content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
From Schwarzschild to Droste
Love's not Time's fool, though rosy lips and cheeks
Within his bending sickle's compass come:
Love alters not with his brief hours and weeks,
But bears it out even to the edge of doom.
If this be error and upon me proved,
I never writ, nor no man ever loved.
... | 4 | [
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0.02331542968... | 20,000 | 20000 | |
Strange data fitting problem
sunjin09
maximize [itex]\frac{<x,y>}{||x||_2||y||_2}[/itex],
I don't know an easy way to do this. You may as well consider only unit vectors, so the problem becomes to maximize [itex] <\hat{x},\hat{y}> [/itex]. As far as I can see this problem falls under the
heading of a "bilinear opti... | 4 | [
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Finding Nth Term
February 11th 2009, 09:14 AM
AlgebraicallyChallenged
Finding Nth Term
Dear Forum , I have to Find the nth term of the geometric sequence for the following,
8,-4/3,2/9...
I was curious if my following work is correct , please let me know what you think:
8,(-4)/(3),(2)/(9)
Remo... | 4 | [
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... | 20,002 | 20002 | |
evaluation
when $c=-7$and $d=4$ $\sqrt{d} - dc^2$ $\sqrt{4} - 4 x (-7)^2$ $2 - 4 x (-7)^2 = -194$ this right?
Ok so i'm not sure what to do now then?
did you know that $(-2)^2=4$ $(-4)^2=16$ $(-7)^2=49$ so $\sqrt{4}=\mp 2$ $\sqrt{16}=\mp 4$ $\sqrt{49}=\mp 7$ in general $\sqrt{a^2}=\mp a$ a is real number in you quest... | 4 | [
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Logistic Growth Models (interpreting r value)
thelema418
I originally posted this on the Biology message boards. But I have not received any responses.
In models of exponential growth, we have an intrinsic growth rate (r) that is calculated as the difference of birth rates to death rates.
With the logistic growth ... | 4 | [
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Vector Derivatives
April 4th 2010, 05:35 PM #1
Newbie
Joined
Apr 2010
Posts
2
Vector Derivatives
Given a vector field V(x,y,z) = (xi + yj + zk)/(r^3) where r = sqrt(x^2 + y^2 + z^2)
a) what is the x,y,z components of V(x,y,z)
b) partial derivatives of each component
do i substitute the r^3 w... | 5 | [
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Maximum value of x in an equation: Involves constant to the power of x
March 7th 2011, 01:19 AM
languagelearner23
Maximum value of x in an equation: Involves constant to the power of x
Hi everyone, this is part of a longer question, but the current part involves me finding the value of c in the following equatio... | 5 | [
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Partial Sum For a certain kind of series.
March 27th 2013, 04:03 PM #1
Partial Sum For a certain kind of series.
Hi everyone! Today we were asked to say if this particular series converges or diverges : $1+\frac{10}{4}+\frac{10}{9}+\frac{10}{16}...$. The first thing I though about is to find if the partial
su... | 5 | [
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How far in first minute?
July 16th 2009, 02:30 PM #1
Junior Member
Joined
Feb 2009
Posts
40
hey guys, i think i might have to use dv/dt = -kv. i have no idea how do this problem, help me solve this
Suppose that a motorboat is moving at 40 ft/s when its motor suddenly quits, and that 10sec later the b... | 5 | [
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Patent US20020141372 - Single user detection base station
[0001] This application is a continuation of U.S. patent application Ser. No. 10/052,943, Nov. 7, 2001, which claims priority to U.S. Provisional Patent Application Ser. No. 60/246,947, filed on Nov.
9, 2000, which applications are incorporated herein by referen... | 4 | [
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[Haskell-cafe] Functional progr., images, laziness and all the
rest
[Haskell-cafe] Functional progr., images, laziness and all the rest
Jerzy Karczmarczuk jerzy.karczmarczuk at info.unicaen.fr
Thu Jun 22 04:49:49 EDT 2006
Brian Hulley wrote:
> jerzy.karczmarczuk at info.unicaen.fr wrote:
>> you may transform a recu... | 4 | [
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Constant repair rate (HPP/exponential) model
8. Assessing Product Reliability
8.4. Reliability Data Analysis
8.4.5. How do you fit system repair rate models?
8.4.5.1. Constant repair rate (HPP/exponential) model
This section covers estimating MTBF's The HPP or exponential model is widely used for two reasons:
and... | 5 | [
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Rel. Max and Rel Min, going wrong in my second derivative
November 7th 2008, 05:11 PM #1
Newbie
Joined
Nov 2008
Posts
22
Rel. Max and Rel Min, going wrong in my second derivative
here's the problem, f(x)= s/1+s^2
I've been staring at this problem for almost 30 minutes and i can't see where i go wron... | 4 | [
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Digamma Integral Representation
May 12th 2010, 07:45 PM #1
Junior Member
Joined
Apr 2010
Posts
50
Digamma Integral Representation
Hi,
I'm trying to figure out how the integral representation of the Digamma function works.
