content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Word Problem And Equation
December 4th 2007, 06:08 AM #1
Junior Member
Joined
Jun 2006
Posts
25
Word Problem And Equation
I have two problems right now the 1st is an equation
1, Two people walk 240 meters at a constant speed
Person A takes 100 more steps than the other,
Person B's steps are ... | 4 | [
0.0050048828125,
0.041015625,
-0.060302734375,
-0.036376953125,
-0.03515625,
0.053955078125,
0.00009441375732421875,
0.0240478515625,
-0.1025390625,
0.045654296875,
0.078125,
-0.03515625,
0.0546875,
0.0654296875,
0.052734375,
0.0556640625,
-0.08740234375,
-0.018310546875,
-0.0629... | 32,100 | 32100 | |
Power series, term-by-term integration
April 7th 2010, 03:44 PM
kingwinner
Power series, term-by-term integration
Evaluate
∞
∑ 1 / [n(n+1) $5^n$]
n=1
(hint: start with a geometric series, then use term-by-term integration)
===================================
Attempt:
∞
∑ $x^n$ = ... | 5 | [
-0.047119140625,
0.029296875,
0.07861328125,
0.06982421875,
-0.00982666015625,
-0.046630859375,
-0.034912109375,
0.006439208984375,
0.0218505859375,
-0.008056640625,
-0.076171875,
-0.040771484375,
0.01251220703125,
0.02587890625,
-0.07470703125,
0.014404296875,
-0.040771484375,
-0.... | 32,101 | 32101 | |
8sin^2(v)-2cos(v)=5
August 29th 2006, 03:52 AM #1
Junior Member
Joined
Oct 2005
Posts
54
8sin^2(v)-2cos(v)=5
$8\sin(v)^2-2\cos(v)=5 \Leftrightarrow$
$8(1-\cos(v)^2)-2\cos(v)=5 \Leftrightarrow$
$8-8\cos(v)^2-2\cos(v)=5 \Leftrightarrow$
$1-\cos(v)^2-\frac{1}{4}\cos(v)=\frac{5}{8} \Leftrightarro... | 4 | [
-0.0947265625,
0.04931640625,
0.039794921875,
0.068359375,
-0.03125,
0.033447265625,
-0.12158203125,
0.050537109375,
0.03759765625,
0.03076171875,
0.055419921875,
-0.02978515625,
-0.050537109375,
0.09814453125,
-0.01300048828125,
-0.022216796875,
-0.0322265625,
-0.052001953125,
-... | 32,102 | 32102 | |
On Dimension Extension of a Class of Iterative Equations
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 180184, 7 pages
http://dx.doi.org/10.1155/2013/180184
Research Article
On Dimension Extension of a Class of Iterative Equations
College of Mathematics and Computer Science, Hunan Normal University, C... | 4 | [
-0.08544921875,
-0.0257568359375,
0.0625,
-0.005218505859375,
-0.046630859375,
0.054931640625,
0.00592041015625,
0.0224609375,
0.0177001953125,
-0.025146484375,
0.08837890625,
0.095703125,
0.0255126953125,
0.06884765625,
-0.0206298828125,
0.0201416015625,
-0.10009765625,
-0.0341796... | 32,103 | 32103 | |
Homework Help
Posted by Katie A on Friday, September 30, 2011 at 11:56pm.
how do I solve using the multiplacation method
-2x>1/9
• math - Steve, Saturday, October 1, 2011 at 6:08am
I guess that means that you multiply both sides by the reciprocal of the coefficient thusly:
-2x * 1/-2 < 1/9 * 1/-2
x ... | 4 | [
-0.0260009765625,
0.038330078125,
0.103515625,
-0.033935546875,
-0.09033203125,
0.0024261474609375,
-0.07763671875,
0.0419921875,
-0.0162353515625,
0.0283203125,
0.0242919921875,
-0.038818359375,
0.0693359375,
0.00494384765625,
-0.0556640625,
0.05810546875,
0.0142822265625,
0.06347... | 32,104 | 32104 | |
[SOLVED] Quick Communication Vector Question
February 16th 2009, 06:51 AM #1
Junior Member
Joined
Feb 2009
Posts
27
[SOLVED] Quick Communication Vector Question
a) If u and v are non-zero vectors, but Proj(u onto v) = 0, what conclusion can be drawn?
b) If Proj(u onto v) = 0, does it follow that Proj... | 4 | [
-0.025634765625,
0.01055908203125,
-0.042724609375,
-0.091796875,
0.045166015625,
0.026123046875,
0.08349609375,
-0.0361328125,
-0.0064697265625,
0.02294921875,
0.0478515625,
0.002655029296875,
-0.00775146484375,
0.07080078125,
-0.0037994384765625,
0.0150146484375,
-0.004058837890625... | 32,105 | 32105 | |
MGF Help Please
May 6th 2010, 10:33 PM #1
Newbie
Joined
May 2010
Posts
6
MGF Help Please
Suppose X ~ N(0,1), i.e. X is normally distributed with mean 0 and variance 1.
Let Y = X^2
Find the MGF of Y DIRECTLY...
Can't seem to get a good answer out. Any help would be appreciated.
Also... | 4 | [
0.0198974609375,
0.0228271484375,
0.025634765625,
0.053955078125,
-0.017578125,
-0.04052734375,
0.01556396484375,
0.04052734375,
-0.01348876953125,
0.02001953125,
0.033935546875,
-0.00170135498046875,
0.0576171875,
0.032958984375,
-0.0179443359375,
-0.029296875,
0.0126953125,
-0.05... | 32,106 | 32106 | |
Find all pairs of positive integers a and b such that...
July 5th 2005, 04:33 AM #1
Junior Member
Joined
May 2005
Posts
33
Find all pairs of positive integers a and b such that...
Once again I am stuck on a question. Thanks as always.
Find all pairs of positive integers a and b such that...
a^2... | 4 | [
-0.04345703125,
0.06298828125,
-0.01226806640625,
0.06494140625,
-0.0498046875,
0.056396484375,
0.0615234375,
-0.047607421875,
0.003143310546875,
-0.01007080078125,
-0.02783203125,
-0.0093994140625,
0.08056640625,
0.08984375,
0.0267333984375,
0.012939453125,
-0.04052734375,
-0.0336... | 32,107 | 32107 | |
Prove a cubed inverse matrix is the same as an inverse cubed matrix
March 1st 2010, 03:02 AM #1
Newbie
Joined
Oct 2009
Posts
9
Prove a cubed inverse matrix is the same as an inverse cubed matrix
I have been asked to prove that the for a generic matrix A that, $(A^3)^{-1}$ is the same as $(A^{-1})^3$. I h... | 5 | [
-0.0498046875,
0.00970458984375,
-0.0859375,
0.0634765625,
-0.07958984375,
-0.10498046875,
0.023193359375,
-0.099609375,
0.034423828125,
-0.04150390625,
-0.03564453125,
0.023193359375,
0.031494140625,
0.004730224609375,
0.03759765625,
0.0810546875,
0.031005859375,
0.06494140625,
... | 32,108 | 32108 | |
This integral is doing my head in!
April 6th 2010, 05:40 PM #1
Newbie
Joined
Sep 2009
Posts
5
This integral is doing my head in!
I am trying to do the integral
$<br /> \displaystyle\int^\pi_0 F(\theta)\,d\theta<br />$
...where
$<br /> F(\theta) = \frac{\epsilon(1-cos\theta)}{1+\epsilon(1-c... | 5 | [
-0.0576171875,
-0.01312255859375,
0.064453125,
-0.02294921875,
0.019775390625,
-0.022705078125,
0.03515625,
-0.028564453125,
-0.0673828125,
0.01708984375,
-0.0703125,
-0.06201171875,
0.0191650390625,
-0.0264892578125,
-0.064453125,
-0.002044677734375,
0.04296875,
-0.0133056640625,
... | 32,109 | 32109 | |
General Solutions of Two Quadratic Functional Equations of Pexider Type on Orthogonal Vectors
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 675810, 10 pages
http://dx.doi.org/10.1155/2012/675810
Research Article
General Solutions of Two Quadratic Functional Equations of Pexider Type on Orthogonal Vecto... | 5 | [
-0.07373046875,
0.0054931640625,
0.023681640625,
-0.0322265625,
-0.057861328125,
0.123046875,
0.00014591217041015625,
0.030029296875,
0.019775390625,
-0.01416015625,
0.10107421875,
0.0296630859375,
-0.09326171875,
-0.01519775390625,
-0.06103515625,
0.08154296875,
-0.01068115234375,
... | 32,110 | 32110 | |
Rates of change
March 7th 2009, 04:06 AM
Orangeobe
Rates of change
I'm having trouble fully understanding the following question. Can anyone help please?
p = e^(β0 + β1x) where β0 = 10.17 and β1 = -0.01581
dp/dx = β1e^(β0 + β1x)
The Question
A small change in mileage (x) will lead to a smal... | 5 | [
0.0201416015625,
0.016357421875,
0.095703125,
0.0234375,
0.0849609375,
-0.044921875,
0.002471923828125,
0.07373046875,
0.0203857421875,
0.0014190673828125,
0.087890625,
0.00604248046875,
-0.0262451171875,
0.026123046875,
0.008544921875,
-0.0059814453125,
-0.020263671875,
0.04760742... | 32,111 | 32111 | |
equations planes
1. June 26th 2007, 09:00 AM #1
2. June 27th 2007, 10:55 PM #2
Hello,
maybe this comes a little bit late ...
