content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Pan Balance Equations
March 30th 2010, 06:52 PM
ParisTNK
Pan Balance Equations
Help!
There are two pan balances, the first pan balance has 2 full juice boxes on the left side and on the right side are 18 grapes along with a half-full juice box. The pan balance is equal.
The second pan balance has an em... | 4 | [
-0.00927734375,
0.06591796875,
-0.0306396484375,
0.046875,
-0.06640625,
0.023193359375,
-0.007232666015625,
-0.0030059814453125,
0.024169921875,
-0.0498046875,
-0.0179443359375,
-0.05224609375,
0.032958984375,
0.0390625,
-0.0166015625,
-0.021484375,
0.0108642578125,
0.01708984375,
... | 38,400 | 38400 | |
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: comparison between two value in a sample, please h... | 5 | [
-0.052978515625,
0.1181640625,
-0.06982421875,
-0.05224609375,
0.037109375,
-0.018798828125,
0.003692626953125,
0.08544921875,
-0.0174560546875,
0.0299072265625,
0.00836181640625,
0.000396728515625,
0.10693359375,
-0.0257568359375,
0.0272216796875,
0.04541015625,
0.05078125,
-0.002... | 38,401 | 38401 | |
Stuck with Nilpotents
October 23rd 2008, 11:35 AM #1
Newbie
Joined
Sep 2008
Posts
16
Stuck with Nilpotents
"Suppose that R is a ring. Then an element $a \in R$ is called nilpotent if there exists a positive integer n so that $a^n = 0$"
Ok this is what im stuck with:
Assume that R is commutative.... | 4 | [
-0.006500244140625,
0.07177734375,
-0.0927734375,
0.07275390625,
-0.0908203125,
0.0162353515625,
0.06787109375,
-0.0810546875,
0.061279296875,
-0.0654296875,
-0.033935546875,
-0.021240234375,
-0.0228271484375,
0.0673828125,
0.06787109375,
0.03466796875,
-0.05126953125,
0.0434570312... | 38,402 | 38402 | |
lowest common denominator in fraction(help me with this problems)
1) $\frac{x}{x^2-5x+4} \ \ , \ \ \frac{x+1}{x^2-16}$ First, factor the denominators: $(x-1)(x-4) \ \ , \ \ (x-4)(x+4)$ The LCD is found by using all the different factors the most number of times
they appear in any one denominator. $LCD = (x-1)(x-4)(x+4)... | 4 | [
0.03564453125,
0.027099609375,
0.007232666015625,
-0.042724609375,
-0.0242919921875,
0.060546875,
-0.06982421875,
0.0322265625,
0.009521484375,
0.041015625,
0.0299072265625,
-0.01531982421875,
0.0419921875,
0.11083984375,
0.01080322265625,
0.043212890625,
-0.0238037109375,
0.020996... | 38,403 | 38403 | |
Learning Only 36 of the Times Tables
Date: 11/04/2001 at 10:39:55
From: Unknown
Subject: Multiplying trick
Hi,
My mother told me of a trick to learn times tables more easily.
She said that I only needed to know 36 of the times tables because of
the problems that can be reversed to a higher problem.
Example:
6... | 4 | [
0.021240234375,
-0.0234375,
-0.0037689208984375,
-0.04638671875,
-0.076171875,
-0.024658203125,
-0.05322265625,
-0.03271484375,
-0.06689453125,
0.0810546875,
-0.000827789306640625,
0.020263671875,
0.024658203125,
-0.0303955078125,
-0.06591796875,
0.00885009765625,
-0.07861328125,
0... | 38,404 | 38404 | |
Switching Theory
Logic Design and Switching Theory
[ Up ] [ PLL ] [ Circuit Analysis ] [ Filters ] [ Switching Theory ]
The Logic Design Workbench (LDW) is an amazingly s... | 4 | [
-0.037109375,
-0.03271484375,
-0.034912109375,
-0.01708984375,
-0.0167236328125,
-0.0286865234375,
0.0234375,
0.0169677734375,
-0.06591796875,
0.020263671875,
-0.02783203125,
0.0093994140625,
-0.033447265625,
-0.0306396484375,
0.007171630859375,
0.06494140625,
-0.06591796875,
-0.03... | 38,405 | 38405 | |
Finite groups with elements of order n
up vote 5 down vote favorite
4
Consider a finite group where all elements have the same order $n$. What could be said about such groups?
For $n=2$ it could be proved that such group is isomorphic to $(\mathbb{Z}/2\mathbb{Z})^k$. Could it be somehow generalized on case $n>2$?
ED... | 4 | [
-0.1083984375,
-0.00116729736328125,
0.0654296875,
0.06982421875,
0.064453125,
-0.08544921875,
0.0030059814453125,
-0.0751953125,
0.0211181640625,
-0.072265625,
-0.022705078125,
0.0439453125,
0.00022029876708984375,
-0.056396484375,
-0.032470703125,
0.01708984375,
-0.061279296875,
... | 38,406 | 38406 | |
Finding basis, dimension and other proofs
April 11th 2014, 03:50 AM #1
Newbie
Joined
Mar 2014
From
Alice Springs
Posts
8
Finding basis, dimension and other proofs
Hey guys, here is a linear algebra problem that I need to do, help would be much appreciated.
Consider the functions p1 : R R, p2 :... | 5 | [
-0.06298828125,
-0.046630859375,
0.0004138946533203125,
0.050048828125,
0.04248046875,
0.08251953125,
0.0869140625,
-0.00982666015625,
-0.038330078125,
0.0019683837890625,
0.01513671875,
-0.055419921875,
0.001953125,
0.034912109375,
-0.01904296875,
-0.020263671875,
-0.09423828125,
... | 38,407 | 38407 | |
Maximizing Area.
January 27th 2010, 06:26 PM #1
Newbie
Joined
Jan 2010
Posts
19
Maximizing Area.
A wire 10 cm long is cut into two pieces, one of length x and the other of length 10 - x. Each piece is bent into the shape of a square.
a. Find a function that models the total area enclosed by the two ... | 5 | [
0.02978515625,
0.037841796875,
0.0074462890625,
-0.0595703125,
-0.023681640625,
0.0167236328125,
0.017822265625,
0.134765625,
-0.087890625,
-0.00004649162292480469,
-0.00034332275390625,
0.045654296875,
0.037841796875,
0.12353515625,
-0.026123046875,
0.07861328125,
0.0302734375,
0.... | 38,408 | 38408 | |
Determine is a line is tangent to a curve or not?
October 7th 2010, 09:15 AM #1
Member
Joined
Oct 2010
Posts
95
Determine is a line is tangent to a curve or not?
Sorry if it sounds silly but I am thinking if there is a way to find out if a line is a tanget of a curve?
Say given a curve of $x^2 + 3xy... | 5 | [
-0.056640625,
-0.0830078125,
-0.0966796875,
0.0013275146484375,
0.006805419921875,
0.044677734375,
0.04443359375,
0.05322265625,
0.025146484375,
-0.0191650390625,
0.033447265625,
-0.04541015625,
0.031982421875,
0.078125,
-0.03125,
0.041259765625,
-0.04443359375,
-0.035888671875,
... | 38,409 | 38409 | |
Borel measurable function
March 10th 2010, 06:49 PM
koko2009
Borel measurable function
Hi there,
I have a question on real analysis, I will write my try and could you please help me to solve it.
we need to prove that f(x)=X^2 ,Q(x)= tanx, and J(x)= -sqrt(x) are borel measurable by the formal definition {... | 5 | [
-0.017822265625,
0.052978515625,
0.095703125,
0.080078125,
-0.035888671875,
0.1845703125,
0.1279296875,
0.052978515625,
0.01513671875,
0.0294189453125,
-0.056884765625,
-0.0142822265625,
-0.01611328125,
0.10595703125,
-0.0211181640625,
-0.091796875,
0.062255859375,
-0.0703125,
-0... | 38,410 | 38410 | |
Analysis of Signs of Derivatives of an Inverse Function
Date: 06/22/2005 at 09:37:35
From: Tommy
Subject: The inverse of a concave function
I want to be able to reach conclusions about the first and second
order derivatives of an inverse function. I have a concave function
which I know has f'> 0 and f''< 0. It is a... | 5 | [
-0.006195068359375,
-0.052001953125,
0.0615234375,
0.00933837890625,
0.0054931640625,
-0.0908203125,
-0.018310546875,
0.04638671875,
0.01434326171875,
0.09423828125,
0.076171875,
0.015380859375,
0.0172119140625,
0.004180908203125,
-0.01275634765625,
-0.0032806396484375,
0.05297851562... | 38,411 | 38411 | |
Finding maximal k-degenerate subgraphs
up vote 2 down vote favorite
Given a graph $G$, let $H$ be a $k$-degenerate (not necessarily induced) subgraph of maximal size. Are there any known lower bounds on $|E(H)|$ for particular classes of $G$ and values of $k$?
I've seen several papers on the subject, but only for ind... | 4 | [
0.002655029296875,
0.06884765625,
0.03466796875,
-0.037109375,
0.00762939453125,
-0.033447265625,
-0.00115966796875,
-0.000560760498046875,
-0.134765625,
0.0771484375,
-0.08203125,
0.006500244140625,
-0.0216064453125,
-0.0238037109375,
0.00982666015625,
0.08447265625,
0.09716796875,
... | 38,412 | 38412 | |
About generator and isomorphism problems for free groups operator algebras
up vote 3 down vote favorite
2
Let $H$ be an infinite dimensional separable Hilbert space.
