content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Sparse Cumulants Fitting for Direction-of-Arrival Estimation without Redundancy
International Journal of Antennas and Propagation
Volume 2013 (2013), Article ID 897158, 7 pages
http://dx.doi.org/10.1155/2013/897158
Research Article
Sparse Cumulants Fitting for Direction-of-Arrival Estimation without Redundancy
Key L... | 4 | [
-0.03955078125,
0.031982421875,
0.024169921875,
-0.00023555755615234375,
-0.041015625,
-0.0576171875,
-0.032470703125,
-0.0517578125,
0.0498046875,
-0.00946044921875,
0.0177001953125,
0.018310546875,
0.0693359375,
-0.0888671875,
-0.028076171875,
-0.039794921875,
0.035888671875,
-0.... | 33,700 | 33700 | |
Solutions for Chapter 4
Introduction to Automata Theory, Languages, and Computation
Solutions for Chapter 4
Solutions for Section 4.1
Solutions for Section 4.1... | 5 | [
-0.01806640625,
0.0732421875,
0.0191650390625,
0.031982421875,
0.031494140625,
0.07763671875,
0.0869140625,
-0.006591796875,
-0.05908203125,
-0.11279296875,
0.047607421875,
0.05615234375,
0.0024566650390625,
0.080078125,
-0.056396484375,
0.026123046875,
-0.041748046875,
-0.09179687... | 33,701 | 33701 | |
Homework Help
Posted by Jade on Monday, October 10, 2011 at 9:51pm.
Define the quotient rule.
• Calculus - Steve, Tuesday, October 11, 2011 at 12:12am
If f and g are functions of x
d/dx(f/g) = (f'g - fg')/g^2
This is just a variation of the well-loved product rule, where f/g = f * g^-1
d/dx(f * ... | 5 | [
-0.06298828125,
-0.005401611328125,
0.1455078125,
-0.0038604736328125,
-0.04150390625,
-0.0751953125,
-0.0303955078125,
0.0205078125,
0.005340576171875,
0.0888671875,
0.022705078125,
0.011962890625,
-0.0174560546875,
-0.023193359375,
-0.058837890625,
0.0011749267578125,
-0.0483398437... | 33,702 | 33702 | |
Contour within Contour
June 9th 2007, 06:11 PM #1
Global Moderator
Joined
Nov 2005
From
New York City
Posts
10,616
Thanks
9
Contour within Contour
Let $f(z)$ be a complex function defined on an open non-empty set $S$. Let $\gamma (t)$ be a contour wholly inside $S$. Does there exist another conto... | 5 | [
-0.033935546875,
0.02685546875,
-0.00262451171875,
0.04833984375,
0.060302734375,
-0.0079345703125,
0.080078125,
0.057373046875,
-0.005279541015625,
-0.037109375,
-0.0220947265625,
0.0576171875,
0.0947265625,
0.0159912109375,
0.016357421875,
-0.051513671875,
0.027099609375,
-0.0407... | 33,703 | 33703 | |
need help variance of poisson dist.
July 5th 2008, 03:37 AM #1
Newbie
Joined
Jul 2008
Posts
2
need help variance of poisson dist.
Can anyone provide a proof for the variance of poisson distribution?
Show that it is Var(N(t)) = lamda*t without using the Bernoulli distribution and independence way..( w... | 5 | [
0.034912109375,
0.000457763671875,
0.02685546875,
0.0238037109375,
-0.0712890625,
0.0252685546875,
0.04345703125,
-0.01483154296875,
0.083984375,
-0.03271484375,
0.06884765625,
0.057373046875,
-0.00811767578125,
-0.044921875,
-0.0308837890625,
-0.032958984375,
0.057861328125,
-0.07... | 33,704 | 33704 | |
Homework Help
Posted by weloo_volley on Tuesday, May 8, 2012 at 6:18pm.
weloo.
Consider the function f(x)= -cos3x -4sin3x.
(a)Find the equation of the line normal to the graph of f(x) when x= pie/6 .
(b)Find the x coordinates of the points on the graph of f(x) where the tangent to the graph is horizontal.
(c)Find ... | 4 | [
-0.0240478515625,
0.0291748046875,
-0.0252685546875,
-0.041015625,
-0.038330078125,
0.06396484375,
-0.00421142578125,
0.11279296875,
-0.020263671875,
0.0067138671875,
0.083984375,
-0.0302734375,
0.0380859375,
-0.018798828125,
0.021728515625,
0.01214599609375,
-0.00909423828125,
-0.... | 33,705 | 33705 | |
proving that the euler totient function is multiplicative if (m, n) = 1
September 30th 2011, 05:57 PM #1
Member
Joined
Aug 2008
Posts
249
proving that the euler totient function is multiplicative if (m, n) = 1
i start by showing that there is a one to one correspondence between $\mathbb{Z}_{mn}$ and $\ma... | 4 | [
-0.039306640625,
-0.0208740234375,
-0.0498046875,
-0.0751953125,
0.004913330078125,
0.01611328125,
0.09912109375,
0.0272216796875,
-0.08056640625,
-0.09521484375,
0.025390625,
0.0128173828125,
0.0712890625,
0.00787353515625,
0.01708984375,
0.1328125,
0.0028533935546875,
0.002777099... | 33,706 | 33706 | |
Real-Time Pricing-Based Scheduling Strategy in Smart Grids: A Hierarchical Game Approach
Journal of Applied Mathematics
Volume 2014 (2014), Article ID 329656, 8 pages
http://dx.doi.org/10.1155/2014/329656
Research Article
Real-Time Pricing-Based Scheduling Strategy in Smart Grids: A Hierarchical Game Approach
^1Scho... | 4 | [
-0.11962890625,
0.09765625,
-0.060546875,
0.0595703125,
-0.0184326171875,
-0.05224609375,
-0.0186767578125,
0.004608154296875,
0.045654296875,
0.08642578125,
-0.05517578125,
-0.01043701171875,
0.048583984375,
0.0081787109375,
-0.00946044921875,
-0.03173828125,
-0.01318359375,
-0.08... | 33,707 | 33707 | |
Math(Please help)
Posted by Hannah on Friday, April 29, 2011 at 5:57pm.
Evaluate: f(x,y)=2x^3e^y
a) partial derivative with respect to x.
I know that you have to treat y as a constant but I have no idea what to do. I do not understand partial derivatives at all. Please help!!
b) partial derivative with repsect to y... | 5 | [
0.033935546875,
-0.0498046875,
-0.042724609375,
-0.01025390625,
0.00885009765625,
0.0001316070556640625,
-0.0108642578125,
-0.039794921875,
-0.00341796875,
0.0244140625,
0.0908203125,
0.0012664794921875,
-0.059326171875,
-0.00482177734375,
0.0751953125,
0.0218505859375,
-0.1044921875... | 33,708 | 33708 | |
Research
August 2006
<<July August September>>
Answer:
Let the demand for the contract from A and B be a and b respectively. Negative values of a or b correspond to a desire to sell the contract short. Expected log wealth for A will is
p*log(X+a*(1-r))+(1-p)*log(X-a*r)
This has derivative with respect to a of
p*... | 5 | [
-0.06494140625,
0.06787109375,
-0.023193359375,
-0.03662109375,
-0.03759765625,
-0.04248046875,
0.07861328125,
0.046142578125,
0.0537109375,
0.0908203125,
-0.01904296875,
-0.028076171875,
0.09130859375,
0.049072265625,
0.06787109375,
0.05517578125,
-0.05859375,
-0.03173828125,
-0... | 33,709 | 33709 | |
Topology Closed Neighborhood Proof
September 13th 2012, 04:59 PM
Kiefer
Topology Closed Neighborhood Proof
(8) N is a closed neighborhood of p in R_U iff N=R
Where R represents the real numbers and
R_U is the upper topological space for the real numbers (R, T_U)
T_U = {A is a subset of R | a is an el... | 5 | [
0.027099609375,
0.0172119140625,
0.015625,
-0.0296630859375,
0.060302734375,
0.0625,
0.08154296875,
-0.005615234375,
-0.01129150390625,
0.00897216796875,
-0.0035400390625,
0.01007080078125,
0.018310546875,
-0.0162353515625,
0.030517578125,
-0.06884765625,
0.0281982421875,
-0.134765... | 33,710 | 33710 | |
Homework Help
Posted by Emma on Thursday, July 3, 2014 at 10:35pm.
The vertex of the graph of a quadratic function is (3, 1) and the y-intercept is (0, 10). Which of the following is the equation of the function?
• incomplete---Algebra - DrBob222, Thursday, July 3, 2014 at 10:41pm
• Algebra - Emma, Thursday, Ju... | 4 | [
-0.0732421875,
-0.02587890625,
-0.00701904296875,
-0.033203125,
0.0277099609375,
0.091796875,
0.01226806640625,
0.034423828125,
-0.0537109375,
-0.017822265625,
0.05126953125,
-0.000545501708984375,
-0.0167236328125,
0.05810546875,
0.0029296875,
0.044189453125,
-0.029296875,
-0.0742... | 33,711 | 33711 | |
Homework Help
Posted by Andrew on Wednesday, May 15, 2013 at 11:07pm.
Suppose x and y are real numbers and 4x+3xi+yi−43=2y+2xi−x+2yi+5i . What is the product xy .
