content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Outer measure and measurable sets.
October 2nd 2009, 08:31 PM #1
Super Member
Joined
Mar 2006
Posts
705
Thanks
2
Outer measure and measurable sets.
If $\mu$ is an outer measure on X and $\{ A_n \} ^ \infty _{n=1}$ is a sequence of disjointed $\mu$ measurable sets, prove that $\mu ( E \cap ( \bigcup ^... | 4 | [
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0.0407714... | 9,100 | 9100 | |
[SOLVED] Series
May 11th 2010, 02:24 PM #1
MHF Contributor
Joined
Mar 2010
From
Florida
Posts
3,093
Thanks
5
[SOLVED] Series
Let $x_n$ be the sequence with $x_1=2$ and $x_n=\sqrt{5(x_{n-1})+6}$ for every integer $n\geq 2$. How can this be written in summation notation?
$x_1=2$
$x_2=\sqrt... | 5 | [
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0.0390625... | 9,101 | 9101 | |
A general semi-parametric approach to the analysis of genetic association studies in population-based designs
Abstract
Background
For genetic association studies in designs of unrelated individuals, current statistical methodology typically models the phenotype of interest as a function of the genotype and assumes a ... | 4 | [
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Ideals in Factors
up vote 9 down vote favorite
2
One can easily prove that factors have no nontrivial ultraweakly closed 2-sided ideals as these are equivalent to nontrivial central projections. One can also show type $I_n$, type $II_1$, and type
$III$ factors are algebraically simple (any 2-sided ideal must contain a... | 4 | [
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True/False : 2 Questions
June 4th 2010, 12:58 PM #1
True/False : 2 Questions
1- The following function is one-to-one
f(x)= -x if x belongs to [-1,0]
f(x)=3x+2 if x belongs to [0,1]
2- The following parametric curve represents a line segment from (0,3) to (2,0) :
$x(t)=2sin^2(t)$ and $y(t)=3cos^... | 4 | [
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Eigenvector
December 8th 2010, 12:23 PM
Revy
Eigenvector standardization
I have matrix $A=\begin{pmatrix}0&1&0\\2&-2&-1\\-3&0&0\end{pmatrix}$
and I get that $det(A-LE)=-L^3+2L^2+2L+3$
so
$L^3-2L^2-2L-3=0$
//after this our lecturer takes random numbers and checks if they can be eigenvalues.
Fo... | 5 | [
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[plt-scheme] Graphs
From: Guillaume Marceau (gmarceau at cs.brown.edu)
Date: Tue Feb 8 13:27:33 EST 2005
On Tue, 2005-02-08 at 16:26 +0000, Paulo Jorge de Oliveira Cantante de
Matos wrote:
> For list-related administrative tasks:
> http://list.cs.brown.edu/mailman/listinfo/plt-scheme
>
> Hi all,
>
> Is there an... | 4 | [
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Inquiry Into Inquiry
Peirce’s 1870 “Logic Of Relatives” • Comment 12.1
To get a better sense of why the above formulas mean what they do, and to prepare the ground for understanding more complex relational expressions, it will help to assemble the following materials
and definitions:
$X$ is a set singled out in a par... | 4 | [
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Unirational implies rationally connected
up vote 2 down vote favorite
It is evidently a well-known fact that a unirational variety $X$ over an algebraic closed field (i.e. there is a dominant rational map from $\mathbb P^n$ to $X$) is rationally connected (by which I
mean that any two points can be joined by a chain o... | 5 | [
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LaGrange's Theorem
Date: 03/12/2001 at 17:45:53
From: Joan
Subject: Number theory
Please explain LaGrange's Theorem on the number of roots of a
polynomial.
Thank you.
Date: 03/13/2001 at 10:35:36
From: Doctor Rob
Subject: Re: Number theory
Thanks for writing to Ask Dr. Math, Joan.
This theorem states that a pol... | 5 | [
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A Quartic Diophantine Equation: 10657 + 11579x^2 + x^4 = y^2
Date: 12/29/2008 at 15:16:31
From: colin
Subject: The Diophantine equation 10657 + 11579x^2 + x^4 = y^2
How can you find at least one solution to this Diophantine equation?
10657 + 11579x^2 + x^4 = y^2
Why is it solvable? or is it not? What is the gen... | 5 | [
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Complex Analysis Confusion!
December 4th 2007, 05:53 AM #1
Newbie
Joined
Nov 2007
Posts
23
Hi,
I'm doing revision for an exam in complex analysis at the mo. I've been going through examples and I've found a couple that I've never seen before and have no idea how to do-any help would be
much appre... | 5 | [
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An informal version of the Furstenberg correspondence principle
One of the basic objects of study in combinatorics are finite strings ${(a_n)_{n=0}^N}$ or infinite strings ${(a_n)_{n=0}^\infty}$ of symbols ${a_n}$ from some given alphabet ${{\mathcal A}}$, which
could be either finite or infinite (but which we shall us... | 4 | [
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Norman window and greatest possible area of a rectangle
February 8th 2009, 12:43 PM #1
Junior Member
Joined
Feb 2009
Posts
41
Hi everybody I'm a precalculus student, and I'd like some help to understand these two problems?
1 A rectangle is inscribed with its base on the x-axis and its upper corners o... | 5 | [
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The Importance of the First and Third Quartiles
There are several ways to measure the center of a set of data. The mean, median, mode and midrange all have their advantages and limitations in expressing the middle of the data. Of all of these ways
to find the average, the median is the most resistant to outliers. It ma... | 4 | [
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How do I iso late x in the following eqation:
November 26th 2010, 09:31 PM #1
Newbie
Joined
Nov 2010
Posts
4
How do I iso late x in the following eqation:
Lr = Hx -Lx -r²x -rx²
In other words how do I define x in terms of the other units: x =
Thanks.
