content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Factoring a Degree 2 Polynomial
Date: 3/21/96 at 0:40:13
From: Brandon
Subject: Math
I don't get this. I have tried, but not succeeded!
I am in grade nine.
Questions like x exponent2 - 12x - 85 I don't get these factor
things !
Please help me a.s.a.p
Thanks, Brandon
Date: 3/21/96 at 13:45:12
From: Doctor Ethan... | 4 | [
0.025146484375,
0.08544921875,
-0.0157470703125,
0.044677734375,
-0.024658203125,
0.0732421875,
0.04345703125,
-0.064453125,
-0.029541015625,
0.00689697265625,
0.09375,
0.004302978515625,
0.0498046875,
0.042724609375,
0.07958984375,
0.1201171875,
-0.0294189453125,
0.0289306640625,
... | 39,700 | 39700 | |
Green's Theorem
June 5th 2010, 07:36 PM #1
Member
Joined
Dec 2009
Posts
224
Green's Theorem
Here's a worked example I don't understand:
Use Green's Theorem to evaluate
$\int_C x^2ydx+xdy$
along the triangular path with verticies at: (0,0), (1,0) and (1,2).
Answer:
$\int_C x^2y dx... | 5 | [
-0.01458740234375,
0.0234375,
0.020751953125,
-0.052734375,
0.0595703125,
-0.01708984375,
-0.0260009765625,
0.08154296875,
-0.045166015625,
-0.00113677978515625,
-0.0625,
0.00994873046875,
0.06591796875,
-0.056396484375,
0.0263671875,
0.04296875,
-0.10791015625,
-0.0498046875,
-0... | 39,701 | 39701 | |
Compound interest problem
July 13th 2012, 01:09 AM
camerart
Compound interest problem
Hi, Can anyone help me solve a financial question please. If someone borrows money and agrees to pay back at 'say' 5%. It is possible to borrow more, and payback any time. Using Excel, I want to
know how to have a running t... | 4 | [
0.01611328125,
0.01318359375,
-0.03515625,
-0.056396484375,
0.00091552734375,
-0.05517578125,
-0.0027923583984375,
0.04296875,
-0.01104736328125,
0.134765625,
0.02392578125,
-0.05078125,
-0.004058837890625,
-0.0023651123046875,
0.016845703125,
0.09716796875,
-0.0341796875,
-0.02490... | 39,702 | 39702 | |
Math Forum Discussions
Math Forum
Ask Dr. Math
Discussions
Internet Newsletter
MathTools
Teacher2Teacher
Teacher Exchange
Workshops
Search All of the Math Forum:
Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.
Math Forum » Discussions » Math Topics » geometry.researc... | 4 | [
-0.034423828125,
0.0035858154296875,
-0.095703125,
-0.000507354736328125,
0.037841796875,
-0.0654296875,
0.0390625,
0.03271484375,
0.0498046875,
-0.043701171875,
0.017822265625,
0.024169921875,
0.01416015625,
0.00811767578125,
0.0223388671875,
-0.010009765625,
-0.03662109375,
-0.04... | 39,703 | 39703 | |
[SciPy-User] Sigmoid Curve Fitting
Warren Weckesser warren.weckesser@enthought....
Tue Sep 21 13:36:57 CDT 2010
On 9/21/10 1:30 PM, Chris Spencer wrote:
> Right, I noticed that negating k should theoretically have the same
> effect. However, when I reversed your sample data (i.e. ydata =
> ydata[::-1]), I was surpr... | 4 | [
-0.04638671875,
-0.03857421875,
0.06494140625,
-0.03125,
-0.0107421875,
-0.1328125,
0.055419921875,
0.0712890625,
0.00921630859375,
0.0228271484375,
0.037841796875,
-0.037109375,
0.00726318359375,
-0.030029296875,
-0.001007080078125,
0.0201416015625,
0.006011962890625,
-0.044921875... | 39,704 | 39704 | |
describe subsets of the integers closed under the binary operation Ax+By
up vote 11 down vote favorite
3
Could one describe the subsets of the integers closed under the binary operation Ax+By where A and B are arbitrary fixed integers ? That is, describe the subsets S of the integers such that if $x,y\
in S$ then $A... | 5 | [
-0.0013885498046875,
0.02685546875,
-0.004364013671875,
-0.00014972686767578125,
0.026123046875,
0.0274658203125,
0.134765625,
-0.04541015625,
-0.061767578125,
0.0537109375,
-0.03857421875,
-0.00421142578125,
0.050048828125,
-0.09619140625,
0.015380859375,
0.03955078125,
0.0480957031... | 39,705 | 39705 | |
Why is the Gamma function shifted from the factorial by 1?
up vote 65 down vote favorite
24
I've asked this question in every math class where the teacher has introduced the Gamma function, and never gotten a satisfactory answer. Not only does it seem more natural to extend the factorial
directly, but the integral def... | 4 | [
-0.09423828125,
-0.05810546875,
-0.0084228515625,
0.08056640625,
0.0269775390625,
0.0126953125,
0.0546875,
0.043212890625,
0.0277099609375,
0.09521484375,
0.07421875,
0.04052734375,
0.057373046875,
0.01287841796875,
-0.00408935546875,
-0.05615234375,
0.03271484375,
-0.072265625,
... | 39,706 | 39706 | |
Test the series for convergence or divergence.
Hello, fardeen_gen! Test for convergence: . $\sum^{\infty}_{n=1}(-1)^n\,\frac{n}{\sqrt{n^3+2}}$ The absolute value of the $n^{th}$ term is: . $|a_n| \:=\:\frac{n}{\sqrt{n^3+2}}$ $\text{Divide top and
bottom by }\sqrt{n^3}\!:\;\;\frac{\dfrac{n}{\sqrt{n^3}}} {\dfrac{\sqrt{n^... | 5 | [
-0.0157470703125,
-0.06298828125,
-0.062255859375,
0.0172119140625,
-0.040283203125,
-0.07373046875,
-0.087890625,
-0.027587890625,
0.037353515625,
-0.10302734375,
0.01495361328125,
0.00933837890625,
-0.0247802734375,
0.0439453125,
-0.050048828125,
-0.07861328125,
0.036865234375,
-... | 39,707 | 39707 | |
Why can't the Klein bottle embed in $\mathbb{R}^3$?
up vote 12 down vote favorite
12
Using Alexander duality, you can show that the Klein bottle does not embed in $\mathbb{R}^3$. (See for example Hatcher's book Chapter 3 page 256.) Is there a more elementary proof, that say could be
understood by an undergraduate who ... | 5 | [
-0.05517578125,
0.013916015625,
-0.0086669921875,
-0.0167236328125,
0.0179443359375,
0.06787109375,
0.0269775390625,
-0.0213623046875,
0.03466796875,
-0.0211181640625,
-0.0185546875,
0.064453125,
0.01434326171875,
0.07177734375,
-0.01611328125,
-0.062255859375,
-0.0263671875,
0.051... | 39,708 | 39708 | |
Quadrilaterals and Inscribed Circle
Date: 05/06/99 at 07:57:30
From: Jayant
Subject: Permutations and Combinations
Ten sticks of lengths 1,2,3,....,10 are given. Four are selected to
form the sides of a quadrilateral. Find the number of quadrilaterals
so formed. Also find in how many of these quadrilaterals a circle... | 4 | [
-0.0240478515625,
0.054443359375,
-0.01300048828125,
-0.09765625,
-0.08740234375,
0.11572265625,
0.08984375,
0.09716796875,
0.02685546875,
-0.04296875,
-0.0242919921875,
-0.031494140625,
0.0673828125,
0.03955078125,
-0.0191650390625,
-0.006927490234375,
-0.02587890625,
0.0229492187... | 39,709 | 39709 | |
How to check if an object is moving in direction of a target
February 12th 2011, 10:53 AM #1
Junior Member
Joined
Mar 2009
Posts
42
How to check if an object is moving in direction of a target
Hi,
I need a sanity check on a problem I’m trying to solve. I know where a number of moving objects are pos... | 4 | [
0.0296630859375,
-0.1025390625,
-0.04931640625,
-0.061279296875,
0.06640625,
-0.0198974609375,
0.0277099609375,
0.005859375,
-0.0277099609375,
0.055908203125,
0.006134033203125,
0.0228271484375,
0.017333984375,
0.0458984375,
-0.023681640625,
0.0673828125,
0.0035247802734375,
0.0512... | 39,710 | 39710 | |
Order in two groups
October 3rd 2008, 04:24 AM
snassimr
Order in two groups
I have two groups with n balls marked from 1 to n.
