content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
An Approximation to Solution of Space and Time Fractional Telegraph Equations by He's Variational Iteration Method
Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 290631, 10 pages
http://dx.doi.org/10.1155/2010/290631
Research Article
An Approximation to Solution of Space and Time Fractional Tele... | 5 | [
-0.0537109375,
0.037841796875,
0.10302734375,
0.05615234375,
-0.049072265625,
-0.0145263671875,
0.00177764892578125,
0.10546875,
-0.0125732421875,
-0.01202392578125,
0.01556396484375,
0.0067138671875,
-0.0250244140625,
0.02978515625,
-0.033935546875,
-0.027099609375,
-0.0030822753906... | 30,100 | 30100 | |
Physics Forums - View Single Post - Charge distribution of a uniformly charged disk
1. The problem statement, all variables and given/known data
The problem can be found in Jackson's book, I think in chapter 1 problem 3 or something like this.
I must determine the charge distribution of a uniformly charged disk of rad... | 4 | [
-0.08203125,
0.07080078125,
-0.0018157958984375,
-0.046142578125,
0.03857421875,
-0.0203857421875,
0.0732421875,
-0.0213623046875,
-0.02490234375,
0.03759765625,
0.057861328125,
-0.042724609375,
0.0284423828125,
0.11572265625,
-0.006500244140625,
-0.11279296875,
-0.034912109375,
-0... | 30,101 | 30101 | |
Volume of revolution between y=sinx and y=cosx
May 28th 2009, 08:50 PM #1
Junior Member
Joined
May 2009
Posts
39
Volume of revolution between y=sinx and y=cosx
How would I go about solving the following problem?
Find the volume of revolution defined by rotating, around the x-axis, the area between t... | 5 | [
-0.03662109375,
-0.005462646484375,
-0.0133056640625,
-0.05712890625,
-0.049560546875,
-0.07275390625,
-0.09814453125,
0.0654296875,
-0.00885009765625,
-0.054931640625,
-0.0250244140625,
0.024169921875,
0.09228515625,
0.07958984375,
0.038818359375,
-0.02783203125,
-0.049560546875,
... | 30,102 | 30102 | |
Homework Help
Posted by lia on Tuesday, August 6, 2013 at 9:48pm.
The perimeter of the quadrilateral is 80feet. Find the length of the other sides.
One side is x+9 another is x+13, 4x-5, x^2-8x.
• math - Reiny, Tuesday, August 6, 2013 at 10:20pm
Let's just add up the four sides you gave
x+9 + x+13 + 4x-5... | 4 | [
-0.03271484375,
0.1279296875,
-0.00628662109375,
-0.0205078125,
0.015869140625,
0.056640625,
0.0264892578125,
0.0218505859375,
-0.0257568359375,
-0.099609375,
0.041748046875,
-0.0196533203125,
0.042236328125,
0.0322265625,
0.00811767578125,
-0.06787109375,
-0.005523681640625,
0.003... | 30,103 | 30103 | |
Interior angles of a Parallelogram
April 16th 2009, 04:57 PM #1
Interior angles of a Parallelogram
Hello, Ho do I find the interior angles of this
I know how to find for a triangle using
A.B = |A||B| cos theta
not sure how to find for a parallelogram
You do just that! Draw a line up from point... | 4 | [
-0.055908203125,
0.0208740234375,
-0.04736328125,
-0.1376953125,
-0.0029754638671875,
0.04296875,
0.00848388671875,
0.05908203125,
-0.00665283203125,
0.041259765625,
0.04248046875,
-0.03271484375,
0.0390625,
0.021484375,
0.06298828125,
-0.018798828125,
-0.056640625,
0.0225830078125... | 30,104 | 30104 | |
Circumradius and inradius.
July 7th 2010, 08:35 PM #1
Member
Joined
Feb 2010
From
in the 4th dimension....
Posts
122
Thanks
9
Circumradius and inradius.
prove that for any triangle ,R>= 2r,where R and r are the circumradius and inradius of the triangle respectively.
post in different proofs
... | 4 | [
-0.0576171875,
0.060546875,
-0.00421142578125,
0.036376953125,
0.0380859375,
0.02197265625,
0.03173828125,
0.0791015625,
0.01361083984375,
-0.0028076171875,
-0.072265625,
-0.0791015625,
0.04296875,
0.08935546875,
0.04345703125,
-0.0205078125,
-0.01483154296875,
0.0208740234375,
-... | 30,105 | 30105 | |
Simple and Compound Interest Problem
January 14th 2011, 12:41 AM #1
Member
Joined
Jan 2011
Posts
95
Simple and Compound Interest Problem
Hi All,
Q:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 550 as interest. He invested the remaining in a bo... | 4 | [
0.0478515625,
0.068359375,
0.02001953125,
-0.0074462890625,
0.01519775390625,
-0.05517578125,
0.00543212890625,
0.068359375,
-0.051025390625,
0.0869140625,
-0.0162353515625,
-0.01300048828125,
0.0341796875,
0.023193359375,
0.02783203125,
0.02392578125,
-0.08935546875,
-0.0244140625... | 30,106 | 30106 | |
-Complete Metric Spaces with Applications
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 280817, 11 pages
http://dx.doi.org/10.1155/2014/280817
Research Article
Fixed Point Theory in -Complete Metric Spaces with Applications
^1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, 21589 ... | 5 | [
-0.0137939453125,
0.0037689208984375,
0.03955078125,
-0.078125,
-0.044189453125,
0.061279296875,
0.03466796875,
-0.00927734375,
0.068359375,
-0.01611328125,
0.058349609375,
-0.0089111328125,
0.0322265625,
0.0546875,
-0.01068115234375,
-0.064453125,
0.0537109375,
-0.07763671875,
0... | 30,107 | 30107 | |
Homework Help
Posted by Jon on Friday, February 15, 2008 at 5:53pm.
Find the exact value of sinx/2 if cosx = 2/3 and 270 < x < 360.
A)1/3
B)-1/3
C)sqrt 6/6
D)-sqrt 6/6
C, since I KNOW cosx is always positive but I don't know the work involved. I know the half angle formula
• Trig - drwls, Friday, February 15, ... | 4 | [
-0.0537109375,
0.01251220703125,
-0.01031494140625,
0.001953125,
-0.00096893310546875,
-0.0213623046875,
-0.060546875,
0.0498046875,
0.0186767578125,
0.0240478515625,
0.0218505859375,
-0.0498046875,
0.0186767578125,
0.001922607421875,
0.06396484375,
-0.022705078125,
-0.00102233886718... | 30,108 | 30108 | |
[SOLVED] Hyperbolic Function
February 5th 2009, 04:24 PM
mr_motivator
[SOLVED] Hyperbolic Function
x is a real number and sinh^2(x) = 24/25
a) what are the possible values of sinh(x)?
b) what are the possible values of cosh(x)?
February 5th 2009, 04:56 PM
mr fantastic
Quote:
x is a real nu... | 4 | [
0.0087890625,
0.07666015625,
0.017333984375,
-0.0625,
0.0157470703125,
0.021484375,
-0.002685546875,
-0.01226806640625,
-0.0230712890625,
-0.0128173828125,
0.11279296875,
-0.08203125,
-0.026123046875,
0.039794921875,
0.0247802734375,
-0.03955078125,
0.0062255859375,
-0.11181640625,... | 30,109 | 30109 | |
Combinations with repetition (I think)
December 29th 2012, 09:12 AM #1
Member
Joined
May 2009
Posts
77
Combinations with repetition (I think)
Long time no see...
My greetings to all forum users.
I know that if we have $k$ identical sets that each one of them has $n$ objects and we want to pick $... | 4 | [
0.0595703125,
-0.0245361328125,
-0.042724609375,
-0.009765625,
-0.0208740234375,
0.07470703125,
0.06787109375,
0.002044677734375,
0.003326416015625,
0.014404296875,
-0.095703125,
-0.01287841796875,
0.04345703125,
-0.0167236328125,
0.00360107421875,
0.05517578125,
0.04443359375,
-0.... | 30,110 | 30110 | |
Solving Quadratic Equations & Determining Quadratic Rules
April 18th 2013, 12:52 AM #5
Member
April 17th 2013, 10:22 PM #4
Super Member
April 17th 2013, 08:56 PM #3
Member
April 17th 2013, 05:47 PM #2
April 17th 2013, 05:44 PM #1
Member
Re: Solving Quadratic Equations & Determining Quadratic Rules
Now we h... | 4 | [
-0.0673828125,
0.056884765625,
0.025390625,
-0.0556640625,
-0.031982421875,
0.03369140625,
0.03564453125,
0.1201171875,
-0.021484375,
-0.01190185546875,
0.0751953125,
-0.043212890625,
-0.01220703125,
-0.01141357421875,
-0.08056640625,
0.0201416015625,
-0.046875,
-0.058349609375,
... | 30,111 | 30111 | |
Probability problem about cubes
November 14th 2009, 08:30 PM #1
Member
Joined
Apr 2009
From
california
Posts
121
Probability problem - cubes
Each face of a cube is painted either Red or Blue, each with probability 1/2. The color of each face is determined independently. What is the probabilty that th... | 4 | [
0.06591796875,
0.0203857421875,
0.0302734375,
-0.01531982421875,
-0.040283203125,
0.0203857421875,
0.003692626953125,
-0.080078125,
-0.033203125,
-0.0654296875,
-0.10546875,
-0.040771484375,
0.068359375,
0.029541015625,
0.06982421875,
0.06591796875,
-0.011474609375,
-0.021118164062... | 30,112 | 30112 | |
[SOLVED] Second order differential equations
February 15th 2009, 02:54 PM #1
Junior Member
Joined
Jan 2009
Posts
35
[SOLVED] Second order differential equations
a)
Find the general solution of the second order differential equation
4y′′ + 8y′ + 3y = 0 .
