content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
find the 1991st term
January 13th 2011, 06:37 PM
chris86
find the 1991st term
Let 2,3,5,6,7,10,11,... be an increasing sequence of positive integers that are neither the perfect squares nor the cubes. Find the 1991st term.
January 13th 2011, 06:57 PM
chiph588@
Quote:
Let's define $f(n)$ to be the nu... | 5 | [
-0.052001953125,
0.0240478515625,
-0.0703125,
0.04150390625,
-0.0439453125,
0.0810546875,
-0.072265625,
0.06298828125,
-0.00531005859375,
-0.07177734375,
-0.05615234375,
0.0174560546875,
-0.0419921875,
-0.00372314453125,
0.016845703125,
-0.07275390625,
-0.029541015625,
-0.007537841... | 24,000 | 24000 | |
Gauss Lemma (Number Theory)
November 2nd 2008, 10:55 PM #1
Newbie
Joined
Nov 2008
Posts
5
Gauss Lemma (Number Theory)
Use Gauss Lemma (Number theory) to calculate the Legendre Symbol $(\frac{6}{13})$.
I know how to use Gauss Lemma. However we use the book: Ireland and Rosen. They define Gauss Lemma ... | 4 | [
-0.0247802734375,
-0.0048828125,
0.044189453125,
-0.04150390625,
0.06982421875,
-0.01116943359375,
0.07421875,
0.1572265625,
0.046875,
-0.017578125,
0.057373046875,
0.0732421875,
0.035888671875,
-0.01055908203125,
-0.07421875,
-0.07470703125,
0.0108642578125,
-0.09130859375,
0.08... | 24,001 | 24001 | |
help with proof
December 1st 2009, 04:13 PM #1
Member
Joined
Jan 2008
Posts
175
help with proof
Prove the following:
An accumulation point of a set S is either an interior point of S or a boundary point of S.
This seems very logical to me, I just dont know how to prove it.
I know that an a... | 4 | [
-0.000888824462890625,
0.0054931640625,
0.030517578125,
-0.0263671875,
0.08544921875,
0.05419921875,
0.1376953125,
0.024169921875,
0.1171875,
-0.06201171875,
-0.034423828125,
-0.0810546875,
0.11474609375,
0.0037078857421875,
0.06982421875,
-0.09765625,
0.048583984375,
-0.0966796875... | 24,002 | 24002 | |
Brevet US6922452 - Method and apparatus for estimating Doppler spread
FIELD OF THE INVENTION
The present invention relates to mobile radio communications, and more particularly, to estimating Doppler spread in a mobile radio communications system.
BACKGROUND AND SUMMARY OF THE INVENTION
In mobile radio communication... | 4 | [
-0.03076171875,
0.00142669677734375,
0.0087890625,
-0.005859375,
0.03515625,
-0.0281982421875,
0.0235595703125,
0.08447265625,
0.046142578125,
-0.033935546875,
0.01446533203125,
-0.01068115234375,
0.087890625,
-0.06884765625,
-0.0021820068359375,
-0.046142578125,
-0.01275634765625,
... | 24,003 | 24003 | |
On Uncertainty Principle for Quaternionic Linear Canonical Transform
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 725952, 14 pages
http://dx.doi.org/10.1155/2013/725952
Research Article
On Uncertainty Principle for Quaternionic Linear Canonical Transform
^1Department of Mathematics, Faculty of Scienc... | 4 | [
-0.06396484375,
0.0771484375,
0.011962890625,
-0.0859375,
-0.04541015625,
0.0732421875,
-0.0264892578125,
0.018798828125,
0.06591796875,
-0.002655029296875,
0.1376953125,
-0.00164794921875,
0.07763671875,
-0.0166015625,
-0.06640625,
-0.0098876953125,
-0.0927734375,
0.11669921875,
... | 24,004 | 24004 | |
Patent US8144827 - Method for determining a residual frequency offset, communication system, method for transmitting a message, transmitter, method for processing a message and receiver
FIELD OF THE INVENTION
The invention relates to a method for determining a residual frequency offset, a communication system, a metho... | 4 | [
-0.0615234375,
0.060791015625,
-0.040283203125,
-0.0299072265625,
-0.08251953125,
0.040283203125,
0.023681640625,
0.09814453125,
-0.0242919921875,
0.0262451171875,
0.06201171875,
0.08251953125,
0.049072265625,
-0.06396484375,
-0.09375,
-0.08251953125,
0.10791015625,
-0.025634765625... | 24,005 | 24005 | |
indefinite integral
Can anyone please help to find an antiderivative of this function and the method used? (Please see attatchment) Cheers,
Use trigonometric substitution. Let $x = 3\tan{\theta}$ so that $dx = 3\sec^2{\theta}\,d\theta$. Also note that $\theta = \arctan{\frac{x}{3}}$. So the integral becomes: $\int{\fr... | 5 | [
0.0311279296875,
-0.0341796875,
0.044677734375,
0.00616455078125,
0.041259765625,
0.0380859375,
-0.049072265625,
0.01470947265625,
0.00225830078125,
-0.068359375,
0.06689453125,
-0.04248046875,
-0.0751953125,
0.04150390625,
-0.045166015625,
-0.0213623046875,
0.0673828125,
0.0893554... | 24,006 | 24006 | |
Math Help
December 12th 2009, 05:02 AM #1
Member
Joined
Sep 2006
Posts
134
Ratio
We had this in a quiz, my answer was $\sqrt{2} = 1$
but my friends say the answer is 2 = 1 because they squared both sides. but I don't get why the need to square it. so here's the problem.
A square is inscribed i... | 4 | [
0.0634765625,
0.039306640625,
-0.00579833984375,
0.048095703125,
0.03369140625,
-0.040283203125,
-0.053955078125,
0.0673828125,
0.0751953125,
0.006805419921875,
-0.015869140625,
-0.0174560546875,
0.019775390625,
0.09814453125,
0.028564453125,
-0.047119140625,
0.0174560546875,
0.015... | 24,007 | 24007 | |
Equivalent Norms
June 21st 2009, 02:00 PM #1
Junior Member
Joined
Apr 2009
Posts
39
Equivalent Norms
Let ||.||_1 and ||.||_2 be norms on a vector space X
such that X_1 = (X, ||.||_1) and X_2=(X,||.||_2) are complete.
If ||x_n||_1 ---> 0 always implies ||x_n||_2 -----> 0,
show that converge... | 5 | [
-0.0634765625,
-0.05615234375,
-0.055908203125,
-0.1044921875,
0.025390625,
0.03271484375,
0.1044921875,
-0.038818359375,
-0.04736328125,
-0.099609375,
0.07568359375,
0.02001953125,
0.07958984375,
-0.0228271484375,
0.0194091796875,
0.047119140625,
0.06298828125,
-0.06201171875,
-... | 24,008 | 24008 | |
Action of Lie Brackets on vector fields multiplied by functions
tut_einstein
Is there a specific product rule or something one must follow when applying the lie bracket/ commutator to two vector fields such that one of them is multiplied by a function
Yes.
tut_einstein
This is the expression given in my textboo... | 5 | [
-0.0751953125,
-0.03173828125,
0.0869140625,
-0.022216796875,
-0.01275634765625,
0.033935546875,
0.1171875,
-0.02490234375,
0.037353515625,
0.0012664794921875,
0.004180908203125,
0.000400543212890625,
-0.08544921875,
-0.031982421875,
0.060791015625,
0.036376953125,
-0.0927734375,
0... | 24,009 | 24009 | |
Forming first-order difference equation
June 7th 2012, 08:30 AM #1
Newbie
Joined
Oct 2011
Posts
8
Forming first-order difference equation
Hi,
I was wondering if anyone can help with this mathematical economics problem:
The multiplier-accelerator model of growth has the following three equation... | 5 | [
-0.1376953125,
-0.024169921875,
-0.00811767578125,
-0.0128173828125,
0.047607421875,
0.02783203125,
-0.012939453125,
-0.0211181640625,
0.0267333984375,
-0.00927734375,
0.057373046875,
0.033935546875,
-0.00775146484375,
-0.0191650390625,
-0.005645751953125,
0.057861328125,
-0.07568359... | 24,010 | 24010 | |
Showing a formula is a tautology
October 7th 2012, 03:40 AM
Diligo
Showing a formula is a tautology
I'm currently enrolled in a introductory course on logic and I'm until now everything has been going great. I'm having some trouble with applying monotonicity and the strengthening/weakening of
propositions.
... | 5 | [
0.00592041015625,
-0.0361328125,
0.07421875,
-0.056640625,
-0.0250244140625,
0.031494140625,
-0.047119140625,
0.07421875,
0.0732421875,
0.1328125,
-0.05126953125,
0.0042724609375,
0.0478515625,
0.1259765625,
0.12158203125,
0.052001953125,
0.01287841796875,
0.012451171875,
-0.1171... | 24,011 | 24011 | |
Concavity Question
November 6th 2009, 02:59 PM
frozenflames
Concavity Question
Consider the function f(x) = 7x + 8x ^-1. For this function there are four important intervals: (-\infty, A], [A,B),(B,C), and [C,\infty) where A, and C are the critical numbers and the function
is not defined at B.
