content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Matrix Eigenvectors
May 16th 2007, 09:23 AM #1
Newbie
Joined
May 2007
Posts
4
Matrix Eigenvectors
Hi just wondering if anybody could help me with a problem i've can't see to solve!
I can work out the Eigenvalues fine
Matrix A = [ 2 -1
-1 1 ]
Ax = Lx L = lamda
| [A-LI] | = 0
(... | 5 | [
0.025390625,
-0.04638671875,
-0.00457763671875,
-0.068359375,
0.0169677734375,
0.014404296875,
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-0.03515625,
-0.06640625,
0.0262451171875,
0.08349609375,
-0.1064453125,
0.007110595703125,
-0.036865234375,
-0.02880859375,
0.0169677734375,
-0.059814453125,
-0.0830078... | 37,300 | 37300 | |
Mapping multivariate polynomial inequalities system to subspace
up vote 1 down vote favorite
What I will ask, more than a solution, is better mathematical definition of my problem and directions to find the solution.
I have a set of linear equations, e.g.:
d_1 &= L_1 - 9\,m_1 - 9\,m_2 \\ d_2 &= x_1 + 3\,m_1 + 3\,m_2... | 4 | [
0.01470947265625,
-0.08154296875,
0.00176239013671875,
-0.1298828125,
0.030029296875,
0.0419921875,
-0.059326171875,
0.0225830078125,
-0.125,
0.0186767578125,
0.0400390625,
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0.05712890625,
-0.0361328125,
-0.046630859375,
0.11279296875,
-0.0027313232421875,
0.0144653... | 37,301 | 37301 | |
division of line segment
A line passes through A(1,1) , B(4,3). Find the coordinates of the point on the line which is (1) three times as far from A as from B, (2) three times as far from B as from A.
Treat the coordinates, x from 1 to 4 and y from 1 to 3, separately. "Three times as far from A as from B". Think of th... | 4 | [
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0.0238037109375,
0.045166015625,
-0.0303955078125,
0.05029296875,
-0.07373046875,
-0.0031... | 37,302 | 37302 | |
Coprimes in Fermat's Last Theorem
Date: 06/03/99 at 07:07:38
From: oliver
Subject: Coprime in Fermat's Theorem n = 2
Hi!
I was wondering, in Fermat's Conjecture of n = 2
x^2 + y^2 = z^2
which can be rearranged to:
(y/2)^2 = (z-x)/2 * (z+x)/2
(z-x)/2 and (z+x)/2 are coprime? I have done s... | 4 | [
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0.0037841796875,
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Finding zeros of a polynomial
June 25th 2012, 03:06 PM
daigo
Finding zeros of a polynomial
12x^4 - 9x^3 - 58x^2 + 4x + 36
Is the only way to find the zeros of any given polynomial to guess and check or is there a more mechanical method like the quadratic formula that works on every single polynomial?
P... | 5 | [
-0.0004138946533203125,
0.059326171875,
-0.044677734375,
0.004302978515625,
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0.01336669921875,
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0.01092529296875,
0.0771484375,
-0.0023193359375,
0.019775390625,
-0.... | 37,304 | 37304 | |
Minimizing the Length of a Crease
Date: 11/11/1999 at 13:54:30
From: Jessica J. Johnston
Subject: Minimize the value of L
This is the exact problem in the book:
A rectangular sheet of 8.5 x 11-in. paper is placed on a flat surface,
and one of the corners is lifted up and placed on the opposite longer
edge. With all... | 4 | [
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0.07275390625,
-0.03271484375,
-0.0020751953125,
-0... | 37,305 | 37305 | |
3D Trig. Probs
February 15th 2008, 09:31 PM #1
Newbie
Joined
Feb 2007
From
Australia
Posts
20
3D Trig. Probs
g&t homework, pleasse help draw the diagrams first
thanks.
1. the pilot of an aircraft flying due South, at an altitude of 750m, sees an airfield directly ahead, angle of depression 1... | 4 | [
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0.023193359375,
... | 37,306 | 37306 | |
Conversion
Decimal to Floating-Point Conversions
The Conversion Procedure
The rules for converting a decimal number into floating point are as follows:
1. Convert the absolute value of the number to binary, perhaps with a fractional part after the binary point. This can be done by converting the integral and f... | 5 | [
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0.10595703125,
... | 37,307 | 37307 | |
Finding Equation for a Function given table of value
January 7th 2013, 03:22 PM #1
Newbie
Joined
Jan 2013
From
New York City
Posts
2
Finding Equation for a Function given table of value
I am given a table of values
x | y
------
-3|91
-2| 21
-1|3
0 |1
1 |3
2 |21
3 ... | 4 | [
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-0.07373046... | 37,308 | 37308 | |
[SOLVED] Find a volume
June 12th 2009, 02:05 PM
arbolis
[SOLVED] Find a volume
Find the volume inside the sphere $x^2+y^2+z^2=4a^2$ and outside the cylinder $x^2+y^2=2ax$.
