content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
DEALING-WITH-KEY-COMBINATIONS-OF-FUNCTION-SYMBOLS
how to get rid of key combinations of function symbols
Major Section: INTRODUCTION-TO-THE-THEOREM-PROVER
Suppose REV reverses a list, MEMBER checks that its first argument is an element of its second, and SQUARES-PLUS-3P is some complicated predicate. Suppose you're... | 5 | [
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0.04687... | 46,100 | 46100 | |
Set Theory Problems (please help)
January 26th 2009, 01:33 PM #1
Junior Member
Joined
Nov 2008
Posts
53
1. Prove that
a) $(A-B) \cap C = (A \cap C) - (B \cap C)$;
b) (A symmetric difference B) = $(A U B) - (A \cap B)$
Last edited by mr fantastic; January 26th 2009 at 05:47 PM. Reason: Fixed... | 4 | [
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Contribution Margin Ratio
Contribution Margin Ratio (CM Ratio):
Posted on March 20, 2014 by Robert
Learning Objectives:
• Define and explain contribution margin ratio.
• Calculate CM ratio.
• What is the importance and benefit of calculating CM ratio?
Definition of Contribution Margin Ratio:
The contributi... | 4 | [
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Principal bundles in the etale and Zariski topology and extensions of the structure group
up vote 3 down vote favorite
1
Say $G$ is a reductive group over a field $k$. I usually take $k = \mathbb{C}$ so assume what you want about the field except maybe that its finite. If $X$ is a scheme over $k$ then a principal $G$
... | 4 | [
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Paracompact but not Hausdorff
Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
Do paracompact non-Hausdorff spaces admit partions of unity? I'm just curious.
add comment
The answer is no. Take the "classical" example of... | 5 | [
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in theory
You are currently browsing the monthly archive for February 2011.
In which we give an explicit construction of expander graphs of polylogarithmic degree, state the properties of the zig-zag product of graphs, and provide an explicit construction of a family of
constant-degree expanders using the zig-zag pr... | 4 | [
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A refined version of Krull's height theorem
up vote 3 down vote favorite
3
A classical result in algebraic geometry states that every irreducible component of a variety defined by $r$ polynomials in affine $n$-space has dimension not less than $n-r$. This is a special case
of Krull's height theorem which states that i... | 5 | [
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Series and sequences
November 28th 2008, 03:25 AM #1
Member
Joined
Oct 2008
From
Melbourne
Posts
166
I'm having problem with this question.
Do I use the ratio test for this infinite series? if so, can you show a few steps to get me going, or if not, what should I use?
$\sum\limits_{n=1}^{\in... | 5 | [
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W9 L17 CENTRAL FORCE MOTION
CENTRAL – FORCE MOTION
When a particle moves under the influence of a force directed toward a fixed
center of attraction, the motion is called central-force motion.
Motion of a Single Body
Consider a particle of mass m moving... | 4 | [
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... | 46,108 | 46108 | |
Fourier sine series...
February 10th 2008, 05:05 AM
hunkydory19
Fourier sine series...
Let f(x) = cos x on 0<= x <= pi. Calculate the Fourier sine series representation of f(x).
Can anybody possibly start me off on this question or give me any help at all as I don't understand my lecture notes on this topic... | 5 | [
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Posts about expository on Lewko's blog
A key component in the work of Green, Tao, and Ziegler on arithmetic and polynomial progressions in the primes is the dense model theorem. Roughly speaking this theorem allows one to model a dense
subset of a sparse pseudorandom set by dense subset of the the ambient space. In the... | 5 | [
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what am i doing wrong? finding the inverse of the matrix
February 21st 2013, 01:11 PM
MariaBlood777
what am i doing wrong? finding the inverse of the matrix
the question is find the inverse the matrix.
[3 1][1 0]
[4 2][0 1]
in Calc Chat (step by step) they multiplied 1/2(R2) first then did -R2 + R1... | 4 | [
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Proof dealing with a closed set
February 11th 2011, 05:33 PM #1
Member
Joined
Nov 2009
Posts
79
Show that the set E' of points of accumulation of any set E must be closed.
Not too sure what to do with this; I understand why it is but really don't have a clue how to show it. Help please?
What is ... | 4 | [
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dy
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Here's the question you clicked on:
lindseyharrison Group Title
What is the si... | 4 | [
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... | 46,113 | 46113 | |
What is this measure on the affine Weyl group?
up vote 1 down vote favorite
Let $G$ be $SL(n, F)$ for a non-archimedean local field $F$ with Iwahori subgroup $I$. Let $\mu$ be the Haar measure of $G$.
What are the properties of the function $w\mapsto \mu(IwI)/\mu(I)$ for $w$ being an element of the normalizer $N$ of ... | 4 | [
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Reply to comment
June 2007
Leonhard Euler, 1707 - 1783
Let's begin by introducing the protagonist of this story — Euler's formula:
V - E + F = 2.
Simple though it may look, this little formula encapsulates a fundamental pro... | 4 | [
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Cesaro means and Banach limits
up vote 7 down vote favorite
3
Consider the class of bounded sequences to which every Banach limit (non-negative shift-invariant continuous functional on $l^\infty$ taking convergent sequences in the usual sense to their limits)
assigns the same limit value.
Does a sequence belong to th... | 5 | [
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0.02... | 46,116 | 46116 | |
How Big is a Googolplex?
Date: 05/29/2003 at 08:59:21
From: Jim
Subject: Googolplex
Is there anything on Earth that is as big as a googolplex?