If $\vec{x}=\left(\begin{array}{c}x \\ y \\z \end{array} \right)$ then the equations of the lines can be written like this: $L:\vec{x} = \underbrace{\vec{a}}_{\text... | 5 | [
-0.03662109375,
-0.02197265625,
-0.046875,
-0.0308837890625,
0.05419921875,
0.00738525390625,
0.052001953125,
-0.046630859375,
-0.054931640625,
0.07861328125,
0.0284423828125,
-0.0223388671875,
-0.006500244140625,
0.0021209716796875,
-0.12060546875,
0.0927734375,
-0.1123046875,
-0.... | 32,112 | 32112 | |
Math Help
September 25th 2006, 09:27 PM #1
Junior Member
Joined
Feb 2006
From
Victoria, Australia
Posts
36
Series
ok i really hate series, they are confusing and i almost have no idea how to do them. These questions are really driving me up the wall.
Any help would be greatly appreciated.
... | 5 | [
0.00311279296875,
-0.03173828125,
0.078125,
0.06689453125,
0.0732421875,
-0.00098419189453125,
-0.0025634765625,
0.01708984375,
0.03271484375,
0.044189453125,
0.076171875,
-0.068359375,
-0.009765625,
0.01470947265625,
-0.1328125,
-0.02734375,
-0.056884765625,
-0.0693359375,
0.005... | 32,113 | 32113 | |
The Maximum Segment Sum Problem: Its Origin, and a Derivation
In a previous paper of mine, regrettably, I wrongly attributed the origin of the maximum segment sum problem to Dijkstra and Feijen’s Een methode van programmeren. In fact, the story behind the
problem was told very well in Jon Bentley’s Programming Pearls.... | 4 | [
-0.0556640625,
0.0263671875,
0.0260009765625,
-0.1240234375,
-0.0213623046875,
-0.056884765625,
0.00162506103515625,
0.05224609375,
-0.03076171875,
0.032470703125,
-0.039306640625,
0.0771484375,
0.01019287109375,
0.0184326171875,
-0.055908203125,
0.08642578125,
0.0164794921875,
0.0... | 32,114 | 32114 | |
differentiation
I need help with the following derivatives y= (e^1/x) / x^2 f(t) = t ln(5t) thanks for your help
Could you show us what exactly is giving you trouble? What do you get when you attempt them?
Using the rules you suggested i got dy/dx = ((x^2)(e^1/x) - (e^1/x)(2x)) / x^4 f ' (t) = (1/5t) (t) are they cor... | 5 | [
0.005706787109375,
0.0147705078125,
0.12060546875,
-0.033935546875,
0.038330078125,
-0.06396484375,
-0.0419921875,
0.039794921875,
-0.015625,
0.020263671875,
0.08837890625,
-0.0169677734375,
-0.00909423828125,
0.0419921875,
-0.000812530517578125,
0.0234375,
-0.007293701171875,
-0.0... | 32,115 | 32115 | |
Homework Help
Posted by Jake on Sunday, April 8, 2012 at 3:34am.
Which plane goes through the origin and is perpendicular to the line r=(2,-2,1) + s(2,3,-4), seR?
a) 2x-2y+z=0
b) 2x+3y-4z=0
c) 2x+3y+z-4=0
d) none of the above.
I got D, none of the above. I have substituted and couldn't find the answer equal to ze... | 4 | [
-0.028076171875,
0.05859375,
-0.027099609375,
-0.08740234375,
0.00775146484375,
0.09912109375,
0.04638671875,
0.0615234375,
-0.02587890625,
0.050048828125,
0.007476806640625,
-0.01507568359375,
0.026123046875,
0.01904296875,
-0.06982421875,
0.0546875,
-0.0859375,
-0.08935546875,
... | 32,116 | 32116 | |
Kernal and Range
December 20th 2012, 02:02 AM #1
Junior Member
Joined
Nov 2012
From
United States
Posts
25
HI I am studying for the final which is in less then 7 hours, There is this one question on the review sheet which I really can't do at all, for some reason I just think I can't do Kernal and
... | 5 | [
0.0341796875,
0.00238037109375,
-0.023193359375,
-0.0673828125,
-0.0006561279296875,
0.04248046875,
-0.01611328125,
0.0283203125,
-0.02783203125,
-0.07275390625,
0.04541015625,
-0.0303955078125,
-0.031005859375,
-0.048828125,
-0.017822265625,
-0.018798828125,
-0.04833984375,
0.0012... | 32,117 | 32117 | |
Prove that both rings are fields but that they are not isomorphic.
March 29th 2011, 02:01 PM #1
Junior Member
Joined
Sep 2010
Posts
42
Prove that both rings are fields but that they are not isomorphic.
Let $\mathbb{Q}[\sqrt{n}] = \{a + b\sqrt{n}\}$
Prove that both $\mathbb{Q}[\sqrt{2}]$ and $\mathbb{... | 5 | [
-0.014892578125,
-0.0537109375,
0.058349609375,
0.001983642578125,
-0.059814453125,
-0.05908203125,
-0.00885009765625,
-0.021728515625,
0.049560546875,
-0.1103515625,
-0.0033721923828125,
0.044189453125,
-0.035888671875,
0.031005859375,
-0.05029296875,
0.043212890625,
-0.005249023437... | 32,118 | 32118 | |
Nordrassil Raiment and Regrowth
Don’t hate me because
I represent only a minor
efficiency increase to an
already marginalized spell.
Because apparently some of you
care
if the math I present is accurate, I’ve been forced to delve a little deeper into the effects of the Nordrassil Raiment on the efficiency of
R... | 4 | [
-0.021728515625,
-0.0164794921875,
0.0400390625,
0.037353515625,
-0.04296875,
-0.01397705078125,
0.0279541015625,
0.03466796875,
-0.021240234375,
-0.04736328125,
-0.0263671875,
-0.0206298828125,
-0.005340576171875,
-0.0279541015625,
-0.05810546875,
0.0020599365234375,
-0.01611328125,... | 32,119 | 32119 | |
12 Cards are delath from 52 playing cards
November 13th 2009, 07:09 AM
desire150
12 Cards are delath from 52 playing cards
Suppose that a hand of 12 cards is dealt from a normal deck of 52 playing cards. What is the probability that of the 12 cards, 3 will be diamonds, 3 will be clubs, 3 will be spades, and 3 wi... | 4 | [
0.01300048828125,
0.0537109375,
-0.05078125,
-0.007293701171875,
-0.10693359375,
0.0059814453125,
0.0283203125,
-0.0208740234375,
0.015380859375,
-0.0032958984375,
0.00147247314453125,
0.0047607421875,
-0.0712890625,
-0.045166015625,
0.028564453125,
0.006195068359375,
-0.0185546875,
... | 32,120 | 32120 | |
Intergration using trig substitution
November 14th 2010, 05:37 PM #1
Member
Joined
Oct 2007
Posts
159
Intergration using trig substitution
I need to integrate 1/ (1 - x^2)^(1/2) dx
I know I can use x = sin theta but... I was also taught that I can use x = cos theta
When I do this I end up with ... | 5 | [
-0.035888671875,
-0.04833984375,
0.01507568359375,
0.01031494140625,
0.0224609375,
-0.08203125,
-0.060546875,
-0.013427734375,
0.01153564453125,
0.042236328125,
0.006561279296875,
-0.0113525390625,
0.00982666015625,
0.033935546875,
-0.031005859375,
0.018310546875,
0.055419921875,
-... | 32,121 | 32121 | |
Homework Help
Posted by how to do this? on Monday, January 30, 2012 at 1:11pm.
a pendulum with a length of .600 m has a period of 1.55 s. what is acceleration due to gravity at the pendulums location
• physics - Damon, Monday, January 30, 2012 at 4:24pm
potential energy = m g h = m g L (1-cosA)
if angle A... | 4 | [
-0.05224609375,
0.01361083984375,
0.007598876953125,
0.0029754638671875,
0.002044677734375,
0.00130462646484375,
-0.032958984375,
0.0888671875,
-0.01068115234375,
-0.0115966796875,
0.07568359375,
-0.005523681640625,
0.0028076171875,
-0.028564453125,
-0.03662109375,
0.056884765625,
-0... | 32,122 | 32122 | |
Help Géo !!!
February 4th 2010, 09:06 AM #1
Junior Member
Joined
Dec 2009
Posts
46
Help Géo !!!
Hii !
I need Help For This Exercice :
Either $ABC$ a triangle and $D$ point belonging to $[BC]$ such as :
$\widehat{DAC} = 90$ , $\widehat{BAD} = 30$ , $BD=AC=1$ .
Find / Calculate $CD$ .
... | 4 | [
-0.03515625,
0.1083984375,
-0.03564453125,
-0.01031494140625,
0.0028839111328125,
0.02880859375,
0.021240234375,
0.0869140625,
-0.0234375,
0.014892578125,
0.038330078125,
-0.10546875,
0.037353515625,
0.026611328125,
-0.0225830078125,
0.00506591796875,
-0.056640625,
0.0150146484375,... | 32,123 | 32123 | |
Double-Angle Formulas
November 2nd 2009, 01:49 PM #1
Member
Joined
Sep 2009
Posts
181
Double-Angle Formulas
Hello,
Can someone please help me with these problems?
