x>0.
- Homework Help - eNotes.com
Find the area enclosed by the three curves: y=`1/x` , y=x, y=`(1/4)x` , x>0.
ย
You need to evaluate the limits of integration `y = 1/x, y = x, y = (1/4)x` such that:
`1/x = (1/4)x => 1/x - x/4 = 0 => 4 - x^2 =... | 5 | [
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Exercicios do Tipler Resolvidos (Volume 2, Capitulo 21 ao 41) -
Exercicios do Tipler Resolvidos (Volume 2, Capitulo 21 ao 41)
(Parte 1 de 11)
Chapter 21 The Electric Field 1: Discrete Charge Distributions
Conceptual Problems
*1 โขโข
Similarities: Differences:
The force between charges and masses varies as 1/r2.
T... | 5 | [
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-0.024658203125,... | 42,524 | 42524 | |
neural_network
Neural Networks and their supervised training, By: Dr. M. Turhan (Tury) Taner , Rock Solid Images Page = 1
NEURAL NETWORKS
and
COMPUTATION OF NEURAL NETWORK WEIGHTS AND BIASE... | 4 | [
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0.0664062... | 42,525 | 42525 | |
proving associative property of any two vectors
January 21st 2013, 10:00 AM
bonfire09
proving associative property of any two vectors
Problem:Prove that any two ways of associating a sum of any number of vectors give the same sum. (Hint. Use induction on the number of vectors.)
Proof: Base Case: Let there b... | 5 | [
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... | 42,526 | 42526 | |
Cross Products; Rotating in Three Dimensions
Date: 10/26/2001 at 00:00:24
From: RJ
Subject: Matrices (Cross-Product)
Hi,
We are currently studying matrices and vectors, and we just came to
the concept of the cross product. Our entire class understands how
it works, but we don't understand why or the proof behind it... | 4 | [
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0.0201416015625,
0.0198974609375,
0.0113525390625,
-0.0040283203125,
0.0498046875,
-0.08837890625,
0.1279296875... | 42,527 | 42527 | |
linear algebra urgent help please
August 2nd 2008, 05:45 PM
happystudent
linear algebra urgent help please
true or false and why?
1) every square matrix can be written as the product of elementary matrices.
2) The inverse of an elementary matrix is an elementary matrix.
3) Every system with 3 equatio... | 5 | [
0.0111083984375,
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-0.0546875,
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0.06494140625,
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0.0111083984375... | 42,528 | 42528 | |
Chapter
Chapter 11: Optimal Portfolio Choice and the CAPM-1
Chapter 11: Optimal Portfolio Choice and the Capital Asset Pricing
Model
Goal: determine the relationship between risk and return
=> key to this process: exa... | 5 | [
0.028564453125,
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0.005950927734... | 42,529 | 42529 | |
Real Analysis/Topology problem
December 8th 2013, 04:13 AM
SMAD
Real Analysis/Topology problem
Let A be a non empty part of โ, such that A and A complement are two open subsets of โ.
1- Prove that A is not bounded above.
2- Assuming that A complement is non-empty and let x in A complement.
and let B... | 4 | [
-0.0289306640625,
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-0.064... | 42,530 | 42530 | |
Finding Equation of a Line Given the Slope and a Point on It
Date: 08/24/2006 at 19:26:45
From: Sara
Subject: getting the equation of a line from y=mx+b to ax+by+c=0
I'm trying to figure out how to convert a line from slope-intercept
form to general form, ax + by + c = 0. I'm given one set of points
and the slope: (... | 4 | [
-0.07568359375,
0.006744384765625,
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0.15625,
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-0.009948730... | 42,531 | 42531 | |
find the probability that Y1 + Y2 is less than 1
December 1st 2011, 11:35 AM
wopashui
find the probability that Y1 + Y2 is less than 1
Suppose that the random variables Y1 and Y2 have a joint probability distribution function f(y1, y2) given by
f(y1,y2)= $6y1^2y2$ 0<=y1<=y2, y1+y2<=2 and f(y1,y2)=0 elsewher... | 4 | [
0.03173828125,
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-0.04760742187... | 42,532 | 42532 | |
Finite Fields Package
A field is an algebraic structure obeying the rules of ordinary arithmetic. In particular, a field has binary operations of addition and multiplication, both of which are commutative and associative.