I understand that the Digamma function is the logarithmic derivative of t... | 5 | [
-0.09326171875,
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... | 20,013 | 20013 | |
Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 361904, 5 pages
http://dx.doi.org/10.1155/2014/361904
Research Article
Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets
^1College o... | 5 | [
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Analysis and Scheduling of Maintenance Operations for a Chain of Gas Stations
Journal of Industrial Engineering
Volume 2013 (2013), Article ID 278546, 7 pages
http://dx.doi.org/10.1155/2013/278546
Research Article
Analysis and Scheduling of Maintenance Operations for a Chain of Gas Stations
Kuwait University, Colleg... | 4 | [
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Entry-Item-Quantity-ABC Analysis-Based Multitype Cigarette Fast Sorting System
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 847591, 9 pages
http://dx.doi.org/10.1155/2012/847591
Research Article
Entry-Item-Quantity-ABC Analysis-Based Multitype Cigarette Fast Sorting System
^1School of Transpor... | 4 | [
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Electric Field due to a line of charge
Yeah, Griffith's book is good.
stunner5000pt
combining the two yields
[tex] \vec{E} = \frac{\lambda}{4 \pi \epsilon_{0}} \left[ \frac{1}{z} -\frac{1}{\sqrt{z^2 + L^2}} \right] \hat{x} + \frac{\lambda}{4 \pi \epsilon_{0}z} \frac{L}{\sqrt{L^2 + z^2}} \hat{z} [/tex]
is there ... | 5 | [
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A Stochastic String with a Compound Poisson Process
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 857678, 8 pages
http://dx.doi.org/10.1155/2013/857678
Research Article
A Stochastic String with a Compound Poisson Process
Department of Mathematics, Southwestern University of Finance and Economics, Chen... | 4 | [
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Covariance question
April 3rd 2012, 05:03 PM #1
Newbie
Joined
Apr 2012
From
-
Posts
23
Covariance question
If Z₁ is Normal (μ₁,σ²), Z₂ is Normal (μ₂,σ²) and Cov(Z₁,Z₂)=ρσ²
For (X₁,X₂)=(Z₁-Z₂,Z₁+Z₂)
How can i find the corresponding covariance matrix?
I know the mean vector is
μ₁-μ₂
... | 4 | [
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Solids Of Revolution
March 4th 2009, 06:17 AM #1
Member
Joined
Oct 2008
Posts
109
Solids Of Revolution
Find the volume of the solid that is generated by rotating around the indicated axis the plane region bounded by the given curves. Sketch the region and a typical rectangle that generates a
'disc' o... | 4 | [
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(Small oscillations) Finding Normal modes procedure.
1. The problem statement, all variables and given/known data
The first part of the problem is just finding the Lagrangian for a system with 2 d.o.f. and using small angle approximations to get the Lagrangian in canonical/quadratic form, not a problem. I am
given nume... | 4 | [
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0.... | 20,021 | 20021 | |
Tycoon Tommy – Follow Up
A follow up to yesterday’s quasi-riddle, on Tycoon Tommy, who despite apparently high average returns, lost money over a 20 year period.
As noted by the commenters, Tommy fell victim to a mathematical illusion. Here’s the full set of returns I postulated when setting up the problem:
... | 4 | [
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0.04... | 20,022 | 20022 | |
Where did I go wrong on this proof? (Mathematical Induction)
October 12th 2010, 07:08 PM #1
Junior Member
Joined
Sep 2010
Posts
48
Where did I go wrong on this proof? (Mathematical Induction)
I apologize in advance for not knowing how to type mathematical notation, I'll do the best I can to make the ques... | 4 | [
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0.045166015625... | 20,023 | 20023 | |
-Symmetrical Coupled System of Identical Cells with Delays
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 417678, 10 pages
http://dx.doi.org/10.1155/2013/417678
Research Article
Multiple Nonlinear Oscillations in a -Symmetrical Coupled System of Identical Cells with Delays
College of Mathematics and Co... | 4 | [
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Math Help
December 14th 2007, 03:22 AM #1
monkyshines
Guest
need help !!
i have 2 question that i need help to solve
1. write an algorithm that writes the binary form of a decimal number n
2. if d divides both n and m the d divides their sum and d divides their difference
Hello, monkyshines!
... | 4 | [
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Another question on Lagrangians (sorry)
diazona
Seems like
[tex]\frac{\partial L}{\partial x^i} \neq 0[/tex]
because the Lagrangian depends on x through the vector potential A.
thanks diazona. You are right:
[I will switch to subscripts, I hope that is okay]
[tex]
L_{i}=\frac{1}{2}m\dot{x}_{i}}^{2}+e\vec{A}.\dot... | 4 | [
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Standard matrix representation of a differentiation operator.
