content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Effects of an electric field on a motion of an electron
1. The problem statement, all variables and given/known data
An electron is projected at an angle of 31.7° above the horizontal at a speed of 8.40×10^5 m/s in a region where the electric field is E = 383j N/C. Neglecting the effects of gravity, calculate the
time... | 4 | [
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0.034912109375,
0.00518798828125,
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-0.021118164062... | 20,200 | 20200 | |
Patent US6396545 - Method for digital synchronization of video signals
BACKGROUND OF THE INVENTION
The present invention is related to digital synchronization of video signals and, more particularly, to a time base error correction scheme to keep video input and output clocks in synchronization in
a multimedia system.... | 4 | [
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0.0260009765625,
0.037... | 20,201 | 20201 | |
Wolfram Demonstrations Project
Representation of Qubit States by Probability Vectors
Any qubit state is associated with a six-dimensional probability vector with components , where is the spin projection and defines a direction of spin projection measurement, . The ends of the
vectors are on the sphere which is illust... | 4 | [
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... | 20,202 | 20202 | |
another exponential limit
Thanks so much! The limit as n--> infinity of [1 + 7/n + 1/(n^4)]^n
Hello, $(1+\frac 7n+\frac 1{n^4})^n$ Taking the logarithm : $n \ln(1+\frac 7n+\frac 1{n^4})$ We know that $\lim_{x \to 0} \ln(1+x)=\lim_{x \to 0} x$ Here, $\lim_{n \to \infty} \frac 7n+\frac 1{n^4}=
0$. So $\lim_{n \to \infty... | 5 | [
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-0.05859375,
-0.... | 20,203 | 20203 | |
Need help solving this logarithm
Write (equation) as the sum, difference, and/or constant multiple of logarithms. Equation is attached.
Hello,For any base of the logarithm, you have : $\log_a (xy)=\log_a(x)+\log_a(y)$ $\log_a \left(\frac xy\right)=\log_a(x)-\log_a(y)$ $\log_a (x^y)=y \log_a(x)$
_______________________... | 4 | [
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... | 20,204 | 20204 | |
Gibbs phenomenon and ringing in square waves: causality?
A seemingly good way to understand the overshoot and decay (ringing) of a square wave on a scope is that it is the result of bandwidth limiting. In that case, the Fourier series of a square wave
[tex]\Pi(t) = \frac{1}{2 \pi} \sum_{n=-\infty}^\infty \frac{\sin(n ... | 4 | [
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0.035888671875,
-0.0456542968... | 20,205 | 20205 | |
Loan repayment
October 7th 2010, 03:59 AM #1
Junior Member
Joined
Nov 2008
Posts
53
Loan repayment
A loan of 5000 can be repaid by payments of 117.38 at the end of each month for n years (12n payments), starting one month after the loan is made. At the same rate of interest, 12n monthly
payments of 1... | 5 | [
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0.01220703125,
-0.06689453125,
-0.0026... | 20,206 | 20206 | |
Part-Time Rules, Part Two
By Tammy Flanagan
March 9, 2007
Last week, we began our exploration of the effects of shifting to part-time work on federal retirement benefits. In that column, I promised that this week we'd look in more detail at how part-time
employment is treated under the Civil Service Retirement Syste... | 4 | [
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finding the area using double integrals
January 16th 2009, 09:25 AM
lllll
finding the area using double integrals
Given $r=\cos(\theta)$ and $r=\sin(\theta)$ find the area inside both circle.
Graphing it out gave me two that intersect in the first quadrant, now I was thinking that it would be
$\int_0^{... | 5 | [
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0.06640625,
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0.0174560546875,
-0.0289306640625,
-0.0147094... | 20,208 | 20208 | |
intersection of the two ellipses
Find the intersection of the two ellipses: $\frac{x^2}{9} + \frac{y^2}{4} = 1$ and $\frac{x^2}{4} + \frac{y^2}{9} = 1$
(x^2)/9 +(y^2)/4 = 1 -------------(1) (x^2)/4 +(y^2)/9 = 1 -------------(2) At the intersection points, the x of one ellipse is the same as the x of the other ellipse.... | 4 | [
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0.0067138... | 20,209 | 20209 | |
Real Analysis - Uniform Convergence
May 11th 2013, 03:56 PM #1
Newbie
Joined
May 2012
From
United States
Posts
17
Real Analysis - Uniform Convergence
Let $f_n(x):=\frac{1}{n\sqrt{2\pi}}\exp{{\frac{-x^2}{2n^2}}}$
and $f(x):=0$
$f_n(x) \rightarrow f(x)$ pointwise.
$\forall n\in\omega\int_... | 4 | [
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Multiple Regression with Two Predictor Variables
Multivariate Statistics: Concepts, Models, and Applications
David W. Stockburger
... | 5 | [
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Brevet US5847714 - Interpolation method and apparatus for fast image magnification
FIELD OF THE INVENTION
This invention relates to transformation of digital images and, more particularly, to interpolation methods and apparatus which result in fast image magnification.
BACKGROUND OF THE INVENTION
A digital image of ... | 4 | [
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Limits & Indeterminate Forms
October 25th 2007, 06:02 AM #1
Hello. I need help on two questions related to limits of indeterminate forms. I've solved at least fifty other such questions, but these just elude me...