A field has two special elements, the additive identity 0 and the multiplicative identity 1. This... | 4 | [
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0.... | 42,533 | 42533 | |
integrals of trigonometric functions
February 21st 2009, 01:42 PM #1
Junior Member
Joined
Jan 2009
From
vancouver
Posts
58
integrals of trigonometric functions
a thief tries to enter a building by placing a ladder over a 9-ft-high fence so it rests against the building,which is 2 ft back from the fen... | 5 | [
-0.0196533203125,
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0.04321289... | 42,534 | 42534 | |
Quickie #8
January 6th 2007, 11:10 AM #1
Super Member
Joined
May 2006
From
Lexington, MA (USA)
Posts
11,682
Thanks
614
Quickie #8
Prove that for any positive integer $n$
. . $n^4 + 2n^3 + 2n^2 + 2n + 1$ is never a perfect square.
$(n^4+2n^2+1)+(2n^3+2n)$
$(n^2+1)^2+2n(n^2+1)$
$... | 5 | [
-0.0255126953125,
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0.0461... | 42,535 | 42535 | |
Example of Leibniz rule for integration
May 6th 2008, 02:47 AM #1
Junior Member
Joined
May 2007
Posts
30
Example of Leibniz rule for integration
Can someone give me a concrete example of using Leibniz rule for evaluating the derivative with respect to x of f(x,y) where the limits of integration are funct... | 5 | [
0.00946044921875,
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-0.09814453125,
0.02893066... | 42,536 | 42536 | |
Graphing a Circle
Date: 04/14/98 at 15:02:55
From: Philip J. Peisch
Subject: algebra
I would like to know how to graph the equation of a circle. I have a
big test coming up - can you please help me?
Thanks -
Philip J. Peisch
Date: 04/14/98 at 15:48:57
From: Doctor Kate
Subject: Re: algebra
The equation of a circ... | 4 | [
-0.01409912109375,
0.0277099609375,
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-0.0247802734... | 42,537 | 42537 | |
ces
International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 30673, 26 pages
doi:10.1155/IJMMS/2006/30673
On semilattices of groups whose arrows are epimorphisms
Department of Mathematics, Faculty of Science, Menoufiya University, Shebin El-Kom 32511, Egypt
Received 6 April 2006... | 4 | [
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Proving Theorems
Date: 07/20/2001 at 06:55:45
From: Condensate
Subject: How to prove Euler's Theorem, i.e., a^f(n) = 1 (mod n) where
f(n) is the phi function.
Dear Dr. Math,
I would like to ask two questions:
(1) How to prove Euler's Theorem, i.e.,
let f(x) be the Euler phi-function. Then a^f(n) = 1 (mod n) fo... | 5 | [
-0.038818359375,
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... | 42,539 | 42539 | |
Unit 2 Linear Equations
Unit 2: Linear Equations and Inequalities 5 weeks
Unit Overview
Essential Questions:
What is an equation?
What does equality mean?
What is an inequality?
How can we use linear equations and linear inequalities to solve real wor... | 4 | [
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... | 42,540 | 42540 | |
Distributional derivative of non continuously differentiable functions
up vote 1 down vote favorite
1
Hello,
let $f$ be a continuously differentiable function on $R^n$. Then its classical derivative and its distributional derivative coincide.
It is known (cf. Rudin, Functional Analysis, Sect. 6.13) that this corresp... | 4 | [
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-0.10986328125,
0.003509521484375... | 42,541 | 42541 | |
probability with combination
December 16th 2011, 01:57 AM
achal
probability with combination
There are k sets of numbers : {0,1,2,โฆ.,m1}, {0,1,2,โฆโฆ..,m2}, โฆโฆโฆโฆ,{0,1,2,โฆโฆโฆ,mk}
Such that m1<m2<โฆโฆโฆ<mk.
1. How many combinations of k elements can be made taken 1 element from each set such that each set has al... | 4 | [
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0.10302734375,
0.018798828125,
-0.07... | 42,542 | 42542 | |
Path length of ball on tilted, perforated plane
up vote 8 down vote favorite
Imagine that an $\epsilon$-radius hole is punched in the plane centered on every integer-coordinate point. Now a point "ball" is dropped on the plane at a random spot $p$. If $p$ has not already
dropped through a hole, the plane is tilted in ... | 5 | [
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-0.07373046875,
-0... | 42,543 | 42543 | |
Differential equation
May 13th 2009, 01:20 PM #1
Junior Member
Joined
Mar 2009
Posts
32
Differential equation
Hi,
I am kinda having trouble with the following problem:
Suppose that the acceleration of a model rocket is proportional to the difference between 120 ft/sec and the rocket's velocity. ... | 5 | [
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-0.078125,
-0.042724609375,
-0.00005078315734863281,
0.035888671875... | 42,544 | 42544 | |
cumulative distribution function
It cannot be done unless you complete that table. You have given no values for $f(x)$.