Find A
... | 4 | [
-0.08544921875,
-0.03173828125,
0.040283203125,
-0.00494384765625,
-0.0150146484375,
0.020751953125,
0.0167236328125,
0.08642578125,
-0.003814697265625,
0.06005859375,
0.0284423828125,
-0.0673828125,
0.0751953125,
0.0198974609375,
-0.0211181640625,
0.04296875,
-0.0673828125,
-0.074... | 24,012 | 24012 | |
Integrability (meaning)
Bill_K
No, integrability means: can a given relationship between derivatives be integrated to yield a relationship between functions. For example, given the system
∂f/∂x = F(x,y)
∂f/∂y = G(x,y)
does f(x,y) exist? Answer, only if an integrability condition is satisfied: ∂^2f/∂x∂y = ∂^2f/∂y∂x... | 5 | [
-0.0167236328125,
-0.045654296875,
0.01251220703125,
-0.10693359375,
0.0380859375,
-0.031494140625,
-0.052734375,
0.02685546875,
-0.10546875,
-0.0247802734375,
-0.060546875,
0.09423828125,
0.0203857421875,
-0.00885009765625,
0.01153564453125,
-0.03466796875,
-0.01904296875,
-0.0120... | 24,013 | 24013 | |
Geometry problem
May 18th 2006, 08:14 AM #1
UFOKatarn
Guest
Geometry problem
First, hello all. Great I found this forum.
Please help me solve this mistery
-----------------------------------------------------------
we have two vertices:
A(1,1)
B(0,2)
and there is also a circle K:
... | 4 | [
-0.015869140625,
0.0634765625,
-0.032470703125,
-0.04638671875,
0.013427734375,
-0.021484375,
0.03857421875,
-0.01104736328125,
-0.001678466796875,
0.00482177734375,
0.01434326171875,
-0.04296875,
-0.0247802734375,
0.06005859375,
0.020263671875,
0.08056640625,
0.02587890625,
-0.031... | 24,014 | 24014 | |
Repeated Game-Inspired Spectrum Sharing for Clustering Cognitive Ad Hoc Networks
International Journal of Distributed Sensor Networks
Volume 2013 (2013), Article ID 514037, 10 pages
http://dx.doi.org/10.1155/2013/514037
Research Article
Repeated Game-Inspired Spectrum Sharing for Clustering Cognitive Ad Hoc Networks
... | 4 | [
0.027587890625,
-0.0380859375,
-0.052490234375,
-0.01190185546875,
0.0341796875,
-0.0281982421875,
0.08251953125,
-0.042724609375,
0.011962890625,
0.050537109375,
-0.020263671875,
0.0181884765625,
0.07275390625,
-0.006195068359375,
0.04052734375,
-0.006317138671875,
0.1279296875,
-... | 24,015 | 24015 | |
Need help w/ pre-calculus summer packet.
August 8th 2009, 04:41 PM #1
Newbie
Joined
Aug 2009
Posts
3
Need help w/ pre-calculus summer packet.
I know my title isn't very descriptive, but there are 3 types of questions i'm in the need of help for. I am very appreciative for any help!
Write the followi... | 4 | [
0.068359375,
0.037353515625,
0.0128173828125,
-0.036376953125,
0.01104736328125,
-0.031494140625,
-0.030029296875,
0.0625,
-0.04296875,
-0.0419921875,
0.03515625,
-0.017578125,
0.06982421875,
0.1005859375,
0.07666015625,
0.11572265625,
0.054443359375,
-0.059814453125,
-0.03833007... | 24,016 | 24016 | |
A Product
September 27th 2006, 10:02 PM #1
Newbie
Joined
Sep 2006
From
New York
Posts
2
A Product
The product (1+x+x^2+x^3+...)(1+x^3+x^6+x^9+...)(1+x^5+x^10+.. .)... is the generating function for the number of partitions of n into odd parts.
How can you replace some of the plus signs with minu... | 5 | [
-0.0849609375,
0.015380859375,
0.06689453125,
0.029052734375,
0.03759765625,
0.0157470703125,
0.0732421875,
0.0286865234375,
-0.02880859375,
-0.052490234375,
0.00689697265625,
-0.076171875,
0.0203857421875,
-0.0072021484375,
-0.002227783203125,
0.013671875,
0.010986328125,
-0.01696... | 24,017 | 24017 | |
Euler problems/181 to 190
From HaskellWiki
< Euler problems
(Difference between revisions)
((183) If we must have a solution here, let's at least have a decent one.) m
← Older edit Newer edit →
Line 34: ... | 5 | [
-0.0267333984375,
0.12060546875,
0.0047607421875,
0.0240478515625,
0.00139617919921875,
-0.0306396484375,
0.0751953125,
0.0576171875,
-0.03564453125,
-0.0341796875,
-0.0849609375,
-0.044921875,
0.005645751953125,
0.078125,
0.006683349609375,
-0.06201171875,
-0.019287109375,
0.00032... | 24,018 | 24018 | |
relateing surface area to volume?
September 5th 2009, 10:53 AM
diver15
relateing surface area to volume?
I have a problem that I can't quite figure out.
If I have a rectangular prism with a length=L width=W and hight=H and L=W, and the volume of this prism is 10,000 then you could write the volume formula a... | 5 | [
0.0126953125,
0.052001953125,
0.00701904296875,
-0.015625,
-0.00157928466796875,
-0.01080322265625,
-0.03271484375,
0.1298828125,
-0.08447265625,
-0.05810546875,
0.00102996826171875,
-0.03173828125,
0.0810546875,
0.08154296875,
-0.049560546875,
0.07666015625,
0.000743865966796875,
... | 24,019 | 24019 | |
flux: surface integral
May 1st 2011, 02:41 AM #1
Junior Member
Joined
Apr 2010
Posts
56
flux: surface integral
Hi,
I need to evaluate the flux integral $\iint F \cdot \hat{n}dS$
for portion of a plane x +2y+3z = 6 in the first octant and vector field F= < xy, -x^2, (x+z) >
How do i go abou... | 4 | [
-0.0196533203125,
0.020751953125,
-0.0087890625,
-0.11279296875,
0.031982421875,
0.0301513671875,
0.0054931640625,
0.08642578125,
-0.1318359375,
0.00689697265625,
-0.072265625,
-0.002655029296875,
-0.0419921875,
-0.0191650390625,
0.02685546875,
-0.01190185546875,
-0.05517578125,
-0... | 24,020 | 24020 | |
Please help solve these system of equations
January 8th 2011, 12:28 PM #1
Newbie
Joined
Dec 2010
Posts
13
Please help solve these system of equations
Y = C + I + G
C = a + bY
Solve for Y and C, assuming I, G, a, and b are known.
I would like someone to show the steps in algebraically solvin... | 5 | [
-0.1376953125,
0.000705718994140625,
0.004302978515625,
0.022216796875,
-0.07861328125,
-0.036865234375,
0.0595703125,
-0.048828125,
-0.043701171875,
0.01806640625,
-0.07080078125,
-0.051513671875,
0.06005859375,
-0.01446533203125,
-0.0286865234375,
0.08056640625,
-0.040283203125,
... | 24,021 | 24021 | |
Determining the best population-level alcohol consumption model and its impact on estimates of alcohol-attributable harms
Abstract
Background
The goals of our study are to determine the most appropriate model for alcohol consumption as an exposure for burden of disease, to analyze the effect of the chosen alcohol con... | 4 | [
0.10009765625,
-0.09521484375,
-0.050048828125,
0.07275390625,
0.046142578125,
0.056640625,
0.004425048828125,
0.058837890625,
0.036376953125,
-0.042236328125,
0.061767578125,
-0.03759765625,
-0.072265625,
0.0211181640625,
-0.0289306640625,
-0.07666015625,
0.0103759765625,
-0.05395... | 24,022 | 24022 | |
Random Attractors for Stochastic Retarded Lattice Dynamical Systems
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 409282, 27 pages
http://dx.doi.org/10.1155/2012/409282
Research Article
Random Attractors for Stochastic Retarded Lattice Dynamical Systems
^1School of Mathematics and Statistics, Henan Un... | 4 | [
-0.0206298828125,
-0.00634765625,
0.0595703125,
0.0220947265625,
0.0576171875,
0.036865234375,
0.08447265625,
-0.05712890625,
0.06787109375,
-0.032470703125,
-0.01416015625,
0.02734375,
0.0947265625,
-0.08447265625,
-0.091796875,
-0.006591796875,
0.040771484375,
-0.00164794921875,
... | 24,023 | 24023 | |
Find theta as a function of phi
May 10th 2011, 03:33 PM #1
Newbie
Joined
May 2011
Posts
18
Find theta as a function of phi
I have found the equation 2\cos \theta \sin \theta \tan \phi +2\sin \theta ^2 -1=0 and want to solve out \theta as a function of \phi .