• Algebra - Steve, Thursday, May 16, 2013 at 12:17am
(4x-43) + (3x+y)i = (2y-x) + (2x+2y+5)i
so, for the two complex numbers above to be equal,... | 4 | [
-0.07666015625,
-0.00970458984375,
-0.01153564453125,
-0.059326171875,
0.01275634765625,
0.0291748046875,
0.06201171875,
0.03076171875,
-0.01416015625,
-0.0179443359375,
0.015869140625,
0.005401611328125,
0.005401611328125,
0.0021820068359375,
0.03564453125,
0.051513671875,
-0.111328... | 33,712 | 33712 | |
Physics Of Hitting A Baseball
The Physics Of Hitting A Baseball
Hitting the "sweet spot" is something that baseball players strive for. This is the location of the bat that is generally regarded as the best spot for hitting the ball. It minimizes vibration of the
bat and results in the maximum energy delivered to the ... | 5 | [
0.07666015625,
0.023681640625,
0.04833984375,
0.016357421875,
-0.007080078125,
0.0203857421875,
0.05419921875,
0.1025390625,
0.07568359375,
0.11865234375,
0.00799560546875,
-0.0181884765625,
-0.06103515625,
0.0625,
0.0869140625,
-0.0035247802734375,
0.1337890625,
-0.06640625,
-0.... | 33,713 | 33713 | |
niche computing science
The AoPA(Algebra of Programming in Agda) library allows one to derive programs in a style resembling that in the book Algebra of Programming in Agda. For example, the following is a derivation of
insertion sort:
sort-der : ∃ ([ Val ] -> [ Val ]) (\f -> ordered? ○ permute ⊒ fun f )
sort-... | 4 | [
-0.126953125,
-0.08056640625,
0.0361328125,
-0.024169921875,
-0.08740234375,
-0.061767578125,
-0.0086669921875,
0.0289306640625,
0.0247802734375,
0.0137939453125,
0.00909423828125,
0.0244140625,
0.00244140625,
0.014892578125,
0.005828857421875,
0.07958984375,
-0.017578125,
-0.00704... | 33,714 | 33714 | |
a few questions I need help with. thank you
August 17th 2007, 03:45 AM
jessicamelia1983
a few questions I need help with. thank you
Okay I am almost done with this lesson. Once again I need help. UGH.. I already did this but received an F and I am fixing all the wrong answers.
Please show me how you got the... | 4 | [
0.0072021484375,
0.04833984375,
-0.0101318359375,
-0.05078125,
0.031494140625,
0.034423828125,
0.017333984375,
0.1064453125,
-0.019287109375,
0.0242919921875,
0.10693359375,
-0.0186767578125,
0.0037078857421875,
0.0203857421875,
-0.045654296875,
0.03125,
-0.08642578125,
-0.01275634... | 33,715 | 33715 | |
Miller-Rabin Primality Test
A Fast Primality Test in JavaScript:
the Miller-Rabin Primality Test
The Miller-Rabin primality test is among the fastest and most widely used primality tests in computational practice. The algorithm of the test is as follows: Given a large odd integer n to be tested,
compute one or more... | 4 | [
-0.050048828125,
-0.0791015625,
-0.119140625,
0.043212890625,
0.07666015625,
-0.06005859375,
-0.00970458984375,
0.08154296875,
0.009033203125,
-0.006378173828125,
-0.11279296875,
0.080078125,
-0.036865234375,
0.000278472900390625,
-0.0252685546875,
-0.07373046875,
0.06396484375,
0.... | 33,716 | 33716 | |
the encyclopedic entry of continuity equation
A
continuity equation
is a
differential equation
that describes the conservative transport of some kind of quantity. Since
mass
,
energy
,
momentum
, and other natural quantities are conserved, a vast variety of physics may be described with continuity equations.
... | 4 | [
-0.0537109375,
-0.056396484375,
-0.00034332275390625,
0.0299072265625,
-0.03271484375,
0.005645751953125,
-0.06005859375,
0.015869140625,
-0.01202392578125,
0.0150146484375,
0.029296875,
0.021728515625,
0.01611328125,
0.048828125,
0.0091552734375,
0.031494140625,
-0.044921875,
0.03... | 33,717 | 33717 | |
Homework Help
Posted by Sergio on Monday, April 23, 2012 at 1:07am.
Determine whether the triangle has no/one/two solutions. Then Find and round measures of sides to the nearest tenth and measures of the angles to the nearest degree.
A= 50 degrees, a=34, b=40
• Math - Henry, Tuesday, April 24, 2012 at 8:16pm
... | 4 | [
-0.0625,
0.138671875,
-0.06591796875,
-0.01092529296875,
-0.03564453125,
0.0322265625,
-0.0322265625,
0.05126953125,
-0.0081787109375,
-0.03076171875,
0.02197265625,
-0.1650390625,
0.007415771484375,
0.03759765625,
0.07861328125,
-0.0191650390625,
-0.072265625,
-0.07275390625,
-0... | 33,718 | 33718 | |
Subgroups and Normal Subgroups
April 18th 2012, 08:37 AM #1
Junior Member
Joined
Jan 2010
Posts
29
Subgroups and Normal Subgroups
Suppose that $A$ and $B$ are subgroups of a group $G$ with $A\subseteq B$ . Prove that $[G:B]$ divides $[G:A]$
Let N be a normal subgroup of a group G and let H be a subg... | 5 | [
-0.042236328125,
0.0081787109375,
0.0595703125,
-0.05517578125,
0.013916015625,
-0.005523681640625,
0.0791015625,
-0.048583984375,
-0.09130859375,
-0.13671875,
-0.014892578125,
-0.0201416015625,
-0.0004177093505859375,
-0.06494140625,
0.0147705078125,
0.07080078125,
0.08935546875,
... | 33,719 | 33719 | |
Indefinite Integral
June 12th 2009, 10:42 PM #1
Super Member
Joined
Jan 2009
Posts
715
Indefinite Integral
a)
solve $\int \frac{\sin{2x}}{ \sin^4{x} + \cos^4{x} } ~dx$
by substituting
i) $u = \tan^2{x}$
ii) $u = \cos{2x}$
b)
Can we deduce that $\tan^{-1}({\cos{2x}}) = - \tan... | 5 | [
-0.0015106201171875,
0.05029296875,
0.0625,
0.040283203125,
0.047607421875,
-0.000965118408203125,
-0.0025482177734375,
-0.0498046875,
-0.052490234375,
0.008056640625,
0.0272216796875,
-0.03955078125,
0.0137939453125,
0.0218505859375,
-0.0284423828125,
0.006378173828125,
0.087890625,... | 33,720 | 33720 | |
Geometry Pattern Formula
September 3rd 2008, 02:17 PM #1
Junior Member
Joined
Aug 2008
Posts
27
Geometry Pattern Formula
Hello All, thank you for your help.
I am at a complete loss in this problem:
Attatched are the triangular numbers used to do the problem, and a table clarifying a few things.... | 4 | [
-0.0361328125,
0.05810546875,
-0.03662109375,
-0.0625,
-0.031494140625,
-0.010498046875,
-0.08447265625,
-0.01953125,
-0.0194091796875,
-0.0120849609375,
-0.09228515625,
-0.0208740234375,
-0.001678466796875,
-0.0096435546875,
0.038330078125,
-0.035888671875,
-0.004119873046875,
-0.... | 33,721 | 33721 | |
How to Calculate Resultant Velocity | The Classroom | Synonym
Physics can be a challenging course for anyone because it combines science with math and introduces potentially difficult concepts. One basic concept is the concept of speed and how it changes.
Calculating the speed of an object can be a simple process if a ... | 4 | [
0.0247802734375,
0.0216064453125,
-0.015380859375,
-0.0146484375,
-0.07421875,
-0.021484375,
-0.103515625,
0.045166015625,
0.0238037109375,
0.06201171875,
0.1337890625,
-0.0791015625,
-0.006591796875,
0.0615234375,
-0.0771484375,
0.012939453125,
-0.037109375,
0.1884765625,
-0.058... | 33,722 | 33722 | |
No Real Solutions
November 8th 2011, 09:26 AM #1
Junior Member
Joined
Apr 2011
From
United States
Posts
32
Hey,
I came upon a problem where I cannot understand why ${x^2} + 6$ has no real solutions for the polynomial equation $f(x) = - 3({x^2} + 6){({x^2} + 4)^2}$ . Any help is greatly appreciate... | 4 | [
-0.033447265625,
-0.038330078125,
-0.0654296875,
0.06689453125,
0.00921630859375,
0.0830078125,
-0.0634765625,
-0.0172119140625,
0.0830078125,
-0.038818359375,
0.1416015625,
-0.080078125,
-0.061767578125,
-0.04638671875,
-0.0167236328125,
-0.015869140625,
-0.037109375,
-0.049560546... | 33,723 | 33723 | |
Speed Distance!!
Author Message
TAGS:
00:00
B
C
... | 4 | [
0.040771484375,
0.033203125,
0.048095703125,
-0.03564453125,
-0.03466796875,
0.0137939453125,
-0.058837890625,
0.01904296875,
-0.04248046875,
-0.024169921875,
0.09326171875,
-0.03857421875,
0.006011962890625,
0.0250244140625,
-0.06298828125,
0.0250244140625,
0.06591796875,
-0.03271... | 33,724 | 33724 | |
Can anyone show me how to complete the square on this
It would be $(x-4)^2-2+(y+1)^2+13$. Which is wrong. Solutions manual says it's supposed to be $(x-4)^2-16+(y+1)^2-1$
so would it be what i had = 0 or = -14. I am so confused.