Two groups are randomized ( i.e. for each ball in each group to get any place in new order from 1 to n the probability is 1/n )
What the probability that in new order I won't s... | 5 | [
-0.0216064453125,
-0.09228515625,
0.025146484375,
-0.057861328125,
-0.048095703125,
-0.0218505859375,
0.03271484375,
-0.07861328125,
0.07421875,
0.047119140625,
0.00061798095703125,
-0.01251220703125,
-0.0235595703125,
-0.031494140625,
-0.056396484375,
-0.03515625,
0.09033203125,
-... | 39,711 | 39711 | |
Generating of the matrix ring by two hermitian matices
up vote 4 down vote favorite
1
Let $p$ be a prime and $q=p^n$. Let $\mathbb F_{q^2}$ be a field with $q^2$ elements and $\sigma$ its authomorhism of order two. A $m$ by $m$ matrix $A$ over $\mathbb F_{q^2}$ is hermitian if $A^\
sigma$ coincides with the traspose o... | 5 | [
-0.031005859375,
0.029296875,
-0.109375,
0.04638671875,
-0.09130859375,
0.00191497802734375,
0.02099609375,
-0.07373046875,
0.07568359375,
-0.01806640625,
0.050537109375,
0.06884765625,
0.0238037109375,
-0.0205078125,
-0.0419921875,
0.091796875,
-0.068359375,
0.053955078125,
0.00... | 39,712 | 39712 | |
quadratic equations and parabolas involving strange exponents
March 31st 2011, 11:51 AM #1
Newbie
Joined
Mar 2011
Posts
7
quadratic equations and parabolas involving strange exponents
I am not sure how to even approach these two equations. Both of them have exponents that are a bit odd and I'm not even s... | 4 | [
-0.050048828125,
-0.033935546875,
-0.091796875,
0.040771484375,
0.034912109375,
-0.0306396484375,
-0.01507568359375,
0.025146484375,
0.0234375,
-0.051025390625,
0.10009765625,
0.038330078125,
-0.005157470703125,
0.1328125,
0.083984375,
0.09716796875,
-0.060791015625,
0.025634765625... | 39,713 | 39713 | |
Choosing Non-Consecutive Integers from a list of N Integers
February 21st 2008, 11:18 AM #1
Newbie
Joined
Feb 2008
Posts
6
Choosing Non-Consecutive Integers from a list of N Integers
Prove that the number of ways choosing k integers from the integers 1,2,3...n, such that no two of the chosen integers are... | 4 | [
-0.0184326171875,
0.0400390625,
0.0157470703125,
-0.060791015625,
0.0196533203125,
0.1162109375,
0.044189453125,
0.040283203125,
-0.0244140625,
-0.0042724609375,
-0.0849609375,
-0.0322265625,
0.03369140625,
-0.0208740234375,
-0.05126953125,
-0.003662109375,
0.04150390625,
-0.050537... | 39,714 | 39714 | |
Subtraction of Trig Functions with a Phase Shift
Date: 09/14/2004 at 14:53:23
From: Jeremy
Subject: Subtraction of Trig Functions
I am a senior Electrical Engineering student and am currently writing
a training manual for my job at an engineering firm. I am now
covering 3-phase voltages and have a trig question pert... | 4 | [
-0.1474609375,
0.049072265625,
-0.06494140625,
0.00994873046875,
-0.005035400390625,
0.046875,
0.01495361328125,
-0.032958984375,
-0.0213623046875,
-0.018310546875,
0.0947265625,
-0.05419921875,
0.01116943359375,
-0.016845703125,
0.1357421875,
-0.07568359375,
-0.09375,
0.0101318359... | 39,715 | 39715 | |
Continuity on rationals?
May 16th 2011, 02:48 AM
cana
Continuity on rationals?
If $g:R \rightarrow R$ is continuous and $f:R \rightarrow R$ is such that f(x)=g(x) for all rational numbers x, is f continuos?
I'm not 100% sure about this because f is clearly continuos on the rationals, but what happens at the... | 4 | [
-0.039794921875,
-0.0157470703125,
-0.05419921875,
0.057373046875,
0.02099609375,
0.0595703125,
0.0830078125,
-0.08447265625,
-0.006103515625,
-0.04638671875,
0.0242919921875,
0.036376953125,
0.01708984375,
0.10986328125,
0.0247802734375,
-0.0478515625,
0.00921630859375,
-0.0084228... | 39,716 | 39716 | |
How to Make Weighted Average Problems Easy
Most people don’t like weighted averages, and for good reason. The formula is complicated, and these often come in the form of story problems, which are hard to set up. We’re going to talk today
about a couple of great little techniques to make these fast and easy well, easi... | 4 | [
0.044189453125,
-0.013671875,
0.0888671875,
0.02734375,
-0.0308837890625,
0.0089111328125,
0.06884765625,
0.053955078125,
-0.0400390625,
0.00848388671875,
-0.0064697265625,
-0.048095703125,
0.01483154296875,
0.08642578125,
0.0252685546875,
0.034423828125,
0.1162109375,
0.0111083984... | 39,717 | 39717 | |
Application of Green's Theorem
May 20th 2011, 08:01 PM #1
Newbie
Joined
Nov 2010
Posts
8
Application of Green's Theorem
Hi, I'm trying to answer the following question:
Basically, I know that you have to use Green's Theorem:
$\displaystyle\oint_C P(x)dx +Q(x)dy = \displaystyle\iint_A (\frac{\... | 5 | [
-0.0272216796875,
0.036376953125,
0.036865234375,
-0.044921875,
0.037841796875,
0.01129150390625,
0.039306640625,
0.0771484375,
0.0218505859375,
0.01318359375,
0.01171875,
0.01495361328125,
0.037109375,
0.046875,
0.0703125,
0.08447265625,
-0.03759765625,
-0.05615234375,
-0.046875... | 39,718 | 39718 | |
580 -Cardinal arithmetic (8)
4. Large cardinals and cardinal arithmetic
In section 3 we saw how the powers of singular cardinals (or, at least, of singulars of uncountable cofinality) satisfy strong restrictions. Here I show that similar restrictions hold at large
cardinals. There is much more than one could sa... | 4 | [
0.07373046875,
-0.020751953125,
0.0107421875,
-0.0177001953125,
0.09130859375,
0.039306640625,
0.01806640625,
0.08544921875,
-0.000396728515625,
-0.00109100341796875,
-0.12060546875,
-0.018310546875,
-0.019287109375,
0.023681640625,
-0.08642578125,
-0.00811767578125,
0.05224609375,
... | 39,719 | 39719 | |
Math Forum Discussions
Re: Help Needed in math
Posted: May 2, 2014 3:34 AM
On Fri, 2 May 2014, quasi wrote:
> William Elliot wrote:
> >quasi wrote:
> >>...
> >>Nevertheless, konyberg's argument is correct.
> >His answer is correct. I don't see his reasoning
> >How does f(x) relate to the missing problem?
>
> This is a... | 5 | [
-0.0291748046875,
0.06982421875,
0.0322265625,
-0.0634765625,
-0.0166015625,
0.0184326171875,
0.00286865234375,
0.0181884765625,
-0.01123046875,
0.08154296875,
0.04150390625,
0.076171875,
-0.03125,
-0.012939453125,
0.0361328125,
0.03662109375,
-0.0011138916015625,
-0.00053405761718... | 39,720 | 39720 | |
Patterns in the Last Digits of the Positive Powers of Two
http://www.exploringbinary.com/patterns-in-the-last-digits-of-the-positive-powers-of-two/
The positive powers of two — 2, 4, 8, 16, 32, 64, 128, 256, … — follow an obvious repeating pattern in their ending digit: 2, 4, 8, 6, 2, 4, 8, 6, … . This cycle of four ... | 4 | [
-0.07666015625,
0.01263427734375,
-0.038330078125,
-0.029052734375,
-0.0006103515625,
-0.01019287109375,
-0.01324462890625,
0.0537109375,
0.021728515625,
-0.03173828125,
0.00927734375,
0.06591796875,
0.054931640625,
0.0211181640625,
-0.00156402587890625,
0.006561279296875,
-0.0922851... | 39,721 | 39721 | |
Matching Linear Equations to x/y Tables
Comments (0)
Please log in to add your comment.
Matching Linear Equations to x/y Tables Ordered Pair- two numbers paired together in the form of (x,y) to represent a point on a graph Vocabulary Any point on a line is a solution to the linear
equation. X/Y Tables You can do a co... | 4 | [
-0.06298828125,
-0.07666015625,
-0.056396484375,
-0.016845703125,
-0.00921630859375,
-0.01806640625,
-0.0174560546875,
-0.0031585693359375,
-0.00408935546875,
0.03759765625,
0.0458984375,
-0.0009307861328125,
0.0576171875,
0.09814453125,
0.048095703125,
0.08740234375,
-0.10546875,
... | 39,722 | 39722 | |
Decomposability of Hausdorff measure
up vote 8 down vote favorite
2
Consider $s$-dimensional Hausdorff measure $\mathcal{H}^s$ on the Borel sets in $\mathbb{R}^n$.
$\mathcal{H}^s$ is not $\sigma$-finite if $s < n$, but it is semifinite (on Borel sets!)