The $C^{*}$-algebras and von Neumann here unital and subalgebras of $B(H)$.
Definition : Let $\mathcal{A}$ be $C^{*}$-algebra (resp. a von Neumann algeb... | 4 | [
-0.125,
0.01470947265625,
-0.01519775390625,
0.026123046875,
-0.05810546875,
0.052978515625,
0.0152587890625,
-0.051025390625,
-0.042236328125,
-0.08251953125,
0.1162109375,
-0.1328125,
0.0128173828125,
-0.056640625,
0.035888671875,
0.06298828125,
-0.03271484375,
-0.04931640625,
... | 38,413 | 38413 | |
Contraction mapping with no fixed point
up vote 5 down vote favorite
1
I am interested in constructing the following "counter-example" to the Banach's fixed point theorem.
Let $K=$ {$ g\in L_1: \|g\|=1, g(\cdot)\ge0 $}. Clearly, $K$ is not a compact and $K$ is [S: not :S] closed.
[S:My:S] A question is: is it possib... | 5 | [
0.01373291015625,
-0.041259765625,
-0.055419921875,
-0.03369140625,
-0.03076171875,
0.049072265625,
0.0654296875,
-0.039306640625,
-0.037353515625,
0.11865234375,
0.01104736328125,
0.06640625,
0.038818359375,
-0.036865234375,
-0.003814697265625,
-0.0115966796875,
0.0159912109375,
-... | 38,414 | 38414 | |
Method of Differences
January 11th 2008, 08:14 PM #1
Method of Differences
Find the sum to $n$ terms of the series
$1(1!)+2(2!)+...+r(r!)+...$
Solution
Let,
$u_r=r(r!)$
If,
$f(r)=r!$
then,
$f(r+1)-f(r)$
$=(r+1)!-r!$
$=(r+1){\color{red}\text{r}}!-r!\quad\leftarrow$ Wher... | 5 | [
-0.044677734375,
0.0218505859375,
-0.0634765625,
-0.00640869140625,
-0.01422119140625,
0.03125,
-0.01318359375,
-0.0034637451171875,
-0.037109375,
0.044921875,
-0.038818359375,
-0.04931640625,
0.00136566162109375,
0.00311279296875,
-0.0111083984375,
-0.09814453125,
-0.012939453125,
... | 38,415 | 38415 | |
solving for X with logs
May 20th 2011, 05:09 AM #1
Member
Joined
Mar 2010
Posts
82
solving for X with logs
Hi could someone please let me know if this is correct?
Log4_X + log4_(x-3)=1
Log4_X + log4_X - Log4_3=1
Change base ln
Log4_X= lnX/ln4
Log4_3=ln3/ln4
1=lne^1=lne
N... | 4 | [
0.0186767578125,
-0.05029296875,
0.0576171875,
-0.055908203125,
-0.001953125,
-0.072265625,
0.02734375,
-0.020263671875,
0.0260009765625,
0.036376953125,
0.05126953125,
-0.052001953125,
0.0235595703125,
0.0107421875,
-0.010986328125,
0.080078125,
-0.1318359375,
0.038330078125,
-0... | 38,416 | 38416 | |
Show that the volume of a pyramid of height h whose base is an equilateral triangle o
December 3rd 2008, 09:28 PM
derrickd
Show that the volume of a pyramid of height h whose base is an equilateral triangle o
Show that the volume of a pyramid of height h whose base is an equilateral triangle of side s is equal t... | 4 | [
0.0010833740234375,
0.056396484375,
0.004486083984375,
-0.06494140625,
-0.040771484375,
0.036376953125,
-0.12255859375,
0.076171875,
0.01123046875,
-0.02294921875,
-0.0302734375,
-0.00021648406982421875,
0.044677734375,
-0.0302734375,
0.02392578125,
0.013916015625,
0.0162353515625,
... | 38,417 | 38417 | |
basic calc two problems! thanks for the help!
December 10th 2007, 08:30 PM #1
wpski
Guest
ok two problems both are totally weird and have no context in my book
please help me!
1) The tangent to y=(ax+b)/(sqaureroot of x) at the point where x=1 is 2x-y=1. find a and b
2) Find a given that the tangent ... | 4 | [
-0.0595703125,
-0.0247802734375,
0.0167236328125,
-0.008544921875,
0.01806640625,
0.054931640625,
0.03955078125,
0.0257568359375,
0.059814453125,
0.038818359375,
0.111328125,
-0.06689453125,
0.01336669921875,
0.016845703125,
-0.055419921875,
0.1083984375,
-0.0947265625,
-0.11425781... | 38,418 | 38418 | |
Is there a connected non-affine scheme $S$ such that it is the union of rings of integers of number fields?
up vote 7 down vote favorite
3
I was woolgathering about the notion of a scheme, and it occurred to me that I know of no non-affine scheme $S$ that is the union of $Spec(O_K)$'s of some number field $K$ (I allow... | 5 | [
0.0205078125,
0.038330078125,
-0.09228515625,
0.0162353515625,
0.056396484375,
-0.056640625,
0.0439453125,
-0.033447265625,
0.048828125,
-0.055419921875,
-0.05078125,
0.0341796875,
0.007598876953125,
-0.004425048828125,
0.0096435546875,
-0.01080322265625,
0.04541015625,
0.062011718... | 38,419 | 38419 | |
find distance
December 10th 2006, 02:05 AM
jim49990
find distance
i have a triangular plot of land through which a stream runs. the point B is due east of A and AB is 50m long. the bearing of C from A 026 degrees and the bearing of C from B is 328 degrees.
calculate the distances AC and BC.
could this p... | 4 | [
-0.039794921875,
0.0986328125,
-0.0830078125,
-0.06787109375,
-0.06494140625,
0.015625,
-0.09033203125,
0.0150146484375,
-0.035400390625,
-0.01043701171875,
-0.01055908203125,
-0.08935546875,
0.00069427490234375,
0.01190185546875,
0.054931640625,
0.031494140625,
-0.0986328125,
-0.0... | 38,420 | 38420 | |
How do I solve this with a direct proof?
November 8th 2012, 05:39 AM #1
Newbie
Joined
Nov 2012
From
Unknown
Posts
7
How do I solve this with a direct proof?
Prove that for all sets X and Y, (X ∩ Y) ∪(Y-X)=Y
I'm stuck and I'm not fully sure how to solve this.
Re: How do I solve this with a direc... | 4 | [
0.0250244140625,
0.0272216796875,
0.006103515625,
-0.0439453125,
0.00909423828125,
-0.00151824951171875,
0.1640625,
-0.041748046875,
-0.0751953125,
-0.0419921875,
-0.0235595703125,
-0.04150390625,
0.0576171875,
0.00592041015625,
0.052978515625,
0.010009765625,
0.01483154296875,
-0.... | 38,421 | 38421 | |
how many blue marbles than red?
July 31st 2006, 08:32 PM
Judi
how many blue marbles than red?
A jar contained twice as many red marbles as blue marbles. Jill removed n% of the red marbles and increased the number of blue marbles by n%. What is the smallest integer value of n that will
result in the jar's now... | 4 | [
-0.005462646484375,
0.03515625,
0.0189208984375,
0.0089111328125,
-0.050537109375,
0.04833984375,
0.10546875,
0.05126953125,
-0.033935546875,
-0.00439453125,
-0.07470703125,
-0.055908203125,
0.03466796875,
-0.006195068359375,
0.00921630859375,
0.09912109375,
0.08935546875,
0.005706... | 38,422 | 38422 | |
Generating-functions: is there a relationship between a generating function and the corresponding squared generating function
up vote 2 down vote favorite
Let's say we have a sequence $T(n)$ with the corresponding generating function
$$A(t) = \sum_{n = 0}^\infty T(n) t^n$$
Is there some relationship between the two ... | 5 | [
-0.12353515625,
0.0274658203125,
-0.031982421875,
0.11376953125,
-0.09716796875,
0.029296875,
0.0029144287109375,
-0.08544921875,
0.1337890625,
-0.0030670166015625,
0.0208740234375,
0.0211181640625,
0.024169921875,
0.0159912109375,
-0.0111083984375,
-0.03369140625,
0.013916015625,
... | 38,423 | 38423 | |
Number of Combinations
August 20th 2008, 10:04 PM #1
Newbie
Joined
Aug 2008
Posts
3
Number of Combinations
G'day,
not sure if this the right place to post this...
I have 20 dice/triangle-like objects, each with a 1, 2 and 3 on it.
How many possible combinations can be made from the 20 obje... | 4 | [
0.03125,
-0.015380859375,
-0.0242919921875,
0.015869140625,
-0.060791015625,
0.0303955078125,
-0.004150390625,
-0.00531005859375,
0.004547119140625,
-0.0059814453125,
0.015625,
-0.060791015625,
0.0286865234375,
-0.0091552734375,
0.033447265625,
0.038818359375,
-0.0242919921875,
-0.... | 38,424 | 38424 | |
finding the equation of a hyperbola!