Start with your initial equation, then whatever you add to complete the square on the x t... | 4 | [
-0.0284423828125,
0.057861328125,
0.0201416015625,
-0.0002880096435546875,
-0.01324462890625,
0.05126953125,
-0.07568359375,
-0.0021514892578125,
0.0213623046875,
-0.057373046875,
0.07470703125,
0.0029144287109375,
-0.032958984375,
0.06201171875,
-0.038330078125,
0.05419921875,
-0.04... | 33,725 | 33725 | |
Uniform convergence vs pointwise convergence
April 23rd 2011, 11:34 PM #1
Newbie
Joined
Jan 2011
Posts
18
Uniform convergence vs pointwise convergence
Hi guys,
Can someone please explain to me the advantages of uniform convergence over pointwise convergence? I was told that pointwise convergence doe... | 4 | [
-0.07763671875,
0.0047607421875,
-0.0703125,
-0.0157470703125,
0.091796875,
0.0238037109375,
0.037353515625,
0.003448486328125,
0.04638671875,
-0.032470703125,
-0.029541015625,
0.1083984375,
0.06298828125,
-0.010498046875,
0.07763671875,
-0.08935546875,
0.045166015625,
-0.126953125... | 33,726 | 33726 | |
find all possible values
Let $a,b,c,d$ positive real numbers such that $a+b+c+d=12$ , and $abcd =27+ab+ac+ad+bc+bd+cd$ find all possible values of $a,b,c,d$
Solution: Given a+b+c+d=12 and abcd=27+ab+ac+ad+bc+bd+cd then a,b,c and d =? let a=b=c=d=3 then 3+3+3+3=12 LHS => abcd=3*3*3*3=81 RHS=> 27+3*3+3*3+3*3+3*3+3*3+3*3... | 4 | [
-0.09912109375,
0.04052734375,
-0.0185546875,
-0.09765625,
-0.06982421875,
0.021728515625,
0.02685546875,
-0.0419921875,
-0.001556396484375,
0.037109375,
0.0233154296875,
-0.0233154296875,
0.0238037109375,
-0.001922607421875,
0.0206298828125,
-0.01153564453125,
-0.04296875,
0.05273... | 33,727 | 33727 | |
Example 1
We illustrate the straightforward solution of a DDE by computing and plotting the solution of Example 3 of [23]. The equations
are to be solved on [0,5] with history y[1](t) = 1,y[2](t) = 1, y[3](t) = 1 for t £ 0.
A typical invocation of dde23 has the form
sol = dde23(ddefile,lags,history,tspan);
The ... | 5 | [
-0.07958984375,
-0.045654296875,
-0.038818359375,
-0.080078125,
0.0322265625,
-0.0654296875,
-0.0079345703125,
0.0299072265625,
-0.038330078125,
-0.01611328125,
-0.0025482177734375,
0.005096435546875,
-0.04150390625,
-0.002227783203125,
-0.03857421875,
-0.044921875,
-0.1025390625,
... | 33,728 | 33728 | |
1966 QST Article
[Table of Contents]These articles are scanned and OCRed from old editions of the ARRL's QST magazine. Here is a list of the QST articles I have already posted. All copyrights (if any) are hereby
acknowledged.
A Passive Limiter
By George Schleicher.* W9NLT
Fig. 1 - The basic limiter circuit. Closing... | 4 | [
-0.154296875,
0.0050048828125,
0.01434326171875,
0.009765625,
0.031982421875,
0.015869140625,
-0.00653076171875,
0.08203125,
-0.0283203125,
0.046630859375,
0.018798828125,
0.0211181640625,
-0.01153564453125,
-0.0196533203125,
-0.06396484375,
0.05615234375,
0.0693359375,
-0.01416015... | 33,729 | 33729 | |
tion
Show that $C(8,4)=C(7,3)+C(7,4)$ Let's manipulate the left side to become the right side $\frac{8!}{4!\cdot (8-4)!}=\frac{8!}{4!\cdot 4!}=\frac{8\cdot 7!}{4!\cdot 4\cdot 3!}=\frac{2\cdot 7!}{4!\cdot
3!}=\frac{7!}{4!\cdot 3!}+\frac{7!}{4!\cdot 3!}$ $\frac{7!}{3!\cdot (7-3)!}+\frac{7!}{4!\cdot (7-4)!}=\boxed{C(7,3)+... | 5 | [
-0.0284423828125,
-0.00311279296875,
-0.0103759765625,
0.05908203125,
-0.10693359375,
0.10205078125,
-0.0018310546875,
0.0123291015625,
-0.005584716796875,
0.021728515625,
-0.03857421875,
-0.11669921875,
-0.042724609375,
0.051513671875,
-0.08935546875,
-0.0274658203125,
-0.0791015625... | 33,730 | 33730 | |
Inverting matrix with unknown.
September 6th 2009, 09:11 PM #1
Member
Joined
Sep 2007
Posts
81
Inverting matrix with unknown.
Hi all,
Quick question.
I'm just unsure of how to handle an unknown in a matrix when talking about finding the inverse.
Usually I simply augment (A|I) and reduce it... | 4 | [
-0.0771484375,
0.021240234375,
-0.051025390625,
0.0274658203125,
0.0732421875,
-0.10107421875,
0.0135498046875,
-0.06591796875,
-0.039794921875,
0.029541015625,
0.03173828125,
-0.0274658203125,
0.053955078125,
-0.01385498046875,
-0.037109375,
0.03271484375,
-0.0196533203125,
0.0228... | 33,731 | 33731 | |
Solving Linear Systems by Graphing
Definition of a Linear System
Real-world applications are often modeled using more than one variable and more than one equation. A system of equationsA set of two or more equations with the same variables. consists of a set of
two or more equations with the same variables. In this se... | 4 | [
-0.03173828125,
-0.0196533203125,
-0.1142578125,
-0.036865234375,
-0.00946044921875,
-0.0311279296875,
-0.03857421875,
-0.0125732421875,
0.0272216796875,
0.03466796875,
0.0732421875,
0.042724609375,
0.0634765625,
0.0267333984375,
0.04833984375,
0.0194091796875,
-0.123046875,
-0.016... | 33,732 | 33732 | |
Pesquisa Operacional
Serviços Personalizados
Artigo
Indicadores
Links relacionados
Compartilhar
versão impressa ISSN 0101-7438
Pesqui. Oper. v.26 n.3 Rio de Janeiro set./dez. 2006
http://dx.doi.org/10.1590/S0101-74382006000300002
Lagrangean relaxation bounds for point-feature cartographic label placement probl... | 4 | [
0.07421875,
-0.02587890625,
-0.03125,
-0.07421875,
0.0172119140625,
0.09130859375,
0.033203125,
0.0634765625,
0.00494384765625,
-0.04736328125,
0.03955078125,
0.046630859375,
0.012451171875,
0.04736328125,
0.01422119140625,
-0.004791259765625,
0.06787109375,
-0.03125,
0.023925781... | 33,733 | 33733 | |
Sum or Difference Formulas
January 4th 2012, 10:27 PM
Nickod777
Sum or Difference Formulas
This is not for homework, nor for a teacher to see, just a test correction so that I know what to do, or what I am doing wrong.
Use the sum or Difference formulas to find the exact value of each expression.
1. si... | 4 | [
-0.041015625,
0.04248046875,
-0.05224609375,
-0.000560760498046875,
-0.0146484375,
0.0311279296875,
-0.0556640625,
-0.0031280517578125,
0.033447265625,
0.011962890625,
0.03955078125,
-0.04296875,
0.0186767578125,
0.0634765625,
0.064453125,
0.005157470703125,
-0.035400390625,
-0.033... | 33,734 | 33734 | |
Generating Functions
February 12th 2010, 03:10 PM #1
Newbie
Joined
Nov 2009
Posts
20
Generating Functions
Hi can someone please help me with the following please:
Find the generating functions for the following sequences, express them in a closed form, without infinite sums:
(i) 1,2,1,4,1,8,1,1... | 5 | [
-0.05712890625,
-0.0177001953125,
0.0169677734375,
0.054931640625,
-0.017822265625,
-0.0191650390625,
0.061767578125,
-0.04052734375,
0.01806640625,
0.00592041015625,
-0.048583984375,
-0.1064453125,
0.035888671875,
-0.01397705078125,
-0.05322265625,
0.029541015625,
-0.034912109375,
... | 33,735 | 33735 | |
Find E(X)
April 7th 2009, 11:56 AM #1
Banned
Joined
Jan 2009
Posts
58
Find E(X)
In a state lottery a three digit integer is selected at random. A player bets $1 on a particular number and if that number is selected, the payoff is $500 minus the $1 paid for the ticket. Let X
equal the payoff to the be... | 4 | [
-0.02587890625,
0.0859375,
0.0036468505859375,
-0.037353515625,
0.01068115234375,
0.042724609375,
0.1591796875,
0.0281982421875,
-0.005645751953125,
0.051513671875,
-0.0281982421875,
-0.0101318359375,
0.06787109375,
0.02734375,
-0.057373046875,
-0.07666015625,
-0.0166015625,
-0.040... | 33,736 | 33736 | |
deleted neighborhood of limit L
July 23rd 2011, 08:59 PM #1
Junior Member
Joined
Jun 2011
From
Colorado, United States
Posts
56
deleted neighborhood of limit L
The question is this true or false. Justify.
