content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Another Charpit PDE
February 8th 2011, 10:38 PM
bugatti79
Another Charpit PDE
Write down the Lagrange-Charpit equations for the equation
$<br /> \displaystyle \frac{\partial u}{\partial x}\frac{\partial u}{\partial y}-y\frac{\partial u}{\partial x}-x<br /> \frac{\partial u}{\partial y}=0<br />$ and use them... | 5 | [
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0.0220947265625,
0.004180908203125,
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0.022216796875,
0.03662109375,
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0.006927490234375,
-0.056640625,
-0.05444... | 8,200 | 8200 | |
Divisibility proof
gcd(a,b) = 1 and a|m and b|m. How to prove ab|m without using unique-prime-factorization theorem?
Hello, $a \mid m \implies m=am' ~,~ \text{where } m' \in \mathbb{Z}$ $b \mid m \implies m=bm'' ~,~ \text{where } m'' \in \mathbb{Z}$ Therefore $am'=bm''$ and hence a divides $bm''$ By Gauss theorem,
if ... | 4 | [
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0.0211181640625,
-0.0446777... | 8,201 | 8201 | |
Sequences/Series
October 18th 2009, 10:58 AM #1
Junior Member
Joined
Oct 2009
Posts
36
Sequences/Series
I'm not sure if this is the right forum for this so I appologise if this is the wrong place.
I think I have worked out the answer to my problem but I'm not sure I have done it right. My question i... | 4 | [
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0.048828125,
-0.08... | 8,202 | 8202 | |
ynamics
2. Eulerian fluid dynamics
2.1. Cosmological fluid equations
A fluid is a dense set of particles treated as a continuum. If particle collisions are rapid enough to establish a local thermal equilibrium (e.g., Maxwell-Boltzmann velocity distribution), the fluid
is an ideal collisional gas. If collisions do not... | 4 | [
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Simultaneous equation problem
Use the method of elimination to solve the following simultaneous equations. http://www.eso.org/sci/software/esom...vola/img49.gif-5p+q/2=-3/2 2p+3q/2=4 What are the following steps?
To eliminate p, multiply the first equation by two, the second by 5 and add the results.
-5p+q/2=-3/2....... | 4 | [
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Rotation and Transformation of Axes
March 14th 2010, 10:48 AM #1
Newbie
Joined
Feb 2010
Posts
24
Hi,I have a question that I have problems with.It's my homework due Thursday.
M1(9,-3);M2(-6,5).Bring the origin to M2 and rotate the system so that M1,M2 agrees with the direction of the new x axis.(tan... | 4 | [
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-... | 8,205 | 8205 | |
Line intersection
July 9th 2010, 06:58 PM #1
Senior Member
Joined
Apr 2010
Posts
487
Line intersection
This is the question:
4x + 3y = 24, x^2 + y^2 = 25
Find where the line intersects the circle.
I tried solving for y, the substituting it into the circle equation, but I don't get the corr... | 4 | [
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parallel lines
August 18th 2009, 11:09 PM
arunachalam.s
parallel lines
If a set of 10 parallel lines are intersected by a set of 13 other parallel lines,then find the number of parallelograms formed?
I m not able to undertsand the question ..is there a standard formula for this type of questions
August 18t... | 4 | [
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Functions
January 25th 2010, 05:17 PM
integral
Functions
If you have
$f(x)=x^{2}+3$
I know f(x) just means the function of x, or just y.
But take this:
If
$\frac{f(x)}{x-k}$
then
$r=f(k)$
Where r= remainder
(Headbang) This makes no since to me. some function divided by x-k y... | 4 | [
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0.07666015625,... | 8,208 | 8208 | |
Integration by trig substitution
March 8th 2009, 12:14 AM
madmartigano
Integration by trig substitution
I need to show that $\int {\frac{x}{{{x^2}+4}}dx} <br /> =\frac{1}{2}\ln \left( {{x^2} + 4} \right) + c<br />$ using trig substitution.
I've tried the following:
$\begin{array}{l}<br /> x = 2\tan \th... | 5 | [
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inverse of an AR(1) or Laplacian(?) or Kac-Murdock-Szegö matrix
up vote 1 down vote favorite
1
My current problem involves having an exact (symbolic) inverse of a scaled AR(1) matrix for n-dimension. (I don't know what this matrix would be called in general; I'm sure it is used often.) This is
used as a smoothing prio... | 4 | [
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Right answer but...not quite ? (Quadratic)
November 1st 2009, 01:43 PM #1
Right answer but...not quite ? (Quadratic)
So here is the question and the way I worked through it
The answer is 55.125 cm^2
I just feel as thought my method used to arrive at the answer is either wrong, or a misinterpretation of ... | 4 | [
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Help! How to foil this cube expression??
September 26th 2006, 12:13 PM
shenton
Help! How to foil this cube expression??
Consider:
(x+y)^2
= (x+y)(x+y)
= x^2 + xy + xy + y^2
= x^2 +2xy + y^2
Question:
(-2-5)^-3
= 1/(-2-5)^3
= 1/(-2-5)(-2-5)(-2-5)
= 1/?
How to foil... | 4 | [
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Trig identities help
November 9th 2008, 06:41 PM
cokeclassic
Trig identities help
Hi i have question
tanx - cotx / tanx + cotx + 1 = 2sinx
so...
sin/cos - cos/sin / sin/cos + cos/sin
then mutlple fracs and get
sin^2x - cos ^2x/ sinxcosx / sin^2x + cos^2x/ sinxcosx
and then what do i ... | 4 | [
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Integral Question
September 14th 2009, 08:12 PM
Sprintz
Integral Question
2 Part Question.
1) How do I use the 'fancy' font to describe formulas on this and other websites? It would make things much easier. I assume some kind of Alt-codes?