Hello, ahztin13! Find an equation of the hyperbola having foci at $\left(5 \pm\sqrt{61},\:-4\right)$ and asymptotes $y \:=\:\pm\frac{6}{5}x - 10$ The equation of a "horizonal" hyperbola is: . $\frac
{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} \;=\;1$ The center of a hyperbola is the midpoi... | 4 | [
0.0174560546875,
0.01531982421875,
-0.049072265625,
-0.0751953125,
0.004150390625,
0.051025390625,
-0.041015625,
0.05126953125,
0.024169921875,
0.0093994140625,
0.0693359375,
-0.02880859375,
-0.017333984375,
0.0169677734375,
-0.007720947265625,
0.1484375,
-0.0419921875,
-0.04077148... | 38,425 | 38425 | |
Fourier transform and orthogonal system
December 15th 2011, 02:02 AM
Opalg
Re: Fourier transform and orthogonal system
I don't understand that. The OP's $\phi_0$ is given by $\phi_0(x) = \begin{cases} 1 & x\in[-\frac{1}{2},\frac{1}{2}],\\ 0 & \text{elsewhere.} \end{cases}$
My f is given by $f(x) = \begin{ca... | 4 | [
-0.062255859375,
0.01263427734375,
0.041015625,
-0.06884765625,
-0.000659942626953125,
0.02001953125,
0.037353515625,
0.0869140625,
-0.00830078125,
0.0498046875,
0.11474609375,
0.06640625,
-0.00482177734375,
-0.07421875,
-0.050048828125,
-0.0439453125,
-0.0035247802734375,
-0.08398... | 38,426 | 38426 | |
figure of eight- need help
November 26th 2008, 11:35 AM
sonia1
figure of eight- need help
Hi. Does anyone know
'What is the largest figure of eight that will stand inside an equilateral triangle of side length one?' (the circles are of the same size).
I have no idea how to start it http://static.thestu... | 4 | [
0.01263427734375,
0.06103515625,
-0.036376953125,
-0.00787353515625,
-0.0279541015625,
-0.047607421875,
-0.017333984375,
0.10986328125,
-0.006011962890625,
-0.025146484375,
-0.091796875,
0.01806640625,
0.03857421875,
0.047607421875,
0.052734375,
0.0302734375,
-0.0211181640625,
-0.0... | 38,427 | 38427 | |
Equilateral Triangle & Circle
January 22nd 2007, 05:36 PM #1
Banned
Joined
Jan 2007
Posts
315
Equilateral Triangle & Circle
A wire 10 meters long is to be cut into two pieces. One piece will be shaped as an equilateral triangle, and the other piece will be shaped like a circle.
(a) Express the total... | 4 | [
-0.041748046875,
0.0517578125,
-0.06884765625,
-0.0634765625,
-0.029296875,
-0.00860595703125,
0.0284423828125,
0.09326171875,
0.01153564453125,
-0.004180908203125,
0.001739501953125,
-0.020751953125,
0.07373046875,
0.05419921875,
0.0849609375,
0.004730224609375,
-0.030029296875,
-... | 38,428 | 38428 | |
Factoring cubic polynomials
November 14th 2012, 06:44 AM #1
Member
Joined
May 2009
Posts
109
Factoring cubic polynomials
I do not understand how we know a cubic polynomial such as
z^3 -3z^2 + 4z - 2 = 0
can be factored as
(z - 1)(z^2 - 2z +2) = 0
I can, of course, work it backwards bu... | 4 | [
-0.059814453125,
-0.0034942626953125,
-0.0556640625,
0.107421875,
0.07177734375,
-0.0289306640625,
-0.012939453125,
-0.00408935546875,
-0.01708984375,
-0.06396484375,
0.021240234375,
-0.058837890625,
0.091796875,
0.03564453125,
-0.00098419189453125,
-0.0045166015625,
0.0220947265625,... | 38,429 | 38429 | |
Operator norm
April 16th 2010, 07:13 AM
notgoodatmath
Operator norm
I'm a bit confused about what an operator norm is.
Can someone explain it to me using a simple matrix?
What value would you use for the Euclidean norm (x) when it is multiplied by A? (before taking the supremum).
April 16th 2010, 07:3... | 5 | [
0.0089111328125,
-0.052978515625,
-0.072265625,
-0.076171875,
-0.002227783203125,
0.0576171875,
0.053466796875,
0.0576171875,
-0.051025390625,
0.0296630859375,
0.020751953125,
0.09521484375,
0.051025390625,
-0.024658203125,
0.0322265625,
0.15625,
0.11865234375,
-0.111328125,
-0.0... | 38,430 | 38430 | |
Why do Clifford algebras determine $KO$ (and $K$-)-theory?
up vote 18 down vote favorite
6
In the paper "Clifford modules" by Atiyah-Bott-Shapiro, they construct a family of Clifford algebras $C_k$ over the real numbers, so that $C_k$ is the algebra associated to a negative definite form
on $\mathbb{R}^k$. Let $M_k$ b... | 4 | [
-0.1005859375,
0.0458984375,
-0.045654296875,
0.0244140625,
-0.0478515625,
0.037353515625,
0.01202392578125,
-0.02685546875,
0.004241943359375,
-0.07958984375,
0.041259765625,
-0.029541015625,
0.0098876953125,
-0.018310546875,
-0.0155029296875,
0.0078125,
0.0274658203125,
0.0639648... | 38,431 | 38431 | |
Re-arranging formula
January 13th 2011, 03:31 AM #1
Newbie
Joined
Jan 2011
Posts
6
Re-arranging formula
Hi, im new here. Just wondering if someone could walk me through solving this for equation for V2. I have a solution but some parts seemed to have been skipped and i dont quite understand why:
150... | 5 | [
-0.043701171875,
0.04443359375,
0.0264892578125,
-0.045654296875,
0.0849609375,
-0.12060546875,
0.0267333984375,
-0.01220703125,
0.05615234375,
0.11865234375,
0.0196533203125,
-0.078125,
-0.00142669677734375,
0.1025390625,
0.07958984375,
0.046875,
-0.12890625,
0.0830078125,
-0.11... | 38,432 | 38432 | |
Help with diff eqn
December 6th 2006, 03:44 AM
ashura
Help with diff eqn
How can I proceed with this? solve the diff eqn: $\left (2y^2 - 4x + 5 \right )dx = \left (4 - 2y + 4xy \right )dy$
$\frac{dy}{dx} = \frac{2y^2 -4x + 5}{4 -2y + 4xy}$
Doesn't seem I can use quotient rule here.
..............?... | 5 | [
-0.064453125,
0.0296630859375,
0.10498046875,
-0.0162353515625,
0.023681640625,
-0.0341796875,
-0.039794921875,
0.005615234375,
0.00982666015625,
-0.00128173828125,
0.1259765625,
-0.07275390625,
0.01123046875,
0.0390625,
-0.03857421875,
0.0294189453125,
-0.04638671875,
0.0007629394... | 38,433 | 38433 | |
Expectation of the time t standard brownian motion stopped at itself's square
up vote 4 down vote favorite
I have a one dimensional standard brownian motion $W$ defined under a stochastic basis with probability $\mathbf{Q}$ and filtration $\left(\mathscr{F}\right)_{t\in{\mathbf{R}}_{+}}$, and I want to
calculate $\mat... | 5 | [
-0.01434326171875,
-0.0030670166015625,
0.047607421875,
0.041748046875,
0.0208740234375,
0.026123046875,
0.0133056640625,
-0.0026397705078125,
0.052490234375,
0.01007080078125,
-0.049560546875,
0.07470703125,
-0.064453125,
0.032958984375,
-0.044921875,
0.07373046875,
0.00564575195312... | 38,434 | 38434 | |
Eigenvalues
November 3rd 2007, 08:01 PM #1
Member
Joined
Sep 2007
From
Calgary, Alberta
Posts
77
Eigenvalues
Find all the eigenvalues (real and complex) of the matrix:
$\left( \begin{array}{ccc} -6 & 22 & 11 \\ -2 & -7 & -2 \\ -1 & 26 & 10 \end{array} \right)$
I started off by using the for... | 5 | [
-0.057373046875,
-0.0181884765625,
-0.06591796875,
0.03662109375,
0.044921875,
0.0294189453125,
-0.049560546875,
-0.0181884765625,
-0.058349609375,
-0.047607421875,
0.11279296875,
-0.014892578125,
-0.0380859375,
-0.0250244140625,
-0.005523681640625,
-0.05224609375,
-0.0269775390625,
... | 38,435 | 38435 | |
How to solve Diophantine equations in $F_{p}$?
up vote 6 down vote favorite
5
For example, how to solve the equation $\sum^{p-1}_{i}x_{i}^{2}=0$ in $F_{p}$? This is not a homework problem. I think it should have a definite answer, so not an open problem. I just don't know how
to solve it.