Find the particular solution that... | 4 | [
-0.083984375,
-0.04736328125,
0.06396484375,
-0.0152587890625,
-0.009765625,
0.060302734375,
-0.01513671875,
0.034423828125,
-0.004150390625,
0.02392578125,
0.1064453125,
-0.126953125,
-0.02392578125,
-0.004150390625,
0.040283203125,
-0.00665283203125,
-0.0262451171875,
-0.05493164... | 30,113 | 30113 | |
find polynomial f(x)
June 19th 2007, 07:44 AM #1
Newbie
Joined
Jun 2007
From
Boston
Posts
10
find polynomial f(x)
I have a test up tomorrow and I really need to know how to solve this; somehow I didn't write explanations in my notes so although I kind of have a vague idea of how to solve it, I don't ... | 4 | [
0.0081787109375,
0.047607421875,
-0.0302734375,
0.0230712890625,
-0.021240234375,
0.047607421875,
0.0263671875,
0.01416015625,
-0.041259765625,
0.0279541015625,
0.0458984375,
-0.1142578125,
0.0281982421875,
0.07763671875,
-0.00018024444580078125,
0.058349609375,
-0.07763671875,
-0.... | 30,114 | 30114 | |
Factoring a quadratic equation
I'm stuck on this one.... 6r^2-r-2=0 Any assistance appreciated. Thanks Thomas
Hi tbradnc, Here's a technique you can use. Multiply the leading coefficient (6) by the constant (-2). This gives you -12. The coefficient of the middle term is -1. You need a pair of numbers whose
product is ... | 4 | [
0.01324462890625,
-0.0106201171875,
-0.01287841796875,
0.0174560546875,
0.040771484375,
0.08251953125,
-0.07177734375,
-0.007354736328125,
-0.01544189453125,
-0.042236328125,
0.01123046875,
0.0634765625,
0.0107421875,
0.046142578125,
0.002288818359375,
0.01171875,
-0.05224609375,
0... | 30,115 | 30115 | |
Poissons equation, gravitational field.
November 21st 2010, 11:06 AM #1
Junior Member
Joined
Jan 2010
Posts
39
Poissons equation, gravitational field.
A spherical planet of radius (3/2)R is composed of two solid regions of different, but constant, mass distributions. The core is located at r<=R and has a... | 4 | [
0.0302734375,
-0.01177978515625,
-0.05615234375,
-0.018798828125,
0.056396484375,
-0.0189208984375,
0.0517578125,
0.072265625,
0.023193359375,
-0.004974365234375,
-0.0184326171875,
-0.025634765625,
-0.053955078125,
-0.00701904296875,
0.123046875,
-0.0673828125,
0.03759765625,
-0.04... | 30,116 | 30116 | |
Hyperbolic Riemann Surface
Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
Let $X$ be a compact Riemann surface and $x\in X$. Is $X - \overline{D(x,r_x)}$ hyperbolic?
If you look at the tags it looks like theOP is int... | 5 | [
-0.0213623046875,
0.0517578125,
0.006866455078125,
-0.0439453125,
0.0284423828125,
-0.04833984375,
0.07080078125,
0.06201171875,
0.049072265625,
-0.031005859375,
0.058837890625,
-0.041748046875,
0.006500244140625,
0.0076904296875,
0.0615234375,
-0.0830078125,
-0.035888671875,
-0.09... | 30,117 | 30117 | |
2-sylow subgroups of S6
August 6th 2008, 02:45 AM #1
Newbie
Joined
Aug 2008
Posts
2
2-sylow subgroups of S6
Can someone suggest some method to find 2-sylow subgroups of S6. From what I know - we first find 2-sylow subgroups of S8 and then find an isomorphism from S6 into S8. Then our desired subgroup
... | 5 | [
-0.0028228759765625,
-0.0264892578125,
0.04052734375,
-0.0115966796875,
0.022216796875,
0.0081787109375,
-0.01025390625,
0.022705078125,
-0.04443359375,
-0.01116943359375,
0.056396484375,
-0.0281982421875,
-0.0181884765625,
-0.057861328125,
0.01025390625,
0.041748046875,
-0.053466796... | 30,118 | 30118 | |
Slope/Standard Form
March 15th 2009, 10:58 AM #1
Newbie
Joined
Mar 2009
Posts
3
Slope/Standard Form
I really can't do this to save my life and It's homework for tomorrow - I didn't know I had it. Help is much appreciated!!
it has to do with slope intercept and standard form
slope intercept for... | 4 | [
-0.05322265625,
-0.0262451171875,
-0.017333984375,
-0.03125,
0.060302734375,
0.07177734375,
-0.036376953125,
0.03369140625,
-0.0947265625,
0.028076171875,
0.06201171875,
-0.0751953125,
-0.01007080078125,
-0.022705078125,
-0.068359375,
0.12158203125,
-0.08154296875,
-0.0130615234375... | 30,119 | 30119 | |
Control for Switched Stochastic Systems with Time-Varying Delay
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 320703, 12 pages
http://dx.doi.org/10.1155/2013/320703
Research Article
Observer-Based Robust Control for Switched Stochastic Systems with Time-Varying Delay
^1School of Automation, Nanjing U... | 4 | [
-0.054443359375,
-0.06982421875,
-0.037109375,
0.044921875,
-0.0279541015625,
0.047119140625,
0.08984375,
0.06640625,
0.02099609375,
0.032470703125,
0.09814453125,
0.01080322265625,
0.0240478515625,
-0.0654296875,
-0.09375,
0.10693359375,
0.056396484375,
-0.00885009765625,
0.0222... | 30,120 | 30120 | |
Finding interval/radius of convergence of power series
May 10th 2009, 05:16 PM #1
Finding interval/radius of convergence of power series
I'm fairly certain I have the correct answer, but I just want to verify.
$\sum_{k=1}^{\infty}\frac{k^{2}x^{k}}{2\cdot 4\cdot 6\cdot \cdot \cdot (2k)}$
So I used the ra... | 5 | [
0.04541015625,
-0.0654296875,
-0.042724609375,
0.05419921875,
0.012451171875,
-0.033203125,
-0.0224609375,
0.00811767578125,
0.00067901611328125,
-0.039306640625,
0.046875,
-0.05224609375,
0.035888671875,
-0.038818359375,
-0.0771484375,
0.023681640625,
0.01263427734375,
-0.03833007... | 30,121 | 30121 | |
Homework Help
Posted by Maths on Friday, October 14, 2011 at 4:50pm.
Please show me the way of using formula log?
• Maths - Steve, Saturday, October 15, 2011 at 12:39pm
Just think of log as another operator, like + or * or √.
We have - to indicate the number you need to add to x to get 0:
3 + (-3) = ... | 4 | [
0.0240478515625,
0.047119140625,
-0.0037078857421875,
0.02294921875,
-0.01409912109375,
-0.078125,
0.068359375,
0.08984375,
0.036376953125,
0.021728515625,
0.003265380859375,
-0.060302734375,
0.056884765625,
0.11083984375,
0.0174560546875,
0.04248046875,
-0.08203125,
0.014099121093... | 30,122 | 30122 | |
Incomplete gamma function
August 8th 2008, 07:26 PM #1
Junior Member
Joined
Jun 2008
Posts
61
Incomplete gamma function
I noticed that the equation for the incomplete gamma function yields an issue for gamma(z,infinity)
It makes the integral representation have infinity for both limits of integratio... | 5 | [
-0.09765625,
-0.023193359375,
0.0296630859375,
0.0150146484375,
-0.0238037109375,
-0.05712890625,
0.033203125,
0.04931640625,
-0.042724609375,
-0.004058837890625,
0.036376953125,
0.003448486328125,
0.109375,
0.0458984375,
0.048828125,
-0.0296630859375,
0.03369140625,
-0.08056640625... | 30,123 | 30123 | |
Whats the chances of...
July 26th 2007, 02:48 PM #1
Newbie
Joined
Jul 2007
Posts
4
Whats the chances of...
Hi,
My very first post so please be gentle lol
Im programming a simple slot machine that has 5 reels and a has 1 "star" on each.
