content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
If you put a pendulum under the influence of a flow, a drag force will move the pendulum creating an angle with respect to the vertical. As the angle is related to the drag force, and because the
drag force is related to the velocity of the flow, you can determine the velocity of the flow by only measuring the ang... | 4 | [
-0.034423828125,
0.0017852783203125,
-0.051025390625,
-0.06787109375,
-0.0296630859375,
0.01611328125,
-0.02392578125,
0.0152587890625,
0.032470703125,
0.011474609375,
0.017333984375,
-0.031494140625,
0.0240478515625,
0.027587890625,
-0.03369140625,
-0.018310546875,
-0.038818359375,
... | 26,000 | 26000 | |
Example of Problem Involving OUTLIERS
Sanderson M. Smith
Home | About Sanderson Smith | Writing... | 4 | [
0.0145263671875,
0.00213623046875,
0.0159912109375,
0.037841796875,
-0.02294921875,
-0.0390625,
0.0238037109375,
0.01806640625,
-0.06787109375,
0.03564453125,
0.036865234375,
0.06396484375,
0.09033203125,
-0.047607421875,
-0.0556640625,
0.04443359375,
0.05810546875,
0.04248046875,
... | 26,001 | 26001 | |
Of GTIs, battery sizing, and capacitor banks
March 16th, 2012, 20:38 PDT #1
New User
Join Date
Mar 2012
Posts
3
Introduction
I work for a fuel-cell R & D. We're building a 5kW (low-voltage) fuel-cell system that I wanted to tie into a grid using an XW6048, a model which requires a 48V-nominal battery... | 4 | [
0.011962890625,
0.1025390625,
-0.10986328125,
0.03173828125,
0.00274658203125,
-0.0299072265625,
0.0101318359375,
0.0849609375,
-0.056396484375,
-0.0031280517578125,
-0.057373046875,
0.01397705078125,
0.0140380859375,
0.060302734375,
0.055908203125,
0.0634765625,
0.025634765625,
-0... | 26,002 | 26002 | |
Controllability of Second-Order Multiagent Systems with Multiple Leaders and General Dynamics
Mathematical Problems in Engineering
VolumeΒ 2013Β (2013), Article IDΒ 587569, 6 pages
http://dx.doi.org/10.1155/2013/587569
Research Article
Controllability of Second-Order Multiagent Systems with Multiple Leaders and General ... | 5 | [
0.043212890625,
-0.0012359619140625,
-0.0693359375,
-0.047119140625,
0.0224609375,
0.052490234375,
0.0201416015625,
-0.01165771484375,
-0.0120849609375,
0.005279541015625,
0.09814453125,
0.0164794921875,
0.0888671875,
-0.0361328125,
-0.07080078125,
0.10986328125,
-0.00872802734375,
... | 26,003 | 26003 | |
A Kind of Infinite-Dimensional Novikov Algebras and Its Realizations
Abstract and Applied Analysis
VolumeΒ 2013Β (2013), Article IDΒ 270937, 5 pages
http://dx.doi.org/10.1155/2013/270937
Research Article
A Kind of Infinite-Dimensional Novikov Algebras and Its Realizations
School of Mathematics and Statistics, Northeast... | 5 | [
-0.14453125,
-0.005615234375,
-0.02685546875,
0.06005859375,
-0.07568359375,
0.0966796875,
0.035888671875,
0.033935546875,
0.060546875,
-0.0830078125,
0.026123046875,
0.0179443359375,
-0.049560546875,
0.064453125,
-0.003631591796875,
-0.0390625,
-0.053955078125,
0.00848388671875,
... | 26,004 | 26004 | |
Quadratic inequality
How many integers satisfy the inequality x(3x-4) is less than or equal to 6x^2-3x+5/10
Perhaps you mean (6x^2- 3x+ 5)/10? Saying that $x(3x- 4)\le (6x^2- 3x+ 5)/10$ is the same as saying $10x(3x- 4)\le 6x^2- 3x+ 5$ which in turn is the same as $30x^2- 40x- (6x^2- 3x+ 5)= 24x^2- 37x- 5\
le 0$. You ... | 4 | [
0.05419921875,
0.009765625,
-0.00897216796875,
-0.044189453125,
-0.053955078125,
0.1318359375,
0.004608154296875,
0.06103515625,
-0.0233154296875,
-0.055419921875,
-0.0546875,
0.00848388671875,
0.109375,
-0.009765625,
-0.000209808349609375,
0.0341796875,
0.033935546875,
0.031494140... | 26,005 | 26005 | |
Pricing interest rate swaps with lambda.r
July 19, 2013
By Brian Lee Yung Rowe
People think Iβm joking when I say something should only take 20 lines of code. More often than not it is possible if you understand how to strip away unnecessary complexity. This example shows how
to calculate the theoretical swap rate f... | 5 | [
-0.08447265625,
0.04052734375,
-0.07275390625,
0.0022430419921875,
-0.047119140625,
-0.033447265625,
0.0556640625,
0.0341796875,
0.007080078125,
0.0859375,
0.02587890625,
0.0218505859375,
-0.0186767578125,
0.046875,
0.1103515625,
0.072265625,
-0.10546875,
-0.0301513671875,
-0.033... | 26,006 | 26006 | |
Integral Domains
βββββββββββββββββββββββββββββββ
β β
... | 4 | [
0.03271484375,
-0.023681640625,
-0.0230712890625,
-0.1259765625,
-0.01141357421875,
-0.10107421875,
0.0208740234375,
0.039306640625,
-0.01153564453125,
-0.04052734375,
0.026123046875,
-0.015625,
0.0869140625,
0.01611328125,
0.019287109375,
0.0203857421875,
-0.0615234375,
0.00573730... | 26,007 | 26007 | |
Find the volume of the solid obtained by rotating the region bounded by the curves...
September 16th 2012, 06:08 PM #1
Newbie
Joined
Sep 2012
From
Philadelphia
Posts
10
Find the volume of the solid obtained by rotating the region bounded by the curves...
The region bounded by: y=1 and y=x^8
Rotat... | 4 | [
0.011474609375,
0.07373046875,
0.044189453125,
-0.054443359375,
-0.0245361328125,
-0.06884765625,
-0.0771484375,
0.09912109375,
-0.0294189453125,
-0.06201171875,
-0.091796875,
0.036865234375,
-0.0181884765625,
0.0556640625,
-0.00299072265625,
0.02490234375,
-0.026611328125,
-0.0057... | 26,008 | 26008 | |
General solution of trigonometric function
March 7th 2013, 06:16 AM #1
Newbie
Joined
Feb 2013
From
India
Posts
17
General solution of trigonometric function
For any real numbers x and y. Sinx = siny implies $n\pi + (-1)^ny, where n \in Z$
If sinx = siny, then sinx -siny = 0
or $2cos\frac{x... | 4 | [
-0.07421875,
-0.051513671875,
-0.0255126953125,
0.09912109375,
-0.023681640625,
0.031982421875,
0.02001953125,
0.005096435546875,
-0.05029296875,
-0.0238037109375,
0.080078125,
-0.02099609375,
-0.0810546875,
0.060302734375,
0.0791015625,
-0.046630859375,
-0.0341796875,
-0.090332031... | 26,009 | 26009 | |
How do you differentiate this with respect to s
How do you differentiate the following with respect to s: Thanks
Last edited by mr fantastic; July 3rd 2010 at 05:01 AM. Reason: Copied title into main body of post.
Let $y = e^{ \lambda ( \frac{ p}{1-qs} - 1 ) }$ $lny = \lambda ( \frac{ p}{1-qs} - 1 )$ $lny = \lambda p... | 5 | [
-0.0189208984375,
0.023681640625,
0.0296630859375,
0.006500244140625,
-0.019287109375,
0.06103515625,
0.0703125,
-0.0054931640625,
0.08447265625,
0.068359375,
0.037353515625,
0.03759765625,
0.017822265625,
0.0791015625,
0.03662109375,
0.0277099609375,
-0.021728515625,
-0.0427246093... | 26,010 | 26010 | |
The Evaluation of Solar Contribution in Solar Aided Coal-Fired Power Plant
International Journal of Photoenergy
VolumeΒ 2013Β (2013), Article IDΒ 197913, 9 pages
http://dx.doi.org/10.1155/2013/197913
Research Article
The Evaluation of Solar Contribution in Solar Aided Coal-Fired Power Plant
School of Energy Power and M... | 4 | [
-0.058349609375,
0.15234375,
-0.033447265625,
0.039306640625,
-0.0040283203125,
-0.0164794921875,
0.03857421875,
0.041748046875,
-0.06494140625,
0.06689453125,
0.017333984375,
-0.0006103515625,
0.078125,
-0.0130615234375,
-0.01123046875,
0.051025390625,
0.0130615234375,
0.052490234... | 26,011 | 26011 | |
The Existence of Solutions for a Nonlinear Fractional Multi-Point Boundary Value Problem at Resonance
International Journal of Differential Equations
VolumeΒ 2011Β (2011), Article IDΒ 401803, 14 pages
http://dx.doi.org/10.1155/2011/401803
Research Article
The Existence of Solutions for a Nonlinear Fractional Multi-Point... | 5 | [
-0.0810546875,
0.0032806396484375,
0.04736328125,
-0.02001953125,
0.02197265625,
0.039794921875,
-0.000377655029296875,
0.00665283203125,
0.0615234375,
-0.06396484375,
0.049560546875,
-0.032958984375,
0.008056640625,
0.0225830078125,
0.06201171875,
0.015380859375,
-0.01495361328125,
... | 26,012 | 26012 | |
sum of coefficients
Next: uniqueness and periodicity Up: the matrizant Previous: Euler's method
The sum rule for exponents requires modification for matrizants, due as usual to problems of noncommutativity. Suppose that the coefficient matrix M is the sum of two others, A and B, and that it is
desired to solve h... | 4 | [
-0.1259765625,
0.037353515625,
-0.0303955078125,
0.0380859375,
-0.0225830078125,
0.01544189453125,
0.049560546875,
-0.06982421875,
-0.00159454345703125,
0.021728515625,
0.07568359375,
-0.03857421875,
0.06787109375,
-0.002593994140625,
0.015869140625,
0.034912109375,
-0.08251953125,
... | 26,013 | 26013 | |
probability with density functions
February 2nd 2009, 01:52 PM #1
Member
Joined
Aug 2007
Posts
96
probability with density functions
A radioactive material emits alpha particles at a rate described by the density function
f(t) = .1e^(-.1t)
Find the probability that a particle is emitted in the fi... | 5 | [
-0.0181884765625,
-0.00811767578125,
0.000453948974609375,
0.004180908203125,
0.0155029296875,
0.02978515625,
0.04296875,
0.049072265625,
0.005889892578125,
0.068359375,
0.0380859375,
-0.0223388671875,
0.0291748046875,
0.08251953125,
-0.01263427734375,
-0.043701171875,
-0.01647949218... | 26,014 | 26014 | |
binomial theorem?