Let f:[a,b]-> $\Re$ and let c $\in$ (a,b). If lim_{x->c} f(x)=L and L>0, then there is a de... | 5 | [
-0.02880859375,
0.00970458984375,
0.024169921875,
-0.006622314453125,
0.11328125,
0.0771484375,
0.020751953125,
-0.034912109375,
-0.00077056884765625,
-0.01397705078125,
0.043701171875,
-0.031982421875,
0.0120849609375,
0.053466796875,
0.06640625,
-0.01904296875,
-0.0279541015625,
... | 33,737 | 33737 | |
Proof of Convergence of a Series
June 30th 2010, 02:45 PM
ragnar
Proof of Convergence of a Series
I'm trying to prove that, if $|z| > 1$ for any complex $z$, then $\displaystyle \sum^{\infty}_{n = 1} \frac{1}{1 + z^{n}}$ converges. I got this far but no farther:
If we try by comparison test, $|\frac{1}{1 + ... | 5 | [
-0.0234375,
0.018310546875,
-0.013427734375,
0.0908203125,
0.05029296875,
-0.08740234375,
-0.04638671875,
0.05224609375,
-0.042236328125,
-0.0164794921875,
-0.09814453125,
0.0206298828125,
0.05908203125,
0.035400390625,
-0.05419921875,
-0.02392578125,
0.061767578125,
-0.11328125,
... | 33,738 | 33738 | |
Related Rates, urgent
February 27th 2007, 05:58 AM #1
estabaaqui
Guest
Related Rates, urgent
I did some of the work but didn't have time to put it up here. I'm really confused...can someone help me.
A baseball diamond has the shape of a square with sides 90 feet long. A player hits the ball and runs toward f... | 5 | [
0.12353515625,
0.057861328125,
-0.041015625,
-0.07763671875,
-0.01397705078125,
0.059326171875,
-0.146484375,
0.11669921875,
-0.004302978515625,
0.0810546875,
0.07421875,
-0.053955078125,
-0.005767822265625,
0.072265625,
0.0244140625,
0.0220947265625,
0.008056640625,
0.003295898437... | 33,739 | 33739 | |
Differential Geometry exam confusion!
December 9th 2007, 04:28 AM #1
Newbie
Joined
Nov 2007
Posts
23
Differential Geometry exam confusion!
Right, I need to show that a(t)=(cost,sint,0)is not a geodesic of the plane.
But I'm not sure what I'm supposed to actually do!
Right I've been thinking abou... | 4 | [
-0.033447265625,
-0.002410888671875,
0.01495361328125,
-0.035888671875,
-0.0201416015625,
-0.0186767578125,
0.08740234375,
-0.00015354156494140625,
0.04541015625,
0.002044677734375,
0.080078125,
-0.000873565673828125,
-0.033447265625,
0.01177978515625,
-0.08935546875,
-0.0517578125,
... | 33,740 | 33740 | |
Fraction Equations With Powers
October 24th 2008, 06:38 PM #1
Newbie
Joined
Oct 2008
Posts
9
Hey, I hate to ask this much of someone to help but im in a real bad spot right now and my college exam is coming up monday and when handed a review to study, my mind went completely blank on
half the review s... | 4 | [
-0.024658203125,
-0.021240234375,
0.0252685546875,
0.04833984375,
0.033203125,
0.00579833984375,
-0.07080078125,
0.039794921875,
0.0157470703125,
-0.04052734375,
0.07421875,
-0.08447265625,
0.09326171875,
0.08154296875,
0.018798828125,
0.0947265625,
0.00933837890625,
0.01953125,
... | 33,741 | 33741 | |
Area of Combined Shapes
Area of combined shape is nothing but more than one shape is combined together we can find the area of the combined shapes. Here we are going to see some example problems for finding the area of the
combine shapes. Normally area is nothing but the space occupied by the 2 dimensional shape. The ... | 4 | [
0.09033203125,
-0.01165771484375,
-0.016845703125,
0.0035400390625,
-0.05322265625,
-0.08447265625,
-0.0380859375,
0.07861328125,
0.004730224609375,
-0.057373046875,
0.0162353515625,
-0.057373046875,
0.043701171875,
0.038818359375,
0.034423828125,
-0.0233154296875,
-0.0255126953125,
... | 33,742 | 33742 | |
Differential Equations
July 26th 2007, 10:08 AM #1
Differential Equations
A water trough, 6 metres long, has uniform cross section in the shape of a semicircle with horizontal diameter 2 metres. It contains water to a depth of x metres. THe centre of the circle is at O
and the triangle POQ is isosceles with a... | 4 | [
-0.0498046875,
0.020263671875,
0.0015869140625,
-0.01611328125,
0.00970458984375,
-0.0634765625,
-0.05224609375,
0.056884765625,
0.00124359130859375,
-0.034912109375,
-0.001312255859375,
-0.115234375,
0.0159912109375,
0.00057220458984375,
0.07421875,
-0.005950927734375,
-0.072265625,... | 33,743 | 33743 | |
Range of 3d function?
Khan
I'm not sure how to approach this problem:
Find the range of f(x,y) = Ax^2 + 2Bxy + Cy^2 (Answer will be in terms of A, B, and C)
Thanks! And we haven't yet been allowed to use partial derivatives, so they can't be used to solve it.
First investigate the cases when one or more coefficient... | 4 | [
0.006744384765625,
0.08154296875,
-0.0400390625,
-0.01385498046875,
-0.050048828125,
0.0771484375,
-0.09130859375,
-0.000035762786865234375,
-0.0013427734375,
-0.035400390625,
0.032958984375,
-0.06591796875,
0.0400390625,
0.09033203125,
0.031982421875,
0.055908203125,
-0.018432617187... | 33,744 | 33744 | |
Induction Proof again :(
November 20th 2007, 04:45 PM #1
Newbie
Joined
Oct 2007
Posts
4
Induction Proof again :(
Hi all,
Once again I'm pretty stumped at this one.
3^3 = 27
3^4 = 81
3^5 =243
3^6 = 729
3^7 = 2187
Now these are the same practically. An even second to last ... | 5 | [
-0.0390625,
-0.01190185546875,
-0.06640625,
-0.00567626953125,
0.03759765625,
0.0155029296875,
0.06884765625,
0.0174560546875,
-0.01611328125,
0.048095703125,
-0.0380859375,
0.0093994140625,
0.01708984375,
0.024169921875,
0.016845703125,
-0.0634765625,
-0.12353515625,
0.064453125,
... | 33,745 | 33745 | |
real hard problem
April 16th 2009, 12:12 PM #1
Junior Member
Joined
Feb 2009
Posts
40
real hard problem
Suppose that $lim_{x\rightarrow a}$$f(x)$ exist and is positive. Show that for any positive integer n we have
$<br /> \lim_{x\rightarrow a} \sqrt[n]{f(x)} = \sqrt[n]{\lim_{x\rightarrow a} {f(x)}}<b... | 5 | [
-0.04541015625,
-0.064453125,
0.01275634765625,
0.04443359375,
-0.1044921875,
0.009765625,
-0.01324462890625,
0.031005859375,
0.009521484375,
-0.03515625,
0.025634765625,
0.072265625,
0.07080078125,
0.04931640625,
0.0208740234375,
0.022705078125,
-0.035888671875,
-0.00909423828125,... | 33,746 | 33746 | |
Interest Rate and Equity Swaps - CFA Level 1 | Investopedia
CFA Level 1
Derivatives - Interest Rate and Equity Swaps
Plain Vanilla Interest Rate Swap
In general, an interest rate swap is an agreement to exchange rate cash flows from interest-bearing instruments at specified payment dates. Each party's payment obligat... | 4 | [
-0.04638671875,
-0.0264892578125,
-0.11376953125,
-0.025146484375,
-0.045654296875,
-0.0400390625,
0.00634765625,
0.025634765625,
0.1318359375,
0.018798828125,
0.0556640625,
0.034912109375,
-0.031494140625,
0.020751953125,
-0.0093994140625,
0.0556640625,
-0.06787109375,
0.008056640... | 33,747 | 33747 | |
Sum and Difference FormulasAlgebraLAB: Lessons
Introduction:
In this lesson, formulas involving the sum and difference of two angles will be defined and applied to the fundamental trig functions.
The Lesson:
For two angles a and b, we have the following relationships:
Sum formulas:
i. sin(a + b) = sin(a)co... | 4 | [
-0.1171875,
0.06689453125,
-0.048583984375,
-0.050048828125,
-0.0498046875,
0.072265625,
-0.0240478515625,
0.002044677734375,
0.04638671875,
0.043701171875,
0.05224609375,
-0.083984375,
0.041259765625,
0.07666015625,
0.09521484375,
-0.03515625,
-0.076171875,
0.04052734375,
-0.021... | 33,748 | 33748 | |
Obtain an expression
Given that $\sum^{n}_{r=1}r^2=\frac{1}{6}n(n+1)(2n+1)$ , obtain an expression , in its simplest term , for $<br /> \sum^{2n}_{r=n+1}(2r-1)^2<br />$ Thanks .
$<br /> \begin{gathered}<br /> \sum\limits_{r = n + 1}^{2n} {\left( {2r - 1} \right)^2 } = \sum\limits_{r = 1}^n {\left( {2(r + n) - 1} \righ... | 4 | [
-0.031982421875,
0.042724609375,
0.03076171875,
0.0751953125,
-0.015380859375,
0.049560546875,
-0.1025390625,
0.0908203125,
0.036865234375,
-0.0546875,
-0.11279296875,
-0.07177734375,
-0.039794921875,
0.0279541015625,
-0.06640625,
-0.033447265625,
0.0244140625,
0.025146484375,
0.... | 33,749 | 33749 | |
surface integral
February 26th 2013, 12:38 PM #1
Newbie
Joined
Aug 2012
From
Croatia
Posts
23
surface integral
Find surface area given when rotating $y=(x+5)^{\frac{1}{2}}$ and $5^{\frac{1}{2}} \leqslant x \leqslant 3$ around y asis.