My attempt : I visualized the volume I must calculate. I can first calculate the volume of the sphere ( $\frac{32\pi a^3}{3}$ ) and then ... | 5 | [
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0.007049560546875,
0.... | 37,309 | 37309 | |
Optimizing time
April 4th 2011, 11:25 AM #1
Junior Member
Joined
Apr 2011
Posts
56
Optimizing time
I learned optimization (distance) but I missed the lesson on optimizing time so I'm having some trouble on this question:
A sailor in a boat 8 km offshore wants to reach a point on shore that is 10 km ... | 5 | [
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0.02685546875,
0.02612... | 37,310 | 37310 | |
Column rank, linear independence and RRE form
April 10th 2010, 10:51 PM #1
Member
Joined
Mar 2009
From
Gold Coast, Queensland, Australia
Posts
105
Column rank, linear independence and RRE form
if I have a matrix A like this:
A = $\left[\begin{matrix}1 & 1 & 0 & 0 & 1 & 0 & 0\\1 & 1 & 0 & 0 & 0 &... | 4 | [
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-0.103515625,
-0.1005859375,... | 37,311 | 37311 | |
Factorising
December 21st 2007, 07:11 AM #1
Newbie
Joined
Dec 2007
From
U.K
Posts
21
hi, just wondering if anyone can give me any help with this maths equation:
X2-6x+9=0
6x2+x-15=0
i have tried to wrk this equation out but un-sure
thanks jenko!
For the first one:
$(x+a)(x+... | 4 | [
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0.0... | 37,312 | 37312 | |
Solution behind a card trick?
March 23rd 2008, 07:19 PM
jacquir
Solution behind a card trick?
I just saw a new card trick tonight and I'm sure there's a mathematical solution to it....just wondering if anyone out there has seen it before. The trick goes like this:
1. Start with a 52-deck of cards
2. Fl... | 4 | [
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0.0756835... | 37,313 | 37313 | |
Mathematical Induction Proof: P(n): (1^3)+(2^3)+...+(n^3)=(1+2+...+n)^2 for all n
January 29th 2013, 04:11 PM #1
Member
Joined
Oct 2010
Posts
150
Mathematical Induction Proof: P(n): (1^3)+(2^3)+...+(n^3)=(1+2+...+n)^2 for all n
Prove: P(n): (1^3)+(2^3)+...+(n^3)=(1+2+...+n)^2 for all natural numbers n
... | 4 | [
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0.08056640... | 37,314 | 37314 | |
YouTube lesson about precalculus wrong?
May 8th 2009, 02:29 PM
Phire
YouTube lesson about precalculus wrong?
YouTube - Precalculus: The Essentials that Students Seem to Forget
It starts at 5:29. Basically, what he is saying is that:
$x^{\frac{1}{3}} + x^{\frac{1}{2}} - 7 = 0$
He's says that you ca... | 4 | [
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0.0693359375,... | 37,315 | 37315 | |
Calc Word problem
February 12th 2011, 06:11 PM
agent2421
Calc Word problem
Can someone please help me out.
Suppose a car is moving along straight road and distanct traveled t hours after starting from rest is given by f (t) = 2t^2+60t. Find the avg velocity of the car over the time intervals (0,2) and
(... | 4 | [
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-0.04199218... | 37,316 | 37316 | |
first order non-linear differential equation
February 2nd 2011, 02:12 PM
Empty
first order non-linear differential equation
I am trying to solve this differential equation and I can't get started and was wondering if I could get some help with a kick start:
$(\frac{dy}{dx})^2 +(\frac{dy}{dx})*x-\frac{dy}{dx... | 5 | [
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0.06640625,
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-0.06640625,
0.0400390... | 37,317 | 37317 | |
finding the equation that relates to set of two numbers
October 7th 2009, 09:18 PM #1
Newbie
Joined
Oct 2009
Posts
1
finding the equation that relates to set of two numbers
can someone help me find the equation that relates to these sets of paired numbers and plz explain the method used
0 - 2
1 ... | 4 | [
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0.1298828125,
-0.037841796875,
-0... | 37,318 | 37318 | |
Topology question
March 1st 2010, 01:23 PM #1
Super Member
Joined
Aug 2009
From
Israel
Posts
976
Topology question
Hi, I would appreciate some guiding with this question. Thanks.