What i want to know is if the Star can be on, above or... | 5 | [
-0.053955078125,
-0.07470703125,
-0.038330078125,
-0.058349609375,
-0.10986328125,
-0.037841796875,
0.00909423828125,
-0.01068115234375,
-0.0291748046875,
0.032470703125,
-0.0390625,
-0.042236328125,
0.025390625,
-0.06884765625,
-0.00138092041015625,
0.00787353515625,
-0.04736328125,... | 30,124 | 30124 | |
Navy Electricity and Electronics Training Series (NEETS)
Module 6—Introduction to Electronic Emission, Tubes, and Power Supplies
Pages
i - ix
,
1-1 to 1-10
,
1-11 to 1-20
,
1-21 to 1-30
,
1-31 to 1-40
,
1-41 to 1-50
,
1-51 to 1-56
,
2-1 to 2-10
,
2-11 to 2-20
,
2-21 to 2-30
,
2-31 to 2-39
,
3-1 ... | 4 | [
-0.0947265625,
0.0184326171875,
0.0211181640625,
0.00836181640625,
0.07666015625,
-0.01409912109375,
0.036865234375,
0.0927734375,
-0.019287109375,
-0.00634765625,
-0.01409912109375,
-0.04443359375,
0.03564453125,
-0.05029296875,
-0.0517578125,
0.08251953125,
-0.0615234375,
0.00160... | 30,125 | 30125 | |
Converting recurring decimals to fractions
In general, suppose x= A.BCCCCC... where "A" is the entire number before the decimal point, "B" is any decimals before repetition, and "C" is the repeating block. Also let "n" be the number of
decimal places in B, "m" the number of decimal places in C.
In your example, 0.77777... | 4 | [
-0.025634765625,
0.06494140625,
-0.01287841796875,
0.01092529296875,
-0.044677734375,
0.05517578125,
0.078125,
0.04150390625,
-0.034423828125,
-0.03173828125,
-0.059326171875,
-0.1416015625,
0.033203125,
0.11962890625,
-0.0189208984375,
-0.0274658203125,
-0.0255126953125,
0.0629882... | 30,126 | 30126 | |
Dirichlet and Neumann Problems Related to Nonlinear Elliptic Systems: Solvability, Multiple Solutions, Solutions with Positive Components
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 760854, 44 pages
http://dx.doi.org/10.1155/2012/760854
Research Article
Dirichlet and Neumann Problems Related to Nonl... | 5 | [
-0.10791015625,
-0.0198974609375,
0.0269775390625,
-0.0213623046875,
0.060302734375,
0.037109375,
0.015625,
-0.0007171630859375,
0.030517578125,
-0.126953125,
0.11083984375,
-0.0216064453125,
0.0186767578125,
-0.0186767578125,
-0.051025390625,
0.00848388671875,
0.006988525390625,
-... | 30,127 | 30127 | |
A divisibility property
June 30th 2010, 11:23 AM
Demandeur
A divisibility property
Prove that if $d\mid{a}$ and $a e 0$, then $|d|\le|a|$.
If $d\mid{a}$ then $a = qd$, for some $q\in\mathbb{Z}$, and $d = \frac{a}{q}$, therefore $|d|\le|a|$. Is this argument correct?
June 30th 2010, 11:44 AM
melese
Q... | 4 | [
-0.043701171875,
0.05859375,
-0.0009918212890625,
-0.08447265625,
0.0498046875,
0.012451171875,
0.054931640625,
0.0361328125,
0.00439453125,
0.00897216796875,
0.04736328125,
-0.0289306640625,
0.09521484375,
0.0810546875,
-0.000446319580078125,
-0.00567626953125,
0.0654296875,
-0.00... | 30,128 | 30128 | |
Homework Help
Posted by sasha on Wednesday, October 31, 2012 at 3:20pm.
a math student borrowed $9300.00 from his local bank at 7% compounded quarterly to pay for his studies. the loan is to be repaid by equal payments at the end of every quarter over a two year term.
a)construct the amortization schedule for the loa... | 4 | [
-0.04638671875,
0.10986328125,
0.0000743865966796875,
-0.040283203125,
-0.00567626953125,
-0.09326171875,
-0.0223388671875,
0.01275634765625,
0.019287109375,
0.09765625,
0.09033203125,
-0.0247802734375,
-0.02490234375,
0.04052734375,
-0.0286865234375,
0.0098876953125,
-0.1171875,
-... | 30,129 | 30129 | |
A debt for a motorbike
September 5th 2009, 11:57 PM #1
Member
Joined
Jan 2009
Posts
98
A debt for a motorbike
Sorry - another question.
For the following, I got $97,800 as an answer. Is this correct? It doesn't seem to make sense. I know I'm doing something wrong here, but what could it be?
Tul... | 4 | [
-0.0703125,
0.1171875,
0.00054168701171875,
-0.00213623046875,
-0.0306396484375,
-0.010498046875,
0.08837890625,
0.1025390625,
-0.02783203125,
0.09912109375,
0.072265625,
-0.047119140625,
0.0235595703125,
0.0247802734375,
-0.0595703125,
0.0546875,
0.0128173828125,
-0.03759765625,
... | 30,130 | 30130 | |
Bayesian Estimation Based on Rayleigh Progressive Type II Censored Data with Binomial Removals
Journal of Quality and Reliability Engineering
Volume 2013 (2013), Article ID 896807, 6 pages
http://dx.doi.org/10.1155/2013/896807
Research Article
Bayesian Estimation Based on Rayleigh Progressive Type II Censored Data wi... | 5 | [
0.0208740234375,
-0.0289306640625,
0.04052734375,
0.0291748046875,
0.006927490234375,
-0.0177001953125,
-0.0002803802490234375,
-0.050048828125,
0.037109375,
0.052001953125,
0.09033203125,
0.0380859375,
0.1259765625,
-0.0279541015625,
-0.12158203125,
0.006256103515625,
0.0810546875,
... | 30,131 | 30131 | |
Optimization in O
Chapter Summaries
Chapter 1: Problem Solving with Mathematical Models
An introduction to the operations research approach of dealing with large-scale, operations problems through mathematical modeling. Basic terminology and modeling a simple problem in several ways to
illustrate the tradeoff between... | 4 | [
0.01068115234375,
0.020263671875,
-0.0126953125,
-0.06591796875,
-0.115234375,
-0.09228515625,
-0.107421875,
0.11181640625,
-0.031494140625,
0.019287109375,
-0.10009765625,
0.0791015625,
0.07568359375,
0.0634765625,
-0.0167236328125,
0.0026397705078125,
0.042236328125,
0.0095214843... | 30,132 | 30132 | |
Greatest common divisor
December 3rd 2008, 11:23 AM #1
Newbie
Joined
Oct 2008
Posts
16
Greatest common divisor
Hi.
Can anybody prove that?
Let $n>4$
$GCD(n, (n-1)!)=1 \Longleftrightarrow{} n$ its prime.
and
if $n$ its not prime $\Longrightarrow{} GCD(n, (n-1)!)=n$
Thanks
... | 4 | [
-0.00396728515625,
-0.0260009765625,
-0.0194091796875,
-0.07958984375,
0.004730224609375,
0.023681640625,
0.036376953125,
0.052001953125,
-0.0751953125,
0.0096435546875,
-0.04638671875,
0.072265625,
0.0235595703125,
-0.05712890625,
0.0164794921875,
-0.004241943359375,
0.010986328125,... | 30,133 | 30133 | |
M-QAM Bit Error Rate in Rayleigh Fading
We have previously discussed the bit error rate (BER) performance of M-QAM in AWGN. We now discuss the BER performance of M-QAM in Rayleigh fading. The one-tap Rayleigh fading channel is generated
from two orthogonal Gaussian random variables with variance of 0.5 each. The compl... | 4 | [
0.049560546875,
-0.037109375,
-0.06103515625,
-0.0096435546875,
-0.060302734375,
0.01708984375,
0.04248046875,
-0.028076171875,
0.005859375,
0.0140380859375,
0.01025390625,
0.01806640625,
0.12890625,
-0.0546875,
-0.0284423828125,
0.0732421875,
0.07373046875,
-0.07763671875,
-0.03... | 30,134 | 30134 | |
[SOLVED] algebra in P.M.I
June 8th 2010, 09:22 PM #1
Junior Member
Joined
Jun 2010
Posts
69
[SOLVED] algebra in P.M.I
I am still having trouble following the simplification of equations in the Induction examples i am studying.
The notes I have use this:
$<br /> [\frac{1}{2}k(k+1)] + (k+1)<br />$... | 4 | [
-0.0208740234375,
0.0281982421875,
0.060302734375,
0.038330078125,
-0.05859375,
-0.0281982421875,
-0.046875,
-0.00335693359375,
0.046875,
-0.014404296875,
-0.07470703125,
-0.06298828125,
0.0615234375,
-0.031005859375,
-0.052001953125,
0.044677734375,
0.051513671875,
0.031494140625,... | 30,135 | 30135 | |
Abelian groups
November 28th 2009, 11:18 AM #1
Member
Joined
Oct 2008
Posts
91
Abelian groups
Let G be an abelian group and let $g,h \in G$.
If $|g| = m$ is finite then prove that, for $n \in \mathbb {Z}$, $ng=0$ iff $m|n$.
