content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
What's the formula for finding the terms in an arithmetic series?
November 28th 2011, 05:31 PM
krstybrght
What's the formula for finding the terms in an arithmetic series?
Here's the math problem....
In an arithmetic series, the terms of the series are equally spread out. For example, in 1+5+9+13+17, consec... | 4 | [
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0.02001953125,
0.020751953125,
-0.00171661376953125,
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-0.09228515625,
-0.026245117187... | 36,800 | 36800 | |
Math Help
1. April 28th 2008, 04:05 AM #1
2. April 28th 2008, 05:11 AM #2
You need to learn Latex my friend.
I see a mistake from the 3rd line to the 4th line when you're FOILing. $x^{\frac{1}{3}} \times x^{\frac{1}{3}} = x^{\frac{2}{3}}$ since you add the exponents in this case. You wrote 1/6 a... | 4 | [
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0.047119140625,
0.000640869140625,
0.07373046875,
-0.1494140625,
0.017456... | 36,801 | 36801 | |
Indeterminancy locus of rational maps
up vote 0 down vote favorite
Let $K=\bar{\mathbb{Q}}(\mathbb{P}^2_\bar{\mathbb{Q}})$, the function field of $\mathbb{P}^2_\bar{\mathbb{Q}}$. Let $C/K$ be a smooth projective curve over $K$ in $\mathbb{P}^2_K$ and let $f$ be a
morphism over $K$, $f: C \longrightarrow C$ and we deno... | 4 | [
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0.04052734375,
-0.051025390625,
0.0568847... | 36,802 | 36802 | |
a difficult geometry proof
May 1st 2009, 02:54 PM #1
Newbie
Joined
May 2009
Posts
3
a difficult geometry proof
Here is the problem.
Consider an isoceles triangle ABC.
Please see the diagram below and IGNORE the dots which are used to show the positions of the points. Point D is a point on side ... | 4 | [
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-0... | 36,803 | 36803 | |
Side Length of Octagon Inscribed in Square
Date: 9/11/96 at 19:38:16
From: Anonymous
Subject: Side Length of Octagon Inscribed in Square
Hello,
I have a piece of plywood (48"x48") and I would like to cut an
octagon out of the middle. How do I get all eight sides equal? What
calculations are needed?
Date: 9/12/96 ... | 4 | [
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0.046... | 36,804 | 36804 | |
Numbers on a Star Brain Teaser
Date: 01/03/2008 at 22:16:17
From: Linda
Subject: 5th grade brain teaser - Mom, Dad & older sister can't solve
We have a number sequence of 20, 21, 22, 23, 24, 25, 27, 28, 29 and
31. The numbers are to be placed on a star so that each line of four
numbers has a sum of 100. Each nu... | 4 | [
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-0.0329589... | 36,805 | 36805 | |
Discrete Mathematics Problem (Proofs)
Prove for all M and N, if M and M-N are even, then N is even.
Assume, by contradiction, that $N$ is odd. Then, $N=2k+1$ for some $k \in \mathbb{N}$ We also know that $M = 2r$ for some $r \in \mathbb{N}$. Then, $M-N = 2r - (2k+1) = 2(r-k) + 1$ which is an odd
number, thus $M-N$ is ... | 4 | [
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0... | 36,806 | 36806 | |
Linear Equation: Removing Negative Variables
July 15th 2012, 07:15 AM
allyourbass2212
Linear Equation: Removing Negative Variables
Problem:
$4x-2>5x+1$
$-x>3$
$x<-3$
In the final step the negative variable was removed. In the book, no additional steps or explanation is given. I am assuming the... | 4 | [
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-0.037841796875... | 36,807 | 36807 | |
inequality involving a fraction
Firslty you want to identify the points at which the expression is equal to zero. That is, solve x-1/x+2 = 0. Multiplying up by x gives x^2 + 2x - 1 = 0, which has solutions x = -1 + sqrt(2) and -1 -
sqrt(2), approximately 0.414 and -2.414 respectively. This particular expression also ha... | 4 | [
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Equilateral Triangle Inscribed in Circle
January 22nd 2007, 05:34 PM
symmetry
Equilateral Triangle Inscribed in Circle
An equilateral triangle is inscribed in a circle of radius r. Express the circumference C of the circle as a function of the length x of a side of the triangle.
HINT GIVEN:
First show ... | 4 | [
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Find the Smallest Triangle
Date: 05/25/2001 at 14:59:13
From: Malau
Subject: To find the triangle length depending on the condition
Hello sir,
Here is the problem:
Given a triangle whose three sides are consecutive numbers, i.e.
x, x+1, and x+2 (where x is an integer, and the area of which is
divisible by 20, find... | 5 | [
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Happy Birthdays
Problem 1170 was solved by Richard Yanco and Joseph DeVincentis. Here is DeVincentis's solution.
There are two cases of happy birthday years to consider.
For years within the century of birth, if the year is AB and the age is BA, then birth year must be (A − B)(B − A), and since A must be grea... | 4 | [
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0.0028076171875... | 36,811 | 36811 | |
Fourier-Mukai transform - a first example
up vote 4 down vote favorite
2
Suppose $X$ and $Y$ are schemes of finite type over a field, and let $f: X\rightarrow Y$ be a morphism. Let $\Gamma_f$ be the closed subscheme of $X\times Y$, then the first example of the
Fourier-Mukai transform says that $$f_*()=p_Y{_*}(p_X^*()... | 4 | [
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Solution of Plateau Problem for a simple, smooth closed curve on a Riemannian Manifold (Kahler) gives a surface that can be parametrized by a closed disk?
up vote 4 down vote favorite
3
Hi,
Perhaps it's a stupid question, in that case i'll delete it. Let M be a compact orientable smooth (Kahler if changes things) man... | 4 | [
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0.01031494140625,
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-0.03271484375... | 36,813 | 36813 | |
Recurrence Relation HELP
May 2nd 2009, 08:13 PM #1
Newbie
Joined
May 2009
Posts
14
Recurrence Relation HELP
1. In predicting future sales of a product, one assumption is to say that the amount sold next year will be the average of the amount sold this year and last year. Suppose that
an is the amoun... | 4 | [
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confuse.....