The history of this equation is from a ph... | 4 | [
-0.0390625,
0.00102996826171875,
0.038330078125,
0.018798828125,
0.01324462890625,
0.0211181640625,
-0.038330078125,
0.08544921875,
-0.00022792816162109375,
0.000843048095703125,
0.028564453125,
0.0634765625,
-0.0322265625,
0.04638671875,
-0.0244140625,
0.005401611328125,
-0.01892089... | 24,024 | 24024 | |
Numerical operations
These procedures implement number-theoretic (integer) division: for positive integers n1 and n2, if n3 and n4 are integers such that then
(quotient n1 n2) => n3
(remainder n1 n2) => n4
(modulo n1 n2) => n4
For integers n1... | 4 | [
-0.06103515625,
0.08642578125,
-0.03564453125,
-0.05615234375,
-0.06884765625,
-0.08740234375,
0.00058746337890625,
0.07080078125,
0.07958984375,
-0.06982421875,
0.0238037109375,
-0.0130615234375,
0.032470703125,
0.03369140625,
-0.06787109375,
-0.0537109375,
-0.052490234375,
0.0380... | 24,025 | 24025 | |
New Exact Solutions of Ion-Acoustic Wave Equations by (
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 810729, 11 pages
http://dx.doi.org/10.1155/2013/810729
Research Article
New Exact Solutions of Ion-Acoustic Wave Equations by ()-Expansion Method
School of Mathematical Sciences, Universiti Kebangsaa... | 5 | [
-0.06787109375,
0.007415771484375,
0.109375,
0.01507568359375,
-0.0693359375,
0.01953125,
-0.0284423828125,
-0.04052734375,
0.000385284423828125,
0.03271484375,
0.09375,
-0.039306640625,
-0.040283203125,
0.004730224609375,
0.027587890625,
-0.09423828125,
-0.032958984375,
-0.0048828... | 24,026 | 24026 | |
-Semigroups and Fractional Abstract Cauchy Problems
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 357821, 9 pages
http://dx.doi.org/10.1155/2014/357821
Research Article
Convoluted Fractional -Semigroups and Fractional Abstract Cauchy Problems
^1School of Mathematics and Statistics, Xi’an Jiaotong Univ... | 4 | [
-0.09423828125,
0.043701171875,
0.06005859375,
0.0015869140625,
-0.01513671875,
0.01470947265625,
0.035400390625,
-0.0810546875,
-0.00897216796875,
0.05224609375,
0.029541015625,
-0.056396484375,
0.001678466796875,
0.0213623046875,
0.0341796875,
-0.0009307861328125,
-0.00297546386718... | 24,027 | 24027 | |
Fractional Linear Transforms
Complex Numbers, Fractional Linear Transforms
Fractional Linear Transforms
Consider the function f(z) = cz, where c is a complex constant. You may recognize this as a linear transform on the xy plane, since c(a+b) = ca+cb, and c(rz) = rcz for any real number r. However, not
all transforms... | 4 | [
-0.1279296875,
-0.0068359375,
-0.0693359375,
-0.01092529296875,
-0.022216796875,
-0.006561279296875,
-0.10107421875,
-0.0693359375,
0.0625,
0.01318359375,
0.0218505859375,
-0.01611328125,
0.020263671875,
0.035400390625,
0.0023345947265625,
-0.0390625,
-0.0849609375,
0.09765625,
-... | 24,028 | 24028 | |
Question regarding angular momentum and velocity.As it relates to a new rate rotation
jayced
To solve this problem, use conservation of angular momentum.
The initial angular momentum is
L = I ω
I is the initial moment of inertia=2.40 kg-m²
ω is the initial angular velocity 1.15 rev / sec
converted to into radians... | 4 | [
-0.0181884765625,
0.0133056640625,
-0.0054931640625,
-0.043212890625,
-0.032958984375,
-0.042724609375,
-0.033203125,
0.0390625,
-0.004119873046875,
0.05126953125,
0.1162109375,
-0.0849609375,
-0.00384521484375,
-0.024658203125,
0.0260009765625,
0.1064453125,
-0.0213623046875,
0.11... | 24,029 | 24029 | |
Test at 7pm, stuck on Trig Integrals.
March 4th 2008, 11:46 AM #1
Junior Member
Joined
Mar 2008
From
Ohio
Posts
26
There are two problems on our practice test/solution that I just can't seem to grasp. The first is: Int(tan^2 (x)dx) ... The solution is tanx-x+c, but I don't understand how the prof. got... | 5 | [
-0.048828125,
0.041259765625,
0.043701171875,
0.047119140625,
-0.003143310546875,
0.0205078125,
0.0517578125,
-0.068359375,
-0.0189208984375,
0.0244140625,
0.010498046875,
-0.0302734375,
-0.060302734375,
0.036376953125,
0.003662109375,
-0.025146484375,
0.028564453125,
0.06689453125... | 24,030 | 24030 | |
Composite function
August 6th 2008, 01:53 PM
Snowboarder
Composite function
So composition function is s(x) = ln(ln(x)) and natural domain is (1, +infinity)
So s(s(x)) = s(ln(ln(x)) = ln(ln(ln(ln(x)))) .
Is natural domain this function also (1,+infinity)????
What is the axes intercepts of y = s(s(x))... | 4 | [
-0.0130615234375,
-0.09912109375,
-0.04638671875,
-0.0274658203125,
0.06982421875,
-0.006439208984375,
-0.0322265625,
-0.00628662109375,
0.006134033203125,
0.0247802734375,
0.1044921875,
-0.035888671875,
0.037353515625,
0.0274658203125,
0.04296875,
-0.0294189453125,
-0.1259765625,
... | 24,031 | 24031 | |
Area Integral
January 25th 2011, 11:24 PM
menco
Area Integral
I need to find the area of the region between the parabpla y^2 = 16x an the line 4x-3y=4.
I understand that i need to get them to both equal y but when i do that i seem to confuse myself and get really odd values.
January 26th 2011, 12:22 AM
Fe... | 5 | [
0.031494140625,
-0.0240478515625,
-0.059326171875,
-0.027587890625,
-0.033447265625,
-0.055419921875,
-0.0264892578125,
0.02734375,
-0.01434326171875,
-0.08447265625,
0.06005859375,
0.0189208984375,
-0.003387451171875,
0.087890625,
0.0283203125,
0.0830078125,
-0.01043701171875,
-0.... | 24,032 | 24032 | |
How do I find the mean of categorical data?
April 21st 2010, 06:56 AM
Warrenx
How do I find the mean of categorical data?
here is my problem:
I am doing this lab on streaks in basketball, like 0=miss, 1=hit once, 2= hit two in a row.. so on.
I need to find the mean of this data in terms of its streak, ... | 4 | [
0.05126953125,
0.022705078125,
0.02197265625,
-0.05712890625,
-0.06494140625,
0.033203125,
-0.02880859375,
0.06689453125,
0.0257568359375,
0.014404296875,
0.00848388671875,
-0.046142578125,
0.01422119140625,
-0.06201171875,
0.031982421875,
-0.02197265625,
-0.07177734375,
-0.0432128... | 24,033 | 24033 | |
Maximum Likehood Estimator
February 6th 2009, 06:12 PM #1
Junior Member
Joined
Nov 2007
Posts
58
Maximum Likehood Estimator
If f_Y(y;theta) = (theta*k^theta)*(1/y)^(theta+1), y>=k, theta>=1,
a) Find the maximum likelihood estimator for theta if information has been collected on a random sample of 25... | 4 | [
-0.03173828125,
-0.06298828125,
0.017578125,
-0.1044921875,
0.02294921875,
-0.05517578125,
0.06494140625,
-0.0234375,
0.006744384765625,
0.0810546875,
0.056640625,
0.015869140625,
0.052734375,
-0.0157470703125,
-0.09228515625,
0.0849609375,
-0.01129150390625,
0.0062255859375,
-0.... | 24,034 | 24034 | |
Calculating Work and Mechanical Energy - Block on Ramp
A lot of the time, I don't know exactly where to start (at all). My instinct here was to draw a force diagram, figure out friction, do a billion different things to get Forcenet.
But actually I asked my teacher and all I needed was to draw a triangle to figure out... | 4 | [
-0.042236328125,
0.02099609375,
0.0240478515625,
-0.0242919921875,
-0.0137939453125,
-0.0537109375,
-0.04296875,
0.0869140625,
-0.0263671875,
0.0693359375,
-0.035888671875,
-0.03955078125,
-0.04248046875,
0.0264892578125,
0.00885009765625,
0.06298828125,
0.014892578125,
0.047607421... | 24,035 | 24035 | |
Proof (Problem Solving)
October 20th 2010, 09:18 AM
matgrl
Proof (Problem Solving)
Prove that is p is a prime number greater than 3, then p^2 leaves a reamainder of 1 when it is divided by 12.
Is there a form I could use as a prime number to show this works for all odd numbers?
October 20th 2010, 06:05 PM... | 4 | [
-0.0274658203125,
0.0712890625,
0.01239013671875,
0.034423828125,
0.0277099609375,
0.0206298828125,
0.05419921875,
0.04150390625,
0.044189453125,
-0.0020751953125,
-0.06689453125,
0.06298828125,
-0.0283203125,
0.0439453125,
-0.06982421875,
-0.107421875,
-0.02978515625,
0.0649414062... | 24,036 | 24036 | |
Random Variables
April 5th 2010, 09:44 PM
jjbrian
Random Variables
A special deck of 50 cards has 5 colors (red, white, blue, purple, and gold); for each color, there are cards numbered 1 through 10. 15 cards are picked at random without replacement from this
deck. Let X be the number of purple cards picked.... | 5 | [
-0.021484375,
0.059814453125,
0.0625,
-0.0048828125,
0.039306640625,
0.031982421875,
0.08447265625,
0.0030517578125,
0.0245361328125,
-0.02734375,
0.045654296875,
-0.037841796875,
0.0152587890625,
0.056884765625,
-0.032958984375,
0.08447265625,
-0.01055908203125,
-0.04248046875,
... | 24,037 | 24037 | |
Von Neumann Entropy of GHZ state
Register to reply
by neu
Tags: entropy, neumann, state
P: 245 I just wanted to run this working by some of you.
