content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Stagnation Temperature - Real Gas Effects
As an object moves through a gas, the gas molecules near the object are disturbed and move around the object. Aerodynamic forces are generated between the gas and the object and the magnitude of
these forces depend on many factors associated with the object and the gas. The spe... | 4 | [
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-0... | 19,500 | 19500 | |
Integration question
Note $\frac{4x^2 + 3x + 1}{x(2x + 1)} = \frac{1}{x} - \frac{1}{2x + 1} + 2$.
How do you know to break it up like this?
For integrands involving improper polynomial fractions, it's a common technique to rewrite the integrand as a proper polynomial fraction. Improper polynomial fractions are fracti... | 5 | [
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0.08203125,
0.0... | 19,501 | 19501 | |
Inverse Laplace Transform
November 6th 2009, 05:24 PM
harbottle
Inverse Laplace Transform
Hi,
I need to find the inverse Laplace transform of
$F(s) = s^{-2} \tanh(sT/2)$.
I suspect I have to use the period definition for Laplace transforms but I can't see how to make it fit. Any tips?
November 6t... | 5 | [
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-0.056... | 19,502 | 19502 | |
Does a diffeomorphism between manifolds induce a diffeomorphism on cotangent space?
I'm reading a book, and this seems to be true, but they don't say why, and I'm not sure.
Re: Does a diffeomorphism between manifolds induce a diffeomorphism on cotangent spac
I'm a little confused. While it is true that the cotangent... | 5 | [
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Explanation Please
April 1st 2009, 07:19 AM
bearej50
Explanation Please
Mark found the mean of 26, 32, 22, 35, 25 using the strategy below. Why is his strategy valid???
"I guessed the mean was 30. Then I found the difference between each data point and 30 and I got -4, 2, -8, 5, -5. The average of these num... | 4 | [
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Trigonometric Formulas Learning
Introduction:
Trigonometric formulas used to express the trigonometric functions. Trigonometric individuality and formulas are based on trigonometric functions. The essential trigonometric functions are Sine,
Cosine and tangent functions of a triangle takes an angle and give the sides ... | 4 | [
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-... | 19,505 | 19505 | |
Integrating over a Manifold
October 17th 2010, 06:42 AM #1
Member
Joined
Aug 2009
Posts
130
Integrating over a Manifold
First let me write out the definition of a manifold given in my book:
Let $k > 0$. A k-manifold in $\mathbb{R}^n$ of class $C^r$ is a subspace $M$ of $\mathbb{R}^n$ having the foll... | 4 | [
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Angle between 2 vectors using 1) Dot product and 2) cross product gives diff. answer?
1. The problem statement, all variables and given/known data
Using these 2 vectors:
[itex] \vec u = (3,-4,0)[/itex]
[itex] \vec v = (1,1,1)[/itex]
I must verify that theta is the same with these 2 equations:
Dot product
[itex] \v... | 4 | [
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k-th convergent
January 10th 2009, 03:24 AM #1
Dear friends, I have a problem with the following question.
I will denote
$\langle a_{0},a_{1},\ldots,a_{k}\rangle:=a_{0}+\dfrac{1}{a _{1}+\frac{1}{\frac{\vdots}{a_{k-1}+\frac{1}{a_{k}}}}}$
and call by $k$-th convergent.
And define
$<br /> p_{k}:=<... | 5 | [
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Try to solve that Question of Green theorm
$\oint_C (y^2dx + x^2 dy) = \iint_D \left( \frac{\partial x^2}{\partial x} - \frac{\partial y^2}{\partial y} \right) \ dA =\iint_D (2x - 2y) dA = 2\int_0^1 \int_0^{1-x} x - y \ dy \ dx$ You should be
able to do it frum heir.
[quote]Find $\oint_C y^2 \, dx + x^2 \, dy$ where t... | 5 | [
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multiplying squared fractions
(1/6 squared) multiplied by 9/25 then that answer is divided by 2/5 squared
duckpluckie Hi, duckpluckie, expand all squares: $\frac{\left(\frac{1}{6}\right)^2\codt\frac{9}{25}} {\frac{2}{5}}$$=\frac{1}{36}\cdot\frac{9}{25}\cdot\frac{5}{2}$ Simplify and you'll get: $\frac{1}
{40}$ Bye EB
... | 4 | [
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2, 5, 8, 11, 14... (q3)
February 12th 2006, 01:58 PM #1
Junior Member
Joined
Oct 2005
Posts
50
2, 5, 8, 11, 14... (q3)
Sequence given: 2, 5, 8, 11, 14...
Investigate which products of the sequence members are in the sequence and prove it?
Natasha
Sequence given: 2, 5, 8, 11, 14...
Inve... | 4 | [
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The CircuitCalculator.com Blog
I published the following Zoho Sheet to calculate the PCB copper surface area to cool a device based on its power dissipation.
It is embedded below and can also be opened in its own window.
Regarding the PCB Trace Width Calculator [1], Regit asks:
(a.) What is the relationship between ... | 4 | [
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What is temperature?