2) The actual question: Integral of (secxcos2x)dx/(sinx + secx)... | 4 | [
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... | 8,214 | 8214 | |
Power Series Proof
August 13th 2009, 06:25 PM
JG89
Power Series Proof
Problem:
If a_v > 0 and $\sum_{v=0}^{\infty} a_v$ converges, then prove that $\lim_{x \rightarrow 1^-} \sum_{v=0}^{\infty} a_v x^v = \sum_{v=0}^{\infty} a_v$.
Attempt:
Since $\sum a_v$ converges, then we can say that $\sum a_v x... | 5 | [
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Interval Proof
August 18th 2007, 06:24 PM #1
Member
Joined
Aug 2007
Posts
239
Interval Proof
We want to prove that $(a, \infty) \subseteq [b, \infty) \Leftrightarrow a \geq b$.
Proof: $x \in (a, \infty) \Rightarrow x \in [b, \infty) \Rightarrow a \geq b$.
$a \geq b \Rightarrow x \in (a, \infty)... | 4 | [
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0.0... | 8,216 | 8216 | |
Agda by Example: Sorting
2013-04-01 Agda by Example: Sorting
Agda?
The Haskell programmer is used to the pleasure of collaborating with a nice type system. Haskell itself hits quite a sweet spot of expressivity and manageability—type inference is (mostly) decidable,
no subtyping, etc. However, in the past 30 years, ... | 4 | [
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How do i determine the wall thickness of a Cylinder if it gets expanded.
February 27, 2014 11:41 AM Subscribe
I would like to use a mathematical formula in Excel to try and determine how much the wall thickness of a Cylinder or tube changes if it is expanded.
Example of what I would like to be able to calculate if ... | 4 | [
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digits
February 5th 2010, 09:17 AM
sri340
digits
Of all the four-digit positive integers containing only digits from the set {2, 4, 6, 8}, what fraction of them have at least one of their digits repeated? Express your answer as a common
fraction.
February 5th 2010, 09:46 AM
Archie Meade
Quote:
H... | 4 | [
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Linear subspace!
December 12th 2010, 03:39 AM
tom27
Linear subspace!
Hi!
I have problem because I do not know how to prove this:
I have a set:
$T_n (\mathbb{R})=\big\{[a_i_j] \ : \ a_i_j \in \ \mathbb{R} \ , \ i,j \ = 1,...,n, \ a_i_j=0 \ for \ i>j\big\}$
and I must show that the $T_n (\mathbb... | 5 | [
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... | 8,220 | 8220 | |
Integration of trig functions
September 9th 2008, 08:00 AM #1
Junior Member
Joined
Sep 2008
Posts
27
Integration of trig functions
Ok so here is my integral:
INTEGRAL of [sin(5x)][cos(6x)]dx
Now this is a pretty simple u-substitution problem, i know that. Except i have one problem. The 5x and 6... | 5 | [
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Find mass by linear density?
July 13th 2010, 11:19 AM #1
Newbie
Joined
Jul 2010
Posts
15
Find mass by linear density? ......SOLVED........
A thin wire is bent into the shape of a semicircle x^2+y^2=4 x>0
If the linear density is 3, find the mass of the wire.
Anyone have a clue how to tackle thi... | 4 | [
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Exponential and logarithmic equations
April 29th 2011, 02:59 PM #1
Member
Joined
Jun 2009
Posts
108
Exponential and logarithmic equations
I was having trouble with the following:
1)An expression for y in terms of x by rearranging 18loge(x)=6-3loge(y).
2) solutions for x in (log6(x))^2+4log3(6)+... | 4 | [
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Approximation
June 26th 2009, 01:17 AM
Amer
Approximation
I have a question in numerical analysis and I do not know where to put it so I post it here ok the question
Find the largest interval in which $p^{*}$ must lie to approximate $p$ with relative error at most $10^{-4}$ for each value of p
$a.\pi... | 5 | [
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0.040527... | 8,224 | 8224 | |
long question, help needed!
January 1st 2009, 08:48 AM
14041471
long question, help needed!
This is a long question whilch i think involves the quadratic formula, but i generally dont know where to start with this so any help would be much appreciated.
"In an engineering test, a rocket sled is propelled int... | 4 | [
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... | 8,225 | 8225 | |
Kinematics: The Motion of Particles
October 9th 2009, 11:02 AM
BabyMilo
Kinematics: The Motion of Particles
A train takes 5 minutes to cover 3km between stations P and Q. Starting from rest at P, it accelerates at a constant rate to a speed of 40km/hr and maintains this speed for a while and then is
brought ... | 4 | [
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0.00... | 8,226 | 8226 | |
7a^2+b^2=2^N
Prove that if $N$ is any integer greater than 2 then there exist odd integers $a$ and $b$ such that $7a^2+b^2=2^N$
Test manually for N = 3, 4, 5. Any N > 5 can be written in the form 3p+4q, where p and q are non-negative integers. So, $2^N=2^{3p}2^{4q}=2^32^3\ldots 2^3(\text{p times})*2^42^4\ldots 2^4(\te... | 5 | [
-0.0224609375,
0.05810546875,
-0.028564453125,
0.056884765625,
-0.0517578125,
0.0517578125,
0.0260009765625,
-0.019287109375,
-0.009765625,
0.009521484375,
-0.072265625,
-0.0235595703125,
0.01611328125,
0.060791015625,
-0.0230712890625,
0.0576171875,
-0.045654296875,
0.013000488281... | 8,227 | 8227 | |
Graph the function?