Sorry for confusion: 0 = 1/27 1 = 6/27 2 = 12/27 3 = 8/27
So for an answer maybe something along the lines... F(x) = 0 if x<0 F(x) = 1/27 if 0<=x<1 F(x) = 6/27 if 1<=x<2 F(x) = 12/27 if 2<=x<3 F(x) ... | 4 | [
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0.0303955078125,
-0.080078125,
-0.05810546875,
-... | 42,545 | 42545 | |
Clarification of Problem
February 11th 2014, 07:30 PM
petenice
Clarification of Problem
I have just completed a section on Second ODE and Second Order Linear Homogenous equations. Topics were the superposition principle, the wronskian, and linear dependence and independence.
But Part A of this exercise ques... | 4 | [
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-0.034... | 42,546 | 42546 | |
Distance between poisson points in two disjoint unit discs
up vote 3 down vote favorite
2
Two disjoint unit discs $D_1$ and $D_2$. Inside them there are random poisson points with intensity $\lambda$. For a given real $r>0$, what is the probability that there exist a poisson point $x_1\in
D_1$ and a poisson point $x_2... | 5 | [
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0.037841796875,
-0.12060546875,... | 42,547 | 42547 | |
Looping Syntax in Various Languages
May 27, 2009 by Jared
Okay, this post is going to be quite long. Iโm going to start with a basic problem I was solving in emacs lisp. From there Iโll segue into thinking about looping syntax and finally Iโll do a bit of
benchmarking as Iโve got the code already and people seem to l... | 5 | [
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-0.0712890625,
0.08007... | 42,548 | 42548 | |
Complex numbers with a polenom!
March 19th 2011, 01:56 AM #1
Newbie
Joined
Mar 2011
Posts
9
Hello,
So here is this combined polynomial & complex numbers; I couldn't solve it!
F(z)= z^7 + a(6)*z^6 + a(5)*z^5 + a(4)*z^4 + a(3)*z^3 + a(2)*z^2 + a(1)*z^1+a(0)
It is given that z=-4-2i is a root ... | 5 | [
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0.022216796875,
0.01806640625,
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0.031494140625,
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-0.126953125,
-0.007... | 42,549 | 42549 | |
Bisector of an acute angle Q2 (Help)
June 27th 2009, 12:13 AM #1
Member
Joined
Jan 2009
Posts
197
[FONT="Arial"]Find the equation of the bisector of the acute angle whose equation is
$4x-5y-10$ and $x-4y+6$
Attempt
L1= $\frac{4x'-5y'-10}{-\sqrt{41}}$
L2= $\frac{x'-4y'+6}{-\sqrt{17}}$
... | 4 | [
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-0.004180908203125,
0.0172119140625,
0.01141357421875,
0.10302734375,
-0.05859375... | 42,550 | 42550 | |
Levi-Civita permutation symbol
Levi-Civita permutation symbol
Definition 1.
Let $k_{i}\in\{1,\cdots,n\}$ for all $i=1,\cdots,n$. The Levi-Civita permutation symbols $\varepsilon_{{k_{1}\cdots k_{n}}}$ and $\varepsilon^{{k_{1}\cdots k_{n}}}$ are defined as
$\varepsilon_{{k_{1}\cdots k_{m}}}=\varepsilon^{{k_{1}\cdot... | 5 | [
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-0.07763671875,
0.1591796875,
-0.03759765625,
0.049072265625,
-0.... | 42,551 | 42551 | |
Find an equation of the line tangent to the graph of y= x^2 + sin(pi/2)x at x=-1 - Homework Help - eNotes.com
Find an equation of the line tangent to the graph of y= x^2 + sin(pi/2)xย at x=-1
Let the equation for the line be :
y-y1 = m(x-x1)ย
where (x1,y1) is any point on the line and m is the slope.
ย ย ย We know th... | 4 | [
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-0.0537109375,
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0.0908203125,
0.0028839111328... | 42,552 | 42552 | |
Proof of Heron's Area Formula
Associated Topics || Dr. Math Home || Search Dr. Math
Proof of Heron's Area Formula
... | 5 | [
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... | 42,553 | 42553 | |
Trig eqn cos(x+TT/6) + cos(x-TT/4) = 0
February 25th 2011, 11:14 AM
flashylightsmeow
Trig eqn cos(x+TT/6) + cos(x-TT/4) = 0
Hi there, I was wondering if someone would be able to help me solve this equation :
cos(x+TT/6) + cos(x-TT/4) = 0
It's driving me insane. I use compound angle theorem to expand th... | 5 | [
-0.056396484375,
0.00653076171875,
0.047607421875,
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-0.031982421875,
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0.0225830078125,
0.002593994140625,
-0.00994873046875,
0.10107421875,
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-0.060302734375,
-0.00311279296875,
0.0390625,
-0.052978515625,
-0.044921875,
-0.01... | 42,554 | 42554 | |
sup and inf
March 29th 2011, 02:59 PM #1
Junior Member
Joined
Mar 2011
Posts
49
sup and inf
Let $f,g:A\to\mathbb R$ so that $f\le g,$ then prove that if $g$ is bounded above, so is $f$ and $\inf f\le \sup g.$
First part is easy, now since $\inf f\le f\le g,$ we have that $\inf f\le g\implies \inf f\... | 4 | [
-0.0184326171875,
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0.0458984375,
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0.043701171875,
0.04248046875,
-0.072265625,
0.07373046875,
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0.09765625,
0.07177734375,
0.0001678466796875,
0.07177734375,
0.0013275146484375,
0.08740234375,
-0.03320... | 42,555 | 42555 | |
System of DE's.
