content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Math Help
September 24th 2008, 09:19 PM #1
Junior Member
Joined
Aug 2007
Posts
71
Roulette
A gambling book recommends the following winning strategy for the game of roulette. It recommends that the gambler bets $\1$ on red. If red appears (which has probability $\frac{18}{38}$), then
the gambler sho... | 5 | [
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0.0654296875,
-0.00775146... | 36,200 | 36200 | |
Relation between Sheaf and Group Cohomology
up vote 2 down vote favorite
4
Let $E=\mathbb{C}/L$ be an elliptic curve. Then $\mathbb{C}$ is contractible, and $L$ is the fundamental group of $E$. What's interesting is that we can find the cohomology of $E$, which is the same
as the sheaf cohomology $H^i(E,\mathbb{Z})$ f... | 4 | [
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-0.054931640625,... | 36,201 | 36201 | |
Greatest common divisor
March 15th 2009, 09:50 PM #1
Newbie
Joined
Mar 2009
Posts
8
Some help with these would be appreciated
1. Prove that if gcd(a,b)=1 and gcd(a,c)=1 then gcd(a,bc)=1
2. Prove that if a and b are relatively prime and c|a, then c and b are relatively prime
3. Prove that if... | 4 | [
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-0.040771484... | 36,202 | 36202 | |
Vector valued DE system
August 23rd 2011, 12:19 AM #1
Junior Member
Joined
Feb 2010
From
New Jersey
Posts
73
Vector valued DE system
In the last equal sign of the last line below, why is $- \lambda z = \ddot{z}$? Thanks.
Given the DE system
$\ddot{\mathbf{x}}=-kA\mathbf{x}$
where $\math... | 4 | [
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0.02... | 36,203 | 36203 | |
Is zero a hydrogen eigenvalue?
up vote 12 down vote favorite
4
This question has been bugging me for some time.
Take the hamiltonian for the hydrogen atom: $$\hat{H}=-\frac{1}{2}\nabla^2-\frac{1}{r},$$ acting on (a domain contained in) $L^2(\mathbb{R}^3)$. It is standard fact that this is an unbounded operator
which ... | 5 | [
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Why Factor?
Date: 08/18/2001 at 16:54:19
From: Kevin O'Neil
Subject: Factoring in algebra
I haven't seen this answer yet anywhere I've looked. WHY specifically
does one have to factor out a problem? My daughter is homeschooling
and we have an excellent Algebra 1 teacher, but it seems to be a
hard question to answer.... | 4 | [
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Does the bordism homology theory satisfy the weak equivalence axiom?
up vote 11 down vote favorite
5
There is an interesting and important homology theory called bordism. Briefly speaking, a singular manifold in a space $X$ is a pair $(M, f)$ where $M$ is a closed smooth manifold and $f : M \to X$
is a map. Two singul... | 4 | [
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Matrices
8-1.6 Factoring Polynomials TEACHER INSTRUCTIONS
ALGEBRA
2. Use algebraic concepts to identify patterns, use multiple representations of relations and functions, and apply
operations to expressions, equations... | 4 | [
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... | 36,207 | 36207 | |
Can analysis detect torsion in cohomology?
up vote 48 down vote favorite
20
Take, for example, the Klein bottle K. Its De Rham cohomology with coefficients in $\mathbb{R}$ is $\mathbb{R}$ in dimension 1, while its singular cohomology with coefficients in $\mathbb{Z}$ is $\
mathbb{Z} \times \mathbb{Z}_2$ in dimension 1... | 4 | [
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integrate (secx)^4
If you want the easy way out, use the general formula: $\int{sec^{n}(u)}du=\frac{1}{n-1}sec^{n-2}(u)tan(u)+\frac{n-2}{n-1}\int{sec^{n-2}(u)}du$ or proceed: $\int{sec^{4}(x)}dx=\int(1+tan^{2}(x))sec^
{2}(x)dx$ $=\int(sec^{2}(x)+tan^{2}(x)sec^{2}(x))dx$ $=\int{tan^{2}(x)}dx+\int{tan^{2}(x)sec^{2}(x)}dx... | 5 | [
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Math Forum Discussions
Re: Riemannian Metric Topology
Posted: Apr 2, 2012 4:57 AM
On Apr 1, 7:49 pm, Jeff Rubin <JeffBRu...@gmail.com> wrote:
> On Sunday, April 1, 2012 3:45:47 PM UTC-7, smn wrote:
> > On Mar 31, 8:12 am, Jeff Rubin <JeffBRu...@gmail.com> wrote:
> > > This is a question about a step in a proof that ap... | 4 | [
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Ratios
March 24th 2010, 01:05 AM
harold
Ratios
If the ratio of 2a to 3b is 1:4, what is the ratio of 4a to 3b?
How can I show that it's 1:2? (What's the algebra behind it?)
March 24th 2010, 01:12 AM
Bacterius
Quote:
Hello,
$\frac{2a}{3b} = \frac{1}{4}$
Multiply by 2 each side of the e... | 4 | [
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Find x-coordinate of stationary point
September 13th 2010, 11:31 PM
Punch
Find x-coordinate of stationary point
Find the x-coordinate of the stationary point of the curve $y=\frac{(x-1)^3}{x+1}$, $x>0$
What I did
$\frac{dy}{dx}=\frac{(x+1)(3)(x-1)^2-(x-1)^3}{(x+1)^2}$
Stationary Point, dy/dx=0
... | 4 | [
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Factorial Notation
August 17th 2011, 11:10 AM
momofmaxncoop
Factorial Notation
I keep having a hard time solving this factorial notation question. I know the steps but I'm having a brain fart of what the correct answer be to input into the next step.
(n+2)! =110
(n)!