I need some help with this one. Thanks in advance Graph the function. f(x) = log3(x - 3)
When you are trying to graph logs, the easiest way to do it (if you can't use a graphing calculator) is to plot points. We know that logs are undefined for negative values of x and also for x = 0.
For this part... | 4 | [
0.0106201171875,
-0.03564453125,
-0.07421875,
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0.0274658203125,
0.04150390625,
0.0223388671875,
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0.0242919921875,
0.037109375,
0.09130859375,
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-0.091796875,
-0.0830078125,
-0.... | 8,228 | 8228 | |
How do I know what the inner and outer function is?
February 28th 2009, 04:33 PM #1
Junior Member
Joined
Mar 2008
Posts
58
How do I know what the inner and outer function is?
Some equations are easy to figure out because you can add brackets around them, but sometimes it's really difficult!
For exam... | 5 | [
0.0191650390625,
0.039794921875,
0.061279296875,
0.0030517578125,
0.0027618408203125,
-0.060791015625,
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0.0128173828125,
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-0.00099945068359375,
-0.00994873046875,
0.091796875,
-0.08837890625,
0.00360107421... | 8,229 | 8229 | |
SAT Tip: A Primer on Triangles
This tip on improving your SAT score was provided by Vivian Kerr at Veritas Prep.
Triangles often appear on the SAT, and there are some basic properties you’ll need to know to rock the SAT math section. A triangle is a three-sided figure. The sum of the interior angles is always
180 degr... | 4 | [
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0.0830078125,
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-0.0517578125,
0.044921875,
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0.037353515625,
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0.034912109375,
0.0908203125,
-0.050048828125,
0.024658203125,
0.005279541015625... | 8,230 | 8230 | |
An invariant method of stationary phase
up vote 9 down vote favorite
6
The method of stationary phase is very well-known and employed in many areas of physics and mathematics, and, of course, included in various versions as theorem in textbooks, especially on pseudors
and microlocal analysis.
However, it always is so... | 4 | [
-0.04931640625,
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-0.00469970703125,
-0.017578125,
-0.048095703125,
0.0150146484375,
-0.008483886... | 8,231 | 8231 | |
Math Virus Formula
Date: 10/23/2001 at 05:49:48
From: Victor Lee
Subject: I cannot figure out the formula to a math virus
Hello Dr. Math,
I have to figure out a formula for a math virus. The virus spreads to
all the squares directly touching each other (not including
diagonally), and I have found the formula for th... | 4 | [
0.01068115234375,
0.051025390625,
0.00185394287109375,
-0.06982421875,
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0.12890625,
0.056396484375,
0.042724609375,
-0.0032196044921875,
0.0225830078125,
0.0159912109375,
0.0859375,
-0.058837890625,
0.0302734375,
-0.07666015625,
0.... | 8,232 | 8232 | |
When do blow-up and quotient commute?
up vote 5 down vote favorite
Let a finite group $G\subset SL(n,\mathbb{C})$ act on $\mathbb{C}^{n}$ in a natural way. Assume there is a crepant resolution of $f:X\rightarrow \mathbb{C}^{n}/G$. When is it possible to write $X$ as
$Y/G$ for some $Y$ and $G$-action on $Y$?
This is ... | 4 | [
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-0.09765625,
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0.03515625,
-0.0019378662109375,
-0.020263671875,
0.0... | 8,233 | 8233 | |
Time that Period!
Day 2
Materials
Introduction
Students should again be encouraged to discuss the definition of a cycle or periodicity. Students should recall the lab that was completed on Day 1 and how it relates to determining the "period of
the periodicity". In the lab, they should have determined the length of t... | 4 | [
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0.0098876953125,
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0.05712890625,
-0.00016021728515625,
-0.000743865966796875,
-0.0625,
-0.00860595703125,
-0.0257568359375,
-0.086... | 8,234 | 8234 | |
Difficult examples for Frankl's union-closed conjecture
up vote 30 down vote favorite
7
Frankl's well-known union-closed conjecture states that if F is a finite family of sets that is closed under taking unions (that is, if A and B belong to the family then so does $A\cup B$), then
there must be an element that belong... | 4 | [
-0.0556640625,
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0.06640625,
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0.07861328125,
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-0.08447265625,
0.043212890625,
0.0014190673828125,
0.031005859375,
-0.005615234375,
-0.03271484375,
-0.00... | 8,235 | 8235 | |
Geometric series and such..
February 21st 2007, 05:10 PM
Mr_Green
Geometric series and such..
The sum of an infinite geometric series is 36. The second term of the series is 8. Find two possibilities for combinations of a (the first term) and r (the common ratio).
Thanks
February 21st 2007, 05:21 PM
Aryth... | 4 | [
-0.05712890625,
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0.009765625,
0.053466796875,
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0.0118408203125,
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0.07666015625,
0.0164794921875,
0.0250244140625,
-0.09326171875,
... | 8,236 | 8236 | |
GLOBE III - Bulk Density
┌────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────┬────────────────────────────────────────────────┐
│ ... | 4 | [
0.002838134765625,
-0.046142578125,
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0.03662109375,
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0.0634765625,
0.0235595703125,
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0.... | 8,237 | 8237 | |
Types Summer School 2007
The Types Summer School 2007 is held in Bertinoro, Italy, August 19 - 31.