$\displaystyle L\,r = H\,x - L\,x - r^2... | 4 | [
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Solving Quadratic Equations by Factoring - Concept
Brightstorm is like having a personal tutor for every subject
See what all the buzz is about
Check it out
Solving Quadratic Equations by Factoring - Concept 47,174 views
Solving rational equations is substantially easier with like denominators. When solving rationa... | 4 | [
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How Much Material to Purchase?
Date: 11/01/97 at 16:58:05
From: kim peterson
Subject: Ramp
Sanchez warehouse wants to install a 3-foot wide ramp from the level
floor to the top of the 4-foot high platform. A regulation states that
for every 2 feet that such a ramp rises vertically, the bottom of the
ramp must be pla... | 4 | [
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Question - tangents and their equation
September 30th 2007, 12:25 AM #1
Junior Member
Joined
May 2007
Posts
35
Question - tangents and their equation
Hello everyone
I am studying tangents and come across this kind of problem where I am going to find the equation for one or more tangent with a specif... | 4 | [
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solve this Differential equation by indicial equation
Hint: $z=\ln(x)$ Use the chain rule $\frac{dy}{dx}=\frac{dy}{dz}\frac{dz}{dx}=\frac{1}{ x}\frac{dy}{dz}$ Now we need the 2nd derivative using the product and chain rule $\frac{d^2y}{dx^2}=-\frac{1}{x
^2}\frac{dy}{dz}+\frac{1}{x}\left( \frac{d^2y}{dz^2} \cdot \frac{1... | 5 | [
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... | 9,119 | 9119 | |
[Numpy-discussion] Here's what I've done to numpy.fft
Jochen Schröder cycomanic@gmail....
Mon Jul 12 21:08:56 CDT 2010
On 13/07/10 08:47, David Goldsmith wrote:
> In light of my various questions and the responses thereto, here's what
> I've done (but not yet committed) to numpy.fft.
>
> There are many ways to define... | 4 | [
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Tensor product of acyclic complexes of free abelian groups
up vote 1 down vote favorite
1
I am trying to find a relatively elementary proof of the following result: If $(K,d^K)$ and $(L,d^L)$ are acyclic chain complexes of free abelian groups, then their tensor product $(K \otimes L,d^{K
\otimes L})$ is acyclic. I am ... | 5 | [
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Almost Complex Structure approach to Deformation of Compact Complex Manifolds
up vote 14 down vote favorite
5
I don't know much about the deformation of compact complex manifolds, I've only read chapter 6 of Huybrechts' book Complex Geometry: An Introduction. There are two parts to this chapter. The second
goes throug... | 4 | [
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Exponential Taylor Series
April 19th 2010, 12:52 PM #1
Member
Joined
Aug 2008
Posts
88
Exponential Taylor Series
Obtain the Taylor series $e^z=e \sum_{n=0}^{\infty}\frac{(z-1)^n}{n!} (\left |z-1 \right |< \infty)$ for the function $f(z)=e^z$ by using $f^{(n)}(1) (n=0,1,2,...)$.
So it would seem to m... | 4 | [
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Simplify then find derivative
June 9th 2009, 01:52 AM #1
Simplify then find derivative
Hi All,
Can you help me with this please.
For this function below simplify f(x + h) – f(x) / h
then take lim to find the derivative.
h → 0
f(x) = x²+ 3x + 2 =
To me, this is a calculus question, ... | 4 | [
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Etale cohomology analogue for the semistable reduction theorem
up vote 4 down vote favorite
Let $K$ be a field, $X/K$ a smooth projective variety, $l\neq char(K)$ a prime number and $q\ge 0$. Then we define $\overline{X}:=X_{K_{sep}}$ and denote by $\rho_{X, l}^{(q)}$ the representation of
$Gal_K$ on $H^q(\overline{X}... | 4 | [
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Math Logic - Determining Truth
Date: 04/13/99 at 19:29:50
From: Ricky De Hamer
Subject: Math Logic
A number divisible by 2 is divisible by 4. I'm suppose to figure out
the hypothesis, the conclusion, and a converse statement, say whether
the converse statement is true or false, and if it is false give a
counterexamp... | 4 | [
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Induction Trig Proof
Prove by induction: For every integer n > 1 [cos(x) + i * sin(x)]^n = cos(nx) + i * sin(nx)
Base Step: n = 1 \displaystyle \begin{align*} LHS &= \left(\cos{x} + i\sin{x}\right)^1 \\ &= \cos{x} + i\sin{x} \end{align*} \displaystyle \begin{align*} RHS &= \cos{\left(1 \cdot x \right)} + i\sin
{\left(... | 5 | [
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Green's Theorem
March 1st 2013, 06:37 AM #1
Senior Member
Joined
Apr 2009
Posts
306
Green's Theorem
For the above expression, I was told that it can be proven using Green's Theorem on the line integral on the RHS, however I can't seem the prove the equality.
Note that $G$, $H$, $f$ are functi... | 4 | [
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Game theory: problem of the shooters
July 29th 2011, 09:19 PM #1
Member
Joined
May 2009
Posts
146
Game theory: problem of the shooters
n shooters numbered 1~n play a game. Their probability of hitting a target are 0<p1<p2<p3<...<pn<1.
Before the game, the referee arranges the n players in some order... | 5 | [
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Libniz Group Title
Shuffle a deck of card ... | 4 | [
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[SOLVED] Complex Stiffness Solution
October 9th 2009, 10:49 AM
jfortiv
[SOLVED] Complex Stiffness Solution
Hi,
I'm trying to solve a differential equation of a 1 degree of freedom mechanical system with a complex stiffness:
m*d^2u/dt^2 + k*u = A*e^(i*w*t), where k is complex (k = a + i*b), i = sqrt(-1)... | 5 | [
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Euler's Number
Date: 01/28/98 at 16:29:49
From: Jeffery Holcomb
Subject: Euler's number
During a recent math assignment I came in contact with Euler's number.