Is it known whether $\mathcal{H}^s$ can be decomposable, i.e. can ... | 4 | [
-0.01263427734375,
-0.0322265625,
-0.0020599365234375,
-0.0177001953125,
0.0927734375,
0.09619140625,
0.1416015625,
-0.05908203125,
-0.0067138671875,
-0.0032806396484375,
-0.08544921875,
0.01318359375,
0.05517578125,
0.036865234375,
-0.0322265625,
-0.06689453125,
0.0517578125,
0.02... | 39,723 | 39723 | |
Being a subgroup: proof by character theory
up vote 27 down vote favorite
14
Let me first cite a theorem due to Frobenius:
Let $G$ be a finite group, with $H$ a proper subgroup ($H\ne (1)$ and $G$). Suppose that for every $g\not\in H$, we have $H\cap gHg^{-1}=(1)$. Then $$N:=(1)\cup(G\setminus\bigcup_{g\in G}gHg^... | 4 | [
-0.0272216796875,
-0.0223388671875,
0.078125,
0.09228515625,
-0.0162353515625,
0.0230712890625,
0.0220947265625,
-0.004364013671875,
0.04443359375,
-0.0498046875,
-0.0052490234375,
0.032470703125,
0.042724609375,
-0.08154296875,
-0.11962890625,
0.034912109375,
0.0263671875,
-0.0115... | 39,724 | 39724 | |
Probability
August 10th 2008, 10:25 AM #1
Newbie
Joined
Jan 2008
Posts
17
Probability
A manufacturer of teddy bears has three assembly lines: 1, 2 and 3. The percentages of total daily output that are produced by the lines are 25%, 35% and 40%, respectively. The percentages of
defective units produc... | 5 | [
0.0322265625,
-0.00909423828125,
0.0439453125,
0.03173828125,
-0.044921875,
-0.0625,
0.0380859375,
0.035888671875,
-0.0478515625,
0.059326171875,
0.024169921875,
-0.059326171875,
0.0634765625,
0.017578125,
0.000583648681640625,
0.00028228759765625,
-0.03271484375,
-0.016357421875,
... | 39,725 | 39725 | |
Converting Fahrenheit to Celsius
Date: 9/29/95 at 8:47:9
From: Anonymous
Subject: Temperature
Is there a temperature that is the same on both the Celsius and
Fahrenheit scales?
Date: 9/29/95 at 11:20:0
From: Doctor Ken
Subject: Re: Temperature
Hello!
Nice question. There's a formula that you can use to get from... | 4 | [
0.00823974609375,
0.055419921875,
-0.01495361328125,
0.03662109375,
0.0035400390625,
0.037109375,
-0.0419921875,
0.07080078125,
-0.008544921875,
-0.032958984375,
0.0274658203125,
-0.2001953125,
-0.01904296875,
0.06298828125,
-0.004913330078125,
-0.10595703125,
-0.08349609375,
0.026... | 39,726 | 39726 | |
rate question
December 15th 2006, 05:05 AM #1
Newbie
Joined
Nov 2006
Posts
18
rate question
I haven't seemed to get rate problems down yet. Can anyone help me with this one?
water is poured into a conical funnel at a rate of 1cm"3 per second. The radius of the top of the funnel is 10cm and the heigh... | 4 | [
0.0225830078125,
0.06494140625,
0.01104736328125,
0.00156402587890625,
-0.0244140625,
-0.0306396484375,
-0.08154296875,
0.05078125,
0.0125732421875,
-0.003326416015625,
-0.0458984375,
-0.0201416015625,
0.00811767578125,
0.09716796875,
0.0167236328125,
0.0078125,
-0.04638671875,
-0.... | 39,727 | 39727 | |
Meteosoft - Climate Change Views
Climate Change – How’s it Panning Out?
Introduction
Updated June 2013 with latest temperatures and base period change to 1981-2010.
This paper asks the question: “Does the empirical observational data support the climate scientists’ computer models output?”. A top-down approach is ta... | 4 | [
-0.0673828125,
0.03466796875,
0.0703125,
0.0751953125,
0.04931640625,
-0.0157470703125,
-0.10546875,
0.0220947265625,
-0.022216796875,
0.041015625,
-0.058349609375,
-0.08837890625,
0.0022735595703125,
0.01422119140625,
0.047119140625,
-0.01025390625,
-0.1630859375,
-0.0106201171875... | 39,728 | 39728 | |
linear programming
June 24th 2009, 03:11 PM #1
Newbie
Joined
Apr 2009
Posts
12
linear programming
A travel agent has to fly 1000 people and 35000 kg of baggage from Hong Kong to Shanghai. Two type of aircraft are available:
"A" which takes 100 people and 2000 kg of baggage, or "B" which takes 60 peop... | 4 | [
0.048095703125,
0.054931640625,
-0.05712890625,
-0.03125,
-0.0439453125,
0.0361328125,
0.08203125,
-0.0291748046875,
-0.11328125,
0.0830078125,
0.05712890625,
-0.0294189453125,
0.07763671875,
0.0673828125,
0.0220947265625,
0.15234375,
0.02978515625,
-0.052978515625,
-0.103515625,... | 39,729 | 39729 | |
Implication theorem
November 8th 2009, 01:40 PM #1
Junior Member
Joined
Oct 2009
Posts
32
Implication theorem
The following theorem has the form of an implication.
If n is an integer and 3n+2 is even, then n is even.
a) Prove this theorem by contradiction.
b) Give a direct proof of this the... | 4 | [
-0.08544921875,
0.03076171875,
0.04296875,
0.0213623046875,
0.0791015625,
0.04736328125,
0.09912109375,
0.0322265625,
-0.05322265625,
-0.005523681640625,
0.030029296875,
-0.0703125,
0.056640625,
-0.055908203125,
-0.0025177001953125,
-0.05517578125,
-0.040283203125,
0.018310546875,
... | 39,730 | 39730 | |
BASIC: How to Simpliy Powers for Induction
May 30th 2011, 08:57 PM #1
Newbie
Joined
Nov 2008
Posts
12
BASIC: How to Simpliy Powers for Induction
Hey guys, I'm just a bit unsure how to simplify numbers so that this induction can be proved. Any help would be appreciated.
$2\frac{{[k(k+1)}]^{ 4} }{ 16} ... | 4 | [
0.0703125,
0.11181640625,
0.0003757476806640625,
0.04833984375,
-0.00946044921875,
-0.0247802734375,
-0.0185546875,
-0.0262451171875,
-0.06103515625,
0.072265625,
-0.05859375,
-0.05029296875,
0.005340576171875,
0.09765625,
-0.052490234375,
0.08935546875,
-0.047607421875,
0.09765625... | 39,731 | 39731 | |
Finding trig functions given constraints
January 25th 2013, 04:11 PM #1
Finding trig functions given constraints
A function value is given along with constraints and I must find all other trig functions based on the given values.
Function value: $tan \theta$ is undefined
Constraints: $\pi \le \theta \le ... | 4 | [
-0.050048828125,
-0.0322265625,
-0.062255859375,
0.01416015625,
-0.01373291015625,
0.03515625,
-0.020263671875,
-0.0146484375,
0.05810546875,
-0.03466796875,
0.068359375,
-0.033203125,
0.00537109375,
0.016845703125,
0.07470703125,
-0.0026397705078125,
0.0084228515625,
-0.0184326171... | 39,732 | 39732 | |
Finding a Binomial Coefficient
April 10th 2012, 11:09 AM #1
Junior Member
Joined
Oct 2011
Posts
28
What is the coefficient of x^5 in the binomial expression (x - 2x^-2)^20 when multiplied by (1+3x^3)
So far I have:
(20 over k)(-1)^k (2)^k x^(20-3k)
so then 20-3k = 5 such that k = 5
So... | 4 | [
0.00518798828125,
-0.029052734375,
-0.01495361328125,
0.072265625,
-0.0255126953125,
0.0189208984375,
0.07421875,
-0.052734375,
-0.0115966796875,
0.0595703125,
0.053466796875,
-0.06298828125,
0.055908203125,
-0.0023193359375,
0.032470703125,
0.11669921875,
0.020751953125,
0.0314941... | 39,733 | 39733 | |
Number Theory 1
July 20th 2012, 10:26 PM #1
Newbie
Joined
Jul 2012
From
Delhi
Posts
12
Number Theory 1
I add first N natural numbers and finds the sum to be 1850 . But actually one number was added twice by mistake .
Find the difference between N and that number ?
Re: Number Theory 1
Re: Number... | 4 | [
-0.107421875,
0.1005859375,
0.053466796875,
0.004425048828125,
-0.016845703125,
0.011474609375,
0.044921875,
0.023193359375,
-0.006805419921875,
-0.01177978515625,
-0.01544189453125,
0.01422119140625,
0.09619140625,
-0.052978515625,
-0.0284423828125,
-0.005615234375,
0.017822265625,
... | 39,734 | 39734 | |
How do I remove these discontinuities?
September 24th 2010, 07:53 AM #1
Member
Joined
Nov 2009
Posts
87
How do I remove these discontinuities?
So I understand how to find where a discontinuity is, but I am not sure how to remove it. Any tips?
Question 1: Identify and remove the discontinuities of f(... | 4 | [
-0.033203125,
0.051513671875,
-0.048828125,
0.04052734375,
0.01129150390625,
0.0703125,
0.026123046875,
-0.06640625,
0.00946044921875,
-0.07666015625,
0.09716796875,
-0.064453125,
-0.028564453125,
0.022216796875,
-0.0032806396484375,
-0.047119140625,
-0.056640625,
-0.057373046875,
... | 39,735 | 39735 | |
Car Buying-Compound interest
March 29th 2011, 04:14 PM #1
Newbie
Joined
Mar 2011
Posts
3
Car Buying-Compound interest
I'm checking answer for my sister. But since I no longer have the background in how to appropriately use the financial formulas, I post it here for help.