August 13th 2008, 11:37 AM
linearalgebradunce
Standard matrix representation of a differentiation operator.
q. let P sub 3 denote the subspace consisting of all polynomials of degree no greater than 3. Let E: P sub 3 ---> P sub 3 denote the differenti... | 5 | [
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0.0230712890625,
0.04150390625,
0.033203125,
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0.04443359375,
0.0234375,
0.021728515625,
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0.0107421875,
0.080078125,
-0.06787109375,
0.09228515625,
-0.... | 20,027 | 20027 | |
2nd Derivative Implicit
October 25th 2012, 02:18 PM #1
Member
Joined
Jul 2012
From
United States
Posts
87
Thanks
3
2nd Derivative Implicit
Find $\frac {d^2y}{dx^2}$
$e^{2y}+x = y$
I didn't get very far after differentiating with respect to x; here's my step 1): $2\frac{dy}{dx}*e^{2y}\fr... | 5 | [
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0.042724609375,
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0.044189453125,
0.06396484375,
-0.0072021484375,
-0.09375,
0.05419921... | 20,028 | 20028 | |
Calculus of variations
May 16th 2010, 04:25 AM #1
Calculus of variations
Write down the Euler-Lagrange equations for critical points of the functional $I(y)=\int_{x_1}^{x_2}y^2+y'y'''-(y'')^2~dx$
I'm finding this odd since the only functions i've looked at are of the form $g(x,y,y')$ not $f(y',y'',y''')$.
... | 4 | [
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0.0003814697265625,
-0.061279296875,
0.054931640625,
0.037841796875,
-0.061279296... | 20,029 | 20029 | |
Integrating tan(x)
The absolute value sign is needed in order to gain the proper integral value of the function [tex]\frac{1}{x}[/tex] on intervals where x<0
(Remember, you can't find the natural logarithm of a negative real number among the reals!)
To illustrate:
Given x>0, we may show that a proper anti-derivative is... | 5 | [
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0.068359375,
-0.06933... | 20,030 | 20030 | |
Understand the science behind color mixing
High-brightness (HB) LEDs continue to increase in popularity due to the numerous advantages they offer when compared to the conventional lighting solutions. One of the advantages of HB LEDs is their
ability to generate different colors, opening a new dimension to the world of ... | 4 | [
0.0240478515625,
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... | 20,031 | 20031 | |
geometry length
September 3rd 2008, 04:02 AM #1
Newbie
Joined
Sep 2008
Posts
9
geometry length
see attatched pic
the diagram shows a running track with the 'straights' 90m ling and with semicircular end sections.if the inside distance is 400m and the track is 8m wide, how much further is it to run ar... | 4 | [
0.032470703125,
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0.05859375,
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0.000560760498046875,
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0.0024566650390625,
-0.028442... | 20,032 | 20032 | |
Proof of square root 3 irrational using well ordering
hi bonfire09!
(just got up
bonfire09
So do I have it right?
Since t=s√3 we can rewrite as t√3=s ⇔ 3t=s√3. So we subtract s from both side and we get 3t-s=s√3-s ⇔ 3t-s=s√3-t√3⇔3t-s=√3(s-t)
(why do you say "subtract s from both sides"?
what you're
actually
... | 4 | [
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-0.0009155273437... | 20,033 | 20033 | |
Implicit Differentiation Help
August 22nd 2012, 03:01 PM #1
Newbie
Joined
Aug 2012
From
Colorado
Posts
17
Implicit Differentiation Help
How can I find the derivative of this implicit relation?
How do I find dG/dt for G=(bv)/(1-(v^2/c^2))^(1/2)
*b and c are constants
*v depends on t
I... | 5 | [
-0.039306640625,
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0.0703125,
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0.0322265625,
-0.0329589843... | 20,034 | 20034 | |
Non-homogeneous Equations problem 1
October 22nd 2009, 01:04 PM
Phyxius117
Non-homogeneous Equations problem 1
Here is the problem:
y''-10 y' +25y = -16 e^(5t)
And I am trying to find the particular solution!
I tried using the method of undetermined coefficients but no matter what my initial guess ... | 5 | [
-0.111328125,
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-0.016479492... | 20,035 | 20035 | |
Math Help
April 7th 2008, 02:00 PM #1
Member
Joined
Sep 2006
Posts
221
Limits
Calculate the following limits:
1.) $\lim_{x \to \infty} \frac{\ln{x}}{x^{\frac{2}{3}}}$
I know the answer is 0. Can I simply use L'Hopitals?
So, $\frac{\frac{1}{x}}{\frac{2}{3}x^{\frac{-1}{3}}}$? Something like... | 5 | [
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... | 20,036 | 20036 | |
Derivative of General Solution
April 9th 2009, 06:39 PM #1
Newbie
Joined
Mar 2009
Posts
10
Derivative of General Solution
this should be simple but I can't get it to come out right
i have the general solution as x(t)= C1e^(-t)cos4.36t + C2e^(-t)sin4.36t
can someone get the first deriv of x(t)? ... | 5 | [
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Patente US6780645 - Diagnostic kit with a memory storing test strip calibration codes and related methods
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates, in general, to diagnostic kits for the measurement of a fluid sample characteristic and, in particular, to diagnostic kits that... | 4 | [
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0.0610351... | 20,038 | 20038 | |
Free electrons in solid sphere of copper
CAF123
For the first calculation, I said $$m=\frac{4 \rho \pi r^3}{3},$$ with ρ = 8.96 g/cm^3 and r = 4mm →4 x 10^-1cm. I realise I made a stupid mistake. I now get ≈ 2.4g and 2.27 x 10^22 atoms. Thanks for
making me aware of my mistake.