I also heard it referred to as the natural base. When I asked why it
was called this my teacher said that he did not know. Since then I
have looked in several... | 5 | [
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Cauchy's Integral theorem
March 18th 2010, 05:47 AM
Tekken
Cauchy's Integral theorem
Quick question
im trying to calculate the integral around the closed curve C of
z(bar) dz where z(bar) is the complex conjugate of z
where C is the unit circle.
Using the subsitution z = e^it i calculated the... | 5 | [
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Find integers
What do they mean by 'for all x' in (a)?
a) $x^2-8x=(x-p)^2+q\Leftrightarrow x^2-8x=x^2-2px+p^2+q,\forall x\in\mathbf{R}$. That means all coefficients of both members are equal. Then $\left\{\begin{array}{c}-2p=-8\\p^2+q=0\end{array}\right.
\Rightarrow p=4,q=-16$. b) The equation can be written $x^2-8x+1... | 4 | [
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Kodaira-Spencer map in a concrete instance
up vote 8 down vote favorite
3
Let $\pi:X_{\epsilon} \rightarrow \Delta$ be a family of (say smooth) projective plane curves parametrized by $\Delta:=\operatorname{Spec}(k[\epsilon])$, and let $X=X_0$ be the closed fiber. Suppose
that $X_\epsilon$ is given by a polynomial $f(... | 4 | [
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Length of the crossed belt.
September 16th 2011, 10:37 AM
Niosama
Length of the crossed belt.
Hi I am new to the university and yet now I face one problem I cannot solve! Pls help me x.x!
Attachment 22288
Thanks :)
September 16th 2011, 11:07 AM
HallsofIvy
Re: Length of the crossed belt! Pls Help!
... | 4 | [
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Determining and Checking Saddle Point for Autonomous System
Associated Topics || Dr. Math Home || Search Dr. Math
Determining and Checking Saddle Point for Autonomous System
... | 4 | [
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Solving Linear Trig Equations?
November 12th 2007, 04:29 PM #1
Junior Member
Joined
Sep 2007
Posts
55
Solving Linear Trig Equations?
Hello again!
I need some help on solving linear trig equations!
1. 1 - tan (2x + pi/2) = 0 0 ≤ Θ ≤ 2 pi
I was told that there are 4 answers possible for thi... | 4 | [
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Trig Word Problem Help!
October 13th 2013, 05:16 PM #1
Newbie
Joined
Oct 2013
From
Cincinnati, OH
Posts
2
Trig Word Problem Help!
I need help with this word problem:
If you stand in shallow water and look at an object below the surface of the water, the object will look farther away from you than... | 4 | [
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Galactic Orbits
Here are some examples of how to compute realistic Galactic orbits within NEMO. Again, as shown in the previous example, we first need to select a Galactic potential. To first order the motion in XY
and Z are decoupled. We do have a very nice feature in NEMO, called potentials (and the newer 'accelera... | 5 | [
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Lévy's C-curve
From Math Images
Lévy's C-curve
Field: Fractals
... | 5 | [
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Jacobian transformation
November 17th 2008, 06:20 AM #1
Newbie
Joined
Nov 2008
Posts
5
Jacobian transformation
Here is a second one I'm not too sure what to do next :
Let $X_1$ and $X_2$ be independent, with respective probability density functions of the forms $f_{X_1}(x_1) = x_1 e^{\frac{-x_1^2}{2... | 5 | [
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Can brute force algorithms scale?
up vote 7 down vote favorite
4
I have a math problem that I solve by trial and error (I think this is called brute force), and the program works fine when there are a few options, but as I add more variables/data it takes longer
and longer to run.
My problem is although, the prototyp... | 5 | [
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Foundation Statistics Mod
October 27th 2012, 04:39 AM
Jon123
Foundation Statistics Mod
Hello everyone!
I am having trouble getting in contact with my lecturer so I am hoping for assistance here with a few questions and would like support in answering them.
The set data given are arrival times e.g. 11.59... | 5 | [
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Ratios of line segments in a triangle
March 28th 2009, 01:02 PM #1
Newbie
Joined
Apr 2008
Posts
11
Ratios of line segments in a triangle
I found this problem in one of those foreign Mathematical Olympiad books. The solution is provided, but even then I still can't grasp the steps that lead to it.
We... | 4 | [
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Isomorphism beetwenn vector space and sub space
November 30th 2008, 09:04 AM
Herbststurm
Isomorphism beetwenn vector space and sub space
Hi,
I have to find a vector space V with a real sub space U and a bijective linear map.