(n+2)x(n+1)x(n)(n-1)(n-2)....x... | 4 | [
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tangentes
January 14th 2013, 06:19 AM
Boo
tangentes
Please:
if
f(x)=x^2-7x+6
and
g(x)= (x-1)(x^2+ax-2)
a)for which a afre graphs of the f and g functions in the (1,0) intersect under the angle of pi/4?
b) for which dots x tangent on graph of the function f in the point (x,f(x)) goes th... | 4 | [
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Trapezoid Rule is really ruling, need to be free, help!
March 23rd 2006, 04:09 AM #1
Newbie
Joined
Mar 2006
Posts
7
Trapezoid Rule is really ruling, need to be free, help!
--------------------------------------------------------------------------------
I am sitting here stuck on these three problems... | 5 | [
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Is this finite surjective flat morphism of 2 dimensional schemes a local complete intersection
up vote 8 down vote favorite
3
Let $X$ be a regular integral noetherian scheme of dimension 2 and let $D$ be a simple normal crossings divisor in $X$.
EDIT: Let $U = X-D$.
Consider a finite etale morphism $V\longrightarrow... | 5 | [
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A quadratic form represents all primes except for the primes 2 and 11.
up vote 14 down vote favorite
2
By computer calculations, I found the following conjecture that the quadratic form $4x^2 + 2xy + 3y^2 + 4w^2 + 2wz + 3z^2$ represents all primes except for the two primes 2 and 11. Is it possible to
prove the conjec... | 4 | [
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function growing/decresing on surroundings
November 27th 2010, 02:10 AM
transgalactic
function growing/decresing on surroundings
2y''+(y')^3=0
y(0)=5
y'(0)=0
i need to deside on :
A.is it increasing or decreasing or a constant on the surroundings of 0
B.does it has a solution
C.does it ha... | 4 | [
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0.0... | 36,218 | 36218 | |
Moschovakis Coding Lemma
up vote 2 down vote favorite
I trying to study the Coding Lemma (in descriptive Set Theory) and there is a small point in the proof that I don't understand. Let me first recall the version I'm studying ( there are different
version of the Moschovakis Coding lemma).
Assume AD. Let $\Gamma$ be ... | 4 | [
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Numerical differentiation
August 17th 2013, 02:44 PM #1
Hello,
I'm having "big" issue recalling formula for numerical differentiation... using front differences $(y[n+1]-y[n])$... and can't find any of my old textbooks... so if anyone could guide me a little
bit, i would be very grateful
let's say i h... | 4 | [
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Strength of Transfinite Induction on the Difference Hierarchy
up vote 6 down vote favorite
I'm wondering if a particular theory of second order arithmetic has been studied or is known to be equivalent to some other theory.
Consider the formulas generated by $\Pi^1_1$ and $\Sigma^1_1$ formulas by propositional combina... | 5 | [
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Parameter Ray Atlas
This page illuminates various interesting points of reference on the M-set, giving then the corresponding ray arc angle. This is a visual map; the corresponding tables of angles and formulas are on
the Tables page.
Visually, the stuff here is pretty boring. Don't expect any hot graphics. The inter... | 4 | [
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-0... | 36,222 | 36222 | |
Easy proof by induction
March 26th 2008, 02:10 PM #1
Newbie
Joined
Oct 2006
Posts
6
Easy proof by induction
Hey everyone, I'm new here. I've taken a few classes which dealt with proofs by induction, and recently a friend came to me for help with one. I'm so rusty now though, but I know it should not be
... | 5 | [
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ASSIMILATION OF SPA AND PMT FOR RANDOM SHOCKS IN MANUFACTURING PROCESS-2
International Journal Industrial Engineering Research and Development (IJIERD), ISSN 0976 –
InternationalJournal of of Industrial Engineering Research
6979(Print), ISSN 0976 – 6987(Online) Volume 2, – 6979... | 4 | [
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Help with Complex Numbers
September 22nd 2012, 01:36 AM #1
Newbie
Joined
Sep 2012
From
Lithuania
Posts
1
Help with Complex Numbers
Hi,
I need help with this task:
Given that $z_1=1+2i$ and $z_2 =-3i$ find $(\frac{\bar {z_2}}{z_1})^6$.
My solution so far
$(\frac{\bar {z_2}}{z_1})= \... | 5 | [
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Derived push-forward and pull back.
up vote 3 down vote favorite
1
All functors are derived and all categories are bounded derived categories of coherent sheaves. Suppose that we have got an inclusion of a smooth divisor $j:D\rightarrow X$ in a smooth projective
variety. Is it true that $$j^*j_*F=F\otimes j^*j_*O_D?$$... | 5 | [
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... | 36,226 | 36226 | |
How to prove that the multiplication table of two isomorphic groups are the same
May 6th 2012, 07:43 AM
kasper90
How to prove that the multiplication table of two isomorphic groups are the same
Prove:
G[1] en G[2] are isomorphic if and only if the multiplication tables are the same
How do you prove some... | 5 | [
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-0.052490234375,
-0.0849609375,
0.0157470703125,
-0.0244140625,
0.03955078125,
-0.023193359375,
-0.09033203125,
0.00726318359375,
-0.0135498046875,
0.07958... | 36,227 | 36227 | |
Cartesian equation of tangent of ellipse
February 27th 2009, 05:30 AM #1
Cartesian equation of tangent of ellipse
Show that for all values of m, the straight lines with equations $y=mx\pm \sqrt(b^2+a^2m^2)$ are tangents to the ellipse with equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
Heelp
The system for... | 4 | [
-0.0208740234375,
-0.041748046875,
-0.0001239776611328125,
0.024169921875,
0.02099609375,
0.032470703125,
-0.0322265625,
0.055908203125,
0.06396484375,
-0.03173828125,
0.1455078125,
0.01422119140625,
0.00494384765625,
-0.0634765625,
-0.01611328125,
0.1943359375,
-0.03515625,
-0.010... | 36,228 | 36228 | |
stuck on matlab simplex method
January 7th 2011, 11:51 AM #1
Member
Joined
Nov 2009
Posts
75
hi all,
can anyone help me with this?ive been stuck for days!