Date: 05/29/2003 at 10:16:17
From: Doctor Ian
Subject: Re: Googolplex
Hi Jim,
It's pretty easy to set up a situation in which the number of possible
_arrangements_ of a se... | 5 | [
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When the Lovász theta-function saturates its upper bound
up vote 7 down vote favorite
1
The Lovász $\vartheta$-function of a graph $G$, $\vartheta(G)$, is well-known to be "sandwiched" between the independence number of the graph, $\alpha(G)$, and the chromatic number of its complement,
$\chi \(\overline{G})$. When $G... | 5 | [
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Area of a Crescent
Date: 06/18/2001 at 10:34:37
From: John Dixon
Subject: Area of a crescent - as in an eclipse
When observing a total eclipse of the sun we need to determine the
area of the sun that has not been covered by the moon. The important
point is that the eclipse magnitude (the ratio of the apparent size o... | 4 | [
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vector independence proof question..
March 4th 2009, 01:06 PM #1
MHF Contributor
Joined
Nov 2008
Posts
1,401
vector independence proof question..
prove that vectors $v_1$,.., $v_n$ on a vectorinc space V over feild F
are linearly dependant if and only if there is an index 1<=i<=n
so $v_i$ is a le... | 4 | [
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Depreciation
Straight-line Method of Depreciation
In straight line depreciation method, depreciation is charged uniformly over the life of an asset. We first subtract residual value of the asset from its cost to obtain the depreciable amount. The
depreciable amount is then divided by the useful life of the asset in n... | 4 | [
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-... | 46,121 | 46121 | |
Flushing Dreams: Part I
Brian Alspach
Poker Digest Vol. 3, No... | 5 | [
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Math Forum Discussions
Re: The ambiguity of 0^0 on N
Posted: Sep 19, 2013 11:34 AM
On 09/19/2013 09:51 AM, Dan Christensen wrote:
> On Thursday, September 19, 2013 7:26:55 AM UTC-4, Peter Percival wrote:
>> Dan Christensen wrote:
>>
>>> On Wednesday, September 18, 2013 7:11:53 PM UTC-4, Rotwang wrote:
>>
>>
>>
>>>>
>>... | 4 | [
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Find an expression for B inverse in terms of B
March 16th 2011, 03:34 PM #1
Newbie
Joined
Nov 2010
Posts
11
Find an expression for B inverse in terms of B
Hi everyone,
I am stuck on this question, because I do not know any properties for square matrices when you multiply them together. I'm not sure ... | 5 | [
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-... | 46,124 | 46124 | |
Easy integration problem.
let $x=3\sin(t) \implies dx=3\cos(t)dt$ $\int \sqrt{9-x^2}dx=\int \sqrt{9-9\sin^2(t)}(3\cos(t))dt=$ $9\int \cos^2(t)dt =\frac{9}{2}\int 1+\cos(2t)dt=\frac{9}{2}t+\frac{9}{4}\sin(2t)+c=$ $\frac{9}{2}
t+\frac{9}{2}\sin(t)\cos(t)+C$ Now we need to solve for t and cos(t) $x=3\sin(t) \iff \frac{x}{... | 5 | [
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0.058349609... | 46,125 | 46125 | |
Mersenne primes problem
up vote 0 down vote favorite
1
Well, I need someone here with programming skills (because I have none of it) to check if this problem that I am proposing is at least true for the known Mersenne primes, and here is the list of the
exponents of the known Mersenne primes :
http://wwwhomes.uni-bie... | 5 | [
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0.00103759765625,
-0.0703125,
0.0... | 46,126 | 46126 | |
Proving that every term of the sequence is an integer
up vote 15 down vote favorite
2
Let $m,n$ be nonnegative integers.
The sequence $\{a_{m,n}\}$ satisfies the following three conditions.
1. For any $m$, $a_{m,0}=a_{m,1}=1$
2. For any $n$, $a_{0,n}=1$
3. For any $m\ge0, n\ge1$, $a_{m+1,n+1}a_{m,n-1}=a_{m+1,n-1}... | 5 | [
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0.032470703125,
-0.032... | 46,127 | 46127 | |
Is there a maximum to the amount of disjoint non-measurable subsets of the unit interval with full outer measure?
up vote 9 down vote favorite
4
This question arose a few years back when I was an assistant teacher on a course of basic (Lebesgue) measure theory, but I didn't find an answer or anyone able to solve the p... | 4 | [
0.03515625,
-0.05810546875,
0.032470703125,
-0.00634765625,
-0.04052734375,
-0.017333984375,
0.05859375,
0.0125732421875,
0.004913330078125,
-0.021240234375,
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-0.04833984375,
0.1337890625,
0.000606536865234375,
0.021484375,
0.012939453125,
0.095703125,
-0.03112792968... | 46,128 | 46128 | |
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Topic: Matrix Proofs
Replies: 0
Matrix Proofs
Posted... | 4 | [
-0.046142578125,
0.06396484375,
-0.04443359375,
-0.03369140625,
-0.0546875,
-0.0174560546875,
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0.0050048828125,
0.00677490234375,
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0.03466796875,
0.035888671875,
-0.0537109375,
0.00118255615234375,
0.125,
0.04931640625,
-0.032470703... | 46,129 | 46129 | |
Finding covariant derivative of a riemanian submanifold
up vote 0 down vote favorite
1
Hi, I have a question about properties which are common to a manifold and its submanifolds. I start with the metric. $ M \subset N, dim(M) = m, dim (N) = m+1 $ let $ g^N $ be the metric of N, so that
$ (N,g^N) $ is a riemanian manif... | 4 | [
0.0255126953125,
0.028076171875,
0.076171875,
-0.03662109375,
-0.040771484375,
0.02685546875,
0.054931640625,
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-0.038818359375,
-0.03271484375,
0.0247802734375,
0.035888671875,
-0.056884765625,
-0.04833984375,
0.0191650390625,
0.049560546875,
-0.000010132789611816406,
... | 46,130 | 46130 | |
Finding the value of variables
January 21st 2014, 07:51 PM #1
Newbie
Joined
May 2010
Posts
22
Thanks
1
Finding the value of variables
Hi there,
I have a question I'd like some help with please. I need to find the values for r and h in a cylinder. I have the volume from which to work. This needs t... | 4 | [
0.03173828125,
0.05078125,
-0.0654296875,
-0.032958984375,
0.020751953125,
0.0810546875,
-0.052734375,
0.0888671875,
-0.020751953125,
0.00144195556640625,
-0.05126953125,
0.0306396484375,
0.06103515625,
0.1064453125,
0.0277099609375,
0.003753662109375,
-0.0172119140625,
0.011474609... | 46,131 | 46131 | |
Multi-variable pdf.