polynomials nt.number-theory... | 5 | [
0.01055908203125,
-0.038330078125,
-0.004486083984375,
0.003143310546875,
0.03369140625,
-0.05615234375,
0.039794921875,
0.06201171875,
0.035888671875,
-0.0166015625,
-0.04150390625,
-0.0234375,
-0.0322265625,
0.017578125,
-0.033447265625,
0.01031494140625,
-0.07373046875,
-0.04858... | 38,436 | 38436 | |
alpha is a square of an element in Fq star
March 16th 2011, 04:22 PM #1
Junior Member
Joined
Jan 2011
Posts
46
alpha is a square of an element in Fq star
if q be a power of an odd prime. we need to prove that an element alpha belongs to the multiplicative group Fq star, is a square element of Fq star if ... | 5 | [
0.005706787109375,
0.099609375,
0.049072265625,
0.0751953125,
-0.0361328125,
0.031005859375,
0.10205078125,
-0.025634765625,
0.033447265625,
-0.078125,
-0.052001953125,
0.00640869140625,
0.0400390625,
0.00153350830078125,
-0.09228515625,
-0.006744384765625,
-0.072265625,
-0.0466308... | 38,437 | 38437 | |
Dijkstra's Algorithm
Notes:
• This algorithm is not presented in the same way that you'll find it in most texts because i'm ignored directed vs. undirected graphs and i'm ignoring the loop invariant that you'll see in any
b... | 4 | [
-0.06689453125,
0.06591796875,
0.00335693359375,
-0.0164794921875,
0.016357421875,
-0.027587890625,
0.001190185546875,
-0.0311279296875,
-0.0220947265625,
-0.01611328125,
-0.035888671875,
0.03857421875,
-0.0150146484375,
0.005889892578125,
-0.0703125,
0.013671875,
0.04052734375,
0.... | 38,438 | 38438 | |
Surface integration
October 22nd 2011, 05:51 AM #1
Junior Member
Joined
Mar 2011
Posts
68
Surface integration
I think my method is correct here, but i must of gone wrong somewhere (note i cannot use divergence theorem)
I have a vector field:
$F = ax\vec{i}$
Where a is a constant and a sphere... | 5 | [
0.0208740234375,
0.0279541015625,
0.0205078125,
-0.1279296875,
0.041748046875,
0.0034637451171875,
0.0166015625,
0.047607421875,
-0.031982421875,
0.06201171875,
-0.05712890625,
0.048583984375,
0.01092529296875,
0.031005859375,
-0.036376953125,
0.01904296875,
-0.003265380859375,
0.0... | 38,439 | 38439 | |
Cyclic groups. Prove that <x^m> intersection <x^n> = <x^ (LCM,m,n)>
November 28th 2011, 10:14 AM
okoolo
Cyclic groups. Prove that <x^m> intersection <x^n> = <x^ (LCM,m,n)>
prove the following property of cyclic
groups: Let G = <x> be a finite cyclic group.
Prove that <x^m> intersection <x^n> = <x ^ LCM(m... | 5 | [
0.044677734375,
0.06396484375,
-0.00341796875,
-0.042236328125,
-0.00396728515625,
0.00070953369140625,
0.0673828125,
-0.0240478515625,
-0.033203125,
-0.06640625,
0.03662109375,
-0.0157470703125,
0.0810546875,
-0.0732421875,
0.056884765625,
0.119140625,
-0.03466796875,
0.0086669921... | 38,440 | 38440 | |
Need help with an inequality
October 1st 2012, 09:11 PM
Halcyon
Need help with an inequality
Hi, could anybody please help with this inequality? I've tried it several times, but my answers are always absurd.
Find a constant A for which abs(log(cos(x))+(x^2)/2) =< Ax^4 for -pi/3 <= x <= pi/3
Any help at... | 5 | [
-0.04248046875,
0.0220947265625,
-0.0546875,
-0.03662109375,
-0.042236328125,
0.0111083984375,
-0.046630859375,
-0.0081787109375,
0.00946044921875,
0.006439208984375,
0.03662109375,
0.0012359619140625,
0.08837890625,
-0.00457763671875,
0.055419921875,
0.0341796875,
0.00494384765625,
... | 38,441 | 38441 | |
[SOLVED] Taylor Series Expansion help!!!
April 27th 2010, 02:38 AM #1
Junior Member
Joined
Nov 2009
Posts
27
[SOLVED] Taylor Series Expansion help!!!
I have to perform a Taylor Expansion in both for $S_i$ where $i=1,2,......,n$ and $t$ for the function $V(S_1,S_2,.......,t)$
I have started it, and s... | 4 | [
-0.031494140625,
-0.0291748046875,
0.0751953125,
-0.0191650390625,
0.01300048828125,
0.0194091796875,
-0.07080078125,
-0.00543212890625,
0.0079345703125,
0.006195068359375,
0.0172119140625,
0.005035400390625,
-0.03662109375,
-0.0498046875,
-0.058349609375,
-0.0322265625,
0.021484375,... | 38,442 | 38442 | |
Proof of DeMoivre's Theorem
Date: 05/01/97 at 20:17:29
From: LIYA
Subject: Proof of Demoivre's Theorem
Dr. Math,
Could you please help me prove DeMoivre's theorem by mathematical
induction? I figured out the first part of the proof, but I can't
prove that assuming that if it's true for n = k, then it's true
for n ... | 5 | [
-0.130859375,
0.0791015625,
0.0142822265625,
0.03466796875,
0.003173828125,
0.0191650390625,
0.083984375,
-0.05419921875,
0.00732421875,
0.04931640625,
0.044677734375,
-0.0135498046875,
0.0296630859375,
0.00250244140625,
0.02197265625,
-0.0302734375,
-0.04833984375,
0.026611328125,... | 38,443 | 38443 | |
Help with this problem please
October 20th 2007, 07:15 AM #1
Newbie
Joined
Oct 2007
Posts
3
Help with this problem please
$\\ \mbox{Give that,} \\ x_A , x_B >1 \\ \mbox{ and } \\ Y_A,Y_B\geqslant0 \mbox{ (but strictly positive for at least one)}$
$Y_A + Y_B = 100$
$P_A=Y_A(x_A -1) - Y_B$
$P_... | 4 | [
-0.080078125,
0.060546875,
-0.01116943359375,
-0.14453125,
-0.025390625,
0.01092529296875,
0.07177734375,
0.01141357421875,
-0.0029754638671875,
0.0390625,
0.0045166015625,
-0.00396728515625,
0.06005859375,
0.06005859375,
0.10107421875,
0.1455078125,
-0.007049560546875,
-0.04882812... | 38,444 | 38444 | |
Can any smooth hyperelliptic curve be embedded in a quadric surface?
up vote 4 down vote favorite
4
Let's consider algebraic curves over a fixed algebraically closed field $K$.
It's well known, that every smooth elliptic curve (genus $g = 1$) can be embedded in a quadric surface in $\mathbb{P}^3$. This fact follows s... | 5 | [
-0.005523681640625,
-0.01336669921875,
0.040283203125,
-0.0162353515625,
-0.0230712890625,
-0.080078125,
0.007049560546875,
-0.025146484375,
-0.00408935546875,
-0.06689453125,
0.055419921875,
-0.0003185272216796875,
-0.027099609375,
0.002471923828125,
0.011962890625,
0.00408935546875,
... | 38,445 | 38445 | |
More log stuff
May 12th 2008, 01:39 AM #1
Newbie
Joined
May 2008
Posts
17
More log stuff
1. $\log_{2}(25^(x+3) - 1) = 2 + \log_{2}(5 ^ (x+3) + 1)$
2. $\log_{4}(2 \cdot 3^(x) - 6) -\log_{2}(9^(x) - 6)$
3. $\log_{4}(2 \cdot 4^(x-2) - 1) + 4 = 2x$
I attempted the first to come as far as this-:
... | 4 | [
-0.03173828125,
0.00022411346435546875,
0.031494140625,
-0.03173828125,
0.027587890625,
-0.11962890625,
0.0517578125,
0.0196533203125,
0.0274658203125,
0.044189453125,
-0.03271484375,
-0.0771484375,
0.039794921875,
0.0517578125,
0.06591796875,
0.080078125,
-0.11474609375,
0.0539550... | 38,446 | 38446 | |
COMPUTE (ABAP Keyword)
COMPUTE (ABAP Keyword) introduction & details
COMPUTE
Basic
form
COMPUTE n = arithexp.
Effect
Evaluates the arithmetic
expression arithexp and places the result in the field n .
Allows use of
the four basic calculation types + , – , * and / , the whole number division
operators DIV (quotient... | 5 | [
-0.048828125,
0.0673828125,
-0.0179443359375,
0.003997802734375,
-0.05810546875,
-0.08837890625,
0.031982421875,
0.0235595703125,
0.034912109375,
-0.00823974609375,
0.0194091796875,
-0.021240234375,
0.033203125,
0.033447265625,
-0.0036773681640625,
0.04296875,
-0.033935546875,
0.01... | 38,447 | 38447 | |
Connected components of schemes over $\mathbb{F}_1$
up vote 4 down vote favorite
I'm reading Deitmar's paper on Schemes over $\mathbb{F}_1$. Proposition 2.4. states that for a scheme $X$ over $\mathbb{F}_1$ there is a bijection between $X(\mathbb{F}_1)$ and the set of connected
components of $X$. I don't understand th... | 4 | [
0.020263671875,
-0.035400390625,
0.05322265625,
-0.00457763671875,
0.12158203125,
-0.056640625,
0.1318359375,
0.03369140625,
0.058349609375,
-0.08203125,
0.042236328125,
-0.0033416748046875,
0.00494384765625,
-0.037841796875,
0.0022430419921875,
0.0012969970703125,
-0.00994873046875,... | 38,448 | 38448 | |
Stickelberger's congruence for Gauss sums
up vote 12 down vote favorite
1
We begin with (unfortunately, quite a bit of) notation necessary to state Stickelberger's congruence: Fix an integer $k>1$, and let $p$ be a prime number not dividing $k$. Let $r$ be the smallest
positive integer such that $p^r\equiv 1 \pmod{k}$... | 4 | [
-0.03564453125,
0.033447265625,
-0.00946044921875,
0.02734375,
0.05517578125,
0.024658203125,
0.11669921875,
0.10009765625,
-0.0107421875,
-0.08251953125,
-0.00147247314453125,
0.052001953125,
0.09765625,
-0.01416015625,
-0.033935546875,
0.0234375,
-0.02197265625,
0.048828125,
-0... | 38,449 | 38449 | |
Show that the system of equation is consistent
May 3rd 2009, 10:24 PM #1
Banned
Joined
Dec 2008
From
Mauritius
Posts
523
Show that the system of equation is consistent
Show that the system of equation $<br /> x - 3y -8z = -10;<br />$$<br /> 3x+y-4z=0;<br />$ and $<br /> 2x+5y+6z =13<br />$ is consist... | 5 | [
-0.130859375,
-0.048828125,
-0.0830078125,
-0.0234375,
0.0169677734375,
0.042724609375,
0.02197265625,
-0.060791015625,
0.01397705078125,
-0.0262451171875,
0.1259765625,
-0.005157470703125,
0.126953125,
-0.01806640625,
-0.0184326171875,
0.060791015625,
-0.037109375,
-0.0439453125,
... | 38,450 | 38450 | |
Find zeros
November 17th 2007, 04:24 PM #1
Super Member
Joined
Mar 2006
Posts
705
Thanks
2
Find zeros
Show that $x^2 + 3x + 2$ has four zeros in $Z_{6}$.