Now the obvious cases are if $n=0$, $ng=0$ and $m|n$ trivially. Same fo... | 5 | [
-0.0927734375,
0.0478515625,
0.01214599609375,
0.039794921875,
0.00726318359375,
-0.010986328125,
0.024658203125,
-0.060791015625,
-0.0380859375,
-0.044189453125,
0.0098876953125,
-0.00057220458984375,
0.0135498046875,
0.006011962890625,
0.000732421875,
0.08740234375,
0.0272216796875... | 30,136 | 30136 | |
the encyclopedic entry of Truss
In architecture and structural engineering, a truss is a structure comprising one or more triangular units constructed with straight slender members whose ends are connected at joints referred to as
nodes. External forces and reactions to those forces are considered to act only at the no... | 4 | [
0.047607421875,
0.032470703125,
-0.0947265625,
-0.0284423828125,
-0.01324462890625,
-0.052978515625,
-0.07373046875,
0.00921630859375,
0.05517578125,
0.052978515625,
-0.021728515625,
0.00909423828125,
0.039306640625,
0.0294189453125,
0.022705078125,
-0.057373046875,
-0.047119140625,
... | 30,137 | 30137 | |
complex values and residuee theorem
May 9th 2011, 10:20 AM #1
Junior Member
Joined
Mar 2010
Posts
46
complex values and residuee theorem
I have two questions, I have tried to find stuff on them but failed
(1) find all complex values z such that e^(z+2)=1+i
I tried to put z=log(1+i)-2 but dont th... | 4 | [
-0.0106201171875,
0.08740234375,
-0.0157470703125,
-0.002105712890625,
0.0947265625,
-0.053466796875,
0.1083984375,
0.095703125,
0.012451171875,
0.087890625,
0.052978515625,
-0.06982421875,
-0.055419921875,
0.06396484375,
0.000514984130859375,
-0.10205078125,
-0.043701171875,
-0.01... | 30,138 | 30138 | |
Math Help
July 12th 2010, 06:59 PM #1
Newbie
Joined
Jun 2010
Posts
5
Help needed.
Be $\alpha\in\mathbb{R}$ and $p_{0}, p_{1}, p_{2},\cdots, p_{n}$ distintict positive intergers. I must prove there's an interger $r$ and indices $i$ and $j$ with $0\le i<j \le n$ such that $\mid\
alpha(p_{i} - p_{j}) -... | 4 | [
-0.00714111328125,
-0.0068359375,
-0.0289306640625,
-0.0478515625,
0.04248046875,
0.049560546875,
0.15625,
0.08251953125,
-0.0216064453125,
-0.09716796875,
-0.11376953125,
0.0166015625,
0.058837890625,
-0.006500244140625,
-0.0172119140625,
-0.08935546875,
0.07861328125,
-0.01232910... | 30,139 | 30139 | |
Chapter 3(Immersed Surfaces) Corrected by Reviewer
FLUID MECHANICS AND MACHINERY
47
HYDROSTATIC FORCES
Chapter-3HYDROSTATIC FORCES ON IMMERSED SURFACESINTRODUCTION
:When a solid object like a plane or curved surface is immersed in a static fluid (fluid at rest), thesurface experiences an upward pushing pressure exe... | 4 | [
-0.056884765625,
-0.0634765625,
0.0634765625,
-0.01031494140625,
0.0089111328125,
-0.032958984375,
0.056884765625,
0.07568359375,
0.0157470703125,
0.0311279296875,
-0.08642578125,
-0.0255126953125,
0.0172119140625,
0.03466796875,
-0.0693359375,
-0.056884765625,
-0.044921875,
0.0273... | 30,140 | 30140 | |
I'm completely lost with matrix differentiation.
November 12th 2010, 04:29 PM #1
Newbie
Joined
Oct 2010
Posts
17
I'm completely lost with matrix differentiation.
So I'm really kinda bummed out because I just don't get how to solve numerical differentiation problems with linear algebra. As an example :
... | 4 | [
0.032470703125,
0.01416015625,
-0.006072998046875,
-0.09814453125,
-0.05908203125,
-0.026611328125,
-0.06884765625,
-0.00982666015625,
-0.09130859375,
0.07421875,
0.0869140625,
-0.05126953125,
0.023681640625,
-0.03759765625,
-0.04443359375,
0.053955078125,
-0.044921875,
0.059082031... | 30,141 | 30141 | |
Posts about Algorithm on COME ON CODE ON
Archive for the ‘Algorithm’ Category
In mathematics a combination is a way of selecting several things out of a larger group, where (unlike permutations) order does not matter. More formally a k-combination of a set S is a subset of k
distinct elements of S. If the set has n el... | 5 | [
0.0400390625,
0.042236328125,
-0.02978515625,
-0.035888671875,
-0.0167236328125,
-0.00762939453125,
-0.040283203125,
-0.000701904296875,
-0.0169677734375,
0.040771484375,
-0.057861328125,
0.00872802734375,
0.01263427734375,
-0.05078125,
-0.052490234375,
0.0186767578125,
-0.0505371093... | 30,142 | 30142 | |
Setting up a quadratic equation from a worded question...
January 4th 2011, 01:35 AM #1
Newbie
Joined
Jan 2011
Posts
4
Setting up a quadratic equation from a worded question...
Hi, not sure whether this is Pre-uni or uni mathematics but any help would be greatly appreciated. The question states:
"Th... | 4 | [
0.0576171875,
0.0439453125,
0.040771484375,
-0.046142578125,
-0.06298828125,
-0.00970458984375,
-0.0654296875,
0.03369140625,
-0.060302734375,
0.038818359375,
0.0216064453125,
-0.052734375,
0.05517578125,
0.03173828125,
0.052734375,
0.058837890625,
0.01953125,
-0.0033416748046875,
... | 30,143 | 30143 | |
partial differential equation
May 13th 2011, 01:40 PM #1
Newbie
Joined
May 2011
Posts
2
partial differential equation
Hi, I have the differential equation
$\frac{ \partial z }{ \partial x } + \frac{ \partial z }{ \partial y } = z^2$. Satisfied by $z(x,y)$, where $z = f(x)$ on y=0 and x is between min... | 4 | [
-0.080078125,
0.0439453125,
0.05908203125,
0.05908203125,
-0.0074462890625,
0.035400390625,
0.006744384765625,
0.002227783203125,
-0.0673828125,
0.064453125,
-0.03955078125,
0.01806640625,
0.1181640625,
0.026123046875,
-0.033935546875,
-0.003875732421875,
0.022705078125,
-0.0427246... | 30,144 | 30144 | |
Problem 43
December 4th 2007, 08:26 PM
ThePerfectHacker
Problem 43
1)Let $a_1,a_2,...,a_n$ be real (or complex) distinct numbers where $n\geq 2$. Define $P_k = \prod_{jot = k} (a_k - a_j)$. Can it be that $P_1=P_2=...=P_n$?
(For example, let $a_1=1,a_2=2,a_3=3$ then $P_1 = (1-2)(1-3)=2$, $P_2 = (2-1)(2-3)=-1... | 5 | [
-0.09033203125,
0.0205078125,
-0.03857421875,
-0.053466796875,
-0.055908203125,
0.0281982421875,
0.1357421875,
0.0034332275390625,
-0.004669189453125,
-0.0111083984375,
0.053955078125,
-0.026123046875,
0.04052734375,
0.0264892578125,
-0.0093994140625,
-0.01171875,
0.00555419921875,
... | 30,145 | 30145 | |
Triple Integral Problem ><
June 2nd 2009, 05:44 AM #1
Triple Integral Problem ><
Hello there!
I have a question I've been stuck on for a couple days...would really appreciate some help! =) =) =)
Find the volume of the region bounded by...
the cone x^2 + y^2 = z^2 (z >= 0)
and the paraboloid z = ... | 5 | [
0.03173828125,
0.034912109375,
-0.004058837890625,
-0.055419921875,
0.060791015625,
-0.05126953125,
-0.0869140625,
0.11181640625,
-0.048095703125,
0.046875,
-0.03466796875,
0.053466796875,
-0.02392578125,
0.0576171875,
-0.018798828125,
0.0164794921875,
-0.0115966796875,
-0.04809570... | 30,146 | 30146 | |
On Absolute Continuity of Conjugations between Circle Maps with Break Points
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 134701, 12 pages
http://dx.doi.org/10.1155/2012/134701
Research Article
On Absolute Continuity of Conjugations between Circle Maps with Break Points
^1School of Mathematical Scien... | 4 | [
-0.022216796875,
-0.007659912109375,
0.0087890625,
-0.07373046875,
0.058349609375,
0.00555419921875,
0.01318359375,
-0.02490234375,
0.0159912109375,
-0.0615234375,
0.06591796875,
0.0113525390625,
0.0230712890625,
-0.029541015625,
0.038330078125,
-0.0126953125,
-0.056640625,
-0.0346... | 30,147 | 30147 | |
Solutions
Note. The incentre of a triangle is the centre of the inscribed circle that touches all three sides. A set is connected if, given two points in the set, it is possible to trace a continuous path from
one to the other without leaving the set. [X¼Z] refers to the area of the plane figure X ¼Z.
121.
Let n ... | 5 | [
-0.056640625,
0.044677734375,
-0.05078125,
-0.0224609375,
-0.095703125,
0.01806640625,
0.154296875,
-0.06787109375,
0.02294921875,
-0.0849609375,
-0.0849609375,
-0.0245361328125,
0.01275634765625,
-0.009765625,
-0.0224609375,
-0.00909423828125,
0.0174560546875,
-0.048095703125,
0... | 30,148 | 30148 | |
Gaussian Elimination
June 8th 2012, 02:58 AM #1
Junior Member
Joined
Apr 2008
Posts
35
Gaussian Elimination
I would normally use Gaussian Elimination to solve a linear system. If we have more unknowns than equations we end up with an infinite number of solutions. Are there any real life applications of
... | 5 | [
-0.1484375,
-0.0186767578125,
-0.0128173828125,
0.024658203125,
0.00168609619140625,
-0.033203125,
-0.046142578125,
-0.002471923828125,
-0.0169677734375,
0.04296875,
0.0400390625,
0.10693359375,
0.06787109375,
0.0047607421875,
-0.0869140625,
-0.006103515625,
0.02490234375,
-0.01452... | 30,149 | 30149 | |
Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 841367, 10 pages
http://dx.doi.org/10.1155/2014/841367
Research Article
Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments
Key ... | 5 | [
-0.03515625,
-0.032958984375,
0.052490234375,
0.0341796875,
-0.01177978515625,
-0.0458984375,
-0.03369140625,
-0.029296875,
0.022705078125,
0.03662109375,
0.05859375,
-0.0859375,
0.061279296875,
0.04443359375,
0.055419921875,
0.0081787109375,
-0.034912109375,
-0.06396484375,
-0.0... | 30,150 | 30150 | |
Homework Help
Posted by andy on Monday, February 1, 2010 at 9:25am.