August 1st 2008, 07:55 PM
yong
confuse.....
what is limit? how to link limit with differentiation? how to link limit with the first principle when i learnt in form 5? how they work out the first principle?
question :
1) modulus X+4 smaller or equal to modulus X-3.
why can we square both ... | 5 | [
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rf directional coupler
RF Directional Couplers
Copyright by Michael G. Ellis, Ph.D.
... | 4 | [
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Solving Harmonic Motion Problems with a period/seconds in decimals
March 12th 2011, 09:19 AM #1
Junior Member
Joined
Jul 2010
Posts
55
Solving Harmonic Motion Problems with a period/seconds in decimals
An object is attached to a coil spring, the object is propelled downwards fromits rest prosition at tim... | 5 | [
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Curvature formula
up vote 4 down vote favorite
1
Suppose I have a homogeneous cubic polynomial $f(w,x,y,z)$ and I let $X$ be the set of points in $\mathbb{R}^4$ where $f(w,x,y,z)=0$ and $w^2+x^2+y^2+z^2=1$. Suppose that this is a smooth surface,
and I give it the metric inherited from $\mathbb{R}^4$. Does anyone know ... | 5 | [
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0.0308837890625... | 36,818 | 36818 | |
circle geometry
August 21st 2010, 05:10 AM #1
Junior Member
Joined
May 2009
Posts
29
circle geometry
points A, B, C, D, E and F lie on the circumference of a circle.
Prove that angle ABC + angle CDE + angle EFA = 360 degrees
Draw a circle with all the points on the circumference and the centre ... | 4 | [
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0.02807617187... | 36,819 | 36819 | |
OFR Design
For a printable, formatted version of this document, click here (requires Adobe Acrobat Reader)
The Paired-Comparison: A Good Design for
Fa... | 5 | [
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[SOLVED] Differentiate
March 1st 2009, 03:19 PM
ronaldo_07
[SOLVED] Differentiate
I want to differentiate this $2e^{2x}(Acos(x)-Bsin(x))+e^{2x}(-Asin(x)+Bcos(x))$
I have put the a terms together to make it simpler am i right in doing so?
$Ae^{2x}(2cos(x) - sin(x)))+ Be^{2x}(2sin(x) + cos(x))$
I ne... | 5 | [
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$\Phi: Hom_R(A,B) \to Hom_R(A,R)\otimes_R B$
up vote 1 down vote favorite
Let $R$ be a commutative ring and $A$ and $B$ two $R$-module. Suppose that $A$ is free of rank $n$ with basis $a_1,\dots,a_n$. Then there is an isomorphism $\Phi: Hom_R(A,B) \to Hom_R(A,R)\otimes_R
B$ defined by $\Phi(\sigma)=\sum_{i=1}^n \psi_i... | 4 | [
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... | 36,822 | 36822 | |
complex number question
October 25th 2006, 08:56 PM
scorpion007
complex number question
1) Use De Moivre’s theorem to show that $(1 + i \tan(x))^5 = \frac{1}{\cos^5(x)} cis (5x)$
2) Hence, find expressions for cos (5x) and sin (5x) in terms of tan(x) and cos(x).
October 25th 2006, 09:01 PM
scorpion007
... | 5 | [
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0.0044250... | 36,823 | 36823 | |
A form of cohomology and base change
up vote 3 down vote favorite
Let $f \colon X \to Y$ be a proper morphism of (Noetherian) schemes, $\mathcal{F} \in \mathop{Coh}(X)$. Let $i_Z \colon Z \hookrightarrow Y$ be a closed subscheme and take the inverse image $W := X \
times_Y Z \overset{i_W}{\hookrightarrow} X$.
If we a... | 5 | [
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-0.05346679687... | 36,824 | 36824 | |
Matrix Determinant / Complex numbers.
1. November 21st 2008, 01:21 PM #1
2. November 21st 2008, 01:31 PM #2
For the first one, try to turn that matrix into a left triangular one, then you'll get easily the determinant.
As for the second question, it's just Euler's formula application.
3. Novemb... | 5 | [
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-0... | 36,825 | 36825 | |
Math Help
April 3rd 2009, 09:39 AM #1
Newbie
Joined
Apr 2009
Posts
4
Please help
Hi,
I am clueless on how to do the attached questions...Will be grateful if someone could help me here...
Thanks a ton
Regards,
Last edited by nodi1310; April 4th 2009 at 10:42 AM.
Hello,
Questi... | 5 | [
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Solving Linear Systems
October 8th 2008, 07:53 PM #1
Member
Joined
May 2008
Posts
103
Solving Linear Systems
use elementary row operations to reduce the given matrix to (a) row echelon form and (b) reduced row echelon form.
[-2 -4 7
-3 -6 10
1 2 -3]
$\begin{bmatrix}-2&-4&7\\-3&-6&10\\1&... | 4 | [
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0.0927734375,
0.00927734375,
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0.01171875,
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0.055908203125,
0.000698089599609375,
-0.050537109375,
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0.015869140625,
-0.07763671875,
0.... | 36,827 | 36827 | |
application of differentiation
October 29th 2009, 08:17 AM #1
Newbie
Joined
Oct 2009
Posts
2
hello everyone, i have this question which i am unsure what to start with..