im using the matlab code:
%
options=optimset('LargeScale','off','Simplex','on' );
%
% This code solves the problem:
%
... | 5 | [
0.002197265625,
-0.00860595703125,
-0.0380859375,
-0.06201171875,
0.034912109375,
-0.0115966796875,
0.050537109375,
-0.0189208984375,
-0.09228515625,
0.0196533203125,
0.0233154296875,
-0.08056640625,
-0.009521484375,
-0.01171875,
-0.00982666015625,
0.09033203125,
-0.03955078125,
-0... | 36,229 | 36229 | |
Does the following Diophantine equation have nontrivial rational solutions?
up vote 2 down vote favorite
2
Are there any solutions to the equation $s^{2}(1+t^{2})^{2}+t^{2}(1+s^{2})^{2}=u^2$ where $s,t,u\in \mathbb{Q}$ and $0 < s,t<1$? If so, is there a simple way to parametrize them all?
If I am understanding the ge... | 5 | [
-0.0189208984375,
0.0123291015625,
-0.020751953125,
0.06982421875,
0.0038299560546875,
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0.052490234375,
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0.0703125,
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0.0242919921875,
0.00006103515625,
0.007354736328125,
0.0419921875,
-0.00604248046875,
-0.0220947265625,
0.01409912109375,... | 36,230 | 36230 | |
different optimization problem
December 9th 2008, 01:39 PM #1
different optimization problem
Here's one that's a little different than the usual cylinder in a cone, cone in a sphere, etc.
Find the tetrahedron of largest volume that can be inscribed in a sphere of radius R.
If the tetrahedron has edge le... | 5 | [
0.061279296875,
0.05859375,
-0.057373046875,
-0.08203125,
-0.051513671875,
-0.0751953125,
0.0146484375,
0.06640625,
0.017333984375,
0.0693359375,
-0.099609375,
0.045654296875,
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0.09716796875,
-0.0390625,
-0.060791015625,
0.064453125,
-0.0035552978515625,
-0.0659... | 36,231 | 36231 | |
joint pmf
November 20th 2010, 01:09 PM #1
Junior Member
Joined
May 2010
Posts
42
joint pmf
if X and Y are discrete RVs with pmf $p(x,y) = a\; \dfrac{k!}{x!y!(k-x-y)!}$ where x and y are $non \; negative \; integers \; and\; x+y\leq k$.
I want to find the value of a.
I know that I need to show ... | 5 | [
0.006256103515625,
0.00555419921875,
-0.0289306640625,
-0.05126953125,
-0.0341796875,
0.01806640625,
0.1220703125,
-0.09521484375,
0.0245361328125,
0.005035400390625,
0.02734375,
-0.00341796875,
0.006683349609375,
0.038330078125,
0.044189453125,
0.08056640625,
0.0208740234375,
-0.0... | 36,232 | 36232 | |
Find y'' by implicit differentiation help!
March 9th 2013, 11:13 PM #1
Junior Member
Joined
Sep 2012
From
canada
Posts
45
Find y'' by implicit differentiation help!
x^3 + y^3 =6xy
No need for d/dx just dy/dx for when you find the derivative of y only.
My steps:
y'= 3x^2+3y^2(dy/dx)= 6y... | 5 | [
-0.038330078125,
-0.08154296875,
-0.051513671875,
0.0147705078125,
0.008544921875,
0.0673828125,
-0.052490234375,
-0.02294921875,
0.0245361328125,
0.00118255615234375,
0.09130859375,
0.0284423828125,
-0.03564453125,
-0.11328125,
0.002410888671875,
0.036376953125,
-0.125,
-0.0085449... | 36,233 | 36233 | |
Substituting
October 5th 2009, 07:34 PM
I-Think
Substituting
Show that, with a suitable value of the constant $\alpha$, the substitution $y=x^{\alpha}w$ reduces the differential equation
$2x^{2}\frac{d^{2}y}{dx^2}+(3x^2+8x)\frac{dy}{dx}+( x^2+6x+4)=f(x)$
to
$2\frac{d^{2}w}{dx^2}+3\frac{dw}{dx}+w=f... | 4 | [
-0.083984375,
-0.0042724609375,
0.025390625,
0.11279296875,
0.055419921875,
0.08740234375,
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0.01300048828125,
0.0027618408203125,
-0.007110595703125,
0.12060546875,
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-0.07470703125,
0.0286865234375,
-0.06591796875,
0.11279296875,
-0.09375,
0.041259765... | 36,234 | 36234 | |
combinations
In how many ways can the letters in "mississippi" be arranged such that there are no consecutive s's?
Hello jmedsyIf, to begin with, we ignore the $4$s's, there are $\frac{7!}{4!2!}$ arrangements of the remaining $7$ letters, which have $4$ repeated i's and $2$ repeated p's. Now imagine that these 7
lette... | 4 | [
0.00799560546875,
-0.048583984375,
0.08251953125,
0.026123046875,
-0.10791015625,
0.10791015625,
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0.007568359375,
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0.12158203125,
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0.03173828125,
0.06982421875,
-0.0133056640625,
-0.10888671875,
0.00116729736328125,
-0.04443359375... | 36,235 | 36235 | |
range of a function of 3 variables ...
October 6th 2008, 05:08 PM #1
Junior Member
Joined
Sep 2008
Posts
33
Thanks
1
range of a function of 3 variables ...
Let g(x,y,z) = ln(25 - x^2 - y^2 - z^2)
Find the range of g.