Problem: A car that costs $1... | 4 | [
0.06201171875,
0.05712890625,
0.01275634765625,
-0.046630859375,
-0.010009765625,
-0.056884765625,
-0.0177001953125,
0.1044921875,
-0.01318359375,
0.06689453125,
0.0004100799560546875,
-0.03271484375,
0.0037384033203125,
0.002838134765625,
0.0322265625,
0.08056640625,
-0.026245117187... | 39,736 | 39736 | |
The Sustainability of Fiscal Policy in Mexico_ 2000
THE SUSTANABILITY OF FISCAL POLICY IN MEXICO, 2000-2025
Julio A. Santaella
ITAM
June 2000
... | 4 | [
-0.072265625,
0.033935546875,
-0.051025390625,
0.005950927734375,
0.0035400390625,
-0.0010833740234375,
0.000522613525390625,
0.05859375,
-0.07666015625,
0.024658203125,
-0.0269775390625,
0.0771484375,
0.05517578125,
-0.0115966796875,
-0.0009918212890625,
-0.00616455078125,
-0.048095... | 39,737 | 39737 | |
S=Rθ and Circumference * ratio of arc angle to 360 degrees
August 23rd 2013, 04:53 PM
roadran422
S=Rθ and Circumference * ratio of arc angle to 360 degrees
I don't know if I'm doing this proof right. But, there are 2 ways to figure out an arc length of a circle s=rθ, and finding the circumference of a circle and... | 4 | [
0.0089111328125,
0.0203857421875,
-0.00994873046875,
0.027587890625,
0.057861328125,
-0.0281982421875,
-0.0419921875,
0.0703125,
0.07861328125,
-0.02197265625,
0.01141357421875,
-0.037109375,
0.0869140625,
0.0576171875,
0.01171875,
-0.03662109375,
-0.05908203125,
0.107421875,
-0.... | 39,738 | 39738 | |
Calculus BC Problem
April 21st 2009, 12:59 PM #1
Junior Member
Joined
Dec 2008
Posts
37
Calculus BC Problem
A taxi driver is going from LaGuardia Airport to Kennedy Airport at an average speed of v miles per hour. The distance is 30 miles and gas costs $1.33 per gallon. The taxi consumes gas at a rate
... | 5 | [
0.07568359375,
0.083984375,
-0.0303955078125,
-0.00604248046875,
0.0361328125,
0.05615234375,
-0.046630859375,
0.09423828125,
-0.0693359375,
0.083984375,
-0.006378173828125,
-0.03515625,
0.003387451171875,
0.0986328125,
-0.0177001953125,
0.06298828125,
-0.00726318359375,
0.04565429... | 39,739 | 39739 | |
Elliptic regularity on bad domain
up vote 3 down vote favorite
1
Let $\Omega \subset R^n$ be an open bounded set. Consider the Dirichlet problem $$ -\triangle u = 0, x \in \Omega, \quad u = \varphi, x \in \partial \Omega. $$ If $\varphi$ is a continuous function,
then the problem is solvable for rather general $\Omega... | 4 | [
0.0341796875,
0.048828125,
0.051513671875,
0.0032196044921875,
0.07666015625,
0.006744384765625,
-0.00885009765625,
0.0235595703125,
0.033203125,
-0.08740234375,
0.0037078857421875,
0.056396484375,
-0.041748046875,
-0.01446533203125,
0.08056640625,
-0.0087890625,
-0.01068115234375,
... | 39,740 | 39740 | |
Derifferentiating a "lemniscate"
April 5th 2010, 08:26 AM #1
Derifferentiating a "lemniscate"
"Find the points on the lemniscate $(x^2+y^2)=25(x^2-y^2)$"
I found the derivative of the equation, and solved for $y'$, getting $(x^2+y^2)=\frac {25} {4}$, but i don't know where to go from here.$x^2-y^2=(x^2+y^2)-... | 5 | [
0.01458740234375,
0.007171630859375,
0.016357421875,
-0.053955078125,
0.037353515625,
-0.05322265625,
0.0181884765625,
0.08447265625,
0.023193359375,
0.00537109375,
0.048583984375,
0.0118408203125,
0.01348876953125,
0.0208740234375,
-0.0198974609375,
0.0927734375,
0.0177001953125,
... | 39,741 | 39741 | |
Converse of Poincaré-Hopf theorem
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
Let $M$ be a connected, compact, oriented manifold of dimension $n<7$. If any two maps $M \to M$ having equal degrees are homotopic, must ... | 5 | [
-0.0322265625,
-0.003936767578125,
-0.03564453125,
0.0419921875,
-0.060791015625,
0.04443359375,
0.049072265625,
-0.00885009765625,
0.0035552978515625,
-0.0250244140625,
0.046142578125,
0.0286865234375,
-0.0194091796875,
-0.0084228515625,
0.044189453125,
0.007598876953125,
-0.1069335... | 39,742 | 39742 | |
Putnam proof
August 29th 2006, 12:42 PM
Jameson
Putnam proof
I am studying for the Putnam competition in December and I want just a hint at how to do this problem, not a full solution please. I'm trying to develop a good methodology to approaching proofs.
A1. Determine, with proof, the number of ordered tri... | 5 | [
-0.01251220703125,
-0.03369140625,
0.01025390625,
0.00433349609375,
-0.02587890625,
0.05078125,
0.06494140625,
-0.0267333984375,
-0.047119140625,
0.0859375,
-0.09716796875,
-0.1064453125,
0.043701171875,
0.03564453125,
0.00848388671875,
0.035888671875,
0.0125732421875,
-0.026489257... | 39,743 | 39743 | |
Diophantine Equation? Or something?
$4x^2 - y^2 = (2x + y)(2x - y) = 480$. Now list all the pairs of numbers that can multiply to 480: $(480, 1); (240, 2); (160, 3); (120, 4); (96, 5); (80, 6);$ $(60, 8); (48, 10); (40, 12); (32, 15);
(30, 16); (24, 20)$ The pairs with one odd number and one even number will result in ... | 4 | [
0.026123046875,
0.0771484375,
-0.0211181640625,
-0.0040283203125,
-0.001983642578125,
0.060302734375,
0.05029296875,
0.0361328125,
-0.09619140625,
-0.051513671875,
-0.03271484375,
0.04150390625,
0.043701171875,
-0.00128173828125,
-0.0179443359375,
0.026611328125,
-0.01483154296875,
... | 39,744 | 39744 | |
tvm
The Time Value of Money
Introduction to Time Value of Money, TVM
Future Value, FV
Lump-sum amount
Annuity
Uneven cash flow
Present Value, PV
Lump-sum amount
Annuity
Uneven cash flow
FV and PV Comparison
Solving for r and n
Intra-year Interest Compounding
Amortiz... | 5 | [
0.00098419189453125,
0.051025390625,
-0.061279296875,
-0.034912109375,
-0.0054931640625,
-0.0301513671875,
0.03564453125,
0.0654296875,
0.08056640625,
0.049072265625,
-0.0322265625,
-0.014404296875,
-0.014404296875,
0.0238037109375,
0.0625,
-0.038818359375,
-0.03759765625,
-0.04150... | 39,745 | 39745 | |
Supersingular elliptic curves
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
I've read that an elliptic curve is supersingular if and only if its endomorphism ring is an order in a quaternion algebra. Does anyone have a si... | 4 | [
-0.05810546875,
0.0089111328125,
-0.000942230224609375,
0.0576171875,
-0.006805419921875,
-0.0018463134765625,
-0.03125,
0.01953125,
0.04833984375,
-0.0277099609375,
0.078125,
-0.00872802734375,
-0.08447265625,
-0.025634765625,
-0.0478515625,
-0.00109100341796875,
-0.0888671875,
-0... | 39,746 | 39746 | |
Ffinding the difference quotient of x + (4/x).
October 3rd 2010, 12:32 PM #1
Newbie
Joined
Jul 2010
Posts
17
Ffinding the difference quotient of x + (4/x).
Given x + (4/x) finding the difference quotient I am wondering how to get started.
I don't know why but, for the life of me I can't clear the f... | 4 | [
-0.0079345703125,
0.0029296875,
0.06494140625,
0.01275634765625,
-0.025390625,
-0.01708984375,
-0.0361328125,
0.001922607421875,
0.0751953125,
-0.023193359375,
0.026123046875,
-0.06005859375,
-0.0615234375,
0.0625,
-0.052001953125,
0.0069580078125,
0.0166015625,
0.080078125,
-0.0... | 39,747 | 39747 | |
Complementary Angle
Notice the 53° angle on the far right side of the same row. This is the other angle in the 3-4-5 triangle and is called the complementary angle. A complementary angle is found by subtracting the
reference angle from 90° (90° - 37° = 53° ).
Since the reference and complementary angles a... | 4 | [
-0.07568359375,
0.04833984375,
-0.06103515625,
-0.06201171875,
-0.0240478515625,
-0.0235595703125,
-0.01953125,
0.0277099609375,
0.01953125,
-0.00634765625,
0.050537109375,
-0.0478515625,
0.004547119140625,
-0.0279541015625,
0.004669189453125,
-0.048095703125,
-0.08056640625,
0.022... | 39,748 | 39748 | |
Reference for representations of quaternion group
up vote 6 down vote favorite
To satisfy a referee, I need a reference for the following well-known fact (which is not hard to prove, but it seems silly to prove it in a paper). I can't find it in either Serre or Fulton-Harris's
books on representation theory. Can anyon... | 5 | [
-0.1044921875,
0.000118255615234375,
-0.0203857421875,
0.09912109375,
-0.036865234375,
0.10205078125,
-0.024658203125,
0.0257568359375,
0.025390625,
-0.10693359375,
0.03125,
0.0169677734375,
-0.00185394287109375,
0.055419921875,
-0.1171875,
0.09521484375,
-0.037353515625,
0.0197753... | 39,749 | 39749 | |
Ramanujan's sum - help with proof.