D H
A relation between entropy and internal energy:
$$\frac 1 T = \left(\frac {\partial S} {\partial E}\right)_{V,N}$$
You should have used the Stefan-Boltzman law. What are you using here? The units aren't even correct with your equation. The left-hand side has units of mass/time^3, the righ... | 5 | [
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Approximating the Inverse of a Square Matrix with Application in Computation of the Moore-Penrose Inverse
Journal of Applied Mathematics
Volume 2014 (2014), Article ID 731562, 8 pages
http://dx.doi.org/10.1155/2014/731562
Research Article
Approximating the Inverse of a Square Matrix with Application in Computation of... | 5 | [
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Graphical Tools for Network Meta-Analysis in STATA
Abstract
Network meta-analysis synthesizes direct and indirect evidence in a network of trials that compare multiple interventions and has the potential to rank the competing treatments according to the
studied outcome. Despite its usefulness network meta-analysis is ... | 4 | [
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Derivation of relationship between carrier density and current
March 15th 2011, 08:09 AM
jonm84
Derivation of relationship between carrier density and current
Hi there,
I'm new here so I'm not sure if this is in the best section, but here goes...
I'm trying to establish how a formula (relating the carr... | 5 | [
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Why holomorphic ?
June 17th 2011, 02:25 AM
Aki
Why holomorphic ?
I cannot understand the following statement in the proof of Lemma 8.7 in "Lectures on Riemann Surfaces" by Otto Forster.
Quote:
$\phi(z)=\frac{1}{2 \pi i}\int_{|w-w_0|=\epsilon}w\frac{F_w(z,w)}{F(z,w)}dw, \;\;\; \left( F_w := \frac{\part... | 4 | [
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A few College Algebra questions
January 26th 2008, 02:57 PM #1
Newbie
Joined
Jan 2008
Posts
17
A few College Algebra questions
Hello Math Help Forum!
Determine how many solutions exist-
Use either elimination or substitution to find the solutions (if any)
1) 4x = 8 and 5y = 15
I was thi... | 4 | [
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Patent US6453442 - Two stage S—Random interleaver
Publication number US6453442 B1
Publication type Grant
Application number US 09/378,281
Publication date Sep 17, 2002
Filing date Aug 20, 1999
Priority date Aug 20, 1999
Fee status Paid
Publication number 09378281, 378281, US 6453442 B1, US 64534... | 4 | [
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0.0... | 19,519 | 19519 | |
What are the hamilton equations of motion for homogeneous lagrangians?
For a Lagrangian [itex]L(x^k,\dot{x}^k)[/itex] which is homogeneous in the [itex]\dot{x}^k[/itex] in the first degree, the usual Hamiltonian vanishes identically. Instead an alternative conjugate
momenta is defined as
[itex]y_j=L\frac{\partial L}{\... | 4 | [
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New partition function record:
fredrikj.net / blog /
New partition function record: p(10^20) computed
March 2, 2014
The partition function p(n) counts the number of partitions of n, i.e. the number of ways n can be written as a sum of positive integers when disregarding the order of the terms. For example, 4 has
th... | 4 | [
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Mean curvature of a surface (just stuck with some simplifying!)
February 1st 2013, 06:52 AM #1
Newbie
Joined
Feb 2013
From
Guernsey, CI
Posts
16
Mean curvature of a surface (just stuck with some simplifying!)
Hi everyone, new here and trying to calculate the mean curvature for the following surface:
... | 4 | [
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Trigo question. Help needed. Need to pass up on tomorrow.
July 15th 2008, 06:53 AM
simonsong
Trigo question. Help needed. Need to pass up on tomorrow.
Given that $\cos x = -\frac{2}{3}$ and $\sin y = -\frac{1}{\sqrt 6}$, that $0^\circ\le x \le360^\circ$ and that $x$ and $y$ are in the same quadrant, find, withou... | 4 | [
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integration problem
December 23rd 2008, 08:46 AM #1
Newbie
Joined
Dec 2008
Posts
6
integration problem
hallo all,
I have the following problem:
Sorry, made an error and typed the wrong one.
$<br /> \int<br />$ x^(-2 ). e^x dx is the one I mean.
Is it even possible to solve this?
... | 5 | [
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Find the last 2 digits of 65*29*37*63*71*87*62
Author Message
TAGS:
Find the last 2 digits of 65*29*37*63*71*87*62 [#permalink] 04 Nov 2009, 00:14
... | 4 | [
0.0291748046875,
0.052978515625,
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0.042724609375,
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0.00811767578125,
-0.138671875,
0.0... | 19,525 | 19525 | |
Distance and Time Problem
May 19th 2011, 06:49 AM #1
Newbie
Joined
May 2011
Posts
11
Distance and Time Problem
A train leaves a station at noon and travels east at the rate 30 mi/hr. At 2 P.M. of the same day a second train leaves the station and travels south at the rate 25 mi/hr. Express the distance d... | 4 | [
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0.038330078125,
0.0152587890625,
0.... | 19,526 | 19526 | |
Polynom over finite field
May 12th 2008, 02:07 PM #1
Member
Joined
May 2008
Posts
75
Hi people! I would like to show that the polynom f=x^4-16x^2+4 is reducible over any finite field K. Unfortunately I do not have any ideas how to do this (maybe by using that any element in K can
be written as sum of ... | 5 | [
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0.0074462890625,
-0.03271484375,
0.0419921875,
-0.10595703125,
0.068359375,
0.02587890625,
0.01239013671875,
-0... | 19,527 | 19527 | |
Uniform Approximate Estimation for Nonlinear Nonhomogenous Stochastic System with Unknown Parameter
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 421754, 20 pages
http://dx.doi.org/10.1155/2012/421754
Research Article
Uniform Approximate Estimation for Nonlinear Nonhomogenous Stochastic System... | 4 | [
-0.059814453125,
-0.0380859375,
0.018310546875,
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0.037109375,
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0.034423828125,
0.0098876953125,
-0.0263671875,
... | 19,528 | 19528 | |
Counters - Math Genius
Answer
Move the counters in the following order.