$x^2 + 3x + 2 = (x+2)(x+1)$, by the factor theorem, -1 and -2 are zeros of the poly.
However, -2 = 4 and -1 = 5 in $Z_{6}$. But what are ... | 4 | [
-0.036865234375,
0.046142578125,
0.0016326904296875,
0.058837890625,
0.045166015625,
0.04052734375,
0.0238037109375,
-0.00823974609375,
0.01416015625,
-0.0230712890625,
0.01544189453125,
-0.0654296875,
0.0289306640625,
-0.0198974609375,
-0.078125,
-0.0390625,
-0.05419921875,
-0.039... | 38,451 | 38451 | |
Infinte Sets
November 21st 2009, 06:12 AM
aman_cc
Infinte Sets
Some notations:
$J_n = \{x|x \in N, 1\leq x \leq n\}$
For any two sets A,B; $A \cong B \Rightarrow$ there exists a bijection between A and B
I have read following two definitions of infinite sets:
1. Set S, is finite if $S \cong J_n... | 5 | [
-0.044189453125,
-0.00732421875,
0.059326171875,
-0.06396484375,
0.0113525390625,
0.0986328125,
0.0927734375,
0.062255859375,
-0.041015625,
-0.036376953125,
-0.072265625,
-0.01226806640625,
0.0791015625,
-0.06005859375,
-0.01080322265625,
-0.0146484375,
0.1484375,
0.01190185546875,... | 38,452 | 38452 | |
lines through A_n reflection arrangement and permutations
up vote 4 down vote favorite
2
(updated; apologies for way too much room left for interpretation in the original post)
Let $\mathcal{A} =A_{n-1}$ be the $A_{n-1}$ arrangement in $\mathbb{R}^{n}$, i.e. the set of hyperplanes $H_{ij}$ specified by equations $x_i... | 4 | [
-0.07275390625,
-0.09228515625,
0.049560546875,
-0.005645751953125,
-0.0859375,
0.06591796875,
0.06201171875,
-0.03564453125,
0.01708984375,
-0.03662109375,
-0.0084228515625,
-0.000701904296875,
-0.054443359375,
-0.123046875,
-0.171875,
0.10791015625,
0.023193359375,
-0.01611328125... | 38,453 | 38453 | |
Isomorphism of the function field of the projective line with $\mathbf{C}(s)$
up vote 3 down vote favorite
Suppose I chose two rational functions, say,
$$u = \frac{t(4+t)^5}{(1+4t)^5}, \qquad v = \frac{t^5(4+t)}{(1+4t)}.$$
Then I know that $K(X) = \mathbf{C}(u,v)$ is the function field of the projective line (Proof:... | 5 | [
-0.0654296875,
0.05517578125,
-0.0013427734375,
-0.0267333984375,
-0.004058837890625,
0.000576019287109375,
0.003875732421875,
-0.064453125,
-0.007568359375,
-0.023681640625,
0.039306640625,
-0.05517578125,
-0.10400390625,
0.05615234375,
-0.06103515625,
-0.008056640625,
0.00296020507... | 38,454 | 38454 | |
representability of consecutive integers by a binary quadratic form
up vote 12 down vote favorite
4
I have two related questions on the representability of integers by quadratic forms in two variables :
(1) Let $f: {\mathbb Z} \times {\mathbb Z} \to {\mathbb Z} $ be such a quadratic form, i.e. we have $f(x,y)=ax^2+bx... | 5 | [
-0.026611328125,
0.060302734375,
-0.0517578125,
-0.052490234375,
-0.0026702880859375,
0.109375,
0.01385498046875,
-0.039794921875,
-0.033935546875,
-0.07470703125,
-0.03125,
-0.007537841796875,
0.057373046875,
0.040283203125,
-0.003692626953125,
-0.0263671875,
0.01531982421875,
-0.... | 38,455 | 38455 | |
[SOLVED] Rearrangements of alternating harmonic series
January 25th 2010, 09:34 PM
tonyc4l
[SOLVED] Rearrangements of alternating harmonic series
Hey guys, I'm pretty stuck on the following problem. It involves rearrangements of the terms in the alternating harmonic series to produce different sums:
Let s =... | 4 | [
-0.1044921875,
-0.0294189453125,
0.06591796875,
-0.064453125,
-0.0400390625,
0.02197265625,
0.0269775390625,
0.0181884765625,
0.0240478515625,
-0.021484375,
-0.052490234375,
-0.06201171875,
0.0361328125,
-0.00958251953125,
-0.07861328125,
-0.06689453125,
0.048828125,
0.002258300781... | 38,456 | 38456 | |
points in proof of homogeneous DE
May 28th 2014, 10:58 PM #1
Member
Joined
Aug 2011
Posts
84
points in proof of homogeneous DE
I have a question about the proof of this elementary DE, the calculations are easy
$\frac{dy}{dt}+a(t)y=0\rightarrow \left | y(t)\right|=exp(-\int a(t)dt+ca)\rightarrow |cexp... | 4 | [
-0.140625,
-0.0458984375,
0.047607421875,
0.03271484375,
0.04296875,
0.06689453125,
0.0595703125,
0.01385498046875,
0.00994873046875,
0.045166015625,
0.1181640625,
0.0013427734375,
0.025634765625,
0.04345703125,
-0.0274658203125,
-0.01336669921875,
-0.0216064453125,
-0.03369140625,... | 38,457 | 38457 | |
Looking for final interest payment on a loan just paid off
May 15th 2012, 06:42 PM #1
Newbie
Joined
May 2012
From
Melfort, SK
Posts
7
Hi there,
It has been over 7 years since I have had to use any of my mathematics of finance knowledge and wow does it disappear when you do not use it.
i have p... | 4 | [
-0.027099609375,
0.052978515625,
0.0230712890625,
-0.05810546875,
0.0184326171875,
-0.031494140625,
-0.05126953125,
0.07861328125,
0.01080322265625,
0.058837890625,
0.00286865234375,
-0.023193359375,
-0.0537109375,
-0.03466796875,
-0.0238037109375,
0.0291748046875,
-0.107421875,
-0... | 38,458 | 38458 | |
A Few Integrals
February 12th 2009, 09:49 PM #1
Newbie
Joined
Feb 2009
Posts
7
A Few Integrals
I'm stumped on these:
The integral of x^3 (1+x^2)^3/2
The integral of the square root of (x^2 - 1)dx/x^3
The integral of x^3 dx/(4-x^2)^2
do a substitution, $u = 1 + x^2$
The integral o... | 4 | [
0.041015625,
-0.03466796875,
0.02392578125,
0.02783203125,
0.0223388671875,
-0.091796875,
-0.05810546875,
-0.00555419921875,
-0.0009918212890625,
-0.0791015625,
-0.01483154296875,
-0.0111083984375,
-0.0703125,
-0.005889892578125,
-0.072265625,
0.0286865234375,
0.02685546875,
-0.007... | 38,459 | 38459 | |
Sup and inf of bounded variations
December 12th 2009, 05:05 PM #1
Super Member
Joined
Mar 2006
Posts
705
Thanks
2
Sup and inf of bounded variations
Suppose that v is a signed measure on $(X, \mathbb {M} )$ and $E \subset \mathbb {M}$
Prove that:
a) $v^+(E) = sup \{ v(F) : F \in \mathbb {M} , ... | 4 | [
0.0084228515625,
0.09326171875,
0.0908203125,
-0.05029296875,
0.07763671875,
0.16796875,
0.125,
0.06689453125,
-0.056396484375,
-0.0087890625,
-0.0189208984375,
-0.052490234375,
-0.0267333984375,
-0.036865234375,
0.03759765625,
-0.0223388671875,
0.08984375,
0.0166015625,
-0.07128... | 38,460 | 38460 | |
What is the volume of a \delta-ball in the orthogonal group O(n)? Is there a (simple) lower bound?
up vote 6 down vote favorite
5
The volume in the orthogonal group is measured by the Haar measure, which is the up to scaling unique measure that is invariant under the group operation. I consider the usual metric that i... | 4 | [
0.010009765625,
-0.0247802734375,
-0.0284423828125,
-0.06884765625,
-0.078125,
0.012451171875,
0.018798828125,
-0.021484375,
0.035888671875,
-0.07763671875,
0.004058837890625,
0.06396484375,
-0.04248046875,
-0.057861328125,
0.00180816650390625,
-0.045166015625,
0.083984375,
0.03735... | 38,461 | 38461 | |
find eqaution of a plane
March 11th 2008, 06:59 PM #1
Junior Member
Joined
Feb 2008
Posts
29
find eqaution of a plane
find the equation of the plane that goes through (1,2,-1) and making equal angles with the positive directions of the coordinate axes
Hello, ramzouzy!
