content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Derivatives of Inv Trig Functions
Try this... $y=\sin^{-1}(x/2) \iff \sin(y)=\frac{x}{2}$ by implicit $\cos(y) \cdot \frac{dy}{dx}=\frac{1}{2}$ solve for the derivative $\frac{dy}{dx}=\frac{1}{2 \cos(y)}$ note that $\cos(y) =\sqrt{\
cos^2(y)}=\sqrt{1-sin^2(y)}=\sqrt{1-(\frac{x}{2})^2}=\frac{1}{2}\sqrt{4-x^2}$ $\frac{dy... | 5 | [
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0.00022411346435546875... | 20,100 | 20100 | |
Gaussian elimination in MATLAB
1. The problem statement, all variables and given/known data
The point of this homework is to experiment with Gaussian elimination, and to
develop an appreciation for partial pivoting. Questions 1 & 2 can be done with a
calculator (though a computer is preferred). Question 3 requires a c... | 5 | [
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0.... | 20,101 | 20101 | |
Converting a Repeating Decimal to a Fraction
July 22nd 2011, 10:58 AM #1
Newbie
Joined
Apr 2011
Posts
14
Converting a Repeating Decimal to a Fraction
Having no guidance but my textbook, which explains basic concepts, but leaves to more in depth stuff to the teacher (of which I have none), I turn yet agai... | 4 | [
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Some help on mathematical induction?
November 29th 2009, 09:06 AM #1
Newbie
Joined
Nov 2009
Posts
4
Some help on mathematical induction?
Have some trouble completing these questions:
Any help will be greatly appreciated:
1 Use mathematical induction to prove that 5^n+9^n+2 is divisible by 4 for ... | 5 | [
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Help with Algebraic Number Theory
June 11th 2008, 12:45 PM #1
Member
Joined
Jun 2008
Posts
148
Help with Algebraic Number Theory
Hello
I'm currently working through a text titled 'Introductory Algebraic Number Theory' by Saban Alaca and Kenneth S. Williams, and I'm having trouble with some of the pr... | 5 | [
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Translation and then a rotation of a triangle
April 12th 2010, 09:15 AM
dolkam
Translation and then a rotation of a triangle
I have a triangle and the vertices were A(3,−1), B(−2,1) and C(2,3). I made a translation on a triangle (in another part of the paper) and now its new
vertices are A(5,−2), B(0,0) and ... | 5 | [
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0.0244... | 20,105 | 20105 | |
Contour Integration
October 27th 2010, 09:01 AM #1
Newbie
Joined
Oct 2009
Posts
16
Contour Integration
Integrate (z^2 - 4)/(z^2 + 4) counterclockwise around the circle |z - i| = 2.
Here's my attempt.
|z - i| = 2
|z - 2| = i
z0 = 2
(z^2 - 4)/(z^2 + 4)
= ((z + 2)(z - 2))/(z^2 + ... | 5 | [
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Patent US7711058 - Determination of the time delay and/or power of a multicarrier signal
FIELD OF THE INVENTION
The present invention relates to a method of determining the time shift and/or the power of a received signal transmitted between one or more user terminals and a base station or between a base
station and o... | 4 | [
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Double Discontinuous Inverse Problems for Sturm-Liouville Operator with Parameter-Dependent Conditions
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 794262, 7 pages
http://dx.doi.org/10.1155/2013/794262
Research Article
Double Discontinuous Inverse Problems for Sturm-Liouville Operator with Parameter-D... | 5 | [
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Patent US5007101 - Auto-correlation circuit for use in pattern recognition
BACKGROUND OF THE INVENTION
This invention relates to an auto-correlation unit for use in pattern recognition to obtain auto-correlation coefficients as for stored signal samples.
Auto-correlation coefficient C.sub.τ used in pattern recognitio... | 4 | [
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Integration using partial fraction-Irreducible Quadratic Factor 1
Integrate x^3 + 4x^2 + 9x + 14 .................x^2 + 4x + 3
The function can be decomposed in partial fractions as follows... $f(x)= \frac{x^{3}+ 4\cdot x^{2} + 9\cdot x + 14}{x^{2} + 4\cdot x + 3}= x + \frac {6\cdot x + 14}{x^{2} + 4\cdot x + 3}= x + ... | 4 | [
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l’Hopital’s rule
Find $\lim_{x\to\infty}\frac{e^{2x}}{(x+5)^3}$. Apply l’Hopital’s rule as many times as necessary, verifying your results after each application
$\lim_{x\to\infty}\frac{e^{2x}}{(x+5)^3}$ First both the numerator and denominator go to infinity in the limit, so we can apply L'Hopital's rule. Thus: $\lim... | 5 | [
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Calculating Square Roots - Matrix Algorithm
Hi. I only just recently found out about an algorithm for calculating the square roots of a number.