The moves in brackets are to be made four times in succession. 12, 1, 3, 2, 12, 11, 1, 3, 2 (5, 7, 9, 10, 8, 6, 4), 3, 2, 12, 11, 2, 1, 2.
The grasshoppers will then be reversed in forty-four moves.
.But to employ a full economy of moves we have ... | 5 | [
-0.00128173828125,
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-0.125,
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0.0161132... | 19,529 | 19529 | |
Math Help
April 22nd 2006, 05:33 PM #1
Newbie
Joined
Apr 2006
Posts
8
translate
translate and solve
twicw the difference of three and n is the same as nine subtracted from negative one times n
maxmac97
translate and solve
twicw the difference of three and n is the same as nine subtrac... | 4 | [
-0.0947265625,
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0.0267333984375,
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0.03369140625,
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-0.0615234375,
... | 19,530 | 19530 | |
Linear Regression: Mean square error (MSE)
May 20th 2009, 03:11 AM
kingwinner
Linear Regression: Mean square error (MSE)
Simple linear regression model:
Y_i = β0 + β1*X_i + ε_i , i=1,...,n
where n is the number of data points, ε_i is random error
Let σ^2 = V(ε_i) = V(Y_i)
Then an unbiased est... | 4 | [
-0.00165557861328125,
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0.08984375,
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0.062255859375,
-0.0053100585... | 19,531 | 19531 | |
Properties of the product topology
February 10th 2010, 11:04 PM #1
Properties of the product topology
Hello friends. I am doing an independent study course, and it is a bit of the Moore method style. So, right now I am studying product topology and have come up with some conjectures. I have
"proof" for all of... | 4 | [
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-0.001228332519... | 19,532 | 19532 | |
Improving Streaming Capacity in Multi-Channel
International Journal of Digital Multimedia Broadcasting
Volume 2012 (2012), Article ID 807520, 9 pages
http://dx.doi.org/10.1155/2012/807520
Research Article
Improving Streaming Capacity in Multi-Channel P2P VoD Systems via Intra-Channel and Cross-Channel Resource Alloca... | 4 | [
-0.0081787109375,
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0.0986328125,
-0.0072326... | 19,533 | 19533 | |
test statistics/critical regions
June 24th 2009, 05:51 PM #1
Newbie
Joined
Jun 2009
Posts
18
test statistics/critical regions
Please help me! I am stuck on this chapter and this question seemed to have it all, so its probably the best one to ask. Thank you!
Let X and Y denote the weights in grams o... | 5 | [
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-0.0432... | 19,534 | 19534 | |
Finding integers when I have their lcm and gcd
March 17th 2009, 12:27 PM
gianni
Finding integers when I have their lcm and gcd
Find all pairs of integers (m, n) such that their greatest common divisor is 1155 and their least common multiple 86625.
This problem confuses me quite a bit. I just don't see how ... | 4 | [
-0.031982421875,
0.0205078125,
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0.0673828125,
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0.07373046875,
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0.01141357421875,
0.005706787109375,
-0.01171875,
0.0283203125,
-... | 19,535 | 19535 | |
Why are quadratic equations set equal to 0?
First, quadratic equations are NOT necessarily set equal to 0. That is one way of solving a quadratic equation because then if we
can
factor we can use the "zero product property": if ab= 0 then either a= 0 or b= 0. If ab equals any number other than 0, that there are many ... | 4 | [
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0.10791015625,
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0.037353515625,
0.01141357421875,
-0.0... | 19,536 | 19536 | |
On the 2-MRS Problem in a Tree with Unreliable Edges
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 743908, 11 pages
http://dx.doi.org/10.1155/2013/743908
Research Article
On the 2-MRS Problem in a Tree with Unreliable Edges
^1Zhejiang University of Water Resources and Electric Power, Hangzhou, Zhejia... | 4 | [
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0.0478515625,
-0.07421875,
0.046875,
-0.06591796875,
0.026123046875,
0.0168... | 19,537 | 19537 | |
Zany probablity problem.....
February 11th 2009, 06:35 AM #1
Senior Member
Joined
Jan 2009
Posts
296
Zany probablity problem.....
A lady had a biopsy on a possibly cancerous tumor. She instructs the doctor to flip a coin. If it comes up heads, will call if the news is good but not if it is bad. If it com... | 5 | [
-0.00531005859375,
0.03515625,
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0.056640625,
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0.0169677734375,
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0.08544921875,
0.0296630859375,
-0.0620117187... | 19,538 | 19538 | |
Ratio (J/S) - Constant Power
JAMMING TO SIGNAL (J/S) RATIO - CONSTANT POWER [SATURATED] JAMMING
The following table contains a summary of the equations developed in this section.