1. $\lim_{x\rightarrow\infty}(\sinh(x)-x)$
2. $\lim_{x\rightarrow0}\frac{x-\tan^{-1}(x)}{x\s... | 5 | [
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0.03662109375,
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-0.021484375,
0.09521484375,
-... | 20,213 | 20213 | |
Patent US5937364 - Automatic selection of statistical quality control procedures
BACKGROUND OF THE INVENTION
Health care providers in the United States have entered a new competitive era. Changes in government reimbursement policies have limited the amount of money that is paid for medical care. Payment of
flat fees, ... | 4 | [
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Patent US4804269 - Iterative wavefront measuring device
BACKGROUND OF THE INVENTION
It is known that a light beam can be distorted as it passes through the atmosphere. In addition, other distortions are induced by the imperfections of receiving optical systems. Hence, adaptive optic
systems have been devised to improv... | 4 | [
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Taylor Polynomial & Remainder
May 7th 2008, 10:57 AM
kithy
Taylor Polynomial & Remainder
given f(x) = x/(1-x)
a) determine the Taylor polynomial of order 3 to f expanded about x=0
b) write an equation for the remainder term of order 3, R3(x), in the taylor series for f
I don't know how to solve th... | 5 | [
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-0.01... | 20,216 | 20216 | |
Intergral help
August 16th 2008, 05:52 PM #1
Junior Member
Joined
Aug 2008
Posts
35
Over what open interval does the formula F(x)=[int (from 1 to x) dt/t]
represent an antiderivative of f(x)=1/x? and find a point where the graph of F crosses the x-axis.
I don't even how to start calculating this... | 5 | [
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0.029296875,
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-0.11962890625... | 20,217 | 20217 | |
gamma distribution.
March 6th 2010, 01:44 AM
alexandrabel90
gamma distribution.
using gamma random variable, how do you find the variance of L= 30Y + 2Y^2 given that alpha = 3 and beta = 2?
may i know what is the formula for V(Y^2) and how do i work out the formula in terms of alpha and beta?
March 6th 201... | 5 | [
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-0.00... | 20,218 | 20218 | |
Saddle points = sore points
September 20th 2009, 12:11 PM #1
Newbie
Joined
Sep 2009
Posts
4
Saddle points = sore points
Hi, I'm trying to solve the following maths problem and have fallen at the first hurdle... which is funny as it relates to a maxima minima "Saddle" Point question
Find the stationa... | 4 | [
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0.0022125244140625,
0.0419921875,
... | 20,219 | 20219 | |
Upper and Lower Bounds
March 9th 2010, 06:08 AM #1
Junior Member
Joined
Jul 2008
Posts
33
Upper and Lower Bounds
Question
The length of a side of a square is 6.81 cm, correct to 3 significant figures.
(a) Work out the lower bound for the perimeter of the square.
(b) Give the perimeter of the... | 4 | [
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Negate a statement
Exercise 1(e) in Section 2.2 of Daniel Velleman's How to prove it:
Negate the statement and then reexpress the result as an equivalent positive statement:
$A \cup B \subseteq C \backslash D$
My attempt at the solution is by expressing it in the logical form as
Step 1: $\forall ... | 4 | [
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0.0014724731... | 20,221 | 20221 | |
Positive Solutions of Advanced Differential Systems
The Scientific World Journal
Volume 2013 (2013), Article ID 613832, 7 pages
http://dx.doi.org/10.1155/2013/613832
Research Article
Positive Solutions of Advanced Differential Systems
^1Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering... | 5 | [
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Problem with Fourier Series
February 6th 2011, 04:46 AM #1
Member
Joined
Nov 2009
Posts
103
Problem with Fourier Series
I have a problem with the below fourier series
-2, -2 < t < -1
-1, -1 < t < 0
f(t) = 1, 0 < t < 1
2, 1 < t < 2
f(t + 4) = f(t)
I want to intergrate by parts t... | 5 | [
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-0.011535644531... | 20,223 | 20223 | |
Binary subtraction using 2's complement
April 11th 2010, 11:08 AM #1
Junior Member
Joined
Aug 2007
Posts
37
Binary subtraction using 2's complement
Subtract 1010 from 1110 using 2's complement subtraction.
I got the following:
1110
0001
+1
0010
1010
0010
1100
0100
... | 4 | [
0.01275634765625,
0.054931640625,
0.03662109375,
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0.0279541015625,
0.07275390625,
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0.058837890625,
-0.052001953125,
-0.05908203125,
0.047607421875,
0.000503540039... | 20,224 | 20224 | |
Almost there...
February 18th 2011, 03:39 PM #1
Almost there...
Hey, I got most of the way through this reduction of order problem, but then my brain gave out right at the end.
Given the equation $y''-4y'+4y=0$ and the solution $y_1=e^{2x}$, write the general solution.