August 6th 2010, 06:39 AM #1
Member
Joined
May 2008
Posts
140
Ramanujan's sum - help with proof.
Hi
Let $c_{k}(n)=\underset{d|(n,k)}{\sum}d\mu(\frac{k}{d})<br />$
I am trying to prove that
$\underset{m=1}{\overset{n}{\Sigma}}c_{k}(m)=\under set{d|k}{\Sigm... | 5 | [
0.00885009765625,
-0.0184326171875,
0.04833984375,
-0.04296875,
-0.02685546875,
0.02392578125,
0.059326171875,
0.07373046875,
-0.040771484375,
-0.043212890625,
0.01373291015625,
-0.042724609375,
0.0262451171875,
-0.07568359375,
-0.0556640625,
0.07275390625,
0.12060546875,
0.0568847... | 39,750 | 39750 | |
Using implicit differentation for second deriviate
May 17th 2010, 04:46 PM #1
Newbie
Joined
Oct 2009
Posts
6
Using implicit differentation for second deriviate
Hello,
I am stuck on the following problem:
sorry i don't know how to write in math on here
i have
on the curve at (1, 1 ) us... | 5 | [
-0.042724609375,
-0.130859375,
0.016357421875,
0.0230712890625,
-0.0189208984375,
-0.038818359375,
0.01226806640625,
0.0654296875,
0.02099609375,
-0.0223388671875,
0.130859375,
0.0026397705078125,
0.013916015625,
-0.00469970703125,
-0.0157470703125,
0.0322265625,
-0.06494140625,
-0... | 39,751 | 39751 | |
Surface Laplace-Beltrami without coordinates, exterior calculus?
up vote 4 down vote favorite
2
Let $f: M \rightarrow \mathbb{R}^3$ be an immersion of a surface $M$. For pedagogical purposes (i.e., I'm teaching a class!) I am looking for an expression for the scalar Laplace-Beltrami operator $\
Delta$ applied to a rea... | 4 | [
-0.048095703125,
-0.01080322265625,
0.08740234375,
-0.058349609375,
-0.03466796875,
-0.0240478515625,
0.005615234375,
-0.021484375,
-0.04541015625,
0.03857421875,
0.0673828125,
0.005126953125,
-0.0294189453125,
0.024169921875,
0.036865234375,
-0.0120849609375,
0.03173828125,
0.1152... | 39,752 | 39752 | |
Method for NDSolve
"EventLocator" Method for NDSolve
Introduction
It is often useful to be able to detect and precisely locate a change in a differential system. For example, with the detection of a singularity or state change, the appropriate action can be taken,
such as restarting the integration.
An event for a ... | 4 | [
-0.06640625,
0.0068359375,
0.0159912109375,
-0.0234375,
0.00020885467529296875,
-0.041015625,
-0.0264892578125,
0.04541015625,
0.1298828125,
0.00750732421875,
0.07080078125,
0.0264892578125,
-0.042236328125,
0.00860595703125,
-0.11328125,
-0.04541015625,
-0.022705078125,
0.05859375... | 39,753 | 39753 | |
Figurate and Polygonal Numbers
Date: 11/21/98 at 18:24:55
From: Megan
Subject: Figurate numbers
I need to know everything about figurate numbers - no one here knows
anything.
Date: 11/22/98 at 15:48:54
From: Doctor Floor
Subject: Re: Figurate numbers
Hi Megan,
Thank you for your question.
Figurate numbers are n... | 4 | [
0.0478515625,
0.021240234375,
0.0189208984375,
-0.00390625,
-0.0625,
0.0284423828125,
-0.08056640625,
-0.0011444091796875,
0.043701171875,
0.0230712890625,
-0.04345703125,
0.017822265625,
-0.0234375,
0.06982421875,
-0.0211181640625,
-0.0908203125,
-0.054931640625,
-0.01055908203125... | 39,754 | 39754 | |
Intersecting Vectors and the Dot Product
Date: 04/24/98 at 03:05:47
From: Tony Lu
Subject: Geometry (vector)
Each of the following geometrical theorems can be proved by
vectors using dot product(scalar product). Prove that:
i) the altitudes of a triangle are concurrent
ii) the perpendicular bisectors of the side... | 5 | [
-0.07373046875,
0.00982666015625,
-0.029296875,
-0.1171875,
0.0203857421875,
0.0252685546875,
0.04296875,
-0.022705078125,
-0.046142578125,
0.0223388671875,
-0.01806640625,
-0.059814453125,
0.037353515625,
0.00494384765625,
-0.00213623046875,
0.1005859375,
-0.0634765625,
0.02355957... | 39,755 | 39755 | |
[SOLVED] quadrilateral QABR
September 29th 2008, 03:51 PM
fabxx
[SOLVED] quadrilateral QABR
Hi, This question is from the SAT OG Book on page 746 # 12.
Note: Figure not drawn to scale
In the figure above, points P, A and B are equally spaced on line L and points P, Q, and R are equally spaced on line M... | 4 | [
-0.0002803802490234375,
0.0810546875,
-0.07666015625,
-0.0712890625,
-0.068359375,
0.1201171875,
0.01129150390625,
0.05419921875,
0.05078125,
-0.019775390625,
0.0303955078125,
-0.0186767578125,
0.0274658203125,
0.0220947265625,
0.05908203125,
0.046875,
-0.08642578125,
-0.0139770507... | 39,756 | 39756 | |
Solving Trigonometric Equations
Solve the following equation algebraically. Give a general solution. 3cos2x+cosx=2
in the interval $[0, 2\pi]$ ... $\cos{x} = {\color{red}+}\frac{2}{3}$ ... $x = \arccos\left(\frac{2}{3}\right)$ and $x = 2\pi - \arccos\left(\frac{2}{3}\right)$ $\cos{x} = -1$ ... you tell me what x
value... | 4 | [
-0.08349609375,
-0.049072265625,
-0.0027008056640625,
0.052490234375,
-0.0223388671875,
-0.05419921875,
0.04638671875,
0.056884765625,
0.0380859375,
-0.036376953125,
0.0458984375,
-0.08447265625,
0.03515625,
0.0025634765625,
0.0634765625,
-0.08544921875,
0.003875732421875,
-0.05200... | 39,757 | 39757 | |
compactness
May 3rd 2009, 03:25 AM #1
Junior Member
Joined
Mar 2009
Posts
42
compactness
The Hilbert cube Q is the subset of l∞ given by {a : N→R││a(i)│≤2-i}.
Show that Q is a compact subspace of l∞ (with the norm ∥a∥=supn∈N│a(n)│).
can anyone please help me to do this question ?? ,,
Let $... | 5 | [
-0.0032501220703125,
-0.031494140625,
-0.04541015625,
0.009033203125,
-0.034423828125,
0.11376953125,
0.1455078125,
-0.042236328125,
-0.059814453125,
-0.08740234375,
0.025146484375,
0.04638671875,
0.0947265625,
-0.0115966796875,
-0.045166015625,
0.05517578125,
0.0021820068359375,
-... | 39,758 | 39758 | |
Is there a theory about these kinds of recurrence equations? Is this a known formula?
up vote 5 down vote favorite
3
(New information at bottom)
Hi.
For a while, I've been toying around with solving recurrence equations of the form
$$a_1 = r_{1,1}$$ $$a_n = \sum_{m=1}^{n-1} r_{n,m} a_m$$
What are these kind of rec... | 4 | [
-0.15625,
-0.0439453125,
-0.017822265625,
0.10400390625,
-0.0654296875,
0.032470703125,
-0.0262451171875,
0.0245361328125,
0.0224609375,
0.0146484375,
0.040771484375,
-0.00994873046875,
0.0107421875,
0.01348876953125,
-0.00140380859375,
-0.003692626953125,
-0.03857421875,
-0.03125,... | 39,759 | 39759 | |
Finiteness of injective hull of residue field for Artin local ring
up vote 0 down vote favorite
$(A,\mathfrak{m})$ an Artin local ring, $E(A/\mathfrak{m})$ the injective hull of $A/\mathfrak{m}$. How do I see that $E(A/\mathfrak{m})$ is a finite $A$-module?
ac.commutative-algebra
2 You can prove, for example, tha... | 5 | [
0.00811767578125,
0.0966796875,
-0.0133056640625,
0.028564453125,
0.043701171875,
0.020751953125,
0.024169921875,
-0.0234375,
0.0206298828125,
-0.048095703125,
0.07373046875,
-0.04443359375,
0.027587890625,
-0.0037841796875,
-0.033203125,
0.08203125,
-0.038330078125,
0.055419921875... | 39,760 | 39760 | |
Boxplot IQR and confidence interval
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
Hi
Just a short question. How are the IQR of the boxplot related to the confidence interval of a sample? I... | 5 | [
0.0014801025390625,
0.0164794921875,
0.072265625,
0.01177978515625,
-0.023681640625,
-0.0091552734375,
-0.024658203125,
0.072265625,
0.0289306640625,
-0.0002994537353515625,
0.00738525390625,
-0.01953125,
0.0002727508544921875,
-0.1015625,
-0.036376953125,
-0.0306396484375,
0.0011749... | 39,761 | 39761 | |
gambling problem/ standard deviation
May 24th 2007, 11:24 AM
JakeD
Quote:
I think you mistype the above formula:
$[8500- 1.28 S / sqrt{450}, 8500+1.28 S /sqrt{450}].$
I've computed the standard deviation as you said:
The mean is M=7500/450
S = sqrt (( sum after i of pow( R[i]-M , 2) ) / (... | 4 | [
0.0208740234375,
0.091796875,
0.01226806640625,
0.055908203125,
-0.017578125,
-0.0186767578125,
0.0208740234375,
0.1298828125,
-0.002227783203125,
0.01251220703125,
-0.010498046875,
-0.031982421875,
0.1318359375,
-0.061767578125,
-0.0126953125,
0.0146484375,
0.023681640625,
-0.0336... | 39,762 | 39762 | |
Terms of the Series 1/n
Date: 05/03/2001 at 14:24:18
From: Tony Steer
Subject: Series 1/n
With the series:
1/1 + 1/2 + 1/3 + ... + 1/n
and given an answer that the series must exceed, how do I calculate
the value of n? I am really stuck on this one; any help would be
really appreciated.