A pole a+b meters high stands vertically in a river b meters deep. Assume a > b. How many meters above the surface of the water must... | 5 | [
-0.0654296875,
-0.001678466796875,
0.023193359375,
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0.046142578125,
0.040771484375,
0.031982421875,
0.181640625,
-0.021484375,
0.04467773437... | 36,828 | 36828 | |
Precise Def of a Limit Problem
July 19th 2010, 01:32 PM
bobsanchez
Precise Def of a Limit Problem
Given the limit as x approaches 1 of (4 + x -3x^3) = 2 find the value of delta that correspond to sigma = 0.25.
I never got to these with my self-study. Can someone explain this type of problem quickly? I under... | 5 | [
-0.0303955078125,
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0.0159912109375,
-0.08... | 36,829 | 36829 | |
method of cylindrical shells
August 29th 2006, 04:00 PM
FLTR
method of cylindrical shells
Use the method of cylindrical shells to find the volume of the solid rotated about the line $x=-1$ given the conditions: $y=x^3-x^2; y=0;x =0$
August 29th 2006, 04:10 PM
ThePerfectHacker
Look at the picture.
Let ... | 5 | [
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0.05029296875,
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0.00121307373046875,
-0.... | 36,830 | 36830 | |
Lecture 2: Differential Eqns and Difference Eqns
The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare offer high quality educational resources for free. To make a donation or to view
additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at o... | 5 | [
-0.0966796875,
0.002288818359375,
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0.02001953125,
-0.05126953125,
-0.044677734375,
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-0.051025390625... | 36,831 | 36831 | |
comparision test
December 31st 2009, 06:17 AM
Abbas
comparision test
Use a comparison to determine whether the integral converges or diverges:
A $\int \frac{x^2e^x}{lnx}dx =$ from 2 to infinite
This integral diverges , but how can I show that using the comparison test?
B $\int \frac{1000}{pi^(2x)+... | 5 | [
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0.03564453125,
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0.00555419921875,
-0.02978515625,
0.044921875,
-0.02416... | 36,832 | 36832 | |
Counting Odd Coefficients
Date: 05/27/98 at 20:12:23
From: Ehsan
Subject: Number Theory
Hi.
The question is: If (1+x)^100 is multiplied out, how many of the
coefficients are odd? How would you generalize?
The way I tried to tackle the problem was that I set the equation
equal to ((1+x)^4)^25. Then I multiplied out... | 4 | [
0.052490234375,
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-0.010498046875,
-0.07617... | 36,833 | 36833 | |
Grade 11 High School Circles Question
November 29th 2008, 07:34 PM #1
Super Member
Joined
Nov 2008
Posts
597
Grade 11 High School Circles Question
I really do not understand how to do this:
"An athlete uses a sling to throw a projectile at a target 15m away. He spins the sling in a circle above his ... | 4 | [
0.046142578125,
0.0712890625,
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0.07080078125,
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0.068359375,
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0.0031... | 36,834 | 36834 | |
Eigenvalues and Eigenvectors
From Math Images
Introduction
If you are familiar with matrix multiplication, you know that a matrix times a vector produces a vector, and most of these products turn out to be different from the original vector,
i.e. $A\vec{v}=\vec{x}$ where $\vec{v}eq\vec{x}$
What if I told you t... | 5 | [
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0.0717773437... | 36,835 | 36835 | |
I need HELP FAST!!!
June 25th 2006, 04:42 PM #1
Newbie
Joined
Jun 2006
Posts
15
I need HELP FAST!!!
it takes Bill 2 hours longer to do a job than jerry. they work together for 2 hours; then jerry takes over and completed the job in 1 hour. how long would it take arch along to do the job?
Brooke
... | 4 | [
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-0.0458984375,
-0.0537... | 36,836 | 36836 | |
Math Help
September 16th 2007, 06:06 AM #1
Series
I need help with these four questions (If possible, can it be explained in steps):
1.
Work out $\displaystyle\sum_{r=n}^{2n}\frac{r^2}{1}$
2.
Given that $f(r) \equiv 1 \frac{1}{r(r+1)}$, show that $f(r) - f(r+1) \equiv \frac{2}{r(r+1)(r+2)}$
... | 4 | [
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0.053466796875,
-0.016845703125,
0.0712890625... | 36,837 | 36837 | |
Why is a monoid with closed symmetric monoidal module category commutative?
up vote 9 down vote favorite
5
Given a symmetric monoidal category and a monoid object A in it, one can form the category of modules over this monoid object, i.e. objects are $A \otimes M \rightarrow M$ satisfying the natural
properties analog... | 4 | [
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-0... | 36,838 | 36838 | |
calculating flux through a surface
April 21st 2009, 12:20 PM
TheRekz
calculating flux through a surface
My question is:
Compute the flux of the vector field, $\vec{F}$ , through the surface, S.
$\vec{F} = 7\vec{r}$ and S is the part of the surface $z = x^2 + y^2$ above the disk $x^2 + y^2 \leq 4$ orient... | 5 | [
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0.050... | 36,839 | 36839 | |
btech
www.jntuworld.com
Code No: 09A1BS01 R09 Set No. 2
I B.Tech Examinations,June 2011
MATHEMATICS-1
Common to CE, M... | 4 | [
-0.06884765625,
-0.0087890625,
0.0093994140625,
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... | 36,840 | 36840 | |
Cardinality, Area, and Probability
Date: 09/05/2003 at 19:04:36
From: Giuseppe Urbani
Subject: Cantor, cardinality and randomness the infinite
Divide a rectangle into two parts, one with twice the area of the
other. Pick a point randomly within the rectangle. It would appear
that the probability of choosing a point... | 5 | [
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-0.07470703125,
-0.01422119140625,
-0.05... | 36,841 | 36841 | |
Tempered distributions
February 28th 2010, 07:18 AM #1
Tempered distributions
Hi
Problem: Show that if $b\in \mathbb{R}$ and $b eq 0 \; , e^{-a|\mathbf{x}|^{2}}$ converges temperately to
$e^{-ib|\mathbf{x}|^{2}}$ as $a$ approaches $ib$ from the right half-plane. Deduce that
$<br /> \mathcal{F}\left[... | 4 | [
-0.007415771484375,
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0.00007152557373046875,
-0.00640869140625,
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0.042724609375,
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0.0322265625,
-0.02197265625,
0.05517578125,
-... | 36,842 | 36842 | |
Perfect Square?
