content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Related rates concept question (Lengthy)
April 10th 2010, 09:30 PM #1
Junior Member
Joined
Dec 2009
Posts
30
Related rates concept question (Lengthy)
(I know this is long, but I tried to be as clear and thorough as possible.)
Here's a problem I have. There is a man walking alongside the edge of a lo... | 5 | [
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x is the sum of y consecutive integers. w is the sum of z
Author Message
TAGS:
x is the sum of y consecutive integers. w is the sum of z co [#permalink] 18 Nov 2009, 20:37
... | 4 | [
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Volumes - Linear Relationships
July 17th 2010, 08:34 PM #1
Junior Member
Joined
Apr 2010
Posts
29
Hi
For this question:
A symmetrical pier of height 5 m has an elliptical base with equation x^2/25 + y^2/4 = 1 and slopes to a parallel elliptical top with equation x^2/9 + y^2 = 1. If the cross sec... | 4 | [
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0.031494... | 22,002 | 22002 | |
Equiv. Class Problem
In Q[t], define the equivalence relation ~ as f(t) ~ g(t) precisely when f(t) - g(t) is a multiple of t^2 - 5. We define the addition and multiplication of equivalence classes as [f(t)] + [g(t)] = [f
(t) + g(t)] and [f(t)] * [g(t)] = [f(t) * g(t)]
(Assume: ~ is an equivalence relation, Addition/Mut... | 4 | [
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Stress Analysis of Piping
The analysis of piping under pressure, weight and thennal expansion is complex. This complexity can be understood by knovledge of Principal Axis System.
Stress is considered as the ratio of Force to Area. To find the stress in the small element, say cube of a piece of pipe, construct a thre... | 4 | [
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0... | 22,004 | 22004 | |
Combinatorics problem - rescursion
October 18th 2009, 02:24 PM
tautology
Combinatorics problem - rescursion
Hey everyone, first post! I have been stuck on this problem for a very long time and can't see to make any headway.
For n>=1, let h_n be the number of ways to express n as the sum of a sequence of pos... | 4 | [
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An Interesting Limit...
May 9th 2008, 09:07 PM
Chris L T521
An Interesting Limit...
I already evaluated the limit, and got the answer, but I want to see if you guys can come up with an easier way to solve it (Sun):
$\lim_{b\to \infty}\int_{0}^{b}\frac{\sqrt{1-e^{-x}}}{b}\,dx$.
May 9th 2008, 10:43 PM
mr f... | 5 | [
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A problem!
June 25th 2010, 01:54 PM
Also sprach Zarathustra
A problem!
$f(x)=x-\frac{3}{2}x^2+\frac{11}{6}x^3-\frac{50}{24}x^4+\frac{274}{120}x^5+...$
This is Taylor series of function $f(x)=\frac{ln(1+x)}{1+x}$
My question is:
$f(x)=x-\frac{3}{2}x^2+\frac{11}{6}x^3-\frac{50}{24}x^4+\frac{274}{120}... | 4 | [
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Speed Bump Dynamics
March 8th 2011, 05:36 PM #1
Newbie
Joined
Mar 2011
Posts
3
Speed Bump Dynamics
so far i have found the problem for when the tire is before the bump and during but i am having trouble with finding after it always turns out to be equal to the before so im looking for someone
to chec... | 5 | [
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Differentiable Functions on Manifolds
Let http://data.artofproblemsolving.com/...bf94102d1b.gif, http://data.artofproblemsolving.com/...37c18dc40f.gif and http://data.artofproblemsolving.com/...40e93223f0.gif, http://
data.artofproblemsolving.com/...4e0c5c8d8f.gif be two functions. If http://data.artofproblemsolving.co... | 5 | [
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How come when a reaction causes an increase of entropy, it is able to do more work?
If the pressure is kept the same, is all the energy exchanged turned into heat?
Not necessarily. Work can still be done by change of volume.
It is worth getting these ideas clear before proceeding further. So let us look at a few real... | 5 | [
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Brevet US6556958 - Fast clustering with sparse data
FIELD OF THE INVENTION
This invention relates generally to data modeling, and more particularly to efficient data modeling utilizing a sparse representation of the initial data set.
BACKGROUND OF THE INVENTION
Data modeling has become an important tool in solving c... | 4 | [
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There are five flavors of icecream: banana, chocolate, lemon
Author Message
TAGS:
There are five flavors of icecream: banana, chocolate, lemon [#permalink] 24 Sep 2009, 19:06
... | 4 | [
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A-level Physics (Advancing Physics)/Vectors/Worked Solutions
From Wikibooks, open books for an open world
1. Which of the following are vectors?
• 20 cm is scalar, not a vector - it does not have a directional component.
• 9.81 ms^-2 towards the centre of the earth is a vector.
• 5 km south-east is a vector.