Lets say i want to evaluate [tex]\sqrt {n}[/tex]. I can make an approximation by inspection, and say [tex]\sqrt n \approx \frac{a}{b}[/tex]. Now, using this approximation, i c... | 4 | [
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Number Algebra
Genius Maker - School software - Maths software
COMPLEX NUMBER ALGEBRA
Features:
The Complex Number Algebra is a mathematics software, which facilit... | 4 | [
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Need some help with solving equations
November 18th 2007, 10:55 AM #1
Junior Member
Joined
Sep 2007
Posts
55
Need some help with solving equations
I am having a lot of trouble with these questions.
6. 5(sin 6t - 4cos 4t) = 0
-----------------------------------------------------
10. a) 3sin... | 4 | [
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Gene Expression Data Classification With Kernel
Principal Component Analysis
• We are sorry, but NCBI web applications do not support your browser and may not function properly.
More information
•
J Biomed Biotechnol. 2005; 2005(2): 155–159.
Gene Expression Data Classification With Kernel Principal C... | 4 | [
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Negative Exponent Problem
Hi,
The problem states:
"Write the following expression with only positive exponents and in simplest form. Variables are not equal to zero".
$x^{-1} + x^{-5}$
The answer is:
$\frac{x^4+1}{x^5}$
From the initial expression I get:
$\frac{1}{x} + \frac{1}{x^5}$
It's here that I get stuck. The ... | 4 | [
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The Klein-Gordon equation with a potential
andrien
Second one makes sense,first one does not.
The KGE is the Euler-Lagrange eqn. for the action defined as [itex]S = \int{d^d x \, \mathcal{L}}[/itex], where the Lagrangian (density) is:
[tex]
\mathcal{L} = \mathcal{L_0} + \mathcal{L}_{\mathrm{int}}
[/tex]
Here [i... | 4 | [
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0.068847656... | 20,117 | 20117 | |
Trigonometric Equations
August 15th 2008, 12:17 AM #1
Junior Member
Joined
Apr 2008
Posts
45
Trigonometric Equations
I'm not sure how to tackle this question, can anyone help me out? It asks;
a) Show that $\frac{1 - cos2x}{1 + cos2x} = tan^2x$.
b) Hence find the value of $tan22.5^o$ in simplest... | 4 | [
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... | 20,118 | 20118 | |
Linear equations addition
March 20th 2013, 05:48 PM #1
Member
Joined
Oct 2011
Posts
170
Thanks
3
Linear equations addition
I'm probably making a silly mistake or Wolfram Alpha is lying to me.
Question: Find the value of c and d.
$3d=13-2c$
$\frac{3c+d}{2}=8$
Rearranged, simplified ... | 4 | [
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Patent US5528527 - Sampling frequency converter
This application is a Continuation of Ser. No. 08/024,202, filed Feb. 23, 1993, now abandoned.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a sampling frequency converter for converting input data sampled at a sampling frequenc... | 4 | [
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Torque: Why F*r?
Originally posted by Dissident Dan
We all know that torque = force x lever arm, through education and experience, but I can't recall ever being taught an explanation for why this is. It's always just been explained to me as a
definition without underlying reasons.
Suppose that we begin by assuming the... | 4 | [
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Patent US4544229 - Apparatus for evaluating a polynomial function using an array of optical modules
FIELD
This invention relates to systolic pipeline processing for evaluation of polynomial functions with optical methods and apparatus. It is especially useful for analog computation at very high speeds,
and has a wide ... | 4 | [
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Radius of convergence
April 10th 2013, 03:21 AM
Educated
Radius of convergence
Attachment 27884
I can do part a) and b) but I'm not getting how to do part c)
So I'm guessing the part under the square root cannot be negative, and so $\dfrac{64b^2}{a^4}x^2 \le 1$
Solving that I would get:
$x^2 ... | 4 | [
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-0.10498046... | 20,123 | 20123 | |
Laplace Transform
April 14th 2010, 09:48 AM #1
Junior Member
Joined
Mar 2009
From
Berkeley, California
Posts
26
Laplace Transform
I've been working on a problem, this one in particular:
$f(t) = cosh(bt)$
where $(e^{bt} + e^{-bt})/2$ is equal to cosh bt
I attempt to take the Laplace tr... | 5 | [
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-0.1171875,... | 20,124 | 20124 | |
Rhombus coordinates
December 31st 2009, 12:42 AM #1
Newbie
Joined
Dec 2009
Posts
3
Rhombus coordinates
Can someone find a solution of this problem....