I make the substitution $y_2(x)=u(... | 5 | [
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-0.064453125,
0.0... | 20,225 | 20225 | |
challenging proof(section idea needed)
also prove that between every two rationals there exists an irrational(this proof requires some thinking!!)
a<b Then, $\frac{a+b}{2}$ is between them and rational. also prove that between every two rationals there exists an irrational(this proof requires some thinking!!) I am not... | 5 | [
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... | 20,226 | 20226 | |
A Study of Non-Euclidean
ISRN Mathematical Physics
VolumeΒ 2012Β (2012), Article IDΒ 896156, 11 pages
http://dx.doi.org/10.5402/2012/896156
Research Article
A Study of Non-Euclidean s-Topology
Department of Mathematics, Faculty of Science, Dayalbagh Educational Institute (Deemed University), Dayalbagh, Agra 282 110... | 4 | [
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finite difference method, coupled wave equations, chickens & eggs
November 4th 2010, 10:54 PM
apchar
finite difference method, coupled wave equations, chickens & eggs
I'm reading a book (Numerical Techniques in Electromagnetics by Sadiku) & just finished the section on finite difference methods. As what I though... | 4 | [
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Lagrange error bound to estimate sin4° to five decimal places( maclaurin series)
March 21st 2010, 10:28 AM #1
Junior Member
Joined
Jan 2010
Posts
26
Lagrange error bound to estimate sin4° to five decimal places( maclaurin series)
Lagrange error bound to estimate sin4° to five decimal places( maclaurin se... | 5 | [
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mathematical induction recursion
May 27th 2007, 06:19 AM
polymerase
mathematical induction recursion
How do I prove by induction,
If t1 = 1, tn+1 = 1 + Ö(1 + tn) prove a) tn < 3 for all n Î N
b) tn+1 > tn for all n Î N
May 27th 2007, 07:18 AM
Soroban
Hello, polymerase!
I'll help you with par... | 4 | [
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% share problem
May 17th 2005, 11:52 PM #1
mmouse
Guest
% share problem
Hi All,
I am trying to workout the the formula to show what % share of the total market you would have, if your % growth is different to the market % growth.
Example
You currently have 4% of the market.
The market grows by ... | 4 | [
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slope of a tangent to a curve
April 7th 2008, 02:59 PM
OzzMan
slope of a tangent to a curve
I could use some help on this one. Calculate the slope of a line tangent to the curve of each of the functions $y = f(x)$ for the given point $P$.
$Y = x^2$ ; $P$ is $(2,4)$
April 7th 2008, 03:05 PM
Mathstud28
... | 4 | [
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Thermodynamics, Exact differentials
Here's a long-winded description of the difference between exact differentials and inexact differentials:
A generalized differential can be written in the form:
[itex]\sum_j Q_j dx_j[/itex]
where the [itex]x_j[/itex] are independent state variables, and [itex]Q_j = Q_j(x_1, x_2, .... | 4 | [
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Math Help
October 20th 2007, 07:56 AM #1
Member
Joined
Nov 2006
Posts
142
sequences
Could someone just tell me if the following sequences converge or not:
Let an = the summation of (1/x) beginning with x = n+1 and ending with 2n.
For example, if n =2, x =3, then the sequence is (1/3) + (1/4).
... | 5 | [
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Geodesics VS Projectile
I don't think this approach can give the Newtonian result because you are using kinematic equations. The full equation for r is
[tex]
\ddot{r}=-\frac{\left( m\,{r}^{2}-4\,{m}^{2}\,r+4\,{m}^{3}\right) \,{\dot{t}}^{2}-m\,{r}^{2}\,{\dot{r}}^{2}}{{r}^{4}-2\,m\,{r}^{3}}
[/tex]
setting [itex]\dot{t}=... | 4 | [
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Proving Integral of an Irrational Function
Hey,
1. The problem statement, all variables and given/known data
(From an Integration Table)
Prove,
[tex]
{\int}{\sqrt {{{a}^{2}} - {{x}^{2}}}}{dx} = {{\frac {1}{2}}{\left(}{{{x}{\sqrt {{{a}^{2}} - {{x}^{2}}}}} + {{{a}^{2}}{\arcsin{\frac {x}{a}}}}}{\right)}}{,}{\,}{\,}{\,}{\... | 4 | [
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-0.0356445312... | 20,236 | 20236 | |
Math Help
August 13th 2009, 05:26 AM #1
Senior Member
Joined
Jan 2009
Posts
381
trigo(4)
A triangle ABC is right angled at A . The angle bisector of angle A meets BC at D . If BC = a , CA =b , and AB=c , prove that
c/b = BD/DC
i just couldn't get the sketch right .
The line that meets BC ... | 4 | [
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Patent US20030115559 - Hardware validation through binary decision diagrams including functions and equalities
BACKGROUND OF THE INVENTION
[0001] 1. Technical Field
[0002] The present invention relates generally to the validation of digital hardware designs using formal methods. Specifically, the present invention is... | 4 | [
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Physics Forums - View Single Post - Model involving SOD of two variables
1. The problem statement, all variables and given/known data
I'm going to model the velocity of a river stream v(y,z) as a function of the location (y,z) in the cross-section of the river. Here y represents the distance from one of the shores an... | 5 | [
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Need Help with this distance problem
November 23rd 2006, 10:48 PM
adamnn2006
Need Help with this distance problem
• Two cars start off at the same point on a straight road facing opposite directions. Each car drives for six miles, takes a left turn, and drives for eight miles. How far apart are the two cars?