November 26th 2010, 05:47 PM
rafi98
System of DE's.
Please help. Solve
dx/dt + y = sint , x(0)=2
dy/dt + x = cost , y(0)=0
this is one problem that comes in my laplace transform chapter. Any method can be used
November 26th 2010, 06:09 PM
Prove It
From DE 1: $\displaystyle \fr... | 5 | [
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0.0517578125,
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0.01470947265625,
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-0.02783203125,
-0.0081787109375,
-0.0311279296875,
-0.0216... | 42,556 | 42556 | |
properties of radical ring
April 12th 2011, 01:40 AM #1
Junior Member
Joined
Feb 2011
Posts
72
properties of radical ring
Show that $\sqrt{I}=\cap{P}$, where the intersection is over all prime ideals of $R$ that contain $I$.
I know how to verify the one inclution $\sqrt{I}\subset\cap{p}$, but how ca... | 5 | [
-0.00390625,
0.006317138671875,
0.026123046875,
-0.002655029296875,
0.09423828125,
-0.057373046875,
0.08740234375,
0.07177734375,
0.01373291015625,
-0.08544921875,
-0.0205078125,
0.0208740234375,
0.056640625,
0.040283203125,
-0.06103515625,
-0.00167083740234375,
-0.0218505859375,
0... | 42,557 | 42557 | |
Solving Constant Differencial Equations
June 15th 2007, 09:10 AM #1
Global Moderator
Joined
Nov 2005
From
New York City
Posts
10,616
Thanks
9
Solving Constant Differencial Equations
Somebody asked me if I can teach how to solve equations:
$ay''+by' + cy = 0$ on $-\infty < x <\infty \ \ \ (1)$... | 4 | [
-0.08984375,
0.004302978515625,
-0.0011138916015625,
0.056396484375,
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0.06396484375,
0.0264892578125,
-0.007293701171875,
0.06591796875,
0.01214599609375,
0.11865234375,
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0.017333984375,
0.0118408203125,
0.005340576171875,
-0.017333984375,
0.00811767578... | 42,558 | 42558 | |
How can I solve this system of linear equations?
February 8th 2013, 03:16 PM #1
Junior Member
Joined
Apr 2012
From
canada
Posts
38
How can I solve this system of linear equations?
Using either Gaussian or Gauss-Jordan elimination, find the value(s) of k, if any, for which the following system will ha... | 5 | [
-0.09423828125,
-0.045166015625,
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0.049560546875,
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0.0693359375,
0.07177734375,
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0.0107421875,
-0.0283203125,
0.00982666015625,
-0.01263427734375,
-0.07666015625,... | 42,559 | 42559 | |
Linear Recursion and Iteration
We begin by considering the factorial function, defined by
There are many ways to compute factorials. One way is to make use of the observation that n ! is equal to n times (n - 1)! for any positive integer n:
Thus, we can compute n ! by computing (n - 1)! and multiplying the result by ... | 4 | [
-0.06640625,
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0.02490234375,
0.01708984375,
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0.01904296875,
-0.04931640625,
-0.04296875,
0.0028533935546875,
-0.0203857421875,
0.0257... | 42,560 | 42560 | |
Equilateral triangle and complex numbers
March 12th 2011, 07:02 AM
Glitch
Equilateral triangle and complex numbers
The question:
Show that the triangle in the complex plane whose verticies are the origin and the points $w_1$ and $w_2$ is equalateral if and only if $w_1^2 + w_2^2 = w_1w_2$
I have a feeli... | 4 | [
-0.0693359375,
0.0166015625,
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0.01104736328125,
-0.0303955078125,
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0.04345703125,
0.034423828125,
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0.064453125,
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0.0186767578125,
0.00396728515625,
-0.0... | 42,561 | 42561 | |
Derivative, worked problem need help on eval
December 9th 2006, 02:56 PM #1
fa3a
Guest
Derivative, worked problem need help on eval
I have a function for a university's tuition and I'm supposed to find f'(3) and f('12). Eval and Interpret. Also, I'm supposed to do the same for the second derivative. I just want t... | 5 | [
0.0166015625,
-0.0198974609375,
0.0035400390625,
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-0.04638671875,
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-0.02294921875,
-0.07958984375,
-0.000... | 42,562 | 42562 | |
Integers sequence
March 12th 2010, 06:48 AM #1
Member
Joined
Aug 2008
Posts
91
Integers sequence
Show that the sequence of positive integers given by $a_{2n} = 3a_n -1, \ \ a_{2n+1}=3a_n +1$ is strictly increasing.