December 2nd 2011, 08:27 PM #1
Junior Member
Joined
Jan 2010
Posts
33
Multi-variable pdf.
Hello,
Would someone please help explain this to me?
Given:
$f(x,y) = {\rm{ \{ }}{e^{ - y}},{\rm{ }}0 < x < y$ and = 0 elsewhere
Find P(x>1, y>1)
So the set up happen to be as... | 5 | [
-0.0478515625,
0.037109375,
0.0155029296875,
-0.08447265625,
0.068359375,
-0.0546875,
-0.03271484375,
-0.000579833984375,
-0.06787109375,
-0.0213623046875,
0.0034942626953125,
0.0257568359375,
0.0267333984375,
0.040771484375,
0.00165557861328125,
-0.034912109375,
-0.060546875,
-0.1... | 46,132 | 46132 | |
Non-negative quadratic maximization
up vote 5 down vote favorite
3
For a given symmetric and positive semidefinite $n \times n$ matrix $A$, we want to solve the problem $$\max_{||x|| = 1, \ x\geq 0} x^T A x.$$ Here, $x\geq 0$ indicates that $x$ must be
component-wise non-negative. Without the $x\geq 0$ constraint, the... | 4 | [
0.02734375,
-0.03173828125,
-0.0279541015625,
-0.09765625,
-0.01153564453125,
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-0.041748046875,
-0.0478515625,
0.06591796875,
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0.09814453125,
0.0322265625,
0.052490234375,
0.038330078125,
0.06396484375,
0.1298828125,
-0.050537109375,
... | 46,133 | 46133 | |
A Question on Random Matrices
up vote 11 down vote favorite
6
Consider the following $n\times n$ random matrix $V_{n}$ where the $(p,q)$ entry is given by $$ V_{n}(p,q):= \frac{1}{\sqrt{n}}\exp(2\pi i(p-1) x_{q}) $$ where $x_{1},x_{2},\ldots,x_{n}$ are iid
random variables with uniform distribution on $[0,1]$.
It is ... | 4 | [
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0.0059814453125,
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-0.046630859375,
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0.0262451171875,
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0.05615234375,
0.00927734375,
0.01007080078125,
0.0224609375,
-0.02978515625,
0.0458984375,
-0.039306... | 46,134 | 46134 | |
trig sub integral?
March 1st 2009, 06:58 PM #1
Member
Joined
Feb 2009
Posts
106
trig sub integral?
so, the problem is integral sq rt (1-4x^2)dx
i really didn't know how to start, other than the fact that it looks sort of like the a^2-x^2 form of trig sub (in which i think you're supposed to make x= ... | 5 | [
-0.00145721435546875,
-0.05126953125,
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0.0205078125,
-0.055419921875,
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0.03173828125,
0.0233154296875,
0.00885009765625,
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0.06689453125,
-0.00946044921875,
0.05224609375,
0.0703125,
-0.... | 46,135 | 46135 | |
Finding Area of Shaded Region - Thomas' Calculus P. 385 #39
March 1st 2009, 10:12 AM
scherz0
Finding Area of Shaded Region - Thomas' Calculus P. 385 #39
Hello everyone,
Could someone please check my work to see where I've erred? My answer is slightly below the one given by my textbook.
Thank you!
... | 5 | [
-0.00848388671875,
0.018798828125,
0.07861328125,
-0.03125,
0.048583984375,
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0.06005859375,
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0.034423828125,
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0.0257568359375,
-0.03662109375,
-0.050048828125,
0.006256103515625,
0.0211181640625,
-0.08... | 46,136 | 46136 | |
Which endomorphism algebras are not Morita-trivial?
up vote 4 down vote favorite
Let $\mathcal C$ be a symmetric monoidal category — for example, $\mathcal C$ might be the category of $R$-modules for a commutative ring $R$. At a minimum, I request further that:
1. $\mathcal C$ is closed under coequalizers. (I genera... | 4 | [
0.0026092529296875,
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0.03125,
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0.010986328125,
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0.08984375,
0.095703125,
0.0732421875,
0.042236328125,
0.083984375,
-... | 46,137 | 46137 | |
Finding two linearly independent solutions (power series)
April 24th 2013, 03:57 PM #1
Newbie
Joined
Apr 2013
From
USA
Posts
7
Finding two linearly independent solutions (power series)
for (x^2+2)y'' +3x-y = 0 about the ordinary point x = 0
my guess was y = sum c_nx^n
I think that I did my ... | 4 | [
-0.08203125,
-0.0194091796875,
-0.0028228759765625,
0.0279541015625,
0.04443359375,
0.05908203125,
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-0.029541015625,
0.005950927734375,
-0.033447265625,
0.06396484375,
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-0.020751953125,
-0.083984375,
-0.033447265625,
-0.002349853515625,
-0.052978515625,
-0.... | 46,138 | 46138 | |
How fast can we numerically calculate Kloosterman sums?