I have 500mmX500mm rhombus ( Rhombus A ). This is divided into 2500 equal size rhombuses of size 10mmX10mm ( R1 - R2500) . Now what I need to find i... | 5 | [
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... | 20,125 | 20125 | |
A Comparative Study of VaR Estimation for Structured Products
Economics Research International
Volume 2010 (2010), Article ID 838469, 16 pages
http://dx.doi.org/10.1155/2010/838469
Research Article
A Comparative Study of VaR Estimation for Structured Products
Department of Finance, Shih Hsin University, no. 111, Sec... | 4 | [
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Solving Inequalities / Check my work?
October 7th 2013, 08:23 AM #1
Junior Member
Joined
Oct 2011
Posts
62
Thanks
2
Can someone please check my work / make sure I am doing these correctly? Really appreciate the help!
1) x^2 + x -2 > 0
....do I just factor then that what x can not be?
x... | 4 | [
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0.01422119140625,
0.000057220458984375,
0.005859... | 20,127 | 20127 | |
Jordan Normal Form Issues
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,345
Let's take the simple example where the matrix, A, is 3 by 3 and has the single eigenvalue 3. Then the Characteristic equation is [itex](x- 3)^3= 0[/itex]. Since every matrix satisfies its own
characteristice equiation, it must be true t... | 5 | [
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0.029052734375,
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0.01403808593... | 20,128 | 20128 | |
Patent US20050171828 - A method for considering hierarchical preemptive demand priorities in a supply chain optimization model
CROSS REFERENCE TO RELATED APPLICATIONS
The present application is related to pending U.S. patent application Ser. No. 10/______, filed concurrently herewith to Denton et al., entitled “A METH... | 4 | [
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-0... | 20,129 | 20129 | |
Patent US20040010397 - Modification of the normalized difference method for real-time optical tomography
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit of U.S. provisional patent application No. 60/370,306, filed Apr. 6, 2002.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Inv... | 4 | [
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Lie Groups, Physics
Lie Groups, Physics, and Geometry
Prof. Robert Gilmore
Physics Department
Email: robert.gilmore@drexel.edu
This book has been published by Cambridge University Press during Janaury, 2008 (ISBN13 978-0-521-88400-... | 4 | [
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... | 20,131 | 20131 | |
Volume of the solid revolving about y-axis
October 4th 2009, 08:09 AM #1
Member
Joined
Feb 2009
Posts
91
Volume of the solid revolving about y-axis
This involves trig functions so I am not sure if I am on the right track
y = (tan^2 x)/x 0 <= x <= pi/4
a = 0; b=pi/4 on the x-axis
so I think... | 5 | [
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0.... | 20,132 | 20132 | |
Semigroups Characterized by Their Generalized Fuzzy Ideals
Journal of Mathematics
Volume 2013 (2013), Article ID 592708, 7 pages
http://dx.doi.org/10.1155/2013/592708
Research Article
Semigroups Characterized by Their Generalized Fuzzy Ideals
Department of Mathematics, COMSATS Institute of Information Technology, Ab... | 5 | [
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sum of a series
June 24th 2006, 07:41 PM #1
Junior Member
Joined
Jun 2006
Posts
53
sum of a series
It's been awhile since I have done these types of problems.
Can the sum of a series have a factorial in the answer?
this is my problem: Summation of (n/(n+1)!) with n>= 1
while working it out... | 5 | [
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0.035888671875... | 20,134 | 20134 | |
Problem Solving
November 22nd 2010, 03:21 PM #1
Member
Joined
Sep 2010
Posts
98
Thanks
1
Problem Solving
A and B are positive integers such that (i) A=7B and (ii) the sum of the digits of A is
twice the sum of the digits of B. If C is the number formed by writing the digits of B
immediately ... | 4 | [
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Reverse Digit problem help
August 18th 2009, 03:25 PM #1
Newbie
Joined
Aug 2009
Posts
2
Reverse Digit problem help
I need help on understanding and do a reverse digit problem.
problem is:
If you take two-digit number to make a second two-digit number, and add these numbers together, their sun w... | 4 | [
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... | 20,136 | 20136 | |
Parabola exercise.
January 29th 2011, 11:30 AM #1
Newbie
Joined
Jan 2011
Posts
4
Parabola exercise.
Currently working on a assignment with the graph to be plotted
R = 1500p-50p^2(squared)
it should be a Parabola with a positive U shape, but using the Parabola equation it is a slight curve from ... | 4 | [
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-... | 20,137 | 20137 | |
three-variable solution using elimintation: I'm stuck!
October 14th 2008, 08:29 PM #1
Newbie
Joined
Oct 2008
Posts
1
three-variable solution using elimintation: I'm stuck!