Let X be some topological space and Y a compact, Hausdorff topological space. Let $f:X \to Y$ and define $\Gamma_f =... | 5 | [
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-0.0283203125,
... | 37,319 | 37319 | |
slight extension to classification of finitely generated abelian groups
up vote 3 down vote favorite
1
Is there a classification theorem for "finitely generated abelian groups with a distinguished element"? If it helps, you can restrict this to the cases where the order of each element divides the
order of the disting... | 4 | [
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-0.0285644531... | 37,320 | 37320 | |
Math Help
Prove that a congruent b(modn) if and only if a^2 + b^2 congruent 2ab(mod n^2) Help please
$a \equiv b(mod n) \Leftrightarrow a^2 + b^2 \equiv 2ab (mod n)$ let's take first $\Rightarrow$ we have $a \equiv b (mod n)$ want the right side $a \equiv b (mod n )$ this mean $n \mid a-b$ and this
mean there exist a... | 4 | [
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0.006805419921875,
-0.017822265625,
0.052001953125,
-0.0296630... | 37,321 | 37321 | |
The integral....
Do the inside integral, aka the y integral, first: Int[(4x + 2)dy, x^2, 2x] = [(4x + 2)y, x^2, 2x] <-- x is a constant for the y integral = (4x + 2)*2x - (4x + 2)*x^2 = 8x^2 + 4x - 4x^3 - 2x^2 = -4x^
3 + 6x^2 + 4x Now do the outside integral, aka the x integral: Int[(-4x^3 + 6x^2 + 4x)dx, 0, 2] = [-4*(... | 5 | [
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-0.04248046875,
-0.000873565673828125,
-0.021240234375... | 37,322 | 37322 | |
Collinearity
Questions: What is collinearity? Why is it a problem? How do I know if I've got it? What can I do about it?
Materials... | 4 | [
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-0.014404296875,
-0.004638671875,
-0.0... | 37,323 | 37323 | |
The Ambiguous Case
Date: 04/01/2003 at 13:38:38
From: Les
Subject: The Ambiguous Case
I do not understand how to use the ambiguous case to determine the
number of triangles that can be constructed. Is there a simple way to
answer the following question:
How many triangles can be constructed if, for example, a=4, A=3... | 4 | [
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-... | 37,324 | 37324 | |
Simplify using the exponent laws #2
September 6th 2012, 10:52 AM #1
Junior Member
Joined
Aug 2012
From
Winnipeg
Posts
57
Simplify using the exponent laws #2
Hi guys,
the task: Simplify using the exponent laws. Write the final answer using only positive exponents. Evaluate where possible.
1.... | 4 | [
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0.154296875,
-0.015991210937... | 37,325 | 37325 | |
exponential word problem
Can someone please help me with part b and c.
to a) Plug in D = 10 and t = 5. Use a calculator. I've got $x \approx 5.353\ \rm{mg}$ to b) Now D = 10 + 5.353 and t = 1. Use a calculator. I've got $x \approx 13.54897\ \rm{mg}$ to c) Solve the
equation for t: $3 = 15.353\cdot e^{-\frac18 t}~\impl... | 4 | [
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0.0133056640625,
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-0.100585... | 37,326 | 37326 | |
SA and volume of half a sphere?
May 20th 2006, 12:46 AM #1
Newbie
Joined
Apr 2006
Posts
8
SA and volume of half a sphere?
Hello,
I need help with volume and surface areas of half a sphere (hemispheres)
I know that v= 4/3x pi x r cubed
SA= 4x pi x r squared
However, when I do this for hal... | 4 | [
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0.03125,
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0.05224609375,
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0.042236328125,
-0.078125,
0.01287841796875,
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-0.... | 37,327 | 37327 | |
finding a function
So here's my problem: Given $f\prime\prime(x)=-9sin(3x)$ $f\prime(0)=-4$ and $f(0)=-1$ Find $f(\frac{\pi}{2})=$ Any suggestions are greatly appreciated.
