content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Competition Questions
Date: 25 Feb 1995 16:19:42 -0500
From: Anonymous
Subject: math problems
Dear Dr. Math,
Do you also answer questions from teachers? We are trying to
prepare students for competitions and have (at present) two problems
that we cannot ourselves work! Here they are:
[1+{28-6... | 5 | [
-0.037841796875,
0.00579833984375,
0.0230712890625,
0.044189453125,
-0.0279541015625,
0.02734375,
-0.03125,
0.032470703125,
-0.02685546875,
0.06640625,
0.0166015625,
0.0126953125,
0.022705078125,
0.0830078125,
0.02587890625,
0.09228515625,
-0.08056640625,
-0.01080322265625,
-0.08... | 46,000 | 46000 | |
factor the trinomial by grouping
Posted by Adriana on Thursday, June 14, 2012 at 12:29pm.
15x^3-9x^2-6x
Can someone please show me how to factor completely.. trying to learn how to do factoring
• factor the trinomial by grouping - Steve, Thursday, June 14, 2012 at 12:53pm
Usually factoring by grouping is usef... | 4 | [
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0.04248046875,
0.038818359375,
-0.031494140625,
0.0703125,
... | 46,001 | 46001 | |
Could someone please check my math on this question involving equivalent rates?
August 20th 2012, 08:40 PM #1
Newbie
Joined
Aug 2012
From
Canada
Posts
2
**Funny side note: While typing this up, as a question, half way through I think I figured it out, which is why this is now a "check my math" post**
... | 4 | [
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-0.00811767578... | 46,002 | 46002 | |
Can one really construct an "ordinal table"?
up vote 4 down vote favorite
1
Many books describe how one can construct "by hand" a table of ordinals $1,\ 2,\ \ldots,\ \omega,\ \omega +1,\ \omega +2,\ \ldots,\ \omega\cdot 2,\ \omega\cdot 2 +1,\ \ldots,\ \omega^{2},\ \ldots,\ \
omega^{3},\ \ldots\ \omega^{\omega},\ \ldot... | 4 | [
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Posts about probability on Annoying Precision
Previously I mentioned very briefly Granville’s The Anatomy of Integers and Permutations, which explores an analogy between prime factorizations of integers and cycle decompositions of permutations.
Today’s post is a record of the observation that this analogy factors throu... | 4 | [
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-0.0556640625,
0.00939... | 46,004 | 46004 | |
Logs - Without calculator
January 16th 2009, 03:52 PM #1
Member
Joined
Sep 2007
Posts
81
Logs - Without calculator
Hi all,
What's the best way to work out log's without a calculator / other aids?
The question is $\log_{8}\frac{1}{4}$ what is the answer.
I know the answer is $-\frac{2}{3}$ ... | 4 | [
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0.0079345703125,
0.052001953125,
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0.0712... | 46,005 | 46005 | |
The Date of Easter for 2014
All of the calculations are done using whole numbers. Whenever you are asked to divide and keep only the whole number, simply ignore the decimal part. For example, in Step 2, you are asked to divide
the year by 4. If the year were 2007, this would give 501.75, but you ignore the decimal part... | 4 | [
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... | 46,006 | 46006 | |
Why Pi?
Date: 01/25/2001 at 11:41:06
From: crystal
Subject: Why Pi?
Dr. Math, I was just wondering...
Why do we use pi when we calculate the circumference and area of a
circle? I think one of my professors once told my class but I can't
remember and am curious.
Thanks.
Date: 01/25/2001 at 13:06:19
From: Doctor P... | 4 | [
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-0.0255126953125... | 46,007 | 46007 | |
Congruences Involving the Totient Function
For any integer n>1 let f(n) denote the number of positive integers less than and relatively prime to n. This is called Euler's totient function. There are some interesting congruences involving f
(n) that don't seem to be mentioned in most of the standard reference texts.... | 5 | [
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0.00008487701416015625,
-0.0224609375,
-0.072... | 46,008 | 46008 | |
Similar Pyramids and Measurement Ratios
Date: 08/10/2002 at 21:12:19
From: Deanna
Subject: Similar Pyramids
Dear Dr. Math,
The volumes of two similar pyramids are 27 and 64. If the smaller has
lateral surface area of 18, how would I find the lateral surface area
of the larger one?
I have tried to go backward since ... | 4 | [
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Turning Word Problems to Equations
Date: 03/08/2001 at 17:13:12
From: Agatha
Subject: Word Problems
How do you turn English sentences into math equations?
Date: 03/08/2001 at 18:50:26
From: Doctor Achilles
Subject: Re: Word Problems
Hi Agatha,
Thanks for writing to Dr. Math.
Word problems can be difficult to tr... | 4 | [
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proof of Riesz representation theorem for separable Hilbert spaces
proof of Riesz representation theorem for separable Hilbert spaces
Let $\{{\bf e}_{0},{\bf e}_{1},{\bf e}_{2},\ldots\}$ be an orthonormal basis for the Hilbert space $\mathcal{H}$. Define
$c_{i}=f({\bf e}_{i})\qquad\mbox{ and }\qquad v=\sum_{{k=0}}^... | 5 | [
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[SciPy-user] Optimization Working only with a Specific Expression of the input Parameters
Lorenzo Isella lorenzo.isella@gmail....
Sat Mar 3 14:23:16 CST 2007
Can you post your code, including the data?
Christian
Hi Cristian,
Actually I already posted this on the mailing list, but nevertheless I
will give it anoth... | 4 | [
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... | 46,012 | 46012 | |
Probability question
GROUPS:
I would appreciate help with this question: What is the probability that two nine digit numbers, each using all of the digits 1 through 9, will have exactly two of the digits in the same
place in the number?