I am helping my daughter and this one has me stumped - it is a three-variable equation and their asking her to use "elimination" to s... | 4 | [
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Calculate the Electric Potential
Actually, nothing. Shoulda done it your way.
dV = kα(L/2 + btanθ)bsec^2θdθ/bsecθ
dV = kα(L/2 + btanθ)secθdθ
V = kαL/2 ∫secθdθ + kαb ∫tanθsecθdθ
V = kαL/2 {ln|secθ + tan&t... | 5 | [
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0.0131... | 20,139 | 20139 | |
Uniform Electric Fields
1. The problem statement, all variables and given/known data
A proton (m=1.67x10^-27) is suspended at rest in a uniform electric field E. Take into account gravity and determine E.
2. Relevant equations
F[E]=|q|E
F[g]=mg
3. The attempt at a solution
F[G] = mg
F[G] = (1.67x10^-27)(9.8)
F[G] =... | 4 | [
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0.00408935... | 20,140 | 20140 | |
Some Limit Questions
July 31st 2009, 11:13 PM #1
Junior Member
Joined
May 2009
Posts
47
Some Limit Questions
Having some issues with these questions:
1.) limit as x ---->4 $\frac{x^2-x-12}{2x^2-5x-12}$
I know I can factor the numerator to have: (x-4 (x+3).
2.) limit as x---->infinity $\frac... | 5 | [
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0.051025390625,
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0.01507568359375,
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Patent US7324432 - Apparatus of compensating for frequency offset using pilot symbol in an orthogonal frequency division multiplexing system
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates generally to a frequency offset compensation apparatus for an OFDM/CDMA (Orthogonal Frequency... | 4 | [
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Missing mass conjecture
up vote 6 down vote favorite
3
Let $n,t$ be positive integers and $p_1,p_2,\ldots,p_n$ positive numbers summing to 1. Conjecture: $$ \sum_{i=1}^n p_i (1-p_i)^t \le \frac{n(1-1/n)^n}{t} $$ always holds.
The motivation comes from my missing mass question; the quantity $\sum_{i=1}^n p_i (1-p_i)^t... | 5 | [
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0.070800781... | 20,143 | 20143 | |
generators and relations
June 13th 2013, 10:04 AM #1
Super Member
Joined
Mar 2010
Posts
979
Thanks
236
generators and relations
Here is the problem I'm working on, from an old qualifying exam:
Let M be the $\mathbb{Z}$-module generated by a, b, c with the relations $4a+3b+3c=2a-b+3c=0$. Express ... | 5 | [
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0.00653076171875,
0.0177... | 20,144 | 20144 | |
Math Help
October 18th 2008, 06:23 PM #1
Junior Member
Joined
Oct 2008
From
baltimore
Posts
61
Cubic
Let C be a cube where the length of its diagonal is the same as its volume..what's the length of each side?
Well let the length of one side = x.
Volume = $x^3$
length of diagonal = $\s... | 4 | [
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0.053710937... | 20,145 | 20145 | |
Positive Integer is Prime Like
Last edited by Aquafina; June 10th 2009 at 05:58 AM.
Hi there, I'm a totally non maths guy. But I've looked at primes for fun over the last few weeks... By your definition (not divisible by 2,3,5) I can tell you there are 26 'prime like' numbers
between 0-100 28 in 100-200 & 26 between 2... | 5 | [
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The motorcyclist's problem reformed: feasibility in the general case (Hard!!!)
June 25th 2011, 12:42 AM
godelproof
Re: The motorcyclist's problem reformed: feasibility in the general case (Hard!!!)
Hi Sudharaka my friend!
If m is very large, it can ignore A3 and first carry A1 forwards, drop him before A2 a... | 5 | [
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Find angle between 0 and pi that's coterminal with 17pi/6?
September 2nd 2012, 05:51 AM #1
Newbie
Joined
Sep 2012
From
Cincinnati
Posts
2
Find angle between 0 and pi that's coterminal with 17pi/6?
I know the answer is 5pi/6.
I just have no idea how to get that answer!