$f'(x) = \int f''(x)\ dx = \int -9\sin{(3x)}\ dx = 3\cos{(3x)} + C$ $f'(0) = -4 \implies 3\cos{(3\cdot 0)} + C = -4 \implies 3 + C = -4 \implies C ... | 5 | [
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0.08935546875,
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0.0021209716796875,
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-0.046875,
0.05371093... | 37,328 | 37328 | |
Statistics Lab 4 - Z-Score, Raw Score, Probability Formulas
Hi,
Today you will:
So How'd You Do On The Test?
In high school your teachers graded your tests and placed a grade on the top, or, placed a fraction on the paper to indicate how well you'd performed. That fraction is on your paper. Find the
fraction with a ... | 5 | [
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0.041015625,
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0.078125,
0.017578125,
... | 37,329 | 37329 | |
POW card counting game
August 21st 2013, 11:30 AM
nofeynmanme
POW card counting game
Hello all. Please forgive me if I do not post in accurate mathematical language. My last math was a beginning calculus course in 1979. My first dilemma is whether to post irrelevant background. I
shall do so. Please skip to ... | 5 | [
-0.0228271484375,
0.1328125,
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... | 37,330 | 37330 | |
Asymptotic series for roots of polynomials
up vote 4 down vote favorite
3
Let $f(z) = z + z^2 + z^3$. Then for large $n$, $f(z) = n$ has a real solution near $n^{1/3}$, which we call $r(n)$. This appears to have an asymptotic series in descending powers of $n^{1/3}$, which
begins $$ r(n) = n^{1/3} - {1 \over 3} - {2 \... | 5 | [
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-0.01361083984375,
... | 37,331 | 37331 | |
Which Measure of Average is the Best to Use?
Date: 08/17/2006 at 04:54:22
From: brian
Subject: Finding AVERAGE of internet bandwidth speed
I have collected over 120 observations of broadband internet
connection speeds achieved through my service provider. The values
range from 5 kilobits per sec. to 256 kbps. I nee... | 4 | [
0.032470703125,
0.0255126953125,
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Help with proof, Given 0<n<m, show that there exists some t, n≤t<m, so that m-n divid
July 4th 2011, 09:04 AM
scruz10
Help with proof, Given 0<n<m, show that there exists some t, n≤t<m, so that m-n divid
Given 0<n<m, show that there exists some t, n≤t<m, so that m-n divides t.
Please help! Thanks!
I sta... | 4 | [
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0.057861328125,
0.0179443359375,
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0.07275390625,
-0.050... | 37,333 | 37333 | |
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Topic: Computation of the matrix exponential
Replies: 6 L... | 4 | [
-0.0732421875,
0.0211181640625,
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0.0238037109375,
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0.058837890625,
... | 37,334 | 37334 | |
Help putting system of equations into Reduced Row Echelon Form?
August 31st 2011, 05:38 AM #1
Newbie
Joined
Aug 2011
Posts
3
I am having a lot of trouble solving systems of equations by putting them in RREF.
I don't understand how you know what to do after each step. I keep working the same problem a... | 4 | [
-0.1025390625,
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0.04443359375,
-0.10546875,
0.01806640... | 37,335 | 37335 | |
Fraction Equalities
October 20th 2009, 06:48 PM
nmbala
Fraction Equalities
I am working on a class project on the derivation of the quadratic formula, and i understand the process of completing the square, up until the very last process of simplifying back to the
quadratic forumla...
Can someone explain... | 4 | [
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... | 37,336 | 37336 | |
Natural log and smallest number
1. November 1st 2012, 06:19 PM #1
2. November 1st 2012, 06:30 PM #2
Re: Natural log and smallest number
Hey Eraser147.
Try undoing the transformations. You can apply an inverse cosine to get the possible solutions (and use the fact that cos is periodic).
... | 5 | [
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-0.0439453125,
-0.0... | 37,337 | 37337 | |
Lagrange Multipliers
Date: 01/28/2001 at 04:56:22
From: li
Subject: Lagrange Multipliers
The temperature of a point(x,y,z) on the unit sphere is given by
T(x,y,z)=xy+yz. Using Lagrange multipliers, find the temperature of
the hottest point on the sphere.
Date: 01/28/2001 at 06:03:18
From: Doctor Mitteldorf
Subject... | 5 | [
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... | 37,338 | 37338 | |
Polynomial Rings over Fields
December 31st 2012, 06:54 PM #1
Polynomial Rings over Fields
Let F be a field.
Let f(x) be a polynomial in F[x].