I have written down a reductio-ad-absurdum-proof, but it's based largely on tedious re... | 4 | [
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0.03027343... | 42,563 | 42563 | |
Reference needed for negative curves on blowup of the projective plane at generic points
up vote 4 down vote favorite
2
Hello,
I usually see the following theorem without seeing any reference or explanation
Theorem: Let X be a blowup of $P^2$ at generic r points. If $r\leq 8$ then there are only finitely many (-1) c... | 5 | [
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... | 42,564 | 42564 | |
category
Contex
Category theory
Concepts
Universal constructions
Theorems
Extensions
Applications
There are several concepts often called a path category.
Contents
Free category on a directed graph
There is a forgetful functor from small strict categories to quivers. This forgetful functor has a left adjoin... | 4 | [
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0.0634765625,
0.0859375,
0.03271484375,
... | 42,565 | 42565 | |
Invariant measures for Cellular automata
up vote 3 down vote favorite
1
An easy question that I have never been able to answer. Suppose we have the CA on $\{ 0,1,2 \}^{\mathbb{N}}$ with local rule given by $f(x,y)=A_{x,y}$ and $A$ the $3\times 3$ matrix $A=
(0,1,2,0,1,2,1,2,0).$ For example $(0,1,2,0,0,0,1,2,0,\ldots)... | 4 | [
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0.0703125,
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-0.021728515625,
0.00061798095703125,
0.0... | 42,566 | 42566 | |
Got this one in my test today...
April 16th 2008, 08:09 AM
janvdl
Got this one in my test today...
Hello everyone (Hi)
I got this one in my test today and would like to know what the answer should have been, please. (EDIT: I used partial integration on it)
Thanks in advance.
$\int \frac{1 - t}{\sq... | 5 | [
-0.003662109375,
0.007659912109375,
0.0419921875,
0.06298828125,
0.010498046875,
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0.0888671875,
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0.0712890625,
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-0.0751953125,
-0.00153350830078125,
-0.03... | 42,567 | 42567 | |
Permutations with ordering constraints
May 18th 2011, 12:44 PM #1
Newbie
Joined
May 2011
Posts
3
Permutations with ordering constraints
Hello,
Let's say we have a set of n balls, consisting of m green balls, l red balls and k grey balls (so, m+l+k=n). The balls will be arranged in some order, using ... | 4 | [
0.040283203125,
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0.068359375,
0.0211181640625,
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0.01513671875,
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0.044677734375,
0.1259765625,
0.034912109375,
-0.027954101... | 42,568 | 42568 | |
In an n-dimensional linear 2nd-order ODE, why is the transpose-inverse to a system of solutions also a solution?
up vote 2 down vote favorite
2
I'm at a sticky spot in my research. Namely, I have a particular fact, and it ought to have a short proof, but the only way I know how to show it is long and drawn out, and I ... | 5 | [
-0.08740234375,
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0.026611328125,
0.0303955078125,
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-0.0296630859375,
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0.06298828125,
0.031494140625,
... | 42,569 | 42569 | |
Find one & all polynomial of degree 4
March 23rd 2011, 11:09 AM
chipwager
Find one & all polynomial of degree 4
If someone can advise me how to approach the following problem it would be greatly appreciated.
Q: Find one & all polynomials of degree 4 such that p(-1)=1, p(0)=0, p(1)=2, p(2)=1
I tried...
... | 5 | [
0.005401611328125,
0.08154296875,
-0.0096435546875,
-0.006622314453125,
0.00897216796875,
-0.024169921875,
-0.0128173828125,
-0.056640625,
-0.0142822265625,
-0.0242919921875,
0.00982666015625,
-0.0859375,
0.052001953125,
0.05126953125,
-0.05419921875,
0.00075531005859375,
-0.06347656... | 42,570 | 42570 | |
Helmet Metal Mass Compensation For Helmet-mounted Sighting System - Patent 4394831
United States Patent: 4394831
( 1 of 1 )
United States Patent
4,394,831
Egli
, et al.