This section derives the J/S ratio from the one-way range equation for J and the two-way range equation for S, and deals exclusively wit... | 5 | [
-0.0225830078125,
0.014892578125,
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0.0155029296875,
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-0.001007080078125,
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0.01470947265625,
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0.10986328125,
-0.0625,
0.037841796875,
0.0018310546875,
0.0986328125,
0.... | 19,539 | 19539 | |
Calculus II integration by parts of exponent functions
July 10th 2013, 05:54 PM #2
July 10th 2013, 05:29 PM #1
Newbie
Calculus II integration by parts of exponent functions
Re: Calculus II integration by parts of exponent functions
Re: Calculus II integration by parts of exponent functions
Topsquark is correct... | 5 | [
-0.0269775390625,
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0.06982421875,
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-0.0576171875,
-0.0205078125,
0.013671875,
-0.0079345703125,
-0.00772094... | 19,540 | 19540 | |
Correlation of combined variables
August 6th 2010, 02:54 AM
mpb
Correlation of combined variables
Dear all
I have got the following problem:
Given are two correlated, normally distributed variables A and B and corresponding variances and correlation. Both means are zero.
Now each variable is combi... | 5 | [
-0.05517578125,
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0.08154296875,
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0.047119140625,
-0.045166015625,... | 19,541 | 19541 | |
A Generalized Alternative Theorem of Partial and Generalized Cone Subconvexlike Set-Valued Maps and Its Applications in Linear Spaces
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 370654, 9 pages
http://dx.doi.org/10.1155/2012/370654
Research Article
A Generalized Alternative Theorem of Partial and Ge... | 4 | [
0.061279296875,
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Show it converges uniformly
November 15th 2009, 11:18 AM #1
Show it converges uniformly
Suppose that g : R $\rightarrow$ R is such that there exists r $\in$ (0,1) with the property that |g'(x)| $\leq$ r for every x $\in$ R. Let $F_{0}$ : R $\rightarrow$ R be a bounded function and
define recursively $F_{n}(x)... | 5 | [
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0.041015625,
-0.05859... | 19,543 | 19543 | |
Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems
International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 174796, 31 pages
http://dx.doi.org/10.1155/2011/174796
Research Article
Hybrid Proximal-Point Met... | 5 | [
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0.046142578125,
0.031982421875,
-0.0683... | 19,544 | 19544 | |
Topology Boundry Question
March 1st 2009, 03:47 PM
flaming
Topology Boundry Question
For each $n\in Z_+$, let $B_n = {n, n+1, n+2, ....}$ and consider the collection B = ${B_n | n\in Z_+}$
(a) Show that B is a basis for a topology for $Z^+$
(b) Show thte the topology on X generated by B is not Hausdorf... | 4 | [
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0.0205078125,
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-0.... | 19,545 | 19545 | |
Rate-Independent Constructs for Chemical Computation
Abstract
This paper presents a collection of computational modules implemented with chemical reactions: an inverter, an incrementer, a decrementer, a copier, a comparator, a multiplier, an exponentiator, a
raise-to-a-power operation, and a logarithm in base two. Unl... | 4 | [
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... | 19,546 | 19546 | |
Page:Mars - Lowell.djvu/283
From Wikisource
This page has been
validated
.
The critical velocity at the surfaces of the planets is found as follows: —
Using the usual symbols we have:
$fdt=dv\,$
... | 4 | [
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0.010986328125,
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0.0123291015625,
0.1181640625,
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0.11669921875,
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0.0272216796875,
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-0.1044921875,
-0.041748046875,
-0.000568389892578125,
0.041259... | 19,547 | 19547 | |
Physics Homework Help
Circular motion is caused when an object experiences just the right amount of net force directed toward the center of the circle or curve. The acceleration of an object in uniform circular motion is
always toward the center of the circle. The acceleration and the force causing it are called centr... | 5 | [
0.02490234375,
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0.0218505859375,
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0.0267333984375,
0.003692626953... | 19,548 | 19548 | |
Find curves C1 and C2 that are not closed
March 18th 2008, 07:25 AM #1
Newbie
Joined
Mar 2008
Posts
2
Find curves C1 and C2 that are not closed
f = gradƒ, where ƒ(x,y)=sin(x-2y)
Find curves C1 and C2 that are not closed and satisfy the equations
i) ∫C1 F•dr = 0
ii) ∫C2 F•dr = 1
1)... | 5 | [
-0.0026397705078125,
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0.046875,
0.01708984375,
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0.0185546875,
-0.027587890625,
0.005523681640625,
-0.09375,
-0.0952148437... | 19,549 | 19549 | |
Wolfram Demonstrations Project
Diocles's Solution of the Delian Problem
The Demonstration constructs a cissoid and and uses it to show Diocles's solution of the problem of doubling the cube, also known as the Delian problem.
Suppose that a cube of side length is given; it has volume . To double the cube means to cons... | 4 | [
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-0.0791015625,
0.088... | 19,550 | 19550 | |
Ideal gas - monatomic or diatomic?