Date: 02/18/2002 at 14:34:15
From: charles
Subject: Advanced algebra
If we use the digits 1,2,3,4,5,6,7 each only once to form a 7-digit
number, can the resulting number be a perfect square?
Date: 02/18/2002 at 20:47:51
From: Doctor Paul
Subject: Re: Advanced algebra
No. There are 7! = 5040 differ... | 5 | [
0.006927490234375,
0.047119140625,
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0.052001953125... | 36,843 | 36843 | |
Question about ordered topology
April 6th 2010, 11:16 AM #1
Junior Member
Joined
Feb 2010
Posts
37
Question about ordered topology
This is a Munkres's problem: Let Y be an ordered set with the ordered topology and f,g functions from X to Y, show that the set $\{x:f(x)\leq g(x)\}$ is closed. I can show th... | 5 | [
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-0... | 36,844 | 36844 | |
im stuckk on polymonial equation.. need help!
October 6th 2009, 01:12 AM
fvaras89
im stuckk on polymonial equation.. need help!
So i was following the textbook with dividing the polynomial to find a quadratic factor..
the polynomial is 4x^3 -10x^2 -8x +6 =0
and i was dividing it by x-3 as it is a root o... | 4 | [
0.0123291015625,
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0.007110595703125,
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-0.051025390625,
0.0625,
-0.... | 36,845 | 36845 | |
Russian Peasant Multiplication
Date: 11/01/97 at 19:07:59
From: Karl Gabzdyl
Subject: Russian peasant multiplication
Dear Dr. Math,
Could you please tell us what Russian peasant multiplication is?
The parent of a gifted 4th grader.
With great respect,
Karl A. Gabzdyl
Date: 11/05/97 at 14:59:04
From: Doctor Terr... | 4 | [
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0.104003... | 36,846 | 36846 | |
System of Equations
January 27th 2009, 06:39 PM #1
Newbie
Joined
Jan 2009
From
New York
Posts
5
I am familair with these type of problems but I am having a hard time setting it up. I would normally use mathematics but I cannot identify the variables. (ie x+y+z+?)
A student has money in three acco... | 4 | [
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... | 36,847 | 36847 | |
Chinese Rem. Thm.
March 24th 2007, 01:51 PM #1
Member
Joined
Sep 2006
Posts
221
Chinese Rem. Thm.
1.) Utilizing the Chin. Rem. Thm., find 5 consec. pos. integers such that the following conditions hold: the first is div. by 2, the 2nd is div by 3, the 3rd is div by 5, the 4th is div. by 7 and
the fin... | 5 | [
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-0.0218505859375,... | 36,848 | 36848 | |
solving an equation
Determine k and solve the equation x^3 -kx^2 + 20x +12 = 0. Thanks
my bad... Determine k and solve the equation x^3 - kx^2 +20x + 12 = 0, if one of its zeros is the triple of another.
Let $a,b,c$ be zero's (counting multiplicity). One of its zeros, say $c$, is triple of another, say $a$. Thus, $c=... | 4 | [
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0.00714111328125,
-0.03515625,
0.04223... | 36,849 | 36849 | |
Practice problems help:
November 13th 2013, 06:36 AM #1
Newbie
Joined
Nov 2013
From
Pittsburgh
Posts
3
Practice problems help:
#1
The top and bottom margins of a poster are 8 cm and the side margins are each 9 cm. If the area of printed material on the poster is fixed at 384 square centimeters, f... | 5 | [
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0.091796875,
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0.05078125,
-0.0712890625,
... | 36,850 | 36850 | |
Power and Energy
Homepage
Professional Pages
Personal Pages
The Nutshell Essays:
Power and Energy (Watts and kWh) in a Nutshell
Larry Miloshevich
ON THIS WEBSITE, as in life, it's often useful to understand how electricity is measured (Watts and kWh). This is useful, for example, to plan the size of a solar ... | 4 | [
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0.059814453125,
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-0.035888671875,
-0.01055908203125,
-... | 36,851 | 36851 | |
The Final Frontier
June 30th 2009, 12:02 PM
VonNemo19
The Final Frontier
Hey Guys
A Satellite weighs 10lbs on the surface of the earth. A rocket carrying the satellite is leaving the earth at a rate of 2000mph. Assume that the radius of the earth is approximately 3960mi. and
that the force describing th... | 5 | [
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... | 36,852 | 36852 | |
Solve the radical equation
Hi all, I need help/directions on how to solve this problem: Thank you much.
Just to clarify, do you mean $\sqrt3x-2$ or $\sqrt{3x}-2$ or $\sqrt{3x-2}$?
Oh, sorry, the third one. The square root of 3x-2
Ok. Here's my attempt: $x-\sqrt{3x-2}=4$ $x-4=\sqrt{3x-2}$ $(x-4)^2=\sqrt{3x-2}^2$ $x^2... | 4 | [
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... | 36,853 | 36853 | |
CS345 Data Mining (PowerPoint download)
Link Analysis Algorithms
Page Rank
Slides from Stanford CS345, slightly modified.