... | 4 | [
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How to prove if all elements of [10] random in circle, sum 3 consecutive at least 18
January 20th 2013, 03:41 AM
RuWel
How to prove if all elements of [10] random in circle, sum 3 consecutive at least 18
Hi,
Let X = {1, 2,..., 10} =[10]. Suppose the elements of X are scattered at random around a circle. Sho... | 4 | [
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Physics Forums - Time-retarded E-field and Gaussian surface integral
Let's say we have a sphere with radius R=1 centered on the origin.
http://www.physicsforums.com/attachm...1&d=1329604621
When evaluating field intensity over the sphere, let's do it for each angle phi over the domain [0,pi].
phi represents degrees... | 4 | [
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the encyclopedic entry of Exact sequences
In
mathematics
, especially in
homological algebra
and other applications of
abelian category
theory, as well as in
differential geometry
and
group theory
, an
exact sequence
is a (finite or infinite)
sequence
of objects and
morphisms
between them such that the
... | 4 | [
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-0.0480957031... | 20,243 | 20243 | |
Constrained Lagrangian equetion (barbell)
Hi!
I tried to compute an ideal barbell-shaped object's dynamics, but my results were wrong.
My Langrangian is:
## L = \frac{m}{2} ( \dot{x_1}^2 + \dot{x_2}^2 + \dot{y_1}^2 + \dot{y_2}^2 ) - U( x_1 , y_1 ) - U ( x_2 , y_2 ) ##
And the constraint is:
## f = ( x_1 - x_2 )^2 +... | 4 | [
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Solving for a*x=b-c*log(d*x)?
Not really sure where this question belongs in this forum...
I was solving an engineering problem and I got to the form
[tex]ax=b-cln(dx)[/tex]
where a, b, c and d are constant real values. I had a peek at the answer and they got a unique positive real valued answer for x but I have no ... | 4 | [
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Definition of a Derivative and Limits
For the first, use \displaystyle \begin{align*} \frac{dy}{dt} = \lim_{h \to 0}\frac{y(t + h) - y(t)}{h} \end{align*} For the second... \displaystyle \begin{align*} 3^x\lim_{h \to 0}\frac{3^h - 1}{h}
&= \lim_{h \to 0}\frac{3^x\left(3^h - 1\right)}{h} \\ &= \lim_{h \to 0}\frac{3^x3^h... | 5 | [
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Quasi-Linear
August 18th 2007, 06:22 PM #1
Quasi-Linear
hi all...
i have 2 Q:
1-what is the diffrent between Quasi-Linear pde and Linear pde ?
2- How we can solve Quasi-Linear ??
any body can help !!!
Let $u_1 \mbox{ and }u_2$ solve a PDE, if it happens that $c_1u_1+c_2u_2$, i.e. any line... | 4 | [
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Wholly Whexagons!
Dear Dr. Math,
I've noticed that hexagons show up in a lot of different places. Now that I've started looking for them, I see them everywhere! What's the deal with hexagons?
Jules, Canton OH
Dear Jules,
I know I'm not supposed to play favorites with mathematical objects, but I have to confess, the h... | 4 | [
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Gaus Jordan ELimination compared to cofactor inverse matrix
November 19th 2009, 06:04 PM #1
Newbie
Joined
Mar 2009
Posts
15
Hey guys i am stuck with the gaus jordan method of the following matrix.
A = 1 2 3
4 5 6
3 1 -2
For the co factor i worked out the C transpose as:
1/3 (-16 7 3... | 4 | [
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-0.0142211914062... | 20,249 | 20249 | |
Partial derivative in spherical coordinates
I am facing some problem about derivatives in spherical coordinates
in spherical coordinates:
x=r sinθ cos[itex]\phi[/itex]
y=r sinθ sin[itex]\phi[/itex]
z=r cosθ
and
r=[itex]\sqrt{x^{2}+y^{2}+z^{2}}[/itex]
θ=tan[itex]^{-1}[/itex][itex]\frac{\sqrt{x^{2}+y{2}}}{z}[/itex... | 4 | [
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Contour Integration help with understanding an example
December 30th 2010, 03:12 AM #1
Junior Member
Joined
Mar 2009
Posts
49
Contour Integration help with understanding an example
Hi
I have attached an example from my notes for contour integration.
However I don't understand how they derive th... | 4 | [
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Calculation of Thrust and Wing Area
I posted I question in regards to shock angles on this very same problem earlier but now I have a new problem. I need to calculate the heat rate required in the combuster in order to ensure that the
vehicle will cruise (delta z=0). I also need to find the mass flow rate of the fuel. ... | 4 | [
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Restricted outcomes for die thrown six times.
July 17th 2011, 05:57 AM
Blizzardy
Restricted outcomes for die thrown six times.
Hi guys, need help with a question:
An unbiased die is thrown 6 times. Calculate the probabilities that the six scores obtained will be such that a 6 occurs only on the last throw a... | 4 | [
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0.... | 20,253 | 20253 | |
Trigonometry to seld complex shapes
May 19th 2007, 05:28 AM #1
Trigonometry to seld complex shapes
how do i work out the angles for A, B and C
all in mm
cheers
also how do i find the angles A & B in this triangle ?
is it 20cos60?