The examples from the lectures can be found here: examples/SummerSchool07/Lecture
Exercises
1. Natural numbers
1.1. Define a datatype of Nat natural numbers with constructors zero and suc.
1.2. Define an addition fu... | 4 | [
-0.11376953125,
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0.0294189453125,
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0.06103515625,
-0.03955078125,
0.044... | 8,238 | 8238 | |
vectors help
April 21st 2007, 10:40 AM #1
Member
Joined
Mar 2007
Posts
80
vectors help
Hi, is this categorized as number theory?....the only text book my college libary has for this kind of stuff is like, 30 years old and not the easiest read!
This is an example in my workbook...if someone could spa... | 4 | [
-0.07861328125,
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0.0166015625,
-0.035888671875,
0.055419921875,
-... | 8,239 | 8239 | |
supremum and infimum
December 4th 2010, 06:11 AM #1
Junior Member
Joined
Oct 2009
Posts
31
supremum and infimum
Hello!
can someone help me to prove this
Let A*B={a*b;a,b>0 a is element of A,b element of B.Prove that:
inf(AB)=inf(A)inf(B)
sup(AB)=sup(A)sup(B)
i've done the proof with... | 4 | [
-0.0230712890625,
-0.04931640625,
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0.057861328125,
0.08251953125,
0.10009765625,
-0.03... | 8,240 | 8240 | |
Find a unit vector that is orthogonal to the plane
March 17th 2010, 12:00 AM #1
Newbie
Joined
Mar 2010
Posts
3
I was given a vector A = [2 2 2] and a vector B = [4 6 5] from a plane and supposed to find a vector orthogonal to this plane. The vector has to intersect with the plane at [0 0 0]
and have ... | 5 | [
-0.0703125,
-0.0120849609375,
-0.056884765625,
-0.07763671875,
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0.032958984375,
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0.02978515625,
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-0.011474609375,
-0.07080078125,
0.08203125,
-0.080078125,
-0.004760... | 8,241 | 8241 | |
Differentiation help
April 22nd 2007, 12:11 PM
johnnyboy
Differentiation help
I have a problem with this exercise:
"The curve with equation: y = ax^3 + bx^2 + cx + d has a local maximum point where x=-3 and a local minimum point where x=-1. If the curve passes through the points (0;4) and (1;20), find the
... | 4 | [
-0.037109375,
-0.0155029296875,
-0.0238037109375,
-0.048095703125,
-0.0625,
0.06396484375,
-0.01422119140625,
0.060791015625,
0.0498046875,
0.00042724609375,
0.0673828125,
-0.076171875,
0.05322265625,
0.0537109375,
0.006591796875,
0.09521484375,
-0.0194091796875,
-0.0380859375,
-... | 8,242 | 8242 | |
Linear (in)dependence of minors of a matrix
up vote 0 down vote favorite
From (Italian, very nice book):"Lezioni di Geometria Analitica e Proiettiva" by Beltrametti, CArletti, Gallarati, Bragadin (pag. 21):
Let $K$ a field, $V:= K^{n+1}$ and let $e_1,\ldots, e_{n+1}$ a base (canonical or not) of $V$. Let $W\subset K^... | 5 | [
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0.06396484375,
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0.07177734375,
-0.05078125,
0.063476... | 8,243 | 8243 | |
Need explanation for basic factoring...
July 26th 2010, 10:13 PM #1
Newbie
Joined
Jul 2010
Posts
5
Need explanation for basic factoring...
Hi guys,
I've just started a discrete mathematics course at university, and one of the things that is assumed knowledge is being able to factor expressions. The ... | 4 | [
-0.0654296875,
0.037109375,
0.0020751953125,
0.057373046875,
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-0.0634765625,
0.00579833984375,
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-0.005035400390625,
-0.0038604736328125,
0.08203125,
-0.03173828125,
-0.0046691... | 8,244 | 8244 | |
Is it normal to have two differing gradients for one point?
September 15th 2007, 08:08 PM #1
Newbie
Joined
Sep 2007
Posts
7
I have an exam tomorrow and part of it will consist of dervitives...
I was given a revision sheet and this is one of the questions:
Find the average rate of change of f(x) ... | 4 | [
0.0269775390625,
-0.03857421875,
0.08203125,
0.007232666015625,
-0.00506591796875,
-0.013427734375,
-0.0257568359375,
0.020263671875,
0.0380859375,
-0.00634765625,
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-0.078125,
0.04345703125,
0.027099609375,
-0.00982666015625,
0.0042724609375,
-0.04345703125,
-0.012451... | 8,245 | 8245 | |
I'm having a hard time factoring this
April 2nd 2009, 05:56 PM
robo_robb
I'm having a hard time factoring this
Hi everyone, I'm trying the find the zeros of the derivative 4x^3 + 9x^2 + 6x +1 so I set it to zero but I am stuck as to how I can factor this. btw the original function is x*(x+1)^2
I've asked a ... | 4 | [
-0.00127410888671875,
-0.0208740234375,
-0.017333984375,
0.087890625,
0.03662109375,
0.031494140625,
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0.03369140625,
0.0311279296875,
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0.08154296875,
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0.07373046875,
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0.045654296875,
-0.080078125,
0.0654296... | 8,246 | 8246 | |
quick interest question ...
January 8th 2007, 05:14 PM #1
Newbie
Joined
Oct 2006
Posts
6
quick interest question ...
To provide an annual scholarship for 25 years, a donation of $50,000 is invested in an account for a scholarship that will start a year after the investment is made. If the money is invest... | 5 | [
0.043701171875,
0.061767578125,
0.0361328125,
-0.07080078125,
0.0220947265625,
-0.06494140625,
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0.005889892578125,
0.0147705078125,
0.12890625,
0.0089111328125,
-0.0859375,
-0.0225830078125,
0.06396484375,
-0.024658203125,
0.038818359375,
-0.09765625,
-0.02416992187... | 8,247 | 8247 | |
Finding region positive/negative regions.