up vote 13 down vote favorite
Define the usual Kloosterman sum by $$S(m,n;c) = \sum_{\substack{x \pmod{c} \\ (x,c) = 1}} e\Big(\frac{mx + n\overline{x}}{c}\Big),$$ where $x \overline{x} \equiv 1 \pmod{c}$, and $e(x) = e^{2 \pi i
x}$. I'm interested in knowing if ... | 4 | [
-0.047607421875,
0.035888671875,
0.0096435546875,
0.029541015625,
-0.007080078125,
0.03271484375,
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0.095703125,
0.0068359375,
-0.0341796875,
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0.01336669921875,
-0.05029296875,
-0.046875,
-0.05908203125,
0.08447265625,
0.0927734375,
-... | 46,139 | 46139 | |
The product of sines and the product of cosines of (k\pi)/(2n+1) for 0<k<n+1
October 17th 2011, 12:11 PM #1
Member
Joined
Feb 2011
Posts
147
Thanks
3
The product of sines and the product of cosines of (k\pi)/(2n+1) for 0<k<n+1
I have to prove the following identities:
$\prod_{k=1}^n \cos\frac{k\... | 4 | [
-0.10009765625,
0.020751953125,
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0.076171875,
0.00000622868537902832,
0.0081787109375,
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0.035400390625,
0.0126953125,
-0.06298828125,
-0.034912109375,
0.031005859375,
0.02... | 46,140 | 46140 | |
Horizontal tangents to an implicitly defined function
October 1st 2008, 10:37 AM #1
Junior Member
Joined
Sep 2008
Posts
55
Horizontal tangents to an implicitly defined function
Consider the implicit function: y-y^5=x^4-2x^3+x^2
dy/dx = 2x(2x^2-3x+1)/1-5y^4
Solving for dy/dx=0, there are 3 solut... | 5 | [
-0.03955078125,
-0.060791015625,
0.011962890625,
0.033203125,
0.0556640625,
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0.0216064453125,
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0.00677490234375,
0.0166015625,
0.0155029296875,
0.02783203125,
-0.0810546875,
-0.053955... | 46,141 | 46141 | |
Deterministic selection
ICS 161: Design and Analysis of Algorithms
Lecture notes for January 30, 1996
Deterministic selection
Last time we saw quick select, a very practical randomized linear expected time algorithm for selection and median finding. In practice, this is all you need to use. But for theoretical purpos... | 4 | [
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0.0185546875,
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-0.0615234375,
0.008544921875,
0.09228515625,
... | 46,142 | 46142 | |
mixing problem
August 9th 2009, 12:49 PM #1
Senior Member
Joined
Jun 2009
Posts
251
mixing problem
tank contains 1000L of water with 15kg of salt dissolved in it. Pure water enters tank at 10L/min and the mixture leaves at the same rate. How much salt is in the tank after t minutes?
Work:
let y(... | 5 | [
-0.09375,
0.0162353515625,
0.0556640625,
-0.04736328125,
0.021728515625,
-0.0986328125,
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0.068359375,
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0.09716796875,
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0.0634765625,
-0.0169677734375,
-0.033935546875,
-0.... | 46,143 | 46143 | |
Ordinary Differential Equation Problem
September 30th 2008, 02:51 PM #1
Member
Joined
Jan 2008
Posts
78
Ordinary Differential Equation Problem
Show that if Y (t); an n by n matrix, is the unique maximal solution of the
matrix IVP
Y'(t) = A*Y(t); Y (0) = I;
then Y has the characteristic proper... | 4 | [
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0.01104736328125,
0.0115966796875,
0.018798828125,
-0.0133056640625,
-0.018310546... | 46,144 | 46144 | |
Geometric series
May 7th 2011, 08:52 AM
elieh
Geometric series
A geometric series has first term a and common ratio r where r\geqslant 1
The sum of the first four terms of this series is 15 times the first term.
a) show that r^3 + r^2 +r -14=0
and having S4 = 15a
I've done the first part
Bu... | 4 | [
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0.02734375,
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0.0380859375,
0.1357421875,
-0.000865936279296875,
-0.006500244140625,
-0.0500488281... | 46,145 | 46145 | |
Parameterization
December 7th 2011, 11:48 AM #1
Member
Joined
Aug 2011
Posts
117
Parameterization
I have a problem that seems easy enough but i cant seem to find x and y
Problem: find a Parametrization for the graph of the function $y = x^2$
Starting at (3,9) and moving towards the origin,using ... | 4 | [
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0.06494140625,
0.0419921875,
0.095703125,
-0.0361328125,
-0.01055908203125,... | 46,146 | 46146 | |
Proof: An Isosceles Triangle inscribed in a Circle
September 6th 2011, 12:21 AM
goby
Proof: An Isosceles Triangle inscribed in a Circle
http://img69.imageshack.us/img69/5044/imagemta.jpg
Hypothesis: AC = CB
DE is the diameter
CH is perpendicular to AB (the altitude)
Thesis: DE : BC = BC : CH (BC^... | 4 | [
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-0.036376953125,
0.019409... | 46,147 | 46147 | |
LECTURE OUTLINE PART ONE
Part One: Multiple Correlation/Regression Analysis
I. Introduction
A. Syllabus: Schedule, Content, and Grading
B. Course Content: Correlations and Causal Models
II. Review and Overview: Critical Distinctions
A. Constants versus Variables
B. Dependent versus Independent Var... | 4 | [
0.10986328125,
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0.06884765625,
-0.044677734375,
-0.08837890625,
0.00897216796875,
0... | 46,148 | 46148 | |
The Brokentoaster Blog
UPDATE: Nophead now covers this better in this post.
In the course of building my extruder I chose not to modify my stepper motor. Instead of having a splined shaft on the motor I decided to use a splined pinch wheel similar to the brass M4 insert used
in the geared extruder driver. My pinch whe... | 4 | [
-0.1259765625,
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0.043212890625,
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0.07470703125,
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0.12109375,
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0.03662109375,
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-0.05615234375,
0.049560546875,
-0.001251220703125,
-0.01733398437... | 46,149 | 46149 | |
induction problem
October 26th 2008, 10:09 AM #1
Member
Joined
Sep 2008
Posts
76
induction problem
I have to prove that for all integers n>= 1
$1/3 = (1+3)/(5+7) = (1+3+5)/(7+9+11) = ... = 1+3+.....+$
$(1+3+...+(2n-1))/(2n+1)+....+(4n-1)$
don't know how to go about it.