In a diagram of circle, chords AB and CD
intersect at E. If AE = 3, EB = 4, CE = x, and ED = x - 4, what is the
value of x?
• trig - Reiny, Monday, February 1, 2010 at 9:47am
you have similar triangles, so set up a ratio
(x-4)/4 = 3/x
... | 4 | [
0.00360107421875,
0.06689453125,
-0.0634765625,
-0.07177734375,
-0.020751953125,
0.0079345703125,
0.05810546875,
0.07763671875,
0.10107421875,
-0.0308837890625,
0.0732421875,
-0.06982421875,
0.0419921875,
-0.033935546875,
0.046875,
0.016357421875,
-0.01220703125,
-0.0625,
-0.1367... | 30,151 | 30151 | |
How should I deal with this system of equations?
December 27th 2012, 09:03 PM
Nervous
How should I deal with this system of equations?
$0 = \frac{2}{3} + 2C + D$
$0 = 2 +6B +6C + 4D + 4E$
$6 = 10 + 12B - 6C +10D -5E$
$0 = \frac{1}{3} + B + D$
I dont know where to start, since the first and last ... | 4 | [
-0.1083984375,
-0.02587890625,
0.0306396484375,
-0.0712890625,
0.037841796875,
0.06591796875,
-0.0301513671875,
0.01129150390625,
-0.03125,
0.09228515625,
0.03662109375,
-0.10986328125,
-0.0137939453125,
-0.022216796875,
-0.06201171875,
-0.0086669921875,
-0.038818359375,
0.05834960... | 30,152 | 30152 | |
Finding perimeter of a square.
February 17th 2009, 03:41 PM #1
Newbie
Joined
Feb 2009
Posts
14
Finding perimeter of a square.
A square on a coordinate grid has horizontal and vertical sides. The upper left vertex of the square is located at (-3,4). The perimeter of the square is 40 units.
What are ... | 4 | [
0.0556640625,
0.0205078125,
-0.0255126953125,
-0.05517578125,
-0.03173828125,
0.001495361328125,
0.0174560546875,
0.05615234375,
-0.015625,
-0.01007080078125,
0.060791015625,
0.00616455078125,
0.0419921875,
0.1474609375,
0.061767578125,
-0.035888671875,
0.01104736328125,
0.02124023... | 30,153 | 30153 | |
Conditional Distribution
January 22nd 2011, 12:42 PM #1
Member
Joined
Oct 2009
Posts
218
Conditional Distribution
A card is picked at random from N cards labeled 1,2,...,N and the number that appears is X. A second card is picked at random from cards numbered 1,2,..., X and its number is Y. Find the
... | 5 | [
0.005279541015625,
-0.01483154296875,
-0.03857421875,
-0.017578125,
0.0771484375,
-0.0556640625,
0.0791015625,
-0.058349609375,
0.0035400390625,
-0.10693359375,
0.0032501220703125,
0.026611328125,
-0.040283203125,
0.053955078125,
0.057373046875,
0.05712890625,
0.03662109375,
-0.050... | 30,154 | 30154 | |
How do you gind domain and range of these logarithmic functions?
January 28th 2009, 03:52 PM #1
Super Member
Joined
Nov 2008
Posts
597
How do you gind domain and range of these logarithmic functions?
l(x)=log base 5 of (sqrt(x+5))
AND
m(x)=log(|x|)
AND
n(x)=log((x+1)/(x-1))
I'd l... | 4 | [
-0.0015869140625,
-0.055908203125,
0.023193359375,
-0.05224609375,
0.01129150390625,
-0.05615234375,
-0.0201416015625,
0.01708984375,
0.0283203125,
-0.0167236328125,
0.0238037109375,
-0.00762939453125,
0.0693359375,
0.06494140625,
0.01300048828125,
0.011474609375,
-0.036376953125,
... | 30,155 | 30155 | |
Homework Help
Posted by rakesh on Saturday, December 13, 2008 at 5:42am.
Find a common factor of (527 to the power 379 + 473 to the power 379) and (527 to the power 166 - 473 to the power 166)
• indices - Reiny, Saturday, December 13, 2008 at 8:17am
did you know that for
x^n + y^n, x + y is a factor if n ... | 4 | [
-0.00738525390625,
0.033935546875,
-0.031494140625,
0.017333984375,
0.06982421875,
-0.022216796875,
0.04052734375,
0.00726318359375,
-0.10546875,
-0.0255126953125,
-0.047607421875,
0.0164794921875,
0.024169921875,
0.01019287109375,
0.0103759765625,
0.0113525390625,
-0.095703125,
0.... | 30,156 | 30156 | |
8th grade algebra
Posted by val on Thursday, February 11, 2010 at 11:17pm.
the length of a rectangular garden is 5 feet longer than its width. The garden is surrounded by a 2-foot-wide-sidewalk. The sidewalk has an area of 76 square feet. Find the dimensions of the garden
• 8th grade algebra - Reiny, Thursday, Febr... | 4 | [
0.0111083984375,
0.0693359375,
0.08984375,
0.0306396484375,
0.06494140625,
0.0390625,
-0.05615234375,
0.00225830078125,
-0.052001953125,
0.01092529296875,
0.08203125,
0.0028228759765625,
0.00439453125,
0.035400390625,
-0.01019287109375,
0.068359375,
-0.0458984375,
0.060302734375,
... | 30,157 | 30157 | |
Problem Solve Equation (Any Help - Greatly Appreciated)
April 27th 2012, 12:54 AM
jase03
Problem Solve Equation (Any Help - Greatly Appreciated)
A flower-bed can be schematicly represented as two concentric circles with two different flowers in the inner circle area and outer ring area as shown in the figure bel... | 4 | [
0.0093994140625,
-0.01434326171875,
-0.04052734375,
-0.00885009765625,
0.0517578125,
0.031494140625,
-0.014892578125,
0.0751953125,
0.01080322265625,
-0.08251953125,
-0.026123046875,
-0.01055908203125,
-0.022216796875,
-0.0289306640625,
0.038330078125,
0.05908203125,
-0.029296875,
... | 30,158 | 30158 | |
Homework Help
Posted by pooja on Tuesday, November 8, 2011 at 4:14am.
from the top of a light house the angle of depression of a ship sailing towards it was found to be 30 degrees . after 10 seconds the angle of depresion changes to 60 degrees. assuming that the ship
is sailing at uniform speed. find how much time it ... | 4 | [
-0.002532958984375,
0.06005859375,
0.00433349609375,
0.020263671875,
0.0380859375,
0.01416015625,
-0.0186767578125,
0.0576171875,
-0.0546875,
0.032470703125,
0.0458984375,
-0.0830078125,
0.00836181640625,
0.00543212890625,
0.07275390625,
0.052734375,
-0.09521484375,
0.0103149414062... | 30,159 | 30159 | |
proving limit law by definition
August 2nd 2011, 03:18 AM #1
MHF Contributor
Joined
Nov 2008
Posts
1,401
proving limit law by definition
there is $lim_{x->x_{0}}g(x)=y_{0}$, $f(x)$is continues in $y_{0}$
point. i need to prove that $lim_{x->x_{0}}f\circ g(x)=f(lim_{x->x_{0}}g(x))=f(y_{0})$
by eps... | 4 | [
-0.0703125,
-0.03564453125,
0.08154296875,
-0.03076171875,
0.0250244140625,
0.032470703125,
0.072265625,
-0.010498046875,
-0.029541015625,
-0.00799560546875,
0.038818359375,
0.029296875,
0.0087890625,
-0.04296875,
0.10009765625,
0.053955078125,
0.02294921875,
0.0037994384765625,
... | 30,160 | 30160 | |
Find a polynomial approaching |x| with error 0.1
How can I find a polynomial approaching |x| such that the maximum error is 0.1?