June 7th 2011, 12:50 PM #1
Senior Member
Joined
Dec 2010
From
CPT
Posts
302
binomial theorem?
Use pascals triangle to expand each binomial
(square root c-1)^6
Can anyone help me expand the binomial I know the row I am supposed to use
1 6 15 20 15 6 1
But the squa... | 4 | [
-0.034912109375,
0.01104736328125,
-0.040771484375,
0.076171875,
-0.083984375,
0.05615234375,
-0.06640625,
-0.00151824951171875,
0.039794921875,
0.018310546875,
-0.0184326171875,
-0.0128173828125,
-0.06591796875,
0.0257568359375,
-0.058837890625,
0.10791015625,
-0.08251953125,
-0.0... | 26,015 | 26015 | |
topology, metric spaces, proving continuity
October 17th 2012, 06:20 PM
gbux512
topology, metric spaces, proving continuity
After seeing all the other topology problems be left out to dry, I'm not exactly confident Ill get help, but ill try anyway.
So heres a photo of my problem, since im not the best at la... | 5 | [
-0.00262451171875,
0.021728515625,
0.019287109375,
-0.076171875,
-0.018798828125,
0.05908203125,
0.045654296875,
0.0419921875,
-0.00665283203125,
-0.00958251953125,
0.08349609375,
-0.044189453125,
0.0137939453125,
0.017333984375,
0.064453125,
0.00009870529174804688,
0.05078125,
-0.... | 26,016 | 26016 | |
On Algebraic Approach in Quadratic Systems
International Journal of Mathematics and Mathematical Sciences
VolumeΒ 2011Β (2011), Article IDΒ 230939, 12 pages
http://dx.doi.org/10.1155/2011/230939
Review Article
On Algebraic Approach in Quadratic Systems
^1Department of Basic Science, Faculty of Civil Engineering, Univer... | 4 | [
-0.10888671875,
-0.0123291015625,
0.05322265625,
0.0107421875,
-0.08740234375,
0.036376953125,
-0.01904296875,
0.04248046875,
0.050048828125,
0.05517578125,
0.06982421875,
0.008544921875,
0.037841796875,
0.0224609375,
-0.068359375,
0.0400390625,
0.01287841796875,
0.03173828125,
-... | 26,017 | 26017 | |
Structural Vibration Control for a Class of Connected Multistructure Mechanical Systems
Mathematical Problems in Engineering
VolumeΒ 2012Β (2012), Article IDΒ 942910, 23 pages
http://dx.doi.org/10.1155/2012/942910
Research Article
Structural Vibration Control for a Class of Connected Multistructure Mechanical Systems
^... | 4 | [
-0.00848388671875,
-0.0341796875,
-0.0037841796875,
-0.00142669677734375,
-0.08154296875,
-0.0262451171875,
-0.045654296875,
0.039794921875,
0.0225830078125,
0.000537872314453125,
-0.0086669921875,
-0.0079345703125,
0.025390625,
-0.044921875,
-0.07470703125,
0.0478515625,
0.020629882... | 26,018 | 26018 | |
limited thoughts on limits :S
Please help me solve this question: lim (x^3-3x-2)/ x->2 (x^2-5x+6)
$\lim_{x \to 2} \frac{x^3 - 3x - 2}{x^2 - 5x + 6}$ Note that $x - 2$ is a factor of $x^3 - 3x - 2$, evidenced by the fact that $2^3 - 3 \cdot 2 - 2 = 0$. Thus, by long or synthetic division we get
that $x^3 - 3x - 2 = (x ... | 4 | [
-0.05078125,
-0.060302734375,
-0.033203125,
-0.00201416015625,
0.046630859375,
0.0654296875,
-0.07568359375,
-0.0286865234375,
0.03564453125,
-0.032470703125,
0.033447265625,
-0.0439453125,
-0.01495361328125,
0.0003204345703125,
0.01416015625,
0.026611328125,
-0.00823974609375,
0.0... | 26,019 | 26019 | |
Help w/ my 1st Calc test!
September 28th 2009, 11:00 AM #1
Newbie
Joined
Sep 2009
Posts
1
Help w/ my 1st Calc test!
Not actually homework, rather sample problems that will be on my test tomorrow. Professor didn't give us the answers to the practice problems (State school...) so I don't know if they're ri... | 4 | [
-0.054443359375,
0.01446533203125,
0.03857421875,
-0.00665283203125,
-0.01458740234375,
0.005584716796875,
-0.037841796875,
-0.0106201171875,
0.00811767578125,
0.0390625,
0.1142578125,
-0.0673828125,
0.0194091796875,
0.0128173828125,
0.030517578125,
0.00274658203125,
-0.1650390625,
... | 26,020 | 26020 | |
ractice skills needed
Standard 1 - Number and Operations
Students will recognize, represent, model, and apply real numbers and operations and will demonstrate an understanding of properties and operations of the complex number system.
Level 1
order a given set of real numbers 1. Comparing... | 4 | [
-0.031982421875,
0.0208740234375,
-0.044921875,
0.0166015625,
-0.103515625,
-0.044921875,
0.004669189453125,
0.00775146484375,
-0.01373291015625,
0.002288818359375,
-0.043212890625,
-0.07470703125,
0.107421875,
0.1005859375,
-0.043212890625,
-0.05712890625,
-0.0341796875,
0.0319824... | 26,021 | 26021 | |
Solving Applied Problems (word problem)
March 3rd 2013, 05:26 PM #1
Newbie
Joined
Jan 2013
From
USA
Posts
6
Solving Applied Problems (word problem)
Hi, If you could show how you solve this, that would be great. Thanks.
Mr. Silvester is 5yr older than his wife. Five years
ago his age was 4/3 ... | 4 | [
-0.057373046875,
0.0693359375,
0.049072265625,
0.0135498046875,
-0.021240234375,
0.068359375,
-0.00482177734375,
0.0322265625,
-0.1025390625,
0.031494140625,
0.06005859375,
-0.04248046875,
0.08203125,
0.0712890625,
0.01171875,
0.0634765625,
-0.07275390625,
0.022705078125,
-0.1289... | 26,022 | 26022 | |
need help putting into words
January 8th 2007, 06:24 AM #1
Newbie
Joined
Nov 2006
Posts
18
need help putting into words
I need to show which of the two expressions is larger and explian why. I know which is the larger number,but can not put it into words to explain. Anyone have any ideas?
a) (1/2)'2... | 4 | [
0.032470703125,
-0.003387451171875,
0.0126953125,
0.014404296875,
-0.03515625,
-0.08203125,
-0.05517578125,
0.08056640625,
0.07373046875,
-0.025390625,
-0.028076171875,
-0.019287109375,
0.052978515625,
0.07373046875,
0.004150390625,
0.035888671875,
0.025390625,
0.052490234375,
-0... | 26,023 | 26023 | |
The function is defined if...