How do i do this? Any help
Re: surface integral
Where did... | 5 | [
-0.031494140625,
-0.0225830078125,
0.06591796875,
-0.080078125,
0.0084228515625,
-0.11279296875,
-0.005462646484375,
0.10498046875,
-0.04052734375,
0.024658203125,
-0.0419921875,
0.046630859375,
0.035400390625,
0.09765625,
-0.024169921875,
0.040283203125,
-0.0067138671875,
-0.02502... | 33,750 | 33750 | |
real analysis
March 1st 2009, 07:43 AM
yuan.69
real analysis
1. If ∑an with an >0 is convergent, then is ∑an² always convergent? Either prove it or give a counterexample?
2. If ∑an with an >0 is convergent, then is ∑(anan+1)^(1/2) always convergent? Either prove it or give a counterexample?
3. Show that ... | 5 | [
-0.037841796875,
-0.08984375,
0.080078125,
0.1103515625,
-0.005340576171875,
0.031005859375,
0.02880859375,
0.002105712890625,
0.0830078125,
0.01519775390625,
0.08154296875,
0.0279541015625,
0.04150390625,
0.0810546875,
-0.06494140625,
-0.033447265625,
0.003936767578125,
-0.0087280... | 33,751 | 33751 | |
Extremely Simple Circle Probability Problem! :)
December 15th 2009, 07:06 PM #1
Newbie
Joined
Nov 2009
Posts
13
Extremely Simple Circle Problem! :)
How many ways can 8 boys be arranged in a circle if 3 boys cannot sit next to each other?
Well, I don't actually have the correct answer, but this is ho... | 4 | [
0.0028839111328125,
-0.04345703125,
-0.00689697265625,
-0.024169921875,
-0.037109375,
-0.0299072265625,
-0.0220947265625,
-0.004150390625,
0.03173828125,
0.0272216796875,
0.041748046875,
-0.0272216796875,
0.052490234375,
0.049072265625,
0.02685546875,
-0.0281982421875,
-0.0166015625,... | 33,752 | 33752 | |
Lie Algebra-Roots and Dynkin basis
December 29th 2010, 06:44 AM #1
Junior Member
Joined
Jun 2007
Posts
43
Lie Algebra-Roots and Dynkin basis
Given a Lie algebra I understand all the stuff about the Cartan-Weyl basis, the roots and stuff, so for example, for A2, the roots are
$\alpha=(1,0), \ \ \beta... | 4 | [
-0.087890625,
-0.1220703125,
-0.050048828125,
-0.00799560546875,
-0.0400390625,
-0.042724609375,
0.0018768310546875,
-0.0012664794921875,
0.0169677734375,
-0.0693359375,
0.06640625,
0.057373046875,
-0.0908203125,
-0.028076171875,
-0.019775390625,
0.0245361328125,
-0.12109375,
0.032... | 33,753 | 33753 | |
Homework Help
Posted by Lizzie on Monday, May 7, 2012 at 2:16am.
In a financial deal, you are promised $800 the first day and each day after that you will receive 45% of the previous day's amount. When one day's amount drops below $1, you stop getting paid from
that day on. What day is the first day you would receive ... | 4 | [
-0.0247802734375,
0.0947265625,
0.04541015625,
0.015380859375,
-0.05615234375,
-0.052978515625,
0.047119140625,
0.009033203125,
-0.0390625,
0.033203125,
0.03271484375,
-0.078125,
0.021484375,
0.040283203125,
-0.005615234375,
0.011962890625,
-0.1357421875,
-0.0201416015625,
-0.082... | 33,754 | 33754 | |
Internet Encyclopedia of Philosophy
Rudolf Carnap: Modal Logic
The Journal of Symbolic Logic in 1946 and the book Meaning and Necessity in 1947, Rudolf Carnap developed a modal predicate logic containing a necessity operator N, whose semantics depends on the
claim that, where α is a formula of the language, Nα represe... | 4 | [
-0.046875,
0.0458984375,
-0.031005859375,
-0.0322265625,
0.006683349609375,
0.0262451171875,
0.056640625,
0.056640625,
-0.03173828125,
-0.01019287109375,
0.00921630859375,
0.022705078125,
0.0032501220703125,
0.06640625,
-0.00244140625,
0.036376953125,
-0.04443359375,
-0.04467773437... | 33,755 | 33755 | |
Combination/ Permutation Question
May 18th 2010, 10:39 PM #1
Newbie
Joined
Jan 2010
Posts
22
Combination/ Permutation Question
I have a few questions i don't understand T_T
1. A committe of 4 people is to be chosen form a group of 8 people- 4 women and 4 men. How many ways can the committee be chose... | 4 | [
0.06591796875,
0.044189453125,
0.041748046875,
-0.032470703125,
-0.035888671875,
0.01806640625,
0.04931640625,
-0.03125,
-0.018310546875,
0.039794921875,
-0.08984375,
0.0111083984375,
-0.05078125,
-0.045654296875,
-0.0380859375,
-0.0211181640625,
-0.01806640625,
-0.07373046875,
0... | 33,756 | 33756 | |
Homework Help
Posted by Sam on Wednesday, January 12, 2011 at 10:27pm.
1.In a jar, suppose there are 3 blue marbles, 2 yellow marbles and one red marble.
c. Suppose that 3 marbles are drawn from the jar without replacement. What is the probability that the 3 marbles are all different colors?
d. Suppose that 4 marble... | 4 | [
0.022705078125,
-0.0291748046875,
0.060302734375,
-0.040283203125,
-0.03662109375,
0.046875,
0.052490234375,
0.0184326171875,
0.0155029296875,
0.0203857421875,
0.0027313232421875,
-0.057373046875,
0.03759765625,
0.0244140625,
0.00885009765625,
0.041259765625,
0.0302734375,
0.031494... | 33,757 | 33757 | |
Exponential Functions
Posted by Jus on Tuesday, May 19, 2009 at 7:51pm.
Show that if
log_b (a) = c, and log_y (b) = c, then log_a (y)=c^-2
• Exponential Functions - Reiny, Tuesday, May 19, 2009 at 8:31pm
recall
log[b] a = log a/log b (base 10, or any other base for that matter)
so log[b](a) = loga/lo... | 4 | [
-0.0439453125,
0.002899169921875,
-0.037353515625,
0.029541015625,
-0.0263671875,
-0.046875,
-0.0341796875,
-0.0026092529296875,
0.02880859375,
0.005889892578125,
0.06396484375,
-0.045654296875,
-0.035888671875,
0.142578125,
0.0810546875,
0.0615234375,
-0.13671875,
0.07861328125,
... | 33,758 | 33758 | |
Probability using permutation and combination
September 10th 2012, 10:15 PM #1
Newbie
Joined
Sep 2012
From
Mauritius
Posts
13
Probability using permutation and combination
Question : Four-figure numbers are to be formed from the digits 4,5,6,7,8,9 .How many different four-figure numbers can be formed... | 4 | [
0.01953125,
-0.0263671875,
-0.014404296875,
-0.1201171875,
-0.03857421875,
0.0810546875,
0.00311279296875,
0.01470947265625,
0.0498046875,
0.04248046875,
0.01708984375,
0.01129150390625,
0.00384521484375,
0.02685546875,
-0.01483154296875,
0.04052734375,
-0.078125,
0.0301513671875,
... | 33,759 | 33759 | |
Polar Equations
Given the polar equation r=4/(2+2sin(x)).Find the Directrix,eccentricity and sketch the conic.
Hello, Gracy! You're expected to know the general form for polar conics. . . $r \:=\:\frac{ke}{1 + e\sin\theta}\qquad\text{or}\qquad r\:=\:\frac{ke}{1 + e\cos\theta}$ . where $e$ = eccentricity And
these rule... | 4 | [
0.058837890625,
0.025634765625,
-0.05712890625,
-0.037841796875,
0.087890625,
-0.064453125,
-0.00958251953125,
0.054443359375,
0.0263671875,
0.044189453125,
0.107421875,
-0.07568359375,
-0.0257568359375,
0.033935546875,
0.0595703125,
0.0040283203125,
-0.052734375,
-0.0634765625,
... | 33,760 | 33760 | |
Points in the plane.
I want to find some arbitrary point in the plane $2x+4y-2z + 10 =0$ Thank you.