Register to reply
by shyguy79
Tags: diatomic, ideal, monatomic
P: 102 1. The problem statement, all variables and given/known data
5 moles of an idea gas at 300K at ... | 4 | [
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0.02099609375,
-0.039306640625,
0.0... | 19,551 | 19551 | |
Unique fixed point
March 12th 2011, 11:29 AM #1
Newbie
Joined
Mar 2011
Posts
6
Unique fixed point
I'm having a problem understanding this:
Show that if $U$ is a continuous map such that $U^n:M \rightarrow M$ is a strict contraction for some fixed integer $n$, then $U$ has a unique fixed point.
... | 5 | [
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-0.0220947265625,
0.01324462890625,
0.0301513671875,
-0... | 19,552 | 19552 | |
Random sample
May 8th 2008, 11:52 AM #1
Member
Joined
Apr 2008
Posts
132
Random sample
A simple random sample of size 10 drawn from a normal distribution yielded a sample mean of 100 and a sample variance of 64.
i) Obtain a 99% confidence interval for the true mean of the population
ii) What wou... | 4 | [
0.09033203125,
0.0546875,
0.044921875,
0.00653076171875,
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0.01953125,
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0.0206298828125,
-0.048828125,
0.0390625,
-0.00331115722656... | 19,553 | 19553 | |
Another Squeeze Theorem Question
January 22nd 2011, 11:19 AM #1
Member
Joined
Jan 2011
Posts
156
Another Squeeze Theorem Question
OK, I think that I have this Squeeze Theorem figured out. Can somebody please look at this to tell me if I do?
Proove: $\displaystyle \lim_{x\to 0 } \sqrt{x^3+x^2}sin \fr... | 4 | [
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0.06298828125,
-... | 19,554 | 19554 | |
Trigonometry/The sine of 18 degrees
The trigonometric functions of angles that are multiples of 3º can all be expressed as surds. This page will only deal with angles that are multiples of 18º.
Consider the equation
sin(5x) - 1 = 0.
Clearly, the only solutions are that 5x = 90º, 90º + 360º, 90º + 2x360º, 90º + 3... | 4 | [
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0.08056640625,
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-0.053466796875,
0... | 19,555 | 19555 | |
I need help on a few things
June 20th 2008, 10:48 AM
wren17
I need help on a few things
1. The limit, as x tends to 2, of the function $y=\frac{x^2 + bx - 28}{x - 2}$ exists, and is equal to 16. What is the value of the whole number coefficient b?
2. The first derivative of $y = (6x^3 + 11)^9$ is of the for... | 5 | [
-0.0361328125,
0.04345703125,
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0.0625,
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0.0859375,
0.003265380859375,
-0.05615234375,
0.0390625,
-0.0419921875,
-0.04150390625,
-0.0546875,
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0.032958984375,
-0.010986328125,
-0.0264892578125,
-0.092773437... | 19,556 | 19556 | |
linear transformation
April 30th 2008, 11:19 AM
fatboy
linear transformation
getting ready for final need some help
(1) 1
Question: R squared through R cubed is a linear transformation.if T(1)= (1),
1 1
T(1 = (0) find T(2)
-1) 1 (4)
have no idea
May 1st 2008, 12:29 AM
Opalg
Quote... | 5 | [
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0.0030670166015625,
0.0010986328125,
-0.0034332275390625,
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0.028564453125,
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0.0081787109375,
0.035888671875,
-0.064453125,
-0.00133514404296875,
-0.034179... | 19,557 | 19557 | |
Category theory/Natural transformation
From HaskellWiki
< Category theory
(Difference between revisions)
m (Fix empty line tricks at tables) m (Vertical arrows: sides of objects: rephrase non-scientific expression)
← Older edit Newer edit →
Line 15... | 5 | [
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Cucker-Smale Flocking with Bounded Cohesive and Repulsive Forces
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 783279, 9 pages
http://dx.doi.org/10.1155/2013/783279
Research Article
Cucker-Smale Flocking with Bounded Cohesive and Repulsive Forces
^1School of Electronics and Information, Hangzhou Dianz... | 4 | [
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Counterdiabatic mode-evolution based coupled-waveguide devices
« journal navigation
Counterdiabatic mode-evolution based coupled-waveguide devices
Optics Express, Vol. 21, Issue 18, pp. 21224-21235 (2013)
http://dx.doi.org/10.1364/OE.21.021224
Abstract
The goal in designing mode-evolution based devices is to reali... | 4 | [
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Question from the proof in euler's forumla
micromass
Have you seen Wilson's theorem? This states that (p-1)!=-1 (mod p) for prime p.
Can you adjust the proof so that it also works in this case?
I have tried, but fail in the last step:
In Wilson's proof, the number satisfy a^2=1(mod p) -> (a-1)(a+1) = p*n. Since 0... | 4 | [
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... | 19,561 | 19561 | |
Finding X in y = mx + b equations
August 12th 2009, 03:23 AM #1
Newbie
Joined
Jul 2009
Posts
6
Finding X in y = mx + b equations
Hello:
I am doing a math worksheet that I was given by my teacher, the sheet is full of slope problems. y = mx + b. You are given two points:
Example:
(4,1) (5,3... | 4 | [
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0.004150390625,
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-0.02... | 19,562 | 19562 | |
Mean Value Theorem Please Help
ok here it is another try to justify that my claim in post #2 holds.