Hello, NidhiS
... | 4 | [
-0.061279296875,
-0.016845703125,
0.055908203125,
-0.0869140625,
-0.0164794921875,
0.03466796875,
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0.0135498046875,
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0.015869140625,
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-0.02099609375,
-0.1103515625,
-0.0595703125,
0.045166015625,
-0... | 46,150 | 46150 | |
Calculate decay of medicine in human body
May 12th 2009, 09:12 AM
Uwe
Calculate decay of medicine in human body
This is basically a repost to Dr. Math over a week ago where I didn't receive an answer. Maybe they thought it was for homework.
A friend of mine is an internist who is going to carry out some stu... | 5 | [
0.017578125,
0.061279296875,
0.034423828125,
-0.029052734375,
-0.05859375,
-0.08837890625,
0.0067138671875,
0.1435546875,
-0.006378173828125,
-0.0208740234375,
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0.051025390625,
0.01397705078125,
0.103515625,
-0.0625,
0.017333984375,
0.00506591796875,
-0.014404296875... | 46,151 | 46151 | |
Hochschild Cohomology of Differential Operators in characteristic 0
up vote 11 down vote favorite
8
In Mariusz Wodzicki's paper "Cyclic homology of differential operators," the following result is mentioned: for $D_M$ the algebra of differential operators on a smooth manifold $M$ we have that $HH_n
(D_M) \cong H_{DR}^... | 4 | [
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0.0159912109375,
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0.01263427734375,
0.0888671875,
-0.056396484375,
0.08544921875,
... | 46,152 | 46152 | |
Reducible trinomials $x^{odd}+x^2+s(t)$ in characteristic $2$
up vote 3 down vote favorite
Let $F$ be a finite field of characteristic $2$. Let $m \geq 2 $ be a positive integer. Seems unknown if the trinomial $$ T(t,x) = x^{2m+1}+x^2+s(t) \in F[t][x] $$ (more explicitly, the constant
coefficient $s(t)$ is a polynomia... | 5 | [
-0.017333984375,
-0.0023956298828125,
-0.01495361328125,
0.039794921875,
0.021728515625,
0.0546875,
0.039794921875,
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-0.05322265625,
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0.08984375,
-0.019775390625,
0.039306640625,
-0.032470703125,
0.00885009765625,
0.0216064453125,
-0.018798828125,
... | 46,153 | 46153 | |
Math Forum Discussions
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Topic: Pairings
Replies: 1 Last Post: Jul 19, 1996 3:04 A... | 5 | [
0.01129150390625,
0.028076171875,
0.00156402587890625,
-0.07177734375,
-0.044189453125,
0.0654296875,
-0.0272216796875,
-0.00970458984375,
-0.06591796875,
-0.0712890625,
-0.068359375,
0.052734375,
0.0031585693359375,
0.001495361328125,
0.009033203125,
0.1015625,
0.0186767578125,
0.... | 46,154 | 46154 | |
Feeding Chickens - Arithmetical Progression
Date: 7/6/96 at 20:53:51
From: Wong Cheong Siong
Subject: Feeding Chickens
Dear Dr. Math,
1) On a certain date a farmer has 3000 hens. One week later he
sells 20 and he continues to do this each week.If each hen costs 8p
per week to feed, calculate the total cost of feedi... | 4 | [
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0.032470703125,
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0.01171875,
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0.031005859375,
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0.03466796875,
-0.06494140625,
-0.0084228515625,
-0.03125,
-0.07666015625... | 46,155 | 46155 | |
maximum velocity of a particle with 3d vector equation
February 6th 2010, 06:14 PM
shawli
maximum velocity of a particle with 3d vector equation
Find the maximum speed of a particle whose velocity v m/s, at any time t seconds is given by v $=2sin(t)$i $+ cos(t)$j $+ 3$k.
February 7th 2010, 12:36 AM
Sudharaka
... | 5 | [
-0.054931640625,
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0.0220947265625,
0.060546875,
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0.06005859375,
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0.0341796875,
0.04150390625,
0.056884765625,
0.00408935546875,
0.032470703125,
0.00994873046875,
-0.0084228515625,
0.08837890625,
0.069335... | 46,156 | 46156 | |
solving logarithmic complex variable equation
November 13th 2012, 04:28 PM #1
Newbie
Joined
Nov 2012
From
Canada
Posts
16
solving logarithmic complex variable equation
Can someone please verify if I have solved this equation properly
$Log (z^{2} -1)$ = $\frac{i \pi}{2}$
taking exp on both s... | 4 | [
-0.044189453125,
0.0308837890625,
0.02783203125,
0.0908203125,
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0.01318359375,
0.046875,
0.045166015625,
0.07568359375,
-0.053955078125,
0.042724609375,
0.11669921875,
0.0003910064697265625,
-0.0007476806640625,
-0.0081787109375... | 46,157 | 46157 | |
r
February 22nd 2008, 04:05 PM #1
Member
Joined
Sep 2007
Posts
76
2nd order diff eq
im having problems again with the constant at the end!! just need a bit of help trying to figure it out..
$<br /> \begin{gathered}<br /> \frac{{d^2 y}}<br /> {{dx^2 }} - 8\frac{{dy}}<br /> {{dx}} + 7y = 0 \hfill \\<... | 4 | [
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0.002960205078125,
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0.09375,
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0.00799560546875,
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0.01104736328125,
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-... | 46,158 | 46158 | |
Ages of Three Children
Date: 9/4/96 at 20:40:5
From: Jason
Subject: Ages of Three Children
During a recent census, a man told the census taker that he had three
children. When asked their ages, he replied, "The product of their
ages is 72. The sum of their ages is the same as my house number."