Thanks,
Tony
Date: ... | 5 | [
-0.0703125,
-0.038330078125,
0.09814453125,
0.01220703125,
-0.0233154296875,
-0.06640625,
-0.015869140625,
0.09033203125,
0.041259765625,
-0.072265625,
-0.1552734375,
0.019287109375,
-0.01251220703125,
0.007659912109375,
-0.08447265625,
-0.0556640625,
0.037353515625,
-0.02014160156... | 39,763 | 39763 | |
Tutorial on Equation of Line
REVIEW
Slope of a Line:
If a line passes through two distinct points P[1](x[1] , y[1]) and P[2](x[2], y[2]), its slope is given by:
m = (y[2] - y[1]) / (x[2] - x[1])
with x[2] not equal to x[1].
This is ano... | 4 | [
-0.12109375,
-0.002410888671875,
-0.0299072265625,
0.02294921875,
0.0400390625,
-0.028076171875,
-0.007598876953125,
0.03271484375,
-0.00128173828125,
0.0252685546875,
0.05908203125,
-0.03369140625,
0.0673828125,
-0.005340576171875,
-0.009521484375,
0.1455078125,
-0.10498046875,
0.... | 39,764 | 39764 | |
Finding infinite set of solutions, X and Y
March 24th 2009, 11:54 PM #1
Finding infinite set of solutions, X and Y
Q. Find an infinite set of integers x any y such that $4973x+9743y=h$. Write answer in terms of the arbitrary integer L (Lambda, hehe).
Here's what I've got:
(i) First find HCF
(after ... | 4 | [
-0.038818359375,
-0.0306396484375,
-0.06689453125,
-0.03515625,
0.0546875,
-0.0098876953125,
0.08349609375,
0.00262451171875,
-0.068359375,
-0.064453125,
0.0145263671875,
-0.0179443359375,
0.031982421875,
0.037353515625,
0.018798828125,
0.006103515625,
-0.059814453125,
-0.118164062... | 39,765 | 39765 | |
Calculating the Curvature of a Complex Manifold
January 20th 2009, 12:39 PM #1
Newbie
Joined
Jul 2008
Posts
18
Calculating the Curvature of a Complex Manifold
Hey everyone,
(First off, this is not a HW question, but I can move it there if you are unhappy about my choice) I'm trying to figure out how ... | 4 | [
-0.0869140625,
-0.00021457672119140625,
0.050048828125,
0.0024261474609375,
-0.0361328125,
-0.0186767578125,
0.0172119140625,
0.0771484375,
-0.003936767578125,
-0.03369140625,
0.03857421875,
-0.0400390625,
-0.046875,
0.0107421875,
-0.01055908203125,
0.01953125,
-0.0986328125,
0.007... | 39,766 | 39766 | |
Explanation requested
February 12th 2011, 03:12 PM
dwsmith
Explanation requested
Given this equation
$\varphi''+\lambda\varphi=0$
$\varphi_1(x)=\cos(x\sqrt{\lambda})$
$\displaystyle\varphi_2(x)=\frac{\sin(x\sqrt{\lambd a})}{\sqrt{\lambda}}$
The book goes from equation to solution without expl... | 4 | [
-0.0830078125,
-0.03857421875,
0.042236328125,
0.1005859375,
-0.0025787353515625,
0.05224609375,
-0.035888671875,
-0.0120849609375,
0.076171875,
0.04541015625,
0.212890625,
0.0322265625,
-0.0028533935546875,
0.0185546875,
0.041748046875,
0.034423828125,
-0.0286865234375,
-0.0683593... | 39,767 | 39767 | |
Catalan's Conjecture
Date: 06/02/2007 at 21:31:49
From: Thomas
Subject: Solve a^b = b^a + 1
Solve a^b = b^a + 1. How many integer solutions are there? Are there
an infinite number? How are the solutions distributed?
I need some clues as to how to analyze this equation. I noticed that
8 is 2^3 while 9 is 3^2. I s... | 5 | [
-0.05615234375,
-0.035888671875,
-0.0196533203125,
0.0908203125,
-0.045654296875,
0.015625,
0.046142578125,
-0.005859375,
0.0283203125,
-0.006103515625,
-0.09033203125,
0.007476806640625,
0.061279296875,
0.059814453125,
0.0299072265625,
0.052490234375,
-0.1162109375,
-0.08154296875... | 39,768 | 39768 | |
About the combination of Projections (Halmos' Finite Dim. Vector Spaces section 42)
June 2nd 2014, 10:00 PM #1
Newbie
Joined
Jun 2014
From
India
Posts
4
About the combination of Projections (Halmos' Finite Dim. Vector Spaces section 42)
Hi! I am having some trouble visualizing the theorems about the ... | 4 | [
-0.042236328125,
-0.0291748046875,
0.01904296875,
0.0380859375,
0.01434326171875,
0.041015625,
0.04931640625,
-0.080078125,
0.03515625,
-0.030517578125,
0.003387451171875,
-0.0703125,
0.0022735595703125,
-0.003082275390625,
-0.08447265625,
-0.0089111328125,
0.0189208984375,
0.04809... | 39,769 | 39769 | |
Perturbation of Morse function
up vote 1 down vote favorite
The following question is probably classic in Morse theory, so a reference to an existing result should be sufficient. I don't know much about Morse theory and I am dealing with the following
situation. I have a compact manifold $X$ and I have a Morse functio... | 5 | [
-0.10546875,
-0.03173828125,
0.036865234375,
-0.0003299713134765625,
-0.04052734375,
0.0615234375,
0.0712890625,
0.0390625,
0.026611328125,
0.0517578125,
0.0400390625,
0.024658203125,
0.06201171875,
0.0247802734375,
-0.02099609375,
0.042236328125,
-0.03125,
-0.059814453125,
0.032... | 39,770 | 39770 | |
Rotated Ellipse
October 21st 2007, 02:27 PM #1
Member
Joined
Oct 2007
Posts
209
Rotated Ellipse
1. Given the equation of the rotated ellipse x^2+xy+y^2=3
a. Find the equation of the normal line (line perpendicular to the tangent line at the given point) to it at x=1
I got 2 points for the probl... | 5 | [
-0.05810546875,
-0.0380859375,
0.0390625,
-0.054931640625,
0.0179443359375,
-0.007171630859375,
-0.0294189453125,
0.0247802734375,
0.04052734375,
0.01434326171875,
0.0908203125,
0.0556640625,
0.03955078125,
0.007720947265625,
0.007476806640625,
0.11328125,
-0.1005859375,
-0.0300292... | 39,771 | 39771 | |
divisibility proof
January 24th 2010, 08:13 AM #1
Newbie
Joined
Jan 2010
Posts
20
divisibility proof
The question I am working on is
Prove that a/b if and only if a^3/b^3.
I know that if p/a^n then p/a...but how can i apply that here..can i make a prime on my own despite the question did not say... | 4 | [
-0.06201171875,
0.035888671875,
-0.083984375,
0.0174560546875,
-0.00099945068359375,
-0.0322265625,
0.0791015625,
-0.1064453125,
0.01397705078125,
-0.05810546875,
-0.0155029296875,
0.01104736328125,
0.046875,
0.058837890625,
0.0703125,
0.056396484375,
-0.0087890625,
0.045654296875,... | 39,772 | 39772 | |
Volume 9,
Volume 9, Issue 4, April 1968
•
View Description Hide Description
The dyadic formalism is applied to cosmological models, and leads to a convenient set of first‐order ordinary differential equations. The Bianchi‐Behr type of any model is shown to be constant in
time, regardless of the state ... | 4 | [
-0.0634765625,
-0.0166015625,
0.07421875,
0.0546875,
0.060546875,
0.072265625,
-0.0257568359375,
0.04541015625,
0.083984375,
-0.033935546875,
0.034423828125,
-0.044189453125,
-0.0078125,
-0.0050048828125,
0.0277099609375,
-0.055419921875,
-0.08740234375,
0.032470703125,
-0.142578... | 39,773 | 39773 | |
Find the domain and range
g(x) = sqrt.(25 - x^2) r(x) = |2x - 3| plz help me thanks!