... | 4 | [
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Proving Limits
July 27th 2011, 09:32 AM
Arron
Proving Limits
I need to prove the following statement
lim
x---> Infinity
3x^5-5logex/5e^x-2x^5
I have
logex/x^5 --> 0 as x---> Infinity
not sure about the other bit.
Also need to prove the following
lim
x--->o
x^2/1-e^... | 5 | [
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0.001808166503... | 22,014 | 22014 | |
Neutrino Oscillation Formula
which part of the formula is confusing you?
how to express [itex]E_{i} t[/itex] in terms of [itex]L, m_{i}[/itex]?
This is done by some easy calculations, I think you can find them easy if you search... eg
http://www2.ph.ed.ac.uk/~vjm/Lecture...s/PPNotes5.pdf
eq 16.3
and also by saying... | 4 | [
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0... | 22,015 | 22015 | |
Distance and the Hubble’s Constant
Marcus: First and foremost:
You mean the figure 92? 92 is twice 46. Diameter is twice radius.
D’Oh - obviously must have contracted horizon blindness due to an overload of horizons
Popular science books written by astrophysicists, astrophysics textbooks and to some extent professio... | 4 | [
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cot(x) and ln sin(x)
May 17th 2012, 11:28 AM #4
May 17th 2012, 08:41 AM #3
May 17th 2012, 07:41 AM #2
May 17th 2012, 07:34 AM #1
Re: cot(x) and ln sin(x)
Sorry. yes . $\frac{\pi}{2}\leq x \leq \pi$ thanks
Re: cot(x) and ln sin(x)
I beg your pardon, the functions are negative in the given range so we need t... | 4 | [
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Help with this PDE
October 1st 2009, 09:05 PM
policebox
Help with this PDE
Hello,
I'm currently taking a course in partial differential equations. We are currently solving boundary value problems using the method of separation of variables. I'm attemping to find the seperated
solutions and have gotten s... | 5 | [
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Fourier transform and orthogonal system
December 12th 2011, 09:47 AM #1
Member
Joined
Sep 2010
From
Germany
Posts
112
Thanks
4
Fourier transform and orthogonal system
Let $\phi_{n}(x)=\begin{cases} 1 ,\ x\in[n-\frac{1}{2},n+\frac{1}{2}]\\ 0, \ elsewhere \end{cases}$
a) Compute the Fourier tr... | 5 | [
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Viscosity Iterative Schemes for Finding Split Common Solutions of Variational Inequalities and Fixed Point Problems
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 470354, 25 pages
http://dx.doi.org/10.1155/2012/470354
Research Article
Viscosity Iterative Schemes for Finding Split Common Solutions of Var... | 5 | [
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... | 22,020 | 22020 | |
System of equations solution description
April 8th 2009, 11:10 AM
Oijl
System of equations solution description
If I have
x' = Ax
where A is the matrix below
(1, -2
3, -4)
then the direction field of the solutions would have everything moving towards (0, 0) as t --> infinity. My question ... | 4 | [
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... | 22,021 | 22021 | |
How many elements in a group Z*81?
October 25th 2008, 07:08 PM
apsis
How many elements in a group Z*81?
The subject says it all. The question is How many elements does the group Z*81 have?
I'm really not too sure what the question is asking. I know if I laid the table out it'd be 81 x 81, but there would on... | 5 | [
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Radio Receiver First Stage Noise
Noise in amplifying valves and mixer noise gives my understanding of valve internal noise. What does this mean for a radio receiver system? There are two main sources of noise in a receiver: internal
device noise and thermal noise. For the moment let us assume that the noise performanc... | 5 | [
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Dyadic Product and Index of Refraction
Manuel_Silvio
Dear readers,
In my recent study of dyadic products I found out that physical quantities expressend as 2nd rank tensors can also be expressed as a dyadic product of two vectors. Similarly 2nd rank tensor fields
can be expressed as pointwise dyadic products of two... | 4 | [
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Equinumerous
September 18th 2008, 11:28 AM #1
Junior Member
Joined
Apr 2008
Posts
30
Equinumerous
Show that the following pairs of sets S and T are equinumerous by finding a specific bijection between the two sets in each pair.
a. S= [0,1] and T = [1,3]
b. S= [0,1] and T = [0, infinity]
Th... | 5 | [
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Fundamental Theorem of Calculus Help Needed
August 29th 2006, 05:18 PM #1
Newbie
Joined
Aug 2006
Posts
9
Fundamental Theorem of Calculus Help Needed
Hello all, I am new here, and would like some help please. I did look around at LaTex first in an effort to make my questions more readable.
$h(x)=\int... | 5 | [
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Transitive closure relation.
March 6th 2009, 04:22 PM
scorpion007
Transitive closure relation.