Using the mean value theorem we get that:[tex]\exists c\in(0,1)[/tex] such that
[tex]f'(c)=f(1)-f(0)=0[/tex] so now
[tex]f'(x)=(sin\frac{c\pi}{6}- \frac{x}{2})'=\frac{\pi}{6}cos\frac{\pi x}{6}-\frac{1}{2}[/tex]
so
[... | 5 | [
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Mathematical Modelling
April 16th 2009, 09:56 AM #1
Newbie
Joined
Feb 2009
Posts
7
Mathematical Modelling
Hey guys
I'm so close to finishing this course I can taste it!
I've been stuck on this question forever because I just don't even know what I'm supposed to do. I have a feeling I'm overthinki... | 4 | [
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Patent US3605625 - Curve liners
Sept.
Filed 1971 o. s. BENCSICS 3,605,625
CURVE LINERS Sept. 15, 1969 4 Sheets-Sheet l RADIOID CLOTHOID 8 Y m Q a Y X0 Xb INVENTOR ODON S. BENCSICS ATTORNEYS.
20, 1971 o. s. BENCSICS 3,605,625
. CURVE LINERS Filed Sept. 15. 1969 A Sheets-Sheet 2 INVENTQR QDON S. BENCSICS ATORNEYS.
P... | 4 | [
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Verify that this is the solution to an ordinary differential equation
NCyellow
1. The problem statement, all variables and given/known data
I am given dy/dt -2yt = 1
and y(t) = (e^(t^2))[e^(-s^2)ds] + e^(t^2)
integrate from t to 0 within the brackets
2. Relevant equations
3. The attempt at a solution
I know that... | 5 | [
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... | 19,566 | 19566 | |
Math Help
September 1st 2008, 04:21 AM #1
Please help me with the circled qns (ii) and qn (a) and (b)
see if you can get the paper's answer: (ii): -0.962
qn (a) -13/9 < k<3
(b) a=1,b=-10
if u can pls tell me yr workings
II
I agree with the Paper's answer. It seems to me that it would b... | 4 | [
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-0.0057... | 19,567 | 19567 | |
A cipher problem
November 29th 2009, 06:45 AM
ps1313
A cipher problem
Consider the 26 letters of the alphabet together with the set of symbols {_, . , , , ;, :}
to complete a 31-character alphabet. Associate a->0, b->1, … ,z->25,_->26, .->27, ,->28, ;->29, and :->30. Consider all maps of the form:
f(x) =... | 5 | [
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-0.06... | 19,568 | 19568 | |
trigonometric equation
$\displaystyle \frac{dy}{dx}\,\sin{x} - y\cos{x} = -\frac{\sin^2{x}}{x^2}$ $\displaystyle \frac{dy}{dx} - y\,\frac{\cos{x}}{\sin{x}} = -\frac{\sin{x}}{x^2}$. The integrating factor is $\displaystyle
e^{\int{-\frac{\cos{x}}{\sin{x}}\,dx}} = e^{-\ln{(\sin{x})}} = e^{\ln{(\sin{x})^{-1}}} = \frac{1}{... | 5 | [
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Sets and Probability
August 30th 2008, 12:05 PM #1
Sets and Probability
Prove:
$<br /> <br /> P\{ (A \cup B) \cap C\} = P\{ A \cap C\} + P\{ B \cap C\} - P\{ A \cap B \cap C\} <br /> <br /> <br />$
Last edited by kid funky fried; August 30th 2008 at 09:56 PM. Reason: add content
The expression $P\l... | 4 | [
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-0.0191... | 19,570 | 19570 | |
Truth Tables
October 4th 2008, 11:16 AM #1
Newbie
Joined
Oct 2008
Posts
1
Truth Tables
I am confused on how to due to this problem
(A). No A is B some of C is A. some C is not B
(B). All B is A All C is A All C is B
I need to give a logical statement and complete a Truth table
This ass... | 4 | [
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-0... | 19,571 | 19571 | |
Question #2: Prime
September 23rd 2008, 04:19 PM #1
Junior Member
Joined
Sep 2008
Posts
36
Adapt the proof of Theorem 1.5.9 to prove:
Theorem 1.5.9 - There is an infinit number of primes.
(a) There is an infinite number of primes of the form 4n + 3.
(b) There is an infinite number of prime... | 5 | [
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-0.0246... | 19,572 | 19572 | |
Physics Forums - View Single Post - Bessel Functions / Eigenvalues / Heat Equation
phioder
Hello
The temperature in the cylinder is given by the above equation, but is dimensionless, what about if one would like to calculate the temperature of cylinders of different materials?