October 3rd 2011, 11:55 PM
Kuma
Finding region positive/negative regions.
Hi there.
I am given these functions and I want to find out in which areas they are positive or negative.
x^y - 1
|x+y| - |x-y|
so the way i tried the first one is i set the fun... | 4 | [
0.0693359375,
-0.0032806396484375,
-0.0654296875,
-0.032470703125,
0.051025390625,
-0.1015625,
0.0057373046875,
0.028076171875,
-0.0576171875,
-0.0308837890625,
0.076171875,
0.0034027099609375,
0.044677734375,
0.11962890625,
0.029052734375,
0.091796875,
-0.08935546875,
-0.090332031... | 8,248 | 8248 | |
Uniform continuity and boundedness
up vote -1 down vote favorite
Hi.
I have come across a proof which I understand almost completely, except for one part:
THEOREM: If $f$ is uniformly continuous on a bounded interval $I, [a,b]$ then $f$ is also bounded on $I$.
PROOF: Fix an $\epsilon > 0$, for instance $\epsilon = ... | 5 | [
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0.0810546875,
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0.0927734375,
-0.058349609375... | 8,249 | 8249 | |
solve the inequality
December 10th 2011, 03:28 PM
slapmaxwell1
solve the inequality
ok im not sure about this problem
i am supposed to solve the inequality
$(x-6)^{2}(x+8)<0$ the zero's are 6 and -8
so the answer would be $(\infty ,-8)$?
December 10th 2011, 03:30 PM
skeeter
Re: solve the inequa... | 4 | [
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0.02978515625,
-0.01531982421875,
-0.028076171875,
0.06591796875,
-0.0184326171875,... | 8,250 | 8250 | |
Last 5 digits
find the final 5 digits of, $9^{9^{9^{^{.^{.^{.^{.^{9}}}}}}}}$ that is 1001 nines
Define $f(x)=9^x$. So $f^2(x)=f(f(x))=9^{9^x}$ and so on. Phrased this way, we are asked to calculate $f^{1000}(9) (\bmod 100000)$. By nature of modular arithmetic, it does not matter if we calculate
$f^{1000}(9)$ first, th... | 5 | [
-0.033935546875,
0.07470703125,
-0.0208740234375,
-0.013916015625,
0.054931640625,
0.0115966796875,
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0.06884765625,
-0.01611328125,
-0.0177001953125,
0.0299072265625,
0.0024261474609375,
0.0198974609375,
0.0615234375,
-0.05517578125,
-0.03857421875,
-0.056884765625,
... | 8,251 | 8251 | |
Explaining Bayes' Theorem
Associated Topics || Dr. Math Home || Search Dr. Math
Explaining Bayes' Theorem
Date: 0... | 5 | [
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0.0027618408203125,
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0.0130615234375,
0.0245361328125,
0.028564453125,
0.00518798828125,
... | 8,252 | 8252 | |
Tackling Multi-Bit Attenuator Designs
Eric E. Austin, Dr. Haki Cebi, and Dr. Jay Yang
Digital step attenuators (DSAs) are versatile components that allow precise control of amplitude levels in a variety of RF/microwave systems. Of course, the requirements for different applications,
from wireless and cellular communic... | 4 | [
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0.00494384765625,
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-0.04150390625,
-0.0322265625,
-0.00921630859375,
0.0849609375,
0.0693359375,
... | 8,253 | 8253 | |
Invariant subspaces for compact restrictions
up vote 3 down vote favorite
Suppose $Y$ is a closed hyperplane in $X$, so we can write $X=Y\oplus[x_0]$. Let $y_n$ be a normalized basis of $Y$. Define an operator $S:Y\to Y\oplus[x_0]$ by $Sy_n=\alpha_ny_n+\beta_nx_0$, for any
$n=1,2,\dots$. We can choose $\alpha_n\to 0$ ... | 5 | [
-0.016357421875,
-0.05126953125,
-0.053466796875,
0.048828125,
0.017822265625,
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0.0283203125,
-0.0142822265625,
-0.0037994384765625,
0.020263671875,
0.017822265... | 8,254 | 8254 | |
boolean functions and averaging / counting
up vote 0 down vote favorite
1
Hey guys,
I have a slightly imprecise question. I would like say something about a whole set of binary strings evaluated by a binary function by just looking at some type of average. The easiest example I can
think of is probably a binary funct... | 4 | [
0.0289306640625,
-0.0159912109375,
0.007354736328125,
0.04296875,
0.008544921875,
-0.0177001953125,
0.0162353515625,
0.0150146484375,
-0.03466796875,
-0.00604248046875,
-0.0888671875,
-0.0712890625,
0.056640625,
-0.019287109375,
-0.0289306640625,
0.07763671875,
-0.014892578125,
-0.... | 8,255 | 8255 | |
Szemerédi's Theorem
From Scholarpedia
Ben Joseph Green and Terence Tao (2007), Scholarpedia, 2(7):3446. doi:10.4249/scholarpedia.3446 revision #91851 [link to/cite this article]
Szemerédi's theorem states that any "positive fraction" of the positive integers will contain arbitrarily long arithmetic progressions \(a... | 4 | [
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0.026611328125,
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-0.07421875,
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0.03076171875,
0.08544921875,
-0.0133056640625,
-0.03076171875,
-0.06494140625,
-0.007659912109375,
0.016235... | 8,256 | 8256 | |
geometry (3)
November 7th 2009, 06:42 AM
thereddevils
geometry (3)
In the diagram , AOB is a diameter of the circle with centre O . ACX , BDY and DEC are tangents to the circle at A , B and E respectively . Show that
(1) angle COD =90
(2) OC . OD = 1/2 AB . CD
November 7th 2009, 07:22 AM
Grandad
... | 4 | [
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Finding the length of line