Hi,
The question is as follows:
The transitive closure of a relation R on S x S is another relation on S x S called Tr(R) such that $(s,t) \in Tr(R)$ iif there exists a sequence $s=s_1, s_2, s_3, \ldots, s_n =... | 4 | [
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0.0546875,
0.04833984375,
-0.0859375,
-0.049072265625,
0.022216796875,
0.01171875,
-0.01062011718... | 22,027 | 22027 | |
Patent US6023573 - Apparatus and method for analyzing circuits using reduced-order modeling of large linear subcircuits
RELATED APPLICATIONS
This application is a continuation-in-part of U.S. application Ser. No. 09/144,767 filed on Sep. 1, 1998, abandoned.
FIELD OF THE INVENTION
The invention pertains to a method a... | 4 | [
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0.06494140625,... | 22,028 | 22028 | |
newton's method
use newtons method to find the roots of the equation sinx=x^(2)+3^(x)-1 correct to sic decimal places
Newton's methof gives us an itterative methof for finding a root of the equation $f(x)=0$. This is: $x_{n+1}=x_n-\frac{f(x)}{f'(x)}$ So for this we have: $f(x)=x^2+3^x-1-\sin(x)$ with: $f'(x)=2x+\ln
(3... | 4 | [
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-0.06591796875,
... | 22,029 | 22029 | |
Power series for 1/cosh(z)
January 12th 2010, 09:32 AM #1
Newbie
Joined
Jan 2010
Posts
2
Power series for 1/cosh(z)
How would I go about computing the series expansion of 1/cosh(z), or at least the first few terms? I know the series of cosh(z), but trying to manipulate that, or trying to form it using th... | 5 | [
-0.000823974609375,
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-0.0... | 22,030 | 22030 | |
Multi - Step Integral Problem
October 19th 2010, 06:58 PM
auntjamima
Multi - Step Integral Problem
Problem
f(x) = $(1-x^4)^\frac{1}{6}\$
R is the area under the curve from 0 to 1.
Part A: Write down an integral that represents the volume of this solid using the slice method, rotating around the x-a... | 4 | [
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Exact values in radians of θ, goven cosec & tan
December 6th 2011, 09:47 AM #1
Exact values in radians of θ, goven cosec & tan
Given cosecθ= -2, tanθ= 1/3√3 and -π < θ < π.
I must find the exact value of θ in radians, justifying my answer.
It shouldn't be too difficult;
An answer is
cosec theta =... | 4 | [
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Branch cut question
jasonRF
You should be able to write arccot in terms of logarithms by solving the following equation for z as a function of y:
[tex]
\cot z = y = i \frac{e^{i z} + e^{-i z}}{e^{i z} - e^{-i z}}
[/tex]
Then you have already (I Hope!) worked with branch cuts of log.
jason
OK... So:
Let w = cot(z... | 5 | [
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Patent US5602761 - Machine performance monitoring and fault classification using an exponentially weighted moving average scheme
CROSS-REFERENCE TO CO-PENDING APPLICATIONS
The following applications are assigned to the assignee of the present application:
U.S. patent application entitled "Machine Fault Diagnostics Sy... | 4 | [
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... | 22,034 | 22034 | |
Recurrence Relations with 2n? Where am I going wrong?
March 24th 2013, 06:27 PM
ob1
Recurrence Relations with 2n? Where am I going wrong?
hello guys,
I have been working on this problem for hours... And I am banging my head against the wall.. Please tell me where I went wrong, and whats the right answer.
... | 5 | [
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0.0... | 22,035 | 22035 | |
Theory of Algebraic Numbers 3RD Edition
A brief introduction for undergraduate students and teachers, presenting detailed proofs and explanations of the elementary components of classical algebraic number theory. Begins with divisibility
and Gaussian primes, and proceeds to ideal classes and class numbers and the Ferma... | 4 | [
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0.... | 22,036 | 22036 | |
Patent US5852567 - Iterative time-frequency domain transform method for filtering time-varying, nonstationary wide band signals in noise
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to time-frequency (TF) domain transform filtering of time-varying, nonstationary wide band signals in no... | 4 | [
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Physics Forums - Derivation of the kinetic energy equation in terms of distance.
Derivation of the kinetic energy equation in terms of distance.
I have seen the derivation of the kinetic energy equation using
F=M*v'
and
E=F*x
And I can see how this works, however if you try to do this without thinking about veloc... | 4 | [
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Evaluating limits using change of variable/ variable substitution
February 27th 2013, 06:38 PM
Bri22
Evaluating limits using change of variable/ variable substitution
Hi there! I am currently in grade 12, studying calculus 30 which is just calculus. I have a question about the above topic posted. One contains ro... | 5 | [
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Circle Geometry Help Please
February 26th 2010, 12:36 PM #1
Newbie
Joined
Feb 2010
Posts
10
A (-6,2) and B (-4,-2) are endpoints of a chord of a circle. C (2.-4) and D (8,4) are endpoints of a second chord.
a) Determine the coordinates of the center of the circle.
b) Determine the radius of the ... | 4 | [
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-0.0... | 22,040 | 22040 | |
Why do we get oscillations in Euler's method of integration and what i
ErezAgh
When using Euler's method of integration, applied on a stochastic differential eq. :
For example - given
d/dt v=−γvΔt+sqrt(ϵ⋅Δt)Γ(t)
we loop over
v[n+1]=v[n]−γv[n]Δt+sqrt(ϵ⋅Δt)Γn.