Using this larger number of 2.27 x 10... | 4 | [
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0.039306640625,
-0.00982666015625,... | 20,039 | 20039 | |
Reduction of Order
November 2nd 2009, 04:14 PM #1
Member
Joined
Nov 2008
Posts
75
Reduction of Order
y''-2y'+y=0 ; With Solution y = e^x
So far I got:
let y=f(x)*v = e^xv
y'=e^xv+e^xv'
y''=e^xv+e^xv'+e^xv'+e^xv''
substituting that into y''-2y'+y=0 gets=
e^xv'' and then v''=w'... | 4 | [
-0.0007476806640625,
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0.001495361328125,
0.0025177001953125,
-0.033935546875,
-0.002... | 20,040 | 20040 | |
prove or disprove
October 25th 2008, 07:16 AM #1
Member
Joined
Feb 2008
Posts
125
prove or disprove
Let G be an Abelian group. Prove or disprove that
H={g^2|g is a member of G}
is a subgroup of G.
Indeed it's true, take $a,b\in G$ then $a^2*b^2=a*a*b*b=a*b*a*b=(a*b)*(a*b)=(a*b)^2$ (*)
W... | 5 | [
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... | 20,041 | 20041 | |
Help with solving graph equation (use of implicit differentiation)
December 7th 2012, 08:10 PM
adamwth
Help with solving graph equation (use of implicit differentiation)
Equation of graph : 2x^5 + 2y^2= 5xy
The vertical tangent line and the horizontal tangent line to the curve intersect at the point A(a,b). ... | 4 | [
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Balance
Weight and Balance Forces Acting on an Airplane
SUBJECT: Physics
TOPIC: Torques and Moments
DESCRIPTION: A set of mathematics problems dealing with torques and moments.
CONTRIBUTED BY: Carol Hodanbosi
EDITED BY: Jonathan G. Fairman - August 1996
Principle: Balance of forces produces Equilibrium
Gravity al... | 4 | [
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... | 20,043 | 20043 | |
Little orbits?
tony873004
You're right. I didn't realize little m would represent Earth on the Earth velocity formula.
I swear my 2 formulas worked last night. But they don't work today! I entered them into Visual Basic but I probably made a typo.
That's okay, I just realised that I misplaced a decimal point while e... | 4 | [
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0.001129150390625,
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0.03955078... | 20,044 | 20044 | |
Questions related to waves.
malawi_glenn
So how can anyone help you if you are not showing what you did?
And WHAT are you trying to convert to Joules?
have you seen this formula:
[tex] E_{\gamma} = hf = hc/\lambda [/tex]
?
I have shown you everything I know how to do. For question 1, I would have thought I would ... | 4 | [
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0.00811767578125,
0.01977539... | 20,045 | 20045 | |
Trigonometric Identities
June 3rd 2011, 09:28 AM #1
Newbie
Joined
Feb 2011
Posts
10
Trigonometric Identities
Hi guys.
So, twenty hours of my life have passed. I'm never going to get them back, but I can prevent another twenty hours elapsing and that cold, hard feeling of my head hitting the desk one... | 4 | [
-0.0220947265625,
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0.... | 20,046 | 20046 | |
Motorboat Speed
January 11th 2007, 01:03 PM
symmetry
Motorboat Speed
A motorboat heads upstream on a river that has a current of 3 mph. The trip upstream takes 5 hours, while the return trip takes 2.5 hours. What is the speed of the motorboat?
Assume that the motorboat keeps a constant speed relative to the... | 4 | [
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... | 20,047 | 20047 | |
Physics Forums - Linear circuit problems
linear circuit problems
In solving linear circuit problems using complex currents, charges etc. I have stumbled upon something I never really understand. You are basically solving 1st and 2nd order differential equations by
algebraic means, right? Well at what point do you a... | 4 | [
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0.04736328125,
-0.0... | 20,048 | 20048 | |
Finding the Exact Value of an Inverse Trigonometry Function
January 21st 2013, 09:04 PM #1
Newbie
Joined
Jan 2013
From
British Columbia
Posts
9
Finding the Exact Value of an Inverse Trigonometry Function
Hello,
I want to find the exact value of $csc(-\frac{5\pi}{3})$
I know that $csc(\theta)... | 4 | [
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0.05712890625,
-0.0220947265625,
0.01544189453125,
0.0036010742187... | 20,049 | 20049 | |
Limits approaching infinity
October 2nd 2012, 01:03 PM #1
Member
Joined
Mar 2012
From
USA
Posts
92
Limits approaching infinity
If b>0 prove that lim[n->infinity] ^1/1+nb=0 using the limit definition.