(e^( cos^(-1) (log x^2) ))^1/2 The base of log is 4
$f(x) = \sqrt{e^{\arccos{[\log{(x^2)}]}}}$. Note that the logarithm is only defined for $x > 0$. Since $x^2 \geq 0$, we can already see that we can not let $x = 0$. Also note that $\arccos{x}$ is
only defined for $-1 \leq x \leq 1$. The ... | 4 | [
0.06591796875,
0.0283203125,
-0.032470703125,
0.052490234375,
-0.038818359375,
-0.1357421875,
-0.060791015625,
0.056640625,
0.0673828125,
0.0286865234375,
0.05517578125,
-0.0133056640625,
0.04345703125,
0.0439453125,
-0.03466796875,
-0.068359375,
-0.0257568359375,
-0.1708984375,
... | 26,024 | 26024 | |
Standard Deviation
September 5th 2007, 12:28 AM #1
Newbie
Joined
Sep 2007
Posts
7
Standard Deviation
Can anyone help me with this question
Baby Pty Ltd. is planning to launch a new brand of makeup product. Based on market research, if sales are high they can make a profit of $3.4 million per year. I... | 4 | [
0.08740234375,
0.0703125,
-0.01611328125,
-0.048095703125,
-0.0498046875,
-0.001251220703125,
-0.05029296875,
0.1103515625,
0.047607421875,
0.0419921875,
0.0537109375,
-0.048583984375,
0.0294189453125,
-0.049560546875,
0.041015625,
-0.03857421875,
-0.04833984375,
0.05078125,
-0.0... | 26,025 | 26025 | |
logarithm/exponential equations
1. January 12th 2010, 03:04 AM #1
2. January 12th 2010, 03:52 AM #2
Assuming $\log a=\log_{10}a$ , and assuming you made a typo and meant $\log\log x$ in the first exer., then
$\log\log x=3\Longrightarrow 10^3=\log x \Longrightarrow 10^{10^3}=x$
$x^{\log_... | 5 | [
0.04443359375,
-0.005035400390625,
-0.00555419921875,
-0.0301513671875,
-0.0021820068359375,
-0.052978515625,
0.10498046875,
0.01611328125,
-0.006927490234375,
0.04736328125,
0.06982421875,
-0.000400543212890625,
0.033935546875,
0.09765625,
0.0595703125,
0.10986328125,
-0.1533203125,... | 26,026 | 26026 | |
On Fibonacci Functions with Period
Discrete Dynamics in Nature and Society
VolumeΒ 2013Β (2013), Article IDΒ 418123, 4 pages
http://dx.doi.org/10.1155/2013/418123
Research Article
On Fibonacci Functions with Period
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum... | 5 | [
-0.1533203125,
0.046142578125,
-0.0196533203125,
0.00927734375,
-0.0439453125,
0.0208740234375,
-0.010986328125,
-0.01519775390625,
0.1123046875,
0.051025390625,
0.0030975341796875,
-0.0927734375,
-0.04638671875,
0.0634765625,
-0.035888671875,
-0.052978515625,
-0.146484375,
-0.0314... | 26,027 | 26027 | |
Dependence of the path
June 8th 2009, 09:05 AM #1
Super Member
Joined
Jun 2008
Posts
829
Dependence of the path
To check whether a vector field depends on the path just check if the rotation is equal to 0 ?
How can I check if the integral curvilinear depends on the path ?
If $abla \times F = 0$... | 5 | [
-0.01458740234375,
0.009765625,
-0.048583984375,
-0.0157470703125,
-0.01416015625,
-0.00194549560546875,
0.039306640625,
-0.0191650390625,
0.002166748046875,
0.01263427734375,
-0.002471923828125,
0.09375,
0.025634765625,
0.04736328125,
-0.0198974609375,
0.0240478515625,
-0.09765625,
... | 26,028 | 26028 | |
Solve matrices using Gaussian elimination or...
May 4th 2007, 02:54 PM #1
Junior Member
Joined
Feb 2007
Posts
53
Solve matrices using Gaussian elimination or...
Gauss-Jordan elimination.
This is a word problem and I'm not very good at these, so please help.
eAuction.com spent a total of $11 mil... | 5 | [
0.021484375,
0.0128173828125,
-0.07958984375,
-0.0517578125,
-0.01031494140625,
-0.034423828125,
0.0218505859375,
-0.0712890625,
-0.068359375,
0.029052734375,
0.04150390625,
0.06689453125,
0.07373046875,
-0.0037384033203125,
0.0189208984375,
0.0057373046875,
0.03173828125,
0.055664... | 26,029 | 26029 | |
Eigenvectors/values
April 29th 2010, 10:18 AM #1
Junior Member
Joined
Feb 2010
Posts
56
Eigenvectors/values
Let A = $\begin{bmatrix}1&-1&0\\-1&1&0\\0&0&1\end{bmatrix}$ and $T: R^3 \rightarrow R^3$ by T(X) = AX.
Find eigenpairs for A, find a basis for Ker(T) using the eigenvectors previously found, fi... | 5 | [
-0.03857421875,
-0.0037994384765625,
-0.0576171875,
-0.06591796875,
0.0017852783203125,
-0.0703125,
0.035888671875,
-0.027587890625,
0.009765625,
-0.039306640625,
0.0625,
-0.06884765625,
0.0048828125,
0.0233154296875,
-0.00970458984375,
-0.056884765625,
-0.07373046875,
-0.041748046... | 26,030 | 26030 | |
arithematic progressions.
Hello, anjana! What a strange problem . . . Find $d$ if sum of first $m$ terms is: . $xm^2 + ym$ The sum of the first $m$ terms is: . $S_m\;=\;\frac{m}{2}\left[2a + d(m-1)\right]$ . . where $a$ is
the first term and $d$ is the common difference. So we have: . $\frac{m}{2}\left[2a + d(m-1)\righ... | 4 | [
0.037353515625,
0.0054931640625,
0.041748046875,
-0.0177001953125,
-0.0302734375,
0.045654296875,
-0.05517578125,
0.031005859375,
0.0004749298095703125,
-0.0172119140625,
0.0908203125,
-0.0150146484375,
0.040283203125,
-0.029052734375,
-0.036376953125,
0.061279296875,
0.025146484375,... | 26,031 | 26031 | |
Homework Help
Posted by amit sharma on Thursday, May 9, 2013 at 4:15pm.
Uncle Bert was making porridge in a cylindrical pan of diameter 24cm. The spoon he was using is 26 cm long. It accidentally falls and sinks into the porridge. Calculate the minimum volume of porridge
necessary to hide the spoon. You may ignore the... | 4 | [
-0.039794921875,
0.040771484375,
0.0101318359375,
-0.056396484375,
-0.0296630859375,
-0.00958251953125,
-0.00012683868408203125,
0.072265625,
0.0106201171875,
-0.0079345703125,
-0.028076171875,
-0.07470703125,
0.030029296875,
0.0281982421875,
-0.047119140625,
-0.10693359375,
0.013366... | 26,032 | 26032 | |
Length of a Curve
Consider x=(e^t)+(e^-t), y=5-2t, 0<t<3. Find the length of the curve.
Recall the arc length integral: $= \int_{ {t }_{i } }^{ {t }_{f } } \left | r'(t) \right | dt$ Where, $r'(t) = \sqrt[ ]{x'(t)^{2}+y'(t)^{2} }$ So we have: $x(t) = e^{t}+e^{-t} = 2cosh(t)$ $y(t) = 5 -
2t$. Then, $x'(t) = 2sinh(t)$ $... | 5 | [
0.0322265625,
-0.00909423828125,
0.0615234375,
-0.046630859375,
0.1064453125,
-0.002716064453125,
-0.072265625,
0.12158203125,
-0.0245361328125,
0.032958984375,
0.07666015625,
-0.02587890625,
-0.0308837890625,
0.0093994140625,
-0.020751953125,
0.034423828125,
-0.0576171875,
-0.0654... | 26,033 | 26033 | |
Limits: Epsilon & Delta
October 6th 2010, 05:10 PM
lilaziz1
Limits: Epsilon & Delta
Hey everyone. I have a question on the definition of limits basically. First, the definition states:
----------------------------------------
Let f be a function defined on some open interval that contains the number a, e... | 5 | [
-0.0294189453125,
-0.01068115234375,
0.01287841796875,
-0.031982421875,
0.056640625,
0.048095703125,
0.023193359375,
0.023193359375,
-0.00830078125,
-0.024169921875,
0.1318359375,
-0.022216796875,
0.08154296875,
-0.000021696090698242188,
0.08251953125,
-0.010498046875,
0.006256103515... | 26,034 | 26034 | |
Pricing Options with Credit Risk in Markovian Regime-Switching Markets
Journal of Applied Mathematics
VolumeΒ 2013Β (2013), Article IDΒ 621371, 9 pages
http://dx.doi.org/10.1155/2013/621371
Research Article
Pricing Options with Credit Risk in Markovian Regime-Switching Markets
^1College of Sciences, Minzu University of... | 4 | [
-0.08203125,
-0.0068359375,
0.000827789306640625,
-0.00173187255859375,
0.0189208984375,
0.040283203125,
0.03369140625,
0.0634765625,
0.1640625,
0.037841796875,
0.03662109375,
-0.04931640625,
0.0022735595703125,
0.0115966796875,
-0.039794921875,
-0.0654296875,
-0.08935546875,
-0.03... | 26,035 | 26035 | |
Quick Algebra question (logs and stuff)
May 17th 2008, 11:44 AM #1
Quick Algebra question (logs and stuff)
I'm having trouble with this word problem:
Assume $150 is deposited in a savings account. If the interest rate is 4.5% compounded continuously, after how many years will the investment be worth $450? (R... | 5 | [
0.064453125,
0.048095703125,
0.0177001953125,
-0.0303955078125,
0.007049560546875,
-0.058837890625,
0.036865234375,
0.0023956298828125,
-0.01904296875,
0.1318359375,
0.0751953125,
-0.040283203125,
0.0228271484375,
0.0712890625,
0.0206298828125,
0.083984375,
-0.1337890625,
-0.042480... | 26,036 | 26036 | |
Sufficient Conditions of Asymptotic Stability of the Time-Varying Descriptor Systems
International Journal of Engineering Mathematics
VolumeΒ 2013Β (2013), Article IDΒ 920851, 4 pages
http://dx.doi.org/10.1155/2013/920851
Research Article
Sufficient Conditions of Asymptotic Stability of the Time-Varying Descriptor Syste... | 5 | [
-0.080078125,
0.0150146484375,
-0.00372314453125,
0.0167236328125,
0.0277099609375,
0.03271484375,
-0.0009918212890625,
0.056396484375,
0.0830078125,
0.000972747802734375,
0.064453125,
0.00482177734375,
0.03759765625,
-0.0087890625,
-0.08203125,
0.043212890625,
0.058349609375,
-0.0... | 26,037 | 26037 | |
Convert Mohr Circle Stress Data to Real-World Stresses
Steven Dutch, Natural and Applied Sciences,
... | 4 | [
-0.015380859375,
0.0279541015625,
0.023193359375,
0.0020599365234375,
0.016357421875,
-0.07861328125,
0.005767822265625,
0.01336669921875,
-0.0030670166015625,
0.0157470703125,
0.00151824951171875,
-0.07861328125,
0.01214599609375,
0.0234375,
0.0361328125,
0.041015625,
-0.01623535156... | 26,038 | 26038 | |
Isomorphism between groups...