(where −γv[n] is a force term, can be any force and Γn i... | 5 | [
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... | 22,041 | 22041 | |
zeros of sum of two (matrix-valued!) polynomials
April 28th 2010, 05:05 AM #1
Junior Member
Joined
Aug 2008
Posts
74
Thanks
1
zeros of sum of two (matrix-valued!) polynomials
hi,
I have a nontrivial problem. let f(z) and g(z) be two (possibly monic) matrix-valued polynomials (i.e. of the form $\... | 4 | [
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... | 22,042 | 22042 | |
Poisson distribution moment generating function
March 13th 2010, 08:08 PM #1
Newbie
Joined
Mar 2010
Posts
17
Poisson distribution moment generating function
Let Y1, Y2,...,Yn be independent Poisson random variables with means ƛ1, ƛ2, ...,ƛn, respectively.
Find the: Probability function of Yi using th... | 4 | [
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Difference of the squares of two integers
October 18th 2006, 12:36 PM #1
Member
Joined
Sep 2006
Posts
75
Difference of the squares of two integers
Which one of the following numbers cannot be expressed as the difference of the squares of two integers?
A:314159265
B:314159266
C:314159267
D... | 4 | [
0.0146484375,
0.04443359375,
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-0.01293945312... | 22,044 | 22044 | |
Error function
Could anybody know formulation of integration $f(x)=\int _0 ^x e^{-t^2}dt$ Formulation is not series.
Last edited by math2009; March 18th 2009 at 04:36 PM.
you cannot integrate this, unless you let x go to infinity. However you can approximate it via it's Taylor Series
I try to solve it, and get a app... | 5 | [
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On Differential Subordinations of Multivalent Functions Involving a Certain Fractional Derivative Operator
International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 952036, 10 pages
http://dx.doi.org/10.1155/2010/952036
Research Article
On Differential Subordinations of Multivalent... | 5 | [
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Need to find four-figure number.
February 19th 2013, 03:15 AM #1
Newbie
Joined
Feb 2013
From
Earth
Posts
15
Hello
I need to find a four-figure number which can be divided by 7 and which can be written as a sum of square and cube of any natural number..
My English is not perfect, but I hope yo... | 4 | [
0.000881195068359375,
0.050537109375,
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-0.0279541... | 22,047 | 22047 | |
Vector problem involving orthogonal
March 5th 2011, 05:41 PM #1
Junior Member
Joined
Aug 2008
Posts
40
Vector problem involving orthogonal
Hi, I'm struggling with this problem:
For $\vec{u} =$[-4, 1, 10]^T and $\vec{v} =$ [−12, −6, 8]^T find the vectors $\vec{u1}$ and $\vec{u2}$ such that:
(i) ... | 5 | [
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0.... | 22,048 | 22048 | |
Patent US7760526 - Method and device for the control of a three-phase inverter
CROSS-REFERENCES TO RELATED APPLICATIONS
This application is a Non-Provisional Utility application which claims benefit of co-pending European Patent Application Serial No. EU 05425059.2 filed Feb. 9, 2005, entitled “Method and Device for
t... | 4 | [
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... | 22,049 | 22049 | |
polar coordinates-changing bounds of integration
November 15th 2010, 11:31 PM
isuckatcalc
polar coordinates-changing bounds of integration
When I change the integral to polar form, how do i adjust the bounds of integration? Do i have to look at the graph of the new function and determine r and theta from that? o... | 5 | [
0.004913330078125,
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-0.00390625... | 22,050 | 22050 | |
Log
$\log_2 3+\log_3 4+\log_4 5+\log_5 6+\log_6 7+\log_7 8$ How to find the value for this? Find the range for x? $3x+4<x^2-6x<9-2x$
first one i can't done more but in second one i solve finally i get answers in root then i can't do more>>
First One, $\log_2 3+\log_3 4+\log_4 5+\log_5 6+\log_6 7+\log_7 8$ $\log_2 3+\... | 4 | [
0.0198974609375,
0.0216064453125,
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0.0240478515625,
-0.0291748046875,... | 22,051 | 22051 | |
Physics Forums - View Single Post - Convolution integrals with Dirac's delta and its derivatives
Hello everybody,
I am new in this forum and I have a problem. First of all, I am not a mathematician, I am an engineer that is using the Laplace transform. Considering this, please do not be too formal in the
answers...