If you know that AC=3,AB=4,XY=1,then what is XW=? WXYZ and ABCD are rectangulars
Hello, Mhmh96! $\text{Given: }\:AC=3,\;AB=4,\;XY=1.$ . . . . . . $W\!XYZ\text{ and }ABDC\text{ are rectangles.}$ $\text{Find the length of }XW.$ Draw diagonal $BC.$ Triangle $ABC$ is a 3-4-5 right
triangle. We f... | 5 | [
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Thermal expansion
International Chapter 1.4. Thermal expansion
Tables for
Crystallography H. Küppers^a^*
Volume D
Physical This chapter discusses the reduction in the number of independent tensor components by crystal symmetry, representation surfaces, the quasiharmonic approximation and t... | 4 | [
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0.0... | 8,259 | 8259 | |
rdering at the boundary crisis point
Scaling and ordering at the boundary crisis point
At the crisis point m[o] = -2 the Mandelbrot set is self-similar with the scaling factor |λ[mo]| = 4 . Each new view below is zoomed in 4 times. m[1] = m[1,0] is the chaotic bands merging Misiurewicz
point with the pattern [CLR]L. C... | 4 | [
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-0.06396484375,... | 8,260 | 8260 | |
trying to slove ıntegration
1) INT 1/[x[(4+x^2)^2](1+x^2)] dx On an earlier problem (on one of the other posts) I explained how to use "Partial Fractions" to solve a particular integration. This one involves the same principle:
Set up the Partial Fractions as: INT [ A/x + (Bx + C)/(4 + x^2) + (Dx + E)/(4 + x^2)^2 + (Fx... | 4 | [
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-0.03173828125,
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0.11181640625,
-0... | 8,261 | 8261 | |
panning
template <class Graph, class OutputIterator, class P, class T, class R>
OutputIterator
kruskal_minimum_spanning_tree(Graph& g, OutputIterator tree_edges,
const bgl_named_params<P, T, R>& params = all defaults);
The kruskal_minimum_spanning_tree() function find a minimum spanning tree (MST) in an undirecte... | 4 | [
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0... | 8,262 | 8262 | |
stupid me
September 4th 2006, 07:00 PM #1
Newbie
Joined
Sep 2006
Posts
5
I know the answer to the equation however i cant seem to get the math to work out. Here is the equation.
x-5/3 - x-4/3 = x-3/2 - (x-2)
skittles900
I know the answer to the equation however i cant seem to get the math to... | 4 | [
-0.09619140625,
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0.0283203125,
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-0.0098... | 8,263 | 8263 | |
special set of permutations
June 22nd 2012, 12:14 PM
andrews
special set of permutations
Hi,
I define a subset of permutations as a subset where there is no more then 1 element the same on the same place
For example a permutation of 4 elements
1 2 3 4
1 3 4 2
1 4 2 3
2 1 4 3
2 3 1 4
... | 4 | [
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0.019775390625,
-0.062255859375,... | 8,264 | 8264 | |
Math Help
November 15th 2011, 12:29 AM #1
Senior Member
Joined
Oct 2009
Posts
459
Integral
With this question do I simply replace x in the integral, simplify and integrate?
"Using the substitution x=(a+b)/2 +((b-a)/2)cos t, evaluate Integral from a to b of square root of((x-a)(b-x))dx".
Do I n... | 5 | [
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-0.0... | 8,265 | 8265 | |
Need help finding out what the variable x is equal to in this exponential decay eq.
November 12th 2012, 09:31 PM #1
Newbie
Joined
Nov 2012
From
New York
Posts
2
(√5 / 25) = 5^3-x
How do you find the value of x? My calculator says that x is equal to 4.5. However, can someone please show me the wor... | 4 | [
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0.0947265625,
-0.08984375,
0.0021514892578125... | 8,266 | 8266 | |
prove convexity
February 28th 2010, 01:38 AM
bravegag
prove convexity
Hello,
I need to prove the following but I am struggling to see where to start:
The image of a convex set $S \subseteq \mathbb{R}^n$ under an affine transformation i.e. the set $f(S)$ for $f(x)=Ax + b$, where $A \in \mathbb{R}^{m \ti... | 5 | [
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0.0859375,
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0.020263671875,
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0.034423828125,
0.07373046875,
-0.057373046875,
... | 8,267 | 8267 | |
Angle sum.
How do I show that $x(t)=\frac{\omega\cos(\omega t)+(1-\omega^{2})\sin(\omega t)}{\omega^{2}+(1-\omega^{2})^{2}}$ is the same as $x(t)=K\sin\left[\omega\left(t-t_{0}\right)\right]$ where $K=\frac{1}
{\sqrt{\omega^{4}-\omega^{2}+1}}.$
Last edited by Cairo; March 4th 2010 at 12:34 PM.
Hello, The idea is to f... | 5 | [
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-0.025... | 8,268 | 8268 | |
is this logical expression equivalent?
it is equivalent, wikipedia actually has this as an example. i figured you wanted to show it though. i'd use a truth table. do you know how to construct one?
yes I do know how, actually my question is to show -(p+q) and p biimplication q are logically equivalent, and I am trying ... | 4 | [
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0.0529785156... | 8,269 | 8269 | |
Basic Complex Number Operations
Complex number
does has the same set of basic math operations as normal algebra. The basic operations are the familiar addition, subtraction, multiplication and division.