Thank you.
Ronald
Bliss -Ron
... | 5 | [
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... | 46,013 | 46013 | |
what is the pattern?
t1=0, find the first few terms tn=1/tn-1+2, what is the pattern?
Hello, nithujaa! Given: . $t_1=0,\;\;t_n\:=\:\frac{1}{t_{n-1}+2}$ Find the first few terms. .What is the pattern? $\begin{array}{ccccccc} t_1 &=& 0 \\ t_2 &=& \frac{1}{0+2} &=& \frac{1}{2} \\ \\
[-4mm] t_3 &=& \frac{1}{\frac{1}{2} + ... | 4 | [
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User Mark Meckes
bio website case.edu/artsci/math/mwmeckes
location Toulouse, France
age 37
visits member for 4 years, 9 months
seen yesterday
stats profile views 3,961
Assoc. Prof. at CWRU. My main research interests are in probability, geometry, and fun... | 5 | [
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Proving Limits of a
January 10th 2013, 02:55 PM #1
Junior Member
Joined
Nov 2012
From
fefw
Posts
31
Proving Limits of a
$\lim_{x \rightarrow a} x = a$
this is my scratch work *
$0< \left | x-a \right | < \delta$
$\left | x-a \right | < \epsilon$
I let
$\delta = \epsilon$
Im... | 4 | [
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Kleisli Monad bijection
up vote 3 down vote favorite
1
For a monad $(T,\mu,\eta)$ if $T(A) = T(B)$, does this imply that $\mu_A = \mu_B$? I want to know because in the bijection between Kleisli triples and monads, given a monad, we define $f^* := T(f) ;
\mu_B$ if $f : A\to T(B)$ (c.f. Prop 1.6), but this needs to be w... | 4 | [
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Arrangements of the word MATHEMATICS with restriction.
February 16th 2013, 11:31 AM #1
Member
Joined
Feb 2011
Posts
83
Thanks
2
Arrangements of the word MATHEMATICS with restriction.
Hello all, I am trying to count the number of arrangements of the word MATHEMATICS where each consonant in adjacent in... | 4 | [
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Lucas Number Proof By Induction
July 26th 2008, 12:48 AM #1
Member
Joined
May 2008
From
Melbourne Australia
Posts
210
Thanks
22
Lucas Number Proof By Induction
I am having some trouble proving the relationship
$F_n$$L_n$= $F_{2n}$
where $F_n$, $L_n$ are the Fibronachi and Lucas numbers ... | 5 | [
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Ok, what am I doing wrong??
September 23rd 2006, 08:33 AM #1
Ok, what am I doing wrong??
Find the area of the minor segment formed on an arc of length 36cm drawn on a circle of radius 50cm.
Chord length = 2rsin(theta/2)
2 * 50sin(theta/2) = 36
theta = 0.7365
Area of segment = 0.5r^2(theta-sinthe... | 4 | [
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Posts from July 2010 on Aaron Meurer's SymPy Blog
Integration of primitive functions
July 31, 2010
Integration of Primitive Functions
So this past week, I had another break through in my project. The first break through, as you may recall, was the completion of the integrate_hyperexponential() function, which allowe... | 5 | [
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... | 46,021 | 46021 | |
Limit law for the number of local maxima in a square lattice of IID random variables
up vote 6 down vote favorite
2
For $i, j \in \{ 1, \ldots, n \}$, let $X_{i,j}$ be a real-valued random variable uniformly distributed on the interval $[0,1]$. The $X_{i,j}$ are independent.
Let $A_{i,j}$ be the indicator random vari... | 4 | [
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Have I finished this?
May 21st 2008, 04:24 AM
Taylor Fylde
Have I finished this?
I'm asked to find the the times (0<t<2pi) that two vectors are perpendicular.
The two vectors are perpendicular when their Dot product is zero. Taking the Dot product, and equating to zero gives:
2.Cos(2t).Sin(2t) - 4.Cos(... | 4 | [
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-0.06494140625,
-0.02600097... | 46,023 | 46023 | |
Proving...
October 1st 2009, 10:03 AM
GreenDay14
Proving...
The question asks:
Prove that if (v1, ... , vn) is a basis of V, then so is(v1, v2-v1, ... , vn - vn-1).
I made the initial assumption that if V remained the same number that by subtracting v1, youd always end up with v1, and so on. But obviou... | 4 | [
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Magnetic Viscosity in Accretion Disks
Previous abstract Next abstract
Session 44 -- Radio Galaxies, Jets and Disks
Display presentation, Wednesday, 9:20-6:30, Pauley Room
[44.14] Magnetic Viscosity in Accretion Disks
T.Tajima, R.Matsumoto (UT Austin), M.Kaisig (Univ.Wuerzburg)
Differentially rotating magnetized d... | 4 | [
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Homework Help
Posted by Kenneth on Sunday, January 29, 2012 at 8:59am.
Q: Convert 4x^2 + 4y^2 -8x -16y -29 = 0 into standard form.