... | 4 | [
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0.0166015625,
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0.03759765625,
-0.01470947265625,
-0... | 22,052 | 22052 | |
Finding this derivative
December 3rd 2008, 08:00 AM
fattydq
Finding this derivative
So here's the deal, I already have the answer to a derivative related problem I was doing because I gave up and used an online derivative calculator, which usually (because it shows the steps
involved) makes me realize where ... | 5 | [
0.00897216796875,
-0.00994873046875,
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0.027587890625,
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0.005584716796875,
0.023193359375,
0.043212890625,
-0.030517578125,
-0.09375,
0.02... | 22,053 | 22053 | |
another implicit differentiation question
Here's another: If $ax^2 + by^2 = c$ show that the second derivative is equal to $-ac/b^2y^3$ Thanks
Because the second derivative will have an "x" in it and eliminating that reintroduces the "c". Since $ax^2+ by^2= c$, $2ax+ 2byy'= 0$. Differentiating again, $2a+ 2by'^2+ 2byy... | 5 | [
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-0.035400390625,
... | 22,054 | 22054 | |
Please help me with coding, statistics? How do I do this?
February 10th 2013, 06:27 AM #1
Newbie
Joined
Jan 2013
From
uk
Posts
15
Please help me with coding, statistics? How do I do this?
I can find out the mean, but not S.D /variance. How can I do this? Please show your steps so that I can understan... | 4 | [
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0.0223388671875,
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0.09521484375,
-0.031494140625,
0.05712890625,
0.08544921875,
0.0517578125,
0.103515625,
-0.0203857421875,
-0.0537109375,
-0.0517578125,
-0.06982421875,
0.046142578125,
... | 22,055 | 22055 | |
how do I find the maximum values?
June 1st 2010, 09:00 AM #1
Banned
Joined
May 2010
Posts
22
Mr. MacGregor's Shop makes bookcases and desks. Each bookcase requires 5 hours of woodworking and 4 hours of finishing. Each desk requires 10 hours of woodworking and 3 hours of finishing. Each
month the shop ... | 4 | [
0.044921875,
0.01129150390625,
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0.0272216796875,
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0.08544921875,
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0.0458984375,
0.02490234375,
0.09130859375,
0.0089111328125,
-0.00503540039062... | 22,056 | 22056 | |
Calculating elliptical orbits
and w = V Sin
X
/ R
:edited X:
and from Polar Direction we have :
R er
=> derivate (d f(x) / dt i`m not sure about the English word)
Velocity = R' er + Rw e(theta)
=> derivate again for acceleration
R'' er + R'w e[tex]\theta[/tex]+ R'w e[tex]\theta[/tex]+ Rw' e[tex]\theta[/tex]... | 4 | [
-0.00347900390625,
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0.14453125,
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0.03857421875,
0.018310546875,
-0.0303955078125,
0.0308837890625,
-0.039306640... | 22,057 | 22057 | |
Patent US6332136 - Fuzzy filtering method and associated fuzzy filter
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to a fuzzy filtering method and associated fuzzy filter.
2. Discussion of the Related Art
As is known, a large number of mass-market applications (such as hi-fi, telecomm... | 4 | [
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... | 22,058 | 22058 | |
Log/Exponential problem
April 18th 2010, 08:24 PM #1
Junior Member
Joined
Apr 2010
Posts
43
Log/Exponential problem
$<br /> \frac{e^x-e^{-x}}{2}=10<br />$
Answer:
$<br /> x = ln (10 + \sqrt{101} )<br />$
What I'm doing (More than likely wrong)
$<br /> \frac{e^x - e}{2^x} = 10<br /> <br... | 5 | [
-0.030517578125,
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0.06640625,
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-0.003509... | 22,059 | 22059 | |
Volume Integral - Cylinder & Cone
January 13th 2012, 01:25 PM
Juggernaut
Volume Integral - Cylinder & Cone
Hello all,
In mathematical terms, I've got a problem where I'd like to calculate the volume of a cylinder whose upper surface is bounded by a right circular cone. A brief discription of the geometries
... | 5 | [
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0.125,
-0.02880859375,
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-0.056884765625,
-0.0185546875,
-0.06494140625,
0.002593994140625,
-0.1... | 22,060 | 22060 | |
A Sharp RIP Condition for Orthogonal Matching Pursuit
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 482357, 3 pages
http://dx.doi.org/10.1155/2013/482357
Research Article
A Sharp RIP Condition for Orthogonal Matching Pursuit
School of Mathematics and Statistics, Guangdong University of Finance & Econo... | 4 | [
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0.03808... | 22,061 | 22061 | |
Characteristic Polynomial
March 29th 2010, 06:15 PM #1
Junior Member
Joined
Oct 2009
Posts
30
Characteristic Polynomial
Given that the characteristic polynomial of $A$ is $t^4 + t + 1$. How would I go about calculating the characteristic polynomial of $A^2$?