The expression for complex number however differs in that it is splitted into 2 parts, namely, the REAL and IMAGINA... | 4 | [
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-0.121... | 8,270 | 8270 | |
Prove that triangle ABC is isosceles
March 13th 2011, 12:58 PM #1
Newbie
Joined
Mar 2011
Posts
9
Prove that triangle ABC is isosceles
Triangle ABC has the following properties: there is an interior point P such that angle PAB = 10 degrees, angle PBA = 20 degrees, angle PCA = 30 degrees and angle PAC = 40... | 5 | [
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... | 8,271 | 8271 | |
Analytical Mechanics
212 ANALYTICAL MECHANICS
the potentials due to a negative charge and a negative pole are negative, while the potentials due to a positive charge and a positive pole are positive.
179. Potential Due to Any Distribution of Mass. — When the field of force or the potential field i... | 4 | [
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-0.0255126953125,... | 8,272 | 8272 | |
solving this equation.
$y - 2 = 2 \cdot \sqrt{3}(x - \frac{\pi}{3})$ any ideas, just confused with the gradient
Solve for $y$ or $x?$ This is a recent question that belongs to other thread, so I'll assume that you want to isolate $y:$ $y-2=2\sqrt{3}\left( x-\frac{\pi }{3} \right)\implies y=2\sqrt{3}x-\frac{2\
sqrt{3}}... | 4 | [
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0.... | 8,273 | 8273 | |
Implicit Differentiation
March 25th 2008, 07:12 PM
lyzzi3
Implicit Differentiation
I think my teacher was talking about turning y into y(x) or something but I'm just completely lost on this one
March 25th 2008, 07:23 PM
TheEmptySet
$5x^2+4x+xy=2$ using implicit we get
$10x+4+y+xy'=0$
$y(2)=-13$
... | 5 | [
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... | 8,274 | 8274 | |
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Topic: Question about linear algebra matrix p-norm
Replie... | 5 | [
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-0.033935546875,
0.05908203125,
0.0301513671875,
-... | 8,275 | 8275 | |
Math Help
February 2nd 2010, 04:31 AM #1
Member
Joined
Nov 2009
Posts
107
vector
The diagram shows non-collinear points O , A , B with P on the line OA such that OP:PA=2:1 and Q on the line AB such that AQ:QB=2:3 . The lines PQ and OB produced meet at the point R . If $\vec
{OA}=a$ and $\vec{OB}=b$
... | 4 | [
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0.099609375,
-0.005218505859375,
-0... | 8,276 | 8276 | |
Solving Trig Equations
November 21st 2007, 06:11 PM
Macleef
Solving Trig Equations
Incorporate the use of the double angle formulas identities and other identities to solve for the following on $0 \leq \theta \leq 360$
$tanx = sin2x$
My Attempt:
$\frac{sinx}{cosx} = 2sinxcosx$
$sinx = 2sinx$
... | 4 | [
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0.0203857421875,
0.01... | 8,277 | 8277 | |
Proving a Set
May 9th 2006, 07:01 PM #1
Newbie
Joined
May 2006
Posts
9
Proving a Set
Note: ^ = "intersects"; U = "union"
Prove that A ^ B ^ C "is a subset of" D, where D = (B ^ (A U C)) U (C ^ A)
Obviously, when drawing a Venn diagram, they all will meet at the very middle. How can I prove this... | 5 | [
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Transformations Across functions
September 9th 2008, 03:06 PM
mike_302
Transformations Across functions
So our lesson in class was about transforming any function, f(x) using generalization (stating: y=f(x), y= -3f(1/2(x-2))+3 etc.)
The homework question is the one thing that may have been the most basic, b... | 4 | [
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-0.1142578125,... | 8,279 | 8279 | |
Limit Question
November 7th 2006, 05:13 PM #1
Member
Joined
Sep 2006
Posts
221
Limit Question
I'm confused:
Why is the limit(as x -> 0) sin(x)/(x-sin(x)) = infinity?
I have done this 10 times now, and I get that it equals -1.
We have an indeterminant form when we plug 0 in (0/0). Thus, I c... | 5 | [
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Hard Problem
April 21st 2005, 10:25 AM
NICEKID
Hard Problem
A sample of 40 families is taken, and a sample mean income of $44,000 with a sample standard deviation of $9,500 is calculated. Determine a 90% confidence interval for the population means
income.
a. $41,469, 46,531
b. $41,529, $46,471
... | 4 | [
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1 problem only
November 23rd 2007, 03:49 PM #1
Newbie
Joined
Nov 2007
Posts
2
Hi! Please help. I will go to class in a few minutes. I don't have an equation for it. Thanks!!!
A merchant has 3 items on sale: namely, a radio for $50, a clock for $30, and a flashlight for $1. At the end of the day, she... | 4 | [
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Third Order Taylor Polynomial
April 16th 2009, 01:29 PM
TAG16
Third Order Taylor Polynomial
If the function f had the following properties: f(2)=1 f'(2)=-3 f''(2)=2 and f'''(x)= (1+x^3)^1/2 for all x> 1 , then use a third order Taylor polynomial to approximate f(2.1). How would you
solve this?
also anot... | 5 | [
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pascal triangle
This is a discussion on pascal triangle within the C++ Programming forums, part of the General Programming Boards category; i am wondering if anyone knows an easy way to write a c++ program that asks
for a number and ...
i am wondering if anyone knows an easy way to write a c++ program that asks for a ... | 4 | [
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how to determine eigenvectors of 2x2 matrices like MatLab does?