For the first triangle use either the Law of Sines or the ... | 4 | [
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0.045166015... | 20,254 | 20254 | |
distribution of the mean of an exponential distribution (mgf)
March 22nd 2009, 05:49 PM
Zithuan
distribution of the mean of an exponential distribution (mgf)
Let $\overline{X}$ be the mean of a random sample from the exponential distribution, Exp( $\theta$). Using the mgf technique determine the distribution of ... | 5 | [
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0.0849609375,
0.01708984375,
0.0546875,
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0.0947265625,
0.025634765625,
0.09375,
-0.0634765625,
-0.048583984375,
0.012939453125,
0.0252685546875,
-0.0654296875,
0.006072... | 20,255 | 20255 | |
Dumb tangent line question
November 2nd 2008, 04:08 PM #1
Newbie
Joined
Nov 2008
Posts
1
Dumb tangent line question
f(x) = x^3 - 3x^2 - x +3
I need to find the slope of the tangent line at x=2 using lim as x->2
(f(x) - f(2)) / (x-2)
I cannot for the life of me factor the equation in order t... | 4 | [
-0.06103515625,
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0.018798828125,
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0.0517578125,
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-0.0294189453125,
0.05126953125,
0.044677734375,
-0.05078125,
-0.05395... | 20,256 | 20256 | |
Physics Forums - (1.0 / 2) process repeated 5 times; what is the algrabraic formula?
-
General Math
(
http://www.physicsforums.com/forumdisplay.php?f=73
)
mr magoo Mar31-12 02:27 PM
(1.0 / 2) process repeated 5 times; what is the algrabraic formula?
1 / 2 = 0.5
0.5 / 2 = 0.25
0.25 / 2 = 0.125
0.125 / 2 = 0.... | 4 | [
-0.05712890625,
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0.0294189453125,
0.056884765625,
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-0.047119140625,
-0.002685546875,
-0.018798828125,
0.059326171875,
-0.04882... | 20,257 | 20257 | |
triple integral problem
October 26th 2009, 09:25 PM #1
Newbie
Joined
Sep 2009
Posts
10
triple integral problem
use a triple integral to find the volume of the given solid
the solid enclosed by the cylinder x^2+y^2=9 and the planes y+z=5 and z=1
i attempted to draw a picture..
and i ended u... | 5 | [
-0.019775390625,
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... | 20,258 | 20258 | |
Is 13 divisible by this incredibly huge number?
January 25th 2010, 07:50 PM #1
Junior Member
Joined
Sep 2009
Posts
32
Is 13 divisible by this incredibly huge number?
Does 13 divide 6^13 + 33^49?
I can't seem to think of a way to make this number more manageable.
(2^13 * 3^13) + (3^49 * 11^49)
... | 5 | [
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0.048583984375,
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0.00994873046875,
-0.0283203125,
-0.04150390625,
-0.10791015625... | 20,259 | 20259 | |
63-gon and the sum
You have [itex]d[/itex] edges with different numbers on the vertices (product =-1) and [itex]s[/itex] edges with the same number on each vertex (product =1), and you're constrained to have
- [itex]s+d=63[/itex];
- [itex]d[/itex] an even number (because of the cyclical arrangement);
- [itex]d\leq s[/i... | 5 | [
-0.0213623046875,
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0.01031494140625,
-0.0264892578125,
-0.050537109375,
0.029296875,
0.028442... | 20,260 | 20260 | |
Circle Geometry: Difficult Proving Parrallel Lines
July 11th 2010, 05:34 PM
Lukybear
Circle Geometry: Difficult Proving Parrallel Lines
AB and AC are equal chords of a circle. AD and BE are parallel chords through A and B respectively. Prove that AE is parallel to CD.