Link Analysis Algorithms
Page Rank
Hubs and Authorities
Topic-Specific Page Rank
Spam Detection Algorithms
Other interestin... | 4 | [
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0.03930... | 36,854 | 36854 | |
List of Classifying Spaces and Covers
up vote 30 down vote favorite
34
I am looking for a list of classifying spaces $BG$ of groups $G$ (discrete and/or topological) along with associated covers $EG$; there does not seem to be such cataloging on the web. Or if not a
list, just some further fundamental examples. For in... | 4 | [
-0.10302734375,
-0.07861328125,
-0.0361328125,
0.07275390625,
0.08154296875,
0.068359375,
0.02294921875,
-0.0634765625,
-0.027099609375,
-0.0712890625,
0.02880859375,
-0.05615234375,
-0.0274658203125,
-0.003936767578125,
-0.0216064453125,
0.021484375,
-0.026123046875,
-0.0170898437... | 36,855 | 36855 | |
Exponential and logarithmic
April 8th 2008, 03:52 AM #1
Junior Member
Joined
Dec 2007
Posts
41
Exponential and logarithmic
hey, i haven't been for quite a while
1. If you invest $100 at 2% per day, compounding daily, the amount of money you would have after x days is given by y=100(1.02)^x. For how ... | 4 | [
0.0439453125,
-0.0101318359375,
0.0015106201171875,
0.0045166015625,
0.0025177001953125,
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0.0966796875,
0.03515625,
-0.05126953125,
0.0478515625,
0.000492095947265625,
-0.06298828125,
0.02880859375,
0.06298828125,
0.11865234375,
0.064453125,
-0.08837890625,
-0.04028320... | 36,856 | 36856 | |
Kinematic #3
September 6th 2009, 10:49 AM #1
Junior Member
Joined
Oct 2008
Posts
68
Kinematic #3
Can someone help me with this problem. Thank you very much! Here is what I did so far.
Question: A train is traveling at 100 m/s. The engineer applies the brake b/c he sees a bike on the tracks ahead. Th... | 4 | [
-0.04931640625,
0.059814453125,
0.060546875,
-0.01263427734375,
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0.055419921875,
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0.0908203125,
-0.0023345947265625,
0.0296630859375,
0.09716796875,
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0.050048828125,
0.036865234375,
-0.07275390625,
0.107421875,
0.06396484375,
-0.0324... | 36,857 | 36857 | |
Maths online
Permutations and Combinations.
1. How many numbers less than `n!` are divisible by all prime numbers less than `n`? What is the number for `1000`? Please show the work-out.
2. Prove that `2nCn` is always divisible by `2^{2}`, except when n is a power of 2.
3. Prove that `2^{n+1}C2^{n}` is divisible by 2... | 5 | [
0.07080078125,
0.005767822265625,
-0.01446533203125,
0.0289306640625,
0.0194091796875,
0.025634765625,
0.09228515625,
0.091796875,
-0.0205078125,
-0.01324462890625,
-0.055908203125,
0.00592041015625,
0.037109375,
0.03564453125,
-0.049560546875,
-0.016357421875,
0.036376953125,
-0.0... | 36,858 | 36858 | |
Convergence of mountain pass solutions of $-\Delta u+u=u|u|^{p-2}$
up vote 2 down vote favorite
2
Consider the following equation in $\mathbb{R}^N, N \ge 3$: $$ (E) \quad -\Delta u +u=|u|^{p-2}u, $$ where $2 < p < 2^{*} =2N/(N-2)$.
Denote by $J: H^1(\mathbb{R}^N) \to \mathbb{R}$ the functional that's naturally associ... | 5 | [
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0.022216796875,
0.0322265625,
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0.0537109375,
0.06005859375,
0.040283203125,
0.03173828125,
-0.1044921875,
-0.08203125,
-0.036376953125,
0.02880859375,
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-0.042724609375,
0.0238037109375,
-0.001617431640625,
-0.01092529296875,
-0.04516... | 36,859 | 36859 | |
How much?
August 30th 2006, 09:46 AM
Neffets...:P
How much?
Hi...
In a triangle ABC are AB= 7 cm, BC= 4cm and angle BAC = 32 degrees...
How much can you increase angle BAC, while AB and BC are unchanged?
Can you guys help me on this?
Would be appreciated! :)
August 30th 2006, 10:11 AM
ThePe... | 4 | [
-0.0235595703125,
0.0439453125,
0.0037841796875,
0.056396484375,
-0.0703125,
0.0029296875,
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0.07666015625,
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0.033935546875,
0.002471923828125,
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0.00823974609375,
0.048583984375,
0.01055908203125,
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0.0106201171875,
... | 36,860 | 36860 | |
Proof by Induction - Divisibility Proofs
September 20th 2011, 11:50 AM
GrigOrig99
Proof by Induction - Divisibility Proofs
Q. Prove by induction that...
Please see attachment.
The end result should be divisible by 6, but it hasn't worked out that way for me. Can someone help me spot where I've gone wro... | 4 | [
-0.0194091796875,
0.031494140625,
-0.016357421875,
0.09228515625,
0.076171875,
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0.051513671875,
0.047607421875,
-0.035400390625,
0.01300048828125,
-0.0625,
-0.052490234375,
0.07275390625,
0.055419921875,
-0.07763671875,
-0.047119140625,
-0.0615234375,
0.01635742187... | 36,861 | 36861 | |
Quadrature, interpolation and observability
Abstract: Methods of interpolation and quadrature have been used for over 300 years. Improvements in the techniques have been made by many, most notably by Gauss, whose technique applied to
polynomials is referred to as Gaussian Quadrature. Stieltjes extended Gauss's method t... | 4 | [
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0.03857421875,
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0.021728515625,
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-0.00177764892578125,
-0.00009012222... | 36,862 | 36862 | |
Differentiation?
April 25th 2009, 10:38 PM #1
Differentiation?
If u = e^(arcsin (y/u)), then prove that d^2y/dx^2 = 2(x^2 + y^2)/(x - y)^3 , where u = √(x^2 + y^2)
Hello,
This is equivalent to $\ln(u)=\arcsin(y/u)$
-> Implicit differentiation with respect to x...