I understand cotermina... | 4 | [
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0.05517578125... | 20,148 | 20148 | |
prove that φ(n/p^K) is even
so in this problem i no that gcd(a,n)=1 and the question i need to answer is : let p be any prime factor of n and let k be the number of times that p appears in the prime factorization of n.
prove that φ(n/p^K) is even
so far i have
If p is prime, then φ(p^k) = p^(k-1)(p-1). ... | 4 | [
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... | 20,149 | 20149 | |
Physical equivalence of Lagrangian under addition of dF/dt
Favicon
Chain rule: [itex]\frac{dF}{dt} = \sum\limits_k{\frac{∂F}{∂q_k}\frac{∂q_k}{∂t}}[/itex]
Correctly: [tex]\frac{dF}{dt} = \sum\limits_k{\frac{∂F}{∂q_k}\frac{dq_k}{dt}}+ \frac {∂F}{∂t}[/tex],
that is
[tex]\frac{dF}{dt} = \sum\limits_k{\frac{∂F}{∂q_k}... | 4 | [
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If a and b are positive integers divisible by 6, is 6 the
Author Message
TAGS:
If a and b are positive integers divisible by 6, is 6 the [#permalink] 02 Sep 2010, 22:28
... | 4 | [
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... | 20,151 | 20151 | |
Hello! Nonlinear Differential Equation
September 2nd 2012, 02:25 PM
Nekoteko
Hello! Nonlinear Differential Equation
Hello, new here. Really need help with this one nonlinear differential equation problem from my Calc IV homework. :( Any help or hints would be greatly appreciated!
xy' - y = 1/(x^3)
Than... | 5 | [
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0.00988769531... | 20,152 | 20152 | |
Physics Forums - View Single Post - When does gravitational force = electromagnetic force?
Thanks
As for your question about protons... if I understand correctly, you're asking how many protons it would take to produce an electric force equivalent to Earth's gravity? That depends on what's being
attracted to the prot... | 5 | [
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Differential Equation question
February 10th 2008, 06:53 AM #1
Junior Member
Joined
Apr 2007
Posts
38
Differential Equation question
The problems in the section of the book list the questions in this way:
dy/dx = 4y+e^4xsin(5x) and y(0)=1
First I get P(x)= -4 and then Q(x) = e^4x sin(5x)
then... | 5 | [
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-0.03881835937... | 20,154 | 20154 | |
Review Material -- Exponents
February 10th 2008, 10:51 AM
Mad
Review Material -- Exponents
I just started Pre-Calc last week and am already stuck. I added the course late (college freshman) and consequently missed three classes. Those three classes were, apparently, focused on
reviewing College Algebra.
... | 4 | [
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0.078125,
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Gamma Distribution Help!!
October 30th 2009, 09:20 AM #1
Junior Member
Joined
Sep 2009
Posts
47
Gamma Distribution Help!!
Suppose the reaction time X of a randomly selected individual to a certain stimulus is a standard gamma distribution with (alpha=2)
What is F(5;2) using gamma
show steps i ... | 5 | [
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Maxwell boltzman distribution
1. The problem statement, all variables and given/known data
A sealed bottle at 1 atm of pressure holds 1 mole of neon and 1 mole of argon gas at a temperature of 295 K.
Find the number of molecules of neon which have velocities between 100 and 200 (m/s).
2. Relevant equations
boltzman... | 4 | [
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... | 20,157 | 20157 | |
Math Problem!! Solid Figures and Volume
February 6th 2006, 04:08 AM #1
gabextreme
Guest
24.A quarter of a rectangular tank is filled with oil. The space remaining in the tank measures 80cm by 14cm by 8 cm. Find the Volume of the tank.
26. 3/4 of a rectangular tank, measuring 40cm by 12cm by 4cm is filled wi... | 4 | [
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singularity
October 8th 2012, 06:29 PM #1
Junior Member
Joined
Sep 2012
From
New York
Posts
55
singularity
Can someone help me with this, I don't really understand how to do it, if you help me with one step by step i could figure out the rest.
For each real function described , give all the valu... | 4 | [
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Finite rings
August 7th 2009, 04:49 AM #1
Finite rings
Given a ring $R$ with multiplicative identity, let $U(R)$ denote the set of its units.
What is the smallest positive integer $n$ such that there does not exist any finite ring such that $U(R)$ contains exactly $n$ elements?
Emm...I think you natural... | 5 | [
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Euclidean algorithm proof
Can anyone help me on the following question show that if a< 0 then a=qb+r 0=<r<b thankss so much
You can prove it by using mathematic induction. let P(n) be the following proposition: if the integer a is in [-nb,-(n-1)b), then there exist integer q and r, such that a=qb+r, where 0=< r < b.
... | 5 | [
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Patent US7411523 - Hardware efficient implementation of finite impulse response filters with limited range input signals
RELATED APPLICATIONS
The present application is a continuation of U.S. patent application Ser. No. 11/058,388 entitled “HARDWARE EFFICIENT IMPLEMENTATION OF FIR FILTERS WITH LIMITED RANGE INPUT SIGN... | 4 | [
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Sum to infinity.. (don't know enough to phrase problem correctly)
April 12th 2010, 03:27 AM #1
Newbie
Joined
Jan 2010
Posts
5
Sum to infinity.. (don't know enough to phrase problem correctly)
This problem is a basic one from finance/economics about obtaining the Present Value; but the math is general
... | 5 | [
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Easy Integrals!!