July 11th 2010, 09:50 PM
simplependulum
... | 4 | [
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0.0712890625,
-0.0009002685546875,
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0.041748046875,
0.061767578125,
0.038818359375,
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0.057861328125,
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0.024169921875,
-0.0830078125,
-0.0234375,
0.01409912109375,
-0.07177734375,
0.... | 20,261 | 20261 | |
Vectors and Projectiles
Mechanics: Vectors and Projectiles
Vectors and Projectiles: Problem Set Overview
This set of 34 problems targets your ability to perform basic vector operations such as vector addition and vector resolution, to use right angle trigonometry and vector addition principles to
analyze physical sit... | 4 | [
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-0.0023956298828125,
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0.037841796875,
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0.0947265625,
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0.0458984375,
0.02197265625,
0.05859375,
-0.041259765625,
0.0087890625,
-0.0186767578125,
0.0429687... | 20,262 | 20262 | |
Cauchy Sequence
October 19th 2012, 04:10 PM
lovesmath
Cauchy Sequence
I need to prove that every Cauchy sequence is bounded. Here is my work thus far:
{a(sub n)}n=1 to infinity is a Cauchy sequence. A sequence is said to be Cauchy if for all E>0 there exists N in the natural numbers such that if m,n>=N, the... | 5 | [
-0.042724609375,
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0.03515625,
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0.0257568359375,
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0.054931640625,
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0.0419921875,
0.07470703125,
-0.... | 20,263 | 20263 | |
Eigenvalues of a 2 by 2 matrix
Benny
Edit: The question is from a non-calculator exam so I can't take decimal approximations. :(
When you see all those multiples of 0.1, simply multiply everything by 10. You'll be looking for eigenvalues of (15 +- sqrt(37))/2. Try (A,B) and get the equation:
8A + 3B = (15 +- sqrt(37... | 4 | [
0.005767822265625,
0.040283203125,
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0.076171875,
-0.0390625,
-0.037353515625... | 20,264 | 20264 | |
Stat and prob help
April 21st 2007, 04:18 PM
schinb64
Stat and prob help
I have three questions that I am not sure of: Help on any of them is greatly appreicated
1) Assume the probability that you will make a sale on a given phone call is .19
a) Find the probability that you will not make a sale on the ... | 5 | [
0.08935546875,
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0.0250244140625,
0.013305664062... | 20,265 | 20265 | |
advanced functions intro calc questions
February 22nd 2009, 09:22 PM #1
Newbie
Joined
Feb 2009
Posts
24
advanced functions intro calc questions
ok so im very new to calculus and just started learning limits...were exiting logs and entering limits (im a grade 12 student) my teacher has given me 2 question... | 5 | [
-0.00750732421875,
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0.12890625,
-0.09326171875,
-0.07714... | 20,266 | 20266 | |
Some questions from old exams??
March 25th 2010, 06:13 AM #1
Junior Member
Joined
Mar 2010
Posts
44
Some questions from old exams??
1)
a) $\lim_{(x,y)\rightarrow(0,0)}\frac{sin(xy)}{x}$
b) $\lim_{(x,y)\rightarrow(0,0)}\frac{xy^2}{x^4y^4}$
2) Without using distance formula, find the distance... | 5 | [
0.03271484375,
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0.05712890625,
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-0.0004119873046875,
-0.049072265625,
-0.074707031... | 20,267 | 20267 | |
z-score question
January 27th 2009, 03:09 PM #1
Newbie
Joined
Oct 2008
Posts
11
z-score question
A university aacepts only applicats scoring in the top 16% on an entrance exam. Each year the test scores are normaly distributed with a standard deviation of 30. What is the highest value that
the mean c... | 5 | [
0.0302734375,
0.06884765625,
-0.036865234375,
-0.0025787353515625,
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0.0380859375,
0.003936767578125,
-0.00592041015625,
0.0191650390625,
-0... | 20,268 | 20268 | |
inverse function question
November 11th 2007, 09:09 AM
synnr
inverse function question
the function is f(x) = 6x + x^2
I need to find the largest restricted domain for which f has an inverse
and to explain the answer carefully..
2nd part is to find the inverse using the original function and the doma... | 4 | [
-0.017822265625,
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0.057373046875,
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0.051513671875,
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0.06787109375,
-0.007720947265625,
-0.0198974609375,
0.032958984375,
0.103515625,
0.006378173828... | 20,269 | 20269 | |
matrix question
December 3rd 2012, 06:05 PM #1
Junior Member
Joined
Sep 2012
From
Toronto
Posts
36
matrix question
The population of rats in my farm moves constantly back and forth between the house and the field. Every week 40% of the rats in the field move to my house while 30% of those in my house... | 5 | [
0.050048828125,
0.00921630859375,
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-0.10107421875,
0.07470703125,
0.11572265625,
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-0.031494140625,
0.06982421875,
0.024169921875,
0.00994873046875,
-0.06982421875... | 20,270 | 20270 | |
A Cluster-Based Consensus Algorithm in a Wireless Sensor Network
International Journal of Distributed Sensor Networks
Volume 2013 (2013), Article ID 547124, 14 pages
http://dx.doi.org/10.1155/2013/547124
Research Article
A Cluster-Based Consensus Algorithm in a Wireless Sensor Network
^1Graduate School of Global Inf... | 4 | [
-0.06982421875,
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0.0012664794921875,
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0.022705078125,
0.07861328125,
-0.064941... | 20,271 | 20271 | |
Complex Analysis -- convergence
September 15th 2011, 06:46 AM #1
Member
Joined
Oct 2009
Posts
82
Complex Analysis -- convergence
Let M be a complete metric space. Suppose that $f_n$is a sequence of
continuous functions in $(\mathcal{C}(U, M), \rho)$ which converges to f and $z_n$ is a
sequence in... | 5 | [
-0.05322265625,
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0.006591796875,
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0.034912109375,
-... | 20,272 | 20272 | |
Log and Exponent Questions
December 17th 2006, 10:29 AM #1
Member
Joined
Oct 2006
From
Toronto
Posts
86
Log and Exponent Questions
Here are five log and exponent questions. I'm wasn't sure where to post them at so if this isn't the right place to make this thread, could someone please move it to wher... | 4 | [
-0.0242919921875,
-0.01806640625,
0.005401611328125,
0.1005859375,
0.08447265625,
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0.058837890625,
-0.000019788742065429688,
-0.00122833251953125,
0.080078125,
0.044677734375,
-0.03857421875,
0.051513671875,
0.16015625,
0.0079345703125,
0.08203125,
-0.10791015625,
-0... | 20,273 | 20273 | |
A New Iterative Scheme of Modified Mann Iteration in Banach Space
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 264909, 9 pages
http://dx.doi.org/10.1155/2014/264909
Research Article
A New Iterative Scheme of Modified Mann Iteration in Banach Space
College of Applied Mathematics, Chengdu University of... | 5 | [
0.05224609375,
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-0.0634765625,
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0.010498046875,
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0.064453125,
0.0133056640625,
0.01190185546875,
-0.0322265625,
0.01080322265625,
-0.... | 20,274 | 20274 | |
Solving a cubic equation.