The census taker ran t... | 4 | [
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0.015380859375,
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-0.0... | 46,159 | 46159 | |
Proof by Induction (Diving a Plane into regions)
April 23rd 2008, 07:59 PM #1
Newbie
Joined
Apr 2008
Posts
6
Proof by Induction (Diving a Plane into regions)
Show that n lines separate the plane into (n^2 + n + 2) / 2 regions if no two of these lines are parallel and no three pass through a common point.... | 4 | [
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-0.... | 46,160 | 46160 | |
Arthimetic Series 2
February 25th 2013, 07:48 AM
Mathnood768
Arthimetic Series 2
1. The first three terms of an arithmetic sequence are given by x, (2x-5), 8.6.
Determine the first term and the common difference.
I know that d = t2 - 1 = t3 - t2
So, (2x-5)-(x) = 8.6 - (2x-5) (Trying to solve for d... | 4 | [
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-0.0712890625,
... | 46,161 | 46161 | |
Homomorphism more than 3/4 the inverse
up vote 11 down vote favorite
2
Suppose $G$ is a finite group and $f$ is an automorphism of $G$. If $f(x)=x^{-1}$ for more than $\frac{3}{4}$ of the elements of $G$, does it follow that $f(x)=x^{-1}$ for all $x$ in $G\ ?$
I know the answer is "yes," but I don't know how to prove... | 5 | [
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0.06640625,
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0.043212... | 46,162 | 46162 | |
Why are the following varieties symplectomorphic?
up vote 6 down vote favorite
3
I saw a statement somewhere that for the Hirzebruch surfaces $F_n:=\mathbb{P}_{\mathbb{P}^1}(\mathcal{O}\oplus\mathcal{O}(n))$, $F_n$ and $F_m$ are symplectormorphic when $m$ and $n$ have the same
parity.
My question is: Why is this true... | 5 | [
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0.033935546875,
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-... | 46,163 | 46163 | |
Examples of asymptotic formulas with optimal error term
up vote 12 down vote favorite
5
Many problems in analytic number theory regard the error term in asymptotic formulas. These problems usually take the form: prove that the number theoretic quantity $f(n)$ satisfies $f(n) = G(n) + O
(n^{e})$ for some exponent $e$ w... | 4 | [
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-0.037109375,
0.007446289... | 46,164 | 46164 | |
Solving Logarithms with the Quotient Rule
Date: 11/11/98 at 20:22:25
From: Tierney Sparks
Subject: Logarithms and dividing them
Dr. Math,
I have a test in a few days and really need your help. This problem is
bound to be on the test:
log(base5) (9x+2) - log(base5) (3x+8) = 2
My first step was to use the quotie... | 4 | [
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0.076171875,
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-0.134765625,
0.11816406... | 46,165 | 46165 | |
Probability of Hitting Safely
Date: 11/06/2001 at 09:44:38
From: Jacob Garvin
Subject: Probability
Calculate the probability that a baseball player batting .357 would
hit safely in at least 56 straight games, during the course of a 162-
game regular season, assuming 4 at bats per game.
I don't even know where to st... | 5 | [
0.083984375,
0.08984375,
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0.005035400390625,
0.06494140625,
0.039794921875,
-0.0693359375,
-0.00299072265625... | 46,166 | 46166 | |
Kolmogorov probability axioms without non-negativity condition
up vote 4 down vote favorite
3
What is a minimal consistent modification of probability axioms to include negative values? Is it enough to use a minimal modification of axioms obtained by formal exclusion of non-negativity
requirement, i.e.:
There are sam... | 4 | [
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0.0021209716796875,
0.053955078125,
0.018188476... | 46,167 | 46167 | |
The Problem-Independent Mapping
Next: Phases for Nogoods Up: A Search Algorithm Previous: A Search Algorithm
To take advantage of the potential cancellation of amplitude in nogoods described above we need a unitary mapping whose behavior is similar to the ideal mapping to supersets. There are two general
ways to a... | 4 | [
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0.0673828125,
-0.0184... | 46,168 | 46168 | |
Ternary sequence
April 30th 2007, 04:11 AM
smoothi963
Ternary sequence
A ternary sequence is a sequence of digits made up entirely of 0's, 1's, and 2's such as 002221102. (this is also known as a base three number)
A. How many 3-digit ternary sequences have exactly one 1?
B. How many 4-digit ternary se... | 4 | [
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0.005950927734375,
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0.0419921875,
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-0.0289306640625,
-... | 46,169 | 46169 | |
A question on Generalized Gauss-Bonnet Theorem
up vote 14 down vote favorite
15
Hello all,
I am trying to learn about basic characteristic classes and Generalized Gauss-Bonnet Theorem, and my main reference at the moment is 'From Calculus to Cohomology' by Madsen&Tornehave. I know the
statement of the theorem is as f... | 4 | [
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-0.0703125,
-0.0097656... | 46,170 | 46170 | |
So I'm having some trouble...
August 2nd 2008, 02:47 PM #1
Newbie
Joined
Aug 2008
Posts
16
So I'm having some trouble...
On a good number of questions. I realize I'm new here, but I hope to stick around. I have left a more sizable message after the problems, in case you're interested.
Here goes:
... | 5 | [
0.0262451171875,
0.00003123283386230469,
0.05859375,
-0.058349609375,
0.01025390625,
-0.051025390625,
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0.07275390625,
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-0.001922607421875,
0.103515625,
-0.0033416748046875,
0.0244140625,
0.004486083984375,... | 46,171 | 46171 | |
Line Tangent to an Ellipse
Date: 03/29/2003 at 18:21:40
From: Maya
Subject: A line tangent to an ellipse
Find the equation of the tangent to the ellipse x^2 + y^2 = 76 at each
of the given points. Write your answers in the form y = mx + b.
a. (8,2)
b. (-7,3)
c. (1,-5)
My main problem is finding the slope o... | 5 | [
-0.056396484375,
0.01904296875,
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0.0181884765625,
0.046142578125,
0.0272216796875,
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0.03271484375,
0.052978515625,
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0.0634765625,
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-0.05810546875,
-0.01019287109375,
0.035888671875,
0.140625,
-0.08251953125,
-0.00... | 46,172 | 46172 | |
Analytic Proof that Midpoints Form a Circle
Date: 03/10/98 at 06:10:03
From: Allan Dunlavy
Subject: Circle Geometry
I am doing a math project that investigates a "What if....?" game.