Here my Ideas and my questions:
If the linear map is bijective, than dim ... | 4 | [
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The Golden Ratio
The Golden Ratio
From Math Images
(Difference between revisions)
← Previous diff Next diff →
Line 18: Line 18:
The golde... | 5 | [
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Dynamics question involving impulse momentum
April 20th 2008, 04:40 PM
pakman
Dynamics question involving impulse momentum
The question is:
A 5oz baseball is 3ft above the ground when it is struck by a bat. The horizontal distance to the point where the ball strikes the ground is 180ft. Photographic studies... | 4 | [
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differentiation and intergration of sinx/x and d/dt P(t)=P`(t)
September 6th 2009, 09:22 PM #1
Newbie
Joined
Sep 2009
Posts
2
differentiation and intergration of sinx/x and d/dt P(t)=P`(t)
(1) problem
differentiation [intergration of sint/t], limit from 0 to x^2
let say f(t)=t, F(t)=t^2/2, if f... | 5 | [
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Break even point ( units of the product needs to be sold to achieve a profit )
February 13th 2014, 09:13 PM #1
Member
Joined
Oct 2009
Posts
202
Break even point ( units of the product needs to be sold to achieve a profit )
A company is selling a product at a price of RM40 per unit. Variable cost per unit... | 4 | [
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Writing Algebraic Equations(Help Me)
February 19th 2008, 06:58 AM
huemunyeow
Writing Algebraic Equations(Help Me)
An apple grower finds that an apple tree produces on an average 400 apples per years, if no more than 16 trees are planted in a limit area. For each additional tree planted per unit area, the
gro... | 5 | [
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0.0087... | 9,151 | 9151 | |
Diffusion Curves
From Inkscape Wiki
Diffusion Curves are a way of specifying very free form gradients. It works by letting colors diffuse from curves, seeding the colors along both sides of the curves using gradients (along the
curves). Additionally a varying amount of blur can be applied along the curves. This makes... | 4 | [
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0.021606445... | 9,152 | 9152 | |
Differential equations - seperation of variables
October 15th 2009, 08:46 PM
wyasser
Differential equations - seperation of variables
Solve the given differential equation by Separation of variables.
(1+x^4)dy + x(1+4y^2)dx = 0, y(1)=0
(3x^2 + 9xy + 5y^2)dx – (6x^2 +4xy)dy = 0, y(2) = -6
(3y^2-x^2 /... | 4 | [
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Combinatorial Probability
October 11th 2010, 11:18 AM
NOX Andrew
Combinatorial Probability
There are two exercises in my probability and statistics textbook with which I am experiencing difficulty.
Exercise 1-28 A high school lottery uses two sets of numbered balls. One set consists of ten white balls numbe... | 4 | [
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0.01385498046875,
-0.0756835... | 9,154 | 9154 | |
determinant of T linear operator
March 26th 2011, 07:51 PM #1
Newbie
Joined
Mar 2010
Posts
4
determinant of T linear operator
Let T be a linear operator on a finite-dimensional vector space V, and let β be an ordered basis for V, we define det(T) = det ( [T]β )
i) 1) Prove that det(T – tIv) = det ( ... | 5 | [
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0.01953125,
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0.083984375,
-0.047607421875,
0.0147705078125,
0.0166015625,
0.044189453125,
0.031982421875,
-0.0257568359375,
0.037353515625,
-0.041748046875,
-0.046142578125,
0.0000069141387939453125,
-0.02355... | 9,155 | 9155 | |
[SOLVED] Time period of simple pendulum(with a catch!)?
June 1st 2009, 10:09 PM #1
[SOLVED] Time period of simple pendulum(with a catch!)?
Find the time period of a simple pendulum if the mass of the bob is $m$ and mass of the rod is $M$.
Answer:
Anyone?
Last edited by fardeen_gen; June 1st 2009 a... | 5 | [
0.0050048828125,
0.0016937255859375,
0.0089111328125,
-0.059814453125,
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0.0016021728515625,
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0.03515625,
0.11767578125,
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0.02734375,
-0.0859375,
0.0252685546875,
0.1240234375,
-0.032958984375,
0.0... | 9,156 | 9156 | |
Telescoping Series
April 13th 2010, 06:11 AM #1
Member
Joined
Nov 2009
Posts
76
Telescoping Series
Can somebody help with this?
Evaluate as a telescoping series: The summation from k=1 to infinity of (k-1)/2^(k+1).
The answer is 1/2 but I need to see the workings so I can figure out how it was ... | 5 | [
-0.057861328125,
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0.0252685546875,
0.09033203125,
0.0216064453125,
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-0.001739501953125,
-0.039794921875,
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-0.125,
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0.0172119140625,
0.00830078125,
-0.08251953125,
-0.00830078125,
0.0269775390625,
-0.0... | 9,157 | 9157 | |
Possible arrangements
November 29th 2006, 02:03 PM #1
Member
Joined
Nov 2006
From
San Francisco
Posts
145
Possible arrangements
Four congruent triangular gardening plots form a square. Each plot will contain one kind of flower, and the flowers in plots that share an edge will be different. How many d... | 4 | [
0.021240234375,
0.004425048828125,
0.006622314453125,
-0.057373046875,
-0.0517578125,
0.060302734375,
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0.0303955078125,
0.03515625,
0.04296875,
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-0.00099945068359375,
0.04443359375,
0.0517578125,
-0.0751953125,
-0... | 9,158 | 9158 | |
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countonme123 Group Title
One man starts ou... | 4 | [
0.0179443359375,
-0.0164794921875,
-0.010986328125,
-0.051513671875,
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0.03173828125,
-0.030151... | 9,159 | 9159 | |
Trigonometric Limit Question
January 14th 2009, 10:20 PM #1
Trigonometric Limit Question
Please refresh my memory on how I would take the limit as x -> infinity of
$[3x + sin(x)] / [4x - cos(2x)]$
Thanks.
This isn't a rigorous way to do it, but it makes sense I think. I feel like a proper proof wou... | 5 | [
-0.039306640625,
0.01806640625,
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0.046875,
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0.0130615234375,
-0.0211181640625,
0.0849609375,
... | 9,160 | 9160 | |
Statistics - Median & Mean
June 2nd 2008, 03:56 AM
Risrocks
Statistics - Median & Mean
The table gives marks out of 50 by 40 candidates:
Class Frequency
1-10 7
11-20 8
21-30 15
31-40 7
41-50 3
(i) In which class deos the median mark lie?
(ii) calculate the mean mark.