Left side :
$\frac{\partial... | 5 | [
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0.052490234375,
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0.0230712890625,
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0.0252685546875,
-0.048828125,
-0.0473... | 36,863 | 36863 | |
taylor series
how would you do this? Find the Taylor series for ln(x) about 2.
see here if you need further explanation, just say so topsquark showed you the main process of deriving something like this, but again, memorization could be used here, the page i gave you has the
general formulas
Just for the record, let ... | 5 | [
0.008056640625,
-0.1279296875,
0.04541015625,
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-0.0181884765625,
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0.0517578125,
0.044921875,
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-0.05029296875,
-0.058837890625,
0.01513671875,
-0.043212890625,
0.0084228515625... | 36,864 | 36864 | |
inhomogeneous linear differential equation
February 1st 2009, 09:38 AM
rajr
inhomogeneous linear differential equation
b)
Determine the general solution of the inhomogeneous linear differential equation
y′ = [xy / (1+x^2)] + SQRT [ (1+x^2) / (1-x^2)]
by the method of integrating factor.
Februa... | 5 | [
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0.11474609375,
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0.0322265625,
0.05419921875,
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0.033935546875,
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-0.0128173828125,
0.0234375,
-0.064453125,
... | 36,865 | 36865 | |
Trying to go back to school to learn calculus (x-2) / (x+4) <7
September 11th 2012, 11:32 PM
Blafin
Trying to go back to school to learn calculus (x-2) / (x+4) <7
Ok, I know this problem is an algebra one and not a calculus but the issue is that I am trying to get back into maths (mature age student here) and h... | 4 | [
0.01409912109375,
-0.0005035400390625,
0.004547119140625,
-0.01116943359375,
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0.0205078125,
-0.053466796875,
0.023193359375,
-0.0262451171875,
0.027099609375,
0.006378173828125,
0.005126953125,
0.05908203125,
0.06005859375,
-0.0174560546875,
0.053466796875,
-0.001586914... | 36,866 | 36866 | |
High dimensional beta integral (a typo in Stein's book "singular integrals")
up vote 1 down vote favorite
1
Hello,
When I read Stein's book of Singular Integrals, at p. 118, there is an obvious mistake:
$$ \int_{R^n} |x-y|^{-n+\alpha} |y|^{-n+\beta}=\frac{\gamma(\alpha)\gamma(\beta)}{\gamma(\alpha+\beta)},\quad 0<\a... | 5 | [
0.00567626953125,
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0.1494140625,
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-0.02197265625,
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0.006561279296875,
0.03955078125,
-0.069335... | 36,867 | 36867 | |
Critical Points
October 13th 2009, 03:18 PM #1
Banned
Joined
Sep 2009
Posts
35
Critical Points
Fine the absolute minimum and absolute maximum of the function on the interval [0,6]
$F(x) = \frac{x}{x^2+16}$
I did the minimum already, it's just the maximum.
f(x) = x
f'(x) = 1
$g(x) =... | 5 | [
-0.00396728515625,
0.00726318359375,
-0.01080322265625,
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0.03173828125,
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0.111328125,
0.0274658203125,
0.0032806396484375,
0.07373046875,
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0.0810546875,
0.0703125,
-0.07568359375,
0.036376953125,
0.10791015625,
-0.... | 36,868 | 36868 | |
Solve for Variable
May 30th 2009, 11:49 AM
suddenlysmarter
Solve for Variable
S= n/2[2a + (n - 1)d]
please solve and show the steps to get there. I'm confused at how they reached the answer the book has. Thanks
May 30th 2009, 01:24 PM
pberardi
May 30th 2009, 02:57 PM
mr fantastic
Quote:
This i... | 4 | [
-0.09033203125,
0.046142578125,
0.099609375,
0.0439453125,
-0.0281982421875,
0.0576171875,
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0.00116729736328125,
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0.0400390625,
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-0.04296875,
-0.0869140625,
0.04296875,
0.004974365234375,
-0.039306640... | 36,869 | 36869 | |
Party Solution
The problem can be solved by applying the spectral theory of graphs (see for instance Bollobas' excellent book, Extremal Graph Theory).
The problem's condition is vacuous if there is only N=1 person at the "party", impossible if N=2 (If you aren't your own friend, nor I mine, somebody else must be our m... | 5 | [
-0.007598876953125,
0.007537841796875,
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0.0361328125,
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0.08203125,
0.0625,
-0.057373046875,
-0.... | 36,870 | 36870 | |
generating an equation for a problem
March 6th 2009, 05:27 PM #1
Newbie
Joined
Mar 2009
Posts
7
generating an equation for a problem
I am trying to help my grade 9 daughter solve this problem
Man has e mail about concert
Man sends email to 10 friends on day 1 so 10 people know about event
Ea... | 4 | [
0.0537109375,
0.032958984375,
0.052490234375,
0.0010528564453125,
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0.03759765625,
0.00567626953125,
0.0673828125,
-0.01153564453125,
-0.0588... | 36,871 | 36871 | |
topological type of smooth manifolds with prescribed homotopy type and pontryagin class
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
Can someone help explain the following result:
If the ... | 4 | [
-0.06298828125,
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0.002685546875,
-0.0859375,
0.07421875,
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-0.01904296875,
-0.025146484375,
-0.0732421875,
0.00173187255859375,
-0.14550781... | 36,872 | 36872 | |
Equicontinuity of continuous families of maps between topological vector spaces
up vote 2 down vote favorite
Let $X$ and $Y$ be locally convex, Hausdorff topological vector spaces and let $[a,b] \subset \mathbb{R}$. Let $f: [a,b] \to \hom(X,Y)$ be continuous, where $\hom(X,Y)$ is the space of continuous
linear maps fr... | 4 | [
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-0.0380859375,
0.091796875,
-0.01123046875,
-0.034912109375,
-0.014770... | 36,873 | 36873 | |
Fun With Numbers!
I have always had a certain love for math and the neat things you can do with it. Here is a bit of information and shortcuts I have picked up in a few of my math classes.