Find Sin2x, Cos 2x, and Tan2x for:
1. tan x= -4/3 quadrant II
2. csc x = 4, tan x<0
how do I start the problem?
f... | 4 | [
-0.0673828125,
0.02978515625,
0.05224609375,
-0.0400390625,
-0.05078125,
0.0198974609375,
0.001678466796875,
0.064453125,
0.0015106201171875,
-0.01434326171875,
0.0849609375,
-0.0712890625,
0.07421875,
0.04296875,
0.0291748046875,
0.01165771484375,
0.0419921875,
-0.027099609375,
... | 32,124 | 32124 | |
Synchronization of Neural Networks with Mixed Time Delays under Information Constraints
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 510903, 7 pages
http://dx.doi.org/10.1155/2013/510903
Research Article
Synchronization of Neural Networks with Mixed Time Delays under Information Constraints
^1School ... | 5 | [
-0.04833984375,
-0.041015625,
-0.0086669921875,
-0.01409912109375,
0.009765625,
0.05615234375,
0.021240234375,
-0.1201171875,
0.02490234375,
-0.11474609375,
0.09912109375,
0.0203857421875,
-0.0069580078125,
-0.07275390625,
-0.1298828125,
0.0086669921875,
-0.0079345703125,
0.0083618... | 32,125 | 32125 | |
the encyclopedic entry of integer
The integers (from the Latin integer, literally "untouched", hence "whole": the word entire comes from the same origin, but via French) are the set of numbers consisting of the natural numbers
including 0 (0, 1, 2, 3, ...) and their negatives (0, −1, −2, −3, ...). They are numbers that... | 4 | [
0.002471923828125,
-0.0093994140625,
-0.028564453125,
0.01904296875,
-0.0250244140625,
-0.04833984375,
0.049072265625,
0.053955078125,
0.072265625,
0.001953125,
-0.0311279296875,
-0.01385498046875,
0.07373046875,
0.007781982421875,
-0.0419921875,
-0.12060546875,
0.004791259765625,
... | 32,126 | 32126 | |
definitions
March 21st 2010, 04:22 AM
alexandrabel90
definitions
what is the difference between the joint probability density function and the joint distribution function when they are both denoted as F(x,y)?
March 21st 2010, 11:02 AM
CaptainBlack
Quote:
The joint density is normally a lower case fu... | 4 | [
-0.00408935546875,
-0.0281982421875,
0.01226806640625,
-0.095703125,
0.036376953125,
0.0023193359375,
-0.080078125,
0.0390625,
0.045654296875,
-0.02978515625,
0.01483154296875,
0.1123046875,
0.0771484375,
0.032470703125,
0.07861328125,
-0.0205078125,
0.01904296875,
-0.10400390625,
... | 32,127 | 32127 | |
Subnormal Weighted Shifts on Directed Trees and Composition Operators in
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 791817, 6 pages
http://dx.doi.org/10.1155/2014/791817
Research Article
Subnormal Weighted Shifts on Directed Trees and Composition Operators in ^2-Spaces with Nondensely Defined Power... | 5 | [
-0.05078125,
-0.001739501953125,
0.07275390625,
0.08154296875,
0.0299072265625,
-0.035888671875,
0.0167236328125,
-0.08349609375,
0.042236328125,
0.0022430419921875,
-0.054443359375,
0.01007080078125,
0.04736328125,
0.002197265625,
-0.031494140625,
0.03271484375,
0.0009307861328125,
... | 32,128 | 32128 | |
Homework Help
Posted by Danny on Sunday, May 11, 2008 at 10:14am.
Suppose you conduct a study and find that the probability of having a baby boy is 60%. Now suppose three of your relatives are going to have babies.
a) Build a tree diagram showing all the conditional probabilities and joint probabilities associated wi... | 4 | [
0.0213623046875,
0.038818359375,
-0.0322265625,
0.0037841796875,
0.02099609375,
0.010009765625,
0.03369140625,
0.0157470703125,
0.04296875,
0.12890625,
0.03125,
-0.052734375,
0.0086669921875,
0.039306640625,
0.1005859375,
0.0234375,
-0.054443359375,
-0.058837890625,
-0.0766601562... | 32,129 | 32129 | |
Formula for Arithmetic sequence
September 27th 2009, 07:23 PM #1
Junior Member
Joined
Sep 2009
Posts
61
Formula for Arithmetic sequence
find the formula for an for the arithmetic sequence.
a3=94, a6=85
ok i know how to solve a similar problem when i am given a1 and d. but i dont have either A... | 4 | [
-0.1083984375,
-0.017578125,
0.025390625,
-0.1103515625,
-0.0791015625,
0.0277099609375,
-0.04833984375,
0.00885009765625,
0.047607421875,
0.05712890625,
0.10009765625,
-0.028076171875,
-0.041259765625,
-0.048095703125,
-0.03759765625,
-0.01116943359375,
-0.07275390625,
0.018066406... | 32,130 | 32130 | |
Homework Help
Posted by sh on Wednesday, March 24, 2010 at 12:24am.
Find an equation of the tangent line to the given curve at the given point
y=(1/cosx)-2cosx at((pi/3),1)
y'=0+2sinx
slope = √3
y=mx+b
1=(√3)(pi/3)+b
b=(3-√3pi)/3
3√3x-3y+3-√3pi=0
What did I do wrong? Thanks in advance.
• Calculus - sh, Wedn... | 4 | [
-0.09814453125,
-0.0703125,
-0.008056640625,
0.018310546875,
-0.020263671875,
0.022705078125,
0.01312255859375,
0.02392578125,
0.04833984375,
0.005279541015625,
0.04736328125,
-0.02099609375,
0.026123046875,
0.0230712890625,
0.015380859375,
0.068359375,
-0.10205078125,
-0.058105468... | 32,131 | 32131 | |
Signless Laplacian Polynomial and Characteristic Polynomial of a Graph
Journal of Discrete Mathematics
Volume 2013 (2013), Article ID 105624, 4 pages
http://dx.doi.org/10.1155/2013/105624
Research Article
Signless Laplacian Polynomial and Characteristic Polynomial of a Graph
^1Department of Mathematics, Gogte Instit... | 5 | [
-0.029541015625,
0.07666015625,
-0.0115966796875,
-0.000858306884765625,
0.031494140625,
-0.02099609375,
0.000255584716796875,
-0.049560546875,
0.03515625,
-0.034912109375,
0.1005859375,
0.01409912109375,
0.042724609375,
-0.00006866455078125,
0.040771484375,
0.0089111328125,
-0.06298... | 32,132 | 32132 | |
Finding the order of a group element
November 10th 2009, 08:49 PM #1
Newbie
Joined
Nov 2009
Posts
1
Finding the order of a group element
I'm stuck on the following problem: if a and b are in a group G, and a^5=e and b^2=a*b*a^-1, what is the order of b (assuming b is not e). Any ideas where to start? I'v... | 5 | [
-0.042236328125,
0.054931640625,
0.1005859375,
0.0771484375,
-0.040283203125,
-0.0185546875,
-0.0284423828125,
-0.076171875,
-0.001129150390625,
-0.021484375,
0.0208740234375,
0.02001953125,
0.055908203125,
-0.001953125,
-0.0302734375,
0.08251953125,
0.00927734375,
-0.018310546875,... | 32,133 | 32133 | |
Dense matrices over the integer ring
sage: m = matrix([(-2, 1, 9, 2, -8, 1, -3, -1, -4, -1),
... (5, -2, 0, 1, 0, 4, -1, 1, -2, 0),
... (-11, 3, 1, 0, -3, -2, -1, -11, 2, -2),
... (-1, 1, -1, -2, 1, -1, -1, -1, -1, 7),
... (-2, -1, -1, 1, 1, -2, 1, 0, 2, -4)]).sta... | 4 | [
-0.099609375,
0.00830078125,
-0.10107421875,
-0.0245361328125,
-0.0255126953125,
-0.05126953125,
0.017822265625,
-0.03955078125,
-0.1015625,
-0.07666015625,
0.037841796875,
-0.0023651123046875,
-0.02197265625,
-0.0205078125,
-0.0791015625,
0.00616455078125,
-0.0235595703125,
-0.017... | 32,134 | 32134 | |
[SOLVED] Limits
March 26th 2009, 06:43 PM
nzmathman
[SOLVED] Limits
Have come across a limits questions I am having trouble with.
(1) $\lim_{x\to \pi}~\frac{\pi-x}{\sin{x}}$
$= \lim_{x\to \pi}~\left(\frac{\pi}{\sin{x}} - \frac{x}{\sin{x}}\right)$
I get stuck after that...I know that $\lim_{x\to 0}... | 5 | [
-0.11669921875,
-0.002044677734375,
0.0027008056640625,
0.01025390625,
-0.00787353515625,
0.043212890625,
0.032958984375,
-0.03857421875,
-0.01092529296875,
-0.016357421875,
0.050537109375,
-0.07373046875,
-0.00732421875,
0.061767578125,
0.04931640625,
-0.038330078125,
0.039794921875... | 32,135 | 32135 | |
what is the probability of drawing two red marbles...