November 4th 2010, 09:58 PM
matt.qmar
Isomorphism between groups...
Hello!
I am trying to show that $\alpha$ is an ismorphism,
$\alpha:U(st) \rightarrow U(s) \oplus U(t)$
defined by $\alpha(x) = (x\ mod\ s, x\ mod\ t)$ where $x \in U(st)$
where U(n) is the multiplic... | 4 | [
-0.041015625,
-0.01214599609375,
-0.043212890625,
-0.0206298828125,
0.0167236328125,
-0.0016021728515625,
0.125,
-0.0281982421875,
-0.0234375,
-0.1923828125,
0.03271484375,
-0.0096435546875,
-0.024169921875,
-0.003021240234375,
0.0260009765625,
-0.0250244140625,
0.00970458984375,
-... | 26,039 | 26039 | |
Math Help
f(t) = (2e^t + 3e^-t) / (e^t + 2e^-t) find f^-1 (t)
I will start you off. let $y = f(t)$ we have: $y = \frac {2e^t + 3e^{-t}}{e^t + 2e^{-t}}$ For inverse, switch $y$ and $t$ and solve for $y$ $\Rightarrow t = \frac {2e^y + 3e^{-y}}{e^y + 2e^{-y}}$ $\
Rightarrow t \left( e^y + 2e^{-y} \right) = 2e^y + 3e^{-y... | 4 | [
-0.04638671875,
0.007537841796875,
-0.01190185546875,
-0.040283203125,
0.04248046875,
-0.00604248046875,
-0.058837890625,
0.06103515625,
-0.0023956298828125,
0.05908203125,
0.1376953125,
-0.13671875,
-0.01470947265625,
-0.0196533203125,
0.0142822265625,
-0.0181884765625,
-0.109375,
... | 26,040 | 26040 | |
Exponential growth
December 9th 2009, 09:15 AM #1
Member
Joined
May 2009
Posts
129
Exponential growth
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420.
a) Find an expression for the number of bacteria afte... | 4 | [
-0.02001953125,
0.111328125,
0.0228271484375,
-0.036376953125,
-0.0177001953125,
-0.039306640625,
0.0299072265625,
0.0546875,
0.031494140625,
0.08642578125,
0.126953125,
-0.1318359375,
0.046142578125,
0.0927734375,
-0.0004425048828125,
0.02490234375,
-0.0927734375,
0.00885009765625... | 26,041 | 26041 | |
Conditinal Probability with numbers selected at random
October 6th 2010, 07:23 PM #1
Junior Member
Joined
Mar 2009
From
Madison, WI
Posts
42
Conditinal Probability with numbers selected at random
Suppose that three numbers are selected one by one, at random, and without replacement from the set of nu... | 4 | [
-0.0380859375,
-0.064453125,
-0.07470703125,
-0.10400390625,
-0.04541015625,
0.044189453125,
0.0791015625,
-0.0225830078125,
0.04296875,
0.027099609375,
-0.08837890625,
0.01611328125,
0.01123046875,
-0.0703125,
0.050048828125,
-0.03466796875,
0.003143310546875,
-0.06787109375,
-0... | 26,042 | 26042 | |
On Radiation by a Heavy Quark in
Advances in High Energy Physics
VolumeΒ 2012Β (2012), Article IDΒ 592854, 10 pages
http://dx.doi.org/10.1155/2012/592854
Research Article
On Radiation by a Heavy Quark in SYM
Physics Department, University of Bielefeld, 33501 Bielefeld, Germany
Received 10 April 2012; Accepted 20 July... | 4 | [
-0.111328125,
-0.0498046875,
-0.0101318359375,
0.0771484375,
0.04150390625,
0.01806640625,
0.0791015625,
0.046142578125,
-0.0303955078125,
0.0086669921875,
0.1005859375,
0.038330078125,
-0.06103515625,
0.048828125,
0.09716796875,
0.038330078125,
0.043701171875,
0.015869140625,
-0... | 26,043 | 26043 | |
Plane-Based Sampling for Ray Casting Algorithm in Sequential Medical Images
Computational and Mathematical Methods in Medicine
VolumeΒ 2013Β (2013), Article IDΒ 874517, 5 pages
http://dx.doi.org/10.1155/2013/874517
Research Article
Plane-Based Sampling for Ray Casting Algorithm in Sequential Medical Images
^1School of ... | 4 | [
-0.0257568359375,
-0.001373291015625,
0.04296875,
-0.10888671875,
-0.05615234375,
-0.049072265625,
0.04345703125,
0.01080322265625,
0.028564453125,
0.003204345703125,
-0.0859375,
0.080078125,
0.03125,
0.08544921875,
-0.12060546875,
-0.059326171875,
-0.0302734375,
-0.0301513671875,
... | 26,044 | 26044 | |
Homework Help
Posted by Math asap on Wednesday, November 10, 2010 at 6:28pm.
1)3/4+x>1 answer:x>1/4
2)10-3x<5 answer:x>5/3
3)|7-x|>2 answer:x>-5 x<-9
4)|x+0.5|=0.25 answer:x=-o.25,-0.75
thank you very very much!!!
β’ please check - Henry, Thursday, November 11, 2010 at 10:09pm
Prob.1 and 2 are correct.
... | 4 | [
-0.07275390625,
0.0299072265625,
0.080078125,
-0.031005859375,
-0.01483154296875,
-0.09130859375,
0.052734375,
0.003814697265625,
-0.0712890625,
0.01092529296875,
-0.0174560546875,
-0.08984375,
0.0771484375,
0.0020751953125,
-0.0302734375,
0.017822265625,
-0.045166015625,
-0.072265... | 26,045 | 26045 | |
Integration of Rational Functions By Partial Fractions
June 21st 2008, 09:41 PM
auslmar
Integration of Rational Functions By Partial Fractions
I have this problem that needs to be solved by integration by partial fractions and I can't seem to get the right answer. Here's the problem as written:
"Find $\int\... | 5 | [
-0.0211181640625,
0.0185546875,
0.06982421875,
-0.01141357421875,
-0.03369140625,
0.05029296875,
-0.04345703125,
0.0135498046875,
0.0111083984375,
-0.01116943359375,
0.02099609375,
-0.078125,
0.00171661376953125,
0.030029296875,
-0.0302734375,
0.055419921875,
0.0177001953125,
0.022... | 26,046 | 26046 | |
Question about the correct variance to use
April 5th 2011, 07:34 AM #1
Member
Joined
Oct 2008
Posts
206
Question about the correct variance to use
I am currently analysing a longitudinal study regarding a treatment group and measurements were taken over 5 intervals. (for example week 1, week 2, week 3, w... | 4 | [
0.0281982421875,
-0.03955078125,
-0.00185394287109375,
-0.013916015625,
-0.0113525390625,
0.0245361328125,
-0.015625,
0.0308837890625,
-0.07861328125,
-0.00628662109375,
-0.0123291015625,
0.0225830078125,
-0.0908203125,
0.047119140625,
-0.022705078125,
-0.0267333984375,
0.01141357421... | 26,047 | 26047 | |
Exponentially Distributed RV - MGF
November 1st 2009, 01:04 PM #1
Newbie
Joined
Nov 2009
Posts
2
Exponentially Distributed RV - MGF
I need help. The problem is this:
X is an exponentially distributed random variable with p.d.f.