I originally thought of using the fact th... | 5 | [
0.0478515625,
0.0673828125,
0.01708984375,
-0.03466796875,
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0.02099609375,
-0.017578125,
-0.0220947265625,
-0.046142578125,
-0.014831... | 22,062 | 22062 | |
On The Solution of Matrix Ricatti Equation ODE
I've become a little confused about why noone cares to actually explicitly solve the Matrix Ricatti Differential Equation (RDE) of the form:
$$ -{\dot{P}} = Q + PA^T + A^TP + PBB^TP $$ where [itex] BB^T, Q, P [/itex] are a positive-definite matrices, and [itex] A, BB^T, Q... | 4 | [
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0.06787109375,
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0.02099609375,
-0.009033203125,
... | 22,063 | 22063 | |
Hyperplane Arrangements
Before talking about hyperplane arrangements, let us start with individual hyperplanes. This package uses certain linear expressions to represent hyperplanes, that is, a linear expression \(3x + 3y -
5z - 7\) stands for the hyperplane with the equation \(x + 3y - 5z = 7\). To create it in Sage, ... | 5 | [
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-0.037109375,
0.00057220458984375,
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0.034912109375,
-0.0747070312... | 22,064 | 22064 | |
proofs by induction
Show true for n=1: 4(1)-2=2(1)^2. True. Assume true for $2+6+10+....+(4k-2)=2k^{2}$ Show true for $P_{k+1}$: $2+6+10+....+(4k-2)+(4k+2)=2k^{2}+4k+2=2(k+1)^{2}$ It is true for the $P_{k+1}$ case.
Try this one on your own. All these induction proofs with sums follow the same pattern Show for a base (... | 4 | [
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0.02197265625,
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0.03125,
0.0498046... | 22,065 | 22065 | |
Newton's method of approximation
Procedure for Newton’s Method 1. Guess a first approximation to a solution of the equation $f(x) = 0$. A graph of $y = f(x)$ may help. 2. Use the first approximation to get a second, the second to
get a third, and so on, using the formula $x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}, \text{ ... | 5 | [
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-0... | 22,066 | 22066 | |
On Period of the Sequence of Fibonacci Polynomials Modulo
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 731482, 3 pages
http://dx.doi.org/10.1155/2013/731482
Research Article
On Period of the Sequence of Fibonacci Polynomials Modulo
^1Department of Mathematics, Faculty of Science, Ataturk Un... | 5 | [
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... | 22,067 | 22067 | |
solving inequalities
December 29th 2009, 09:56 PM #1
Member
Joined
Dec 2009
Posts
122
solving inequalities
Please solve the inequalities, (the results in set notation)
1) -2 (3+x)< 4x +4 < 8x
2) [2x - 4] < 10
3) 4 < -z - 4 < 11
1. 2 < x < 5 or (2, 5)
2. x < 7 or (-inf, 7)
3. -15 ... | 4 | [
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0.11669921875,
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0.03955078125,
0.0159912109375,... | 22,068 | 22068 | |
Logarithmic differentiation
September 10th 2012, 08:09 AM #1
Member
Joined
Nov 2011
Posts
86
Use logarithmic differentiation to find the derivative of y with respect the independent
variable x, where
y = x^ln x
thanks to everyone who takes a look
Re: Logarithmic differentiation
\displa... | 5 | [
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0.015869140... | 22,069 | 22069 | |
Do derivatives belong to unique functions?
The fact that "derivatives belong to unique functions" or, more correctly, that if f(x) and g(x) have the same derivative then f(x) and g(x) differ at most by a constant, is given in most calculus
books and follows from the mean value theorem:
Lemma: Suppose f(x) is continuo... | 4 | [
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... | 22,070 | 22070 | |
A question on photons
Just to make sure, here are the key steps in my calculation, so you or someone else can check them if you like:
In the rest frame of the laser pointer, the photon travels horizontally. Assuming it has energy E, its four-momentum is
[tex]Pc = \left( \begin{array}{cccc} E \\ p_x c \\ p_y c \\ p_z ... | 5 | [
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0.076171875,
-0.048583984375,... | 22,071 | 22071 | |
| sinh (z) |^2 = sinh^2(x) + sin^2(y)
December 21st 2010, 01:20 PM #1
MHF Contributor
Joined
Mar 2010
From
Florida
Posts
3,093
Thanks
5
| sinh (z) |^2 = sinh^2(x) + sin^2(y)
I am having trouble proving this identity $|sinh(z)|^2=sinh^2(x)+sin^2(y) \ \ z\in\mathbb{C} \ \ x,y\in\mathbb{R}$.
$\... | 5 | [
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0.125,
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0.034912109375,
0.0035552978515625,
-0.0... | 22,072 | 22072 | |
Finite-dimensional subspaces..?
May 5th 2009, 05:51 AM
fardeen_gen
Finite-dimensional subspaces..?