I first started by pairing the like terms together, getting:
4x^2 -8x + 4y^2 -16y = 29
The next step, I'm a little confused. I know I need to complete the square, but I'm not sure how t... | 4 | [
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Please help me with this challenging math question probabilty
February 17th 2010, 10:53 AM
john002
Please help me with this challenging math question probabilty
Please answer any of the following question and please show your work
For [ 2x^2 - 1/x]^6, determine
a) The middle term
b) The term contain... | 5 | [
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0.035400390625,
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-0.0810546875,
0.0299072265625,
0.003997802734375,
-0.0272216796875,
0.00102996826171875... | 46,027 | 46027 | |
lifetime value formulaThe (almost) magic formula of Lifetime Value estimation
The (almost) magic formula of Lifetime Value estimation
In a previous blog post, Reinier wrote about the importance of assessing LTV. He brings as an example a corporate case study, and says “It’s not the calculation that is so interesti... | 4 | [
-0.056884765625,
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0.10498046875,
0.09375,
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0.06591796875,
0.01513671875,
0.044921875,
-0.041259765625,
0.0198974609375,
-0.036376953125,
-0.059570... | 46,028 | 46028 | |
ube roots
The Babylonian Algorithm for the square root of a number N is
x[n+1] = (x[n] + N/x[n])/2, where x[n+1] is the n+1-th approximation to the square root, obtained from x[n] which is the n-th approximation. The Babylonian Algorithm can be modified to obtain cube
roots to give the formula
x[n+1] = (2x[n] + N/x[n]^... | 5 | [
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0.03759765625,
0.0561... | 46,029 | 46029 | |
Sample Variance
Date: 08/08/97 at 21:12:31
From: craig murray
Subject: Sample variance
4,5,2,6,4,3,4
Could you please help me understand the sample variance using the data
above?
n = 7
X = 3.52
I am having a hard time understanding the problem. Thank you for any
help.
Craig
Date: 08/09/97 at 07:29:35
From: Doc... | 4 | [
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-0.030639648... | 46,030 | 46030 | |
Decomposition of a dynamical system into ergodic componenents
up vote 8 down vote favorite
1
Quick version of the question. Let $(X, \mu)$ be a probability measure space and let $Z$, the group of integers, act on $X$ in a measure preserving way. How can I decompose $X$ into ergodic
componenets? More precisely,... | 5 | [
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0.0... | 46,031 | 46031 | |
Prime divisor of finite group
up vote 0 down vote favorite
We know that the number of elements of order $k$ in a finite group $G$ is equal to $\sum |cl_{G}(x_{i})|$=$\sum|G/C_{G}(x_{i})|$ such that $|x_{i}|=k$. It is clear that for a prime $p$ if $p\mid |cl_
{G}(x_{i})|$, then $G$ has an element of order $p$. Now let ... | 5 | [
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Transformation, kernel, image, etc
June 20th 2009, 01:19 PM
arbolis
Transformation, kernel, image, etc
This is an exercise I had on the Linear Algebra final exam I failed. I could only do a part and I'm still stuck for most of it. So I'll write it entirely and I'll ask help only for part 1) until
we finish i... | 5 | [
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-0.09228515625,
-0.0173339843... | 46,033 | 46033 | |
Group theory
January 9th 2009, 10:45 AM #1
Newbie
Joined
Sep 2008
Posts
9
Group theory
Having some trouble figuring this out - any help at all would be greatly appreciated! Thanks
S the group of bijective applications R - > R. x, y elements of S. For every real number t, x(t) = t +1, y(t) = 2t.
... | 5 | [
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-0.0419921... | 46,034 | 46034 | |
Gravitational-wave measurements of the mass and angular momentum of a black hole
Echeverria, Fernando (1989) Gravitational-wave measurements of the mass and angular momentum of a black hole. Physical Review D, 40 (10). pp. 3194-3203. ISSN 0556-2821. http://resolver.caltech.edu/
CaltechAUTHORS:ECHprd89
PDF
See Usag... | 4 | [
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0.010070800... | 46,035 | 46035 | |
Greedy Algorithms
How to contact me. Base B, Circuit C, Closure s, Greedy G, Independence I, Rank r, Rank r'.
Greedy Algorithms
We recall the definition of an I-matroid.
Definition. An I-matroid (or, simply, matroid) M=(S,I) i... | 5 | [
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0.00576782226... | 46,036 | 46036 | |
Is Lebesgue/Borel non-measurability actually caused by non-uniqueness?
up vote 6 down vote favorite
1
In ZFC, every construction of a Lebesgue or Borel non-measurable set uses the axiom of choice. None of them that I've seen use choice to define a unique set, even though it's entirely possible to do
so (e.g. under the... | 4 | [
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Programming Technique for Animal Diet Formulation: A Non-linear Approach
Pratiksha Saxena ^1, Vinay Pathak ^2, Vinod Kumar ^2
^1Assistant Professor, School of Applied Sciences, Gautam Buddha University, Greater Noida 201308, India
^2School of ICT, Gautam Buddha University, Greater Noida 201308, India
Correspondence ... | 4 | [
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0.08056640625,
0.... | 46,038 | 46038 | |
Two Integrals
January 11, 2011
Our functions are straight forward translations of the mathematical formulas, summing the infinite series until the individual terms are less than the desired tolerance:
(define (exp-integral x)
(let* ((gamma 0.5772156649015328606065))
(let loop ((k 1) (fact 1) (z x) (sum (+ gamma (log... | 5 | [
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0.0322265625,
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-0.00347900390625,
0.033... | 46,039 | 46039 | |
Hybrid Gravitational Search Algorithm and Genetic Algorithms for Automated Segmentation of Brain Tumors Using Feature-based Symmetric Analysis
(IJCSIS) International Journal of Computer Science and Information Security,
... | 4 | [
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... | 46,040 | 46040 | |
Nearest and farthest point
November 18th 2009, 05:22 AM
noob mathematician
Nearest and farthest point
The plane $x+y+2z=2$ intersects the paraboloid $z=x^2+y^2$ in an ellipse. Find the points on this ellipse that are nearest to and farthest from the origin.