f(x) = $\lambda{e}^{-\lambda*x}$
0<x<infinity
Show that th... | 5 | [
-0.0517578125,
0.0294189453125,
0.0242919921875,
0.033935546875,
0.0034637451171875,
-0.033203125,
0.06396484375,
0.00122833251953125,
-0.0008544921875,
0.08447265625,
0.04931640625,
0.0274658203125,
0.0400390625,
-0.0206298828125,
0.03466796875,
-0.04248046875,
0.06884765625,
-0.1... | 26,048 | 26048 | |
Delta Shock Waves for a Linearly Degenerate Hyperbolic System of Conservation Laws of Keyfitz-Kranzer Type
Advances in Mathematical Physics
VolumeΒ 2013Β (2013), Article IDΒ 958120, 10 pages
http://dx.doi.org/10.1155/2013/958120
Research Article
Delta Shock Waves for a Linearly Degenerate Hyperbolic System of Conservati... | 5 | [
-0.134765625,
0.050048828125,
0.0751953125,
-0.05029296875,
0.052978515625,
0.0027618408203125,
-0.00750732421875,
-0.0284423828125,
0.014404296875,
0.032470703125,
0.125,
-0.0142822265625,
-0.006683349609375,
-0.04345703125,
0.055908203125,
-0.0262451171875,
-0.09765625,
-0.047607... | 26,049 | 26049 | |
Nontrivial Solution of Fractional Differential System Involving Riemann-Stieltjes Integral Condition
Abstract and Applied Analysis
VolumeΒ 2012Β (2012), Article IDΒ 719192, 11 pages
http://dx.doi.org/10.1155/2012/719192
Research Article
Nontrivial Solution of Fractional Differential System Involving Riemann-Stieltjes In... | 5 | [
-0.09228515625,
-0.008544921875,
0.0096435546875,
-0.051025390625,
0.017822265625,
0.03466796875,
-0.0693359375,
0.007781982421875,
0.044677734375,
-0.03271484375,
0.049560546875,
-0.04833984375,
-0.004730224609375,
0.0003566741943359375,
-0.0299072265625,
-0.020263671875,
0.01794433... | 26,050 | 26050 | |
Find the values of M and N
I am lost in this question attached if some kind soul can show the algebra it would be highly appreciated
Hello, waleedrabbani! $\text{Let: }\:\begin{array}{ccc}f(x) &=& mx^2+2x+5 \\ g(x) &=& 2x^2 + nx - 2 \end{array}$ $\text{Define: }\:H(x) \;=\;f(x)\!\cdot\!G(x)$ $\text{Two points that sat... | 4 | [
-0.00897216796875,
0.024658203125,
0.04931640625,
0.002655029296875,
0.01068115234375,
0.05712890625,
0.008056640625,
0.035400390625,
-0.0634765625,
-0.06640625,
0.0859375,
-0.064453125,
0.05419921875,
-0.0751953125,
-0.0341796875,
0.05908203125,
0.02294921875,
-0.0301513671875,
... | 26,051 | 26051 | |
Math Help
December 13th 2009, 01:43 PM #1
Junior Member
Joined
Dec 2009
Posts
71
identity
i don't know how to do this identity:
tan ^4-sec^4=...
can you help me? i hope not to disturb you..but i'm reviewing 2 chapters made so far...and i truly need your help.
Hello, alessandromangione!
... | 4 | [
0.029052734375,
0.080078125,
0.0888671875,
0.019287109375,
-0.0771484375,
0.03466796875,
0.0556640625,
-0.016357421875,
0.003936767578125,
-0.015625,
0.05712890625,
-0.046630859375,
-0.0123291015625,
0.07275390625,
0.0020751953125,
0.04345703125,
0.04248046875,
0.03076171875,
-0.... | 26,052 | 26052 | |
How to find the difference between angles of two complex numbers
May 21st 2013, 06:23 AM #1
Newbie
Joined
May 2013
From
Bangalore
Posts
4
Hi
I have two vectors represented as complex numbers and need to calculate angle between in most efficient way.
This is for implementing in C.
If I use ... | 4 | [
-0.04150390625,
0.0223388671875,
-0.06494140625,
-0.046875,
0.0302734375,
-0.0869140625,
-0.056396484375,
0.0235595703125,
0.017333984375,
-0.0810546875,
0.0179443359375,
0.0225830078125,
0.01141357421875,
0.052001953125,
0.041259765625,
-0.0174560546875,
-0.00830078125,
0.09863281... | 26,053 | 26053 | |
Correcting for Hubris in Project Appraisal
ISRN Economics
VolumeΒ 2012Β (2012), Article IDΒ 478485, 4 pages
http://dx.doi.org/10.5402/2012/478485
Research Article
Correcting for Hubris in Project Appraisal
School of Business & Economics, Wilfrid Laurier University, Waterloo, ON, Canada N2L 3C5
Received 18 April 2012; ... | 5 | [
-0.047607421875,
0.0230712890625,
0.006500244140625,
0.06396484375,
-0.00311279296875,
-0.001251220703125,
-0.048583984375,
0.053466796875,
0.07861328125,
0.12255859375,
-0.0157470703125,
0.03564453125,
-0.01031494140625,
-0.04931640625,
-0.049072265625,
-0.05517578125,
-0.0180664062... | 26,054 | 26054 | |
another mapping question
October 12th 2008, 03:23 PM #1
another mapping question
Let $f$ be a function from $X$ onto $Y$ and let $B \subset Y$. Show that $f(f^{-1}(B))=B$.
I was thinking of something along the lines of
let $b \in B \ \& \ x \in X$ then $f^{-1}(b) = x \longrightarrow f(f^{-1}(b)) = f(x) ... | 4 | [
-0.005706787109375,
-0.0084228515625,
0.01434326171875,
0.029052734375,
-0.03515625,
-0.046142578125,
0.09033203125,
0.083984375,
-0.06689453125,
-0.046875,
-0.047607421875,
0.01220703125,
0.0283203125,
0.039306640625,
0.047607421875,
0.1044921875,
0.0264892578125,
-0.052734375,
... | 26,055 | 26055 | |
Integrating to Find Particular Solution - Question 2
April 25th 2011, 02:27 PM #1
Member
Joined
Feb 2009
Posts
118
Integrating to Find Particular Solution - Question 2
The answer to the following question is C = -3.75. Please tell me where I went wrong:
Question: y = integral (squareroot 3x - cubero... | 5 | [
-0.0177001953125,
0.005584716796875,
-0.047119140625,
0.00390625,
-0.00885009765625,
0.0478515625,
-0.037841796875,
-0.00909423828125,
-0.016357421875,
-0.08203125,
0.07470703125,
-0.07666015625,
-0.03759765625,
0.060302734375,
-0.032958984375,
-0.0400390625,
-0.0291748046875,
0.01... | 26,056 | 26056 | |
Puzzles in Education - Red, White, and Blue Balls Solution
Home / Puzzles in Education / Hands On Puzzles / Grade 7-8 /
This was a really hard and tricky challenge, and we got a lot of different solutions to this clever puzzle. Among them there were wrong solutions too. The main mistake in them was that some
possibl... | 4 | [
0.010498046875,
0.0128173828125,
0.01904296875,
-0.0067138671875,
-0.0035858154296875,
-0.039794921875,
0.043212890625,
0.01483154296875,
0.0255126953125,
0.061767578125,
-0.04638671875,
-0.043701171875,
-0.03515625,
0.08740234375,
0.0098876953125,
0.0022735595703125,
-0.024291992187... | 26,057 | 26057 | |
No integer Solutions
July 14th 2011, 02:51 AM
Learner248
No integer Solutions
Prove that 15x^2 -7y^2=9 has no integer solutions.
I have understood a few steps
15x^2 -7y^2=9 => y=3y1 => 5x^2-21y^2=3 => x-3x1 => 15x1^2-7y1^2=1 =>y1^2=2 mod 3
But this contradiction how???
If there is any other wa... | 4 | [
-0.012939453125,
0.01611328125,
0.0281982421875,
0.064453125,
0.11474609375,
0.0213623046875,
0.057373046875,
0.006500244140625,
-0.0123291015625,
-0.05810546875,
0.0286865234375,
0.0125732421875,
0.0419921875,
0.0556640625,
-0.037109375,
-0.043212890625,
-0.0250244140625,
-0.06054... | 26,058 | 26058 | |
MathGroup Archive: March 2003 [00189]
[Date Index] [Thread Index] [Author Index]
Fwd: RE: Antiderivatives and Definite Integrals
β’ To: mathgroup at smc.vnet.net
β’ Subject: [mg39841] Fwd: [mg39713] RE: [mg39670] Antiderivatives and Defin... | 5 | [
-0.07421875,
-0.0274658203125,
0.07275390625,
0.01416015625,
0.0908203125,
-0.0274658203125,
-0.01214599609375,
-0.03271484375,
-0.01300048828125,
0.07470703125,
0.0439453125,
0.05908203125,
-0.0037994384765625,
0.020263671875,
-0.016357421875,
-0.00982666015625,
0.0235595703125,
-... | 26,059 | 26059 | |
[Haskell] Announce: revamped free theorems generator
Sebastian Fischer sebf at informatik.uni-kiel.de
Tue Jun 22 11:20:41 EDT 2010
On Jun 22, 2010, at 1:32 PM, Janis VoigtlΓ€nder wrote:
>> A variant of the above statement incorporating type classes is:
>> For every given type a and function
>> f :: forall b . Mo... | 4 | [
-0.109375,
0.024169921875,
0.09375,
0.00244140625,
0.0191650390625,
0.04541015625,
0.080078125,
-0.0244140625,
-0.0198974609375,
0.054931640625,
0.02685546875,
-0.06640625,
0.01904296875,
-0.03466796875,
0.09521484375,
0.07373046875,
-0.028564453125,
0.0023651123046875,
-0.039062... | 26,060 | 26060 | |
Math Help
The answers are all here. If $f(t) = t^n$ then $\mathcal{L}(f)(s) = \frac{n!}{s^{n+1}}$. So the Laplace transform of $6t^3$ is $\frac{36}{s^4}$. Also, the Laplace transform converts convolution
products to regular products. So $\mathcal{L}((f*f)(t)) = (\mathcal{L}(f)(s))^2$. Therefore $(\mathcal{L}(f)(s))^2 ... | 5 | [
-0.0198974609375,
0.027099609375,
-0.0216064453125,
0.00787353515625,
-0.00640869140625,
0.06884765625,
-0.07861328125,
-0.00689697265625,
-0.01080322265625,
-0.01953125,
0.02294921875,
0.027587890625,
-0.031494140625,
-0.06689453125,
-0.036376953125,
-0.0341796875,
-0.0966796875,
... | 26,061 | 26061 | |
New Statistical Multiparticle Approach to the Acceleration of Electrons by the Ion Field in Plasmas
International Journal of Spectroscopy
VolumeΒ 2010Β (2010), Article IDΒ 347080, 4 pages
http://dx.doi.org/10.1155/2010/347080
Research Article
New Statistical Multiparticle Approach to the Acceleration of Electrons by the... | 4 | [
-0.047607421875,
-0.00665283203125,
0.057861328125,
0.064453125,
-0.03759765625,
0.007232666015625,
-0.02294921875,
0.046142578125,
-0.01416015625,
0.039794921875,
-0.0191650390625,
-0.056396484375,
0.056640625,
-0.030029296875,
0.0079345703125,
-0.10107421875,
0.0263671875,
0.0157... | 26,062 | 26062 | |
Measurements of the Characteristics of Transparent Material Using Digital Holography
Advances in Materials Science and Engineering
VolumeΒ 2013Β (2013), Article IDΒ 598737, 7 pages
http://dx.doi.org/10.1155/2013/598737
Research Article
Measurements of the Characteristics of Transparent Material Using Digital Holography
... | 4 | [
0.006988525390625,
0.036376953125,
0.068359375,
-0.03662109375,
0.0269775390625,
-0.091796875,
0.0277099609375,
-0.0244140625,
-0.0308837890625,
-0.003662109375,
0.018798828125,
0.036376953125,
0.0322265625,
-0.017578125,
0.00390625,
-0.0712890625,
0.039794921875,
-0.00570678710937... | 26,063 | 26063 | |
, 20
ASPHALTIC EQUATIONS
& EXAMPLE CALCULATIONS
SCOPE
This IM describes the equations associated with asphaltic materials. In addition, there are a number of example calculations showing how to determine various properties.