Let U, V, W be finite-dimensional subspaces of a real vector space. Show dim U + dim V + dim W - dim (U + V + W) greater or equal to max {dim (U intersection V), dim (V intersection W), dim (U
intersection W)}.... | 5 | [
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-0.0947265625,
-0.0050048828125,
-0.0091552734375,
-0.03247070... | 22,073 | 22073 | |
Proof of the ratio test
April 14th 2009, 08:02 PM #1
Proof of the ratio test
Hey, I have a question about the proof of the ratio test. I'm using the Stewart Calculus 6thed book, which gives the following for the proof:
Choose a number $r$ such that $L<r<1$.
Since $\lim_{n \to \infty} \left | \frac{a_{n+... | 4 | [
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Fundamental Theorem of calculus & Estimation Theorem
June 14th 2007, 12:09 AM #1
Member
Joined
Jun 2007
Posts
131
Fundamental Theorem of calculus & Estimation Theorem
Hi Guys
Can you help with the attached problem? I think for part (i) and (ii) the answer is the same - i have this as 0 in both cases... | 5 | [
-0.039306640625,
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-0... | 22,075 | 22075 | |
ation
convert/Sum - convert to inert sum representation - a formal power series
convert/sum - convert to sum representation
Calling Sequence
convert( expr, Sum, opts, Sum_opts );
convert( expr, sum, opts, Sum_opts );
Parameters
expr - valid Maple expression, equation, set, list, or simil... | 4 | [
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0.03466796875,
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0.0159912109375,
0.00518798828125,
-0.0128173828125,
0.06787109375,
-0.0225830078125,
0.053... | 22,076 | 22076 | |
Approximation of Eigenvalues of Sturm-Liouville Problems by Using Hermite Interpolation
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 412028, 14 pages
http://dx.doi.org/10.1155/2013/412028
Research Article
Approximation of Eigenvalues of Sturm-Liouville Problems by Using Hermite Interpolation
^1Depart... | 5 | [
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... | 22,077 | 22077 | |
Triangle question
February 24th 2009, 07:14 AM
WendyM
Triangle question
Hi!
How can I count the surface area of an isosceles triangle + lengths of all sides + count the angles ?
I only know the height of the isosceles triangle and the base angle too.
Thanks for your help!
February 24th 2009, 07:... | 4 | [
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0.020... | 22,078 | 22078 | |
A cubic equation...
May 11th 2008, 11:02 PM #1
Newbie
Joined
Feb 2006
Posts
16
A cubic equation...
Problem 243. A cubic equation $x^3+px^2+qx+r=0$ has three roots $x_1, x_2, x_3$ Find: $(x_1-x_2)^2(x_1-x_3)^2(x_2-x_3)^2$ as an expression containing p, q, and r. This polynomial in p, q, and r
is calle... | 4 | [
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0.0299072265625,
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0.0... | 22,079 | 22079 | |
Fibbo-something sequences
Does anybody understand the concept of analyzing a word problem and turning it into an equation?
EX
Mr. Yazaki discovered that there were 225 dandelions in his garden on the first Saturday of spring. He had time to pull out 100, but by the next Saturday, there were twice as many as he had le... | 4 | [
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0.0576171875,
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-0.013916015625,
-0.0908203125,
0.0111083... | 22,080 | 22080 | |
MATLAB help: Interpolating an array of data to create a function
polyfit()?
http://www.mathworks.com/help/matlab/ref/polyfit.html
the function x(t) will be a polynomial, so you may or may not like that.
you may want to choose another function basis, like adding up exponentials to fit your data. you might want to app... | 4 | [
-0.109375,
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-0.0091552734375,
-0.049560546875,
-0.02624511... | 22,081 | 22081 | |
Math Help
October 1st 2007, 12:45 PM #1
Member
Joined
Jul 2007
Posts
151
use the transformation T(u,v) = < u, u+v> to evaluate the iterated integral
the integral from 1 to 2 the integral from x+3 to x+6 of 1/(sqrt(xy-x^2)) dy dx.
please help if you know how to solve this question. thank you.
... | 5 | [
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... | 22,082 | 22082 | |
Transformation relations tensors
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by roldy
Tags: relations, tensors, transformation
P: 194 I'm trying to understand the transformation relations for 2d stress and the book doesn't show the derivation of the... | 4 | [
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On a Theorem of Khan in a Generalized Metric Space
International Journal of Analysis
Volume 2013 (2013), Article ID 852727, 6 pages
http://dx.doi.org/10.1155/2013/852727
Research Article
On a Theorem of Khan in a Generalized Metric Space
^1Department of Mathematics, COMSATS Institute of Information Technology, Chak ... | 5 | [
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MatLab Frenet-Serret Function
January 19th 2010, 05:10 AM
porkpie
MatLab Frenet-Serret Function
Hello, I'm looking for some help with a function I've made to return the Frenet-Serret vectors for a 'track' defined by a set of x,y,z coordinates. It seems to work except for the curvature which
is certainly wron... | 4 | [
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Angle in a 3-D Parallelogram
June 12th 2010, 01:18 PM #1
Newbie
Joined
Jun 2010
Posts
5
Angle in a 3-D Parallelogram
Hello! I am in Calc III, and I have a question. The answer sheet gives me a different answer than I have, but I feel that I am correct. Could you all point me one way or another?