July 26, 1983
Helmet metal mass compensation for helmet-mounted sighti... | 4 | [
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-0.06884765625,
-0.0279541015625,
0.028564453125,
0.061279296875,... | 42,571 | 42571 | |
Inner Automorphism Groups
February 20th 2014, 07:10 PM #1
Junior Member
Joined
Sep 2010
Posts
36
Inner Automorphism Groups
How does one go about proving that a particular group is isomorphic to the set of its inner automorphisms? Specifically I'm looking at the symmetric group of order 3. I've done the t... | 5 | [
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-0.037353515625,... | 42,572 | 42572 | |
A
6
SOME RULES
OF
ALGEBRA
The rule of symmetry
The commutative rules
The inverse of adding
Two rules for equations
ALGEBRA, we can say, is a body of formal rules. They are rules that show how something written one form may be rewritten in another form. For what is a calculation if not transforming one set of
s... | 4 | [
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-0.06787109375,
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-0.00014972686767578125,
0.043212890625,
0.0194091796875,
0.0556640625,
0.0576171875,
-0.08496093... | 42,573 | 42573 | |
Defining Equations of a Flag Variety
up vote 3 down vote favorite
1
I've been reading Fulton's Young Tableaux, and I'm trying to understand flag varieties. I want to understand the defining equations of a Flag Variety, but the coordinates in Fulton's Plucker
relations, and in the equations defining the flag varieties ... | 4 | [
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0.02392578125,
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0.0986328125,
-0.072265625,
0.005523681... | 42,574 | 42574 | |
Orthonormal Wavelet Basis
An orthonormal wavelet basis is an orthonormal basis of the form
B= 2j2โขฯโข2jโขtโk jโZ and kโZ B 2 j 2 ฯ 2 j t k j k
(1)
The function
ฯโขt ฯ t
is called the wavelet.
The problem is how to find a function ฯโขt ฯ t so that the set BB is an orthonormal set.
The Haar basis (described by Haar in... | 4 | [
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0.0035400390625,
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-0.087890625,
0.023193359375,
0.0201416015625,
-0.041015625,
-0.0213... | 42,575 | 42575 | |
Differentiate using product Rule
June 5th 2009, 08:29 AM #1
Newbie
Joined
May 2009
Posts
22
Differentiate using product Rule
Is This correct?
$(x+20)^4 (x-30)^3$
$u=(x+20)^4$
$du/dx = 4(x+20)^3$
$v=(x-30)^3$
$dv/dx=3(x-30)^2$
$dy/dx=v.du/dx + u . dv/dx$
$dy/dx = (x-30)^... | 5 | [
-0.00518798828125,
0.00164031982421875,
-0.007476806640625,
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0.037841796875,
0.05810546875,
0.0322265625,
0.0279541015625,
-0.011230468... | 42,576 | 42576 | |
C*-algebra
From Encyclopedia of Mathematics
2010 Mathematics Subject Classification: Primary: 46L05 [MSN][ZBL]
$$ \newcommand{\abs}[1]{\left|#1\right|} \newcommand{\norm}[1]{\left\|#1\right\|} \newcommand{\set}[1]{\left\{#1\right\}} \newcommand{\Ah}{A_{\text{h}}} \newcommand{\Cstar}{C^*\!} $$ A Banach algebra
$A$ ov... | 4 | [
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0.013916015625,
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0.020263671875,
-0.0986328125,
0.027587890625,
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0.045654296875,
-0.059814453125,
-0.10302734375,
0.041259765625,
-0.01177978515625,
0.0751953125,
-0.0634765625,
-0.055419921875,
0.05517578125,
-0.0341796875,
-0.0390625,
-0.... | 42,577 | 42577 | |
Order of groups involving conjugates and abelian groups
February 4th 2009, 07:43 PM
Janu42
Order of groups involving conjugates and abelian groups
1. Let G be a group and let a be in G. An element b in G is called a conjugate of a if there exists an element x in G such that b = xax^-1. Show that any conjugate of... | 5 | [
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-0.061279296875,
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-0.09228515625,
0.02587890625,
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0.03564453125,
0.11669921875,
0.0264892578125,
-0.052978515625,
0.019775390625,
0.171875,
-0.0257568359375,
-0.0144653320312... | 42,578 | 42578 | |
Do transvers foliations induce complex structure?
up vote 4 down vote favorite
1
Hallo,
I have the following question: Let $M$ smooth analytic manifold of dimension 4n. Assume furthermore that $M$ admits two foliations $A$, $B$, both with leaves of dimension 2n such that the leaves of
$A$ are transvers to the leaves ... | 4 | [
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0.080078125,
-0.0042724609375,
-0.1015625,
0.1328125,
... | 42,579 | 42579 | |
Elementary number theory
Taking modular powers
How do I compute modular powers in Sage?