Pascal’s Triangle
Pascal’s Triangle is a pretty neat thing. It is very simple to construct and can be used to understand a lot o... | 5 | [
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0.033935546875,
-0.07421875,
-0.060791015625,
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0.007080078125,
-0.0732421875,
0.023193359375,
-0.09619140625,
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0.01007080078125,
-0.02783203125,
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-0.01019287109375,
-0.10791015625,
0.0... | 36,874 | 36874 | |
another simple statics problem
October 16th 2009, 03:33 PM #1
Newbie
Joined
Sep 2009
Posts
10
another simple statics problem
Unfortunately, there are no examples in the book like this and I don't have any physics books.
The answer in the back of the book says k = 11.2 lb/ft. But the spring is only ... | 5 | [
-0.0458984375,
-0.024169921875,
0.0181884765625,
-0.041259765625,
0.0126953125,
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0.05615234375,
-0.05419921875,
0.07861328125,
0.0084228515625,
0.0269775390625,
0.00640869140625,
0.033935546875,
-0.0634765625,
0.1103515625,
-0.06298828125,
0.076171... | 36,875 | 36875 | |
Proving equality of varieties by dimension counting
up vote 5 down vote favorite
2
For finite sets $A$ and $B$, it is clear that $A \subseteq B$ and $|A| \geq |B|$ implies $A = B$. While an obvious fact, it can sometimes be a nice shortcut in proofs.
Analogously, if $V$ and $W$ are finite-dimensional vector spaces su... | 4 | [
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0.0260009765625,
0.053466796875,
0.004913330078125,
0.130859375,
0.02587890625,
... | 36,876 | 36876 | |
A Simple Analog Multiplier
Introduction
I regularly get questions on using solar panels to power our Fiber-To-The-Home gear (FTTH). You might think that sounds kind of odd, but it makes a lot of sense for many businesses and
municipalities. For example, every municipality has water towers, sewage lift stations, and e... | 4 | [
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0.02001953125,
0.0272216796875,
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0.01495361328125,
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0.046630859375,
0.0234375,
-0.00012302398681640625,
0.0301513671875,
0.014404296875,
0.08398... | 36,877 | 36877 | |
Trying to solve a Trig Equation
April 30th 2012, 09:12 AM #1
Newbie
Joined
Apr 2012
From
London
Posts
1
Trying to solve a Trig Equation
Hi There,
I've just joined the forum, and this is my first post. I'm an engineer working on problem with some angle offsets in a device, and would like to be ab... | 5 | [
-0.07373046875,
-0.004302978515625,
0.0172119140625,
0.08740234375,
-0.04541015625,
0.04296875,
-0.0771484375,
-0.00116729736328125,
0.01409912109375,
0.0263671875,
0.038818359375,
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0.10107421875,
0.017578125,
0.05810546875,
0.003662109375,
-0.015625,... | 36,878 | 36878 | |
finding derivatives
For a), apply the chain rule: $\left[f(g(t))\right]^{\prime}=f^{\prime}(g(t))\cdot g^{\prime}(t)$. In you case, let $f(t)=t^4$ and $g(t)=4t+5$. For b), apply quotient rule: $\left[\frac{f(x)}{g(x)}\
right]^{\prime}=\frac{g(x)f^{\prime}(x)-f(x)g^{\prime}(x)}{\left[g(x)\right]^2}$ In your case, let $f... | 5 | [
-0.03271484375,
0.0230712890625,
0.0908203125,
-0.048828125,
-0.0654296875,
0.00860595703125,
0.0289306640625,
-0.006591796875,
-0.0146484375,
0.07275390625,
0.115234375,
0.003509521484375,
0.002777099609375,
-0.0015869140625,
-0.005615234375,
0.044921875,
-0.031494140625,
0.059570... | 36,879 | 36879 | |
gr-cosmology
Cosmology with General Relativity
Foundations
Special relativity
Shortest paths between two points (geodesics) can have
various shapes
Mass alters the shapes of geodesics.
The Metric: How to specify the geometry of
space
Let dl specify an incremental distan... | 4 | [
-0.027587890625,
-0.08544921875,
0.059814453125,
-0.0230712890625,
-0.04541015625,
0.01708984375,
0.0034942626953125,
0.0244140625,
0.0859375,
-0.0927734375,
0.036865234375,
-0.028564453125,
-0.103515625,
0.03271484375,
0.030517578125,
-0.1005859375,
0.041259765625,
0.0091552734375... | 36,880 | 36880 | |
Projective dimension of simple module
up vote 4 down vote favorite
1
Let $R$ be a (not necessarily commutative) ring and $M$ a simple right $R$-module. Then $\mathfrak{m}=Ann(M)$ is a maximal ideal of $R$. It is seems known that $$ pdim_{R}(M)=pdim_{R_{\mathfrak{m}}}
(M_{\mathfrak{m}}) $$ where $R_{\mathfrak{m}}$ is t... | 4 | [
-0.07080078125,
0.0272216796875,
-0.048095703125,
-0.007293701171875,
0.0732421875,
0.0021209716796875,
-0.021728515625,
0.1044921875,
-0.08837890625,
-0.0380859375,
0.003448486328125,
-0.04833984375,
0.043701171875,
-0.006683349609375,
-0.01007080078125,
0.08544921875,
0.04272460937... | 36,881 | 36881 | |
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Topic: can the Maxwell Equations demand magnetic monopole... | 4 | [
-0.09765625,
-0.00020885467529296875,
-0.0089111328125,
-0.004486083984375,
-0.044677734375,
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0.041748046875,
0.0654296875,
0.040283203125,
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0.051025390625,
0.059814453125,
-0.0859375,
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mathschallenge.net
Mean Claim
Problem
The contents of twelve boxes of matches were recorded as:
34, 31, 29, 35, 33, 30, 31, 28, 27, 35, 32, 31
On the box it stated, "Average contents 32 matches", but the sample mean can be shown to be about 31.3.