I'm pretty sure that the answer will depend on what interval you are considering. I say this because most of the approximation theorems I am aware of (that would be useful in this case) rely... | 5 | [
-0.026123046875,
0.0191650390625,
0.02001953125,
0.06787109375,
-0.048583984375,
0.0118408203125,
0.031005859375,
0.017822265625,
-0.05029296875,
-0.02490234375,
-0.09619140625,
-0.0030364990234375,
0.119140625,
-0.03466796875,
-0.036376953125,
-0.004180908203125,
0.052490234375,
-... | 30,161 | 30161 | |
Rating Climbs: rating difficulty using full profile data
There's been two principal weaknesses with the methods I've described so far as ratings of difficulty:
1. They neglect the difficulty associated with extended steep sections embedded withing a longer climb. In extreme cases, the optimal rating comes from rating... | 4 | [
-0.026611328125,
-0.026123046875,
0.034423828125,
0.04248046875,
0.00109100341796875,
0.046875,
-0.11181640625,
0.1142578125,
-0.11572265625,
-0.043701171875,
-0.044921875,
-0.0625,
0.0712890625,
0.11474609375,
0.0439453125,
0.0615234375,
0.0185546875,
0.1123046875,
0.05639648437... | 30,162 | 30162 | |
Find value of expression involving roots of a quadratic
September 27th 2011, 12:01 PM #1
Newbie
Joined
Sep 2011
Posts
2
The roots of the equation x^2 - 2x + 7=0 are alpha and beta. Without finding the value of alpha and beta explicitly, determine 2B^3 - 3a^2 + 6 (a being alpha and B being beta)
i pos... | 4 | [
-0.087890625,
0.032958984375,
-0.0306396484375,
0.09716796875,
-0.00823974609375,
0.08349609375,
0.030517578125,
0.00311279296875,
-0.0068359375,
-0.01495361328125,
-0.00872802734375,
-0.09130859375,
0.007659912109375,
0.047119140625,
-0.003021240234375,
0.0272216796875,
-0.0546875,
... | 30,163 | 30163 | |
Homework Help
Posted by Jocelyn on Saturday, February 26, 2011 at 6:24pm.
Use analytic methods to find the global extreme values of the function on the interval and state where they occur.
y=x(2-x)^(1/2), -2<=x<=2
• calculus - agrin04, Sunday, February 27, 2011 at 6:35am
Find the first derivative of the funct... | 5 | [
0.045654296875,
-0.0546875,
0.0191650390625,
0.01373291015625,
-0.045166015625,
-0.0849609375,
-0.1337890625,
0.052490234375,
-0.01470947265625,
0.048583984375,
0.031982421875,
-0.03857421875,
0.03759765625,
0.042236328125,
0.0032958984375,
-0.00830078125,
0.00921630859375,
-0.1464... | 30,164 | 30164 | |
Integrals Example Number 5
Integrals Example Number 5 Let’s move on to the next one. This is going to be the integral of 3/x3 + 2x3/2 - 1 dx. All of these problems by the way, the reason why I have parenthesis around them like
this, basically the reason that they do that is so that you know that the integral or antider... | 5 | [
-0.0693359375,
0.000942230224609375,
0.06201171875,
0.00689697265625,
0.025634765625,
-0.048828125,
-0.01165771484375,
-0.005889892578125,
-0.0024261474609375,
0.057373046875,
-0.00872802734375,
-0.052978515625,
0.016357421875,
0.021240234375,
-0.04052734375,
0.0341796875,
-0.0255126... | 30,165 | 30165 | |
factoring trinomials with a coefficient in the first expression • /r/Algebra
factoring trinomials with a coefficient in the first expression (self.Algebra)
submitted by Aithne205
sorry, this has been archived and can no longer be voted on
I am totally lost on this. I understand factoring simple trinomials. For examp... | 4 | [
-0.04248046875,
0.043212890625,
0.01495361328125,
0.04541015625,
0.068359375,
0.09326171875,
0.0167236328125,
-0.045654296875,
-0.068359375,
0.019287109375,
0.048828125,
-0.0888671875,
0.0218505859375,
0.03125,
0.033203125,
0.07421875,
-0.029052734375,
0.0006256103515625,
-0.1035... | 30,166 | 30166 | |
closest point on graph
December 17th 2006, 04:54 PM #1
Member
Joined
Oct 2006
Posts
88
closest point on graph
Find the Point(s), P(x,y) on the graph of y=4-x^2 so that the distance between two points P and Q(0,2) is a minimum.
i think what you do is
d=squareroot[(x-0)+(y-2)]
d^2=[(x-0)+(y-... | 5 | [
0.048095703125,
-0.00151824951171875,
-0.012939453125,
-0.052490234375,
-0.038818359375,
0.0615234375,
-0.0234375,
0.10791015625,
0.06884765625,
0.0101318359375,
0.07080078125,
0.0439453125,
0.01318359375,
0.0888671875,
-0.00787353515625,
0.0242919921875,
0.0181884765625,
-0.088378... | 30,167 | 30167 | |
Dv/dt=-2e^-x v=2e^-(x/2) anyone willing to try this one?
September 19th 2009, 07:22 PM #1
Junior Member
Joined
Sep 2009
Posts
34
Dv/dt=-2e^-x v=2e^-(x/2) anyone willing to try this one?
Hi,
I am trying to figure out this question but I really can't understand it. Can someone please work through it a... | 4 | [
-0.0306396484375,
-0.0218505859375,
0.08544921875,
0.013427734375,
0.033203125,
-0.020751953125,
-0.078125,
0.042724609375,
-0.0201416015625,
0.050048828125,
0.103515625,
-0.083984375,
-0.006988525390625,
0.045166015625,
0.0194091796875,
-0.00433349609375,
0.0031585693359375,
-0.01... | 30,168 | 30168 | |
Math - Polygons and Quadrilaterals
Posted by Venus on Tuesday, September 10, 2013 at 11:51am.
A rectangle has a diagonal of length 125. If the ratio fo the length of the short side to the length of the long side of the rectangle is 7:24, what is the length of the shorter side of the
rectangle?
• Math - Polygons and... | 4 | [
0.0537109375,
0.047607421875,
0.029541015625,
-0.0169677734375,
-0.029541015625,
0.038818359375,
-0.059326171875,
0.044189453125,
-0.06396484375,
-0.0185546875,
-0.0030975341796875,
-0.01025390625,
-0.0194091796875,
0.0220947265625,
-0.052490234375,
0.0089111328125,
-0.03955078125,
... | 30,169 | 30169 | |
ommons
Overview Package Class Use Tree Deprecated Index Help
PREV CLASS NEXT CLASS FRAMES NO FRAMES
SUMMARY: NESTED | FIELD | CONSTR | METHOD DETAIL: FIELD | CONSTR | METHOD
org.apache.commons.math3.stat.descriptive.moment
Class Variance
java.lang.Object
org.apache.commons.math3.stat.descr... | 4 | [
-0.0064697265625,
0.00927734375,
0.0244140625,
-0.0269775390625,
0.0634765625,
-0.01611328125,
-0.0267333984375,
0.0771484375,
0.0625,
0.0242919921875,
-0.041259765625,
0.0263671875,
-0.016357421875,
-0.0233154296875,
-0.0225830078125,
-0.045654296875,
0.0123291015625,
0.0145263671... | 30,170 | 30170 | |
CMS/CAIMS Summer 2004 Meeting
A path integral formulation for pricing generally exotic derivative securities is presented. Some main features of the approach will be discussed, such as its applicability for pricing virtually
any type of path dependent and early exercise option. In particular, we discuss the use... | 4 | [
-0.04150390625,
-0.042724609375,
0.0010833740234375,
-0.00011587142944335938,
0.03076171875,
-0.06591796875,
0.0235595703125,
0.010498046875,
0.041748046875,
-0.0186767578125,
-0.021484375,
-0.01458740234375,
0.02783203125,
0.0556640625,
-0.002410888671875,
-0.078125,
-0.011413574218... | 30,171 | 30171 | |
Adjoint of linear operators
November 12th 2009, 11:09 PM
Last_Singularity
Adjoint of linear operators
Question: Let $T$ be a linear operator on a finite-dimensional vector space $V$. Show that:
1. $N(T^*T)=N(T)$
2. $rank(T) = rank(T^*)$
3. $rank(A^*A)=rank(AA^*)=rank(A)$
I figured that if I can ... | 5 | [
-0.08935546875,
0.00701904296875,
0.0400390625,
0.0262451171875,
-0.08447265625,
0.045166015625,
0.059814453125,
-0.01434326171875,
-0.031005859375,
0.0517578125,
0.018310546875,
-0.0191650390625,
-0.02001953125,
0.0155029296875,
0.02294921875,
0.01116943359375,
-0.043212890625,
0.... | 30,172 | 30172 | |
three problems I am stuck on
March 4th 2009, 10:01 AM
minivan15
three problems I am stuck on
1. Find all pairs of positive integers 0 < a < b such that gcd(a,b) = 6 and ab = 2160
obviously I could list all integers of this form and check each, I am wondering if there is a more theoretical, efficient way?
... | 4 | [
-0.031494140625,
0.032958984375,
-0.03759765625,
-0.07421875,
-0.005615234375,
0.0615234375,
0.0086669921875,
0.02685546875,
-0.08935546875,
0.0004482269287109375,
-0.00787353515625,
0.04736328125,
0.010498046875,
-0.012939453125,
0.051025390625,
0.038818359375,
0.01104736328125,
-... | 30,173 | 30173 | |
Calculus 1 Related Rates
Posted by jahil on Sunday, November 21, 2010 at 6:50pm.
Water is discharged from a pipeline at a velocity v(in ft/sec) given by v=1240p^(1/2), where p is the pressure (in psi). I f the water pressure is changing at a rate of 0.406 psi/sec, find the
acceleration(dv/dt) of the water when p=33.0 ... | 4 | [
-0.046875,
-0.00921630859375,
0.041748046875,
-0.00970458984375,
0.003814697265625,
-0.07421875,
-0.0751953125,
0.042236328125,
-0.0250244140625,
0.01220703125,
0.01904296875,
-0.01141357421875,
0.03173828125,
0.0380859375,
-0.06689453125,
0.0184326171875,
-0.0186767578125,
0.01879... | 30,174 | 30174 | |
Fourier Transform
7. Application - The Fast Fourier Transform
1. Digital Audio
Pulse code modulation (PCM) is the most common type of digital audio recording, used to make compact disks and WAV files.