Hello, NeedHelp18! Quote: Find the domain and range. $1)\;\;g(x) \:= \:\sqrt{25 - x^2}$ We can see that $(25-x^2)$ must not be negative. We have: . $25-x^2 \:\geq \:0$ Then we have: . $-x^2 \:\geq
\:-25$ Multiply by -1: . $x^2 \:\leq ... | 4 | [
-0.0130615234375,
0.02685546875,
0.02734375,
-0.06982421875,
-0.052978515625,
-0.045654296875,
0.00830078125,
0.040283203125,
-0.030517578125,
0.00145721435546875,
0.00079345703125,
-0.01171875,
0.064453125,
0.01055908203125,
0.044189453125,
0.020751953125,
0.07373046875,
-0.042236... | 39,774 | 39774 | |
-
Last edited by matsci0000; July 14th 2009 at 07:19 AM. Reason: inadequate information
(cos2A+cos2B)+cos2C =2cos(A+B)cos(A-B)-cos2C =-2cosC cos(A-B)-2cos^2C+1 [ cos(A+B)=cos(pie-C)= -cosC] =1-2cosC[cos(A-B)-cosC] =1-2cosC[cos(A+B) -cos(A-B)] =1-2cosC [2sinA sinB] How to get the term
sinC from 2cosC?
That identity ... | 5 | [
-0.1220703125,
0.026611328125,
0.0057373046875,
0.07275390625,
-0.03271484375,
0.0712890625,
-0.047119140625,
0.0247802734375,
0.055908203125,
0.0079345703125,
-0.022216796875,
-0.1689453125,
0.04833984375,
0.01068115234375,
-0.00933837890625,
-0.04541015625,
0.021728515625,
0.0305... | 39,775 | 39775 | |
Moment Generating Function
March 2nd 2011, 08:57 PM
jzellt
Moment Generating Function
Differentiate the moment-generating function in Exercise 3.147 to find E(Y) and E(Y^2). Then find V(Y).
Exercise 3.147
If Y has a geometric distribution with probability of success p, show that the moment generating f... | 4 | [
0.0291748046875,
0.055908203125,
0.0703125,
0.0152587890625,
0.0087890625,
0.0302734375,
0.0537109375,
0.02490234375,
0.08740234375,
0.0908203125,
0.1103515625,
0.04638671875,
0.007080078125,
0.0234375,
-0.0021514892578125,
0.03466796875,
-0.0380859375,
-0.01953125,
0.06640625,
... | 39,776 | 39776 | |
Math Forum Discussions
Math Forum
Ask Dr. Math
Discussions
Internet Newsletter
MathTools
Teacher2Teacher
Teacher Exchange
Workshops
Search All of the Math Forum:
Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.
Topic: Re: Product of Spherical Harmonics
Replies: 0
... | 4 | [
-0.06005859375,
-0.006744384765625,
0.06591796875,
-0.0693359375,
0.015869140625,
0.03857421875,
-0.051025390625,
0.00182342529296875,
0.041748046875,
0.04443359375,
0.06396484375,
-0.031982421875,
0.01324462890625,
-0.00726318359375,
0.119140625,
0.09033203125,
-0.03857421875,
0.0... | 39,777 | 39777 | |
An Active Multibaseline Stereo System with Real-Time Image Acquisition
Sing Bing Kang, Jon A. Webb, C. Lawrence Zitnick, Takeo Kanade
School of Computer Science, Carnegie Mellon University
Pittsburgh, PA 15213-3891
CMU-CS-94-167
Acknowledgment
This research was partially supported by the Adanced Research Projects... | 4 | [
-0.07373046875,
-0.0150146484375,
-0.04150390625,
-0.1591796875,
0.00677490234375,
0.007293701171875,
-0.10009765625,
0.020751953125,
0.01177978515625,
0.03515625,
-0.027099609375,
-0.028076171875,
0.0458984375,
-0.04638671875,
-0.04443359375,
0.01611328125,
0.018798828125,
0.04443... | 39,778 | 39778 | |
How to calculate X in a series based on 2 correlated arrays
January 22nd 2013, 04:57 AM #1
Newbie
Joined
Jan 2012
Posts
4
How to calculate X in a series based on 2 correlated arrays
Hi -
I have two arrays of numbers that have a -0.99 correlation. Since they are correlated, I assume I can determine w... | 4 | [
-0.007568359375,
-0.0252685546875,
-0.01153564453125,
-0.0191650390625,
-0.0380859375,
-0.040283203125,
0.039794921875,
-0.09326171875,
-0.007171630859375,
-0.0289306640625,
-0.023193359375,
0.04931640625,
0.04296875,
0.0419921875,
-0.031005859375,
0.01226806640625,
-0.08349609375,
... | 39,779 | 39779 | |
Quadratic Equations Using a Formula
January 1st 2010, 09:53 AM #1
Newbie
Joined
Jan 2010
Posts
6
Quadratic Equations Using a Formula
Hi Happy New Year everyone hope you all have had a good one........ I'm doing Maths on New Years Day
This is the equation :
4²-3x-2=0
I use the formula :
... | 4 | [
0.0054931640625,
-0.035400390625,
0.004364013671875,
-0.05126953125,
-0.07666015625,
0.0595703125,
-0.0595703125,
0.0732421875,
0.054443359375,
0.026123046875,
0.0693359375,
-0.036865234375,
0.009765625,
0.0169677734375,
0.03125,
0.12109375,
-0.00616455078125,
-0.0201416015625,
-... | 39,780 | 39780 | |
Assignment on Second Law and Entropy
Mechanical Engg. Dept
D.N.Thatoi, S.N.Das, A.K.Mishra
... | 5 | [
-0.0478515625,
0.07177734375,
-0.03662109375,
0.03955078125,
0.0213623046875,
-0.0260009765625,
-0.0179443359375,
-0.002777099609375,
0.1005859375,
-0.02001953125,
-0.0576171875,
-0.02294921875,
0.06494140625,
-0.0458984375,
-0.00006389617919921875,
-0.091796875,
0.0137939453125,
0... | 39,781 | 39781 | |
Weakly Cauchy
Let X be a reflexive normed linear space.Then show that X is weakly complete..i'e;Every Cauchy sequence is weakly convergent..
Pick a weak Cauchy sequence $(x_n)$ and call $(\hat{x}_n)$ its corresponding sequence in the double dual then for any $l\in X^*$ we have, since Cauchy sequences are bounded, $|\h... | 4 | [
-0.0155029296875,
-0.020263671875,
0.0927734375,
-0.052490234375,
-0.0206298828125,
0.1396484375,
-0.0059814453125,
0.08935546875,
-0.087890625,
-0.00075531005859375,
-0.01275634765625,
0.0302734375,
-0.020263671875,
-0.1083984375,
0.0206298828125,
0.02783203125,
0.0279541015625,
0... | 39,782 | 39782 | |
alculation
FWHM Gaussian FWHM Calculation
Access list of astrophysics formulas download page:
FWHM Calculation for a Gaussian Line Profile
Below, the FWHM Gaussian FWHM calculation is shown with an example of how to estimate velocity broadening of emission or absorption lines. The FWHM is the full width half maxi... | 5 | [
0.01470947265625,
-0.050537109375,
-0.0162353515625,
0.01287841796875,
-0.00152587890625,
-0.1015625,
-0.0751953125,
0.09130859375,
-0.016357421875,
-0.017333984375,
0.0086669921875,
-0.032470703125,
-0.024169921875,
-0.05126953125,
-0.01251220703125,
-0.025390625,
-0.03759765625,
... | 39,783 | 39783 | |
A Graph Problem :?
May 15th 2007, 03:42 AM
IHATECHONGAS
A Graph Problem :?
Graph the line x+y= 5 on the graph provided. Then graph the results.
x|y
5|0
0|?
?|?
Graph the line x-y=1 on the graph.
x|y
?|?
?|?
?|?
What is the point of intersection of the two lines?
Wh... | 4 | [
-0.068359375,
-0.0191650390625,
0.019775390625,
-0.031982421875,
0.044677734375,
0.00933837890625,
0.034912109375,
0.02685546875,
-0.052978515625,
0.007537841796875,
0.008056640625,
-0.01043701171875,
0.025146484375,
0.0546875,
-0.000354766845703125,
0.1435546875,
-0.09619140625,
-... | 39,784 | 39784 | |
8. Evaluation
The quote-quote operator '' (two single quote marks) modifies evaluation in input expressions.
Applied to a general expression expr, quote-quote causes the value of expr to be substituted for expr in the input expression.
Applied to the operator of an expression, quote-quote changes the ope... | 5 | [
-0.08251953125,
0.0142822265625,
0.0162353515625,
0.034912109375,
-0.01177978515625,
-0.0269775390625,
0.045654296875,
0.034912109375,
-0.0023345947265625,
0.041259765625,
-0.0037994384765625,
-0.018798828125,
0.031005859375,
-0.041748046875,
0.03466796875,
0.0267333984375,
-0.039550... | 39,785 | 39785 | |
Solving Linear Systems
Many calculations involve solving systems of linear equations. In many cases, you will find it convenient to write down the equations explicitly, and then solve them using Solve.