December 11th 2011, 07:28 AM
slapmaxwell1
what is the probability of drawing two red marbles...
im not sure why probability problems give me fits....
ok so here is the problem.
a bag contains 3 red marbles and 3 blue marbles. what is the probability... | 4 | [
-0.0145263671875,
-0.09326171875,
0.0283203125,
0.0233154296875,
-0.064453125,
-0.032958984375,
0.058837890625,
0.01251220703125,
0.0238037109375,
0.0128173828125,
-0.0673828125,
-0.08056640625,
0.0135498046875,
0.0004291534423828125,
0.02978515625,
0.0361328125,
0.01434326171875,
... | 32,136 | 32136 | |
partial differentiation
January 17th 2013, 07:49 AM
JacobOCD
partial differentiation
Hello
I have two functions:
$V(x,h)=x^2 \cdot h=4$
and
$A(x,h)=2x^2+4xh$
As someone might guess, this is a optimization problem of sorts (minimization of A(x,h) with V(x,h)=4 as constraint). My problem a... | 5 | [
0.06884765625,
0.04541015625,
0.0299072265625,
-0.0791015625,
-0.047119140625,
0.0634765625,
-0.0098876953125,
-0.0118408203125,
-0.0038299560546875,
-0.0064697265625,
0.0712890625,
0.00738525390625,
0.00946044921875,
-0.013671875,
0.0042724609375,
0.07080078125,
0.04248046875,
0.0... | 32,137 | 32137 | |
Homework Help
physics - tchrwill, Wednesday, October 12, 2011 at 10:51am
Excuse the change in units. 60 year old habits are hard to break.
You left us without a clue as to the weight of the rocket. Propellant fractions of rockets typically range from .85 to .90, i.e., the weight of propellant divided by the fully loa... | 5 | [
0.03759765625,
0.0888671875,
0.043701171875,
-0.0615234375,
-0.02099609375,
0.0208740234375,
-0.035400390625,
0.058837890625,
-0.1142578125,
-0.0186767578125,
0.00799560546875,
-0.04345703125,
-0.003082275390625,
-0.05712890625,
0.0152587890625,
0.043701171875,
0.002349853515625,
0... | 32,138 | 32138 | |
Inequality
October 7th 2007, 01:20 PM #1
Junior Member
Joined
Aug 2007
Posts
32
Inequality
is it true that
$||z| - |w|| \leq |z + w|$??
if so what is the proof?
here is my workin so far.. please verify it
We know $|z+w| \leq |z|+|w|$
let c = z - w, so $|c+w| \leq |c|+|w|$
Now... | 4 | [
-0.1044921875,
-0.01007080078125,
0.0103759765625,
0.027099609375,
0.00872802734375,
-0.03564453125,
0.01080322265625,
0.055419921875,
-0.055908203125,
-0.0093994140625,
-0.002471923828125,
-0.00286865234375,
0.10400390625,
0.04052734375,
-0.0478515625,
0.0517578125,
0.05859375,
0.... | 32,139 | 32139 | |
Trig Identities
Prove that 1-sin^2X/1+cotX - cos^2X/1+tanX = sinXcosX Much thanks in advance.
Yes, I understand, but .. in the original equation, there are no parantheses. I typed the question exactly as it is shown on the paper given to me.
Hello, ahling! Prove that: . $1 - \frac{\sin^2\!x}{1 + \cot x}- \frac{\cos^2... | 4 | [
-0.04150390625,
0.06787109375,
0.055419921875,
0.0458984375,
0.02001953125,
0.04345703125,
0.00299072265625,
-0.00799560546875,
0.01025390625,
0.036376953125,
0.036865234375,
-0.045166015625,
0.0179443359375,
-0.01806640625,
-0.033935546875,
-0.02978515625,
0.0849609375,
0.01190185... | 32,140 | 32140 | |
Equations on the set of complex numbers
October 31st 2010, 10:44 AM #1
Newbie
Joined
Oct 2010
Posts
6
Equations on the set of complex numbers
Hello,
Can someone help, how to solve
x ^ 3 = 1
and/or
x ^ 4 = -4
equations on the set of complex numbers?
Thanks in advance!
I'll do... | 5 | [
-0.0810546875,
0.0213623046875,
-0.043212890625,
0.08984375,
-0.061767578125,
-0.055908203125,
0.045166015625,
-0.0059814453125,
0.06494140625,
-0.05859375,
0.0751953125,
-0.087890625,
0.0361328125,
0.087890625,
0.078125,
-0.000789642333984375,
-0.08740234375,
0.0118408203125,
-0... | 32,141 | 32141 | |
Help with logs please
May 14th 2005, 01:36 PM
jamesh
Help with logs please
We just started doing some work on logs and i cant work out this problem, i think its quite easy but im crap at these.
Two curves:
y=a^x and y=2b^x
Prove that x coord of the point of intersection is 1 / (log(of base2)A-log(... | 4 | [
-0.000499725341796875,
-0.0771484375,
-0.01446533203125,
-0.01611328125,
0.054931640625,
-0.061279296875,
0.06689453125,
0.02783203125,
-0.027099609375,
-0.00848388671875,
0.07421875,
-0.0595703125,
0.06591796875,
0.019775390625,
0.04833984375,
0.08203125,
-0.1220703125,
-0.0322265... | 32,142 | 32142 | |
Another modular arithmetic proof
December 11th 2012, 08:00 AM
dom139
Another modular arithmetic proof
"By considering all possible residue classes modulo 6, or otherwise, prove that n^3 - n is a multiple of 6 for all integers n."
I've been staring at this one for a while now and i've got tunnel vision.
T... | 5 | [
-0.08154296875,
0.037841796875,
-0.0625,
-0.0023193359375,
-0.013671875,
-0.0011138916015625,
0.08447265625,
-0.0283203125,
0.051513671875,
-0.0849609375,
0.00494384765625,
0.072265625,
0.006103515625,
0.0390625,
0.08740234375,
0.031494140625,
-0.099609375,
0.072265625,
-0.053222... | 32,143 | 32143 | |
ODE Integral by partial fractions
April 22nd 2013, 07:06 PM
mathlover10
ODE Integral by partial fractions
the solution technique is easy but I'm exhausted and having surgery...by the way what is the partial fraction expansion for this differential equation? $\LARGE \frac{dy}{dt}+\frac{ty}{1+t^2}=1-\
frac{t^3... | 5 | [
-0.05810546875,
0.07568359375,
0.078125,
0.052734375,
0.060546875,
-0.01226806640625,
-0.047607421875,
-0.03369140625,
-0.0101318359375,
-0.0137939453125,
0.043212890625,
-0.049560546875,
-0.004150390625,
0.001556396484375,
-0.06494140625,
0.01318359375,
-0.0013275146484375,
0.0015... | 32,144 | 32144 | |
Money Problem
January 17th 2013, 03:52 PM #1
Money Problem
Jack's parents have been paying $450 per month into a retirement fund for the last 30 years. The fund is now worth $450 000. What annual interest rate, compounded monthly are Jack's parents
earning? Round to two decimal places.
Please any one, ho... | 5 | [
0.0172119140625,
0.1103515625,
-0.0208740234375,
-0.047119140625,
-0.002349853515625,
-0.0218505859375,
-0.000858306884765625,
0.03173828125,
-0.01068115234375,
0.0869140625,
0.0264892578125,
-0.0693359375,
0.04443359375,
0.0120849609375,
-0.018310546875,
0.0255126953125,
-0.08154296... | 32,145 | 32145 | |
Lessons In Electric Circuits -- Volume I
Lessons In Electric Circuits -- Volume I
Chapter 16
RC AND L/R TIME CONSTANTS
This chapter explores the response of capacitors and inductors to sudden changes in DC voltage (called a transient voltage), when wired in series with a resistor. Unlike resistors, which respon... | 5 | [
-0.019775390625,
0.06494140625,
0.042236328125,
0.02978515625,
0.07421875,
-0.0206298828125,
-0.0072021484375,
0.06982421875,
0.11767578125,
0.08203125,
0.028076171875,
-0.0233154296875,
0.0712890625,
0.0859375,
-0.0673828125,
-0.053466796875,
-0.0322265625,
0.04150390625,
-0.030... | 32,146 | 32146 | |
I need to minimize the surface area of this cylinder
November 23rd 2008, 02:15 PM
la_lo626
I need to minimize the surface area of this cylinder
design a cylinder which can hold a volume of 10ft cubed. so that it's used with minimal material. what are the dimensions (r and h) and what is the relationship between ... | 5 | [
-0.0017852783203125,
0.059326171875,
-0.0294189453125,
0.004302978515625,
0.01025390625,
0.021728515625,
0.023681640625,
0.150390625,
-0.046875,
-0.09716796875,
-0.0966796875,
0.00640869140625,
0.0283203125,
0.03125,
-0.04345703125,
0.000766754150390625,
0.048828125,
0.078125,
-0... | 32,147 | 32147 | |
[SOLVED] Initial height question in vector spaces
February 1st 2010, 07:10 AM #1
Newbie
Joined
Feb 2010
Posts
2
[SOLVED] Initial height question in vector spaces
A stone is thrown from a rooftop at time t = 0. Its position at time t is given by r(t) = (10t,−5t, 6.4−4.9t^2). The origin is at the base of t... | 4 | [
-0.01806640625,
0.0654296875,
0.0224609375,
-0.080078125,
0.003997802734375,
0.033935546875,
-0.05224609375,
0.11376953125,
-0.04541015625,
0.04052734375,
0.042236328125,
-0.005035400390625,
-0.0013275146484375,
0.064453125,
-0.03173828125,
0.043701171875,
-0.03466796875,
0.0393066... | 32,148 | 32148 | |
How to simplify velocity magnitude equations?
September 29th 2009, 09:29 AM #1
Junior Member
Joined
Oct 2008
Posts
32
How to simplify velocity magnitude equations?