1st one comes out to: $\frac{1}{4}x^2 (2log(x) - 1)$ 2nd one comes out to: $\frac{1}{5}(2log(x - 2) + 3log(x + 3))$ I think! not 100% certain there.
HiLet's find the partial fraction decomposition of $\frac{x}{x^2+x-6}$. The discriminant of the denominator is $\Delta = 1^2-4\cdot1\cdot (-6)=25>0$ henc... | 5 | [
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Integration... can't do this one either...
I need to find x. any help would be great: $<br /> v \frac{dv}{dx} = -\frac{g}{b^2}(v^2 + b^2)<br />$
Is this right? $<br /> ln(v + 1) = - gx + C<br />$ or this: $<br /> \frac{1}{2} ln(b^2 + v^2) = - \frac{g}{b^2} + C<br />$
Last edited by billym; March 26th 2008 at 02:04 AM... | 5 | [
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Can't figure out how to set up this modeling problem
January 25th 2011, 10:38 PM #1
Newbie
Joined
Oct 2010
Posts
17
Can't figure out how to set up this modeling problem
So I feel confident that I can solve the differential equation once I set it up, however I'm not able to set up the problem.
The qu... | 5 | [
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Continued Fraction for the Gamma Function
KEYWORDS:
Binet function, Gamma Function, Continued Fraction, qd algorithm,
Akiyama-Tanigawa algorithm, Bernoulli numbers, Jacques Binet,
Thomas Jan Stieltjes, Heinz Rutishauser, Peter Henrici,
OEIS A005146, OEIS A005147.
On Stieltjes' Continued Fraction for the Gamma Function... | 4 | [
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Induction - Divisibility
We have to prove that $n(n^2+5)$ is divisible by 6. How do we go about it?
Re: Induction - Divisibility
Re: Induction - Divisibility
Re: Induction - Divisibility
To use induction, as mentioned, we first check the base case $P_1$:
$1\left(1^2+5\right)=1(6)=6(1)$ true. So we sta... | 5 | [
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Patent US5195052 - Circuit and method for performing integer power operations
TECHNICAL FIELD
The present invention relates generally to data processing systems and, more specifically, to arithmetic circuitry that performs integer power operations.
BACKGROUND ART
Integer power arithmetic is often required in data pr... | 4 | [
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0.127... | 20,169 | 20169 | |
Renormalization Group for dummies
Its not quite like that. You write out the power series and you calculate the terms term by term using perturbation theory. The first term is finite - no problem. Second and higher terms turn out to
be infinite. It took people a long time to figure out why this happened but the answer ... | 4 | [
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Weather Derivatives and Stochastic Modelling of Temperature
International Journal of Stochastic Analysis
Volume 2011 (2011), Article ID 576791, 21 pages
http://dx.doi.org/10.1155/2011/576791
Research Article
Weather Derivatives and Stochastic Modelling of Temperature
^1Center of Mathematics for Applications, Univers... | 4 | [
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... | 20,171 | 20171 | |
Dielectric breakdown
1. The problem statement, all variables and given/known data
Hello:
I am asked to find the maximum voltage in a cylindrical capacitor. The capacitor consists of an inner wire and an outer cylindrical shell. The wire has radius [tex]r_{1}[/tex] and the cylinder has
inner radius [tex]r_{2}.[/tex] The... | 4 | [
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Point of Intersection
September 4th 2010, 12:03 PM #1
Newbie
Joined
Sep 2010
Posts
17
Thanks
1
Point of Intersection
Hi there,
The formula's are:
$y = -\frac{4}{3}x + 12.33$
$y= \frac{3}{4}x + 4$
I'm unsure about how I go about it? I can do simultaneous equations and stuff, but we h... | 4 | [
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0... | 20,173 | 20173 | |
Formula product of sines
January 14th 2012, 03:39 AM #1
Junior Member
Joined
Oct 2011
From
Belgium
Posts
36
Formula product of sines
Does anyone know how to prove this formula?
$2^{n-1}\prod_{k=0}^{n-1}\sin(x+\frac{k\pi}{n}) = \sin(nx)$
All suggestions, ideas are welcome.
Below you fi... | 5 | [
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Help computing derivative of a 2 variable integral
December 4th 2012, 07:09 AM
Maroka93
Help computing derivative of a 2 variable integral
Im not sure if there is a typo, or I'm just not seeing how to solve this:
help please (:
Compute the derivative w.r.t. t of g(t) := ∫[0]^t f(t,x) dx.
sorry for... | 5 | [
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A Puzzle
A Puzzle June 25, 2010
Posted by genericme in Uncategorized.
trackback
Consider a set of $n$ objects from which $m$ are drawn randomly at a time, with replacement. What is $E(n, m)$, the expected number of draws I have to make to have drawn all of the objects?