Prove that F[x]/(f(x)) is a field if and only if f(x) is irreducible.
Would appreciate help with this problem.
Peter
Re: Polynomial Rings over Fields
... | 5 | [
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... | 37,339 | 37339 | |
June
Some interesting facts
• There are 2n non-perfect square numbers between the squares of two consecutive natural numbers n and (n+1) e.g. between 2^2 and 3^2 , there are
2 x 2 = 4 , non-perfect square numbers.
• The square number of an odd natural number n , can be expressed as the sum of two consecutive na... | 4 | [
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-0.... | 37,340 | 37340 | |
Gases #1
October 4th 2009, 10:47 AM
jsu03
Gases #1
Can someone please help me with this problem? Thanks a lot!
One mole of nitrogen and one mole of neon are combined in a closed container at STP.
How big is the container?
I did PV=nRT and V= nRT/P so V= ?(0.08206)(273)/1 atm... so I need to find n... | 4 | [
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0.008... | 37,341 | 37341 | |
Finding area between two graphs
March 23rd 2012, 01:23 PM
makeupgirl1107
Finding area between two graphs
Consider the area between the graphs http://math.webwork.rochester.edu:80...9866f8d281.png and http://math.webwork.rochester.edu:80...7b15d68f41.png
I know how to do this problem by doing it as a sum of ... | 4 | [
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-0.0196533203125,
... | 37,342 | 37342 | |
Exact short sequences of vector spaces
up vote 6 down vote favorite
3
If possible, how could one prove that every short exact sequence $0 \to A \xrightarrow f B \xrightarrow g C \to 0$ of vector spaces (here $A$, $B$ and $C$) splits without using any basis of $A$, $B$
or $C$. I was not able to exhibit a morphism $h \c... | 4 | [
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... | 37,343 | 37343 | |
Inverse function on definite integral
October 20th 2010, 08:03 AM
nvwxgn
Inverse function on definite integral
The function $\displaystyle f$ and its inverse $\displaystyle f^{-1}$ are continuous. If $\displaystyle f(0) = 0$, find $\displaystyle\int^5_0 f(x)\ dx + \int^{f(5)}_0 f^{-1}(t)\ dt$
I really have ... | 5 | [
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... | 37,344 | 37344 | |
Trig equation help please!
April 8th 2014, 01:41 AM #1
Newbie
Joined
Apr 2014
From
United Kingdom
Posts
17
Trig equation help please!
I think I'm having a massive blonde moment...
How would I begin?
edit: also this question:
Here's my working so far:
$\frac{1+\frac{sin^2x}{cos... | 4 | [
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0.032958984375,
0.0142... | 37,345 | 37345 | |
Tricky Integral
November 11th 2010, 05:51 AM #1
Member
Joined
May 2008
Posts
106
Tricky Integral
Hi I'm doing a question to find the pressure of a gas made of massless bosons. I've done everything else and now the question has resulted in me needing to evaluate this integral
$\int_{0}^{\infty}\frac{z... | 5 | [
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0.05810546875,
-0.0458984375... | 37,346 | 37346 | |
Connected tanks.
February 13th 2011, 05:33 AM #1
Newbie
Joined
Feb 2011
Posts
2
Connected tanks.
I have had this problem for a week now. I do not even know where to begin.
You have 26 tanks of water.
1 giant tank that holds a maximum of 27million L
25 smaller tanks that hold a maximum of 130... | 5 | [
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... | 37,347 | 37347 | |
A small problem about primes number
June 25th 2009, 07:52 PM #1
Newbie
Joined
Jun 2009
Posts
9
A small problem about primes number
Conjecture.
Does there exist a real number C such that for all i in N:
tan(p_i)+cot(p_(i+1)) > 0 or tan(p_i)+cot(p_(i+1)) < C,
where C = -0.14627836...
If th... | 4 | [
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0.013244... | 37,348 | 37348 | |
Math Help
August 21st 2009, 10:54 AM #1
Newbie
Joined
Aug 2009
From
United Kingdom
Posts
17
Expanding
Hello,
Could somebody please help me expand the following, going into detail please as I'd like to learn how:
1) (a+b)^6
2) (1-x)^8
Regards,
Recall Pascal's Triangle:
... | 4 | [
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How To Solve Geometry Problems?
Top
Geometrical problems in mathematics are basically those which are related to geometrical shapes like Triangles, circles, quadrilaterals etc. To solve these problems we have well – defined theorems
and formulas. Let us see how to solve Geometry problems with the help of examples.