Simplest Greenberger-Horne-Zeilinger state (entagled) s... | 5 | [
-0.045166015625,
0.00244140625,
-0.08349609375,
-0.0040283203125,
-0.119140625,
0.02294921875,
0.0439453125,
-0.0771484375,
-0.06298828125,
-0.03466796875,
-0.00201416015625,
-0.115234375,
0.058349609375,
0.005584716796875,
-0.05859375,
0.07177734375,
0.004913330078125,
-0.11572265... | 24,038 | 24038 | |
Momentum Bar Charts (IF Charts, IFF Charts)
Disclaimer: I most certainly did not come up with this type of diagram, though the name (IF charts) is probably unique to my classes since it’s based on the way one of my first Modeling Physics
students drew her bar charts. This post is meant to be a how-to and a why-to guide... | 4 | [
0.00244140625,
-0.0206298828125,
0.0380859375,
-0.0751953125,
0.042724609375,
0.0294189453125,
-0.0211181640625,
0.04248046875,
0.11376953125,
0.01348876953125,
0.09423828125,
-0.00958251953125,
-0.0296630859375,
0.032470703125,
0.031494140625,
-0.01513671875,
0.0419921875,
-0.0294... | 24,039 | 24039 | |
Why do smaller black holes emit more Hawking radiation?
tensor33
Why is it that the smaller a black hole is, the more Hawking radiation it emits? It seems counterintuitive to me. I would think that a larger black hole with a larger surface area would trap more
antiparticles from virtual particle antiparticle pairs, ... | 4 | [
0.09912109375,
-0.026123046875,
0.0341796875,
0.12109375,
0.07666015625,
-0.05322265625,
0.01019287109375,
0.07177734375,
0.06640625,
-0.031982421875,
-0.07080078125,
-0.048828125,
-0.0198974609375,
0.016357421875,
0.01165771484375,
0.02880859375,
0.126953125,
-0.0155029296875,
-... | 24,040 | 24040 | |
Quadratic proof
February 22nd 2013, 04:22 AM #1
Newbie
Joined
Feb 2013
From
US
Posts
14
Thanks
3
Quadratic proof
I was doing some problems last night, and I came across this one and I am not sure how to get started.
If the polynomial $Eq. A: ax^2+bx+c$ does not have any (real*) roots, prove ... | 4 | [
-0.0712890625,
-0.017578125,
0.000736236572265625,
0.0301513671875,
-0.08154296875,
0.064453125,
-0.04443359375,
0.0247802734375,
0.060302734375,
-0.0013885498046875,
0.06298828125,
-0.019287109375,
0.0196533203125,
0.0673828125,
0.007476806640625,
0.064453125,
0.02880859375,
-0.01... | 24,041 | 24041 | |
On the Generalized Krätzel Transform and Its Extension to Bohemian Spaces
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 841585, 7 pages
http://dx.doi.org/10.1155/2013/841585
Research Article
On the Generalized Krätzel Transform and Its Extension to Bohemian Spaces
^1Department of Applied Sciences, Fac... | 5 | [
-0.0966796875,
0.11572265625,
0.00133514404296875,
0.00469970703125,
-0.0201416015625,
0.051025390625,
0.01385498046875,
-0.005584716796875,
0.049560546875,
-0.026123046875,
0.048583984375,
-0.024658203125,
0.0191650390625,
-0.0257568359375,
-0.00567626953125,
-0.03466796875,
-0.1079... | 24,042 | 24042 | |
Radioactive Decay
December 10th 2005, 07:11 PM #1
Newbie
Joined
Dec 2005
Posts
2
In the formula A=Ie^kt, A is the amount of radioactive material remaining from an initial amount I at a given time t, and k is the negative constant determined by the nature of the material. An
artifact is discovered at a... | 5 | [
-0.0400390625,
0.0927734375,
0.052978515625,
0.064453125,
0.00982666015625,
-0.09228515625,
0.0072021484375,
0.1064453125,
0.0167236328125,
0.05810546875,
0.10107421875,
-0.0703125,
0.050537109375,
0.06005859375,
-0.01806640625,
0.0308837890625,
-0.052001953125,
-0.056396484375,
... | 24,043 | 24043 | |
Most General solution of Laplace's equation
January 16th 2009, 05:35 AM
Jason Bourne
Most General solution of Laplace's equation
Laplace's equation written in plane polar coordinates $(r,\theta)$ is
$T_{rr} + \frac{1}{r}T_r + \frac{1}{r^2}T_{\theta \theta} = 0$
I need to find the most general solution ... | 5 | [
-0.08935546875,
-0.0208740234375,
0.020263671875,
-0.01416015625,
0.06201171875,
0.004730224609375,
0.0079345703125,
-0.0020904541015625,
0.033935546875,
0.03369140625,
0.019287109375,
0.0218505859375,
-0.03271484375,
0.12109375,
-0.01519775390625,
-0.06884765625,
-0.0380859375,
-0... | 24,044 | 24044 | |
Math Help
In a right triangle given a=32.8ft and A= 28 deg 30’15” , solve for b and c
$\left(28+\frac{30}{60}+\frac{15}{360} \right)^\circ =\frac{685 }{24}^\circ$ Using the Sine Rule: $\frac{a}{\sin A}=\frac{b}{\sin B} = \frac{c}{\sin C}$ $\frac{32.8}{\sin(\frac{685}{24})}=\frac{c}{\
sin90}$ $c \approx 68.65$ Use pyt... | 4 | [
-0.026611328125,
0.103515625,
-0.0302734375,
0.041015625,
-0.059326171875,
0.0118408203125,
-0.08544921875,
0.07177734375,
-0.034423828125,
0.03271484375,
0.0260009765625,
-0.07861328125,
0.0157470703125,
0.055419921875,
0.05078125,
0.05859375,
-0.07666015625,
0.07470703125,
-0.0... | 24,045 | 24045 | |
Probability question
January 1st 2012, 06:22 PM #1
Junior Member
Joined
Feb 2011
Posts
56
Probability question
A and B play a series of similar game. The probability that A will win a set is 3/5, and there is no draw for each set. The game will continue until one of them, A or B win 2 sets. Find the
... | 5 | [
-0.0546875,
-0.061767578125,
0.018310546875,
-0.12255859375,
-0.0830078125,
0.068359375,
0.0390625,
-0.055908203125,
0.0546875,
0.10009765625,
-0.0546875,
-0.053466796875,
0.01904296875,
-0.0038299560546875,
0.043701171875,
0.0810546875,
-0.00433349609375,
-0.07666015625,
0.01269... | 24,046 | 24046 | |
Optimization of Training Signal Transmission for Estimating MIMO Channel under Antenna Mutual Coupling Conditions
International Journal of Antennas and Propagation
Volume 2010 (2010), Article ID 213576, 10 pages
http://dx.doi.org/10.1155/2010/213576
Research Article
Optimization of Training Signal Transmission for Es... | 4 | [
0.0233154296875,
-0.04248046875,
-0.00604248046875,
-0.00017642974853515625,
0.0145263671875,
-0.01507568359375,
-0.0341796875,
0.006988525390625,
-0.034423828125,
-0.04248046875,
-0.03466796875,
0.0830078125,
0.10107421875,
0.023193359375,
-0.0213623046875,
0.01531982421875,
0.00299... | 24,047 | 24047 | |
Inequality
November 23rd 2008, 01:51 AM #1
Inequality
Can anyone tell me how my book went from point a to b?
$<br /> |x^2 - 1| < 2 \Rightarrow - \sqrt 3 < x < \sqrt 3 <br />$
I just don't see it...thanks.
Try drawing the graphs of $y = |x^2 - 1|$ and $y = 2$. Now calculate the x-coordinate of the i... | 4 | [
0.01171875,
-0.05419921875,
-0.0107421875,
-0.031982421875,
-0.01263427734375,
-0.034912109375,
-0.034912109375,
0.056640625,
0.0308837890625,
-0.05419921875,
-0.01141357421875,
0.02294921875,
0.10595703125,
0.0166015625,
-0.0289306640625,
0.057373046875,
0.0264892578125,
-0.130859... | 24,048 | 24048 | |
Connected subset
October 19th 2010, 12:35 PM
tarheelborn
Connected subset
If $S \subseteq \mathbb{R}$ is bounded below but not bounded above, then $S$ is either $\left( a,\infty \right]$ or $\left[ a,\infty \right)$ for some $a \in \mathbb{R}$.
I know from a previously proved theorem that if $S$ is a connec... | 4 | [
-0.01953125,
0.006927490234375,
-0.03662109375,
0.01904296875,
-0.01129150390625,
0.13671875,
0.015869140625,
0.04931640625,
0.022705078125,
-0.01336669921875,
-0.1044921875,
0.08154296875,
0.080078125,
-0.01336669921875,
-0.032470703125,
-0.052734375,
0.07373046875,
-0.08837890625... | 24,049 | 24049 | |
Modular Analysis of Sequential Solution Methods for Almost Block Diagonal Systems of Equations
Advances in Numerical Analysis
Volume 2013 (2013), Article ID 563872, 7 pages
http://dx.doi.org/10.1155/2013/563872
Research Article
Modular Analysis of Sequential Solution Methods for Almost Block Diagonal Systems of Equat... | 4 | [
-0.11962890625,
0.0986328125,
0.009765625,
-0.003814697265625,
0.03369140625,
0.00579833984375,
-0.0712890625,
-0.0011138916015625,
-0.00095367431640625,
-0.0274658203125,
0.09423828125,
0.044189453125,
-0.0262451171875,
-0.04931640625,
-0.0537109375,
0.021240234375,
-0.038818359375,... | 24,050 | 24050 | |
Fractions
Last edited by CSG18; February 18th 2010 at 07:34 AM.