I can't seem to make any headway in choosing my delta to make progress in this exercise.
Re: Li... | 5 | [
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0.0869140625,
... | 20,050 | 20050 | |
Patent US5063530 - Method of adding/subtracting floating-point representation data and apparatus for the same
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method of adding/subtracting floating-point representation data suitable for a computer or a digital signal processor a... | 4 | [
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-0.0625,
0.0108642578125,
... | 20,051 | 20051 | |
rational expressions #2
July 23rd 2013, 03:19 PM #1
Member
Joined
Feb 2013
From
Canada
Posts
131
i cannot finish 1 c) and d)... that is how far i got.
i am having some problems with turning trinomials with no common factors into binomials
thank you
Re: rational expressions #2
In (... | 4 | [
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0.00885009765625,
0.103515625,
0.0111083984375,
0.0... | 20,052 | 20052 | |
Reflection and Rotation Matrices
January 31st 2009, 11:35 AM #1
Member
Joined
Jan 2009
Posts
91
Reflection and Rotation Matrices
calculate [R][S]
where R is the reflection matrix
[ 4/5 -3/5 ]
[-3/5 -4/5 ]
and S is the reflection matrix
[ -3/5 4/5 ]
[ 4/5 3/5 ]
i found [R][S... | 4 | [
-0.076171875,
0.003662109375,
0.0019683837890625,
-0.059814453125,
0.0045166015625,
-0.033447265625,
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-0.04345703125,
-0.0179443359375,
0.00089263916015625,
-0.00086212158203125,
0.03955078125,
0.0299072265625,
0.020751953125,
-0.0302734375,
0.01165771484375,
0.0120239... | 20,053 | 20053 | |
Dots, line
Perhaps it would be better to say 5 points. A 'dot' is not a mathematical object. Of course, if the 5 points happened to lie on a single line, there would be only one line through them so the
question really should be "What is the largest number of lines that can be drawn through 5 points in a plane?"
Choos... | 4 | [
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0.07373046875,
-0.052001953125,
-0.0839843... | 20,054 | 20054 | |
Verifying trig identities
October 28th 2009, 02:34 PM
l flipboi l
Verifying trig identities
Hello,
I'm having difficulties verifying this problem, can some please help me out?
Problem: (tan-cot) / (tan^2) - (cot^2) = sin cos
if I'm right the problem should look like this...
((sin/cos)-(cos/sin... | 4 | [
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0.060302734375,
-... | 20,055 | 20055 | |
Solving for H(g(f(x)))
February 15th 2010, 07:19 AM #1
Newbie
Joined
Feb 2010
Posts
4
Solving for H(g(f(x)))
Hi, i've been posed a maths tutorial on functions and i'm just looking for someone to check my answer. I would get a classmate or lecturer to do it, but it's reading week and no-one is around.
... | 4 | [
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0.054931640625,
-0.06591796875,... | 20,056 | 20056 | |
A Triple Fixed Point Theorem for Multimap in a Hausdorff Fuzzy Metric Space
Journal of Mathematics
Volume 2013 (2013), Article ID 812153, 6 pages
http://dx.doi.org/10.1155/2013/812153
Research Article
A Triple Fixed Point Theorem for Multimap in a Hausdorff Fuzzy Metric Space
^1Department of Mathematics, Acharya Nag... | 5 | [
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... | 20,057 | 20057 | |
HELP with Particular solution in the non-homogeneous recurrence relation
May 3rd 2009, 01:41 PM #1
Newbie
Joined
May 2009
Posts
14
HELP with Particular solution in the non-homogeneous recurrence relation
Find the solution of the recurrence relation $a_{n} = 2a_{n-1} + 2n^2$with initial condition a1 = 4.
... | 5 | [
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Consider the equation.
January 1st 2010, 04:38 PM #1
Newbie
Joined
Jan 2010
Posts
6
Consider the equation.
Consider the equation 10 = 2^x
(a) Solve the equation for x by taking the common logarithm of both sides.
Answer :
log10 = xlog2
x = log10/log2
(b) use the result to show that... | 4 | [
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Prove that cos 20 is irrational
xax: this one has no rational solutions so cos20 is irrational
You are correct. This can be looked at from the standpoint of Euclidean construction. And since, as you may have heard, you can not trisect an angle using the method of the Greeks, so you can not
construct a 20 degree angle ... | 5 | [
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Lost!