Find the equation of the p... | 4 | [
-0.1181640625,
0.0194091796875,
0.006103515625,
-0.0166015625,
-0.009033203125,
-0.010009765625,
0.04541015625,
0.0400390625,
-0.00848388671875,
0.0057373046875,
-0.02001953125,
-0.02197265625,
0.002227783203125,
-0.033935546875,
-0.052490234375,
-0.007171630859375,
-0.076171875,
-... | 38,462 | 38462 | |
Math Forum Discussions - fERMAT'S PROOF 2^n-2 for prime n is mod n
Date: Apr 11, 2013 11:22 AM
Author: DRMARJOHN
Subject: fERMAT'S PROOF 2^n-2 for prime n is mod n
One of Fermat's few proofs is that for prime n, n divides [(2^n) -2], or n is mod n. Can this be expanded for an appropriate formula for (3^n)? Is it possi... | 4 | [
-0.0810546875,
0.0216064453125,
-0.0654296875,
0.0703125,
0.09765625,
-0.0673828125,
0.011962890625,
0.0888671875,
-0.004150390625,
-0.05078125,
-0.0791015625,
0.01123046875,
-0.031005859375,
0.05029296875,
0.07470703125,
-0.0017242431640625,
-0.0625,
-0.0263671875,
0.00573730468... | 38,463 | 38463 | |
Deriving a square root under a square
Suppose that $f(x) = \sqrt{6+\sqrt{8x}}$. Find $f'(x).$ oh man I really need help on this one.
Maybe if the numbers/expressions/surds are shown, your questions can be solved. Two red x's don't help much.
Oh there they are! f(x) = sqrt[6 +sqrt(8x)] Or, f(x) = [6 +(8x)^(1/2)]^(1/2)... | 5 | [
0.05029296875,
-0.0174560546875,
0.08935546875,
0.068359375,
-0.032470703125,
-0.0137939453125,
-0.042236328125,
0.08447265625,
0.042724609375,
0.02587890625,
0.09521484375,
-0.01446533203125,
0.0172119140625,
0.0081787109375,
-0.059326171875,
0.05419921875,
-0.05078125,
0.03015136... | 38,464 | 38464 | |
Ball At Max Height
November 17th 2008, 10:23 PM #1
MHF Contributor
Joined
Jul 2008
From
NYC
Posts
1,489
Ball At Max Height
Vanessa throws a tennis ball in the air.
The function h(
t) = –16t^2 + 45t + 7 represents the distance, in feet, that the ball is from the ground at any
time t. At w... | 4 | [
-0.009521484375,
0.07666015625,
0.032470703125,
-0.119140625,
-0.034423828125,
0.0257568359375,
-0.03271484375,
0.1669921875,
-0.027099609375,
0.07373046875,
0.037841796875,
0.028564453125,
0.0037078857421875,
0.11865234375,
0.005584716796875,
0.06591796875,
0.0537109375,
-0.083496... | 38,465 | 38465 | |
I have a quiz
August 14th 2006, 07:43 PM
Candy
I have a quiz
If the distance to a sound source is halved, how will the sound intensity level change?
a) increase by a factor of 2
b) depends on the actual distance
c) increase by a factor of 4.
d) increase by 6 dB
e) increase by 3 dB
August 14... | 5 | [
0.034912109375,
-0.037109375,
0.00994873046875,
-0.03564453125,
-0.004486083984375,
-0.0012664794921875,
-0.0208740234375,
-0.01239013671875,
-0.036865234375,
0.01422119140625,
-0.032470703125,
-0.0233154296875,
0.0240478515625,
-0.0230712890625,
0.060302734375,
0.035400390625,
0.088... | 38,466 | 38466 | |
A 200 g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At t = 0 s, the mass is at x = 5.0... - Homework Help - eNotes.com
A 200 g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At t = 0 s, the mass is at x = 5.0 cm and has vx = -30 cm/s. Determine the k.
We know th... | 4 | [
0.017578125,
0.04248046875,
-0.0205078125,
-0.006072998046875,
-0.08544921875,
0.01495361328125,
-0.021240234375,
-0.015625,
-0.0238037109375,
0.0732421875,
0.0830078125,
-0.0791015625,
0.0225830078125,
-0.0272216796875,
0.05078125,
0.0218505859375,
-0.0159912109375,
0.07421875,
... | 38,467 | 38467 | |
ervi
Overview of the RegularChains[ConstructibleSetTools] Subpackage
Calling Sequence
RegularChains[ConstructibleSetTools][command](arguments)
command(arguments)
Description
• The RegularChains[ConstructibleSetTools] subpackage is a collection of commands for manipulating these two types of algebraic objec... | 5 | [
-0.07373046875,
0.05322265625,
-0.08642578125,
-0.0084228515625,
-0.048095703125,
-0.025390625,
-0.0002155303955078125,
0.029296875,
-0.048583984375,
-0.055908203125,
0.004302978515625,
-0.072265625,
0.032958984375,
-0.045166015625,
-0.00848388671875,
-0.038330078125,
-0.06494140625,... | 38,468 | 38468 | |
What is the limit of the sequence an=(n^2-n+7)/(2n^3+n^2) ?n tends to infinite - Homework Help - eNotes.com
What is the limit of the sequence an=(n^2-n+7)/(2n^3+n^2) ?
n tends to infinite
We'll force the factor n^2 to numerator and we'll get:
lim an = lim n^2*(1 - 1/n + 7/n^2)/(2n^3+n^2)
We'll force the factor n^3 ... | 5 | [
-0.0419921875,
0.05029296875,
-0.035888671875,
0.10498046875,
-0.016845703125,
0.026611328125,
-0.00154876708984375,
-0.01446533203125,
0.02783203125,
-0.04248046875,
-0.002227783203125,
-0.07861328125,
-0.0032958984375,
0.1005859375,
-0.057373046875,
-0.09619140625,
-0.0225830078125... | 38,469 | 38469 | |
Infinitely uniform line charge
April 7th 2009, 06:27 AM
august
Infinitely uniform line charge
Hi all,
In fact, this is a classical integral, whose answer is always given without showing the steps, in electromagnetism.
In Cylindrical coordinates
$<br /> \int_{+\infty}^{-\infty} \! \frac{\rho r \hsp... | 5 | [
-0.0888671875,
0.05908203125,
-0.0546875,
-0.01556396484375,
0.056884765625,
-0.078125,
0.0272216796875,
0.018798828125,
-0.08154296875,
0.0022430419921875,
0.0184326171875,
-0.0135498046875,
0.058837890625,
0.0751953125,
-0.03662109375,
-0.035400390625,
0.00165557861328125,
-0.039... | 38,470 | 38470 | |
Trivial canonical bundle of a Ricci-flat, simplyconnected Kähler manifold
up vote 3 down vote favorite
1
Hallo,
I have two questions where I do not really know how to deal with them. Let $(M,J,g)$ be a Kähler manifold, where $g$ is the Riemannian metric and denote by $\omega(\cdot , \cdot) = g(J \cdot , \cdot)
$ the ... | 5 | [
-0.078125,
-0.0203857421875,
0.02978515625,
0.050537109375,
-0.064453125,
0.087890625,
0.0191650390625,
0.042724609375,
-0.01513671875,
-0.046875,
0.10205078125,
-0.014892578125,
-0.05322265625,
0.00107574462890625,
0.068359375,
0.004547119140625,
-0.0546875,
0.047607421875,
-0.0... | 38,471 | 38471 | |
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: The integration test suites for Sage.
Replies: 14 ... | 4 | [
-0.056396484375,
-0.029296875,
0.042724609375,
0.050537109375,
0.021240234375,
-0.061767578125,
-0.056884765625,
0.029052734375,
-0.03271484375,
0.0146484375,
0.06201171875,
0.0283203125,
-0.0235595703125,
0.099609375,
0.0021209716796875,
0.0252685546875,
0.044921875,
-0.0390625,
... | 38,472 | 38472 | |
product rule in norm space
November 17th 2012, 05:28 AM #1
Junior Member
Joined
Oct 2012
From
uk
Posts
41
product rule in norm space
the product rule fn->f , gn->g implies fngn->fg true in the normed
vector space (C[0,1],||.||) depends on the the norm||.||. Give a proof or a
counterexample fo... | 5 | [
-0.0517578125,
-0.07421875,
0.004425048828125,
-0.0296630859375,
-0.0281982421875,
0.025634765625,
0.103515625,
0.0004520416259765625,
-0.041748046875,
-0.0048828125,
0.0107421875,
0.0400390625,
0.0390625,
-0.02587890625,
-0.06884765625,
-0.0283203125,
-0.054443359375,
-0.012390136... | 38,473 | 38473 | |
Differentials
Hi guys! I ve got this very difficult exercise for my uni. Could someone please help? Thank you in advance. http://img2.immage.de/200270494rszexercise2.jpg
Thanks for looking into my problem Prove It. I have inserted a picture of the exercise but it seems that you could not see it. I have now uploaded it... | 5 | [
-0.0947265625,
0.0113525390625,
0.0986328125,
-0.007781982421875,
0.045654296875,
0.11279296875,
0.041259765625,
0.0703125,
0.00634765625,
0.05322265625,
0.055908203125,
-0.023681640625,
0.042724609375,
0.005157470703125,
-0.0537109375,
0.006439208984375,
-0.040283203125,
0.0366210... | 38,474 | 38474 | |
Series Solution of PDE Non-Homogeneous BCS
August 2nd 2010, 09:55 AM
lvleph
Series Solution of PDE Non-Homogeneous BCS
I thought I had these problems down, but I found one for which I am having trouble.