The LCD of 6 and 216 is 216. Multiply the first term by 36/36 $\frac{36}{36} \cdot \frac{3\sqrt{2}}{6} = \frac{108 \sqrt2}{216}$ Now they have the same denominator they can be combined $\frac{108 \
sqrt{2} - 8 \sqrt{2}}{216}$ Factor out $\sqrt{2}$ $\frac{... | 4 | [
0.02197265625,
-0.0250244140625,
-0.02294921875,
-0.025390625,
-0.060791015625,
-0.007232666015625,
-0.083984375,
0.04833984375,
0.052978515625,
0.0034332275390625,
-0.04248046875,
-0.0107421875,
0.0024871826171875,
0.0262451171875,
0.0013580322265625,
0.01708984375,
-0.053955078125,... | 24,051 | 24051 | |
Are numbers : (-1)^(i) , 1^(-i) , 1^(i) transcendental numbers?
November 30th 2011, 05:24 AM #1
Senior Member
Joined
Nov 2011
From
Crna Gora
Posts
420
Thanks
64
Are numbers : (-1)^(i) , 1^(-i) , 1^(i) transcendental numbers?
According to Euler's formula : $e^{ix}=\cos x + i\cdot \sin x$ we may w... | 5 | [
-0.0184326171875,
0.00299072265625,
-0.007171630859375,
0.09765625,
-0.046875,
-0.091796875,
0.054443359375,
0.03662109375,
0.07470703125,
0.00897216796875,
0.05859375,
-0.038330078125,
0.056884765625,
0.07373046875,
0.04248046875,
-0.0306396484375,
-0.0458984375,
-0.0284423828125,... | 24,052 | 24052 | |
Integrate - Area Under the Curve
November 12th 2008, 11:26 PM #1
Newbie
Joined
Nov 2008
Posts
8
This is the question in my book and I can't seem to get an answer:
14 (a) For the function:
It then says
(b) With the same function (
And finally.. (however, if we can get the right answer t... | 5 | [
-0.05908203125,
0.0284423828125,
-0.00537109375,
0.06298828125,
0.0191650390625,
-0.049560546875,
0.0064697265625,
0.07177734375,
-0.042236328125,
-0.04052734375,
-0.017333984375,
-0.0771484375,
-0.0093994140625,
0.0361328125,
-0.03564453125,
0.0234375,
-0.05224609375,
-0.087890625... | 24,053 | 24053 | |
Order of element
November 26th 2006, 05:08 PM #1
Member
Joined
Nov 2006
Posts
142
Order of element
How do you prove that the order of a in Zn (where n is an integer greater than or equal to 1) viewed as a group of order n with respect to addition is
n/(gcd(a,n))?
Do you mind elaborating on this?... | 4 | [
-0.0595703125,
0.08935546875,
0.0147705078125,
0.0380859375,
-0.031982421875,
-0.01531982421875,
0.0164794921875,
-0.0198974609375,
-0.00518798828125,
0.004150390625,
-0.03759765625,
0.031982421875,
0.10595703125,
-0.095703125,
-0.0281982421875,
0.07861328125,
-0.019287109375,
0.01... | 24,054 | 24054 | |
regression
Cox proportional-hazards regression
Description
Whereas the Kaplan-Meier method with log-rank test is useful for comparing survival curves in two or more groups, Cox regression (or proportional hazards regression) allows analyzing the effect of
several risk factors on survival.
The probability of the end... | 5 | [
-0.0184326171875,
0.01007080078125,
-0.06982421875,
-0.020263671875,
0.1181640625,
0.0260009765625,
0.005828857421875,
0.1279296875,
0.1142578125,
0.006500244140625,
0.06787109375,
0.0021514892578125,
0.07666015625,
0.05126953125,
-0.037109375,
-0.038330078125,
-0.056640625,
-0.035... | 24,055 | 24055 | |
limits of sequences
April 3rd 2007, 06:23 PM #1
Newbie
Joined
Mar 2007
Posts
21
limits of sequences
find the limit of each sequence:
A) Sn = (1 + 1/2n)^(2n)
B) Sn = ( 1 + 1/n)^(2n)
C) Sn - (1 + 1/n) ^ (n-1)
D) Sn = (n/(n+1))^n
E) Sn = (1+ 1/2n)^n
F) Sn = ((n+2)/(n+1))^(n+3)
I... | 5 | [
0.0020904541015625,
-0.018310546875,
-0.0107421875,
-0.02783203125,
-0.01318359375,
0.03759765625,
-0.0157470703125,
0.062255859375,
0.031982421875,
0.05078125,
-0.0115966796875,
-0.062255859375,
-0.0439453125,
0.057861328125,
-0.0125732421875,
-0.0242919921875,
-0.026123046875,
-0... | 24,056 | 24056 | |
partial differential equation
How to solve the attached coupled equations for $\psi$ and $u$. Please help me. Its very complex.
You can try separation of variables. The given equation is $\dfrac{\partial^2 \psi}{\partial x^2}+\dfrac{\partial^2 \psi}{\partial y^2}=k^2\psi$. Let $\psi(x,y)=a(x)b(y)$ then $\dfrac{\mathrm... | 4 | [
-0.09814453125,
0.00084686279296875,
-0.00927734375,
-0.0025634765625,
-0.10400390625,
0.08203125,
0.0035400390625,
-0.1298828125,
-0.0162353515625,
0.014404296875,
0.0277099609375,
-0.01025390625,
-0.05419921875,
-0.0147705078125,
0.041748046875,
0.1240234375,
-0.043212890625,
-0.... | 24,057 | 24057 | |
Sensitivity of a Fractional Integrodifferential Cauchy Problem of Volterra Type
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 129478, 8 pages
http://dx.doi.org/10.1155/2013/129478
Research Article
Sensitivity of a Fractional Integrodifferential Cauchy Problem of Volterra Type
Faculty of Mathematics an... | 4 | [
-0.1171875,
-0.0262451171875,
0.06298828125,
-0.0145263671875,
-0.01434326171875,
0.04541015625,
0.0240478515625,
0.042236328125,
0.004058837890625,
0.01483154296875,
-0.0439453125,
-0.02685546875,
0.03564453125,
0.042724609375,
-0.0260009765625,
-0.042724609375,
0.06298828125,
-0.... | 24,058 | 24058 | |
real analysis one sided limits
October 2nd 2012, 02:10 PM
biga415
real analysis one sided limits
hey guys. so im in an introductory real analysis course and I am finding it quite challenging, partially because my teacher isnt great. i went to ask for help on some limit problems but im not
sure if his advice ... | 4 | [
-0.10107421875,
0.0301513671875,
0.022216796875,
0.02783203125,
0.0908203125,
0.045654296875,
0.00360107421875,
0.0223388671875,
-0.04345703125,
-0.03759765625,
0.13671875,
-0.09130859375,
0.05126953125,
0.0400390625,
0.00299072265625,
0.031982421875,
0.051513671875,
-0.04370117187... | 24,059 | 24059 | |
Eigenvalue Questions
June 20th 2011, 04:33 AM #1
Senior Member
Joined
Apr 2009
Posts
306
Eigenvalue Questions
I can do i) but just a bit stuck on ii).
my working for i) is: E^2-E=0 so that means $\lambda^2-\lambda$ is an eigenvalue of E^2-E=0, since the zero vector only has an eigenvalue of 0... | 5 | [
0.055419921875,
0.059814453125,
-0.0296630859375,
-0.0113525390625,
-0.059814453125,
0.07373046875,
0.07421875,
-0.03466796875,
-0.004608154296875,
0.004547119140625,
0.046142578125,
-0.0576171875,
-0.016357421875,
0.01312255859375,
0.10986328125,
0.125,
0.0194091796875,
-0.0712890... | 24,060 | 24060 | |
Optimization of a 12.5 GHz Microstrip Antenna Array Using Taguchi's Method
International Journal of Antennas and Propagation
Volume 2011 (2011), Article ID 458569, 9 pages
http://dx.doi.org/10.1155/2011/458569
Research Article
Optimization of a 12.5 GHz Microstrip Antenna Array Using Taguchi's Method
^1Department of... | 4 | [
0.018310546875,
0.09765625,
-0.064453125,
-0.07958984375,
-0.037353515625,
-0.08349609375,
0.006103515625,
0.034912109375,
-0.1171875,
0.02099609375,
0.0029754638671875,
0.08740234375,
0.01513671875,
-0.0771484375,
-0.0556640625,
0.0224609375,
0.02197265625,
-0.0771484375,
0.0031... | 24,061 | 24061 | |
Squared Weights in MBH98
A couple of weeks ago, I said that I would document (at least for Jean S and UC) an observation about the use of squared weights in MBH98. I realize that most readers won’t be fascinated with this
particular exposition, but indulge us a little since this sort of entry is actually a very useful ... | 4 | [
-0.14453125,
-0.00921630859375,
0.0003185272216796875,
0.05615234375,
-0.054443359375,
0.00970458984375,
0.0361328125,
0.0908203125,
-0.0703125,
-0.041015625,
-0.0247802734375,
-0.007537841796875,
0.0281982421875,
-0.053466796875,
-0.0277099609375,
-0.04345703125,
0.08447265625,
0.... | 24,062 | 24062 | |
Composite f, g, and/or h
January 21st 2007, 04:53 AM
symmetry
Composite f, g, and/or h
For questions 1 and 2 below, let f(x) = x^2, g(x) = 3x and
h(x) = (sqrt{x}) + 1. Express each function as a composite of f, g and/or h.