Find the derivative of the function. h(x)=(10/sqrt x) - (2x)
If you rewrite the function as h(x) = 10(x^-0.5) - 2x you might be able to see how to do it from there. If not.... look below. {h'(x) = -5(x^-3/2) - 2}
h(X) = (10/sqrt(X)) - 2X = 10X^-0.5 -(2X) d/dx = -5X^-3/2 - (2) = -(5/sqrt(X^3)) -2
Quote: Origina... | 4 | [
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Solving some equations :)
March 6th 2007, 12:52 AM #1
Newbie
Joined
Jan 2007
Posts
8
Hello everyone, i have a few questions
a) 3x(2) - 16x +5 = 0
b) 2x(2) - 5x - 3 = 0
c) 6x(2) - 13x + 6 = 0
d) x(2) + 2x +4 = 0
e) x(2) + 8x - 4 = 0
f) x(2) - 4x +1 = 0
the number in the b... | 4 | [
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0.059570... | 20,062 | 20062 | |
Math Help
December 31st 2006, 09:06 PM #1
Junior Member
Joined
Dec 2006
Posts
48
Gcd
Let a = 242, b = 142. Let g be the gretest common divisor of a and b, Find g, and find integers m,n such that g = m*a+n*n
I found g = 2
So 2 = 242m + n^2
how can i find m and n?
Also what is the fast... | 5 | [
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0.04296875,
... | 20,063 | 20063 | |
really cant do
Hello, For question (a): Each number n in the sum is lower than p. So, (n,p)=1. Hence, we can apply Fermat's Little Theorem: $n^{p-1}\equiv 1\text{ mod }p$ Let's multiply both sides by n. $n^{p}\
equiv n\text{ mod }p$ Thus $\sum_{n=1}^{p-1} n^p\equiv \sum_{n=1}^{p-1} n\equiv \frac{(p-1)(p)}{2}\text{ mod ... | 5 | [
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0.0128173... | 20,064 | 20064 | |
derivative problem
May 24th 2007, 06:33 AM #1
Newbie
Joined
May 2007
Posts
11
derivative problem
assuming that the volume of the trunk is directly proportional to the cube of its diameter,and that the latter increases uniformly from year to year,show that the rate of increase in the volume
when the d... | 4 | [
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... | 20,065 | 20065 | |
Complex limit
June 13th 2012, 09:50 PM #1
Complex limit
Bit confused about a limit
I need to find this limit
$lim_{z\rightarrow{0}} \frac{Re(z)Im(z)}{|z|^2}$
Wolframalpha gives this limit as $0$
Shouldn't this problem be equivalent
$lim_{(x,y)\rightarrow{(0,0)}} \frac{xy}{x^2+y^2}$
Wolf... | 5 | [
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-0.0981... | 20,066 | 20066 | |
COmplex number uestion
November 19th 2012, 11:45 PM
Tutu
COmplex number uestion
Hi again,
I need help with this question,
Find the complex number z that satisfies the equation 50/z* - 10/z = 2 + 9i given | z | = 2sqrt(10).
I had put 50 and 10 to the same denominator ie. zz* which then gives me |z|... | 5 | [
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0.00354003906... | 20,067 | 20067 | |
Inverse functions
The function f(x)= px+q such that f-1(6)=3 and f-1(-29)= -2. Find f-1(27). Thanks.
Could you please explain the steps to reach the answer thanks.
$\frac{1}{p}(6-q) = 3$...............(eq1) $\frac{1}{p}(-29-q) = -2$.............(eq2) Rearrange eq2 to make q the subject: Spoiler: $q = -29+2p$............ | 4 | [
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0.0269775390625,
0.0224609375,
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-0.078125,
-0.0196533203125,
0.0281982... | 20,068 | 20068 | |
Finite abelian group.
October 27th 2009, 11:26 AM #1
Member
Joined
Nov 2008
Posts
76
Finite abelian group.
Can someone give me a hand on this problem? I want to show that $G_1 \cong G_2 \Leftrightarrow G_1(p_i) \cong G_2(P_i)$ for all $i \in \{1,2,...,n\}$. Given that $G_1, G_2$ are abelian groups
su... | 4 | [
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0.0625,... | 20,069 | 20069 | |
Calulating the minimum value of f(x) in a given range of x?
March 12th 2008, 03:55 AM #1
Newbie
Joined
Mar 2008
Posts
13
Calulating the minimum value of f(x) in a given range of x?
Given the function below, where a, b, c, d, e are constants.
f(x) = ax^4 + bx^3 + cx^2 + dx + e
How do I get the m... | 4 | [
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0.052001953125,
0.0194091796875,
0.0074... | 20,070 | 20070 | |
[SOLVED] Integral of abs(x)^(1/2)
Hello there, I was wondering how to integrate $|x|^{1/2}$. I don't think that $\frac{2|x|^{3/2}}{3} + C$ is correct. Thank you!