NAMING CONVENTION
DEFINITIONS
P[a] = % of air voids in compacted hot mix asp... | 5 | [
-0.038330078125,
-0.0172119140625,
0.007476806640625,
0.007110595703125,
-0.039794921875,
0.0020904541015625,
0.0255126953125,
0.034423828125,
0.0007171630859375,
0.0263671875,
0.015869140625,
-0.08251953125,
0.08447265625,
-0.05078125,
0.0230712890625,
0.0927734375,
-0.0283203125,
... | 26,064 | 26064 | |
Closed set problem
March 18th 2007, 06:22 PM
tttcomrader
Closed set problem
Let n be in the set of Natural Numbers, let S = {u in R^n : ||u|| = 4}. Prove S is closed.
March 18th 2007, 09:48 PM
CaptainBlack
Quote:
Here a set is closed if all limit points of the set are in the set.
Let x be a lim... | 5 | [
0.0277099609375,
0.0537109375,
0.0191650390625,
-0.06591796875,
-0.005157470703125,
0.0927734375,
0.142578125,
-0.0031280517578125,
0.0196533203125,
-0.03662109375,
-0.04150390625,
-0.017822265625,
0.06396484375,
-0.02783203125,
-0.03515625,
-0.019775390625,
0.01043701171875,
-0.11... | 26,065 | 26065 | |
Calculate Volume using the Method of Cylindrical Shells - Urgent
October 7th 2012, 04:58 AM #1
Newbie
Joined
May 2012
From
North America
Posts
11
Calculate Volume using the Method of Cylindrical Shells - Urgent
Here are some things I have done. I already found the volume since the other part o... | 5 | [
0.01239013671875,
0.030517578125,
0.01177978515625,
-0.0654296875,
0.0186767578125,
-0.07177734375,
-0.06689453125,
0.1279296875,
-0.04150390625,
0.0096435546875,
-0.004913330078125,
0.01953125,
0.030029296875,
0.07958984375,
0.01165771484375,
-0.0225830078125,
-0.0390625,
-0.00418... | 26,066 | 26066 | |
A word problem
May 14th 2009, 06:59 AM
dizizviet
A word problem
I've always had a problem with word problems...
1)A baseball team is trying to determine what price to charge for tickets. At a price of $10 per ticket, it averages 45,000 people per game. For every increase of $1, it loses 5,000 people.
Ev... | 4 | [
0.05908203125,
0.07666015625,
0.0267333984375,
-0.08935546875,
-0.01373291015625,
0.0125732421875,
-0.037353515625,
0.12255859375,
-0.01385498046875,
0.11083984375,
-0.0184326171875,
-0.0072021484375,
0.0250244140625,
0.1015625,
-0.033935546875,
0.058349609375,
-0.0054931640625,
0.... | 26,067 | 26067 | |
astroid: vectors, curvature, arc length
April 14th 2010, 05:16 AM #1
Member
Joined
May 2008
Posts
77
astroid: vectors, curvature, arc length
Hope someone can help me out here, to check the work I've done and set me on the right path of the work I'm stuck at (or getting the wrong answer for!)
Astroid ... | 5 | [
-0.058837890625,
0.0036468505859375,
-0.0299072265625,
-0.051513671875,
-0.035400390625,
-0.00101470947265625,
-0.0084228515625,
0.10986328125,
-0.019775390625,
-0.0284423828125,
0.0625,
0.05078125,
-0.05908203125,
-0.0206298828125,
-0.083984375,
0.01470947265625,
-0.06298828125,
-... | 26,068 | 26068 | |
greatest least bound and least upper bound proof
November 4th 2009, 12:21 PM
tae1466
greatest least bound and least upper bound proof
I've been struggling with this one.
Let A be a partially ordered set. Suppose XβYβA.
1. Assuming that all the least upper bounds and greatest lower bounds exist, prove t... | 5 | [
-0.05615234375,
-0.0201416015625,
0.142578125,
-0.061279296875,
0.0174560546875,
-0.004638671875,
0.0771484375,
0.0693359375,
-0.00238037109375,
-0.0595703125,
-0.017578125,
0.023681640625,
0.043212890625,
-0.068359375,
0.038330078125,
0.06396484375,
0.1083984375,
-0.06103515625,
... | 26,069 | 26069 | |
geomertric and arithmetric sequences
February 1st 2009, 05:20 AM
hmmmm
geomertric and arithmetric sequences
a geometric sequence of posotive terms has first term 2 and the sum of the first three terms is 266 calculate the common ratio
an arithmetric sequense A has first term a and a common difference of 2 a... | 4 | [
-0.06201171875,
-0.016357421875,
-0.00830078125,
-0.058349609375,
-0.109375,
0.06494140625,
-0.055908203125,
-0.0001983642578125,
0.0147705078125,
0.000560760498046875,
0.046142578125,
-0.041259765625,
-0.0062255859375,
-0.0257568359375,
0.0250244140625,
0.02197265625,
-0.09912109375... | 26,070 | 26070 | |
the encyclopedic entry of young modulus
In
solid mechanics
,
Young's modulus (E)
is a measure of the
stiffness
of an isotropic elastic material. It is also known as the
Young modulus
,
modulus of elasticity
,
elastic modulus
(though Young's modulus is actually one of several
elastic moduli
such as the
bu... | 4 | [
-0.056396484375,
0.036376953125,
-0.033203125,
0.07666015625,
0.0189208984375,
-0.04345703125,
0.0228271484375,
0.099609375,
-0.012939453125,
0.0439453125,
0.08935546875,
-0.03076171875,
0.0177001953125,
0.07177734375,
-0.087890625,
-0.061279296875,
-0.045166015625,
0.03369140625,
... | 26,071 | 26071 | |
Robust Exponential Stability Criteria of LPD Systems with Mixed Time-Varying Delays and Nonlinear Perturbations
Abstract and Applied Analysis
VolumeΒ 2012Β (2012), Article IDΒ 348418, 20 pages
http://dx.doi.org/10.1155/2012/348418
Research Article
Robust Exponential Stability Criteria of LPD Systems with Mixed Time-Vary... | 5 | [
-0.095703125,
0.0002269744873046875,
0.0218505859375,
0.009765625,
0.018310546875,
-0.015869140625,
-0.0322265625,
-0.00445556640625,
0.06884765625,
-0.0012054443359375,
0.08154296875,
0.053466796875,
0.04541015625,
-0.09033203125,
-0.0517578125,
0.005096435546875,
0.008056640625,
... | 26,072 | 26072 | |
need help proving a statment with subspaces dimensions
January 11th 2013, 09:47 AM
Stormey
need help proving a statment with subspaces dimensions
Hi.
Let $U,W$ be subspaces of $V$.
Suppose $dim(V)=n$, and $dim(U)=dim(W)=n-1$
I need to prove that $dim(U\cap W)=n-2$
Thanks in advanced!
January 1... | 5 | [
-0.013427734375,
-0.0225830078125,
0.04736328125,
0.07568359375,
0.035400390625,
0.06982421875,
0.048828125,
-0.044677734375,
-0.04736328125,
-0.11376953125,
-0.0478515625,
-0.05517578125,
-0.0128173828125,
-0.006317138671875,
-0.0830078125,
-0.053466796875,
-0.0140380859375,
-0.09... | 26,073 | 26073 | |
Math Help
If a, b and c are positive real numbers, prove that: bc(b+c)+ca(c+a)+ab(a+b)β₯6abc
OK. Now expand the given expression, and divide it by abc. You get $[b^2c + bc^2 + c^2a +ca^2 + a^2b + ab^2]/abc$ = b/a + c/a + c/b + a/b + a/c + b/c Now consider b/a + a/b = (b^2 + a^2)/ab = [(a+b)^
2- 2ab]/ab = [(a+b)^2/ab] ... | 4 | [
-0.040283203125,
0.07177734375,
0.0189208984375,
0.0703125,
-0.1064453125,
0.00408935546875,
-0.0732421875,
-0.019775390625,
0.06640625,
-0.0308837890625,
-0.05419921875,
-0.0810546875,
0.041748046875,
0.055908203125,
-0.00069427490234375,
0.039306640625,
-0.01611328125,
0.07617187... | 26,074 | 26074 | |
another method of solving this ODE..