This game takes a circle and then you choose a point P within the
circle. Lines are then drawn from this point to points on the edge o... | 4 | [
-0.058837890625,
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0.078125,
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0.043212890625,
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0.0361328125,
0.026611328125,
0.03564453125,
-0.07275390625,
-0.01... | 46,173 | 46173 | |
Making CW-complexes metrizable
up vote 8 down vote favorite
2
It is a basic topological fact that CW-complexes aren't typically metrizable (they must satisfy a certain local finiteness condition) and the quotient topology is to blame.
Suppose $X$ is a finite dimensional CW-complex with countably many cells in each di... | 5 | [
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-0.05810546875,
-0.011596679687... | 46,174 | 46174 | |
slope of tangent
October 28th 2009, 10:13 AM #1
Member
Joined
Oct 2009
Posts
86
slope of tangent
Use "implicit differentiation" to find the slope of tangent when x= sqrt 3 for x^2 + y^2 = 4
i did
dx^2/dx + dy^2/dx = d4/dx
dx^2/dx = 2x
dy^2/dx = 2yy'
d4/dx = 0
2x + 2yy' = 0
... | 4 | [
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0.043701171875,
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0.06787109375,
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0.000188827514648437... | 46,175 | 46175 | |
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Topic: Volume of a Pyramid
Replies: 4 Last Post: Jan 29, ... | 4 | [
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0.030517578125,
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0.030517578125,
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0.041259765625,
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0.003204345703125,
0.015380859375,
0.08203125,
-0.00811767578125,
0.00750732421875,
0.0045776367187... | 46,176 | 46176 | |
Sample Paper for CLASS IX CCE CBSE MATHEMATICS Summative Assessment SA 2 - AVTE
Sample Paper
(Based on CBSE CCE SA - 2)
(IX) MATHEMATICS
[Time allowed: 3 hours] ... | 4 | [
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-0.039794921875,
... | 46,177 | 46177 | |
Math Help
June 11th 2006, 04:53 PM #1
Newbie
Joined
May 2006
Posts
20
Help
I don't know if this the right thread to get help, but here it goes.
Prove that:
|x + y|^2 + |x-y|^2 = 2|x|^2 + 2|y|^2 if x is an element of R^k and y is an element of R^k.
Interpret this geometrically, as a statem... | 4 | [
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... | 46,178 | 46178 | |
Proving
\displaystyle \begin{align*} \frac{2\tan{x}}{1 - \tan^2{x}} = \frac{2}{\cot{x} - \tan{x}} \end{align*} Please prove.
Hello, gashbell1! Quote: $\displaystyle\frac{2\tan{x}}{1 - \tan^2{x}} \;=\; \frac{2}{\cot{x} - \tan{x}}$ Left-to-Right: We have: . $\frac{2\tan x}{1 - \tan^2x}$ Divide numerator and denominator ... | 4 | [
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0.0179443359375,
-0.0101318359375,
0.070800... | 46,179 | 46179 | |
Convergence of an empirical distribution w.r.t. the Hellinger distance
up vote 5 down vote favorite
3
Let $P$ be a probability distribution on a finite set $\mathcal{X}$ and let $X_1, X_2, \ldots, X_n$ be drawn i.i.d. according to $P$. Define the empirical distribution:
$\hat{P_n}(x) = \frac{1}{n} \sum_{i=1}^{n} 1_{X... | 5 | [
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0.04052734375,
-0.07568359375,... | 46,180 | 46180 | |
Sequences
September 29th 2007, 10:45 AM
alikation0
Sequences
1a) Define $(x_n)$ as being the sequence:
$x_1 = 3$
$x_{n+1} = \frac{1}{2}\cdot (x_n + \frac{3}{x_n})$
Prove $x_n$ converges and find the lim.
b) Let $b > 1$ and define $(x_n)$ as being the sequence:
$x_1 = b$
$x_(n+1) = \... | 5 | [
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-0.076171875,
-0.0198974609375,
-0.0111083984375,
0.0296630859375,
0.039794921875,
-0.01599121... | 46,181 | 46181 | |
Differentiating an integral-defined function
July 31st 2013, 11:04 PM #1
Newbie
Joined
Jul 2012
From
Seoul, South Korea
Posts
8
Differentiating an integral-defined function
hi, i have a problem with differentiating please help
(I think) It is well known that for an integral-defined function, dif... | 5 | [
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0.033935546875,
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0.0152587890625,
0.02294921875,
0.02734375,
-0.0098876953125,
-0.000690460205078125,
0.0... | 46,182 | 46182 | |
Leaving single variable by itself.
September 9th 2005, 09:30 AM
Bagalk
Leaving single variable by itself.
I have the following equation
and I need to get n by itself. So far what I have done is:
Quote:
I*(R+nr) = nE
IR+Inr = nE
But I don't know what to do next since everything I do doesn't... | 4 | [
-0.07275390625,
0.08984375,
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0.03125,
0.07373046875,
0.03271484375,
-0.0191650390625,
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0.00090... | 46,183 | 46183 | |
Exponentials and trig functions
Hi, I'm having some trouble understanding the relationships between trig functions and exponential functions. I have a question with answers and just can't see how they simplify down to get to
where they do
$C_{k}= 1/{2\pi} \int_{-\pi}^{\pi} te^{-ikt} dt = - {(-1)^k}/{ik}$
... | 4 | [
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0.033447265625,
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0.05712890625,
0.0380859375,
-0.0595... | 46,184 | 46184 | |
Proof by Induction
Date: 7/3/96 at 19:0:59
From: Scott Turner
Subject: Proof by Induction
I'm trying to prove that 1 + 1/4 + 1/9 + ... 1/n^2 < 2 - 1/n for all
n > 1.