To compute \(51^{2006} \pmod{97}\) in Sage, type
sage: R = Integers(97)
sage: a = R(51)
sage: a^2006
12
Instead of R = Integers(97) you can also type R = IntegerModRing(97). Another option is to use the interface with GMP:
sag... | 5 | [
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-0.02490234375,
-0.06494140625,
-0.024658203125,
0.0177001953125,
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0.0098876953125,
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0.01312255859375,
0.04443359375,
0.0771484375,
0.0284423828125,
-0.07275390625,
0.02880... | 42,580 | 42580 | |
Finding Pythagorean Triplets
Date: 02/02/2006 at 17:07:24
From: Faizan
Subject: Pythagorean triplets
Without using the standard a = n^2 - m^2, b = 2nm, c = n^2 + m^2, how
can you work out primitive Pythagorean triplets?
For example, you can work out an equation for cases when c and b
differ by 1 using (2n+1)^2 + b^2... | 4 | [
-0.05419921875,
0.05908203125,
0.007659912109375,
0.02783203125,
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0.046630859375,
0.0108642578125,
-0.0162353515625,
-0.00086212158203125,
0.005218505859375,
-0.07177734375,
0.0458984375,
0.02099609375,
-0.00860595703125,
-0.0216064453... | 42,581 | 42581 | |
Finding the 1000th Term in a Sequence
Date: 1/19/96 at 15:34:21
From: Anonymous
Subject: Number
Our class was given the following problem in class: Two kids are on a
car trip, and there's nothing to do, so they decide to count telephone
poles. One kid counts normally, 1,2,3,4,5...25,26,27...31,32,33, etc.
But the ot... | 4 | [
-0.041748046875,
0.04150390625,
0.00946044921875,
-0.0673828125,
-0.045654296875,
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0.0400390625,
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0.027587890625,
0.009765625,
0.016357421875,
0.03466796875,
-0.064453125,
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-0.01904296... | 42,582 | 42582 | |
rational expression
simplify. 1. (x^2+3)/x^2 + (x-1)/5 I get (x+2)/5, is this correct?
I don't know how you arrived at your conclusion so I don't know where to correct you. If you're simplifying by putting everything over one denominator, then we need an LCD. That would be $5x^2$ $\
frac{x^2+3}{x^2}+\frac{x-1}{5}=\fra... | 4 | [
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-0.01470947... | 42,583 | 42583 | |
"Ill-founded Recursion" without Fund
up vote 2 down vote favorite
It is a basic fact of set theory that the following holds:
Let $(X,\leq)$ be a linear ordered set. Then it holds that, for each finite sequence $y_{1}$,...,$y_{n}$ of sets and each formula $\phi(x,y_{1},...,y_{n})$ of set theory, we have
$$\forall{y_{... | 5 | [
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0.02490234375,
0.0008010... | 42,584 | 42584 | |
Essential geometric morphisms on the รฉtale site.
up vote 5 down vote favorite
2
Hi!
There is a risk that this question might be utterly trivial, and if it is, my sincerest apologies, but I haven't been able to find anything in the literature.
Let $f:X \rightarrow Y$ be an รฉtale morphism of schemes. This gives rise ... | 4 | [
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-0.03125,
-0.00... | 42,585 | 42585 | |
Characteristic subgroups of extra-special p-groups
up vote 4 down vote favorite
2
Let $G$ be a extra-special $p$-group of order $p^{1+2r}$ with exponent $p$ (p odd). I want to know if $G$ has only $3$ characteristic subgroups?
Background: From [2], if $G$ is extra-special $5$-group of order $5^5$ with exponent $5^2$,... | 5 | [
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-0.01062... | 42,586 | 42586 | |
"Sums-compact" objects = f.g. objects in categories of modules?
up vote 16 down vote favorite
8
Hello,
Let us call an object of an additive category sumpact (contraction of "sums" and "compact") if taking $Hom$ from it (considered as functor from the category to $Ab$) commutes with coproducts. Note
that to be sumpact... | 4 | [
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0.0712890625,
0.1132... | 42,587 | 42587 | |
HELP with cauchy sequences
February 9th 2011, 10:56 PM #1
HELP with cauchy sequences
I am so confused with Cauchy Sequences. I was sick the day we learned about them. Here are two problems that I am absolutely unsure about. (just two of many)
1. Prove straight from the definition that $(n + \frac{(-1)^n}{n})... | 5 | [
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0.055664... | 42,588 | 42588 | |
Help with the bounds on this double integral
August 17th 2008, 06:32 PM #1
Help with the bounds on this double integral
double integral (D) of y^3(x^2+y^2)^(-3/2) DXDY where (D) is the region determined by the ocnditions .5 less than or equal to y less than or equal to 1 and x^2+y^2 less than or equal to 1.