CD-ROM
In PCM recording hardware, a microphone converts sound waves into a varying voltage. Then an analog-to-dig... | 5 | [
-0.029052734375,
0.000453948974609375,
-0.04248046875,
-0.04150390625,
-0.01171875,
-0.018798828125,
0.029052734375,
-0.0216064453125,
0.041015625,
0.025146484375,
0.048828125,
-0.00787353515625,
-0.039306640625,
-0.04931640625,
0.006622314453125,
-0.06982421875,
0.02734375,
0.0732... | 30,175 | 30175 | |
the encyclopedic entry of Hereditarily finite sets
In
mathematics
,
hereditarily finite sets
are defined
recursively
as
finite sets
containing only hereditarily finite sets (with the
empty set
as a base case). Informally, a hereditarily finite set is a finite set, the members of which are also finite sets, as... | 4 | [
-0.00946044921875,
0.0267333984375,
-0.0064697265625,
0.080078125,
-0.0228271484375,
0.04150390625,
0.040283203125,
-0.078125,
0.0791015625,
0.00194549560546875,
-0.03564453125,
-0.0284423828125,
0.05322265625,
-0.02099609375,
-0.01531982421875,
-0.040283203125,
-0.0277099609375,
-... | 30,176 | 30176 | |
proving the failure of riemann integrability
May 10th 2008, 07:28 PM
squarerootof2
proving the failure of riemann integrability
i want to prove that the function f:[0,1] -> R where [0,1] is the closed interval 0,1 and R is the set of reals, defined by f(x)=1 if x is rational and 0 otherwise, is not riemann integ... | 5 | [
0.001800537109375,
-0.033203125,
0.032958984375,
-0.01129150390625,
0.03466796875,
0.00872802734375,
0.0615234375,
0.08642578125,
-0.0206298828125,
-0.055908203125,
-0.126953125,
-0.0140380859375,
0.0184326171875,
0.0439453125,
-0.0849609375,
-0.11376953125,
0.0390625,
-0.057128906... | 30,177 | 30177 | |
Polar Curve
February 19th 2008, 12:27 PM #1
Polar Curve
A polar curve is defined by $r=1+cos\theta$.
Show that $\frac{dy}{dx} = -cot\frac{3\theta}{2}$.
I was wondering if anyone could help me with this. This is what I have.
Let $r=f(\theta)$
$tan\alpha=\frac{f(\theta)}{f'(\theta)}=\frac{1+cos \... | 4 | [
-0.018310546875,
-0.061279296875,
-0.068359375,
0.017333984375,
0.0208740234375,
0.057373046875,
-0.012939453125,
0.042724609375,
0.0240478515625,
0.07861328125,
0.039306640625,
0.00933837890625,
-0.08642578125,
0.1044921875,
0.032958984375,
-0.0045166015625,
-0.10791015625,
0.0561... | 30,178 | 30178 | |
Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 847317, 8 pages
http://dx.doi.org/10.1155/2013/847317
Research Article
Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance
^1Department of Math... | 4 | [
-0.0137939453125,
0.07763671875,
-0.053466796875,
-0.042236328125,
-0.00067138671875,
-0.0155029296875,
-0.036376953125,
-0.037353515625,
-0.0286865234375,
0.047119140625,
-0.02099609375,
0.0281982421875,
0.05810546875,
0.0201416015625,
-0.0361328125,
0.060546875,
-0.0007896423339843... | 30,179 | 30179 | |
What 4-digit number abcd satisfies this equation?
What 4-digit number abcd satisfies this equation? 4 * abcd = dcba
Last edited by chinchu; June 8th 2010 at 02:45 AM. Reason: Re-titled.
Since $4 \times 3000 = 12000 > 9999$ so $0 < a \leq 2$ but if $a=1$ from the unit digit of $dcba$ we conclude that $dcba$ is odd but... | 4 | [
-0.05859375,
0.03564453125,
-0.00927734375,
-0.068359375,
-0.0927734375,
0.0615234375,
-0.03271484375,
0.1298828125,
-0.01275634765625,
-0.0264892578125,
-0.031005859375,
-0.0322265625,
0.08447265625,
0.032958984375,
-0.05126953125,
0.00836181640625,
0.0289306640625,
0.0498046875,
... | 30,180 | 30180 | |
Questions I'm struggling with Part 1
October 25th 2009, 11:17 AM
helpmeplease2323
Questions I'm struggling with Part 1
1.)
The table below gives the number of people who attended the U.S. Open tennis tournament in Flushing Meadows for the past 7 years. However, due to a typing error the attendance for 2005 ... | 4 | [
0.060302734375,
0.02392578125,
0.078125,
0.029052734375,
-0.0517578125,
0.12451171875,
0.004547119140625,
0.0174560546875,
-0.021484375,
0.0250244140625,
0.021484375,
-0.000347137451171875,
0.00004506111145019531,
-0.05029296875,
-0.0264892578125,
-0.056396484375,
0.0198974609375,
... | 30,181 | 30181 | |
Exponential Distribution
1. Exploratory Data Analysis
1.3. EDA Techniques
1.3.6. Probability Distributions
1.3.6.6. Gallery of Distributions
1.3.6.6.7. Exponential Distribution
Probability Density The general formula for the probability density function of the exponential distribution is
Function
... | 4 | [
-0.052490234375,
-0.001953125,
0.0125732421875,
0.030517578125,
-0.0284423828125,
-0.043212890625,
0.04638671875,
0.04248046875,
0.0830078125,
0.0172119140625,
0.1328125,
-0.060546875,
0.036376953125,
0.03271484375,
0.0281982421875,
-0.06494140625,
0.025634765625,
-0.0751953125,
... | 30,182 | 30182 | |
Application of Chaos Theory in Trucks' Overloading Enforcement
Journal of Engineering
Volume 2013 (2013), Article ID 245293, 5 pages
http://dx.doi.org/10.1155/2013/245293
Research Article
Application of Chaos Theory in Trucks' Overloading Enforcement
^1Department of Industrial Engineering, Payame Noor University (PN... | 4 | [
-0.0078125,
0.04052734375,
0.0947265625,
-0.0026397705078125,
0.041748046875,
-0.06982421875,
-0.005645751953125,
0.0047607421875,
-0.0091552734375,
-0.00579833984375,
-0.006072998046875,
0.09375,
0.0771484375,
-0.0361328125,
-0.07763671875,
0.04248046875,
0.07470703125,
0.00424194... | 30,183 | 30183 | |
Precalculus angle-side-side, please help!!
October 14th 2008, 01:31 PM #1
Newbie
Joined
Oct 2008
Posts
1
Precalculus angle-side-side, please help!!
Hi, I really need help on this problem please. I realize that because it's angle side side, and one is shorter than the other, there will be two sets of solu... | 4 | [
-0.10400390625,
0.1396484375,
-0.03857421875,
-0.007110595703125,
0.0238037109375,
0.018310546875,
-0.0191650390625,
0.027099609375,
-0.00933837890625,
-0.0291748046875,
0.04638671875,
-0.0791015625,
-0.03857421875,
0.1181640625,
0.052490234375,
-0.0224609375,
-0.01385498046875,
-0... | 30,184 | 30184 | |
Help me grasp a better understanding of the Von Neumann universe • /r/math
all 8 comments
[–]protocol_7Arithmetic Geometry11 points12 points13 points
sorry, this has been archived and can no longer be voted on
We're talking about set theory, and in particular ZFC, which is a material set theory — this means that eve... | 4 | [
-0.01513671875,
-0.03369140625,
0.0166015625,
0.016357421875,
0.0341796875,
0.06396484375,
-0.028076171875,
0.03271484375,
-0.0155029296875,
-0.056884765625,
-0.0284423828125,
-0.04052734375,
0.05419921875,
-0.033203125,
-0.00860595703125,
-0.054931640625,
0.0419921875,
-0.05224609... | 30,185 | 30185 | |
Hybrid Viscosity Approaches to General Systems of Variational Inequalities with Hierarchical Fixed Point Problem Constraints in Banach Spaces
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 945985, 18 pages
http://dx.doi.org/10.1155/2014/945985
Research Article
Hybrid Viscosity Approaches to General Syst... | 4 | [
-0.00836181640625,
0.023681640625,
0.099609375,
-0.037353515625,
-0.005218505859375,
0.029541015625,
-0.038330078125,
0.08642578125,
0.0419921875,
-0.022705078125,
-0.03515625,
-0.01043701171875,
0.095703125,
0.0235595703125,
-0.005340576171875,
-0.0019073486328125,
0.068359375,
-0... | 30,186 | 30186 | |
proving if such transformation exists
June 24th 2011, 03:11 AM #1
MHF Contributor
Joined
Nov 2008
Posts
1,401
proving if such transformation exists
is there a transformation which follows these rules:
T: $R^4$-> $R^4$
T(-1,1,0,1)=(1,-1,2,1)
T(1,1,1,0)=(2,3,1,-1)
T(-1,5,2,3)=(3,7,0,-3)
... | 4 | [
-0.03125,
0.033447265625,
0.007293701171875,
-0.027587890625,
-0.002899169921875,
-0.03466796875,
0.032958984375,
-0.044189453125,
-0.000858306884765625,
-0.06298828125,
0.010986328125,
-0.0299072265625,
0.0157470703125,
0.0242919921875,
-0.10693359375,
-0.0361328125,
-0.083984375,
... | 30,187 | 30187 | |
orthogonal matrix
February 6th 2009, 12:30 AM #1
Junior Member
Joined
Dec 2008
Posts
30
orthogonal matrix
two problems that I have problem with:
1. let A be orthogonal matrix that is triangular, prove that A is diagonal.