Hello there, I figured out the answer. Since: $|x|^{1/2} = \left\{\begin{array}{cc}\sqrt{x},&\mbox{ if }<br /> x\geq 0\\\sqrt{-x}, & \mbox{ if } x < 0\end{ar... | 5 | [
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-0.015... | 20,071 | 20071 | |
Find curve that has tangent and normal lines that create a triangle
October 9th 2011, 02:15 PM
Shamako
Find curve that has tangent and normal lines that create a triangle
Find the implicit equation of the curve that goes through the point (3, 1) and whose tangent and normal lines always form with the x axis a tr... | 4 | [
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... | 20,072 | 20072 | |
permutation and combination
December 29th 2012, 06:16 AM #1
Newbie
Joined
Oct 2012
From
BANGALORE
Posts
5
permutation and combination
>>2)the english alphabet contains 21 consonants and five vowels.how many strings of six lowercase letters of the english alphabet contain>a)exactly one vowel? ans:1225... | 4 | [
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0.049072265625,
-0.055908203125,
-0.047363281... | 20,073 | 20073 | |
Sum of Series
April 25th 2010, 12:56 AM #1
Newbie
Joined
Apr 2010
Posts
18
Sum of Series
Find the sum of the first n terms of the series:
(i) 1.3.5 + 3.5.7 + 5.7.9 + ... + (2n - 1)(2n + 1)(2n +3)
(ii) 1/(1.3.5) + 1/(3.5.7) + 1/(5.7.9) + ... + 1/[(2n - 1)(2n + 1)(2n +3)]
I have tried many m... | 5 | [
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-0.0003509521484375,
-0.0388183593... | 20,074 | 20074 | |
Train Word Problem
September 11th 2012, 06:47 PM #1
Newbie
Joined
Sep 2012
From
California
Posts
1
Train Word Problem
Hi all,
I am curious whether there is a better approach to solving this problem than just guessing and checking. Here is the problem.
One hour out of the station, the locomo... | 4 | [
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0.04931640625,
0.00277709960... | 20,075 | 20075 | |
acceleration and velocity
April 25th 2007, 11:16 AM
zachb
acceleration and velocity
I don't understand the reasoning behind a few steps in this problem:
What constant acceleration is required to increase the speed of a car from 30 mi to 50 mi in 5 seconds?
a(t) = C = v'(t)
v'(t) = Ct + K
v(0... | 4 | [
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0.111328125,
-0.0908203... | 20,076 | 20076 | |
Arc length question
March 20th 2008, 03:08 AM #1
Super Member
Joined
Oct 2007
From
London / Cambridge
Posts
591
Arc length question
A curve has equation $9ay^2= x(3a-x)^2$
where a is a positive constant
a) Sketch a graph of the curve and showing stationary points and intersection with the a... | 5 | [
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... | 20,077 | 20077 | |
Help needed with (the point form of) Gauss's law & divergence of E and
Lisa...
I need to show that
[tex]\vec{\nabla} \cdot \vec{E}= \frac{\rho}{\epsilon_0}[/tex]
where [tex]\rho[/tex] is the volume charge density.
I know that if I can show that the net flux of the electric field (in three directions xyz) out of the ... | 5 | [
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0.0129... | 20,078 | 20078 | |
Patent US6910110 - Interleaving apparatus and method for a communication system
PRIORITY
This application claims priority under 35 U.S.C. §119 to an application entitled “Interleaving Apparatus and Method for a Communication System” filed in the Korean Industrial Property Office on Jan.
9, 2002 and assigned Ser. No. 2... | 4 | [
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0.05126953125,
-0... | 20,079 | 20079 | |
have answer, need equation...
November 27th 2005, 10:18 AM
Juice
have answer, need equation...
OK, I have a points system where I can have up to 1.3billion points. I need to find a way to convert the points into percentages. I found a way to come up with the points, but I have not been
able to reverse it.
... | 4 | [
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0.0078735351562... | 20,080 | 20080 | |
Water Jug Problem
September 12th 2010, 07:39 PM
My Little Pony
Water Jug Problem
You take a 17 quart jug and a 12 quart jug to a stream, but you want to bring 8 quarts of water back. How do you do it?
Attempt at a solution
I used Bezout's Identity for this:
8 = 17x + 12y
However, the GCD of (... | 5 | [
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Measuring the Globe: An Historical Activity
For centuries educated people believed that the earth was a sphere. The circumference of the sphere we call the earth was first measured by Eratosthenes (c. 276-194 BCE), the third Librarian of the
famous Library at Alexandria, Egypt. A scholar in his own right but not the ve... | 4 | [
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2nd Order Linear PDE - Harmonic Function
April 29th 2011, 01:47 AM #1
2nd Order Linear PDE - Harmonic Function
Folks,
Can anyone assist in solving the attached question?
I believe the PDE is ellipitic becasue B^2-AC = 0 -(1)(1)<0 implies elliptic.
Therefore we can write
$\displaystyle \frac{d... | 5 | [
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Patent US7545932 - Secure authenticated channel
TECHNICAL FIELD OF THE INVENTION
The invention relates generally to secure authenticated channels, and in particular to calculation of session keys for establishment of such channels for protection of digital content, for example in
a digital television system.
BACKGROU... | 4 | [
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Patent US6389410 - Method for minimizing the number of sorts required for a query block containing window functions
FIELD OF THE INVENTION
The present invention relates generally to database query operations performed within computer systems and, more specifically, to minimizing the number of sort operations required ... | 4 | [
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2^x derivitive
If f(x)= a^x, the f(x+h)= a^a+x= a^xa^h so
f(a+ h)- f(a)= a^x(a^h- 1).