What I did:
Let $f(x,y)=x+y+2z-2$ and $g(x,y)... | 5 | [
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Generators of Groups
October 8th 2010, 10:42 PM
jzellt
Generators of Groups
a) List all the cyclic subgroups of <Z10, +> (Z10 = integers mod 10)
b) Show that Z10 is generated by 2 and 5
c) Show that Z2 x Z3 is a cyclic group
Any help is appreciated.... Thanks.
October 9th 2010, 02:47 AM
Swlabr
... | 4 | [
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-0.0016021728515625,
0.039306640625,
-0.00787353515625,
0.0267333984375,... | 46,042 | 46042 | |
Universal beam calculation
Hi, I'm replacing a section (2.2m) of first floor internal suporting wall with a universal beam (2.5m).
The beam will have to support floor joists, p/b, flooring only (no walls etc.)
Rooms above whose floor joists will be supported by the universal beam (ub):
1. have an area o... | 5 | [
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0.0314941... | 46,043 | 46043 | |
Simultaneous maximization of two Generalized Rayleigh Ritz Ratios
up vote 5 down vote favorite
1
Consider hermitian positive semi-definite matrices $A_1$ and $A_2$. Consider also positive definite matrices $B_1$ and $B_2$. I want to maximize the minimum of the two Generalized Rayleigh Ritz
ratios $\frac{x^{H}A_1x}{x^{... | 5 | [
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0.06494140625... | 46,044 | 46044 | |
Rings exam problem
February 18th 2009, 07:36 AM #1
Junior Member
Joined
Nov 2008
Posts
50
Rings exam problem
Let $\mathbb{K}$ be a field, consider the ring $\mathbb{K}[x,y]$.
1) Let $p(x,y) \in \mathbb{K}[x,y]$, prove that there exist $q(x,y) \in \mathbb{K}[x,y]$ and $a(x), b(x) \in \mathbb{K}[x]$ u... | 5 | [
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Introduction to Statistical Quality Control_ 4th Edition_2_
Chapter 12
Factorial and Fractional Factorial
Experiments for Process Design and
Improvement
Introduction to Statistical Quality Control,
4th Edition
General model o... | 5 | [
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X in exponent on both sides, can't make bases the same
July 29th 2010, 12:36 PM
jimmy1
X in exponent on both sides, can't make bases the same
Help:
$7^-^4^x = 2^1^+^3^x$
I should take the ln of both sides, right...?
$-4x ln 7 = (1+3x) ln 2$
How do I simplify?
July 29th 2010, 12:43 PM
Ackbeet
... | 4 | [
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0.06494140625,
0.006103515625,
0.0235595703125,
-0.1591796875,
-0.0205078... | 46,047 | 46047 | |
Fixed points of random permutations
November 7, 2012 by Qiaochu Yuan
The following two results are straightforward and reasonably well-known exercises in combinatorics:
1. The number of permutations on $n$ elements with no fixed points (derangements) is approximately $\frac{n!}{e}$.
2. The expected number of fixed... | 5 | [
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0... | 46,048 | 46048 | |
derivative in the Wasserstein space
up vote 2 down vote favorite
3
Villani gives the following formula to find the gradient of a function $F$ of a probability density function $\rho$ in the Wasserstein space : $$\nabla_W F(\rho) = -\nabla.(\rho \nabla \frac{\delta
F}{\delta \rho})$$ where, if $F$ is given as $F(\rho)=... | 4 | [
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-0.02819824... | 46,049 | 46049 | |
Property testing and Szemeredi's Theorem
After discussing Szemeredi’s Theorem and the analytical approaches of Roth and Gowers, let’s see some ideas and open problems in the combinatorial approach.
The following result is a good starting point.
Triangle Removal Lemma. For every $\delta >0$ there is a constant $\e... | 4 | [
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-0.017... | 46,050 | 46050 | |
Basic Shapes
Text to Supplement Lesson on Basic Area, Perimeter and Volume
In this lesson, we will review area, perimeter and volume. In particular we will first look at the definitions of basic 2-dimensional shapes: rectangles, triangles and circles... | 4 | [
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0.000705718994140625,
-0.0150146484375... | 46,051 | 46051 | |
Long division
Please could somebody tell me how you work out 119/140 using long division, Thanks:)
Unfortunately, I dont know how to show a long division, keeping all digits positioned correctly, so the best I can do is "talk" about it. Since 119 is less than 140, of course, the quotient will be
less than 1. So we wri... | 4 | [
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-0.04931640625,
-0.06201171875,
0.0... | 46,052 | 46052 | |
Is there an irreducible, noncompact commuting, nonnormal operator, with spectrum strictly continuous?
up vote 5 down vote favorite
1
Let $H$ be an infinite dimensional separable Hilbert space.
Definition: The commutant $\mathcal{S}'$ of a subset $\mathcal{S} \subset B(H)$ is $ \{A \in B(H) : AB=BA \ , \ \forall B \in... | 4 | [
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0.01721... | 46,053 | 46053 | |
Breaking down tolerance stack-up
A technique to predict the effects of tolerance stack-up on assembly forces and stresses combines a rigid body assembly model with a finite-element analysis.
KARL MERKLEY
KEN CHASE
Brigham Young University
Provo, Utah
EDITED BY MARTHA K. RAYMOND
Tolerance variation in assemblies res... | 4 | [
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0.04052734375,
0... | 46,054 | 46054 | |
Ordinary differential equations
October 8th 2010, 09:52 AM
ceode
Ordinary differential equations
1 ) SOLVE
dy/dx + y*cot(x) =5*e^cos(x) if y=-4 and x=5/4
2)
solve
dy/dx + (y logy)/x = y(logy)^2/(x^2)
3)SOLVE
(x*y^2)dx - e^(1/(x^3))dx - x^2*y dy = 0
Thank you very much.