In my calculus class a few days ago, my professor was going over how to find three dimensional velocity and its magnitude. In the problem, th... | 4 | [
0.0128173828125,
-0.0263671875,
0.00531005859375,
0.0084228515625,
-0.032958984375,
-0.01519775390625,
-0.11181640625,
0.0211181640625,
0.0211181640625,
-0.00604248046875,
0.08349609375,
0.033447265625,
-0.007354736328125,
0.0194091796875,
-0.01055908203125,
0.042724609375,
-0.069335... | 32,149 | 32149 | |
Homework Help
Posted by RAUNAK on Saturday, February 15, 2014 at 1:26am.
AN AP has 21 term the sum of 10 ,11,12 term is 129 and sum of last 3 term is 237.find AP
• MATH - Steve, Saturday, February 15, 2014 at 6:32am
T10+T11+T12 = (a+9d)+(a+10d)+(a+11d), so
3a+30d = 129
Similarly, for the last three ter... | 4 | [
-0.09130859375,
-0.010986328125,
0.043212890625,
-0.13671875,
-0.06689453125,
0.060791015625,
-0.017333984375,
0.005523681640625,
-0.018310546875,
0.049072265625,
0.031982421875,
-0.0023345947265625,
-0.00408935546875,
0.01116943359375,
-0.02587890625,
-0.035888671875,
-0.02648925781... | 32,150 | 32150 | |
Every nonzero vector space can be viewed as a space of functions
July 22nd 2010, 01:31 PM
buri
Every nonzero vector space can be viewed as a space of functions
The problem statement, all variables and given/known data
Let V be a nonzero vector space over a field F, and suppose that S is a bases for V. Let C... | 4 | [
-0.091796875,
-0.03662109375,
0.00506591796875,
0.055419921875,
-0.006927490234375,
0.1611328125,
0.056396484375,
-0.02001953125,
0.045654296875,
-0.01446533203125,
-0.019287109375,
-0.033935546875,
-0.04833984375,
-0.003936767578125,
-0.04541015625,
0.0159912109375,
-0.022216796875,... | 32,151 | 32151 | |
Help with simple equation needed.
October 25th 2010, 07:18 AM #1
Newbie
Joined
Jul 2010
Posts
2
Help with simple equation needed.
Hi,
I cannot solve the following equation to x.
$27^{\sqrt{2-3x}} = 243^{\sqrt{3x-2}}$
I tried it like this:
$\sqrt{2-3x}lg(27) = \sqrt{3x-2}lg(243)$
... | 4 | [
0.00994873046875,
-0.072265625,
-0.033203125,
0.0220947265625,
-0.054443359375,
-0.004852294921875,
-0.060302734375,
-0.037109375,
0.043212890625,
0.0908203125,
0.050537109375,
-0.06396484375,
0.03076171875,
-0.0169677734375,
0.0771484375,
0.035888671875,
-0.11962890625,
-0.0183105... | 32,152 | 32152 | |
integral test convergence divergence
July 29th 2009, 03:32 PM #1
Junior Member
Joined
Jul 2009
Posts
42
integral test convergence divergence
im confused on this one
$\sum_{n = 2}^{\infty} 6n^2 \exp(-n^3)$
i think the exponential goes to 0 does this mean that i can not use the integral test?
... | 5 | [
-0.048583984375,
-0.06982421875,
-0.06884765625,
-0.0028228759765625,
0.000751495361328125,
-0.06884765625,
-0.0380859375,
0.0269775390625,
0.026611328125,
-0.072265625,
0.0888671875,
0.05078125,
-0.0001277923583984375,
-0.041259765625,
0.01141357421875,
-0.050537109375,
0.0090332031... | 32,153 | 32153 | |
Volumetric expansion problem
August 7th 2011, 10:06 AM #1
Newbie
Joined
Aug 2011
Posts
1
Volumetric expansion problem
Hello, i understand this isnt a calculus question but there seems to be the most people on this forum. Im studying for my Power Engineer 3rd class and have a question. At 5 degrees celciu... | 4 | [
-0.0267333984375,
0.012451171875,
0.057861328125,
0.0032501220703125,
0.0595703125,
0.0135498046875,
-0.0128173828125,
0.044921875,
-0.021240234375,
-0.04638671875,
0.0169677734375,
-0.01531982421875,
-0.03369140625,
-0.000518798828125,
-0.005645751953125,
0.0308837890625,
-0.0351562... | 32,154 | 32154 | |
Trig Identity Problems
November 28th 2008, 08:51 PM
Chouman
Trig Identity Problems
Got two problems for extra credit that I can't seem to figure out if anyone here can.
Prove the following.
1. cosx-(sinx-1)/cosx+(sinx-1) = sinx/1-cosx It says as a hint to multiply
the numerator and
denominator ... | 4 | [
-0.1015625,
0.06005859375,
0.07861328125,
0.044677734375,
0.026123046875,
0.04736328125,
0.03662109375,
-0.049072265625,
-0.0028228759765625,
-0.006744384765625,
0.0133056640625,
-0.08056640625,
0.06689453125,
0.03955078125,
-0.00958251953125,
-0.041748046875,
-0.0269775390625,
0.0... | 32,155 | 32155 | |
Combination Mode of Internal Waves Generated by Surface Wave Propagating over Two Muddy Sea Beds
Advances in Mathematical Physics
Volume 2012 (2012), Article ID 183503, 9 pages
http://dx.doi.org/10.1155/2012/183503
Research Article
Combination Mode of Internal Waves Generated by Surface Wave Propagating over Two Mudd... | 4 | [
-0.06787109375,
-0.0184326171875,
0.138671875,
-0.04150390625,
-0.01324462890625,
-0.095703125,
-0.049560546875,
-0.00836181640625,
-0.05029296875,
0.00286865234375,
-0.031494140625,
-0.056884765625,
0.018310546875,
-0.02197265625,
0.06982421875,
0.109375,
-0.10595703125,
-0.058837... | 32,156 | 32156 | |
An Efficient Pseudospectral Method for Solving a Class of Nonlinear Optimal Control Problems
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 357931, 7 pages
http://dx.doi.org/10.1155/2013/357931
Research Article
An Efficient Pseudospectral Method for Solving a Class of Nonlinear Optimal Control Problems
... | 5 | [
-0.0927734375,
0.0252685546875,
-0.01220703125,
-0.0162353515625,
-0.04443359375,
0.026611328125,
-0.0078125,
-0.03515625,
0.00689697265625,
0.05712890625,
0.0252685546875,
0.0478515625,
0.0703125,
-0.017578125,
-0.07958984375,
0.07275390625,
-0.0216064453125,
-0.033935546875,
0.... | 32,157 | 32157 | |
Solving Polynomial Inequalities
Solving Polynomial Inequalities (page 1 of 2)
The first step in solving a polynomial inequality is to find the polynomial's zeroes (its x-intercepts). Between any two consecutive zeroes, the polynomial will be either positive or negative. Since
the inequality is asking for positivity ("... | 4 | [
-0.040771484375,
0.0291748046875,
0.0034942626953125,
0.01092529296875,
-0.0208740234375,
-0.0027313232421875,
-0.042724609375,
0.044677734375,
-0.0146484375,
0.0361328125,
0.01226806640625,
-0.06884765625,
0.06298828125,
0.06494140625,
0.0042724609375,
0.07275390625,
-0.0078125,
-... | 32,158 | 32158 | |
Simultaneous Equations
January 25th 2009, 09:53 AM #1
Newbie
Joined
Oct 2008
Posts
5
Simultaneous Equations
Hey guys, I have these two questions, which I am confused about. If anyone could help me I would be very grateful!
"Solve the following simultaenous equations using an analytical method (eithe... | 4 | [
-0.0206298828125,
-0.0244140625,
-0.0196533203125,
0.017333984375,
0.006988525390625,
0.051025390625,
-0.05517578125,
0.06591796875,
-0.0196533203125,
-0.022216796875,
0.11181640625,
0.00070953369140625,
0.06591796875,
0.03466796875,
0.0064697265625,
0.0390625,
-0.10009765625,
-0.0... | 32,159 | 32159 | |
Max Profit
April 5th 2009, 05:57 PM
sk8erboyla2004
Max Profit
This problem makes no sense to me
A store can sell 20 bikes per week at $400. For each $10 the store lowers the price by 2 more bicycles sold per week. each buke costs the store 200 dollars what price should be charged to
maximize profit? how... | 5 | [
-0.05126953125,
0.06005859375,
-0.0546875,
-0.10107421875,
-0.060302734375,
0.050048828125,
-0.02734375,
0.095703125,
-0.028564453125,
0.045654296875,
0.01019287109375,
-0.0048828125,
0.09375,
0.047607421875,
0.0537109375,
0.08935546875,
-0.0576171875,
0.0380859375,
-0.0490722656... | 32,160 | 32160 | |
Verifying the divergence theorem
July 30th 2009, 12:51 PM #1
Verifying the divergence theorem
I must verify the divergence theorem in the following case :
$F(x,y,z)=x \vec i + y \vec j + z \vec k$. And $S$ is the surface of the sphere $x^2+y^2+z^2=4$.
My attempt :
$\iint _S F \bold n dS=\iiint _S div ... | 5 | [
-0.004974365234375,
0.038818359375,
-0.00567626953125,
-0.091796875,
0.041748046875,
-0.0234375,
0.00115203857421875,
0.048828125,
-0.0162353515625,
0.10009765625,
-0.0791015625,
0.008544921875,
0.0196533203125,
0.016845703125,
-0.0458984375,
-0.03369140625,
-0.005523681640625,
0.0... | 32,161 | 32161 | |
A rectangular photograph is surrounded by a border that is 1
Question Stats:
82%18% (03:02)based on 99 sessions
D.