The derivative is lim (f(x+h)- f(x))/h= a^xlim {(a^h-1)/h}. Notice that that is a^x time a limit that is independent of x. That is, as long as the derivative exists, it is a^x times a constant. The
problem is showing that the lim{(a^... | 5 | [
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sketch an approximate solution curve through each of the points...
February 5th 2011, 10:11 PM #1
Senior Member
Joined
Aug 2009
Posts
349
sketch an approximate solution curve through each of the points...
by hand sketch an approximate solution curve through each of the points.
ok so the function is:... | 5 | [
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Reciprocal Trigonometric FunctionsAlgebraLAB: Lessons
Introduction:
In this lesson, three trigonometric ratios (secant, cosecant and cotangent) will be defined and applied. These involve ratios of the lengths of the sides in a right triangle.
The Lesson:
In a right triangle, one angle is 90º and the side across ... | 4 | [
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... | 20,088 | 20088 | |
matrices
is there any way you can help me. I know there is a system to solving these equations. such as add the 1st two roles to get the 1st row but i cant remember the rest.
Are you talking about echelon form? The most common way (I think) of doing this is finding the inverse of the matrix. Have you learned how to do... | 4 | [
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Physics Forums - View Single Post - Factor a 4th order polynomial
bob1182006
1. The problem statement, all variables and given/known data
Find the roots of:
[tex] x^5-1=0[/tex]
2. Relevant equations
Polynomial long division.
3. The attempt at a solution
[tex] x^5-1 = (x-1)(x^4+x^3+x^2+x+1) = 0[/tex]
[tex] x^4+x^3... | 4 | [
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finding the limit.
October 23rd 2011, 12:08 PM
hmmmm
finding the limit.
How do I prove that the limit of the function
$limit_{n\rightarrow \infty}(x_1^n+x_2^n+x_3^n+.....+x_k^n)^{(1/n)}$
where $0<x_1,x_2,.....,x_k\leq 1$ is equal to $max\{x_1,x_2,.....,x_k\}$
thanks for any help
solution
... | 5 | [
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How do I determine if the series converges?
Its given that the series are as follows: ∞ ∑ (arctan k)/(1 + kČ) k=1
I did some searchings and readings about basic comparison test but i dont fully understand them. Is the comparison between arctan k/1+kČ with Pi/4 and with (Pi/2)/(1/kČ) necessary? Can i just compare
in th... | 5 | [
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Surface Area
May 8th 2007, 12:51 AM #1
Newbie
Joined
Feb 2007
From
Australia
Posts
20
Surface Area
Many countries extend their borders by making a claim over territorial waters inside a defined km distance from their coastline.
What is the size (radius and area) of a circular island claiming a te... | 4 | [
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Patent US7023912 - Hybrid adaptive equalizer for optical communications systems
FIELD OF THE INVENTION
This invention relates generally to the field of optical communications systems, and more particularly to equalizing signals received via an optical channel.
BACKGROUND OF THE INVENTION
FIG. 1 shows an optical comm... | 4 | [
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Solve Uxx-3Uxt-4Utt=0 (hyperbolic)
solve Uxx-3Uxt-4Utt=0 with u(x,0)=x^2 and Ut(x,0)=e^x
I know that this is hyperbolic since D=(-1.5)^2+4 >0 so I have to transform the variables x and t linearly to obtain the wave equation of the form
(Utt-c^2Uxx=0). The above equation is equivalent to:
(d/dx - 1.5 d/dt)*(d/dx - 1.5... | 4 | [
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Derivatives of partial fractions
I'm having issue with one problem. We're asked to break down the problem into partial fractions to solve for the integral.
Well, I'm stuck on one. I'm being asked for the values of A, B, and C for the following problem.
∫((9x^2+13x-83)/((x-3)(x^2 + 16)))dx
I can get it worked down pr... | 4 | [
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Trigonometry Question
August 9th 2009, 08:54 AM
Programmer
Trigonometry Question
If Sin[x] + Sin[x]^2 + Sin[x]^3 == 1
Find Cos[x]^6 + 4 Cos[x]^4 + 8 Cos[x]^2
Any help/solution would be appreciated.
Thanks.
August 9th 2009, 02:56 PM
adkinsjr
Is this the correct problem?
$\sin(x)+\sin^2(x)... | 4 | [
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Complex numbers
July 3rd 2007, 07:04 AM #1
Newbie
Joined
Jul 2007
Posts
3
Complex numbers
I am trying to solve this set of problems, any ideas:
Let 1, omega, omega squared, ....., omega^n-1 be nth rooots of unity
then
(a) Show the conjugate of any nth root of unity is another root of unity, ... | 5 | [
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search results
Expand all Collapse all Results 1 - 7 of 7
1. CJM 2013 (vol 65 pp. 1287)
$K$-theory of Furstenberg Transformation Group $C^*$-algebras
The paper studies the $K$-theoretic invariants of the crossed product $C^{*}$-algebras associated with an important family of homeomorphisms of the tori $\math... | 4 | [
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