October 8... | 5 | [
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0.0030059814453125,
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-0.00225830078125,
0.0703125,
-0.0242919921875,
-0.06494140625,
-0.0240478515625,
0.0179443359375,
0.030517578125,
0.07666015625,
-0.0289306640625,
-0.04736328125,
0.0308837890625,
0.06787109375,
0.0277099609375,
-0.07763671875,
-0.0... | 46,055 | 46055 | |
Complex Numbers (Loci)
April 12th 2009, 02:57 AM #1
Member
Joined
Jan 2008
Posts
132
Complex Numbers (Loci)
Hello!
Q: The complex number w is represented by the point of intersection of the loci |z -8 -6i| = 5 and arg(z -4 -3i) = 2 $\alpha$, where $\alpha$ = $\arctan$ (0.75). Find w, in the form x +... | 4 | [
-0.060302734375,
0.0235595703125,
-0.068359375,
0.03466796875,
0.034912109375,
-0.0703125,
0.06982421875,
0.0859375,
-0.00194549560546875,
-0.06298828125,
0.0166015625,
-0.0179443359375,
-0.0052490234375,
0.064453125,
-0.0189208984375,
0.00909423828125,
-0.1396484375,
-0.0737304687... | 46,056 | 46056 | |
Determining whether a sequence of partial sums is convergent or divergent
November 2nd 2012, 10:01 AM
MathIsOhSoHard
Determining whether a sequence of partial sums is convergent or divergent
Given the following sequence of partial sums:
$S_N=\frac{1}{N}cos(N\pi)$
My attempt:
If I can find the series... | 5 | [
-0.08447265625,
-0.07275390625,
-0.006866455078125,
0.06103515625,
-0.046142578125,
0.0311279296875,
-0.087890625,
0.03564453125,
0.055908203125,
-0.049072265625,
-0.0289306640625,
0.0186767578125,
0.0084228515625,
-0.043701171875,
-0.04296875,
-0.16015625,
0.0849609375,
-0.1215820... | 46,057 | 46057 | |
Proving irrational
September 25th 2008, 09:48 AM
Sinuyen
Proving irrational
Hi,
I have been reading a lot on here about proving that a number is irrational, which has helped. But I have not seen anything when it is simply variables that are either said to be rational or
irrational. Here is my question:
... | 4 | [
-0.0255126953125,
0.0303955078125,
-0.036865234375,
0.115234375,
0.00347900390625,
0.041748046875,
0.064453125,
-0.1376953125,
-0.0233154296875,
-0.018798828125,
-0.03662109375,
0.006988525390625,
0.095703125,
0.138671875,
-0.0035552978515625,
0.0125732421875,
-0.0145263671875,
0.0... | 46,058 | 46058 | |
Practical Uses of a Model of APL
Kenneth E. Iverson
I.P. ... | 5 | [
-0.0966796875,
-0.02587890625,
0.033203125,
-0.037353515625,
-0.1806640625,
-0.030029296875,
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0.13671875,
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0.0203857421875,
0.00084686279296875,
-0.017578125,
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-0.0114746... | 46,059 | 46059 | |
6.4
Excerpted from Beachy/Blair, Abstract Algebra, 2nd Ed. © 1996
Forward to §6.5 | Back to §6.3 | Up | Table of Contents | About this document
§ 6.4 Splitting fields
Definition 6.5.1. Let K be a field and let f(x) = a[0] + a[1... | 4 | [
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0.04443359375,
0.0458984375,
-0.12890625,
-0.016845703125,
... | 46,060 | 46060 | |
Math Forum Discussions
dpb
Posts: 8,100
Registered: 6/7/07
Re: Plotting a line with variables from a matrix
Posted: Feb 18, 2013 10:44 AM
On 2/17/2013 5:16 PM, Vilius wrote:
> three example matrixes:
> V1=1
> A=[10*1 20*1 ; 30*1 40*1]
> a=inv(A)=[ -0.2000 0.1000; 0.1500 -0.0500]
>
>
> V2=2
> A=[10*2 20*2 ; 30*2 40*2]... | 4 | [
-0.06005859375,
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-0.01904296875,
0.050537109375,
0.04296875,
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0.0186767578125,
0.0400390625,
0.0234375,
0.017578125,
-0.036376953125,
-0.03857421875,
-0.0068... | 46,061 | 46061 | |
Proof of Proposition 2.8
Proposition 2.8
.
L
*
[N]
(
E
) ⊆
K
*
[N]
(
E
), that is, Lewis-common knowledge of
E
implies common knowledge of
E
.
Proof.
Suppose that ω ∈ L*[N](E). By definition, there is a basis proposition A* such that ω ∈ A*. It suffices to show that for each m ≥ 1 and for all agents ... | 4 | [
-0.0250244140625,
0.07177734375,
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-0.046875,
0.01263427734375,
-0.0634765625,
-0.0247802734375,
-0.046142578125,
0.08251953125,
-0.0286865234375,
0.042236328125,
0.0859375,
-0.057373046875,
0.0264892578125,
... | 46,062 | 46062 | |
Just want to verify I am doing this right
February 9th 2010, 07:28 PM #1
Junior Member
Joined
Sep 2009
Posts
34
Just want to verify I am doing this right
I did get the right answers, but I still would like to make sure my thinking is accurate, and also check if I made unnecessary calculations somewhere.