I have yet to find a satisfactory closed-form ... | 5 | [
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Conservation of energy using orientation
Doc Al
Yes, momentum is conserved. Use that to figure out the velocity of the first guy after the collision.
so...
m1v1 + m2v2 = m1v1` + m2v2`
(80 kg)(7.5 m/s [E20S] = (80kg)(V1`) + (90 kg)(3 m/s[N30E])
600 kgm/s [E20S] = (80kg)(V1`) + 270 kgm/s [N30E]
600 kgm/s [E20S] -... | 4 | [
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Schraubenberechnung unter Berücksichtigung der Flankenwinkel, Werkstoffkennwerte und Scherspannungsverfahren.
Englisch Deutsch
Bolt calculation in
... | 5 | [
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0.06591796875,... | 20,178 | 20178 | |
Math Help
October 22nd 2008, 11:02 AM #1
Newbie
Joined
Oct 2008
Posts
22
Ring
Let A be a ring with $0 ot = 1$ and K be the set
$K =${ $x\in A | x^2 - x + 1 = 0$}.
1) If $x\in K$ then $x$ is invertible and $x^{ - 1} = x^5$
2) If $K = A$ \ {0,1} then A is isomorphic with $Z_{3}$ or $1 + 1 = 0$... | 5 | [
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-... | 20,179 | 20179 | |
Real analysis - proving the number of solutions
August 4th 2008, 05:52 AM
kevin28
Real analysis - proving the number of solutions
Hey everyone,
Basically this kinda question comes up every year on the Real Analysis exam, but i really don't know how to do it.
I'm stuck on the last part of the question wi... | 5 | [
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Brevet US4209780 - Coded aperture imaging with uniformly redundant arrays
BACKGROUND OF THE INVENTION
The present invention pertains generally to imaging devices and more specifically to coded aperture imaging of non-focusable radiation.
The concept of using a coded aperture to image nonfocusable radiation was first ... | 4 | [
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dimensional analysis for metric conversions
May 8th 2013, 11:09 AM
dwinns17
dimensional analysis for metric conversions
I need to learn how to solve metric conversions through dimensional analysis. Can someone please help any info would be greatly appreciated.
May 8th 2013, 11:35 AM
topsquark
Re: dimensional ... | 4 | [
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Numerical Simulations of the Impact and Spreading of a Particulate Drop on a Solid Substrate
Modelling and Simulation in Engineering
Volume 2012 (2012), Article ID 687961, 10 pages
http://dx.doi.org/10.1155/2012/687961
Research Article
Numerical Simulations of the Impact and Spreading of a Particulate Drop on a Solid... | 4 | [
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I having a headache proving an identity
March 30th 2009, 08:28 AM #1
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Mar 2009
Posts
9
I having a headache proving an identity
I having some problem proving a identity.
Prove:
$<br /> (sec^2x )/tanx = (cot^2x - tan^2x) / (cotx - tanx)<br />$
i start by the left side so i get... | 4 | [
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-0.... | 20,184 | 20184 | |
arghh!!! please help - new to this hope im posting correctly
March 24th 2009, 01:17 PM #1
Newbie
Joined
Mar 2009
Posts
3
arghh!!! please help - new to this hope im posting correctly
Points A (3,1), B(-1,-11), C(-5,9)
what the slope that passes through A and B
whats the co-ordinates of the midpo... | 4 | [
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help with Riemann integrals
November 7th 2009, 02:26 PM #1
Junior Member
Joined
Sep 2009
Posts
53
help with Riemann integrals
Prove that the function f:[0,1]--> R defined by
f(x) = {1, if x=1/n, n is an element of Z+
{0, otherwise
is Riemann integrable on [0,1].
Thanks!
1) Usi... | 5 | [
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-0.064941406... | 20,186 | 20186 | |
Integration by parts
intergrate (ln(x))^2
so i set u=(lnx)^2...which makes du=2lnx(1/x)
then i set dv=dx...which makes v=x
according to the formula for integration by parts i have
x(lnx)^2- integral x(2lnx)(1/x)
simplifying it i get x(ln)^2-2intergral lnx
and here is where i am stuck....what i the integral of lnx... | 5 | [
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Accretion rate of Earth
1. The problem statement, all variables and given/known data
i) Estimate (in kg/yr) the rate of Earth accreting inter-planetary dust.