... | 5 | [
-0.034912109375,
0.07470703125,
0.029296875,
-0.059814453125,
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0.0181884765625,
-0.0289306640625,
-0.... | 9,161 | 9161 | |
problem on Trace of the sum of two matrices
October 17th 2012, 07:37 AM
MAX09
problem on Trace of the sum of two matrices
The following question is in the exercise of my text book.
A is 4x4 matrix with 1,-1,2 and -2 as its four eigen values. If B = A^4 - 5A^2 + 5I, which of the following is true?
a) det... | 5 | [
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0.0023956298828125,
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0.01092529296875,
-0.07763671875,
0.076171875,
-0.017700195312... | 9,162 | 9162 | |
Chessboard problem
March 29th 2011, 06:32 PM
claws61
Chessboard problem
Problem:
Imagine a King on an 8x8 chessboard.
It's located in a1, bottom left corner.
And it wants to get to a8, top left corner.
It can only move one step at a time, diagonally, vertically and horizontally.(Surprised)
H... | 5 | [
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0.0001621246337890625,
-0.04443359375,
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0.064453125,
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0.0771484375,
0.0341796875,
0.0201416015625,
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0.00185394287109375,
0.01513671875,
-0.04541015625,
0.0556640625,
-0.04150390625,
0.02758... | 9,163 | 9163 | |
Finding Products of a Range of Numbers
Date: 03/28/2002 at 17:55:21
From: M
Subject: Formula for finding products of a range of numbers
What method or formula is there to solve for the product of a range
of numbers? For example, how can I figure out the product of the
numbers from 1 to 100? I know the method for fin... | 4 | [
-0.02294921875,
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0.0001926422119140625,
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0.05810546875,
-0.0038299560546875,
0.03955078125,
0.033447265625,
-0.0010528564453125,... | 9,164 | 9164 | |
Math Forum Discussions - Plot:Connect few points and form a line
Date: Nov 12, 2013 4:30 PM
Author: HsiaoTing Ko
Subject: Plot:Connect few points and form a line
%Elastic Modulus--YM=YA=Y(MPa)
Y=62000;
%Transformation Temp(degree C)
MF=10;
MS=17;
AS=31;
AF=44;
%Transformation Constatns--CM=CA=C(MPa/degree)
C=7;
%Ma... | 4 | [
-0.07568359375,
0.0113525390625,
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0.0947265625,
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0.0128173828125,
-0.1162109... | 9,165 | 9165 | |
Differential Eqns
May 4th 2009, 06:44 PM
ny_chow
Differential Eqns
At time t, t $\ge$ 0, the volume of a sphere is increasing at a rate proportional to the reciprocal of its radius. At t = 0, the radius of the sphere is 1 and at t = 15, the radius is 2. (Volume
of sphere is V = 4/3pir^3)
a) Find the rad... | 5 | [
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0.04931640625,
0.02392578125,
-0.00714111328125,
0.003936767578125,
-0.0106201171875,
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0.05419921875,
0.09228515625,
0.0174560546875,
0.0712890625,
-0.08203125,
0.0267333984375,
0.0712890625,
-0.068359375,
-0.037353515625,
-0.010498046875,
-0.0269775390... | 9,166 | 9166 | |
Line intersecting implicit function
January 18th 2010, 09:28 AM
hciR
Line intersecting implicit function
Hi, I have to find the co-ordinates where the line y=-x+1 intersects f(x,y) = x^2 + y^2 -xy - y -1
I can do this with explicit functions by making them equal, but it doesn't work with this.
The actu... | 5 | [
-0.052734375,
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0.0037689208984375,
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0.04638671875,
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-0.141601... | 9,167 | 9167 | |
Second Order Implicit Partial Derivatives
May 31st 2009, 10:55 PM
wceagles10
Second Order Implicit Partial Derivatives
This problem is doing my head in...
If $z$ is defined implicitly as a function of $x$ and $y$ by the equation
$xze^y + yz^3 = 1$,
find the values of $dz/dx, dz/dy$ and $d^2z/dxdy$... | 4 | [
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0.006072998046875,
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0.017578125,
0.06982421875,
0.0235595703125,
-0.038818359375,
0.05... | 9,168 | 9168 | |
Logarithm problem (sorry if this in the wrong section!)
March 30th 2008, 06:36 AM #1
Newbie
Joined
Mar 2008
Posts
1
Logarithm problem (sorry if this in the wrong section!)
I couldn't seem to find a board on logarithms so apologised if this is in the incorrect section. Apologies for formatting too.
I... | 4 | [
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0.0308837890625,
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0.06176... | 9,169 | 9169 | |
word problem
I claim 103138 divides that number for all positive integer values of n. This is done by observing that $a-b$ divides $a^n - b^n$ and then rearranging the given number into sums of such differences.
For example, $278 = 2141-1863$ and $-278 = 1492 - 1770$ Thus $278|2141^n -1863^n + 1492^n - 1770^n$ Similarl... | 5 | [
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0.07470703125,
-0.06201171875,
-0.00439453125,
-0.00628662109375,
-0.033447265625,
0.... | 9,170 | 9170 | |
Homework Help
Posted by steve on Tuesday, May 24, 2011 at 10:43pm.
which term in the expansion of (1/(3x^2)-x)^15 is the constant term?
A. 10th
B. 11th
C. 12th
D. 13th
• math - MathMate, Wednesday, May 25, 2011 at 12:17am
The constant term is the term where the power of x in the product (1/(3x²))^r*x^(15-r... | 4 | [
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0.0034942626953125,
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0.060546875,
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0.072265625,
0.00921630859375,
-0.047607421... | 9,171 | 9171 | |
proof in modern algebra
October 28th 2012, 02:31 PM
amyw
proof in modern algebra
Prove that (G, *) is an abelian group if an only if f:G--->G defined by f(x)=x^-1 is a homomorphism.