I know this isn't even that complicated I just don't understand how to fi... | 4 | [
0.00421142578125,
-0.0166015625,
0.005126953125,
-0.09033203125,
-0.01611328125,
-0.0791015625,
-0.036376953125,
0.0103759765625,
-0.0003204345703125,
0.00750732421875,
-0.0185546875,
0.09130859375,
0.0277099609375,
0.07177734375,
0.031494140625,
0.019775390625,
-0.0081787109375,
-... | 36,236 | 36236 | |
Prescribing areas of parallelograms (or 2x2 principal minors)
up vote 16 down vote favorite
3
Let $(a_{ij})$ be a $n\times n$ symmetric matrix such that $a_{ij}\geq 0$ for all $i,j$ and $a_{ii}=0$ for all $i$. Under which conditions on the $a_{ij}$'s can one find $n$ vectors $v_1,\ldots,v_n\
in{\mathbb R}^n$ such that... | 5 | [
0.0419921875,
-0.057861328125,
0.052978515625,
-0.09765625,
-0.02978515625,
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0.0037689208984375,
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0.01263427734375,
-0.0031585693359375,
0.07177734375,
0.10400390625,
0.0893554687... | 36,237 | 36237 | |
Factoring Quadratics Without Guessing
Date: 05/28/2002 at 16:41:09
From: Chris
Subject: Quadratic Equations
Hi.
My name is Chris and I am a seventh grader, but I love math and
like to learn on my own. I have already learned basic
trigonometry, logs, etc... I am now learning how to solve
quadratic equations. I found ... | 4 | [
-0.0196533203125,
-0.039794921875,
0.0245361328125,
0.021240234375,
0.057373046875,
0.1064453125,
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-0.017822265625,
-0.03173828125,
0.031494140625,
0.09814453125,
0.022216796875,
0.04931640625,
0.061279296875,
0.033203125,
0.01556396484375,
-0.02490234375,
0.07470... | 36,238 | 36238 | |
Find the Standard Deviation for the given Probability Distribution?
Top
For finding the Standard Deviation for the given Probability distribution, we use following steps -
Step 1: First of all we will find out Probabilities for each and every Random Variable means we will calculate Probability Distribution for that p... | 4 | [
0.060546875,
0.0546875,
0.03173828125,
-0.044677734375,
0.007720947265625,
-0.029052734375,
0.031982421875,
0.018310546875,
-0.0064697265625,
0.017822265625,
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-0.064453125,
0.040771484375,
-0.034912109375,
-0.0238037109375,
-0.0263671875,
-0.07421875,
0.02697753906... | 36,239 | 36239 | |
Coordinate Geometry
December 15th 2013, 05:57 AM #1
Newbie
Joined
May 2013
From
India
Posts
16
Coordinate Geometry
I am not able to solve this problem of Book 'The Element of Co-ordinate of SL Loney'
Find the equations of the two straight lines drawn through
the point (0, a) on which the per... | 4 | [
-0.08837890625,
0.004791259765625,
0.0277099609375,
-0.1025390625,
-0.056640625,
0.056640625,
-0.072265625,
0.061279296875,
-0.00180816650390625,
0.0164794921875,
0.08984375,
0.0244140625,
0.025634765625,
0.004913330078125,
0.00909423828125,
0.09716796875,
-0.04736328125,
0.0012054... | 36,240 | 36240 | |
Random walk: police catching the thief
up vote 24 down vote favorite
8
I posted this problem on stackexchange.com,but haven't get a satifactory answer.
This is a problem about the meeting time of several independent random walks on the lattice $\mathbb{Z}^1$:
Suppose there is a thief at the origin 0 and N policemen ... | 5 | [
-0.06787109375,
0.0146484375,
0.0245361328125,
-0.0302734375,
0.109375,
0.022216796875,
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0.0419921875,
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0.02587890625,
0.042236328125,
-0.0400390625,
-0.0296630859375,
-0.022705078125,
0.061767578125,
-0.09130859375,
0... | 36,241 | 36241 | |
how fast distance is changing
November 28th 2008, 01:02 PM
thecount
how fast distance is changing
A plane flies directly over an observation point. The plane has constant altitude of 5000 ft. How fast is the distance between the plane and the point changing, at the instant the plane is 600ft
past the overhea... | 4 | [
0.01275634765625,
0.0751953125,
-0.0272216796875,
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0.0380859375,
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0.04443359375,
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0.0869140625,
-0.0244140625,
-0.005584716796875,
-0.000926971435546875,
-0.05224609375,
0.08203125,
-0.06982421875,
-0.002... | 36,242 | 36242 | |
Half angle Identities
April 14th 2010, 09:17 PM #1
Member
Joined
Mar 2009
Posts
97
Half angle Identities
Hi
This may take a while and a few posts so be pateint please!!
I can't understand when to use which formula and how to recognise half angle problems.
Can I use either of the formulae belo... | 4 | [
-0.07763671875,
0.0234375,
0.054443359375,
0.0026397705078125,
0.0703125,
-0.0302734375,
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0.087890625,
0.091796875,
-0.00135040283203125,
0.0712890625,
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0.00069427490234375,
0.0615234375,
0.08935546875,
0.0194091796875,
0.00433349609375,
0.030029296875,... | 36,243 | 36243 | |
Question about a derivative problem
September 13th 2012, 04:48 PM
leezgo
Question about a derivative problem
The problem is simply
f(x) = x^(3/2)
using (f(x+h) - f(x)) / h and multiply with the conjugate I get
(x+h)^3 - x^3
/
h(x+h)^(3/2) + z^(3/2)
How do I get forward from this? I h... | 5 | [
0.0084228515625,
-0.026611328125,
0.00151824951171875,
0.01092529296875,
-0.03857421875,
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-0.0654296875,
-0.03125,
0.007415771484375,
0.040283203125,
0.08984375,
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0.033203125,
-0.02880859375,
0.0302734375,
0.087890625,
-0.0194091796875,
0.0275878906... | 36,244 | 36244 | |
Probability of the Same Birthday within a Group
Date: Tue, 22 Aug 95 16:54 EST
From: "Kyra K. Bromley"
Subject: Probability Question
What is the probability that, in a room of 30 people, two people will have
the same birthday?