First, we know that M is the area of the picture AND the border, and that the border is 1 in wide. If you have a border around a picture that is 1" wide, it doesn't add just 1" to the width and
height, ... | 4 | [
0.09326171875,
0.08642578125,
-0.00579833984375,
0.00714111328125,
0.078125,
-0.0284423828125,
-0.01446533203125,
0.08984375,
-0.00738525390625,
-0.025634765625,
0.0196533203125,
-0.0184326171875,
0.06298828125,
0.06689453125,
0.02880859375,
0.01141357421875,
-0.04541015625,
0.0439... | 32,162 | 32162 | |
If |12x−5|>|7−6x|, which of the following CANNOT be the
Author Message
TAGS:
If |12x−5|>|7−6x|, which of the following CANNOT be the [#permalink] 11 Jun 2013, 03:17
... | 4 | [
0.005401611328125,
0.0537109375,
0.01531982421875,
-0.040771484375,
0.00933837890625,
0.01336669921875,
0.053466796875,
-0.0037384033203125,
-0.0255126953125,
0.038818359375,
-0.000133514404296875,
0.0020904541015625,
0.057373046875,
-0.0079345703125,
-0.107421875,
0.08740234375,
-0.... | 32,163 | 32163 | |
Homework Help
Posted by jenny on Thursday, August 25, 2011 at 12:46am.
Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of sin
-pi/6, cos 5/3pi and tan 4pi/3.
I have found the answers to the first three using the special table... | 4 | [
-0.051025390625,
-0.041015625,
-0.004669189453125,
0.01263427734375,
-0.04248046875,
-0.0234375,
-0.0098876953125,
0.01409912109375,
0.04296875,
-0.013671875,
0.050537109375,
-0.05224609375,
-0.01708984375,
0.024169921875,
0.12158203125,
-0.058837890625,
-0.05322265625,
0.000444412... | 32,164 | 32164 | |
Solve The Following Trigonometric Integral. (3)
January 18th 2010, 08:14 AM #1
Member
Joined
Jan 2009
Posts
236
Solve The Following Trigonometric Integral. (3)
Hello
here is it:
$\int ( cos(x) + 1 )^{\frac{3}{2}} dx$
I used $u=cos(x)+1$
Then, I got :
$- \int \frac{u^{\frac{3}{2}} }{ \... | 4 | [
-0.0157470703125,
-0.04541015625,
-0.0101318359375,
-0.004791259765625,
-0.0225830078125,
-0.00482177734375,
-0.0390625,
-0.095703125,
-0.004547119140625,
0.050048828125,
0.0081787109375,
-0.056884765625,
-0.031494140625,
0.04248046875,
-0.024169921875,
-0.033203125,
-0.033935546875,... | 32,165 | 32165 | |
real numbers
July 18th 2008, 10:52 AM
perash
real numbers
a, b, c, d, e are real numbers such that
a + b + c + d + e = 8
a^2 + b^2 + c^2 + d^2 + e^2 = 16.
What is the largest possible value of e?
July 19th 2008, 12:18 AM
JaneBennet
Let’s suppose $a$, $b$, $c$, $d$ are non-negative. (Obviou... | 5 | [
0.039794921875,
0.07958984375,
0.0201416015625,
-0.0654296875,
-0.076171875,
0.0069580078125,
-0.039794921875,
0.08984375,
0.0150146484375,
0.021240234375,
-0.057373046875,
0.0093994140625,
0.056396484375,
0.049560546875,
-0.025146484375,
0.044189453125,
0.07275390625,
-0.032714843... | 32,166 | 32166 | |
More trig review
November 9th 2008, 07:35 PM #1
More trig review
Ok I'm having problems with these 3 problems
Solve each equation in the interval {0,2pi) and round your answer to the nearest hundredth of a radian
A) $3\sin^{x} - \sin{x} - 1 =0$
B) $2\sin{x} - 3\cos{x} = 1$
C) $3\sin{x} - 5 = 0... | 4 | [
-0.048583984375,
0.04638671875,
-0.0162353515625,
-0.041748046875,
-0.049072265625,
-0.0242919921875,
-0.0206298828125,
-0.02001953125,
0.03955078125,
-0.01806640625,
0.0869140625,
-0.0517578125,
0.0224609375,
0.046875,
0.01409912109375,
-0.0703125,
-0.01458740234375,
-0.0018234252... | 32,167 | 32167 | |
Multiple Active Contours Guided by Differential Evolution for Medical Image Segmentation
Computational and Mathematical Methods in Medicine
Volume 2013 (2013), Article ID 190304, 14 pages
http://dx.doi.org/10.1155/2013/190304
Research Article
Multiple Active Contours Guided by Differential Evolution for Medical Imag... | 4 | [
-0.01361083984375,
-0.005859375,
0.01336669921875,
-0.022705078125,
0.0419921875,
-0.0927734375,
0.0179443359375,
0.03125,
0.01556396484375,
-0.031005859375,
-0.00384521484375,
-0.045166015625,
0.02880859375,
0.046875,
-0.07568359375,
-0.01373291015625,
-0.1298828125,
0.02429199218... | 32,168 | 32168 | |
A Survey of Binary Search
If you think you know everything you need to know about binary search, but have not read Netty van Gasteren and Wim Feijen’s note The Binary Search Revisited, you should.
In the FLOLAC summer school this year we plan to teach the students some basics of Hoare logic and Dijkstra’s weakest pre... | 4 | [
0.006683349609375,
0.11328125,
-0.07275390625,
-0.042236328125,
0.00567626953125,
-0.045654296875,
0.01361083984375,
-0.00555419921875,
-0.06591796875,
0.021484375,
-0.0771484375,
0.035400390625,
0.04296875,
-0.01953125,
-0.0439453125,
0.041259765625,
-0.0439453125,
0.0003013610839... | 32,169 | 32169 | |
The class equation of G is 60=1+15+20+12+12. Then G is simple.
April 20th 2012, 06:54 AM #1
Member
Joined
Feb 2009
Posts
138
The class equation of G is 60=1+15+20+12+12. Then G is simple.
I think I found a proof but not sure. Let A_i denote the classes.
Class Number of elements in the class
====... | 5 | [
-0.031494140625,
0.10400390625,
0.05517578125,
-0.0167236328125,
-0.054443359375,
0.035400390625,
0.05859375,
-0.039306640625,
-0.06689453125,
-0.003448486328125,
-0.040771484375,
0.03759765625,
0.033935546875,
-0.08642578125,
-0.040771484375,
0.0294189453125,
-0.033935546875,
0.00... | 32,170 | 32170 | |
Math Help
August 17th 2012, 11:46 AM #1
Newbie
Joined
Aug 2012
From
Canada
Posts
21
Isomorphism
Hey There
I need to show that 2 groups with order 3 is isomorphic
I basically have the answer I just wanted to double check with you guys
I have proven that ab=identity and that simularly cd=i... | 5 | [
-0.061279296875,
-0.02197265625,
0.0390625,
-0.0184326171875,
-0.038818359375,
0.0263671875,
0.1328125,
-0.091796875,
0.0223388671875,
-0.027099609375,
0.040283203125,
-0.10107421875,
0.0269775390625,
-0.027099609375,
0.044921875,
0.051025390625,
-0.0218505859375,
0.0576171875,
-... | 32,171 | 32171 | |
Tiling array data analysis: a multiscale approach using wavelets
• We are sorry, but NCBI web applications do not support your browser and may not function properly.
More information
•
BMC Bioinformatics. 2011; 12: 57.
Tiling array data analysis: a multiscale approach using wavelets
Abstract
Background
T... | 4 | [
-0.03662109375,
-0.004547119140625,
-0.0269775390625,
-0.07861328125,
-0.04931640625,
-0.11474609375,
0.000060558319091796875,
-0.0830078125,
-0.054443359375,
-0.09814453125,
-0.07958984375,
-0.0026092529296875,
-0.0791015625,
-0.00799560546875,
-0.025146484375,
-0.00146484375,
-0.03... | 32,172 | 32172 | |
Computational & Applied Mathematics
Services on Demand
Article
Indicators
Related links
Share
On-line version ISSN 1807-0302
Comput. Appl. Math. vol.28 no.2 São Carlos 2009
http://dx.doi.org/10.1590/S1807-03022009000200003
A filter SQP algorithm without a feasibility restoration phase^*
Chungen Shen^I,II; We... | 4 | [
-0.091796875,
0.0301513671875,
0.0274658203125,
-0.0267333984375,
-0.042724609375,
0.05712890625,
-0.00909423828125,
-0.033447265625,
-0.0166015625,
0.00787353515625,
-0.061279296875,
0.0277099609375,
0.039794921875,
0.06591796875,
-0.064453125,
0.046630859375,
0.09033203125,
0.003... | 32,173 | 32173 | |
What am I doing wrong, differential equation
May 2nd 2008, 02:21 PM
arbolis
What am I doing wrong, differential equation
We're looking for $x(t)$. The data are : $x'=f(t,x)$, $x(0)=0$.
We have $f(t,x)=1+x^2$.
I rewrite it as $\frac{dx}{dt}=1+x^2$. Which is equivalent to $1=\frac{dx}{(1+x^2)dt}$. Equivale... | 5 | [
-0.0002994537353515625,
-0.00135040283203125,
0.10595703125,
0.0634765625,
0.0108642578125,
-0.0233154296875,
0.057861328125,
0.053466796875,
-0.00186920166015625,
-0.018798828125,
0.10302734375,
-0.0380859375,
-0.023193359375,
0.0234375,
-0.11279296875,
0.0037689208984375,
0.0021667... | 32,174 | 32174 | |
Homework Help
Posted by laura on Thursday, March 29, 2007 at 11:22pm.