I understand that I need to prove two things.
1) If (G, *) is abelian, then the function is a homomorphism.
2) If the ... | 5 | [
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-0.055419921875,
0.0272216796875,
0.125,
-0.056640625,
0.06127929... | 9,172 | 9172 | |
Perimeter of Pascal's Triangle
Date: 06/04/2001 at 20:43:23
From: Bobby Mcdonald
Subject: Formula for Pascal's triangle
Is there a general formula for finding the perimeter of Pascal's
triangle using the number of rows?
Formula for Perimeter of Pascal's Triangle
Number of rows Perimeter sum
---------------------... | 4 | [
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0.048583984375,
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0.011962890625,
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-0.029052734375,
-0.0135498046875,
... | 9,173 | 9173 | |
Zonohedra and the Sylvester-Gallai theorem
When I was in Melbourne recently, I spent some time browsing through a copy of “Twelve Geometric Essays” by Harold Coxeter in the (small) library at AMSI. One of these essays was entitled “The
classification of zonohedra by means of projective diagrams”, and it contained a ver... | 4 | [
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0.0306396484375,
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0.017578125,
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0.0208740234375,
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-0.0712890625,
-0.0174560546875,
-0.04052734375,
-0.0859375,
0.1... | 9,174 | 9174 | |
Construction of GL_2(F) counting issues
November 12th 2013, 09:40 AM #1
Construction of GL_2(F) counting issues
Counting principles (however easy they may be) are not something I'm all that good with.
I am trying to find all 2 x 2 matrices with elements in $\mathbb{F}_p = \mathbb{Z}/n \mathbb{Z}$ where p is... | 5 | [
-0.00506591796875,
-0.01904296875,
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0.015869140625,
0.004974365234375,
0.043701171875,
-0.03125,
-0.01007080078125,
-0.0732421875,
0.040283203125,
0.0218505859375,
0.02978515625,
0.01092529296875,
-0.048828125,
0.0244140625,
-0.0537109375,
-0.0610351... | 9,175 | 9175 | |
Equivalent metrics on Fréchet spaces and Lipschitz maps
up vote 4 down vote favorite
Lipschitz maps are defined over metric space as maps $f:(X,d_X) \to (Y,d_Y)$ such that $$ d\left( f(x),f(x^\prime) \right)_Y \le k d(x,x^\prime)_X \ \forall x,x^\prime \in X, $$ where $k$ is a
positive constant. We usually say that $f... | 4 | [
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0.0031890869140625,
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-0.0081787109375,
0.039794921875,
0.0390625,
0.0478515625,
0.037353515625,
0.031494140625,
-0.00927734375,
0.035888671875,
-0.0703125,
0.0478515625,
-0.001014709... | 9,176 | 9176 | |
Mechanical Aptitude Tests -
Are you faced with a mechanical aptitude test as part of an interview?
Do you want to ... | 4 | [
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0.035888671875,
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0.05029296875,
0.020263671875,
-0.02685546875,
0.00408935546875,
0.000457763... | 9,177 | 9177 | |
First Order Ordinary differential Equation
December 1st 2009, 06:19 PM
Fallen186
First Order Ordinary differential Equation
I have the first order Initial Value Problem ODE of
$y' = 1 + 4y^2$ , $y = \frac{1}{2}*tan(2x+C)$ , $y(0) = 0$
I calculate that $y' = sec^2(2x+c)$
$<br /> sec^2(2x+ C) = 1 + ... | 5 | [
-0.00830078125,
-0.00421142578125,
0.08642578125,
0.09912109375,
-0.0038604736328125,
0.0556640625,
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0.040771484375,
0.03564453125,
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0.07958984375,
-0.06396484375,
-0.08740234375,
0.0068359375,
-0.0277099609375,
-0.0238037109375,
0.0478515625,
-0.0088... | 9,178 | 9178 | |
Show n^3 + 11n Divisible by 6
Date: 12/11/2002 at 00:41:56
From: Jasmine
Subject: Algebra
If n is a natural number, show that for all values of n, (n^3+11n) is
divisible by 6.
Date: 12/11/2002 at 10:33:52
From: Doctor Ian
Subject: Re: Algebra
Hi Jasmine,
I would probably try to use induction. That is, I know that... | 4 | [
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0.078125,
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0.00164794921875,
0.0771484375,
-... | 9,179 | 9179 | |
Problem - Onto mapping with power set.
November 11th 2009, 07:29 AM #1
Super Member
Joined
Apr 2009
Posts
677
Problem - Onto mapping with power set.
Let S be a set. S* is the power set of S. Prove there can't be any onto mapping from S->S*
My approach:
1. Let f be a onto mapping from S->S*
2... | 5 | [
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0.051025390625,
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0.08154296875,
-0.00823974609375,
0.007415771484375,
-0.0283203125,
0.0732421875,
0.015869140625,
... | 9,180 | 9180 | |
0!
A silly poem I wrote while in college: Man has wondered Since time immemorial Why 1 is the value Of 0!.
Hello 0! is a convention without demonstration. Same $2^0 = 1$ $<br />$
We can show this is the case using calculus (if this is a bit advanced for you, please bear with me (Nod) ) The Gamma Function is defined b... | 5 | [
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0.017578125,
-0.060791015625,
-0.0194091796875,
0.0002307891845703125,
... | 9,181 | 9181 | |
Determinants and linear transformations
A linear transformation $\vc{T}: \R^n \to \R^m$ (confused?) is a mapping from $n$-dimensional space to $m$-dimensional space. Such a linear transformation can be associated with an $m \times n$
matrix.