December 2nd 2011, 06:59 AM
rollinator
how to determine eigenvectors of 2x2 matrices like MatLab does?
Hi I am attempting to determine the eigenvalues and eigenvectors of a 2x2 matrix.
So how to do the following Matlab instruction "manually":
... | 5 | [
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Solve for B
April 5th 2009, 04:45 PM #1
Junior Member
Joined
Feb 2009
Posts
42
Solve for B
This is driving me nuts!
-Z < (XBar - B) / (B/sqrt(n)) < Z
I want to solve this for B (and keep it in the center). I've burned through an eraser.....can anyone show me the steps?
Thanks!
Do you ... | 5 | [
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[SOLVED] A really hard puzzle involving algebra
July 4th 2009, 01:31 AM #1
Newbie
Joined
Jul 2009
Posts
1
[SOLVED] A really hard puzzle involving algebra
I don't understand the second part:
here is the problem. I have written what I don't understand at the bottom of the problem, I was unable to copy ... | 4 | [
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Largest and smallest possible dimension?
Have you given this any thought at all? Do you know the "rank- nullity" theorem: If L:U-> V, then the rank of L (dimension of the image L(U)) plus the nullity of L (dimension of null space of L) is
equal to the dimension of U. Now, what is the dimension of U?
A "5 by 7 matrix" ... | 5 | [
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Probabilty problem
May 18th 2009, 10:18 PM #1
Junior Member
Joined
Apr 2009
Posts
44
A heavy-equipment salesperson can contact either one or two customers per day with probability 1/3 and 2/3 ,respectively .Each contact will result in either no sale or a 50,000$ sale ,with the
probabilities 0.9 and 0.... | 5 | [
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Math Help
July 26th 2010, 10:53 PM #1
Junior Member
Joined
Jun 2010
Posts
69
Induction
Is the the correct approach to work through this problem
23n – 1 is divisible by 7 for all n>=1
n(1)
23(1) – 1 = (2*2*2) – 1
= 7
23n – 1 = 7m
n(k+1)
23(k+1) – 1 = 2.23k-1
= 2 * (7m+1)... | 4 | [
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User:Pranav Rathi/Notebook/OT/2010/12/10/Olympus Water Immersion Specs
From OpenWetWare
Water immersion objective details
We are using Olympus UPLANSAPO (UIS 2) water immersion IR objective for Optical tweezers ( DNA-overstretching stretching and unzipping experiments). The detail specifications of the objective can... | 4 | [
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Transposing of formulae
October 26th 2009, 10:09 AM
mikewhant
Transposing of formulae
Hi there, thanks in advance for any help
Make A the subject of the formula:
Q = C.A square root (2g.h / (1-A^2/x^2))
I have got this far but unsure what to do with the fraction of a fraction... the (x^2) bit.
... | 4 | [
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Vector Calculus: Flux and divergence theorem
May 19th 2010, 01:20 PM #1
Newbie
Joined
Apr 2010
Posts
2
1. Consider a cube with vertices at A=(0,0,0) B=(2,0,0) C=(2,2,0) D=(0,2,0) E=(0,0,2) F=(2,0,2) G=(2,2,2) H=(0,2,2)
A)Calculate the flux of the vector fieldF=xi through each face of the cube by takin... | 4 | [
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27. atensor
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
27. atensor
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]
27.1 Introduction to atensor
atensor is an algebraic tensor manipulation package. To use atensor, type load(atensor), followed by a call to the init_at... | 4 | [
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... | 8,294 | 8294 | |
Induction on a sequence
June 2nd 2011, 08:25 AM #1
MHF Contributor
Joined
Mar 2010
From
Florida
Posts
3,093
Thanks
5
Induction on a sequence
$a_1=0, \ a_2=3, \ \ \forall n\geq 3 \ \ \ a_n=\frac{1}{2}(a_{n-1}+a_{n-2})$
Show $\forall n\geq 2 \ \ \ a_n=2+4\left(-\frac{1}{2}\right)^n$
and d... | 5 | [
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Geometry - word problem
January 13th 2006, 08:40 AM
The Preacher
Geometry - word problem
Hey, thanks for taking a look at this.
A parallelogram with sides of 6 and 10 has an area of 30(sqrt)2. Find the measure of each angle of the parallelogram.
Small angle _____
Large angle _____
I apologize... | 4 | [
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Operation @
March 17th 2010, 07:26 PM
MATNTRNG
Operation @
If operation @ is defned as: (1) 2 @ 2 = 1; (2) (2n+2) @ 2 = (2n @ 2) + (n²)/2, what is 2010 @ 2?
March 18th 2010, 08:43 AM
hollywood
If you look at the series 2 @ 2, 4 @ 2, 6 @ 2, ...
2 @ 2 = 1 = (1/2) * 2
4 @ 2 = 2 @ 2 + 1/2 = 3/2 = (1/... | 4 | [
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Distance between Lines
Date: 03/04/97 at 23:22:55
From: Brandon Gee
Subject: Geometrical applications with vectors
Dear Dr. Math,
I am in analysis and am struggling. I need help with just problem 6b.
I wrote the other questions because 6b refers to some of them, and I
was not sure which ones, so I wrote them all.
... | 5 | [
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General Approach for Sum of Arithmetic Series
Date: 08/24/2006 at 17:46:55
From: robert
Subject: algebra/geometry
What is the formula for figuring out the sum of adding consecutive
even numbers? 2 + 4 = 6, 2 + 4 + 6 = 12, 2 + 4 + 6 + 8 = 20, etc.
Date: 08/25/2006 at 14:54:39
From: Doctor Greenie
Subject: Re: alge... | 4 | [
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