I have $f(x)= x^4 + 2x^2$ and am trying to solve $f'(x)= 1$, that is $4x^3 + 4x= 1$
The common factor is 4x. Can you try to factor it? Either that, or I'm not understanding what you need to do. Do you need to find the values of x for which 4x^3 + 4x = 1 ?
Indeed, you can't do that You get $4... | 5 | [
0.0184326171875,
-0.045166015625,
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0.07861328125,
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0.053955078125,
-0.0003948211669921875,
0.04248046875,
-0.04150390625,
... | 20,275 | 20275 | |
the integral of a^u where u is a function of x
July 19th 2013, 03:26 AM
kingsolomonsgrave
the integral of a^u where u is a function of x
The integral of a^u where u is a function of x is given as
1/ln(a) a^u + C
but if I take the derivative of that using the product rule we have C=0 because it's a cons... | 5 | [
0.014404296875,
-0.0225830078125,
0.042724609375,
0.01153564453125,
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0.0625,
-0.07373046875,
0.04638671875,
0.11181640625,
0.08544921875,
-0.003326416015625,
0.037841796875,
0.0035247802734375,
-0.027587890625,
0.0107421875,
-0.08349609375,
-0.0280... | 20,276 | 20276 | |
i have four math problems i have been struggling with for a while now
February 24th 2010, 12:51 PM #1
Newbie
Joined
Feb 2010
Posts
1
Questions 1,2: using rational theorem + descartes's rule of sign to determine possible rational & real zeroes. find all zeroes & express the polynomial as a product of linea... | 4 | [
0.01708984375,
0.04638671875,
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0.05322265625,
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0.057861328125,
0.050537109375,
-0.0390625,
0.0791015625,
0.09619140625,
0.01092529296875,
0.0673828125,
-0.044677734375,
-0.01184082... | 20,277 | 20277 | |
Quick question involving integration by parts
April 13th 2010, 06:42 PM #1
Member
Joined
Oct 2009
Posts
229
Quick question involving integration by parts
Here is a solution guide to a problem;
$\int \frac {3}{2x-3} + \frac {2}{(2x-3)^5} dx$
$3*<font color=$\frac{1}{2} \int \frac {1}{u}du + 2*\fr... | 5 | [
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0.002105712890625,
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-0.0021209716796875,
-0.048095703125,
-0.01177978515625,
0.006927490234375... | 20,278 | 20278 | |
Teach me the best way of simplyfying this Long Demoivre's Trig Prooving question.
September 24th 2008, 12:13 PM #1
Newbie
Joined
Sep 2008
Posts
3
Teach me the best way of simplyfying this Long Demoivre's Trig Prooving question.
Hi there,i've attached the question in the image...It's basically some test q... | 5 | [
-0.06591796875,
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0.038330078125,
-0.00933837890625,
0.028564453125,
-0.0185546875,
0... | 20,279 | 20279 | |
G, H groups, phi: G -> H epimorphism, N normal in G, A normal in H. Then ...
March 20th 2012, 04:09 PM #1
Member
Joined
Feb 2009
Posts
138
G, H groups, phi: G -> H epimorphism, N normal in G, A normal in H. Then ...
Hi: Let G be a group and N normal in G such that 1 and N are the only normal subgroups of... | 4 | [
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0.01104736328125,
-0.01123046875,
0.007598... | 20,280 | 20280 | |
Learn about Senior Chemistry: Equilibrium 4
Male Speaker: Lets put some numbers into an expression, and then kind of mess with the equations see what happens, okay watch, lets take H2 plus F2 makes HF all gases when they all go into the
expression, this of course becomes square divided by the concentration of these two... | 4 | [
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0.03564453125,
0.00216674804687... | 20,281 | 20281 | |
Proving if something is even
April 17th 2013, 07:25 PM #1
Member
Joined
Oct 2012
From
san francisco
Posts
92
Proving if something is even
Let A,B,C be integers such that A^2 + B^2 = C^2. Prove at least one of A and B is even.
Please help guide me through this problem so I can understand it bette... | 4 | [
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0.03759765625,
-0.01104736328125,
0.03... | 20,282 | 20282 | |
Initial Value Differential Equation
March 26th 2013, 11:25 AM #1
Newbie
Joined
Mar 2013
From
mathville
Posts
22
Initial Value Differential Equation
I have dy/dx = x^2/y^2
=y^2 dy = x^2 dx
∫y^2 dy = ∫x^2 dx
y^3/3 = x^3/3+ C
y^3 = x^3 + 3C
3C= some constant k
y = (x^3+k)^(... | 4 | [
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Patent US7080313 - Signal evaluation apparatus and signal evaluation method
BACKGROUND OF THE INVENTION
The present invention relates to a signal evaluation apparatus and signal evaluation method for evaluating a reproduction signal of a recording medium.