... | 4 | [
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0.01513671875,
0.00665283203125,
0.009765625,
-0.1308593... | 42,589 | 42589 | |
Questions about the Fourier expansion of $e^{iz\cot(x)}$
up vote 7 down vote favorite
2
Referring to a question I posted on MS, I post it here, as I didn't get an answer:
By analogy with the JacobiโAnger expansion, one expects that $e^{iz\cot(x)}$ has a Fourier expansion of the form : $$e^{iz\cot(\theta)}=\sum_{n=-\i... | 5 | [
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0.007598876953125,
-0.034423... | 42,590 | 42590 | |
of
Internet Data Analysis for the Undergraduate Statistics Curriculum
Juana Sanchez
UCLA
Yan He
UCLA
Journal of Statistics Education Volume 13, Number 3 (2005), www.amstat.org/publications/jse/v13n3/datasets.sanchez.html
Copyright ยฉ 2005 by Juana Sanchez and Yan He, all rights reserved. This text may be freely sh... | 4 | [
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-0.00933837890625,
0.033447265625,
-0.0576171875,
0.0634765625,
-0.0795898437... | 42,591 | 42591 | |
Horizontal Vessel
Summary
The calculation of a horizontal vessels wetted area and volume is required for engineering tasks such fire studies and the determination of level alarms and control set points. However the
calculation of these parameters is complicated by the geometry of the vessel, particularly the heads. T... | 4 | [
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0.0583496... | 42,592 | 42592 | |
Finding the ordered Triplet
November 12th 2006, 06:23 AM #1
Member
Joined
Nov 2006
From
chicago
Posts
156
Find the ordered triplet (A,B,C) if:
(6x^2 - 8x -20) / [(x+2)(x-3)(x-2)] = (A/(x+2)) + (B/(x-3)) + (C/(x-2))
**hint: mulitply both sides by (x+2)(x-3)(x-2)
Multiply through and yo... | 4 | [
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... | 42,593 | 42593 | |
SAS and R
In our
last entry
, we demonstrated how to simulate data from a logistic regression with an interaction between a dichotomous and a continuous covariate. In this entry we show how to use the simulation to estimate the
power to detect that interaction. This is a simple, elegant, and powerful idea: simply sim... | 5 | [
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0.01293945... | 42,594 | 42594 | |
Kirchhoff's Current Law
Kirchhoff's Current Law (KCL)
Why Do You Need To Know About KCL?
Facts About KCL
Using KCL To Write Equations For Circuits
Problems
You are at: Basic Concepts - Kirchoff's Laws - KCL
Return to Table of Contents Kirchhoff's Current Law - Introduction
... | 4 | [
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0.07421875,
... | 42,595 | 42595 | |
solving trace norm equality
up vote 0 down vote favorite
1
Problem Formulation
under what conditions can we solve $\mathrm{trace}(\mathbf{AB})=0$ ? or more specifically, when will $\mathrm{trace}(\mathbf{AB})=0$ implies that $\mathrm{trace}(\mathbf{B})=0$.
Related Art
This occurs to me when $\mathbf{A}$ was a Posit... | 5 | [
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0.0791015625,
0.003677368... | 42,596 | 42596 | |
Stokes Theorum
April 9th 2008, 06:15 AM
joker_900
Stokes Theorum
I'm not sure if this is the right place to put this?
Show that: curl(fu) = fcurlu + (gradf) x u
By using this in relation to Stoke's theorum, show that for a simple closed curve C,
(Line integral) fdS = -(surface integral) (gradf) x ... | 5 | [
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0.0162353515625,
-0.1806640625,
-0.0175... | 42,597 | 42597 | |
What is an exponent?
Associated Topics || Dr. Math Home || Search Dr. Math
What is an exponent?
Date: 8/8/96 at 2... | 4 | [
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... | 42,598 | 42598 | |
Finding the Limit of a Sequence
April 1st 2013, 11:20 AM #1
Hi, I know the answer to the limit of this sequence but I am still unsure about the logic behind it.
So I am given a sequence sqrt(6), sqrt(6+sqrt(6)), sqrt(6+sqrt(6+sqrt6)))...
I know it is monotonic sequence, because it only increases.
So... | 5 | [
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0.0179443... | 42,599 | 42599 |