Now the base step is simple: n = 2: 1 + 1/4 < 2 - 1/2, true
The inductive step is assume true for n. I must show it is also true
for n + 1 so 1 + 1/... | 5 | [
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0.059326171875,
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0.059814453125,
-0.01086425... | 46,185 | 46185 | |
Enterprise and Equity Values
Calculating Enterprise Value
The enterprise value (EV) of the business is calculated by discounting the unlevered free cash flows (UFCFs) projected over the projection period and the terminal value calculated at the end of the
projection period to their present values using the chosen disc... | 4 | [
0.0556640625,
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0.07373046875,
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-0.01361083984375,
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-0.0166015625,
-0.03955078125,
-0.014343261... | 46,186 | 46186 | |
Probability of at Least 45 Heads in 100 Tosses of Fair Coin
Date: 05/15/2004 at 08:14:21
From: Joe
Subject: A different type of coin toss probability question
What is the probability of getting AT LEAST 45 HEADS out of 100
tosses of a fair coin?
I assumed that the answer would be P(45) + P(46) + .... + P(100).
When ... | 4 | [
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-0.037109375,
-0.00958251953125,... | 46,187 | 46187 | |
on product of some spaces
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
I know that $X$ is a topological space, $R$ is the real line, $S^n$ is n-sphere and $X\times R$ is diffeomorphic to $S^n\times R$. Is it true that ... | 5 | [
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0.03662109375,
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-0.051513671875,
0.047119140625,... | 46,188 | 46188 | |
Fibonacci members and powers of the golden ratio
May 22nd 2010, 09:10 AM #1
Newbie
Joined
May 2010
Posts
2
Fibonacci members and powers of the golden ratio
Hello. I searched for a topic for the same question, but my queries were fruitless, although they returned some similar questions. If i have missed i... | 4 | [
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0.0... | 46,189 | 46189 | |
Examples of CAT(0)-groups
up vote 4 down vote favorite
1
My question is the following:
Let M be a simply connected Riemannian manifold whose sectional curvatures are all nonpositive and let G be a group. Suppose that G acts in M properly discontinuous and cocompactly by isometries. Is
G a CAT(0) group?
mg.metric-geo... | 5 | [
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-0.0349121093... | 46,190 | 46190 | |
Trig identities.
May 26th 2010, 11:23 AM #1
Junior Member
Joined
May 2010
Posts
36
Trig identities.
Hi,
Im having a lot of trouble solving the following trig identities:
a) secē x-2 sec x cos x + cosē = tanē x - sinē x
b) $tan x + 1/ tanx = 1/sin x cos x$
My working:
For a):
... | 4 | [
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0.040771484375,
0.039794921875,
-0.0341796875,
0.024169921875,
0.0252685... | 46,191 | 46191 | |
Fast Fourier Transform (FFT)
¡@
Fast Fourier Transform (FFT)
¡@
In this section we present several methods for computing the DFT effic... | 4 | [
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0.098... | 46,192 | 46192 | |
I Already Have The Soltuions But Need The Step ... | Chegg.com
Fourier Transforms Electrical Engineering Signals and Systems/communications
I already have the soltuions but need the step by step process on how to solve
Image text transcribed for accessibility: Suppose x(t) = 2rect(t/2) + tri(t). Plot x(t). Plot y(t ... | 4 | [
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Noisy channel coding theorem
Talk0
34,135pages on
this wiki
Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Individual differences | Personality | Philosophy | Social |
Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology |
Cognitive Ps... | 4 | [
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0.03076171875,
-0.0266... | 46,194 | 46194 | |
Quotient spaces and equivalence relations
March 8th 2009, 02:47 PM #1
Member
Joined
Feb 2009
Posts
103
Quotient spaces and equivalence relations
Let I(x) denote the integer part of a real number x (ie the unique integer n such that $n \leq x < n+1$).
I can show that $x$ ~ $y$ iff $I(x) = I(y)$ is an... | 4 | [
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0.0390625,
-0.0184326171875,
-0.04345703125,
0.0703125,... | 46,195 | 46195 | |
Some Quick Questions for my Exam
June 24th 2007, 04:01 PM #1
Hello! I obviously don't mean for my exam. I mean some questions i want to cover for my studying for the exam. They may seem easy to you, but were not all blessed with gifts in Mathematic's so
here they are in easy order
How would this happen? 6... | 4 | [
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-0.080078125,
-0.004486083984375,
-0.05... | 46,196 | 46196 | |
Solving a System of Modular Equations with Multiple Variables
Date: 12/15/2004 at 15:01:30
From: Colin
Subject: Modular equations with multiple variables
Hello,
I have the following question which looked simple to me at first
glance, but is actually a difficult to solve set of modular equations.
(1919ab) mod 5107 =... | 5 | [
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0.07373046875,
-0.054443359375,
0.02722167968... | 46,197 | 46197 | |
Points of Intersection
Date: 08/31/97 at 17:01:35
From: Lisa Wang
Subject: Points of Intersection
Dear Dr. Math:
I'm a high school student taking calculus. I encountered this
problem, which really made me think. Please help me.
The problem is:
Estimate all points of intersection of the graphs f(x) = x + sin x a... | 4 | [
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... | 46,198 | 46198 | |
Limit of a Trigonometric Function
February 15th 2009, 06:15 PM #1
Newbie
Joined
Feb 2009
Posts
10
Limit of a Trigonometric Function
I need help taking the limit of this problem please:
f(x) = sin(x) / [x + tan(x)] as x approaches 0
Any help would be appreciated, thank you.
I am familiar wi... | 5 | [
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... | 46,199 | 46199 |