The answer would be nice but I'd really love to know how to solve it, i.e.,
what equation... | 5 | [
0.0198974609375,
0.0277099609375,
-0.0012969970703125,
-0.006317138671875,
-0.056396484375,
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0.050048828125,
0.0361328125,
-0.05029296875,
0.027099609375,
0.055419921875,
-0.08154296875,
0.041015625,
0.00311279296875,
0.03125,
0.01806640625,
-0.005279541015625,
-0... | 36,245 | 36245 | |
Right continuous
September 20th 2011, 01:09 PM #1
MHF Contributor
Joined
Mar 2010
From
Florida
Posts
3,093
Thanks
5
Right continuous
Notation:
$(\mathbb{R},\tau_s)$ Standard topology on R
$(\mathbb{R}.\tau_l)$ Lower limit topology on R
Prove $f:\mathbb{R}\to\mathbb{R}$ is right conti... | 5 | [
0.012939453125,
-0.047119140625,
-0.00653076171875,
-0.00408935546875,
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0.0673828125,
0.004241943359375,
-0.046875,
0.01416015625,
-0.001129150390625,
0.040771484375,
0.08251953125,
0.03271484375,
0.04833984375,
0.099609375,
0.0274658203125,
-0.042236328... | 36,246 | 36246 | |
How to simplify after differentiation.
May 14th 2009, 11:38 PM #1
Junior Member
Joined
May 2009
Posts
29
How to simplify after differentiation.
Hi
I have a problem with simplifying after I differentiate, can anyone enlighten me as what are some key ways in simplifying equations
Heres my problem... | 5 | [
0.0093994140625,
-0.0146484375,
0.056640625,
0.00830078125,
0.01275634765625,
-0.08837890625,
0.03271484375,
0.03857421875,
0.0186767578125,
0.027587890625,
0.06494140625,
-0.031005859375,
0.02392578125,
0.04345703125,
0.013671875,
0.04833984375,
-0.035888671875,
0.0260009765625,
... | 36,247 | 36247 | |
Why are hypergeometric series important and do they have a geometric or heuristic motivation?
up vote 13 down vote favorite
5
Apart from telling that the hypergeometric functions (or series) are the solutions to the (essentially unique?) fuchsian equation on the Riemann sphere with 3 "regular singular points", the wik... | 4 | [
-0.09375,
-0.01043701171875,
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0.142578125,
0.03173828125,
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0.03662109375,
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-0.05615234375,
-0.012939453125,
-0.04858398... | 36,248 | 36248 | |
Co terminal Angle?
June 19th 2005, 10:39 AM #1
Newbie
Joined
Jun 2005
Posts
18
Co terminal Angle?
I need to find a positive co-terminal angle for 120 deg. and one for pie/5
and a negative co-terminal angle for 420 deg. and one for 3 pie/5
Positive angle that is co-terminal with 120 deg.
One ... | 4 | [
-0.018310546875,
0.0240478515625,
-0.037353515625,
-0.03955078125,
-0.09326171875,
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0.044921875,
0.015869140625,
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0.07861328125,
0.01458740234375,
0.0191650390625,
-0.03857421875,
-0.0693359375,
0.02624... | 36,249 | 36249 | |
Rate of change question
December 13th 2010, 04:14 PM #1
Junior Member
Joined
Aug 2010
Posts
37
Rate of change question
Hi Guys,
Am currently stuck with this rate of change question.
question is as per attached file.
Please help thanks !
up for help guys !
Thanks !
Hello, liu... | 5 | [
-0.0162353515625,
0.045166015625,
-0.01361083984375,
-0.022216796875,
0.057373046875,
0.03759765625,
0.02587890625,
0.08203125,
0.08447265625,
0.0191650390625,
0.125,
0.053955078125,
-0.017578125,
0.087890625,
0.03369140625,
0.1220703125,
-0.0712890625,
-0.03857421875,
0.00515747... | 36,250 | 36250 | |
Numerical analysis
January 16th 2011, 11:59 AM #1
Numerical analysis
Hello, i dont know if its possible but can someone simply explain me how to solve a third degree equation with numerical analysis?
Are you looking to find the roots of a third degree polynomial with a numerical method?
Yes.
Ok, wh... | 5 | [
-0.072265625,
-0.07666015625,
-0.03173828125,
0.0098876953125,
-0.050048828125,
-0.034423828125,
-0.055908203125,
-0.0164794921875,
-0.011474609375,
0.036376953125,
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-0.00135040283203125,
0.0029144287109375,
0.0216064453125,
0.00145721435546875,
-0.016845703125,
-0.... | 36,251 | 36251 | |
2 integrals...
December 23rd 2010, 07:41 AM
earthboy
2 integrals...
problem 1: $\int \frac{\sin 2x}{\sin ^{4}x+\cos^{4}x } dx$
problem 2 : $\int\limits_{0}^{\pi} \frac{\cos (3x)}{\cos x} dx$
please write the full solutions because i'm a integration newbie(Happy)
and a very happy christmas and new y... | 5 | [
-0.0064697265625,
0.06640625,
0.0081787109375,
-0.0166015625,
0.06103515625,
0.06640625,
-0.0020751953125,
-0.04345703125,
-0.07763671875,
-0.00543212890625,
-0.0098876953125,
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0.01507568359375,
-0.013427734375,
-0.03857421875,
0.009765625,
0.060546875,
0.0319824218... | 36,252 | 36252 | |
Double Integration
November 29th 2007, 11:54 AM #1
Newbie
Joined
Nov 2007
Posts
6
Double Integration
∫∫R (x^1/2 - y^1/2) dydx
where y=x^2, y= x^1/4, x=0, x=1
im struggling to solve this!! i came up with an answer of 1.5 but i dont think i have done it correct!...could anyone help please?
$\i... | 5 | [
0.0625,
-0.0927734375,
-0.00604248046875,
-0.046875,
0.01177978515625,
-0.1201171875,
-0.06787109375,
0.01361083984375,
-0.044677734375,
-0.0498046875,
-0.0341796875,
0.0849609375,
-0.017578125,
0.053466796875,
0.005462646484375,
0.0703125,
-0.0047607421875,
-0.09716796875,
-0.05... | 36,253 | 36253 | |
Need help finding the derivative.