When the company received a complaint that the average contents is l... | 5 | [
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Sorry Guys - One last Improper Integration question (e^x)/ ((e^x) -1) Why Divergent??
December 17th 2012, 05:31 PM
skinsdomination09
Sorry Guys - One last Improper Integration question (e^x)/ ((e^x) -1) Why Divergent??
Sorry. I'm coming to the end of my four hour review. I try not to disturb you guys too much bu... | 5 | [
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Finiteness of stable homotopy groups of spheres
up vote 12 down vote favorite
5
Since the work of Serre in the early 50's on homotopy groups of spheres, it is known that the homotopy group $\pi_k(S^n)$ is finite, except when $k=n$ (in which case the group is $\mathbb{Z}$), or
when $n$ is even and $k=2n-1$ (in which ca... | 4 | [
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... | 36,885 | 36885 | |
nontrivial subgroup
March 17th 2010, 05:47 PM #1
Newbie
Joined
Mar 2010
Posts
4
Show that a group G has no nontrivial subgroups if and only if it is a cyclic group of prime order
If $G=\{e\}$ we're done. So, assume not. Then, let $g\in G-\{e\}$ we must clearly have that $\langle g\rangle\leqslant G$ ... | 5 | [
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... | 36,886 | 36886 | |
Colimits of covers
up vote 3 down vote favorite
1
Suppose I have category $C$ equipped with a Grothendiek pretopology of covers, and let $y:C \to Sh(C)$ be the Yoneda embedding into sheaves and $y/c:C/c \to Sh(C)/y(c)\cong Sh(C/c)$. How can I show
that if $F:J \to C/c$ is any functor such its diagram consists only of ... | 4 | [
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Topic: THE FREQUENCY OF THE PI VALUE IN POINT - Part 22 :... | 4 | [
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-0.07714843... | 36,888 | 36888 | |
Logarithmic differentiation
February 22nd 2010, 10:13 PM #1
Newbie
Joined
Feb 2010
Posts
13
Logarithmic differentiation
Logarithmic differentiation
Having some problems with these question....
f(x) and g(x) are two differentiable functions and f(x)>0 for all x.
Consider h(x) = f(x)^g(x)
... | 5 | [
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Counting Answer Keys
Date: 05/25/2001 at 12:52:38
From: Alison Vickery
Subject: Combinations / Permutations
A multiple-choice test has 30 questions, each with five choices. How
many answer keys are possible?
This is a question on my students' pre-algebra test. I believe the
answer should be 5^30. The book claims th... | 4 | [
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need help with an Eucledian algorthim and gcd involving factorials and large exponets
September 9th 2012, 06:21 PM #1
Newbie
Joined
Sep 2012
From
MD
Posts
14
I have not seen a problem like this before so I would be very grateful for some for some guidance. the problem is to find the gcd(100! + 99, 100... | 5 | [
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Proof that domains of positivity of symmetric nondegenerate bilinear forms are self-dual cones?
up vote 4 down vote favorite
Max Koecher (in, for example, The Minnesota Notes on Jordan Algebras and Their Applications (new edition: Springer Lecture Notes in Mathematics number 1710, 1999)), defined a domain of positivit... | 4 | [
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Optimization for a triangle + square
October 10th 2012, 04:41 PM #1
Newbie
Joined
Oct 2012
From
Colorado
Posts
3
Optimization for a triangle + square
1,000 feet of fencing is going to be cut into two pieces. One of the pieces will be used to enclose a square playground and the other will be to enclos... | 4 | [
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Special values of a doubly periodic meromorphic function
up vote 2 down vote favorite
1
Consider the following function: $G(z) = \prod_{n \in \mathbb{Z}} {1 \over{\tanh^2\left(\pi\left(z-n\right)\right)}}$.
By constuction, it has poles at $z=m+in$ with $m,n \in \mathbb{Z}^2$.
Additionally, it is doubly periodic suc... | 5 | [
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[SOLVED] Metric Space and Inequality
July 31st 2008, 08:28 AM #1
Member
Joined
Jul 2008
Posts
119
[SOLVED] Metric Space and Inequality
Problem:
For any two functions f and g in C([0,1],R), define
a. Prove that this defines a metric on C([0,1],R)
b. Prove that the following inequality relatin... | 5 | [
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Implicit differentiation
October 23rd 2009, 01:36 PM
kodos
Implicit differentiation
Let F: $R^2 \rightarrow R$ be a function $C^2$ for which F(x+y,y+z)=0 defines implicitly z=f(x,y) around a point (a,b,c). Verify that in (a,b)
dz/dx-dz/dy=1
I'm having difficulty with getting rid of some derivatives, the... | 4 | [
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Show x is a unit iff N(x)=1 in Z[w]
January 26th 2008, 07:35 PM #1
Super Member
Joined
Mar 2006
Posts
705
Thanks
2
Show x is a unit iff N(x)=1 in Z[w]
Let $<br /> w = \frac {-1}{2} + \frac {3^{1/2}}{2}i<br />$, let $<br /> N:Z[w] \rightarrow Z \ by\ N(a+bw) = a^2 - ab + b^2<br />$ and suppose that x ... | 5 | [
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Embedding of BV and L^P spaces
up vote 1 down vote favorite
An elementary question about Sobolev spaces:
Is there some explicit theorem about embedding relation between spaces BV(Omega) and L^P(Omega)?
e.g. is BV a subset of L^2 (i.e. BV possess regularities of L^2)?
real-analysis ca.analysis-and-odes fa.functional... | 5 | [
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Can a non-surjective polynomial map from an infinite field to itself miss only finitely many points?
up vote 64 down vote favorite
23
Is there an infinite field $k$ together with a polynomial $f \in k[x]$ such that the associated map $f \colon k \to k$ is not surjective but misses only finitely many elements in $k$ (i... | 4 | [
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