Para... | 4 | [
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Please help with trigonometric functions!
1)Prove this identity $\frac{1-cos\theta}{sin\theta}= \frac{sin\theta}{1+cos\theta}$ 2)Solve this for $-\Pi\leq\theta\leq\Pi$ $sin2\theta=cos2\theta$ thanks if ya can :)
Quote: Originally Posted by Confuzzled? Hello, to 1): Multiply both sides of the equation by $sin\theta$ an... | 4 | [
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Intersection of vector subspaces
March 30th 2009, 05:22 AM #1
Newbie
Joined
Mar 2009
Posts
6
Intersection of vector subspaces
Dear All,
I hope you can help me solving the following problem.
Given several subspaces $S_i$ of a linear $n$-dimensional vector space, each subspace being determined by... | 4 | [
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Motion with Uniform Acceleration
October 4th 2009, 02:27 AM
NathanBUK
Motion with Uniform Acceleration
Though id post this one here becuase its partly mechanics so physcis based etc. This thing is im working with SuVat as in S=displacement u=uniform acceleration V=velocity a=acceleration and t=
time. Ive man... | 4 | [
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Repeated integral with dx and dy
evaluate the following repeated integral
int(0-pi/2) ( int(y-pi/1) cosysinxdxdy)
i have never seen a question like this please help
This is almost unreadable. Is this $\displaystyle \int_0^{\frac{\pi}{2}}{\int_y^{\pi}{\cos{y}\sin{x} \,dx}\,dy}$?
Just separate it... | 4 | [
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Patente US6198248 - Method of controlling a rotary electrical machine, a servo-control system for implementing the method, and a rotary machine fitted with such a system
The invention relates to a method of controlling a rotary machine, to a servo-control system for implementing the method, and to a rotary machine fitt... | 4 | [
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A Domain Decomposition Method for Hybrid Shell Vector Element with Boundary Integral Method
International Journal of Antennas and Propagation
Volume 2012 (2012), Article ID 790164, 6 pages
http://dx.doi.org/10.1155/2012/790164
Research Article
A Domain Decomposition Method for Hybrid Shell Vector Element with Boundar... | 4 | [
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Patent US5274744 - Neural network for performing a relaxation process
FIELD OF THE INVENTION
The present invention relates to a neural network for performing a probabilistic relaxation process.
BACKGROUND OF THE INVENTION A. Relaxation Process
The relaxation process is a technique for using contextual information to... | 4 | [
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Help with integration
April 9th 2008, 08:24 AM #1
Newbie
Joined
Apr 2008
Posts
2
Help with integration
I supposed to integrate (x^2 + x)^(1/2).
I do it this way
int (x^2 + x)^(1/2) = x(x^2 + x)^(1/2) - 1/2* int (x(2x + 1))/(x^2 + x)^(1/2) = x (x^2 + x)^(1/2) - 1/2((xln(x^2 +x)) - ln(x^2 + x))
... | 5 | [
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Differential Equation
March 4th 2010, 08:00 AM #1
Member
Joined
Oct 2008
Posts
80
Differential Equation
How do I find the general solution for this differential equation:
$\frac{dy}{dx} = 2y - 4x$
?
I know how to do them using separation of variables, but I can't figure out this one, because... | 5 | [
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Prove function is differentiable
May 12th 2010, 07:16 PM #1
Prove function is differentiable
Let $f$ be continuous on the reals and let $F(x) = \int_{x-1}^{x+1}f(t)dt$. Show that $F$ is differentiable on the reals and compute $F'$.
So this should seem straightforward but I'm having trouble actually formalizi... | 5 | [
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Global Attractor for a Chemotaxis Model with Reaction Term
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 536381, 8 pages
http://dx.doi.org/10.1155/2013/536381
Research Article
Global Attractor for a Chemotaxis Model with Reaction Term
School of Mathematics and Statistics, Xuchang University, Xuchang ... | 4 | [
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Permanence and Almost Periodic Solutions of a Discrete Ratio-Dependent Leslie System with Time Delays and Feedback Controls
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 358594, 31 pages
http://dx.doi.org/10.1155/2012/358594
Research Article
Permanence and Almost Periodic Solutions of a Discrete Ratio-... | 5 | [
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Inverse function Help
October 27th 2012, 02:57 PM #1
Newbie
Joined
Oct 2012
From
San Diego
Posts
4
Inverse function Help
For this problem, y = f(x) = 3x^2 − 5x − 1
on the domain of all real numbers.
1. Restrict y = f(x)to the domain {a ≤ x} and find the formula for the inverse function f^... | 4 | [
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