If we restrict ourselves to mappings within the same space, such as $\vc{T}: ... | 5 | [
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0.138671875,
0.0216064453125,
0.07666015625,
0.0361328125,
-0.0079345703125,
0.06982421875,
-0.005157470703125,
-0.02880859375,
-0.0159912109375,
0.0339355... | 9,182 | 9182 | |
Fat Tails
COMPUTING SCIENCE
Fat Tails
Sometimes the average is anything but average
By No Means
How different are the statistics of the factoidal process! When I first began playing with the n? function, I was curious about its average value, and so I did a quick computation with a small
sample—100 repetitions of 1... | 4 | [
-0.035400390625,
-0.0419921875,
0.014892578125,
0.021484375,
0.0223388671875,
-0.1318359375,
-0.05224609375,
0.11572265625,
0.07763671875,
0.0027618408203125,
-0.015869140625,
0.0284423828125,
-0.043212890625,
-0.0361328125,
-0.005218505859375,
-0.045654296875,
0.0120849609375,
-0.... | 9,183 | 9183 | |
Rigorous Limits
September 30th 2010, 02:41 PM #1
Rigorous Limits
We've begun limits, but the more rigorous approach I have not fully understood yet, so I'm hoping someone could help me please
Question
$lim_{n\rightarrow{\infty}} \frac{n^2+1}{n^2+2}$
Answer
Determine some real number $L$ such tha... | 5 | [
-0.0625,
0.054931640625,
0.072265625,
0.031494140625,
0.08544921875,
-0.0205078125,
-0.04638671875,
0.0439453125,
-0.001922607421875,
-0.134765625,
-0.0035858154296875,
-0.0255126953125,
0.033935546875,
0.047607421875,
-0.068359375,
-0.027587890625,
0.08349609375,
-0.0284423828125,... | 9,184 | 9184 | |
When the rate of unemployment will fall to 5%? Likely never
Update: A working paper is available with more technical details. The intuition behind Okun’s law is very simple. Everybody can feel that the rate unemployment is likely to rise when real economic
growth is very low or negative. An economy needs fewer employee... | 4 | [
-0.138671875,
0.0252685546875,
0.10205078125,
0.04443359375,
0.04052734375,
0.01287841796875,
-0.049560546875,
0.029296875,
0.061279296875,
0.07763671875,
0.06005859375,
0.00144195556640625,
0.0089111328125,
0.001129150390625,
0.0291748046875,
0.032470703125,
-0.0205078125,
0.03247... | 9,185 | 9185 | |
Is the given expression, monotonically increasing or decreasing with increasing x?
up vote -2 down vote favorite
Is the given expression, monotonically increasing or decreasing with increasing x?
$\frac{1}{x \log(x)} \sum_{i=1}^{\infty} \frac{\mu(i)}{i} x^{1/i}$
EDIT: This is the derivative of the prime counting fu... | 5 | [
-0.091796875,
-0.0869140625,
0.043701171875,
0.048828125,
0.01611328125,
-0.09912109375,
0.06298828125,
0.0712890625,
0.11865234375,
0.005279541015625,
0.0062255859375,
0.023193359375,
0.123046875,
0.05908203125,
-0.010986328125,
0.017333984375,
0.035888671875,
0.016357421875,
-0... | 9,186 | 9186 | |
Math Help
show that 37^n+2 + 16^n+1 + 23^n is divisible by 7 whenever n is natural thank you
I assume you're having trouble with step 3. Then note: $37^{k+3} + 16^{k+2} + 23^{k+1} = 37 \cdot 37^{k+2} + 16 \cdot 16^{k+1} + 23 \cdot 23^{k}$ $= 37 \left( 37^{k+2} + 16^{k+1} + 23^{k} \right) -
21 \cdot 16^{k+1} - 14 \cdo... | 4 | [
0.004425048828125,
0.107421875,
-0.042724609375,
0.0260009765625,
0.06591796875,
0.0037841796875,
0.044921875,
0.08349609375,
-0.095703125,
0.00506591796875,
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0.0267333984375,
0.02001953125,
-0.0037078857421875,
-0.043212890625,
-0.07568359375,
-0.00150... | 9,187 | 9187 | |
Planar Graphs and Skew Binary Spaces
up vote 2 down vote favorite
Let $G$ be a planar triangulation on $3m$ edges and $m+2$ vertices. Let $A$ be the binary matrix obtained from the incidence matrix of $G$ by deleting a row (equivalently we require the rows of $A$
to form a basis of the cocycle space of $G$ over $GF(2)... | 4 | [
-0.01458740234375,
-0.06494140625,
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-0.046142578125,
0.0478515625,
0.01129150390625,
-0.038330078125,
-0.1064453125,
-0.004058837890625,
0.07275390625,
0.07275390625,
-0.01806640625,
0.00921630859375,
-0.036376953125,
0.04052734375,
0.030029296875,
0.000713348388671875,... | 9,188 | 9188 | |
Problem Solving: Using Systems
November 2nd 2008, 12:00 PM #1
Newbie
Joined
Oct 2008
Posts
7
1. Kerry asked a bank teller to cash a $390 check using $20 bills and $50 bills. If the teller gave her a total of 15 bills, how many of each type of bill did she receive?
2. Tickets for the homecoming dance... | 4 | [
0.0216064453125,
0.1005859375,
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0.07373046875,
0.054443359375,
0.0269775390625,
0.04150390625,
-0.007171630859375,
0.016235351... | 9,189 | 9189 | |
Sigma Proof by Induction
August 31st 2012, 05:20 PM
renolovexoxo
Sigma Proof by Induction
Prove 1/1(2)+2/2(3)+...+1/n(n+1)=n/n+1
I've been using induction to prove this.