... | 4 | [
-0.07958984375,
0.07421875,
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0.095703125,
0.00799560546875,
-0.0517578125,
-0.0194091796875,
0.00543212890625,
-0.07275... | 46,063 | 46063 | |
how to cover a set in a grid with as few rectangles as possible
up vote 2 down vote favorite
1
In calculus, when estimating a area of a set in a 2-dimensional space, we use rectangles to approximate. To get sufficient precision, how many rectangles are needed if the shape of the set is close
to a rectangle? I formaliz... | 5 | [
0.06787109375,
0.03515625,
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0.010009765625,
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0.03466796875,
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0.134765625,
-0.0111083984375,
-0.0... | 46,064 | 46064 | |
differentiation
November 23rd 2009, 09:35 AM #1
Newbie
Joined
Oct 2009
Posts
5
the tangent to the curve y= ax^2 + bx 2 at (1,1/2) is parallel to the normal to the curve y= x^2 +6x +10 at (-2,2). find the values of a and b
How much progress have you made with this question?
Find the slope of y= x... | 4 | [
-0.057861328125,
-0.0172119140625,
0.01123046875,
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0.021484375,
0.061279296875,
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0.12353515625,
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0.00677490234375,
-0.0238037109375,
0.126953125,
-0.06640625,
-0.020996093... | 46,065 | 46065 | |
Volume integration problem
August 19th 2008, 06:37 AM #1
Newbie
Joined
Aug 2008
Posts
11
Volume integration problem
Hey I need help with this.
A giant parabolic space dome has a roof described by the equation
z = 1 - x^2 - y^2
where z is the height above the ground and x and y are horizont... | 5 | [
0.03857421875,
0.107421875,
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-0.006866455078125,
-0.0255126953125,
... | 46,066 | 46066 | |
Subset sum problem
March 23rd 2011, 10:54 PM #1
Member
Joined
Jun 2008
Posts
148
Subset sum problem
Subset sum problem - Wikipedia, the free encyclopedia
I thought this problem was solvable in polynomial time using generating functions?
There is a algorithm given in the wiki link above that use... | 4 | [
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0.078125,
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0.050537109375,
-0.053466796875,
0.159... | 46,067 | 46067 | |
Curve Fit.
June 26th 2010, 06:13 PM #1
Junior Member
Joined
Jun 2010
Posts
27
Curve Fit.
Hi All
Thanks for your previous help Ackbeet. Now I have the following data.
data.txt
I wish to fit a power law curve to it of the following type (first equation).
I am particularly interested i... | 4 | [
-0.058349609375,
0.0634765625,
0.055419921875,
0.07861328125,
0.0277099609375,
-0.038330078125,
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0.0115966796875,
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-0.0096435546875,
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0.031005859375,
0.08251953125,
-0.041748046875,
... | 46,068 | 46068 | |
Modelling a quadratic - Systems of linear equations
May 11th 2010, 06:59 PM #16
MHF Contributor
Joined
Mar 2010
From
Florida
Posts
3,093
Thanks
5
$a=15-3c$
$b=10-2c$
$c$
$\begin{bmatrix}<br /> 15-3c\\ <br /> 10-2c\\ <br /> c<br /> \end{bmatrix}\rightarrow \begin{bmatrix}<br /> 15-... | 5 | [
-0.087890625,
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0.01177978515625,
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0.0849609375,
0.05517578125,
-0.03... | 46,069 | 46069 | |
Question on functions & domains
February 10th 2009, 12:02 PM #1
Newbie
Joined
Feb 2009
Posts
1
Question on functions & domains
Im having a hard time wrapping my mind around domains. I have no problem finding the domain of a function but what is stumping me is determining the function of a given domain. A... | 4 | [
-0.042724609375,
-0.028076171875,
0.0272216796875,
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0.005767822265625,
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0.072265625,
0.0264892578125,
-0.01495361328125,
-0.01361083984... | 46,070 | 46070 | |
Is that series-transformation known in the context of divergent summation?
up vote 4 down vote favorite
2
Note: I asked this question in math.stackexchange but did not receive an answer
Background: In the context of divergent summation I'm analyzing the matrix of eulerian numbers for a regular matrix-summation method... | 4 | [
-0.054931640625,
0.003570556640625,
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0.028076171875,
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0.0172119140625,
-0.033203125,
... | 46,071 | 46071 | |
Estimate mean and std dev?
April 8th 2009, 11:50 AM #1
Newbie
Joined
Mar 2009
Posts
15
A random sample of 13 observations from a population yielded $\sum$ x=488.8 and $\sum$$x^2$ = 18950.2. Estimate $\mu$ and $\sigma.$
I can't find this in my notes, I think $\sum$ x = 488.8 would be the sum of the sa... | 4 | [
0.007659912109375,
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0.09423828125,
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0.012939453125,
-... | 46,072 | 46072 | |
Odds in Blackjack
January 14th 2007, 05:31 PM #1
Banned
Joined
Jan 2007
Posts
315
Odds in Blackjack
Question :
In the game of 'Blackjack' or '21' what are the odds of making a hand: 17,
18, 19, 20 and also 14, using 6 or 8 standard deck of 52 cards?
Example:
10+7; 11(ace)+6; 8+6+3; 9+8... | 4 | [
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0.0185546875,
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0.021484375,
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-0.045166015625,
-0.03100... | 46,073 | 46073 | |
The Irrationality of e
Date: 09/04/98 at 00:17:10
From: Shawn Brady
Subject: How is it possible to prove a number is transcendental?
Hi, I was wondering if you could help me.