2.let $<br /> R^n = U_1 + U_2 <br /> <br />$ be true, does $<br /> R^n = U... | 4 | [
-0.09375,
0.0294189453125,
-0.058837890625,
-0.047607421875,
-0.024658203125,
-0.049560546875,
-0.07421875,
-0.0439453125,
-0.01019287109375,
0.047607421875,
0.007049560546875,
0.0751953125,
0.034912109375,
-0.01422119140625,
-0.04248046875,
0.031494140625,
0.021728515625,
-0.05688... | 30,188 | 30188 | |
Homework Help
Posted by Sandra on Sunday, March 22, 2009 at 3:58pm.
-x/9=1/16
This is suppose to be solved using the multiplication principle. If possible please show me not just the answer but how you came up with it so I understand how to do these problems. Thank you
• math 116 - Reiny, Sunday, March 22, 2009 at... | 4 | [
-0.0181884765625,
0.0458984375,
0.05078125,
-0.056396484375,
-0.0400390625,
-0.041259765625,
-0.022216796875,
0.01513671875,
-0.064453125,
-0.05419921875,
0.0517578125,
-0.0673828125,
0.049072265625,
0.08740234375,
-0.044189453125,
0.04248046875,
-0.00372314453125,
0.1201171875,
... | 30,189 | 30189 | |
Common Fixed Points for JH-Operators and Occasionally Weakly g-Biased Pairs under Relaxed Condition on Probabilistic Metric Space
Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 846315, 6 pages
http://dx.doi.org/10.1155/2013/846315
Research Article
Common Fixed Points for JH-Operators and O... | 5 | [
-0.08740234375,
-0.023193359375,
0.08544921875,
-0.0673828125,
-0.01153564453125,
0.00167083740234375,
0.07958984375,
-0.0145263671875,
0.03955078125,
-0.052490234375,
-0.0035247802734375,
0.032958984375,
0.0673828125,
-0.061767578125,
0.0029449462890625,
-0.053955078125,
0.048339843... | 30,190 | 30190 | |
New Calculus Problem
October 29th 2006, 11:13 AM #1
Newbie
Joined
Oct 2006
Posts
14
Sorry to ressurect this, but I have another assignment on similar subject matter. I figured it would be better to ask again her, than make a new thread.
Both of these types I remember covering in class, but can't seem... | 5 | [
-0.031982421875,
0.0830078125,
0.0225830078125,
0.055908203125,
0.00885009765625,
-0.0218505859375,
-0.007293701171875,
-0.0242919921875,
0.06591796875,
0.052490234375,
0.10888671875,
-0.03662109375,
-0.007293701171875,
0.0096435546875,
0.1064453125,
0.0245361328125,
-0.0576171875,
... | 30,191 | 30191 | |
Differentiate by definition - please help
April 17th 2013, 04:34 PM #1
Newbie
Joined
Mar 2013
From
USA
Posts
8
Differentiate by definition - please help
Can someone confirm I have done this correctly?
Y = 3x^4 + 2x^3 + 4x at P (x, y), let Q (X + Δx, y+Δy)
lim(Δx->0)
3(x+Δx)^4 + 2(x+Δx)^3... | 4 | [
0.00946044921875,
-0.026611328125,
-0.0179443359375,
-0.0308837890625,
0.0306396484375,
0.032470703125,
0.0181884765625,
-0.06591796875,
0.04345703125,
-0.017578125,
0.1171875,
-0.041748046875,
-0.015625,
0.017578125,
0.06884765625,
0.0255126953125,
-0.07421875,
-0.0213623046875,
... | 30,192 | 30192 | |
Proposition 17
If magnitudes are proportional taken jointly, then they are also proportional taken separately.
Let AB, BE, CD, and DF be magnitudes proportional taken jointly, so that AB is to BE as CD is to DF.
I say that they are also proportional taken separately, that is, AE is to EB as CF is to DF.
Take equimu... | 4 | [
0.0123291015625,
-0.005645751953125,
0.005889892578125,
-0.0289306640625,
0.0625,
0.053466796875,
0.0184326171875,
-0.011962890625,
0.0013580322265625,
0.007720947265625,
0.083984375,
-0.07275390625,
0.0269775390625,
0.0228271484375,
0.00946044921875,
-0.0191650390625,
-0.08349609375... | 30,193 | 30193 | |
Trig help pls :(
March 17th 2008, 09:48 AM #1
Member
Joined
Dec 2007
Posts
80
I need to solve the following for 0degrees<and equal to x <equal to 360
1) tan x=1 which i did tan^-1=45 +180=225
but i have others such as cos x=0.5 , cos x=-0.9 but i dnt know what to do!
Also without a calcul... | 4 | [
-0.0791015625,
0.03173828125,
-0.06103515625,
0.00433349609375,
-0.05615234375,
0.04736328125,
-0.01043701171875,
-0.0035400390625,
0.001556396484375,
0.033203125,
0.068359375,
-0.0791015625,
0.064453125,
0.052001953125,
0.06591796875,
0.003692626953125,
-0.08203125,
0.02978515625,... | 30,194 | 30194 | |
Iterations of real
Iterations of real quadratic functions
Iteration diagram
We can trace real maps x[n+1] = f( x[n] ) dynamics on 2D the "iteration diagram" to the left below. Dependence x[n] on n is plotted to the right.
Controls: Drag the blue curve to change C and x[o] value. Press <Enter> to set new parameter va... | 4 | [
-0.043701171875,
-0.0458984375,
-0.037109375,
0.07568359375,
-0.034423828125,
-0.0010223388671875,
-0.031005859375,
0.06298828125,
0.06103515625,
-0.11767578125,
0.0771484375,
0.057861328125,
-0.039306640625,
-0.00946044921875,
-0.064453125,
0.06640625,
-0.05419921875,
-0.028442382... | 30,195 | 30195 | |
maths --plse help me..
Posted by Meenakshi on Thursday, December 13, 2012 at 11:36am.
The pilot of an aircraft flying horizontally at a speed of 1200 Km/hr observes an angle of depression of a point on the ground changes from 30 degree to 45 degree in 15 seconds. Find the height of
the aircraft at which it is flying?
... | 4 | [
-0.01519775390625,
0.05078125,
-0.0015106201171875,
-0.06884765625,
0.0859375,
0.048828125,
0.0228271484375,
0.052001953125,
0.035400390625,
0.03955078125,
0.1044921875,
-0.0086669921875,
-0.056640625,
-0.004608154296875,
-0.0390625,
0.03759765625,
-0.00970458984375,
0.010375976562... | 30,196 | 30196 | |
the encyclopedic entry of evolute
In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature. Equivalently, it is the envelope of the normals to a curve. The original curve is an
involute of its evolute. (Compare and )
History
Apollonius
(c. 200 BC) discussed evolutes... | 4 | [
-0.033447265625,
-0.036865234375,
-0.06640625,
0.013427734375,
-0.04931640625,
-0.00701904296875,
0.0341796875,
0.09033203125,
0.0009765625,
-0.0167236328125,
0.0869140625,
0.0634765625,
0.0301513671875,
0.00982666015625,
-0.0673828125,
-0.0002593994140625,
-0.0556640625,
-0.006530... | 30,197 | 30197 | |
Using worksheet functions for quality control
This article is an excerpt from Business Analysis with Microsoft® Excel, Second Edition by Conrad Carlberg and is available in electronic format on Safari® HelpDesk Online.
Safari puts the power of a comprehensive Microsoft Office library right on your desktop. This book ... | 5 | [
-0.05029296875,
0.0400390625,
-0.04833984375,
-0.00482177734375,
-0.0751953125,
0.00775146484375,
-0.0017547607421875,
0.0208740234375,
0.056396484375,
0.052001953125,
-0.00811767578125,
-0.02587890625,
0.061767578125,
-0.06201171875,
-0.0113525390625,
0.034912109375,
0.1201171875,
... | 30,198 | 30198 | |
Find the Maclaurin series for the function using definition of a Mclaurin series
December 8th 2012, 03:35 AM #1
Find the Maclaurin series for the function using definition of a Mclaurin series
Find the Maclaurin series for the function using definition of a Mclaurin series. Also, find the radius of convergence.
... | 5 | [
-0.035888671875,
-0.12353515625,
0.0299072265625,
0.08740234375,
-0.01123046875,
-0.04052734375,
-0.01080322265625,
-0.00299072265625,
0.06689453125,
-0.004669189453125,
0.036376953125,
-0.03759765625,
-0.0274658203125,
0.06640625,
-0.061767578125,
-0.06689453125,
0.00390625,
-0.06... | 30,199 | 30199 |