Hello, MatteNoob! I want to find some arbitrary point in the plane: . $2x+4y-2z + 10 \:=\:0$ The easiest points are the intercepts. .You can "eyeball" the answers! . . $\begin{array}{cccccccc} \text
{Let }y = 0,\:z = 0\... | 4 | [
-0.0125732421875,
-0.0185546875,
-0.05322265625,
-0.0244140625,
0.1103515625,
0.04150390625,
0.103515625,
0.0556640625,
-0.0517578125,
0.001556396484375,
0.0703125,
-0.01513671875,
0.0026702880859375,
0.04052734375,
-0.01239013671875,
0.035400390625,
-0.0390625,
-0.057861328125,
... | 33,761 | 33761 | |
Simulation to Implementation as Good Practices for Teaching Power Electronics to Undergraduate Students: Fuzzy Sliding Mode Control for DC Motors
Advances in Power Electronics
Volume 2014 (2014), Article ID 697263, 9 pages
http://dx.doi.org/10.1155/2014/697263
Research Article
Simulation to Implementation as Good Pra... | 4 | [
-0.06591796875,
0.0673828125,
0.058349609375,
0.0015716552734375,
-0.068359375,
-0.03271484375,
-0.01611328125,
0.0130615234375,
0.0146484375,
0.0732421875,
0.11572265625,
0.0400390625,
0.0986328125,
-0.06884765625,
-0.051025390625,
0.10205078125,
0.03271484375,
-0.07275390625,
0... | 33,762 | 33762 | |
Sum The Series
September 14th 2007, 09:43 PM #1
Newbie
Joined
Sep 2007
Posts
11
How would I solve this?:
Sum The Series-
1 x 2 + 2 x 3 + 3 x 4 + . . . + 1994 x 1995
Thanx
$\displaystyle\sum_{k=1}^{1994}k(k+1)=\sum_{k=1}^{1 994}(k^2+k)=\sum_{k=1}^{1994}k^2+\sum_{k=1}^{1994} k$
Now u... | 4 | [
-0.01190185546875,
0.051025390625,
0.107421875,
-0.007232666015625,
-0.051025390625,
0.07568359375,
-0.06298828125,
0.0146484375,
0.01483154296875,
-0.0830078125,
-0.07421875,
-0.0380859375,
-0.049560546875,
-0.048095703125,
-0.07861328125,
-0.07568359375,
0.031005859375,
0.0722656... | 33,763 | 33763 | |
Huffman Encoding
Bases: sage.structure.sage_object.SageObject
This class implements the basic functionalities of Huffman codes.
It can build a Huffman code from a given string, or from the information of a dictionary associating to each key (the elements of the alphabet) a weight (most of the time, a prob... | 5 | [
-0.058349609375,
0.00469970703125,
-0.138671875,
-0.027099609375,
-0.0712890625,
-0.0263671875,
-0.007293701171875,
-0.0142822265625,
-0.01025390625,
0.0108642578125,
0.0235595703125,
0.036376953125,
0.04833984375,
-0.036865234375,
0.041259765625,
0.07177734375,
-0.05126953125,
0.0... | 33,764 | 33764 | |
Homework Help
Posted by Marcia on Friday, April 27, 2012 at 2:32pm.
A bug is placed on the road. t seconds after it is put down, the function is p(t) = -16tsquared + 64t, where p(t) is measure in feet. At what moment will the bug be 14 feet from where it began?
• Algebra 2 - visoth, Friday, April 27, 2012 at 3:59pm... | 4 | [
-0.08837890625,
0.0888671875,
0.0703125,
0.03076171875,
0.01483154296875,
0.00034332275390625,
-0.0419921875,
0.1005859375,
-0.040771484375,
0.00848388671875,
0.1171875,
-0.003082275390625,
-0.0012054443359375,
0.076171875,
-0.08837890625,
-0.020263671875,
-0.062255859375,
-0.03881... | 33,765 | 33765 | |
Hermitian Matrix
November 9th 2012, 09:57 AM
sfspitfire23
Hermitian Matrix
Let M be an nxn complex orthogonal matrix. Show that for any two column vectors v, w in C,
show that v * w = (Mv) * (Mw)
where * denotes the dot product.
I'm stuck. I know that any vector v^H = v^-1
Thanks
November 9t... | 5 | [
-0.0791015625,
0.003814697265625,
-0.0537109375,
0.02783203125,
-0.0208740234375,
-0.04443359375,
0.030029296875,
-0.08349609375,
-0.03662109375,
-0.0123291015625,
0.0615234375,
-0.0111083984375,
0.00165557861328125,
0.032470703125,
-0.03857421875,
0.0888671875,
-0.040771484375,
0.... | 33,766 | 33766 | |
Sequence and series
April 8th 2009, 01:19 AM #1
Junior Member
Joined
Mar 2009
Posts
52
Sequence and series
Q- Find the sum of the series -
1+1/3+1/6+1/10+1/15+...........
what should be our approach to solve these kind of questions ?
Thanks,
Ashish
Hi
$S = \frac{1}{1} + \frac... | 5 | [
-0.107421875,
0.0111083984375,
0.12451171875,
0.0017852783203125,
0.02294921875,
-0.0050048828125,
0.0172119140625,
0.0791015625,
-0.042236328125,
0.020263671875,
-0.08203125,
-0.0556640625,
-0.06201171875,
0.0179443359375,
-0.078125,
-0.07275390625,
0.0908203125,
-0.00619506835937... | 33,767 | 33767 | |
Homework Help
Posted by TO: Mathmate on Monday, April 23, 2012 at 10:52pm.
This is a substitution equation. Would that change the steps that you did?
Y=3x+1
Y=5x-3
Answer says x=-2 and y=7
Please explain steps. Thanks
math help - MathMate, Monday, April 23, 2012 at 10:25pm
Y=3x+1 ...(1)
Y=5x-3 ...(2)
By compar... | 4 | [
-0.11328125,
0.01092529296875,
0.06591796875,
-0.0038604736328125,
0.00958251953125,
-0.010986328125,
0.04150390625,
0.01092529296875,
-0.0849609375,
0.00078582763671875,
0.004364013671875,
-0.0126953125,
0.012939453125,
-0.0033721923828125,
-0.0205078125,
0.055419921875,
-0.08496093... | 33,768 | 33768 | |
Proving matrix addition theorem
September 19th 2009, 03:37 PM #1
Newbie
Joined
Sep 2009
Posts
7
Proving matrix addition theorem
Hi, I'm in first year university and I'm new to proofs, so I was wondering if anyone here can help me out.
The questions ask to prove:
1) A + (B + C) = (A + B) + c
... | 4 | [
-0.083984375,
-0.00799560546875,
-0.002777099609375,
-0.039306640625,
-0.03125,
0.0517578125,
0.060302734375,
-0.07373046875,
0.00004410743713378906,
0.07470703125,
0.0888671875,
-0.05517578125,
0.0013580322265625,
-0.020263671875,
0.0162353515625,
0.072265625,
0.004638671875,
0.07... | 33,769 | 33769 | |
Greens Theorem
Attachment 27490 How would I use Green's Theorem to prove this area integral?
It is a known deduction of Green's Theorem that, for an area of a disc in a plane, $\displaystyle A = \frac{1}{2}\oint_D xdy-ydx$ Find an expression of x and y in terms of $r=f(\theta)$. and
substitute into this equation. The ... | 5 | [
-0.01226806640625,
-0.02783203125,
-0.04150390625,
-0.0693359375,
0.08544921875,
0.00762939453125,
-0.03662109375,
0.07421875,
0.036376953125,
0.044677734375,
0.004425048828125,
0.0142822265625,
-0.0380859375,
0.06298828125,
0.07470703125,
0.0419921875,
-0.08544921875,
0.0119018554... | 33,770 | 33770 | |
expansion, binomial
May 9th 2009, 09:34 AM #1
Super Member
Joined
Sep 2008
Posts
607
expansion, binomial
In the binomial expansion of $(2k+x)^n$ where k is a constant and n is a positive integer, the coefficient of $x^2$ is equal to the coefficient of $x^3$.
(a) Prove that n=6k+2.
$(2k+x)^n = 2... | 4 | [
-0.003143310546875,
0.00811767578125,
-0.03515625,
0.08837890625,
0.01190185546875,
0.07861328125,
0.0057373046875,
0.004150390625,
0.005767822265625,
-0.01458740234375,
0.01708984375,
-0.095703125,
-0.0693359375,
-0.1015625,
-0.002655029296875,
0.046875,
0.01519775390625,
0.041503... | 33,771 | 33771 | |
Homework Help
Posted by partha on Friday, September 20, 2013 at 1:21pm.
in how many ways can the letters of mahabharat be arranged so that, b and t are never together and m,a,t,h occurs at first four places
• maths - Steve, Friday, September 20, 2013 at 1:38pm
There are 4! ways to arrange m,a,t,h in the 1st 4 ... | 4 | [
0.00439453125,
-0.01519775390625,
0.048095703125,
-0.038330078125,
-0.1630859375,
0.0703125,
-0.0272216796875,
-0.03515625,
0.01806640625,
0.123046875,
0.061279296875,
-0.041015625,
0.07958984375,
-0.05810546875,
-0.051513671875,
0.013671875,
-0.05419921875,
-0.09619140625,
-0.09... | 33,772 | 33772 | |
Study on Driving Stability of Tank Trucks Based on Equivalent Trammel Pendulum for Liquid Sloshing
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 659873, 15 pages
http://dx.doi.org/10.1155/2013/659873
Research Article
Study on Driving Stability of Tank Trucks Based on Equivalent Trammel Pendul... | 4 | [
-0.035888671875,
0.02197265625,
0.01092529296875,
0.0240478515625,
-0.03076171875,
-0.0361328125,
-0.00848388671875,
0.0067138671875,
-0.008544921875,
-0.0634765625,
-0.0625,
0.054443359375,
0.05908203125,
-0.0078125,
-0.0537109375,
0.011962890625,
0.09130859375,
0.0751953125,
-0... | 33,773 | 33773 | |
Probability with random-coefficient quadratic equation
August 14th 2009, 04:43 AM #1
Newbie
Joined
Apr 2009
From
Many
Posts
17
Probability with random-coefficient quadratic equation
Let A, B, and C be independent random variables, and consider the random-coefficient quadratic equation $Ax^2 + Bx + C ... | 5 | [
-0.0091552734375,
-0.0216064453125,
0.0228271484375,
0.041748046875,
-0.053955078125,
-0.00115203857421875,
0.041015625,
-0.0037689208984375,
0.09033203125,
-0.006011962890625,
0.039794921875,
-0.0172119140625,
0.042724609375,
0.00689697265625,
-0.02392578125,
0.01507568359375,
-0.03... | 33,774 | 33774 | |
Indefinite Integral
March 10th 2010, 11:10 PM #1
Junior Member
Joined
May 2008
From
California
Posts
36
Indefinite Integral
Just bummed on this question here.. :
∫(pi/ax+b)dx
Thanks so much!