Find the two consecutive odd integers such that 5 times the first integer is 12 more than 3 times the second.
can some explain to me how to get this
i was thinking the formula would be '
5x+12=3x
No, that's not it. The second integer is x+2, sin... | 4 | [
-0.033935546875,
0.03857421875,
0.02294921875,
-0.10693359375,
0.01806640625,
0.0263671875,
0.0201416015625,
0.044921875,
-0.044677734375,
0.00003910064697265625,
0.0240478515625,
0.052734375,
0.01434326171875,
0.006744384765625,
0.05908203125,
-0.027099609375,
-0.0286865234375,
0.... | 32,175 | 32175 | |
Negation Logic
January 11th 2009, 01:49 PM #1
Negation Logic
Write the negation of the logical expression $(p \rightarrow eg q) \wedge (p \vee q)$. Simplify it to the point where the negation symbol appears only in front of the variables $p$ and $q$, do
not leave the negation symbol in front of a parenthetica... | 5 | [
0.003814697265625,
0.0181884765625,
0.13671875,
0.0003528594970703125,
0.00653076171875,
0.07958984375,
0.01177978515625,
0.003936767578125,
0.052734375,
0.09423828125,
0.029541015625,
0.01190185546875,
0.022216796875,
0.10693359375,
0.1005859375,
0.11279296875,
-0.07080078125,
0.0... | 32,176 | 32176 | |
Help with L'Hospital's Rule question
November 25th 2009, 05:20 PM #1
Junior Member
Joined
Sep 2009
Posts
32
Help with L'Hospital's Rule question
Hey guys,
I was just wondering if you could help me out with a question. I think I've wittled it down enough but I'm having troubles simplifying it and I'm... | 5 | [
0.054443359375,
0.07958984375,
0.07763671875,
0.04931640625,
-0.02392578125,
0.0181884765625,
0.005218505859375,
0.09228515625,
0.052490234375,
-0.033447265625,
0.0634765625,
-0.037353515625,
0.01397705078125,
0.0654296875,
-0.0133056640625,
0.057861328125,
0.031005859375,
-0.04223... | 32,177 | 32177 | |
f(x+y)=f(x)*f(y), f(1)=q. find the followings.
November 14th 2012, 07:11 AM #1
Newbie
Joined
Apr 2010
Posts
7
f(x+y)=f(x)*f(y), f(1)=q. find the followings.
There are 5 questions on this problem. The one I have difficult with is the last one, I think I got the first four.
Given a function f(x+y)=f(x)... | 4 | [
-0.080078125,
0.02197265625,
0.01434326171875,
0.06787109375,
-0.04052734375,
0.0830078125,
0.06787109375,
-0.04052734375,
-0.024169921875,
0.01287841796875,
0.07568359375,
-0.1142578125,
-0.04345703125,
0.10693359375,
0.009765625,
0.035400390625,
-0.126953125,
-0.0252685546875,
... | 32,178 | 32178 | |
Compute E[X(X-1)]
December 14th 2009, 01:39 AM #1
Banned
Joined
Dec 2008
From
Mauritius
Posts
523
Compute E[X(X-1)]
Question : A Binomial variate $X$ has the mean $6$ and standard deviation $\sqrt{2}$. Find its moment generating function. Hence obtain $E[e^{2X+3}]$. Also compute $E[X(X-1)]$
Firs... | 5 | [
0.047607421875,
-0.02099609375,
0.050537109375,
-0.008056640625,
-0.01171875,
0.0390625,
0.05712890625,
0.0111083984375,
0.048583984375,
0.078125,
-0.0281982421875,
0.00714111328125,
-0.0164794921875,
-0.09716796875,
-0.035400390625,
-0.048828125,
-0.048583984375,
-0.00393676757812... | 32,179 | 32179 | |
the encyclopedic entry of symmetrize
In
group theory
, a
word metric
on a
group $G$
is a way to measure distance between any two elements of
$G$
. As the name suggests, the word metric is a
metric
on
$G$
, assigning to any two elements
$g$
,
$h$
of
$G$
a distance
$d\left(g,h\right)$
that measures ho... | 4 | [
-0.04052734375,
-0.038818359375,
-0.00052642822265625,
-0.0184326171875,
-0.103515625,
-0.05810546875,
0.0257568359375,
-0.01373291015625,
0.07421875,
-0.00098419189453125,
0.03955078125,
-0.027587890625,
0.03271484375,
0.03369140625,
-0.054443359375,
-0.039306640625,
0.040283203125,... | 32,180 | 32180 | |
Equation of the tangent line at that point
February 12th 2011, 04:44 PM
agent2421
Equation of the tangent line at that point
Can someone please explain to me how to do this. It seems like a very straight forward question.
Find the slope of the tangent line to the graph of each function at the given point. W... | 4 | [
-0.09033203125,
-0.00579833984375,
0.0211181640625,
-0.0002593994140625,
0.01141357421875,
0.08203125,
0.0111083984375,
0.10546875,
-0.045654296875,
0.03271484375,
0.0303955078125,
-0.0947265625,
0.027587890625,
0.0186767578125,
0.009033203125,
0.060791015625,
-0.12158203125,
-0.02... | 32,181 | 32181 | |
Check derivtives for correctness
January 16th 2011, 11:58 AM
sedemihcra
Check derivtives for correctness
I have not done differential calculus for awhile. I reviewed my calc book, but I am still having some trouble. Could someone please check these derivatives?
$f(x) = e^x + 2^-^x + 2*cos(x)-6$
$f'(x) =... | 4 | [
-0.03662109375,
-0.052490234375,
0.01544189453125,
0.00982666015625,
0.051513671875,
-0.0050048828125,
-0.03759765625,
-0.00665283203125,
-0.031494140625,
0.083984375,
0.1357421875,
-0.119140625,
0.00927734375,
-0.050537109375,
0.017822265625,
-0.02978515625,
-0.05078125,
-0.011047... | 32,182 | 32182 | |
Coordinates where tangent line is vertical?
October 5th 2008, 05:33 PM #1
Newbie
Joined
Sep 2008
Posts
23
Hey anyone know how I can solve this?
The equation is (x^2)+2x+(y^4)+4y=5
How do I find the coordinates of the two points on the curve where the line tangent to the curve is vertical?
A... | 5 | [
-0.0498046875,
-0.0498046875,
-0.004852294921875,
-0.025634765625,
0.047607421875,
0.026611328125,
-0.0128173828125,
0.07275390625,
0.0478515625,
-0.00201416015625,
0.0791015625,
0.0234375,
0.0517578125,
0.0089111328125,
-0.045166015625,
0.11669921875,
-0.026611328125,
-0.046875,
... | 32,183 | 32183 | |
Math Help
April 18th 2010, 06:28 PM #1
Junior Member
Joined
Oct 2009
Posts
56
divisor
If p(x) is a polynomial of degree n in F[x] and if E is the splitting field of p(x) over F, then (E:F) is a divisor of n!
If the polynomial p(x) is separable or characteristic of F is 0, then it can be shown direc... | 4 | [
-0.02978515625,
0.00494384765625,
0.0634765625,
0.00738525390625,
0.09765625,
0.0947265625,
0.07470703125,
0.06298828125,
-0.01025390625,
-0.050537109375,
0.05810546875,
0.013916015625,
-0.007080078125,
-0.038818359375,
-0.0108642578125,
0.004608154296875,
-0.09130859375,
-0.008483... | 32,184 | 32184 | |
Physics Urgent please help
Posted by Ramana on Wednesday, November 13, 2013 at 11:05am.
A physical pendulum consists of a body of mass contained in the xy-plane. The moment of inertia of the object about an axis perpendicular to the plane and passing through the object's center of mass
is I_cm .
The object oscillates... | 5 | [
-0.038330078125,
-0.018798828125,
-0.0230712890625,
-0.03759765625,
-0.02685546875,
-0.005706787109375,
0.00726318359375,
0.019287109375,
0.04638671875,
0.0135498046875,
0.095703125,
0.006683349609375,
0.06298828125,
-0.023681640625,
-0.006317138671875,
0.0654296875,
-0.0206298828125... | 32,185 | 32185 | |
Question about inner product space inequality
November 24th 2009, 04:06 PM #1
Newbie
Joined
Nov 2009
Posts
1
Question about inner product space inequality
Hi guys,
How would I show that $\sum\limits_{j = 1}^n {\left| {\left\langle {x,{v_j}} \right\rangle \left\langle {y,{v_j}} \right\rangle } \right... | 5 | [
-0.007080078125,
0.00286865234375,
0.046142578125,
-0.08642578125,
-0.0302734375,
-0.038818359375,
-0.01953125,
-0.08251953125,
-0.07568359375,
-0.0281982421875,
-0.10546875,
0.0576171875,
-0.004852294921875,
-0.0068359375,
0.00421142578125,
0.08203125,
0.08056640625,
-0.0112915039... | 32,186 | 32186 | |
Numerical Solution of Singular Lane-Emden Equation
ISRN Mathematical Physics
Volume 2013 (2013), Article ID 507145, 9 pages
http://dx.doi.org/10.1155/2013/507145
Research Article
Numerical Solution of Singular Lane-Emden Equation
Department of Applied Mathematics, School of Mathematical Sciences, University of Guila... | 5 | [
-0.08154296875,
-0.0108642578125,
0.02783203125,
-0.060546875,
0.0218505859375,
-0.08837890625,
-0.056884765625,
0.06787109375,
0.01092529296875,
-0.026611328125,
0.06298828125,
0.0205078125,
-0.0206298828125,
-0.05908203125,
-0.08251953125,
0.035888671875,
-0.06689453125,
0.022094... | 32,187 | 32187 | |
An Inventory Model with Time-Dependent Demand and Limited Storage Facility under Inflation
Advances in Operations Research
Volume 2012 (2012), Article ID 321471, 17 pages
http://dx.doi.org/10.1155/2012/321471
Research Article
An Inventory Model with Time-Dependent Demand and Limited Storage Facility under Inflation
... | 5 | [
-0.051025390625,
-0.00092315673828125,
-0.06396484375,
0.045654296875,
-0.07421875,
-0.0322265625,
-0.0908203125,
-0.0189208984375,
0.059326171875,
0.054931640625,
0.07666015625,
-0.00213623046875,
0.04736328125,
0.0419921875,
0.01556396484375,
-0.0390625,
0.04541015625,
-0.0703125... | 32,188 | 32188 | |
exponential function
March 12th 2008, 05:40 AM
mt_lapin
exponential function
A person invests $7000 at 10% interest compounded annually. Let $f(t)$ be the value (in dollars) of the account at t years after he/she has deposited the $7000.