$u_t = u_{xx} - u,\quad 0<x<\pi,\; t>0$
$u_x(0,t) = 1,\; u_x(\pi,t) = -1,\; t>0$
$u(x,0) = 0,\;... | 5 | [
-0.1376953125,
0.006591796875,
0.08251953125,
0.0218505859375,
-0.0157470703125,
0.06640625,
0.0101318359375,
-0.03173828125,
0.0028839111328125,
-0.047607421875,
0.01104736328125,
-0.06884765625,
-0.03173828125,
-0.05322265625,
-0.0296630859375,
-0.0223388671875,
-0.0037078857421875... | 38,475 | 38475 | |
Please Help: find the area of the region
March 18th 2008, 11:29 AM
waite3
Please Help: find the area of the region
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.
y=6cos(x), y=(2sec(x))^2, x=-pi/4, x=pi/4
I keep getti... | 5 | [
0.064453125,
-0.05224609375,
0.0284423828125,
-0.02978515625,
-0.045166015625,
-0.00714111328125,
-0.0439453125,
0.08056640625,
0.0174560546875,
-0.03857421875,
0.047607421875,
0.057861328125,
-0.038330078125,
-0.020263671875,
0.02734375,
0.021728515625,
-0.000946044921875,
-0.0463... | 38,476 | 38476 | |
Finding y-intercepts
Date: 6/12/96 at 19:2:1
From: Ourpond
Subject: Linear Equations
Dear Dr. Math:
I'm having a problem with finding y-intercepts. How do you know what
the y-intercept is for the following equations?
2x + y = 3 or x - 4y + 8 = 0
I'm also having trouble with this: Draw the graph of each line:
x-in... | 4 | [
0.0045166015625,
-0.034912109375,
-0.0537109375,
-0.03125,
0.0439453125,
0.058837890625,
-0.0054931640625,
0.044189453125,
0.009033203125,
0.04150390625,
0.064453125,
-0.000370025634765625,
-0.0291748046875,
0.0032806396484375,
0.00689697265625,
0.09228515625,
-0.1103515625,
-0.050... | 38,477 | 38477 | |
Supplier Order Allocation
Order allocation issues among
multiple suppliers in B2B E-market places
Jishnu Hazra (hazra@iimb.ernet.in)
B. Mahadevan (mahadev@iimb.ernet.in)
Sudhi Seshadri (seshadri@iim... | 4 | [
-0.041748046875,
-0.0223388671875,
-0.06494140625,
0.00799560546875,
-0.058837890625,
0.020751953125,
0.03271484375,
0.045166015625,
0.0274658203125,
-0.024658203125,
-0.02294921875,
0.028076171875,
0.07666015625,
-0.02880859375,
0.027099609375,
0.02978515625,
-0.04833984375,
-0.10... | 38,478 | 38478 | |
Version of Lights-Out Puzzle Using Buttons
Date: 09/02/2004 at 12:04:32
From: James
Subject: Puzzle algebra
You have 36 buttons placed in a 6x6 grid. Each button can be either
visible or invisible. The difference between a visible and an
invisible button is that you cannot press an invisible button. When
you press... | 5 | [
-0.0145263671875,
-0.04345703125,
-0.10693359375,
0.0037384033203125,
-0.052978515625,
0.02294921875,
-0.037109375,
-0.032958984375,
-0.07470703125,
0.0908203125,
-0.0118408203125,
0.0272216796875,
0.03125,
-0.004669189453125,
-0.00032806396484375,
0.010009765625,
-0.06787109375,
-... | 38,479 | 38479 | |
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: Actuarial: An Introduction to Mortality
Replies: 1... | 4 | [
-0.006195068359375,
-0.08642578125,
-0.00885009765625,
0.004730224609375,
0.047607421875,
0.072265625,
-0.007568359375,
0.08447265625,
0.005401611328125,
0.0302734375,
0.1357421875,
-0.0026397705078125,
0.091796875,
0.006622314453125,
-0.040283203125,
0.0032501220703125,
-0.133789062... | 38,480 | 38480 | |
Compound Probabilities
Date: 6/28/96 at 21:6:53
From: Johnny Vogler
Subject: Compound probabilities
Dear Dr. Math,
I want to learn how to find the probability of various values of an
expression that is a linear combination of random numbers with uniform
probability density within a certain range, say zero to one.
... | 5 | [
0.005706787109375,
-0.0028533935546875,
-0.0059814453125,
-0.037841796875,
-0.0137939453125,
0.04443359375,
0.12060546875,
-0.091796875,
-0.00970458984375,
0.0029754638671875,
-0.0693359375,
-0.0556640625,
0.049072265625,
0.06640625,
0.02685546875,
-0.048095703125,
-0.0211181640625,
... | 38,481 | 38481 | |
nontrivial cube root of unity
up vote 0 down vote favorite
Hi,
I have a finite field Fp with p = 11 mod(12) and I am trying to get the third nontrivial root of unity in Fp^2 = Fp^2[x]/(x^2+1). So, i need x where x^3=1.
Somehow I came into a source saying that it would be: (p-1)/2 + (3^((p+1)/4)) mod(p))*i where i^2=... | 4 | [
-0.01708984375,
0.0361328125,
-0.01806640625,
0.06787109375,
0.00885009765625,
-0.0291748046875,
0.0478515625,
0.0228271484375,
-0.01068115234375,
-0.040771484375,
-0.028076171875,
0.056396484375,
-0.00653076171875,
0.0262451171875,
-0.0263671875,
-0.018310546875,
-0.04736328125,
-... | 38,482 | 38482 | |
Relations question
February 16th 2009, 06:14 PM #1
Newbie
Joined
Jan 2009
Posts
21
Relations question
My textbook does an erratic job of presenting relations to the reader, my professor is of no help, and I'm thoroughly puzzled, particularly with this question.
For each of the following relations de... | 4 | [
-0.016845703125,
-0.0537109375,
0.0244140625,
-0.034423828125,
-0.041015625,
-0.025634765625,
-0.027587890625,
-0.0380859375,
-0.0038299560546875,
0.049072265625,
-0.061279296875,
-0.0037078857421875,
0.03564453125,
0.0185546875,
-0.049072265625,
0.031494140625,
0.07177734375,
-0.0... | 38,483 | 38483 | |
Vector / Scalar Projection
April 3rd 2009, 08:59 PM
Russ
Vector / Scalar Projection
This question has me majorly confused. I've been going quite well so far at Calculus (that's the name of the subject) but this question has me completely stumped. Complete answers aren't
necessary since I want to get this don... | 4 | [
-0.0289306640625,
0.0035400390625,
-0.051025390625,
-0.1484375,
0.0250244140625,
0.00136566162109375,
0.0264892578125,
-0.08349609375,
-0.053955078125,
-0.0159912109375,
-0.0269775390625,
-0.0264892578125,
0.0294189453125,
0.06884765625,
-0.060546875,
-0.0458984375,
-0.01416015625,
... | 38,484 | 38484 | |
Different notions of associated prime (in the non Noetherian case)
up vote 7 down vote favorite
2
Most books I have treat primary decomposition only in the Noetherian case. Atyiah-MacDonald goes a step further and prover the uniqueness theorems of primary decomposition without the Noetherian
hypothesis. But it seems t... | 5 | [
-0.058349609375,
0.0260009765625,
-0.033935546875,
-0.0267333984375,
0.087890625,
-0.06787109375,
0.06103515625,
0.0225830078125,
0.0274658203125,
-0.023681640625,
0.03173828125,
0.028076171875,
0.07666015625,
-0.0230712890625,
-0.0196533203125,
0.037353515625,
0.0103759765625,
0.0... | 38,485 | 38485 | |
Indices Algebra
July 17th 2012, 03:59 AM #1
Newbie
Joined
Jul 2012
From
Earth
Posts
3
Indices Algebra
I have two questions that needs to be solved with algebra, please help, i figured out the answers to be -4 for the first and -1 for the second but i dont know the steps solving it with algebra.
... | 4 | [
0.017822265625,
-0.0079345703125,
0.029052734375,
0.0888671875,
0.02197265625,
-0.1220703125,
0.0537109375,
0.0294189453125,
-0.07568359375,
0.02197265625,
-0.001678466796875,
-0.12109375,
0.07275390625,
0.07421875,
-0.0380859375,
0.07080078125,
-0.04931640625,
-0.09521484375,
-0... | 38,486 | 38486 | |
Bayesian Variable Transformation (solve for PDF)
September 15th 2011, 03:03 PM
Dwaffle
Bayesian Variable Transformation (solve for PDF)
Hi I'm struggling with where to start for this variable transformation problem.