April 9th 2008, 01:23 AM #1
Junior Member
Joined
Mar 2008
Posts
60
another method of solving this ODE..
another method of solving this ODE..
$(3x^2y-y^3)dx-(3xy^2-x^3)dy=0$
I ve proved that it is an exact differential equation ..
I need to state another me... | 4 | [
-0.0966796875,
-0.052734375,
-0.0096435546875,
-0.007659912109375,
-0.0167236328125,
0.0013580322265625,
-0.0189208984375,
-0.10107421875,
-0.00579833984375,
-0.050537109375,
0.078125,
-0.016357421875,
-0.03466796875,
0.0174560546875,
0.01904296875,
0.004669189453125,
-0.03662109375,... | 26,075 | 26075 | |
Help with solving linear systems by substitution
March 19th 2008, 05:46 PM #1
Help with solving linear systems by substitution
Okay I was doing well until I stumbled across a question that was backwards if that makes sense.
Like:
a+4b=15
5b=2a+3
or
5=2y-x
7=3y-2x
I have been trying... | 4 | [
-0.05908203125,
0.0172119140625,
0.038330078125,
-0.052978515625,
0.06103515625,
0.050048828125,
0.0004425048828125,
-0.06982421875,
-0.0986328125,
0.0224609375,
0.0673828125,
-0.045654296875,
0.049560546875,
-0.0024871826171875,
0.022216796875,
0.12890625,
-0.036865234375,
-0.0336... | 26,076 | 26076 | |
Help with solving the following integral
February 6th 2013, 07:03 AM #1
Newbie
Joined
Dec 2011
Posts
8
Help with solving the following integral
Hi all,
Any help with the following integral would be much appreciated.
$\int(5x^2+\sqrt x-\frac{4}{x^2})dx$
This what i have so far
$\int \left... | 4 | [
0.025634765625,
-0.09716796875,
0.07763671875,
0.00848388671875,
-0.024169921875,
-0.035400390625,
-0.057373046875,
0.03271484375,
-0.031494140625,
-0.060546875,
-0.033935546875,
-0.0213623046875,
-0.0341796875,
0.0052490234375,
-0.05322265625,
0.05810546875,
0.03173828125,
-0.0192... | 26,077 | 26077 | |
Percentage with apples problem
October 1st 2010, 06:30 AM #1
Member
Joined
Apr 2010
From
dfsdfdf
Posts
160
Percentage with apples problem
Dear sir,
I would be grateful if someone can help me in the below question
thanks
There are more apples in box A than in box B. 30 % of the apples in ... | 4 | [
0.050537109375,
-0.005950927734375,
-0.04833984375,
-0.0458984375,
-0.01953125,
0.0284423828125,
0.05078125,
-0.0252685546875,
-0.01708984375,
0.08251953125,
0.076171875,
-0.09375,
0.07470703125,
0.0267333984375,
0.015869140625,
0.1220703125,
0.0223388671875,
-0.01953125,
-0.1669... | 26,078 | 26078 | |
the encyclopedic entry of indirect proof
In
mathematics
and
logic
, a
direct proof
is a way of showing the
truth
or falsehood of a given statement by a straightforward combination of established facts, usually existing
lemmas
and
theorems
, without making any further assumptions. In order to directly prove ... | 4 | [
-0.0284423828125,
0.021484375,
0.07275390625,
0.0025482177734375,
0.03759765625,
0.00131988525390625,
-0.056640625,
0.1015625,
0.09521484375,
0.11328125,
0.050048828125,
0.006134033203125,
0.041015625,
0.06640625,
0.0478515625,
0.00439453125,
0.038330078125,
0.02685546875,
0.0206... | 26,079 | 26079 | |
A New Estimation of the Growth Bound of a Periodic Evolution Family on Banach Spaces
Journal of Function Spaces and Applications
VolumeΒ 2013Β (2013), Article IDΒ 260920, 6 pages
http://dx.doi.org/10.1155/2013/260920
Research Article
A New Estimation of the Growth Bound of a Periodic Evolution Family on Banach Spaces
^... | 4 | [
-0.1123046875,
0.018310546875,
0.009521484375,
0.0791015625,
0.0284423828125,
0.08447265625,
0.0032806396484375,
-0.0186767578125,
0.0191650390625,
-0.058349609375,
-0.00171661376953125,
-0.06689453125,
0.0595703125,
-0.05615234375,
0.00872802734375,
-0.0458984375,
-0.0791015625,
-... | 26,080 | 26080 | |
Palindromes
February 25th 2007, 06:13 PM #1
Newbie
Joined
Feb 2007
Posts
7
Palindromes
Any help would be appreciated on the following.
A palindrome is a number that reads same backwards as fowards (for instance, 373 and 521125 are palindromes). Prove that any palindrome with an even number of digits... | 4 | [
-0.11767578125,
0.06005859375,
0.004150390625,
-0.068359375,
0.01104736328125,
0.0576171875,
0.06494140625,
0.07861328125,
-0.08203125,
0.01470947265625,
-0.02392578125,
0.0302734375,
0.00823974609375,
0.0133056640625,
-0.09521484375,
-0.036865234375,
-0.047119140625,
0.07421875,
... | 26,081 | 26081 | |
Stress-Strain Law for Confined Concrete with Hardening or Softening Behavior
Advances in Civil Engineering
VolumeΒ 2013Β (2013), Article IDΒ 804904, 11 pages
http://dx.doi.org/10.1155/2013/804904
Research Article
Stress-Strain Law for Confined Concrete with Hardening or Softening Behavior
^1Dipartimento di Ingegneria C... | 4 | [
-0.07666015625,
0.00174713134765625,
0.056640625,
0.05029296875,
0.0703125,
-0.059326171875,
0.0576171875,
0.08251953125,
0.01080322265625,
-0.013916015625,
-0.027099609375,
-0.060302734375,
0.037841796875,
0.0712890625,
0.0072021484375,
0.060546875,
-0.004547119140625,
0.017089843... | 26,082 | 26082 | |
The Shapley Values on Fuzzy Coalition Games with Concave Integral Form
Journal of Applied Mathematics
VolumeΒ 2014Β (2014), Article IDΒ 231508, 13 pages
http://dx.doi.org/10.1155/2014/231508
Research Article
The Shapley Values on Fuzzy Coalition Games with Concave Integral Form
^1Library, Beijing Institute of Technolog... | 5 | [
0.004638671875,
0.003509521484375,
-0.0142822265625,
-0.107421875,
-0.076171875,
0.0654296875,
0.05859375,
-0.083984375,
-0.00799560546875,
0.09326171875,
0.0002689361572265625,
0.0146484375,
0.134765625,
0.03857421875,
0.0106201171875,
0.040771484375,
0.0732421875,
-0.0888671875,
... | 26,083 | 26083 | |
Approximation Integral
July 31st 2008, 01:16 PM #1
Newbie
Joined
Jul 2008
Posts
11
Approximation Integral
Hey all, i asked a question on this the other day, just wanted to check my answer & it might be useful to someone else as a worked example
Evaluate the area correct to 4 significant figures, usi... | 5 | [
0.0712890625,
-0.01470947265625,
0.06884765625,
-0.10302734375,
-0.002471923828125,
-0.10595703125,
-0.01904296875,
0.0361328125,
-0.062255859375,
-0.016845703125,
-0.044921875,
-0.01214599609375,
0.053955078125,
0.023681640625,
-0.039794921875,
0.016845703125,
-0.016357421875,
-0.... | 26,084 | 26084 | |
greatest least bound and least upper bound proof
November 4th 2009, 12:21 PM #1
Newbie
Joined
Nov 2009
Posts
1
greatest least bound and least upper bound proof
I've been struggling with this one.
Let A be a partially ordered set. Suppose XβYβA.
1. Assuming that all the least upper bounds and gr... | 4 | [
-0.037353515625,
-0.034912109375,
0.13671875,
-0.0732421875,
0.0019378662109375,
-0.011962890625,
0.0771484375,
0.0673828125,
-0.00579833984375,
-0.057861328125,
-0.0181884765625,
0.0269775390625,
0.044677734375,
-0.058837890625,
0.0498046875,
0.0693359375,
0.11376953125,
-0.052978... | 26,085 | 26085 | |
Sum and difference identitiees?
February 7th 2011, 06:16 PM
homeylova223
Sum and difference identitiees?