I'm reading through a book, and it's talking about transcendental
numbers. I know that a transcendental number is a number such that it
can't... | 5 | [
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0.03125,
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0.0458984375,
0.0556640625,
-0.0115966796875,
-0.07421875,
-0.0361328125,
-0.0688476562... | 46,074 | 46074 | |
Lattice generators
up vote 0 down vote favorite
3
I hope this question isn't trivial. Let $L$ be a lattice in $\mathbb{C}$ generated by two complex numbers $w_1,w_2$ which are linearly independent over $\mathbb{R}$. Let $\gamma\in\mathbb{C}$ be a
root of unity such that $\gamma\notin\mathbb{R}$ and $\gamma L=L$, and l... | 5 | [
-0.051513671875,
-0.0283203125,
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0.049560546875,
0.033203125,
0.04833984375,
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-0.00970458984375,
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0.054931640625,
0.00171661376953125,
0.060546875,
-0.05078125,
-0.052978515625,
0.040771484375,
-0.09716796875,
-0.04223632... | 46,075 | 46075 | |
In the long integer 36912151821...9999, what is the 1107th digit?
The title question would be a medium level math contest problem.
The following could be the SAT version:
369121518...99
The integer above is formed from consecutive positive integer multiples of 3 from 3 to 99 inclusive. What would be the 50th digit in... | 4 | [
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0.049560546875,
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0.0233154296875,
0.0115966796875,
-0.048583984375,
-0.0615234375,
0.01965332031... | 46,076 | 46076 | |
Differentiation Formulas
Top
Sub Differentiation Formulas are useful in finding a derivative of Functions and we use them in solving differentiation problems. Here, we will discuss useful differentiation formulas and other
Topics properties:-
Derivative of constant is 0:
d (c) = 0
... | 4 | [
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-0.048095703125,
0.068359375,
0.052734375,
-0.0245361328125,
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0.036376953125,
-0.00133514404296875,
0.0279541015625,
-0.058349609375,
0.0830... | 46,077 | 46077 | |
Complete metric space
January 16th 2009, 12:39 PM #1
Senior Member
Joined
Nov 2008
Posts
394
Complete metric space
(a)Give an example of two metric spaces $(X_{1}, d_{1})$ and $(X_{2}, d_{2})$ which are topologically equivalent and for which $(X_{1}, d_{1})$ is complete and $(X_{2}, d_{2})$ is not.
... | 5 | [
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0.00182342529296875,
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0.0245361328125,
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-0.0191650390625,
0.04638671875,
-0.050048828125,
0.07177734375,
... | 46,078 | 46078 | |
L'Hopital's Rule question...
March 22nd 2010, 09:15 AM #1
Newbie
Joined
Feb 2010
Posts
17
L'Hopital's Rule question...
Hi, I have two questions requiring L'Hopital's Rule that I can't seem to get. They are
And
For the first one I didn't even think the rule was necessary. I thought I could just ... | 5 | [
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-0.054931640625,
0.060302734375,
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0.045654296875,
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0.06689453125,
-0.031982421875,
0.038818359375,
-0.0556640625,
-0.02514648437... | 46,079 | 46079 | |
Problem with saving account
April 3rd 2007, 11:21 PM #1
Newbie
Joined
Mar 2007
Posts
3
Problem with saving account
You save 20 000 € on a savings account at the end of each year for 9 years. The annual interest rate is 3%.
a) How much is the total amount immediately after the last deposit?
b) Ho... | 4 | [
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0.07275390625,
0.0185546875,
-0.00823974609375,
-0.1328125,
0.001441955... | 46,080 | 46080 | |
Modal logic - box rules
up vote 0 down vote favorite
Hi guys,
In modal logic i.e. propositional logic with box and diamond, are then any laws to get a box or a diamond from outside a bracket to inside?
I.e. $\Box (x \rightarrow \Box x)$
I want the box inside the brackets :).
lo.logic modal-logic
I don't under... | 5 | [
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0.060546875,
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-0.01507568359375,
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0.031494140625,
0.0242919921875,
0.119140625,
0.0400390625,
0.007537841796875... | 46,081 | 46081 | |
Math Help
September 25th 2008, 08:00 AM #1
Newbie
Joined
Sep 2008
Posts
3
The service time of the first service of a BMW car is found to be normally distributed with a mean of 70 minnutes and a variance of 81 minutes.
1. If a customer brings her BMW car for its first service, what is the probability... | 4 | [
0.00439453125,
0.06494140625,
0.0966796875,
-0.0556640625,
-0.0673828125,
0.01171875,
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0.046630859375,
-0.02783203125,
0.0137939453125,
0.06884765625,
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0.028564453125,
0.04443359375,
0.03662109375,
-0.0233154296875,
0.11181640625,
-0.1376953125,
-0.17382... | 46,082 | 46082 | |
Fractional linear transformations and elliptic curves
March 12, 2010 by Qiaochu Yuan
The following two lemmas might be encountered in a basic course in complex analysis (the first in a basic course in group theory, even).
Lemma 1: Fix a field $F$. The group of fractional linear transformations $PGL_2(F)$ acts trip... | 4 | [
-0.0966796875,
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Primality Checking
May 1, 2009
In a previous exercise you wrote a function that returned a list of prime numbers, and in another exercise you used that function to find a particular prime number. This exercise looks at prime
numbers from a different perspective by considering a function that takes a number and determ... | 4 | [
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0.046630859375,
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... | 46,084 | 46084 | |
Square Root of 3
Date: 5/31/96 at 2:49:5
From: Marie Langley
Subject: Square root of 3
My granddaughter wants to know, what is the square root of 3?