Is there a way to add to that equati... | 4 | [
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0.0517578125,
-0.08... | 19,573 | 19573 | |
Newtons Method
I don't know how to do this question would anyone be able to help thanks nath
Newton's Method solves the equation f(x) = 0 as follows. Let x_1 be an approximation to the true root x, say x_1 = x - h. Then 0 = f(x) = f(x_1 + h) = f(x_1) + h.f'(x_1) + (error) and we assume that
the error is negligible. Th... | 5 | [
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0.042236328125,
-0.052001953125,
0.0295410156... | 19,574 | 19574 | |
Methods
Density Functional (DFT) Methods
DESCRIPTION
Gaussian 09 offers a wide variety of Density Functional Theory (DFT) [Hohenberg64, Kohn65, Parr89, Salahub89] models (see also [Labanowski91, Andzelm92, Becke92, Gill92, Perdew92, Scuseria92,
Becke92a, Perdew92a, Perdew93a, Sosa93a, Stephens94, Stephens94a, Ricca9... | 4 | [
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0.080078125,
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0.048828125,
0.041259765625,
-0.060546875,
0.05322265625,
0.033935546875,
-... | 19,575 | 19575 | |
Replacing the current by the fields in electromagnetism.
hello,
In electromagnetism from the Lagrangian formulation, one can defines a canonical momentum and applying Euler's equation to that momentum gives the lorentz law.
To get the Lorentz law, one uses a vector identity, only available because it is said the speed... | 4 | [
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0.10205078125,
0.0... | 19,576 | 19576 | |
differentials
April 10th 2008, 12:06 PM #1
Newbie
Joined
Apr 2008
Posts
14
differentials
Hi everyone,
Im having trouble with this problem
-use differentials to calculate radical 15.4, to 3 correct decimal places.
-if anyone could help it would be much appreciated
We can use the formul... | 4 | [
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0.051025390625,
0.00982666015625,
0.047607421875,
-0.0247802734375,
0.0456542... | 19,577 | 19577 | |
Patent US6724258 - Highly-linear, wide-input-range, wide control-range, low-voltage differential voltage controlled transconductor
TECHNICAL FIELD OF THE INVENTION
This invention relates to fully differential voltage controlled transconductors, and more particularly relates to such transconductors that operate at low ... | 4 | [
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0.045166015625,
... | 19,578 | 19578 | |
The percentage of carbon dioxide in the air
Beez
Hello. I need a help again for my differential equations class.
The problem is as follows:
The air in a room whose volume is 10,000 cu ft tests 0.15% carbon dioxide. Starting at t=0, outside air testing 0.05% carbon dioxide is admitted at the rate of 5000 cu ft/min.
(a)... | 4 | [
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0.035888671875,
0.05419921875,
0.040283203125,
0.005706787109375,
0.05615234375,
-0.031982421875,
-0.... | 19,579 | 19579 | |
Area and rotation volume
June 10th 2008, 11:25 PM #1
Junior Member
Joined
Jun 2008
Posts
44
Area and rotation volume
a) Calculate the are between the lines $y=x$ and $y^2=2-x$ and the parabola $y^2=2-x$
b) Calculate the rotation volume of the body that comes when the curve $y=xe^x$ rotates around th... | 5 | [
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0.035400390625,
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0.0194091796875,
0.0264892578125,
0.0157470703125,
-0.01275634765625,
... | 19,580 | 19580 | |
Calculus of variations - showing extremal is minimum
October 15th 2013, 12:18 PM #1
Hi,
J[y] = $\int_0^1{e^y(y')^2 dx$
y(0) = 1, y(1) = 2ln(2).
I need to find the extremal and show whether it provides a maximum or minimum.
In this case I only have problems with the second part. I have the extrem... | 4 | [
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0.0159912109375,
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0.00604248046875,
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0.06494140625,
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0.02587890625,
0.0201416015625,
-0.0291748046875,
0.036865234375,
0.035400390... | 19,581 | 19581 | |
Multivariable Vector: Gradient @ particular speed - Find Rate
1. The problem statement, all variables and given/known data
Given: Concentration of Fluid = F(x,y,z) = 2x^2 + 4y^4 + 2*x^2*z^2 at point (-1,1,1)
Found Grad(F(x,y,z)) = <-8,16,4>
----If you start to move in the direction of Grad(F) at a speed of 8, how fast ... | 4 | [
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0.05615234375,
0.06103515625,
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0.045166015625,
0.0085449218... | 19,582 | 19582 | |
Find the equation of the tangent plane to the surface (vector calculus)
Find the equation of the tangent plane to the surface z=x(x^2+y)^1/2 at the point (2,5,6) thank you
That's a pretty straight forward problem, isn't it? The gradient of f(x, y, z) where [tex]f(x, y, z)= x(x^2+ y^2)^{1/2}- z[tex] is a vector perpe... | 4 | [
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0.1416015625,
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-... | 19,583 | 19583 | |
[SOLVED] How can i show this, trig identity
Hello,Do you know about Weierstrass substitution ? Let $t=\tan (\theta/2)$ Then $\sin(\theta)=\frac{2t}{1+t^2}$ and $\cos(\theta)=\frac{1-t^2}{1+t^2}$ Otherwise... : $\frac{1}{\tan(\theta/2)}=\frac
{1}{\frac{\sin(\theta/2)}{\cos(\theta/2)}}=\frac{\cos(\theta/2)}{\sin(\theta/2... | 4 | [
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0.... | 19,584 | 19584 | |
Calculating the equation and slope of a Right Bisector
December 21st 2007, 08:26 AM #1
Junior Member
Joined
Dec 2007
Posts
34
Calculating the equation and slope of a Right Bisector
I'm doing a math course through correspondence and I'm having some trouble with a couple of things that haven't been properl... | 4 | [
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0.... | 19,585 | 19585 | |
Feynman slash identity
1. The problem statement, all variables and given/known data
I am trying to prove that [tex]\displaystyle{\not} a \displaystyle{\not} b + \displaystyle{\not} b \displaystyle{\not} a = 2a\cdot b[/tex] using the relation [tex]\{\gamma^{\mu},\gamma^{\nu}\} = 2g^
{\mu\nu}[/tex]
2. Relevant equation... | 4 | [
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-0.06... | 19,586 | 19586 | |
Residues
October 2nd 2012, 01:39 AM
linalg123
Residues
Calculate $\int_{|z|=3}\frac{e^{iz}}{z^2(z-2)(z+5i)}dz$ So the point Z= -5i is not enclosed by the contour.