In some cases, however, you may prefer to convert the system of linear equations into a matrix equation, and then ap... | 4 | [
-0.028564453125,
0.014892578125,
-0.1064453125,
-0.01226806640625,
-0.007537841796875,
-0.064453125,
-0.07958984375,
0.0011138916015625,
0.02734375,
0.08837890625,
0.004669189453125,
0.06103515625,
0.0390625,
0.0012664794921875,
0.00732421875,
0.055908203125,
-0.0634765625,
0.07568... | 39,786 | 39786 | |
$A_5$-extension of number fields unramified everywhere
up vote 19 down vote favorite
5
So I was having tea with a colleague immensely more talented than myself and we were discussing his teaching algebraic number theory. He told me that he had given a few examples of abelian and
solvable extensions unramified everywhe... | 4 | [
-0.06298828125,
-0.06689453125,
0.050048828125,
-0.0284423828125,
0.08349609375,
0.021240234375,
0.00726318359375,
-0.019287109375,
-0.0390625,
-0.06884765625,
0.095703125,
0.043212890625,
-0.044189453125,
-0.03125,
0.02587890625,
0.0279541015625,
-0.0517578125,
-0.010986328125,
... | 39,787 | 39787 | |
Interior Angles of a Polygon
Date: 05/20/97 at 19:46:32
From: Danielle Deitz
Subject: Interior angles of a polygon
What can you conclude about the sum of the interior angles of a
pentagon? A triangle? A quadrilateral? A hexagon?
Does the sum depend on whether or not the polygon is convex? Why?
What would you predi... | 4 | [
0.0162353515625,
0.058837890625,
0.043701171875,
0.0289306640625,
-0.0291748046875,
-0.02197265625,
0.0244140625,
-0.00628662109375,
0.052734375,
0.06787109375,
-0.05029296875,
-0.0186767578125,
0.05029296875,
0.037109375,
0.053955078125,
-0.0595703125,
-0.0045166015625,
-0.0142822... | 39,788 | 39788 | |
Does the group $\langle a,b,c \mathbin | a^2b^2c^2=1\rangle $ have $\mathbb{Z} \times F_2$ as a subgroup?
up vote 1 down vote favorite
Let $F_2$ denote the free group of rank two and consider the group $G=\langle a,b,c \mathbin | a^2b^2c^2=1\rangle$ which is the fundamental group of the connected sum of three projecti... | 5 | [
-0.03271484375,
-0.05908203125,
-0.0517578125,
0.0277099609375,
-0.0142822265625,
-0.00421142578125,
0.07763671875,
-0.061279296875,
0.06494140625,
-0.02734375,
0.0654296875,
-0.0084228515625,
0.012939453125,
-0.006500244140625,
0.0174560546875,
-0.0201416015625,
-0.0673828125,
-0.... | 39,789 | 39789 | |
Alittle help here please
July 31st 2007, 09:19 PM #1
Newbie
Joined
Jul 2007
Posts
2
Alittle help here please
I am trying to get a formula for the lateral surface area of 2 semi circles that is a right solid that have a height of 14 meters. The small semi circle has a radius of 15 and the large semi
c... | 4 | [
0.015869140625,
0.0546875,
0.032470703125,
-0.0159912109375,
0.0301513671875,
-0.0546875,
-0.0206298828125,
0.146484375,
0.02783203125,
-0.080078125,
0.005645751953125,
-0.036865234375,
-0.01300048828125,
0.109375,
0.032958984375,
-0.0250244140625,
-0.0230712890625,
-0.028930664062... | 39,790 | 39790 | |
Subharmonic function on a twice punctured complex plane
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
is the twice punctured complex plane parabolic or hyperbolic? In this sense: does $\mathbb{C}-\{0,1\}$ admit a nonco... | 5 | [
-0.0458984375,
-0.023193359375,
0.024658203125,
0.0218505859375,
-0.030517578125,
-0.046142578125,
0.00616455078125,
0.01513671875,
0.035888671875,
-0.035888671875,
0.0361328125,
-0.1015625,
0.0133056640625,
0.060302734375,
0.03466796875,
-0.10302734375,
-0.016845703125,
-0.140625,... | 39,791 | 39791 | |
dy
Got Homework?
Connect with other students for help. It's a free community.
• across
MIT Grad Student
Online now
• laura*
Helped 1,000 students
Online now
• Hero
College Math Guru
Online now
Here's the question you clicked on:
LolWolf Group Title
This shouldn't be too ... | 5 | [
-0.059814453125,
0.036865234375,
-0.009521484375,
0.03759765625,
-0.01556396484375,
0.000046253204345703125,
0.06103515625,
0.05322265625,
0.0126953125,
-0.0361328125,
-0.05859375,
-0.058837890625,
0.044189453125,
-0.0390625,
-0.09033203125,
-0.03369140625,
0.031494140625,
-0.09228... | 39,792 | 39792 | |
Cubic Equations in One Formula
Date: 11/27/2001 at 06:37:34
From: Robert Sullivan
Subject: Cubic equations in one formula
To Dr. Math,
I know the formula for solving quadratic equations of the type
ax^2 + bx + c = 0, but is there a formula for cubic equations? I've
seen supposed cubic formulas, but they take severa... | 4 | [
-0.0869140625,
-0.052978515625,
-0.0106201171875,
0.07275390625,
-0.0615234375,
0.02734375,
-0.0859375,
-0.01141357421875,
0.0380859375,
-0.01263427734375,
0.03955078125,
-0.0478515625,
-0.0247802734375,
0.0576171875,
0.03662109375,
0.07763671875,
-0.05810546875,
0.056396484375,
... | 39,793 | 39793 | |
Zariski-closed subsemigroups of SL_n(C) are groups
up vote 5 down vote favorite
4
I would like to show that any Zariski-closed subsemigroup of $SL_n(\mathbb{C})$ is a group. If I understand correctly, this is consequence 1.2.A of http://www.heldermann-verlag.de/jlt/jlt03/
BOSLAT.PDF .
Is there a more elementary proof... | 5 | [
-0.1220703125,
-0.01300048828125,
-0.000835418701171875,
0.134765625,
0.0245361328125,
-0.02587890625,
0.032958984375,
-0.0220947265625,
0.0064697265625,
-0.166015625,
0.060302734375,
-0.01214599609375,
-0.06298828125,
-0.0869140625,
-0.0303955078125,
-0.030517578125,
-0.046875,
0.... | 39,794 | 39794 | |
Complex Projective Space as a $U(1)$ quotient
up vote 4 down vote favorite
2
As is well known, one can view $\mathbb{CP}^n$ as a quotient of the unit $(2n + 1)$-sphere in $\mathbb{C}^{n+1}$ under the action of $U(1)$, since every line in $\mathbb{C}^{n+1}$ intersects the unit
sphere in a circle.
Moreover, we have $S^... | 5 | [
-0.166015625,
0.00958251953125,
-0.03125,
0.0272216796875,
-0.0595703125,
0.052490234375,
-0.004638671875,
-0.0703125,
0.01141357421875,
-0.111328125,
0.07080078125,
-0.00921630859375,
-0.020751953125,
-0.01361083984375,
-0.052001953125,
-0.056396484375,
0.0191650390625,
0.07324218... | 39,795 | 39795 | |
Solution uniqueness for ODE
up vote 5 down vote favorite
5
I have a vectorial, non-linear second order ordinary differential equation $$Z''=f(Z)$$ for which I have a solution $Z^0$ on $[0,1]$ with $Z^0_i(0)=0$ and $Z^0_i(1)=1$. I would like to know under
which kind of conditions on $f$ it is true that no other solutio... | 5 | [
-0.1181640625,
-0.016357421875,
-0.00860595703125,
0.05908203125,
-0.01025390625,
-0.01190185546875,
0.01080322265625,
0.014404296875,
0.01165771484375,
-0.06201171875,
-0.00469970703125,
-0.0201416015625,
0.052490234375,
0.010498046875,
-0.02099609375,
-0.006591796875,
-0.0402832031... | 39,796 | 39796 | |
Ptolemy's Theorem and Double-angle Formulas
Associated Topics || Dr. Math Home || Search Dr. Math
Ptolemy's Theorem and Double-angle Formulas
... | 4 | [
-0.0986328125,
0.0947265625,
-0.0026092529296875,
-0.037353515625,
-0.059326171875,
0.061279296875,
0.051513671875,
-0.006195068359375,
-0.006561279296875,
0.05712890625,
0.036376953125,
-0.041748046875,
-0.023193359375,
-0.0184326171875,
0.033935546875,
-0.0166015625,
-0.0947265625,... | 39,797 | 39797 | |
Outer space: When errors snowball
Issue 50
March 2009
Errors cause problems. But errors are not necessarily mistakes. They are uncertainties in our knowledge of the true state of affairs. Sometimes these are one-offs: we want to measure a baby's weight
and our digital scales are only accurate to a gram, so we have a... | 4 | [
-0.035400390625,
-0.011962890625,
0.1396484375,
0.09130859375,
0.07470703125,
-0.059326171875,
-0.07666015625,
0.0303955078125,
0.0206298828125,
-0.000823974609375,
-0.1162109375,
-0.0223388671875,
0.0098876953125,
-0.00885009765625,
-0.023681640625,
-0.060546875,
-0.032470703125,
... | 39,798 | 39798 | |
I can't solve these Trig Equations
November 30th 2008, 12:33 PM #1
Newbie
Joined
Nov 2008
Posts
3
Hi
Solve these equations in the indicated domain
(1+cos(theta))/(sin(theta))=-1
domain: [-180,180)
cos4(theta) - sin2(theta) = 0
domain: (-90,90)
cos4(theta) - sin2(theta) = 1
... | 4 | [
-0.09912109375,
-0.0135498046875,
-0.0145263671875,
-0.0264892578125,
-0.0301513671875,
-0.07275390625,
-0.05419921875,
-0.01519775390625,
-0.028076171875,
0.005401611328125,
0.0751953125,
-0.107421875,
0.0361328125,
0.042724609375,
0.00982666015625,
0.000148773193359375,
-0.15039062... | 39,799 | 39799 |