June 21st 2009, 09:37 PM #1
Member
Joined
Sep 2007
From
Colorado
Posts
145
I need to find the derivative of
$x-2 \sqrt{x-1}$
I knew to use the power rule, but I was coming up with
$1/2(x-1)^{-1/2}$ Is this the correct answer?
Thanks
Jason
L... | 5 | [
0.047607421875,
-0.057373046875,
0.08349609375,
0.0517578125,
-0.028076171875,
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0.0262451171875,
0.0277099609375,
0.09326171875,
0.016357421875,
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0.04736328125,
0.03564453125,
-0.040771484375,
0.06591796875,
0.0299072265625,
-0.100097... | 36,254 | 36254 | |
L'Hopital
April 8th 2010, 06:35 PM #1
Newbie
Joined
May 2008
Posts
16
L'Hopital
Let $f(x)=x^2\sin{1/x}$ for $xeq 0$ , let $g(x)=\sin{x}$ for $x\in\mathbb{R}$ .
Show that $\lim_{x\to 0}f(x)/g(x) = 0$ but that $\lim_{x \to 0}f'(x)/g'(x)$ does not exist.
You are like the seventh person to post this... | 5 | [
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induction proof
Use Mathematical induction to prove: $(k^3)=((n^2)(n+1)^2)/4$ when the series starts at k=1 and is for n terms
To prove by mathematical induction: first prove for n = 1 ie. substitute n=1 and show that the formula holds for this value. Then assume true for n = b: so in this case assume $\sum_{k=1}^{b} ... | 4 | [
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0.095214843... | 36,256 | 36256 | |
Cubic Formula
The cubic formula
John Kerl January, 2006
In college algebra we make frequent use of the quadratic formula. Namely, if f (x) = ax2 + bx + c, then the zeroes of f (x) are x= −b ± b2 − 4ac . 2a This formula can be derived by completing the square. Note that if b2 − 4... | 5 | [
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Integral with substitution and parts
March 9th 2013, 03:45 PM
Steelers72
Integral with substitution and parts
∫ sin(2t)*e^[cos(t)] dt (from t=0 to π)
My work:
trig identity: sin2t= 2sintcost
bring constant to the outside
=> 2 ∫ sin(t)cos(t)*e^[cos(t)] dt (from t=0 to π)
I did u substituti... | 5 | [
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Integration Problem.
Find the integral of {{(x4 + 1)1/2 }[ ln( x2 + 1 ) + 2lnx]} /x4
I think I made a mistake in writing it the correct question is {{x2 + 1)1/2[ ln(x2 + 1) - 2lnx]}/x4
Last edited by sohamjariwala; July 12th 2012 at 09:41 PM.
integral[Sqrt[x^2 + 1]*(Log[x^2 +... | 5 | [
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Matrices: characterizing pairs $(AB, BA)$
up vote 19 down vote favorite
7
Let $A$ be an $m\times n$-matrix and $B$ an $n \times m$-matrix over the same field. Consider the matrices $C=AB$ and $D=BA$. It is probably well known (and not difficult to show) that the only
difference between the canonic rational forms of $C... | 4 | [
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0.07763671875,... | 36,260 | 36260 | |
Understanding acceleration
Acceleration is related to external force. This relationship is given by Newton’s second law of motion. For a constant mass system,
F = m a F = m a
In words, Newton’s second law states that acceleration (effect) is the result of the application of net external force (cause). Thus, the relat... | 4 | [
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Help choosing branch cuts
October 14th 2010, 08:13 AM #1
Help choosing branch cuts
Q: Define a single-valued branch of the function $f(z)=z^{z}$ on an open set $U$ in $\mathbb{C}$, show $f$ is analytic on $U$.
Here is my work
$f(z)=z^{z}=e^{zlog(z)}$
Let $log(z)$ range over the principle branch. Th... | 4 | [
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NSDL Materials Digital Library Wiki
softmatter:Lennard-Jones Potential
From NSDL Materials Digital Library Wiki
The Lennard-Jones potential (LJ) is used to model the excluded volume interactions and
van der Waals interaction
attraction of neutral atoms. The commonly used 6-12 form of the potential is as follows:
$... | 4 | [
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easy integral
November 11th 2008, 09:00 AM #1
Member
Joined
Sep 2008
Posts
144
easy integral
the integral sign and then x^3 sqrt of x
i know the integral of x^3= x^4/4 +C
i know the integral of the sq rt of x= 2X^(3/2)/3 +C
but when i multiply these together im not getting 2x^(9/2)/9 +C as m... | 4 | [
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Are these the correct derivatives for these functions?
March 8th 2012, 03:38 AM
Orlando
Are these the correct derivatives for these functions?
use the quotient rule to differentiate the function
k(x)= (e^6x)/(x^3+8)
I have got as far as
k '(x) =(x^3+8)(6e^6x)-(e^6x)(3x^2)/(x^3+8)^2
But im uns... | 4 | [
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-... | 36,265 | 36265 | |
probability
November 18th 2006, 04:30 AM #1
Newbie
Joined
Nov 2006
Posts
3
please help me i hate probabilty!
Two students Alan and Brenda are due to take an examination. The probability that Alan will pass is 3/5 the probability that Brenda will fail is 4/7.
a) calculate the probability that bot... | 4 | [
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0.00442504... | 36,266 | 36266 | |
When does a pair of homotopic Lipschitz functions fail to admit a Lipschitz homotopy?
up vote 11 down vote favorite
Let $(M,d)$ and $(N,\rho)$ be metric spaces. A function $f: M \to N$ is Lipschitz if there exists some constant $\kappa \geq 0$ so that $\rho(f(x),f(y))$ is smaller than $\kappa d(x,y)$ for all
points $x... | 5 | [
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Partial Sum of a Sequence
September 21st 2011, 10:32 AM #1
Newbie
Joined
Sep 2011
Posts
4
Partial Sum of a Sequence
This is an exercise in my book that I can't figure out. And there's no answer sheet for it so I don't know if I did it right.
an = 1/n+1 - 1/n+2
I got these as the first terms of ... | 4 | [
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... | 36,268 | 36268 | |
A "holomorphic" Peano curve?
up vote 11 down vote favorite
2
A Peano curve is a continuous map $[0,1]\to [0,1]^2$ whose image is the whole square.