So am i right that we only calculate the residues at z=0 and z=2 and sum them then multiply by 2i*pi to evaluate the integral?
Residue at z=... | 5 | [
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... | 19,587 | 19587 | |
search results
Expand all Collapse all Results 1 - 3 of 3
1. CJM 2014 (vol 66 pp. 902)
Corrigendum to Example in "Quantum Drinfeld Hecke Algebras"
The last example of the article contains an error which we correct. We also indicate some indices in Theorem 11.1 that were accidently transposed.
Keywords:qu... | 4 | [
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Patent US5369404 - Combined angle demodulator and digitizer
FIELD OF THE INVENTION
The invention relates to analog-to-digital (A/D) converters and phase-tracking devices, specifically a device that performs both functions simultaneously.
BACKGROUND OF THE INVENTION
Phase-locked loops are used in a multitude of commu... | 4 | [
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0... | 19,589 | 19589 | |
Proof congruence
November 18th 2007, 11:35 PM
AgentNXP
Proof congruence
Show that if p is a prime, then (a + b)^p ≡ a^p + b^p (mod p)
(Hint: prove and use that p choose k is a multiple of p for every k ∈ {1, . . . , p − 1}). Then expand (a + b)^p via the binomial theorem).
Using the previous formula, pro... | 4 | [
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-0.00... | 19,590 | 19590 | |
Integration by substitution
February 3rd 2009, 07:48 PM #1
Junior Member
Joined
Jan 2009
Posts
74
Someone please help me! I don't get this problem...
Use substitution to find: the integral from 0 to pi/3 of sinx/cos(squared)x dx
Put $u=\cos x$ and don't forget the new bounds for $u.$
Hello ... | 5 | [
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... | 19,591 | 19591 | |
Finding the equation of a plane
June 4th 2010, 02:45 PM #1
Member
Joined
Sep 2009
Posts
83
Finding the equation of a plane
Hey, I was hoping you kind people here at mathhelpforum.com could help me out with a problem that I am stuck on.
Question
Find the equation of the plane that passes through ... | 5 | [
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-0.055908203125,
-0.0245361328125,
-0.087890625,
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Generalized Caratheodory Extension Theorem on Fuzzy Measure Space
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 260457, 11 pages
http://dx.doi.org/10.1155/2012/260457
Research Article
Generalized Caratheodory Extension Theorem on Fuzzy Measure Space
Department of Mathematics, Faculty of Arts and Scien... | 5 | [
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Invertibility of the product matrix-transpose
Why the matrix $AA^T$ is invertible, if the generic real matrix $A$ has full rank?
If a matrix has full rank, then its transpose also has full rank. The product of two invertible matrices is invertible.
I don't think that quite answers the question! The OP didn't say they... | 5 | [
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0.0244140625,
0.04736328... | 19,594 | 19594 | |
Finding the minimum area of triangle, coordinate plane
July 3rd 2011, 08:45 AM
Zellator
Finding the minimum area of triangle, coordinate plane
Hi Forum!
I've been reviewing the things I know so far, and found this question
A line is drawn through (2,1), forming a right triangle at the 1st quadrant. Dete... | 5 | [
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Patent US20060072656 - Estimation of signal-to-noise ratio by processing measured error vector magnitude
BACKGROUND OF THE INVENTION
The present invention generally pertains to communication signal processing and is particularly directed to estimating the signal-to-noise ratio (SNR) of a received modulated signal by p... | 4 | [
-0.0157470703125,
-0.007598876953125,
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0.08935546875,
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0.069... | 19,596 | 19596 | |
Deregressing estimated breeding values and weighting information for genomic regression analyses
Abstract
Background
Genomic prediction of breeding values involves a so-called training analysis that predicts the influence of small genomic regions by regression of observed information on marker genotypes for a given
p... | 4 | [
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... | 19,597 | 19597 | |
Patent US20050195924 - Method and system for predicting signal power to interference metric
FIELD OF THE INVENTION
The present invention relates to methods and systems for the prediction of signal power to interference metrics.
BACKGROUND OF THE INVENTION
High-speed packet data systems rely on carrier-to-interferenc... | 4 | [
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... | 19,598 | 19598 | |
Number identification
Given a real number identify(x) attempts to find an exact formula for None is returned. With full=True, a list of matching formulas is returned.
As a simple example, identify() will find an algebraic formula for the golden ratio:
>>> from mpmath import *
>>> mp.dps = 15; mp.prett... | 5 | [
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