Step by step teaching if possible.. Thank you so much. I want to learn!
Dear gearshifter,
... | 5 | [
-0.08349609375,
-0.045166015625,
0.0296630859375,
-0.03173828125,
-0.0213623046875,
0.06982421875,
-0.0033721923828125,
-0.021240234375,
0.0028533935546875,
0.07373046875,
0.0245361328125,
0.0286865234375,
-0.02783203125,
0.023193359375,
-0.0115966796875,
0.0181884765625,
-0.01928710... | 33,775 | 33775 | |
Contaduría y administración
Servicios Personalizados
Artículo
Indicadores
Links relacionados
Compartir
versión impresa ISSN 0186-1042
Contad. Adm no.229 México sep./dic. 2009
Artículos de investigación
Anticipating turbulent periods in Latin... | 4 | [
0.00897216796875,
-0.0264892578125,
-0.0108642578125,
0.0294189453125,
0.042724609375,
-0.0250244140625,
-0.1142578125,
0.05615234375,
0.0294189453125,
-0.053955078125,
0.033447265625,
-0.03759765625,
-0.09130859375,
-0.041015625,
-0.01068115234375,
-0.00640869140625,
-0.080078125,
... | 33,776 | 33776 | |
Please solve the equation for "Y"? (a few more problems!)
September 18th 2010, 10:24 PM
ADH
Please solve the equation for "Y"? (a few more problems!)
Hello,
I wasn't completly sure on the ones I have solved.
Most of these I have already solved, and have included the answer I got! Please tell me if I ... | 4 | [
-0.039794921875,
-0.06689453125,
0.00775146484375,
-0.0184326171875,
0.0390625,
-0.0244140625,
0.03173828125,
-0.10009765625,
0.012939453125,
0.00445556640625,
0.09765625,
-0.033203125,
-0.0279541015625,
0.06640625,
0.1044921875,
0.08984375,
-0.12255859375,
0.02587890625,
-0.0708... | 33,777 | 33777 | |
Quadratic Functions exam paper question
November 11th 2008, 07:26 AM #1
Member
Joined
Oct 2008
Posts
157
Quadratic Functions exam paper question
Given that the equation
kx^2 - 4x + k - 3 = 0
has equal roots, find the value of "k".
I know that a=k, b=-4, and c=k-3.
Then to put it into ... | 4 | [
0.00408935546875,
0.06640625,
-0.07177734375,
0.005828857421875,
-0.1181640625,
0.0189208984375,
0.020751953125,
-0.033447265625,
0.047119140625,
0.03515625,
0.0400390625,
-0.0732421875,
0.0247802734375,
0.02587890625,
-0.031982421875,
0.10205078125,
-0.014404296875,
0.028442382812... | 33,778 | 33778 | |
does this converge?
Sumation from 1 to infinity of [3^n + 4] / 2^n converges or diverges?
Given $\sum\limits_{n=1}^\infty \frac{3^n+4}{2^n}$, I guess you can apply direct comparison test here. Let $b_n=\frac{3^n+4}{2^n}$, consider another sequence $a_n=\frac{3^n}{2^n}$. We have $0\le a_n\
le b_n,\;\;\forall n$. Since ... | 5 | [
-0.041015625,
-0.0966796875,
-0.06298828125,
-0.01708984375,
-0.01544189453125,
-0.0595703125,
-0.07080078125,
0.006622314453125,
0.0274658203125,
-0.0498046875,
-0.08837890625,
-0.134765625,
-0.01220703125,
0.037353515625,
-0.05224609375,
-0.00106048583984375,
0.02587890625,
-0.05... | 33,779 | 33779 | |
complex numbers
January 28th 2009, 10:15 AM #1
Junior Member
Joined
Oct 2008
Posts
29
complex numbers
Express in the form a + bi, where a and b are real
(a) sin(3pi/2 - i)
(b) cosh(1 + i)
have tried using addition formula on (a) but its not right.
Note that for $z\in\mathbb{C}$, $\sin... | 5 | [
-0.06494140625,
0.0458984375,
-0.0595703125,
-0.055908203125,
0.022216796875,
0.04248046875,
0.02490234375,
0.006744384765625,
0.04052734375,
0.055419921875,
0.05078125,
-0.15234375,
0.020751953125,
0.0299072265625,
0.0498046875,
-0.05517578125,
0.0206298828125,
-0.02880859375,
0... | 33,780 | 33780 | |
Strong Convergence of a Modified Extragradient Method to the Minimum-Norm Solution of Variational Inequalities
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 817436, 9 pages
http://dx.doi.org/10.1155/2012/817436
Research Article
Strong Convergence of a Modified Extragradient Method to the Minimum-Norm... | 5 | [
-0.023681640625,
0.0011444091796875,
0.0634765625,
-0.038330078125,
0.01348876953125,
-0.0086669921875,
-0.0079345703125,
0.0634765625,
-0.0029754638671875,
0.00897216796875,
-0.0012664794921875,
0.028076171875,
0.169921875,
0.0020751953125,
-0.0361328125,
0.008056640625,
0.079101562... | 33,781 | 33781 | |
Calculus ll - Improper Integrals
Posted by Alyssa on Saturday, October 2, 2010 at 9:32pm.
Find the area of the curve y = 1/(x^3) from x = 1 to x = t and evaluate it for t = 10, 100, and 1000. Then find the the total area under this curve for x ≥ 1.
I'm not sure how to do the last part of question ("find the the total... | 5 | [
-0.068359375,
-0.0206298828125,
0.055419921875,
-0.0024871826171875,
0.061279296875,
-0.1455078125,
0.01336669921875,
0.0927734375,
-0.02783203125,
-0.0179443359375,
0.00994873046875,
-0.00080108642578125,
0.07763671875,
0.068359375,
-0.026611328125,
-0.00130462646484375,
0.024291992... | 33,782 | 33782 | |
Homework Help
Posted by Aria on Wednesday, August 31, 2011 at 4:04am.
Could someone verify if I got two answers to two problems right?
f(x)=x^2-9x+15 find x and y intercepts
-9+square root of 21/2,0
-9-square root of 21/2,0
x^2-x+3=0 solve and find x-intercepts
(1+square root of -11/2,0)
(-1-square root of -11/2... | 4 | [
-0.037353515625,
0.009521484375,
0.0263671875,
0.0025177001953125,
0.06689453125,
0.0712890625,
-0.0322265625,
0.023193359375,
-0.0284423828125,
-0.052978515625,
0.09765625,
-0.061767578125,
-0.043701171875,
0.013916015625,
-0.05126953125,
0.072265625,
-0.036865234375,
-0.07421875,... | 33,783 | 33783 | |
Commutators
December 11th 2008, 11:11 PM
csuiter
Commutators
What's up I am working on some quantum chemistry problems and I am somewhat confused about commutators.
The question asks to calculate the commutators, the questions are:
[x,d/dx]
[sqrt,()^2]
There is also one concerning nuclear spin... | 5 | [
-0.03515625,
-0.0284423828125,
0.0771484375,
-0.038818359375,
-0.08251953125,
0.015869140625,
0.0244140625,
0.0225830078125,
-0.05029296875,
-0.0213623046875,
0.07568359375,
-0.029541015625,
0.02685546875,
-0.025390625,
0.0220947265625,
0.049560546875,
-0.08740234375,
0.04711914062... | 33,784 | 33784 | |
Physical Fitness Probability
April 18th 2009, 10:08 AM #1
Newbie
Joined
Apr 2009
Posts
14
Physical Fitness Probability
I need help please....
A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known t... | 4 | [
0.01708984375,
0.09814453125,
0.042236328125,
0.022216796875,
-0.014892578125,
-0.052978515625,
-0.006439208984375,
0.034912109375,
-0.03662109375,
-0.007659912109375,
0.087890625,
-0.054931640625,
0.083984375,
0.05078125,
0.0130615234375,
0.00531005859375,
0.03271484375,
0.0186767... | 33,785 | 33785 | |
Kaplan's Infinite Series for
Kaplan discovered that
d
can be written as a series in the form
where each
a[n]
is rational. The first few terms of this series are:
Although there is no obvious pattern to these terms, they can be calculated from the
Taylor series
of the
inverse
of a certain function.