Assume a particle number density of n=1e-8/m3, a particle mass density of 5 gm/cc, a particle radius 50 microns and a relative velocity equal to Earth's orbital ... | 4 | [
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... | 20,188 | 20188 | |
Very difficult math problem
Your question seemed a bit ambiguous to me, so I hope this is what you are asking for:
We start off with:
Cos(ax) + Cos(bx) + Cos(cx) = 0
Cos(bx) + Cos(cx) = -Cos(ax)
ArcCos[Cos(bx) + Cos(cx)] = ArcCos[-Cos(ax)]
Looking at the right side of the equation after taking the inverse Cos, it ... | 4 | [
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0.0299072265... | 20,189 | 20189 | |
Complex Numbers
February 24th 2007, 11:02 PM #1
Complex Numbers
Note: z = cis(@) here.
I worked out that
z + z^-1 = 2cos(@) ---1
(z + z^-1)^3 = z^3 + z^-3 + 3(z+z^-1) --- 2
Now I need to prove cos(3@) = 4cos^3(@) - 3cos(@)
I try to sub in 2cos(@) into 2 for (z + z^-1), and fiddle around, ... | 5 | [
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Applications of Integration - Work. Please Help
I am currently taking CALC II in the summer. So far we have gone over Applications of Integration(area under the curve, solids of revolution) to Techniques of Integration (integration by parts, Trig
substitution, Partial Fractions, IMproper Integrals, etc.) From all the p... | 5 | [
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-... | 20,191 | 20191 | |
Lifetime of Tires
March 22nd 2009, 08:49 PM #1
Newbie
Joined
Mar 2009
Posts
5
Lifetime of Tires
Here is the question:
For a tire manufacturing company, it is known that only 7% of their tire
products last less than 35 months, whereas 11% of them last more tham 63
months. Assuming the distrib... | 5 | [
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Model Theory - definiable classes
November 17th 2010, 04:12 AM #1
Junior Member
Joined
Oct 2009
Posts
70
Model Theory - definiable classes
Hi,
This time I've problem with following exercise:
Let $L$ be a first-order language and for each $i \in I$ let $\mathbb{K}_i$ be a class of $L$-structures... | 4 | [
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... | 20,193 | 20193 | |
[SOLVED] Limit question
August 3rd 2009, 03:43 AM #1
Junior Member
Joined
Aug 2009
Posts
29
[SOLVED] Limit question
limit as h goes to 0 of $\frac{f(2+h)-f(2)}{h}$ where f(x) = $\sqrt{x}$
It looks similar to differentiation from first principles, but I can't see how to use that...
Hello,
R... | 5 | [
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trig arithmetic series..
December 26th 2009, 06:09 AM
Tweety
trig arithmetic series..
Quote:
The first three terms of an arithmetic series are √3cosθ, sin(θ−30°) and sin θ, where θ is acute. Find the value of θ.
So far I have expanded sin(θ−30°)
to get;
$\sqrt{3}cos\theta + \frac{\sqrt{3}}{2}s... | 5 | [
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0.040771484... | 20,195 | 20195 | |
Showing that the Virial Theorem holds
So I have already calculated correctly that the expectation of the interaction potential for hydrogenic atoms is
<nlm|V(r)|nlm>=-(uZ^2e^4)/((hbar^2)*n^2)
Note that u= mass,and V(r)=-Ze^2/r
I now have to calculate <nlm|T|nlm> where T is the kinetic energy operator, and
T=p^2/(2u... | 4 | [
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Gradients and Directional Derivatives
Alw
1. The problem statement, all variables and given/known data
(a) Find two linear equations in the variables x,y,z such that their solution set is the tangent line to the graph of f(x,y) = [tex]x^{2}[/tex] - [tex]y^{2}[/tex] at (2,1,3) which is parallel to the
x,z plane. (b)... | 5 | [
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0... | 20,197 | 20197 | |
Inverse trig domain
March 21st 2010, 06:48 PM #1
Inverse trig domain
Hi there,
Just wanted to check if my answer to this question is correct. I need to find the implied domain of $sin^{-1}\left [ 2cos(x+\frac{\pi}{2})\right ]$
I'm getting $x\in \left [ -\frac{5\pi}{6} , -\frac{\pi}{6}\right ]$
Than... | 4 | [
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Differential Equations
Well, the second equation is a Cauchy-Euler type if you multiply through by x. Or, since there's no y term, you can reduce the order.
The DE... $\displaystyle y^{'} = -\frac{y}{x} + x^{2}\ y^{2}$ (1) ... is of the type analysed in XVII° century by the Swiss mathematician Jacob Bernoulli. Devidin... | 4 | [
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... | 20,199 | 20199 |