(1) P(x) = 3(sqrt{x}) + 3
(2) Q(x) = sqrt({sqrt{x} + 1}) + 1
NOTE:
... | 4 | [
-0.044677734375,
-0.00457763671875,
0.061279296875,
0.01446533203125,
-0.033935546875,
0.0380859375,
0.0115966796875,
-0.0517578125,
0.041015625,
-0.00396728515625,
0.0196533203125,
0.0181884765625,
0.056884765625,
0.0031585693359375,
-0.00885009765625,
-0.0087890625,
-0.078125,
-0... | 24,063 | 24063 | |
Sylow group question
August 20th 2008, 07:06 PM #1
Newbie
Joined
Aug 2008
Posts
2
Sylow group question
1.Let G be a group with |G|=p^2*q,where p and q are distinct primes,show that G has a normal Sylow p-subgroups or a normal Sylow q-subgroups.
2.if |G| < 100 and G is non-abelian and simple,then sho... | 5 | [
-0.000457763671875,
0.09423828125,
0.0537109375,
0.025390625,
-0.009033203125,
0.051513671875,
0.062255859375,
0.0203857421875,
-0.01263427734375,
-0.0019683837890625,
0.0250244140625,
0.03662109375,
0.013916015625,
0.064453125,
0.01904296875,
0.0291748046875,
-0.0439453125,
-0.022... | 24,064 | 24064 | |
Irrational number between these two?
January 24th 2008, 07:48 PM #1
Newbie
Joined
Jan 2008
Posts
2
Irrational number between these two?
Hi,
I have two questions:
1. Is there an irrational number between 2.6 and 2.6repeating (2.666666...)?
2. Is there an irrational number between 4th root of... | 4 | [
0.0517578125,
-0.045654296875,
0.0224609375,
0.0771484375,
-0.03759765625,
0.03173828125,
-0.01123046875,
0.04541015625,
0.048095703125,
-0.033203125,
-0.07080078125,
0.00933837890625,
0.054443359375,
0.046875,
0.061767578125,
-0.0205078125,
-0.0064697265625,
-0.035888671875,
0.0... | 24,065 | 24065 | |
simple integration by parts
How do you integrate (re^r/2)dr ?
Here is what I have so far, I think I am making a mistake with the integration of e^r/2.
(re^r/2)dr u = r dV = e^r/2dr
du = dr V = (1/2)e^r/2
uV - (integral of) Vdu
so:
(1/2)re^r/2 - (integral of)(1/2)e^r/2 dr
(1/2)re^r/... | 5 | [
0.03125,
0.12158203125,
0.09375,
-0.01556396484375,
0.056396484375,
-0.05712890625,
-0.09814453125,
0.0244140625,
-0.059326171875,
0.056640625,
-0.0025787353515625,
-0.109375,
-0.07666015625,
0.08447265625,
0.015869140625,
-0.134765625,
0.001678466796875,
0.0194091796875,
-0.0576... | 24,066 | 24066 | |
irrational numbers
Can anyone help me with this? "if x is an irrational number, is 2x rational or irrational? explain"
If $2x$ were a rational number then there exist integers $a$ and $b$ such that: $2x=\frac{a}{b}$ but then: $x=\frac{a}{2b}$ but that means $x$ is also rational. So if $x$ is irrational $2x$ must also
... | 4 | [
0.0130615234375,
-0.005706787109375,
0.07275390625,
0.061279296875,
-0.03466796875,
-0.00628662109375,
0.01434326171875,
-0.072265625,
0.003265380859375,
-0.051513671875,
-0.04052734375,
-0.0703125,
0.0908203125,
0.061767578125,
0.053466796875,
-0.004241943359375,
0.03564453125,
0.... | 24,067 | 24067 | |
Combinations
May 4th 2008, 07:41 PM #1
Newbie
Joined
Dec 2007
Posts
15
Combinations
Hi guys!
Havings a problem with this... how many ways can you have 2 cards of one value and 3 other cards each of a different value? (assuming a standard 52 card deck)
My thought process was: C(13,1)xC(4,2)xC(12... | 4 | [
0.0281982421875,
0.0306396484375,
-0.1015625,
-0.054443359375,
-0.0341796875,
0.035400390625,
0.0517578125,
0.0069580078125,
0.0177001953125,
-0.03564453125,
-0.0118408203125,
-0.0947265625,
-0.054443359375,
0.0167236328125,
0.035888671875,
0.05810546875,
-0.0478515625,
-0.01855468... | 24,068 | 24068 | |
Integration by Substitution
February 10th 2008, 07:26 PM #1
Newbie
Joined
Feb 2008
Posts
21
Integration by Substitution
Hello, I'm having trouble doing this one integration problem and it needs to be done using substitution and only substitution (no integration by parts). I can pretty much figure it out ... | 5 | [
0.01287841796875,
0.057861328125,
0.0771484375,
0.05224609375,
-0.0150146484375,
0.0150146484375,
-0.004364013671875,
-0.0189208984375,
-0.03955078125,
-0.00677490234375,
0.028076171875,
-0.06982421875,
-0.0306396484375,
0.0419921875,
-0.0419921875,
-0.0673828125,
0.041015625,
0.00... | 24,069 | 24069 | |
Solving Trig eqations
December 16th 2007, 11:58 AM #1
Newbie
Joined
Dec 2007
Posts
2
Solving Trig eqations
I have two questions:
1-How do I go about solving the equation 3cot² + 5csc =-1
(i couldn't get the angle symbol to appear)
2- I am supposed to solve this eqation (sec(x)=x-3) graphic... | 4 | [
-0.1064453125,
-0.01177978515625,
0.058837890625,
0.07080078125,
0.03759765625,
0.019775390625,
-0.017578125,
-0.03125,
0.057861328125,
0.00360107421875,
0.10498046875,
-0.08349609375,
-0.00384521484375,
0.0380859375,
-0.009033203125,
-0.025390625,
-0.028076171875,
-0.0144653320312... | 24,070 | 24070 | |
Ground State Robustness as an Evolutionary Design Principle in Signaling Networks
Abstract
The ability of an organism to survive depends on its capability to adapt to external conditions. In addition to metabolic versatility and efficient replication, reliable signal transduction is
essential. As signaling systems are... | 4 | [
-0.07763671875,
-0.1201171875,
-0.025390625,
-0.04833984375,
-0.0159912109375,
-0.0086669921875,
-0.00775146484375,
0.058837890625,
0.046875,
-0.024169921875,
-0.045166015625,
0.0013885498046875,
-0.021484375,
0.037353515625,
0.016845703125,
0.0036773681640625,
-0.05126953125,
-0.0... | 24,071 | 24071 | |
Generalized Köthe-Toeplitz Duals of Some Vector-Valued Sequence Spaces
International Journal of Analysis
Volume 2013 (2013), Article ID 862949, 7 pages
http://dx.doi.org/10.1155/2013/862949
Research Article
Generalized Köthe-Toeplitz Duals of Some Vector-Valued Sequence Spaces
Department of Mathematics, Inonu Univer... | 4 | [
-0.1650390625,
-0.0179443359375,
-0.0179443359375,
-0.04052734375,
-0.06103515625,
0.1591796875,
0.019287109375,
0.026611328125,
0.0191650390625,
-0.044189453125,
-0.015869140625,
0.0341796875,
-0.054931640625,
0.0089111328125,
-0.033935546875,
-0.032470703125,
-0.000804901123046875,... | 24,072 | 24072 | |
Calculus Word Problem Ladder
October 25th 2009, 02:00 PM
kashifzaidi
Calculus Word Problem Ladder
A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1.5 ft/s, how fast is the angle between the ladder and the ground changing
when the bottom of... | 5 | [
-0.0888671875,
-0.0198974609375,
-0.01025390625,
-0.0712890625,
0.01300048828125,
-0.004791259765625,
-0.111328125,
0.0771484375,
0.0015106201171875,
-0.024169921875,
0.0751953125,
-0.002197265625,
0.0272216796875,
0.0400390625,
-0.0218505859375,
0.07470703125,
-0.0673828125,
0.022... | 24,073 | 24073 | |
finding the roots
March 22nd 2009, 10:04 AM #1
Newbie
Joined
Mar 2009
Posts
16
finding the roots
what is the easiest way of finding the roots of these kind of equations (except guessing):
x^4+x^3-7x^2-x+6=0
or
x^5-2x^4+2x^3-2x^2+x=0
you can tell rigorously or sth easy. it's OK.
a... | 4 | [
-0.07470703125,
0.0294189453125,
-0.0252685546875,
0.058349609375,
0.00762939453125,
0.029541015625,
-0.037109375,
-0.0018768310546875,
0.0024566650390625,
-0.0615234375,
-0.00165557861328125,
-0.07666015625,
0.03759765625,
-0.0050048828125,
-0.046630859375,
0.04052734375,
-0.0319824... | 24,074 | 24074 | |
Just need confirmation on a circular function question.