In recent years, according to the digitization of various sort... | 4 | [
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Continuous function => Measurable
If a function f:[a,b]->R is continuous a.e, then show that f is a measurable function.
The definition of continuity is that $f^{-1}$ takes open sets to open sets. f is a measurable function if $f^{-1}$ takes open sets to measurable sets. But, every open set is measurable. Thus, all
th... | 5 | [
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... | 20,285 | 20285 | |
Using total differential to find the marginal rate of substitution
March 11th 2010, 10:01 AM
ihatemath09
Using total differential to find the marginal rate of substitution
help please..
Consider the utility function U(x, y) = xy + y.
(a) Use the total differential to find the marginal rate of substituti... | 5 | [
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find solutions to the equation
Hi sorry am i doing this right?
find all solutions to the equation
$x^6 + 2x^3 + 1 = 0$
let $u = x^3$
then $u^2 + 2u + 1 = 0$
$= (u+1)^2 = 0$
thus $u^3 = -1$
$= \sqrt{1} e^{\pi + 2\pi m}$
and then i solve for $m = 0..6$
is that correct?
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... | 20,287 | 20287 | |
area between curves
December 2nd 2007, 10:09 PM #1
Junior Member
Joined
Apr 2007
From
USA
Posts
41
area between curves
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.
From (5/3) to (25/3) 3x^2-5x dx
I kee... | 5 | [
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GMAT 3D Coordinate Geometry
• GMAT Prep (USA)
•
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•
• Favorite GMAT Articles
□ 800score GMAT Course Reviews
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□ GMAT Essay Tips & Grading from 800score
•
• Free GMAT Prep
□ Free GMAT CAT ... | 4 | [
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Exploiting geometric series with power series to find Taylors series
September 28th 2010, 05:34 PM #1
Member
Joined
Jan 2010
Posts
144
I'm confused between some formulae so I'm going to give some examples and you can let me know if what I'm writing is correct.
Find the Taylor series for....
EXAM... | 5 | [
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Biharmonic Operator -Fourier Transform.
September 27th 2012, 03:21 AM #1
Newbie
Joined
Sep 2012
From
Australia
Posts
10
Biharmonic Operator -Fourier Transform.
Hi guys,
just wondering if someone out there could give me a hand with the following problem.
u(x,y) multiplied by a biharmonic ope... | 5 | [
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help with determinant problem....
January 15th 2009, 11:04 AM #1
Ok, here it is. I know how to do every single problem dealing with determinants except THIS one. This problem you have to solve the equation for 'x'.
|0 0 -1|
| 3 x 0 | = x^2
| 2 0 3 |
Any help is appreciated!
Calculate the d... | 4 | [
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Patent US5649084 - Method for performing boolean operations on geometric objects in a computer-aided design system
The invention relates to a method for performing Boolean operations on geometric objects in a computer-aided design (CAD) system. In the design of physical objects, for example machine pads, it is
often ne... | 4 | [
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Sum of Positive Integers
Find the sum of all positive integers less than 1000 that are divisible by 3 but not by 2
Rimas and I are friends, and you seem to have read the problem wrong like I did intially. The problem asks for the sum of the integers, not how many integers. I already determined that the sum of all
inte... | 4 | [
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Thermodynamic Modelling of Dolomite Behavior in Aqueous Media
Journal of Thermodynamics
Volume 2012 (2012), Article ID 723052, 12 pages
http://dx.doi.org/10.1155/2012/723052
Research Article
Thermodynamic Modelling of Dolomite Behavior in Aqueous Media
^1Faculty of Engineering and Chemical Technology, Technical Univ... | 4 | [
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Patent US7103093 - Method and device for estimating a propagation channel
BACKGROUND
1. Field of Invention
The present invention relates to a method and a device for estimating the parameters of a propagation channel, so as to decode digital signals, by using a learning sequence or reference sequence
known to the rec... | 4 | [
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Patent US4509003 - Vector control method and system for an induction motor
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates generally to a vector control method and system for an induction motor and more specifically to a decoupled-vector control method and system for an induction m... | 4 | [
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find a square root of the complex number
December 28th 2010, 05:15 PM
Volga
find a square root of the complex number
Question. Find a square root of the complex number $i$.
Answer.
Let $i^2=w$. By inspection (of i), the modulus of w is 1; we need to find $\theta$.
$(\cos(\frac{\theta}{n}+\frac{2kn}... | 5 | [
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Proof Using Modular Arithmetic
October 18th 2009, 02:29 PM #1
Newbie
Joined
Oct 2009
Posts
14
Proof Using Modular Arithmetic
show that if an integer n has at least two distinct odd prime divisors then there exists k<φ(n) such that
a^k ≡ 1(mod n)
for every a relatively prime to n.
What I h... | 5 | [
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