Hello! I have two problems I need help on.
use sum or difference to find the exact value of each trigonometric function.
cot 113pi/12
I know this equals= 4(360)+255
and 255 is 210+45
So ... | 4 | [
-0.0478515625,
0.043212890625,
0.0537109375,
-0.033203125,
0.017578125,
0.058349609375,
-0.00494384765625,
-0.01068115234375,
0.06982421875,
-0.01904296875,
-0.017333984375,
-0.05126953125,
-0.0341796875,
0.01312255859375,
0.0849609375,
-0.05224609375,
-0.0267333984375,
0.013549804... | 26,086 | 26086 | |
Order of elements in a group
June 25th 2010, 11:51 AM #1
Junior Member
Joined
Aug 2009
Posts
34
Order of elements in a group
This probably just a simple manipulation problem but I keep going in circles. It's from Introduction to Algebra by Cameron
A group which contains elements a,b,c,d,e (none equal... | 5 | [
-0.055908203125,
0.0859375,
0.08837890625,
0.0208740234375,
-0.049560546875,
-0.005767822265625,
0.010009765625,
-0.10302734375,
0.0439453125,
0.0230712890625,
-0.037841796875,
0.056884765625,
0.0546875,
-0.05615234375,
-0.0137939453125,
0.05517578125,
-0.032958984375,
0.0703125,
... | 26,087 | 26087 | |
Anti derivative
April 23rd 2012, 12:39 AM
tankertert
Anti derivative
Confused guys
Whats the most general anti derivative of
f(x) = 4x + (3/x^2)
And
y(x) = 5x e^(1-x^2) + sin x cos x
Plz thanks
April 23rd 2012, 02:28 AM
Prove It
Re: Anti derivative
Quote:
For the first one, s... | 5 | [
-0.08642578125,
0.0712890625,
0.04296875,
-0.002593994140625,
0.052490234375,
-0.020751953125,
-0.006134033203125,
-0.039306640625,
0.0081787109375,
0.01220703125,
0.0277099609375,
-0.034912109375,
-0.045654296875,
-0.06689453125,
-0.01385498046875,
-0.03515625,
0.019287109375,
-0.... | 26,088 | 26088 | |
Another exponential dist.
July 10th 2008, 01:35 PM #1
Junior Member
Joined
Jun 2008
Posts
53
Another exponential dist.
The lifetime of a product is Y = 5X^0.7 , where X has an exponential dist. with mean = 1
Find the distribution function and pdf of Y
I'm not even sure where to start here...
... | 5 | [
-0.0810546875,
-0.0235595703125,
0.06787109375,
-0.06640625,
0.0238037109375,
-0.076171875,
0.052978515625,
0.0380859375,
-0.01348876953125,
0.059814453125,
0.04345703125,
-0.00775146484375,
0.0245361328125,
0.09765625,
0.019287109375,
0.0810546875,
-0.036376953125,
-0.06591796875,... | 26,089 | 26089 | |
[SOLVED] I need help proving that the cross product of 2 countable sets is countable.
October 11th 2008, 12:33 PM
ilikedmath
[SOLVED] I need help proving that the cross product of 2 countable sets is countable.
Statement to prove:
If A and B are countable sets, prove A x B is countable.
My work so far:
... | 5 | [
-0.036865234375,
-0.052001953125,
-0.0306396484375,
-0.0203857421875,
-0.015380859375,
0.115234375,
0.1259765625,
0.045654296875,
-0.023681640625,
-0.0400390625,
-0.04345703125,
-0.0595703125,
0.06494140625,
0.010498046875,
0.01025390625,
0.08984375,
0.033203125,
-0.003311157226562... | 26,090 | 26090 | |
DIFFERENTIAL equation
November 11th 2009, 12:55 AM #1
Newbie
Joined
Nov 2009
Posts
3
hi
can someone please help me with the following equation
y''-y= $x^n$
using method of separation of variables...
the roots come out to be 1,-1
so when i find variable parameters A(X) and B(x)
... | 5 | [
-0.11962890625,
-0.01171875,
0.00872802734375,
0.03662109375,
-0.0201416015625,
0.07861328125,
-0.01904296875,
-0.0185546875,
0.00750732421875,
-0.0274658203125,
0.05615234375,
0.030029296875,
0.024658203125,
-0.0888671875,
-0.052490234375,
0.004913330078125,
0.04736328125,
-0.0607... | 26,091 | 26091 | |
Mean Value Theorem on indicated intervals
November 27th 2012, 07:48 PM #1
Member
Joined
Oct 2011
Posts
153
Mean Value Theorem on indicated intervals
Just making sure if I got mean value theoroms,
Apply the Mean Value Theorem to f on the indicated interval, and find all values of c in the interval (a,... | 5 | [
-0.048828125,
-0.002410888671875,
0.0126953125,
-0.017333984375,
-0.07861328125,
0.0024871826171875,
-0.023681640625,
0.0888671875,
0.044677734375,
-0.00946044921875,
0.0289306640625,
-0.1318359375,
0.07763671875,
0.0361328125,
-0.0201416015625,
-0.000057697296142578125,
-0.048339843... | 26,092 | 26092 | |
The mean and standard deviation
February 17th 2008, 09:18 AM #1
Junior Member
Joined
Nov 2006
Posts
48
The mean and standard deviation
A heavy equipment sales person can contact either one or two customers per day with probability 1/3 and 2/3 respectively. Each contact will result in no sale or a $50 000... | 4 | [
0.00064849853515625,
-0.01214599609375,
0.006927490234375,
-0.048095703125,
-0.083984375,
-0.06494140625,
0.03857421875,
0.03662109375,
-0.0003986358642578125,
-0.0252685546875,
0.08154296875,
-0.035400390625,
0.038330078125,
0.0159912109375,
0.09765625,
-0.015625,
-0.01190185546875,... | 26,093 | 26093 | |
Design of Robust Current Controller for Two-Level 12-Pulse VSC-based STATCOM
Advances in Power Electronics
VolumeΒ 2011Β (2011), Article IDΒ 912749, 7 pages
http://dx.doi.org/10.1155/2011/912749
Research Article
Design of Robust Current Controller for Two-Level 12-Pulse VSC-based STATCOM
^1School of Electrical Engineer... | 4 | [
-0.1279296875,
0.0625,
-0.130859375,
0.068359375,
0.00994873046875,
0.1064453125,
-0.0206298828125,
0.0537109375,
-0.00054168701171875,
0.0673828125,
0.041748046875,
0.0125732421875,
0.0791015625,
-0.046142578125,
0.007232666015625,
0.072265625,
0.09326171875,
0.03515625,
0.00564... | 26,094 | 26094 | |
L'Hospital Rule Indeterminate INF-INF
April 12th 2007, 03:42 PM #1
L'Hospital Rule Indeterminate INF-INF
I was just wanting to know if someone could tell me what to do in this circumstance. I do know that I have to get a common denominator, on both sides of the problem, but what if there are no
fractions in t... | 5 | [
0.00408935546875,
-0.03759765625,
0.04345703125,
-0.0240478515625,
0.06884765625,
-0.07080078125,
-0.08056640625,
0.01507568359375,
0.0263671875,
0.07373046875,
0.0361328125,
-0.12158203125,
0.03857421875,
0.0284423828125,
0.05029296875,
0.004913330078125,
-0.00128173828125,
-0.007... | 26,095 | 26095 | |
On the Accuracy of Fluid Approximations to a Class of Inventory-Level-Dependent EOQ and EPQ Models
Advances in Operations Research
VolumeΒ 2011Β (2011), Article IDΒ 301205, 23 pages
http://dx.doi.org/10.1155/2011/301205
Research Article
On the Accuracy of Fluid Approximations to a Class of Inventory-Level-Dependent EOQ ... | 5 | [
-0.04296875,
-0.01904296875,
0.06494140625,
0.01251220703125,
-0.033935546875,
0.0123291015625,
-0.052490234375,
0.044677734375,
0.10791015625,
0.0390625,
0.0169677734375,
0.0072021484375,
0.0306396484375,
0.038330078125,
-0.030517578125,
-0.08203125,
0.04833984375,
-0.015991210937... | 26,096 | 26096 | |
Complex Integral
December 14th 2009, 03:33 PM #1
Newbie
Joined
Mar 2009
Posts
6
Complex Integral
Show that
$\frac{1}{2 \pi} \int_{-\pi}^{\pi} \frac{1}{1-2r\cos \theta +r^2} d \theta = 1, 0 \leq r < 1$.
Right now, I don't see how to show this. I do see that the integrand is an even function if t... | 4 | [
-0.07470703125,
0.033203125,
-0.0157470703125,
0.028564453125,
0.06884765625,
-0.037353515625,
-0.046630859375,
0.078125,
-0.0361328125,
0.11181640625,
-0.099609375,
0.0167236328125,
0.0247802734375,
0.0244140625,
-0.05224609375,
-0.07861328125,
0.0517578125,
-0.08154296875,
0.00... | 26,097 | 26097 | |
Probability of a random variable
March 29th 2011, 08:20 AM
jabba1
Probability of a random variable
The reading given by a thermometer calivrated in ice water is a random variable with probablility density function
f(x) { k(1-x) -1
{ 0 otherwise where k is a constant
find the value of k.
What ... | 5 | [
0.013671875,
0.031982421875,
-0.0341796875,
0.0234375,
-0.053466796875,
-0.042236328125,
0.0859375,
-0.00057220458984375,
0.00823974609375,
0.08837890625,
-0.0791015625,
-0.072265625,
0.11279296875,
0.0181884765625,
-0.048828125,
-0.051513671875,
0.00213623046875,
-0.11376953125,
... | 26,098 | 26098 | |
A ring becomes a division ring?
December 17th 2012, 10:36 PM
Rita
A ring becomes a division ring?
I got one problem from the textbook:
Prove that a finite ring with more than one element and no zero divisors is a division ring.
It's obvious that the zero element must exist in this ring, so "with more th... | 5 | [
-0.08837890625,
0.052978515625,
-0.050537109375,
0.0556640625,
-0.003204345703125,
-0.10791015625,
0.06884765625,
0.004486083984375,
0.0546875,
-0.064453125,
-0.06396484375,
-0.00457763671875,
0.11328125,
0.01953125,
-0.025390625,
-0.0233154296875,
-0.0390625,
0.02783203125,
-0.0... | 26,099 | 26099 |