Let
f
(... | 5 | [
-0.1298828125,
-0.0130615234375,
0.0169677734375,
0.041748046875,
-0.034423828125,
-0.01104736328125,
-0.05078125,
0.033935546875,
0.095703125,
0.0225830078125,
0.0294189453125,
-0.0057373046875,
-0.01129150390625,
-0.0595703125,
0.0057373046875,
-0.11865234375,
0.0026397705078125,
... | 33,786 | 33786 | |
the encyclopedic entry of neighbor
In
bioinformatics
,
neighbor-joining
is a bottom-up clustering method used for the construction of
phylogenetic trees
. Usually used for trees based on
DNA
or
protein sequence
data, the algorithm requires knowledge of the distance between each pair of taxa (e.g. species or s... | 4 | [
-0.0125732421875,
0.0634765625,
-0.0673828125,
-0.1337890625,
-0.054443359375,
0.0166015625,
-0.1162109375,
0.046875,
-0.035888671875,
0.010986328125,
0.04931640625,
-0.033935546875,
0.0264892578125,
0.02099609375,
-0.1083984375,
0.048828125,
-0.08203125,
-0.003875732421875,
-0.0... | 33,787 | 33787 | |
Counting Principles
April 2nd 2008, 02:46 PM
strgrl
Counting Principles
A homework question:
Twelve children are divided up into three groups, of five, four, and three. In how many ways can this be done if the order within each group is not important?
I'm not quite sure how to attack this question.
... | 4 | [
0.0133056640625,
-0.0380859375,
0.0027008056640625,
-0.07958984375,
-0.0419921875,
-0.01214599609375,
-0.009033203125,
-0.0625,
0.050537109375,
0.1015625,
0.01092529296875,
0.03564453125,
-0.0019683837890625,
0.030029296875,
0.00433349609375,
0.0101318359375,
-0.01806640625,
-0.015... | 33,788 | 33788 | |
Math Help
November 27th 2008, 05:19 PM #1
Newbie
Joined
Nov 2008
Posts
2
basis
let S = { v1 , v2} T = { w1, w2} be bases for R2
Given: V1 = ( 1, -2) V2= ( 3, 0)
Transition matrix from T to S be
[ 1 2 ]
[-1 0]
Find w1 and w2.
Please help me with the steps. I am not sure where... | 4 | [
-0.0283203125,
-0.0123291015625,
-0.045166015625,
-0.006072998046875,
0.07958984375,
0.005340576171875,
-0.017578125,
0.033935546875,
-0.06005859375,
-0.0673828125,
0.0084228515625,
-0.00811767578125,
-0.010986328125,
-0.01324462890625,
-0.076171875,
0.0286865234375,
-0.07958984375,
... | 33,789 | 33789 | |
How to solve this problem algebraically?
November 30th 2011, 01:12 PM
peekayem
How to solve this problem algebraically?
Qs: One number is 6 more than another. Their product is 520. Find the numbers.
-- Let the numbers be: x, x+6
So, x(x+6) = 520
or, x^2+6x=520
then what..?
The numbers are 2... | 4 | [
-0.05712890625,
0.05322265625,
-0.0267333984375,
0.00182342529296875,
-0.0732421875,
0.07373046875,
0.031494140625,
0.00592041015625,
0.0010223388671875,
-0.04443359375,
-0.0179443359375,
0.0927734375,
0.08740234375,
-0.036376953125,
0.01373291015625,
0.0286865234375,
-0.022705078125... | 33,790 | 33790 | |
Decreasing function
October 29th 2008, 02:42 PM #1
Junior Member
Joined
Feb 2008
Posts
48
Decreasing function
$f(x)=x^\frac{1}{n} - (x-1)^\frac{1}{n}$
I need help showing this is decreasing for $x$> $1$
Any suggestions? trying to do this with the derivative.
I get
$f'(x)=\frac{x^\frac... | 5 | [
0.043701171875,
-0.0537109375,
0.0086669921875,
0.0172119140625,
-0.08544921875,
-0.0947265625,
-0.0478515625,
0.064453125,
0.0203857421875,
0.0262451171875,
-0.12353515625,
0.0308837890625,
0.1103515625,
0.00634765625,
0.0019378662109375,
-0.00787353515625,
0.045166015625,
-0.1079... | 33,791 | 33791 | |
This problem looks intimidating at first, but actually is
Author Message
TAGS:
This problem looks intimidating at first, but actually is [#permalink] 11 Nov 2005, 06:15
... | 4 | [
-0.00010156631469726562,
0.054931640625,
-0.048095703125,
-0.026123046875,
-0.0849609375,
0.0169677734375,
0.0242919921875,
-0.054931640625,
0.016845703125,
0.003082275390625,
0.01312255859375,
0.0213623046875,
0.11572265625,
0.00518798828125,
-0.035400390625,
0.0308837890625,
-0.034... | 33,792 | 33792 | |
Pre-Algebra Placement Test problem
November 5th 2010, 11:54 AM
Aravsion
Pre-Algebra Placement Test problem
I'm preparing for college and I got stuck on one of the problems of Pre-Algebra Placement Test.. So can someone please help me find the solution to it.
A total of 50 juniors and seniors were given a ma... | 4 | [
0.0186767578125,
0.068359375,
0.07568359375,
-0.056396484375,
-0.05712890625,
-0.0198974609375,
-0.00604248046875,
0.04345703125,
-0.0712890625,
0.07763671875,
0.043212890625,
-0.032470703125,
0.08837890625,
-0.00799560546875,
0.00604248046875,
0.035888671875,
0.02001953125,
-0.013... | 33,793 | 33793 | |
Econometrics: MR, Revenue, profit.
September 1st 2009, 04:42 PM #1
The cost (in 000's) of producing x thousands of loudspeaker systems is TC = x^3 + 3x^2 - 10x + 2. Price (p) and quantity demanded (x) which are both required to be non-negative are related by p =
130 - 2x. Marginal Cost (MC) = 3x^2 + 6x - 10.
... | 5 | [
0.00970458984375,
-0.0306396484375,
-0.0242919921875,
-0.12255859375,
-0.05810546875,
0.033447265625,
0.08837890625,
0.044189453125,
-0.0242919921875,
0.06884765625,
0.035888671875,
0.010498046875,
0.04248046875,
-0.0023345947265625,
-0.03515625,
0.00616455078125,
0.041259765625,
0... | 33,794 | 33794 | |
Verification problems
October 21st 2009, 04:22 PM #1
Newbie
Joined
Nov 2007
Posts
12
Verification problems
1. sinx+cosx/tan^2x-1 = cos^2x/sinx-cosx
I've tried everything(converting to sines and cosines, factoring, etc.) and even my teacher couldn't figure it out...
2. 1+tanx/1-tanx = sec^2x+2ta... | 4 | [
-0.0299072265625,
0.048583984375,
0.10302734375,
0.0693359375,
0.006256103515625,
-0.0172119140625,
-0.0022735595703125,
-0.048095703125,
0.02197265625,
0.0140380859375,
0.09375,
-0.03271484375,
0.045654296875,
0.1005859375,
-0.0289306640625,
-0.0208740234375,
0.04931640625,
0.0327... | 33,795 | 33795 | |
Reference Sphere Positioning Measurement Based on Line-Structured Light Vision Sensor
Advances in Mechanical Engineering
Volume 2013 (2013), Article ID 587904, 6 pages
http://dx.doi.org/10.1155/2013/587904
Research Article
Reference Sphere Positioning Measurement Based on Line-Structured Light Vision Sensor
State Ke... | 4 | [
-0.0101318359375,
-0.00799560546875,
-0.03515625,
-0.0703125,
0.041015625,
-0.0030670166015625,
0.0026397705078125,
0.042724609375,
0.048095703125,
-0.0052490234375,
0.038330078125,
0.033447265625,
0.00897216796875,
0.019775390625,
-0.0771484375,
-0.045654296875,
0.01123046875,
0.0... | 33,796 | 33796 | |
Electronic Journal of Biotechnology
Services on Demand
Article
Indicators
Related links
On-line version ISSN 0717-3458
Electron. J. Biotechnol. vol.9 no.4 Valparaíso July 2006
Biotechnology Industry Process Biotechnology
Electronic Journal of Biotechnology ISSN: 0717-3458 Vol... | 4 | [
-0.03125,
-0.061767578125,
-0.0673828125,
-0.06591796875,
0.01312255859375,
-0.02490234375,
-0.03271484375,
0.11767578125,
-0.00360107421875,
0.0174560546875,
0.0169677734375,
-0.099609375,
0.050048828125,
-0.0252685546875,
-0.08740234375,
-0.062255859375,
0.025146484375,
-0.056884... | 33,797 | 33797 | |
Boolean Laws, and Theorem
December 5th 2013, 02:27 PM
Jarod_C
Boolean Laws, and Theorem
What's up wonder community of math wizards. I was hoping you could check a problem for me. For every step I need to pick which numbered law from the list was used. HERE IS THE LIST.
Given = $\overline{(A\overline{BC}+\ov... | 4 | [
-0.09228515625,
0.0255126953125,
0.03466796875,
-0.006072998046875,
0.0167236328125,
0.09521484375,
0.041015625,
-0.01611328125,
-0.055908203125,
0.043212890625,
0.046142578125,
-0.0260009765625,
0.06005859375,
0.0263671875,
0.0225830078125,
0.0191650390625,
-0.10791015625,
0.05712... | 33,798 | 33798 | |
Coordinates, vectors and cross products
October 15th 2010, 07:30 AM
yellowFattyBEan
Coordinates, vectors and cross products
Hi
I have 4 3D points and I have been told I need to create 2 vecors out of them. I then need to cross product these vecotrs to then get another vector.
Now with my terrible grasp... | 4 | [
-0.023681640625,
-0.044189453125,
-0.027587890625,
-0.109375,
0.0294189453125,
0.021728515625,
0.0157470703125,
-0.01483154296875,
-0.0634765625,
-0.0001392364501953125,
0.005462646484375,
-0.053955078125,
0.0257568359375,
0.0615234375,
-0.04150390625,
0.11181640625,
-0.07958984375,
... | 33,799 | 33799 |