I would like to know if on can obtain "holomorphic" Peano curves. Namely, is it possible to find a continuous map $\phi$ from the unit disk $|z|\le 1$ to $\mathbb C^1$ suc... | 4 | [
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limit question
$\begin{array}{cc}\lim\\x\rightarrow0\end{array} \frac{\sin2x}{\sin3x}$ How can I solve that without using L'Hôpital's rule (which is considered illegal in my calculus class)?
For small x (which we have here, since we're letting x tend to 0) you can use the first order Taylor expansion for sin(x) which ... | 5 | [
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Subsets of sequences of natural numbers vs. strategies under ZFC
up vote 4 down vote favorite
This question is related to a previous question of mine:
Determinacy interchanging the roles of both players
Given any set A of sequences of natural numbers, every strategy (no matter for which player) is either winning (W)... | 5 | [
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a "basis" in {0,1}^n with operations induced from the boolean algebra {0,1}
October 22nd 2011, 08:47 AM
ymar
a "basis" in {0,1}^n with operations induced from the boolean algebra {0,1}
Let $u_1,...,u_n\in\{0,1\}^n$. Can we impose a condition on these vectors so that every vector $s\in\{0,1\}^n$ has a unique deco... | 4 | [
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Math Forum Discussions
Re: Is there a compact form for n-tuple relativistic additions of
velocities?
Posted: May 31, 2010 10:00 AM
On May 29, 12:00 pm, stargene <starg...@sbcglobal.net> wrote:
> I seek advice on whether a certain very long function can be made
> significantly more compact and therefore easier to compu... | 4 | [
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-0.042724609375... | 36,273 | 36273 | |
Having Trouble Setting up a System...
August 31st 2009, 02:15 PM #1
Newbie
Joined
Aug 2009
Posts
5
Having Trouble Setting up a System...
...of DEs in regards to a written problem we've been given. Here it is, followed by a tentative 'stab' at what is meant to be in the equation.
"Suppose that the ti... | 4 | [
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Soil Processes
WIMOVAC Soil Processes
Soil-Plant Water Relations
Models of water uptake by plant roots generally have one of two purposes. Either they produce estimates of transpirational water loss for water budget models or they provide estimates for predicting
plant water stress {Campbell, 1991 #1958}. Wimovac use... | 4 | [
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0.07128906... | 36,275 | 36275 | |
features of a polynomial function
March 19th 2010, 08:59 AM #1
features of a polynomial function
The the function f(x)=x^3-x^2+4x-3, determine
a) the intervals of increase or decrease
b) the location of any maximum or minimum points
c) the intervals of concavity up or down
d)the location of any po... | 4 | [
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-0... | 36,276 | 36276 | |
Mol
Introduction to the Mole
Before you can do molar math successfully, you must first know what a mole IS. If you are NOT completely clear about what a mole IS, quickly browse the page at the following link. Then come back when
you think you understand enough to go on. What is a Mole?
We use the unit of a "mole" in... | 4 | [
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0.0105590820312... | 36,277 | 36277 | |
Solving/Factoring an equation
The answer is letter B but I got letter D for my answer... What did I do wrong?
Chiro's suggestion for looking for common factors is a good one, but your method is fine as well. When you get to \displaystyle \begin{align*} 10y^2 - 13y - 3 \end{align*}, you should note that \
displaystyle ... | 4 | [
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Date Intervals
This page describes a few methods for working with intervals of dates. Specifically, it address the questions of whether a date falls within an interval, the number of days that two intervals
overlap, and the how many days are in one interval, excluding those days in another interval. These formulas can ... | 4 | [
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0... | 36,279 | 36279 | |
Homework Help
Posted by Lucy on Saturday, January 3, 2009 at 4:06pm.
a red number cube and a white number cube are rolled. Find the probability that the red number cube shows a 2, given that the sum showing on the two number cubes is less than or equal to 5.
My work: (red cube = [1,2,3,4]
white cube = [4,3,2,1]
Pro... | 4 | [
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... | 36,280 | 36280 | |
Similar Matrices
March 8th 2010, 03:25 PM
joe909
Similar Matrices
Little bit stuck on this problem.
Let $A$ and $B$ be similar Matrices. Let $\lambda$ be an eigenvalue of $A$ and $B$
Show that $dim Ker(A-\lambda I) = dim Ker(B-\lambda I)$
Any help would be great. Thanks!
March 8th 2010, 06:11 PM
... | 4 | [
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0.042236328125,
0.01... | 36,281 | 36281 | |
find h'(x): has ln in equation
March 9th 2009, 06:40 PM #1
Junior Member
Joined
Oct 2008
Posts
34
find h'(x): has ln in equation
h(x) = −12 ln( tanx + secx ) + ln( 6 tanx ) − 8 ln( secx)
find h'(x)
alright so this is the third time doing this question, obviously i'm missing something here. i sep... | 5 | [
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0.0157470703125,
0.039306640625,
0.043212890625,
-0.11279296875,
-0.00344... | 36,282 | 36282 | |
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Topic: Algebra 1 the vos Savant way
Replies: 0
Algebr... | 4 | [
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A property of unimodal sequences
up vote 10 down vote favorite
1
It is well-known that $(-1)^j \sum_{i=0}^j (-1)^i\binom{n}{i} \geq 0$. This inequality can be used to prove Bonferroni's inequalities for example. Recently I noticed that a similar inequality applies
to non-negative unimodal sequences with alternating ze... | 4 | [
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0.02... | 36,284 | 36284 | |
Groups whose all normal subgroups are principal
up vote 4 down vote favorite
6
My motivation for this question is from Universal Algebra: A congruence of an arbitrary algebra $A$ is said to be principal, if it is generated by a single element. In the case of rings, this is just
the notion of principal ideal and for gr... | 5 | [
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-0.018066406... | 36,285 | 36285 | |
Math Help
August 2nd 2013, 06:51 PM #1
Newbie
Joined
Aug 2013
From
Mauritius
Posts
12
Thanks
1
Question
(i)Sketch on the same diagram the graphs of y = |2x+3| and y = 1-x
(ii)Find the values of x for which x + |2x+3|= 1
Last edited by Matt512; August 2nd 2013 at 07:00 PM.