July 6th 2008, 08:34 AM #1
Banned
Joined
Jul 2008
Posts
29
Just need confirmation on a circular function question.
determine the value of the following if 0 is less than or equal to theta and theta is less than 2 pie.
sec theta= -2root3/3= -roo... | 4 | [
-0.0419921875,
-0.076171875,
-0.050537109375,
0.001739501953125,
-0.099609375,
-0.036376953125,
-0.0546875,
0.03759765625,
0.08984375,
-0.0250244140625,
0.05908203125,
-0.087890625,
0.05810546875,
0.00628662109375,
0.0830078125,
-0.050537109375,
-0.0299072265625,
0.00897216796875,
... | 24,075 | 24075 | |
Choosing numbers from a bag without replacement
April 23rd 2010, 12:13 PM #1
Member
Joined
Jan 2010
Posts
77
Choosing numbers from a bag without replacement
A bag contains eleven discs numbered 1 to 11. Two discs are selected at random form the bag. Given that the sum of the selected numbers is even, use... | 4 | [
0.00567626953125,
-0.00189971923828125,
-0.00628662109375,
-0.02734375,
0.037109375,
-0.0157470703125,
0.035888671875,
0.06689453125,
-0.016357421875,
0.048095703125,
0.033447265625,
-0.022216796875,
-0.0045166015625,
-0.052001953125,
0.0130615234375,
-0.00104522705078125,
-0.0189208... | 24,076 | 24076 | |
Limit
Let $a_{1}=\frac{5}{2}$ and $a_{n+1}=\sqrt{ a_{n}^{3} -12a_{n}+\frac{20n+21}{n+1}}$ Prove that the sequence $(a_{n})$ converges and find its limit
If the 'recursive relation' is... http://quicklatex.com/cache3/ql_d676...adbc711_l3.png (1) ... it can be written as... http://quicklatex.com/cache3/ql_b7fc...5a37e84... | 5 | [
-0.11328125,
-0.05859375,
-0.0189208984375,
-0.0252685546875,
-0.08349609375,
0.00946044921875,
-0.026611328125,
0.0322265625,
0.02783203125,
0.0113525390625,
0.056884765625,
0.029541015625,
-0.0034637451171875,
0.103515625,
-0.0810546875,
-0.00469970703125,
-0.054931640625,
-0.021... | 24,077 | 24077 | |
Adding and subtracting rational expressions. Please help?
November 14th 2012, 02:19 PM #1
Newbie
Joined
Nov 2012
From
United States
Posts
8
Adding and subtracting rational expressions. Please help?
I have a math problem and the answer to it. The only problem I have is that I cannot figure out how to ... | 4 | [
-0.0181884765625,
0.05517578125,
0.09375,
-0.0537109375,
0.03466796875,
0.0174560546875,
-0.01513671875,
0.01422119140625,
-0.0595703125,
-0.041748046875,
0.03759765625,
-0.044677734375,
0.02978515625,
0.169921875,
-0.0191650390625,
0.0673828125,
-0.0026702880859375,
0.03173828125,... | 24,078 | 24078 | |
What kind of proof to use? Ring Homomorphisms
November 30th 2010, 03:08 PM #1
Junior Member
Joined
Aug 2009
Posts
28
What kind of proof to use? Ring Homomorphisms
Hi here is the question
prove that every ring homomorphism phi from Z_n to itself has the form phi(x)=ax where a^2=a
im just wonderin... | 4 | [
-0.06396484375,
0.10009765625,
0.041015625,
0.06005859375,
-0.08154296875,
0.000583648681640625,
0.08642578125,
-0.043701171875,
0.016845703125,
-0.0654296875,
0.0294189453125,
0.01416015625,
0.01025390625,
-0.0118408203125,
-0.033447265625,
-0.007537841796875,
-0.007293701171875,
... | 24,079 | 24079 | |
Existence of a root between 2 given points
Well if I read your function correctly (if I am not mistaken you're a PhD student, then why don't you use TeX?), it's:
[tex]f(x)=(1-x^2)^2-\sqrt{(1-x^2)(1-\frac{1}{2} x^2)}[/tex]
If this is your function then we can see that at x=1 the function vanishes, and you also know th... | 4 | [
0.00958251953125,
-0.03271484375,
0.0242919921875,
0.00341796875,
-0.031005859375,
-0.0634765625,
-0.022216796875,
0.031494140625,
0.059326171875,
-0.0020294189453125,
-0.0225830078125,
0.01507568359375,
0.0908203125,
0.05517578125,
-0.06591796875,
-0.07275390625,
0.01068115234375,
... | 24,080 | 24080 | |
Problem from Lang
micromass
You must only show that if two of the indices [itex](A:B),(A_f:B_f),(A^f,B^f)[/itex] is finite, then so is the third. Right?
Well, maybe you can start by showing that
[tex]0\rightarrow A_f/B_f\rightarrow A/B\rightarrow A^f/B^f\rightarrow 0[/tex]
is exact.
Apologies for not getting bac... | 4 | [
-0.0079345703125,
0.011474609375,
0.0537109375,
-0.043212890625,
0.00140380859375,
0.09033203125,
0.06640625,
-0.01123046875,
-0.0294189453125,
-0.0284423828125,
0.043212890625,
-0.0908203125,
-0.0291748046875,
0.056640625,
-0.0140380859375,
0.056396484375,
-0.07958984375,
0.061523... | 24,081 | 24081 | |
Sign Inference for Dynamic Signed Networks via Dictionary Learning
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 708581, 10 pages
http://dx.doi.org/10.1155/2013/708581
Research Article
Sign Inference for Dynamic Signed Networks via Dictionary Learning
State Key Laboratory of Information Photonics and... | 4 | [
-0.07666015625,
-0.0196533203125,
0.0216064453125,
0.01068115234375,
0.023681640625,
-0.09423828125,
0.0284423828125,
-0.01483154296875,
0.059326171875,
-0.06494140625,
0.02587890625,
0.06787109375,
0.12060546875,
0.037109375,
0.07080078125,
-0.00250244140625,
-0.0021820068359375,
... | 24,082 | 24082 | |
A Weighted Variant of Riemann-Liouville Fractional Integrals on
Abstract and Applied Analysis
VolumeΒ 2012Β (2012), Article IDΒ 780132, 18 pages
http://dx.doi.org/10.1155/2012/780132
Research Article
A Weighted Variant of Riemann-Liouville Fractional Integrals on
^1Department of Mathematics, Linyi University, Shando... | 5 | [
-0.05078125,
-0.07177734375,
0.0224609375,
0.0089111328125,
0.11376953125,
-0.0145263671875,
-0.003875732421875,
-0.0064697265625,
0.01043701171875,
-0.03271484375,
-0.048095703125,
0.032958984375,
0.036376953125,
0.01123046875,
-0.0208740234375,
-0.0054931640625,
0.059326171875,
0... | 24,083 | 24083 | |
bn_gf2m.c [openssl/crypto/bn/bn_gf2m.c] - Woboq Code Browser
1 /* crypto/bn/bn_gf2m.c */
2 /* ====================================================================
3 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
4 *
5 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
6 *... | 4 | [
-0.1181640625,
0.0157470703125,
-0.08056640625,
-0.0262451171875,
0.056884765625,
-0.0458984375,
-0.0252685546875,
0.0296630859375,
0.04736328125,
-0.02783203125,
0.007354736328125,
-0.0140380859375,
-0.0252685546875,
-0.07470703125,
0.0615234375,
0.0279541015625,
-0.031494140625,
... | 24,084 | 24084 | |
Convergent Geometric Series
Suppose we have two convergent geometric series ∑x^n and ∑y^n. Does it ever occur that ∑x^n∑y^n=∑[(x^n)(y^n)]? THANKS.
I would say yes. Assume that the lead term is $1$ and that $n$ starts at $n = 0$ then $\sum_{n=0}^\infty x^n = \frac{1}{1-x},$$\sum_{n=0}^\infty y^n = \frac{1}{1-y}$ and $\... | 5 | [
-0.072265625,
-0.08837890625,
-0.0244140625,
0.0625,
-0.076171875,
-0.0830078125,
-0.0181884765625,
-0.076171875,
0.064453125,
-0.00787353515625,
-0.06982421875,
0.0050048828125,
0.06396484375,
0.08544921875,
0.01123046875,
-0.00058746337890625,
-0.06689453125,
-0.103515625,
0.07... | 24,085 | 24085 | |
Math Help
May 26th 2007, 02:13 PM #1
Member
Joined
Nov 2006
Posts
139
series..?
I know these are very very basic series(if they are..
If I have the ? [from 1 to 6] of (1/(1.3)^ (s/12)) how do I solve it and why?
Thanks for all the help.
I'm guessing this is the problem you're trying to so... | 5 | [
-0.018310546875,
-0.0220947265625,
-0.01104736328125,
0.0230712890625,
-0.08837890625,
-0.017333984375,
0.0272216796875,
-0.0322265625,
0.046875,
0.0103759765625,
-0.087890625,
-0.0211181640625,
0.00750732421875,
-0.038330078125,
-0.0615234375,
-0.0098876953125,
-0.0108642578125,
0... | 24,086 | 24086 | |
Math Help
January 9th 2010, 02:37 PM #1
Super Member
Joined
Aug 2009
Posts
639
intergral
may i know why the answer for integrate exp (x) sin ( exp x) from x= ln (pi) to x= 0 is not
1- cos (ln (pi))?