a. Find an equation of f.
My answer: $f(t)=7000(1.10)^t$
b. ... | 4 | [
-0.055419921875,
0.0380859375,
-0.05322265625,
0.0145263671875,
0.01263427734375,
0.034423828125,
0.0147705078125,
0.083984375,
0.0030670166015625,
0.1240234375,
0.037841796875,
-0.0703125,
0.0206298828125,
0.0269775390625,
0.004241943359375,
0.0223388671875,
-0.1279296875,
-0.0737... | 32,189 | 32189 | |
Find the area of the finite region
May 6th 2008, 09:07 PM #1
Member
Joined
Sep 2007
Posts
198
Find the area of the finite region
Find the area of the finite region bounded by the curve with equation x^2 - y^2 = 4 and the line x = 5.
So to find the region we've to find, int (x^2 - 4)^1/2 dx with limi... | 4 | [
0.0654296875,
-0.059326171875,
0.0703125,
-0.0093994140625,
-0.004669189453125,
-0.072265625,
-0.053955078125,
0.0654296875,
0.0022430419921875,
-0.0242919921875,
-0.0179443359375,
0.05810546875,
-0.049560546875,
0.057373046875,
-0.06787109375,
0.142578125,
0.00775146484375,
-0.019... | 32,190 | 32190 | |
integral of exp(-x^2)
$e^{-x^2}$ does not have an elementry antiderivative. The integral can be calulated using Taylor series. $e^{-x^2}=\sum_{n=0}^{\infty}\frac{(-1)^nx^{2n}}{n!}$ So we can integrate this term by term to
get $\int_{0}^{1}\sum_{n=0}^{\infty}\frac{(-1)^nx^{2n}}{n!} dx = \sum_{n=0}^{\infty}\frac{(-1)^n}{... | 5 | [
0.009521484375,
-0.033447265625,
0.0234375,
0.040283203125,
-0.0252685546875,
-0.06884765625,
-0.037841796875,
0.05029296875,
-0.0233154296875,
-0.04296875,
0.05615234375,
0.000667572021484375,
-0.00885009765625,
-0.04931640625,
-0.1181640625,
-0.06884765625,
0.0517578125,
-0.06396... | 32,191 | 32191 | |
1. Introduction
With rapid progress of the information age, information itself as well as physical objects has become a major part of economic value and current popularity of information technology (IT)
intensifies the importance of information. For example, in the manufacturing industries, products are mostly re... | 4 | [
-0.004425048828125,
0.0032806396484375,
0.00726318359375,
-0.064453125,
-0.0245361328125,
-0.07080078125,
-0.06005859375,
0.040283203125,
0.033203125,
-0.006072998046875,
-0.0517578125,
0.009765625,
0.03759765625,
0.06103515625,
0.031005859375,
-0.06591796875,
-0.028076171875,
-0.0... | 32,192 | 32192 | |
Math Question Help
October 6th 2009, 06:41 PM #1
Member
Joined
Oct 2009
Posts
123
Math Question Help
Solve for x, ER
-x^3+25x < 0
----
I tried it out and i got:
x = 0, -5, 5
therefore if x is less than 5, x < 0
if x is greater than 5, x <0
not sure if it's right though.
... | 4 | [
-0.030517578125,
0.025634765625,
0.053955078125,
-0.06787109375,
-0.0118408203125,
-0.06884765625,
0.021240234375,
-0.006195068359375,
-0.00069427490234375,
0.02001953125,
0.01336669921875,
-0.019775390625,
0.10107421875,
0.043701171875,
0.0859375,
0.038330078125,
0.0283203125,
-0.... | 32,193 | 32193 | |
Quasilinearization for the Boundary Value Problem of Second-Order Singular Differential System
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 308413, 7 pages
http://dx.doi.org/10.1155/2013/308413
Research Article
Quasilinearization for the Boundary Value Problem of Second-Order Singular Differential Sys... | 5 | [
-0.1162109375,
0.050048828125,
0.01031494140625,
-0.015869140625,
0.0245361328125,
-0.00982666015625,
-0.036376953125,
-0.02734375,
0.013427734375,
0.0283203125,
0.04052734375,
0.052001953125,
-0.037109375,
-0.0068359375,
-0.006561279296875,
-0.024658203125,
-0.0498046875,
-0.01635... | 32,194 | 32194 | |
A Simple Power Management Scheme with Enhanced Stability for a Solar PV/Wind/Fuel Cell/Grid Fed Hybrid Power Supply Designed for Industrial Loads
Journal of Electrical and Computer Engineering
Volume 2014 (2014), Article ID 319017, 18 pages
http://dx.doi.org/10.1155/2014/319017
Research Article
A Simple Power Managem... | 4 | [
-0.0281982421875,
0.154296875,
-0.0458984375,
0.01153564453125,
-0.00131988525390625,
-0.0162353515625,
-0.05224609375,
0.0419921875,
-0.04736328125,
0.00055694580078125,
-0.015625,
0.054443359375,
0.052490234375,
-0.05712890625,
0.01336669921875,
0.07666015625,
0.037353515625,
-0.... | 32,195 | 32195 | |
Andy's Math/CS page
Fun with Censorship: the Finite Case
This post was inspired by Elad Verbin's insights and question about the 'Damn Good Puzzle'. See that post's comments section for the buildup.
Here is a finite version of the censor puzzle (which readers should review for the scenario):
Given
k > 0,
there is... | 4 | [
-0.046142578125,
-0.00714111328125,
-0.06396484375,
-0.06396484375,
0.015869140625,
0.0859375,
0.032958984375,
-0.0625,
0.0233154296875,
0.05615234375,
-0.0223388671875,
0.044677734375,
0.1103515625,
-0.0228271484375,
-0.07275390625,
0.0162353515625,
0.06103515625,
-0.0225830078125... | 32,196 | 32196 | |
4096 has 13 factors WHY
August 31st 2008, 07:45 PM #1
Newbie
Joined
Feb 2008
Posts
21
4096 has 13 factors WHY
Why is 4096 the smallest number with 13 factors. What does 2^n have to do with it? I understand in order to get an odd number of factors you have to use a perfect square.
Thanks for anythin... | 4 | [
0.02587890625,
-0.031982421875,
-0.02734375,
0.03466796875,
0.06689453125,
0.056396484375,
0.00335693359375,
0.099609375,
0.010986328125,
0.044189453125,
0.0003223419189453125,
0.032958984375,
0.0172119140625,
0.05029296875,
0.0252685546875,
0.05126953125,
-0.1103515625,
-0.0451660... | 32,197 | 32197 | |
Finding exact area with the Definite Integral
November 14th 2007, 11:18 PM #1
Finding exact area with the Definite Integral
Okay i was busy trying to figure these things out and then i got stuck.
Now using the Riemann notation to calculate the area under the graph $x^2 + 1$ we get the following:
$R_{6} ... | 5 | [
-0.036865234375,
-0.031005859375,
-0.00872802734375,
-0.05810546875,
-0.005126953125,
-0.052001953125,
-0.038330078125,
0.055419921875,
0.01904296875,
-0.018310546875,
-0.0517578125,
-0.025634765625,
-0.0126953125,
-0.007537841796875,
-0.031982421875,
-0.0306396484375,
-0.06030273437... | 32,198 | 32198 | |
[SOLVED] Checking my result (infinite series)
July 12th 2008, 08:59 AM #1
[SOLVED] Checking my result (infinite series)
Just want to be sure about my results.
Say whether it converges or not :
1) $1-\frac{1}{2}+\frac{2}{3}-\frac{1}{3}+\frac{2}{4}-\frac{1}{4}+\frac{2}{5}-\frac{1}{5}+...$. I wrote it as $\s... | 5 | [
-0.0732421875,
-0.06689453125,
0.05908203125,
0.0036163330078125,
0.0206298828125,
-0.05322265625,
-0.01544189453125,
0.0771484375,
0.0030059814453125,
0.03125,
-0.08984375,
-0.06298828125,
-0.01092529296875,
0.0081787109375,
-0.1025390625,
-0.07763671875,
0.068359375,
-0.1328125,
... | 32,199 | 32199 |