Re: Question
... | 4 | [
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Series: Absolutely convergent, con convergent or divergent
February 21st 2009, 08:54 AM
thehollow89
Series: Absolutely convergent, con convergent or divergent
The series from 1 to infinity of n!/n^n? I tried the ratio and root test and they didn't work, unless I messed up. I was thinking a comparison test, but I... | 5 | [
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0.0269775390625... | 36,287 | 36287 | |
simplification of ODE
March 7th 2010, 08:35 PM #1
Newbie
Joined
Sep 2009
Posts
8
simplification of ODE
I saw this in a book:
$\frac{dy}{dt} = -\frac{y}{\tau} +f(t)$,
can be simplified to $y = f(t)\tau$, if one is interested only in the time scale slower than $\tau$,
I don't know how this is ... | 5 | [
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0.... | 36,288 | 36288 | |
Finite interpolation by nondecreasing indefinitely differentiable functions in a finite-dimensional space
up vote 0 down vote favorite
Some time ago, I asked about inite interpolation by a nondecreasing polynomial here at Finite interpolation by a nondecreasing polynomial. This turned out to be an already solved probl... | 5 | [
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0.012145996093... | 36,289 | 36289 | |
converting from spherical coordinates
October 10th 2010, 05:20 AM #1
Junior Member
Joined
Sep 2010
Posts
47
converting from spherical coordinates
Hey everyone, I really need some help on this one, I just can seem to find a connection anywhere between formulas for each coordinate system.
Convert $\ph... | 4 | [
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SUSY exists because the number 3/2 can't be missing
Paul Frampton: Off-topic sad news: he gets 4.67 years in prison for drug smuggling; Google News. He may be moved to the U.S. in 2014 if he applies. They found a note, "1grm/200U$S. 2000grms/
400000 U$S", handwritten by Frampton himself on which he calculated t... | 4 | [
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-0.0306396484375,... | 36,291 | 36291 | |
Injective and Integrable Mapping from $\mathbb R^3$ to $\mathbb R$
Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
Is there an injective and Riemann integrable map $f:\mathbb R^3\rightarrow\mathbb R$? (Of course such a map... | 5 | [
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0.01... | 36,292 | 36292 | |
I want to see if I'm right...
January 15th 2008, 05:21 AM
Undefdisfigure
I want to see if I'm right...
I am given the series (e^n)/(3^(n-1))...Don't forget the Riemann sum symbol in front of this. It appears to be a geometric series. This would mean its ar^n
and a = 1/3 and r = e. I then do a bit of manipula... | 5 | [
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Second linear differential euqation with variable coefficient how to solve
October 9th 2012, 08:22 AM #1
Second linear differential euqation with variable coefficient how to solve
(1-x^2)y'' - xy' +4y = 2x (1 -x^2)^1/2
Hint use the substitution x =sin t
I used it and end with
cos t y'' + sin t y' - ... | 5 | [
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gcd(a,b)=pi^min{si,ti} and lcm(a,b)=pi^max{si,ti} proof?
October 8th 2008, 11:43 PM #1
gcd(a,b)=pi^min{si,ti} and lcm(a,b)=pi^max{si,ti} proof?
a>1 , b>1 are two integers(whole numbers)
s>=0 , t>=0
a=(P1^s1)*...*(Pr^sr)
b=(P1^t1)*...*(Pr^tr)
for each i=1,2,3,....,r is mi=min{si,ti} and ni=max{... | 4 | [
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Another quad formula word prob
August 28th 2009, 05:30 AM
RaphaelB30
Another quad formula word prob
Block 4 by 5 by 3 feet. Wants to reduce volume by shaving off the same amount from length width and height.
Could you give me a clue as to where I should start? I know I have to make a quad formula.
The ... | 4 | [
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0.... | 36,296 | 36296 | |
inequality
August 20th 2009, 04:23 PM
Random Variable
inequality
Show that $|(Re^{i \theta})^{2} + a^{2} | \ge R^{2} -a^{2} \ \ (R, a >0, \ 0 \le \theta \le \pi)$
$|R^{2}e^{2i \theta} + a^{2} | = |R^{2}(cos 2 \theta + i \sin 2 \theta) + a^{2} |= |(R^{2} \cos 2 \theta + a^{2}) + i R^{2} \sin 2 \theta |$
... | 5 | [
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Congruence subgroups as abstract groups
up vote 10 down vote favorite
4
This is probably well know, and maybe even trivial, but not to me. Consider for concreteness the subgroup $$ \pm\Gamma_0(3)=\left\{\begin{pmatrix}a & b \\ c & d\end{pmatrix}:\;a,b,c,d\in\mathbb
{Z},ad-bc=\pm1, c\equiv 0\pmod 3\right\} $$ of $GL_2(... | 5 | [
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Math Help
February 11th 2008, 01:04 PM #1
Member
Joined
Feb 2008
Posts
79
Proof
Prove the following:
Assume that the average of four integers (all integers are different) is 20. Prove that at least 1 of those 4 integers has to be greater than 21.
Assume that they are all <= 21.
The bigges... | 4 | [
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