My first reaction was to wonder why you think it should be! But I think I see. I suspect you mad... | 5 | [
-0.07080078125,
-0.01275634765625,
0.06103515625,
0.007293701171875,
0.0693359375,
-0.018798828125,
0.02392578125,
0.051513671875,
-0.0693359375,
0.032958984375,
0.095703125,
-0.01263427734375,
0.0059814453125,
-0.0128173828125,
-0.0286865234375,
-0.037353515625,
-0.0281982421875,
... | 24,087 | 24087 | |
Trigonometry problem
Use the
law of sines
. The law of sines for a triangle is just the relation that the ratio of the sine of an angle by the length of the opposite side of the triangle is a constant for each triangle. With this law you can
calculate the size of both sides of the triangle, or quicker you can just co... | 4 | [
0.0050048828125,
0.10205078125,
-0.053466796875,
-0.01483154296875,
-0.0274658203125,
0.04443359375,
-0.034912109375,
0.0380859375,
0.007476806640625,
0.015625,
-0.0062255859375,
-0.03857421875,
0.011962890625,
0.05029296875,
0.0537109375,
0.0162353515625,
-0.07373046875,
0.0038452... | 24,088 | 24088 | |
# of binomial coefficients not divisible by 3 is not divisible by 5
December 29th 2009, 04:46 AM #1
Senior Member
Joined
Nov 2007
Posts
329
# of binomial coefficients not divisible by 3 is not divisible by 5
Show that the number of binomial coefficients not divisible by 3 is not divisible by 5 where the ... | 5 | [
-0.0152587890625,
-0.07275390625,
-0.0205078125,
-0.04150390625,
0.059326171875,
0.07666015625,
0.0771484375,
-0.002532958984375,
-0.0004482269287109375,
0.02294921875,
-0.0927734375,
-0.0211181640625,
-0.00445556640625,
0.00482177734375,
0.01611328125,
-0.0283203125,
-0.037841796875... | 24,089 | 24089 | |
Patent US6282520 - Computer system and methods for allocation of the returns of a portfolio among a plurality of investors with different risk tolerance levels and allocation of returns from an efficient portfolio
FIELD OF THE INVENTION
The present invention relates to computer systems and methods for allocation of in... | 4 | [
-0.00531005859375,
-0.0087890625,
-0.1064453125,
-0.0390625,
-0.00653076171875,
0.01446533203125,
0.09033203125,
0.041748046875,
0.03955078125,
0.04248046875,
-0.053955078125,
0.0888671875,
0.0498046875,
-0.04296875,
-0.11572265625,
-0.08349609375,
-0.04736328125,
0.031982421875,
... | 24,090 | 24090 | |
Muzzle velocity given test range, time of flight and ballistic properties.
This isn't really homework, but I figure this is the most appropriate place to post this... Please do say if you think there is a more likely place it will get answered - I'm new!
The problem statement, all variables and given/known data
I am t... | 4 | [
0.0157470703125,
0.047607421875,
0.03173828125,
0.00830078125,
0.023193359375,
-0.0240478515625,
-0.0146484375,
0.0791015625,
-0.03271484375,
0.0498046875,
0.051513671875,
0.007537841796875,
0.00457763671875,
0.053955078125,
-0.01904296875,
0.0245361328125,
0.03564453125,
-0.028198... | 24,091 | 24091 | |
Intersecting Lines in a Plane
March 31st 2009, 01:25 PM
square
Intersecting Lines in a Plane
Equation of plane: r= (-3,5,6) + s[-1,1,2] + v[2,1,-3]. I need the equation of 2 intersecting lines that lie on this plane. I know I can use s[-1,1,2], but I need to find another vector that is
perpendicular to s[-1,... | 4 | [
-0.032470703125,
-0.0478515625,
-0.041015625,
-0.034912109375,
0.048828125,
0.041748046875,
-0.0260009765625,
0.024169921875,
-0.048828125,
0.041015625,
-0.04833984375,
0.0308837890625,
-0.027099609375,
0.00006198883056640625,
-0.0966796875,
0.035888671875,
-0.05712890625,
-0.05346... | 24,092 | 24092 | |
Mutual Inductance of Two RC Circuits?
1. The problem statement, all variables and given/known data
In the circuit shown in the following figure(Figure 1) the capacitor has capacitance 20 microF and is initially uncharged. The resistor R_0 has resistance 12 Ohms . An emf of 90.0V is added in series
with the capacitor a... | 4 | [
0.00347900390625,
0.0751953125,
-0.0693359375,
-0.0439453125,
0.1103515625,
-0.0177001953125,
0.0306396484375,
0.107421875,
-0.03564453125,
0.01348876953125,
0.0634765625,
-0.061279296875,
0.095703125,
0.06591796875,
-0.0634765625,
0.0546875,
-0.06787109375,
-0.034912109375,
-0.0... | 24,093 | 24093 | |
Sequences and series
March 25th 2008, 10:24 AM #1
Member
Joined
Jul 2007
Posts
147
Sequences and series, a financial application with interest rates, please help me
Dear forum members, could you please verify that my calculations are correct
A person takes a two million euro loan from a bank with ... | 5 | [
-0.0162353515625,
0.0634765625,
-0.0235595703125,
-0.031494140625,
-0.12060546875,
0.005645751953125,
-0.00933837890625,
0.0654296875,
0.0194091796875,
0.031982421875,
-0.068359375,
-0.046142578125,
0.0458984375,
0.07958984375,
-0.01116943359375,
0.11474609375,
-0.06591796875,
-0.0... | 24,094 | 24094 | |
Controllability of state space equation
dabargo
2. Relevant equations
[tex]
u(t) = -B^T\exp^{A^T(t_1-t)}W_c^{-1}(t_1)[\exp^{At_1}x_0-x_1]
[/tex]
[tex]
W_c(t_1) = \int_0^{t_1} \exp^{A\gamma}BB^T\exp^{A^T\gamma} d\gamma
[/tex]
Where did you get those equations, your system is not doing what you want it to do I ag... | 4 | [
-0.08837890625,
-0.0147705078125,
-0.057373046875,
-0.01263427734375,
-0.054443359375,
0.013427734375,
0.06982421875,
-0.01361083984375,
-0.0361328125,
0.0103759765625,
0.07666015625,
-0.060791015625,
0.0198974609375,
-0.08837890625,
-0.048828125,
0.1025390625,
0.0284423828125,
-0.... | 24,095 | 24095 | |
How Far Will It Skid?
Most driver's education classes teach future drivers that the stopping distance of a skidding car is directly proportional to the square of the speed of the car. That is a car traveling 10 mi/hr may
require 4 feet to skid to an abrupt halt; but a car going twice as fast - 20 mi/hr - would require... | 4 | [
-0.01336669921875,
0.01904296875,
-0.006195068359375,
-0.03173828125,
-0.049560546875,
0.047607421875,
-0.09716796875,
0.07958984375,
-0.0034637451171875,
-0.00994873046875,
0.05810546875,
0.08642578125,
0.0247802734375,
0.07275390625,
-0.07763671875,
0.033447265625,
0.018798828125,
... | 24,096 | 24096 | |
Isomorphism of Rings
May 12th 2010, 08:07 PM #1
Member
Joined
May 2009
Posts
86
Isomorphism of Rings
Hello,
I was just trying out problems from Herstein, and I have a doubt in this. I would really appreciate any help.
Let R be a ring with unit element. Using its elements we define a ring R' by d... | 5 | [
-0.0274658203125,
0.031005859375,
-0.07421875,
-0.005859375,
-0.042236328125,
0.022216796875,
0.12158203125,
0.0107421875,
-0.0142822265625,
-0.07763671875,
-0.0096435546875,
-0.09375,
0.06787109375,
-0.032958984375,
-0.0181884765625,
-0.0263671875,
0.0036468505859375,
0.0197753906... | 24,097 | 24097 | |
TRICKY u substitution - are my answers correct
September 26th 2009, 07:51 PM #1
Member
Joined
Dec 2008
From
Australia
Posts
161
QUESTION ONE $\int z^3\sqrt{z^2 + 1}dz$
$u = z^2 + 1$
$\frac{du}{dz} = 2z$
$\frac{z^2}{2}\int u^\frac{1}{2}\ du$
$\frac{z^2}{2}.\frac{2}{3}u^\frac{3}{2}$
... | 5 | [
-0.036865234375,
0.0052490234375,
-0.01226806640625,
0.0233154296875,
0.01287841796875,
-0.041015625,
-0.052001953125,
-0.02880859375,
-0.0244140625,
-0.0260009765625,
-0.006622314453125,
-0.018798828125,
-0.031982421875,
0.11083984375,
-0.052734375,
-0.0277099609375,
-0.0322265625,
... | 24,098 | 24098 | |
stationary points of a function of 2 variables
May 10th 2008, 08:38 AM #1
Newbie
Joined
May 2008
Posts
7
stationary points of a function of 2 variables
hey i have this problem where
z = xy(6-x-y) when multiplying out and differentiating with respect to x i get:
dz/dx = 6y - 2xy -y^2 and y dz/dy... | 5 | [
-0.0235595703125,
-0.052734375,
-0.0693359375,
-0.03125,
-0.0152587890625,
0.01953125,
-0.03271484375,
0.01123046875,
0.01055908203125,
-0.01507568359375,
0.040283203125,
0.0478515625,
0.0252685546875,
-0.002532958984375,
0.021484375,
0.03515625,
-0.08154296875,
-0.052734375,
-0.... | 24,099 | 24099 |