Thanks, Marie Langley
Date: 6/2/96 at 17:46:25
From: Doctor Brian
Subject: Re: Square root of 3
Hello-
In a rare situation, three of our math doctors have addresse... | 4 | [
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Upper bounds on the permanent of dense 0-1 matrix
up vote 6 down vote favorite
2
I am looking for some result useful in deriving following (conjecture?):
Let $A$ be an $n\times n$ matrix with $0-1$ entries. Suppose, that exactly $k\leqslant n$ entries are equal to $0$. Then $\mathrm{Per} A \leqslant n!\left(1-\frac{k... | 5 | [
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-0.041... | 46,086 | 46086 | |
On the order of finite simple groups
up vote 11 down vote favorite
1
About the order of finite simple groups there exists a very interesting result which stated as follows:
Let $G$ be an non-solvable simple group of order $g$. If $p\mid g$, where $p>g^{1\over 3}$ is a prime, then $p>3$ and either $G\cong L_2(p)$ or $... | 4 | [
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Force to hold a spring
December 10th 2009, 08:13 AM
derekjonathon
Force to hold a spring
A force of 4 pounds is required to hold a spring stretched 0.3 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.9 feet
beyond its natural length... | 4 | [
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0.0103759765625,
-... | 46,088 | 46088 | |
Find the range
April 22nd 2009, 05:44 PM #1
Newbie
Joined
Jan 2009
Posts
19
Find the range
Find the range of the following function.
f(x) = (4+x)/(3-2x)
Looking for something like this
y= x^2
x = +/- sqrt(y)
y>0
range of $f(x)$ will be the domain of $f^{-1}(x)$
$y = \fra... | 4 | [
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-0... | 46,089 | 46089 | |
torsion of a non unit speed curve
January 9th 2013, 03:24 AM #1
Junior Member
Joined
Dec 2012
From
Britain
Posts
46
Thanks
2
torsion of a non unit speed curve
calculate torsion of y=(sqrt(5)+3cost, 3+tsqrt(7), 1 - 3sint). The usual way I do this is use the frenet formulae for a USC. But y is not ... | 4 | [
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0.08203125,
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0.049072265625,
-0.0286865234375,
0.007781982421875,
-0.09228... | 46,090 | 46090 | |
Sums of inverses of ``odd'' elements modulo $p$
up vote 0 down vote favorite
1
In a letter to Dirichlet, Gottold Eisenstein stated the congruence: $$ q(u) \equiv u - \frac{u^2}{2}+ \frac{u^3}{3} - \frac{u^4}{4} + \cdots + \frac{u^{p-2}}{p-2}-\frac{u^{p-1}}{p-1} \pmod{p} $$
where $p$ in an odd prime number and $$ q(u)... | 4 | [
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Cartesian equation containing the two lines
October 27th 2008, 06:13 PM #1
Member
Joined
Jun 2008
Posts
175
Cartesian equation containing the two lines
The questions asks to find the Cartesian equation of the lines r=<1,1,0>+t<1,-2,2> and r=<2,0,2>+t<-1,1,0>
Just trying to work out how to solve. Is ... | 4 | [
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-0.106445312... | 46,092 | 46092 | |
Are there "non-constructive" sets in second-order arithmetic?
up vote 7 down vote favorite
Consider $\phi(A)$ a formula of second-order arithmetic with one free variable $A$ of type "set". Suppose $\exists A : \phi(A)$ is a true sentence. Does it follow (not in second order arithmetic
itself, but in a stronger theory ... | 4 | [
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Metrically measured motions
Robert A. Lipsett
Engineering manager
Danaher Motion Inc.
Wood Dale, Ill.
The process of designing with metric motion-control components is quite similar to that with their English-dimensioned counterparts. The same design principles and formulas used for English-based
measurements apply to... | 5 | [
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0.040283203125,
0.096191... | 46,094 | 46094 | |
Surface Area and Volume of a Cube
Solved Examples
Question 1: Solution:
Find the surface area of the cube with the volume of 512 $cm^{3}$ ?
Given : volume =512 $cm^{3}$
Volume of cube = $(side \ length)^{3}$
=>512 $cm^{3}$ = $(side)^{3} $
=>side = cube root of 512
since 512 $cm^{3}$ = 8 cm $\times$ 8 cm $\... | 4 | [
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... | 46,095 | 46095 | |
Homotopy groups and homology groups for the $H\mathbb Z$ module-dg module correspondence.
up vote 5 down vote favorite
2
In Shipley's paper http://arxiv.org/abs/math/0209215 she proves a Quillen equivalence between the category of $H\mathbb Z$-modules and dg $\mathbb Z$-modules. So, to a chain complex $C$, she assigns... | 4 | [
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0.03979492187... | 46,096 | 46096 | |
Algebra y=mx+b
y=mx+b is "Slope-Intercept Form" where "y" is the equation of the line, "m" is the slope of the line, and "b" is the y-intercept. To find the y-intercept (or "b"), you should look for the point where
the line crosses the y-axis. On this graph, the line crosses the y-axis when y=0, so b=0. To find the slo... | 4 | [
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... | 46,097 | 46097 | |
Solutions to the eikonal equation
up vote 4 down vote favorite
5
Theorem. Let V be a $C^\infty$ function on a riemannian manifold $M$ and $p$ be a nondegenerate local minimum with $V(p)=0$. Then there is a unique positive function $\varphi \in C^\infty(U)$ such
that $\varphi$ solves the eikonal equation $$\|\mathrm{gr... | 4 | [
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-0.032226562... | 46,098 | 46098 | |
Question regarding differentiation
March 14th 2014, 08:37 AM #1
Newbie
Joined
Mar 2014
From
Germany
Posts
2
Question regarding differentiation
I have some problems with a differential - don't now what is correct...
Start with $c(t) = t_{EC} + \int_{t_{WA_c}}^{t} \frac{1-\Psi(s)}{2} \frac{\phi(s)... | 4 | [
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... | 46,099 | 46099 |