X~Bin(N,p) so that p(X=x) = (N choose x) * (p^x) * (1-p)^(N-x)
Use a uniform prior p(p)... | 4 | [
-0.040771484375,
-0.0234375,
0.0634765625,
-0.041015625,
0.02197265625,
-0.07177734375,
0.057373046875,
0.0034637451171875,
0.036376953125,
0.054931640625,
0.07177734375,
0.0162353515625,
0.016357421875,
-0.00848388671875,
-0.016357421875,
-0.0284423828125,
0.006866455078125,
-0.03... | 38,487 | 38487 | |
PD3 groups and PD4 complexes
up vote 5 down vote favorite
1
I am interested at the moment in what groups can occur as the fundamental group of a 4-manifold (or more generally, a 4-dimensional CW complex) with prescribed conditions on the intersection form. I
have what I am hoping is a basic homotopy theory question:
... | 5 | [
-0.07958984375,
0.0024261474609375,
0.01312255859375,
-0.050537109375,
-0.0556640625,
0.018798828125,
0.000957489013671875,
-0.06982421875,
0.033447265625,
-0.036865234375,
0.0546875,
-0.033447265625,
-0.056396484375,
-0.034912109375,
0.03759765625,
-0.012451171875,
-0.0771484375,
... | 38,488 | 38488 | |
Simplifying using trig identities
June 3rd 2010, 07:37 AM #1
Junior Member
Joined
Nov 2008
Posts
62
Simplifying using trig identities
Simplify: $\cot(-x) (\cos x) (\tan^2 x + 1)$
I'll show you what I have so far. My problem is I don't really know when I'm finished.
$\cot(-x) (\cos x) (\tan^2 x ... | 4 | [
-0.01495361328125,
0.055908203125,
0.0634765625,
0.052001953125,
-0.01190185546875,
0.03466796875,
0.0189208984375,
-0.0169677734375,
0.046875,
0.007476806640625,
0.12109375,
-0.00634765625,
-0.00994873046875,
0.07177734375,
-0.001678466796875,
-0.01953125,
0.07373046875,
0.0527343... | 38,489 | 38489 | |
Help! Test tomorrow.
December 2nd 2008, 12:42 PM #1
Newbie
Joined
Sep 2008
Posts
10
Help! Test tomorrow.
i have a test tomorrow and i need help with some of the questions on the review. i have like 5 of them. here is the first one.
Find the derivative of the function y=xTanh^-1(lnx)
You need to... | 5 | [
-0.003509521484375,
0.029541015625,
0.11181640625,
-0.005645751953125,
0.07373046875,
-0.0576171875,
0.038818359375,
-0.030517578125,
-0.04296875,
0.041259765625,
0.126953125,
-0.03466796875,
-0.0244140625,
0.06884765625,
-0.041259765625,
0.049560546875,
-0.0654296875,
-0.106445312... | 38,490 | 38490 | |
convergence test
May 13th 2011, 07:28 AM #1
Member
Joined
Nov 2010
Posts
94
convergence test
I have question which to show that sum(1/n)log[1+(1/n)] is convergent. I don't think i can use integral or ratio or raabe's test. I am guessing I have to use limit comparison test ??? Help me !
I haven't lea... | 5 | [
0.04931640625,
0.0145263671875,
-0.02685546875,
0.046630859375,
0.0189208984375,
-0.0966796875,
0.007598876953125,
0.025146484375,
0.0093994140625,
-0.01190185546875,
-0.047607421875,
0.027099609375,
-0.045654296875,
0.08349609375,
-0.091796875,
-0.033447265625,
0.028564453125,
-0.... | 38,491 | 38491 | |
First-order nonlinear DE
November 25th 2010, 05:26 AM #1
First-order nonlinear DE
Hello,
I tried searching similar DE-problems, but I couldn't find one. The problem is following differential equation:
$e^{x}y'+xe^{-y}=0$
So, it seems to be first-order nonlinear DE. But, I don't know how to solve it. ... | 5 | [
-0.08203125,
-0.046142578125,
0.1005859375,
-0.00133514404296875,
-0.032958984375,
-0.01348876953125,
0.0147705078125,
-0.050048828125,
-0.040283203125,
0.09716796875,
0.15625,
-0.037109375,
0.01422119140625,
0.037109375,
0.034423828125,
0.0341796875,
-0.007720947265625,
-0.0087280... | 38,492 | 38492 | |
orsion
General Relativity Tutorial - Torsion
John Baez
Oz asks: "Why do we assume [the connection] in GR is torsion free? A short couple of non-sarcastic information-rich understandable sentences would suffice. Enough to place it in a footnote of the
brain."
Non-sarcastic, eh? You must think I'm really mean and nast... | 4 | [
-0.1162109375,
-0.103515625,
0.035888671875,
-0.0361328125,
-0.01153564453125,
0.0301513671875,
0.0308837890625,
0.001556396484375,
0.111328125,
-0.023193359375,
0.09375,
0.040771484375,
-0.0625,
-0.0625,
0.021728515625,
-0.032958984375,
-0.068359375,
0.02783203125,
-0.0971679687... | 38,493 | 38493 | |
sums and differences of angles
February 20th 2010, 03:47 PM #1
Junior Member
Joined
Sep 2009
Posts
40
sums and differences of angles
If the angles A, B of triangle ABC are such that $cos A = {-4/5}$ and $cos B = {12/13}$, find without using tables the value of Cos C'
Thanks.
$C = \pi - A - B$
... | 4 | [
-0.11865234375,
0.09716796875,
-0.033203125,
-0.02392578125,
-0.06005859375,
0.0908203125,
-0.05810546875,
0.025634765625,
0.0142822265625,
0.00182342529296875,
0.005645751953125,
-0.07421875,
-0.01556396484375,
0.0211181640625,
0.0281982421875,
-0.04638671875,
-0.0240478515625,
-0... | 38,494 | 38494 | |
Is there a good metric under which a sequence of compact sets can converge to an infinite dimensional set?
up vote 3 down vote favorite
I have a sequence of finite-dimensional, compact sets in $L^2(\Omega)$, where $\Omega\subset \mathbf{R}^2$ is closed and bounded. The dimension grows monotonically with the sequence, ... | 4 | [
-0.012451171875,
-0.06201171875,
-0.055419921875,
-0.0181884765625,
0.00927734375,
0.06787109375,
-0.06201171875,
-0.0064697265625,
0.03271484375,
-0.0927734375,
0.0079345703125,
0.07568359375,
0.0164794921875,
-0.032958984375,
-0.0101318359375,
-0.043212890625,
0.00640869140625,
-... | 38,495 | 38495 | |
Linear Damping Model
June 13th 2008, 02:53 AM
moolimanj
Linear Damping Model
Hi all.
I have got the following question regarding a seismograph and what I would like to do is to express the forces acting on the particle in terms of the given variables and parameters and the unit
vector i. Can some one pl... | 4 | [
-0.003143310546875,
0.016845703125,
0.11328125,
-0.00244140625,
-0.031494140625,
0.00897216796875,
-0.00148773193359375,
-0.00994873046875,
-0.00628662109375,
0.05615234375,
0.037841796875,
-0.03271484375,
0.06103515625,
-0.02685546875,
-0.03271484375,
0.05859375,
0.014892578125,
0... | 38,496 | 38496 | |
Help with question on matrices
April 11th 2012, 12:19 AM #1
Newbie
Joined
Apr 2012
From
Texas
Posts
2
Help with question on matrices
Hello
My daughter is doing a college assignment and I managed to help her with the majority of the question but cannot figure out the last part.
I have the cha... | 5 | [
-0.00616455078125,
0.0849609375,
0.034423828125,
0.11376953125,
-0.040283203125,
-0.02734375,
0.01251220703125,
0.01263427734375,
-0.0162353515625,
-0.0211181640625,
0.1376953125,
-0.057373046875,
0.0869140625,
0.016357421875,
-0.0242919921875,
0.08837890625,
-0.0213623046875,
0.01... | 38,497 | 38497 | |
analysis - continuous functions
April 26th 2008, 03:26 AM #1
Member
Joined
Jan 2008
Posts
114
analysis - continuous functions
Just going through past papers as my anaysis exam is on Weds, but I'm quite stuck/unsure about 2 questions I've come across...
If g:[0,1] ---> [0,1] is a continuous function... | 5 | [
-0.04052734375,
-0.01202392578125,
0.06103515625,
0.0263671875,
-0.0478515625,
0.02197265625,
0.11572265625,
0.006866455078125,
-0.041259765625,
-0.03515625,
-0.06494140625,
-0.010986328125,
0.051513671875,
0.041259765625,
-0.04931640625,
-0.035888671875,
0.01904296875,
-0.04003906... | 38,498 | 38498 | |
of
An Exploration of Physics by Dimensional Analysis
The diversity of dimensions of physical quantities and their consequences on how the behaviors of physical systems are shaped, plays an essential role throughout all physics theories. This is somehow
well-known in principle since long ago. However the explanatory ... | 4 | [
-0.0206298828125,
0.0098876953125,
0.046630859375,
0.0859375,
-0.017822265625,
0.009765625,
-0.0771484375,
0.018798828125,
0.06103515625,
-0.007781982421875,
0.0155029296875,
-0.0291748046875,
-0.046630859375,
0.07763671875,
-0.003936767578125,
-0.03173828125,
-0.01031494140625,
0.... | 38,499 | 38499 |