For the base case I got: 1/1(2)=1/2
Then I go on and get a little more stuck:
Assume 1/1(2)+2/2(3)+...+1/n(n+1)=n/n+1 for a... | 4 | [
-0.0810546875,
0.013671875,
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0.0234375,
-0.011962890625,
0.030517578125,
0.045166015625,
0.06982421875,
0... | 9,190 | 9190 | |
Locus of circumcentre?
April 30th 2009, 07:32 AM
fardeen_gen
Locus of circumcentre?
A triangle has two of its sides along the axes. Its 3rd side touches the circle $x^2 + y^2 - 2ax - 2ay + a^2 = 0$. Find the equation of locus of the circumcentre of the triangle.
April 30th 2009, 11:37 PM
earboth
Quote:
... | 4 | [
-0.0216064453125,
0.0166015625,
-0.00201416015625,
0.027099609375,
0.0203857421875,
0.080078125,
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0.10302734375,
0.0576171875,
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0.115234375,
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0.0101318359375,
0.02734375,
0.0595703125,
-0.039794921875,
-0.056884... | 9,191 | 9191 | |
Radicals #1
imgur: the simple image sharer My attempt: imgur: the simple image sharer I'm not sure if I was right about dividing .3 in the beginning from the radical.
You didn't need to divide by 0.3. You also divided 6.3 by 0.3 as well as dividing $\sqrt{48}$ by $\sqrt{0.3}$ so in total you divided by $0.3\sqrt{0.3}$... | 4 | [
0.007049560546875,
0.0216064453125,
-0.0380859375,
0.046875,
-0.058837890625,
-0.0732421875,
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0.046875,
0.026123046875,
0.000885009765625,
0.04345703125,
0.0037841796875,
0.0380859375,
0.06298828125,
-0.01043701171875,
0.042724609375,
-0.1533203125,
0.11083984375,
... | 9,192 | 9192 | |
Basic Electrodynamics (V): Electron Beam Deflection
Electron beam deflection relates to the behavior of a beam of electrons when fired from an electron "gun" and through a defined field. The diagram accompanying shows the path of a beam through an
electric field, E, set up inside a cathode ray tube. Note that althou... | 4 | [
0.0247802734375,
0.07421875,
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0.011474609375,
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0.01324462890625,
0.... | 9,193 | 9193 | |
Cohen-Lenstra Heuristics reference
up vote 3 down vote favorite
3
I am looking for good references (preferably, books) on Cohen-Lenstra Heuristics (on Real Quadratic fields) which explain in detail the reasons behind its fundamental assumption (higher the
cardinality of the automorphism group less likely it is cyclic)... | 4 | [
-0.0869140625,
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-0.002349853515625,
-0.0233154296875,
-0.020... | 9,194 | 9194 | |
Tips on How to Manipulate the Ideal Gas Law
Brightstorm is like having a personal tutor for every subject
See what all the buzz is about
Check it out
Tips on How to Manipulate the Ideal Gas Law 2,484 views
So we are working with Gas Laws. And we're going to be come across the Ideal Gas Law. We want to manipulate th... | 4 | [
-0.04150390625,
0.04736328125,
-0.03515625,
0.0556640625,
-0.00360107421875,
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0.0791015625,
0.019775390625,
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0.00714111328125,
0.044921875,
0.0087890625,
-0.031982421875,
-0.0181884765625,
0.062255859375... | 9,195 | 9195 | |
Partial derivatives of arccos
June 18th 2013, 12:46 PM
Vulpes
Partial derivatives of arccos
Hi All,
To be able to construct a Jacobian, I am asked to find the two partial derivatives of the following inverse trigonometric function:
$w_{1}(u,v) = \frac{1}{2\pi} \arccos (\frac{u}{\sqrt{u^{2} + v^{2}}})$
... | 5 | [
0.00506591796875,
0.003143310546875,
0.064453125,
0.044921875,
-0.018310546875,
-0.0771484375,
-0.03271484375,
-0.03857421875,
-0.036376953125,
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-0.09228515625,
-0.0196533203125,
0.0123291015625,
-0.032958984375,
0.0179443359375,
... | 9,196 | 9196 | |
Trig Problem
June 29th 2010, 11:18 AM #1
Junior Member
Joined
Feb 2010
From
New Jersey, USA
Posts
36
Trig Problem
Hi all.
I'm trying to show that...
1 - ( tan (x/2) )^2 = sec x + tan x
Any help will be appreciated.
Thanks.
expand the difference of squares
given:
$1 - ( \... | 5 | [
-0.01019287109375,
0.01239013671875,
0.125,
0.0576171875,
0.03076171875,
-0.0025177001953125,
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0.037353515625,
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0.04931640625,
0.054443359375,
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0.0859375,
0.00445556640625... | 9,197 | 9197 | |
Find All Three Angles
September 10th 2008, 01:11 PM
magentarita
Find All Three Angles
Gregory wants to build a garden in the shape of an isosceles triangle with one of the congruent sides equal to 12 yards. If the area of his gardenwill be 55 square yards, find, to the nearest
tenth of a degree, the three an... | 4 | [
0.0252685546875,
0.103515625,
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-0.03662109375,
-0.01611328125,
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0.033935546875,
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0.019287109375,
-0.01068115234375,
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0.055908203125,
0.1416015625,
0.056640625,
-0.091796875,
0.03833007812... | 9,198 | 9198 | |
prove this Highest Common Factor property
Hello, Let d=gcd(m,n) and d'=gcd(m+kn,n) 1st part d divides m. It also divides n. So it divides every linear combination of the two, and in particular m+kn. Therefore, d divides both m+kn and n. We
can conclude that d divides d' (because d' is the highest common factor) 2nd par... | 4 | [
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0.043212890625,
0.03466796875,
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0.00194549560546875,
-0.003402709... | 9,199 | 9199 |