Ex... | 4 | [
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triangle area proof
April 26th 2006, 08:35 PM #1
triangle area proof
In triangle ABC, X is the midpoint of AB and Y is the midpont of AC.
XC is joined. Prove
a) ∆AXY = ∆XYC in area
b) ∆AXC = half ∆ABC in area
c) Find what fraction the area of ∆AXY is of the ∆ABC
thanks
jacs
In ... | 4 | [
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Question about some element in a group commutes with its all conjuagates.
up vote 3 down vote favorite
2
Let G be a group and g and h be elements in G. If g commutes with all conjugates of g and h commutes with all conjugates of h, can one conclude that gh commutes with all conjugates of gh?
Thanks!!
gr.group-theory... | 5 | [
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0.0... | 37,352 | 37352 | |
The conditional properties of 2 exponential functions
Suppose $f_{X|Y}(x|y)=\frac{1}{y}e^{-\frac{x}{y}}$ and $f_Y(y)=e^{-y}$ where $0<x,y<\infty$ Why is it obvious that $E(X|Y)=Y$ and $Var(X|Y)=Y^2$ ??
Last edited by noob mathematician; October 16th 2010 at 09:19 PM.
Hello, The distribution of X|Y is that of an expon... | 5 | [
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e
Bayesian Principal Component Analysis
This example provides an implementation of Bayesian principal components analysis as described, for example, in Chris Bishop's book Pattern Recognition and Machine Learning. The code is provided in
the Examples Browser. Most of you will be familiar with standard Principal Compon... | 4 | [
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0.06982421875,
0.00213623046875,
0.02978515625,
0.0157470703125,
0.018310546875,
0.036865234375,
0.0294189453125,
0.017333984375,
-0.0732421875,
0.0140380859375,
0.041259765625,
0.101... | 37,354 | 37354 | |
Math Images
Permutations
From Math Images
Permutations
The image is a tree of permutations which shows all possible orderings for four colors.
Basic Description
A permutation of any set is an arrangement of the set’s elements where order matters. As you can see from the above tree, the number of distinct arr... | 4 | [
0.09814453125,
-0.024169921875,
0.0211181640625,
-0.0537109375,
-0.0400390625,
0.0228271484375,
0.009521484375,
0.0262451171875,
0.142578125,
0.0634765625,
-0.04052734375,
0.07373046875,
0.130859375,
0.0322265625,
-0.0576171875,
0.07080078125,
-0.083984375,
-0.00579833984375,
-0.... | 37,355 | 37355 | |
quick complex number question
Last edited by yellow4321; March 6th 2008 at 05:13 AM.
There are three possible values of z. $z = 2e^{\frac{{\pi i}}{6}} \,,\,2e^{\frac{{ - \pi i}}{2}} \,\mbox{or} \,2e^{\frac{{5\pi i}}{6}}$
ok thanks i understand how to get 2e^i*(pi/6) but the over two solutions i do not understand how ... | 4 | [
-0.09228515625,
0.0185546875,
0.00787353515625,
0.1279296875,
0.01373291015625,
-0.0264892578125,
-0.006072998046875,
0.058349609375,
0.01263427734375,
-0.047607421875,
-0.005126953125,
-0.060302734375,
0.04833984375,
-0.0233154296875,
0.0067138671875,
-0.00897216796875,
-0.054931640... | 37,356 | 37356 | |
Convexity of Jacobi's theta function with zero argument
up vote 9 down vote favorite
2
This question may be elementary, I have asked it on math.stackexchange.com but have not received any answer yet. Note that I am not an expert on theta/elliptic functions.
Define Jacobi's theta function with argument zero and nome $... | 5 | [
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-0.017822265625,
0.03662109375,
0.00124359130859375,
-0.054443359375,
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0.0224609375,
0.09619140625,
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0.02392578125,
-0.1025390625,
0.02783203125,
-0.01092529296875,
-0.1... | 37,357 | 37357 | |
Degrees of Generality
Date: 03/13/99 at 00:17:30
From: Pete
Subject: Different types of Integrals
In my calculus class, I learned the Riemann integral. However, in my
side readings, I came across terms like Riemann-Stieltjes integral and
even Lebesgue integral. They seem to be different; could you explain
why we nee... | 5 | [
0.01171875,
-0.03173828125,
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0.049560546875,
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0.08544921875,
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0.038818359375,
-0.022705078125,
... | 37,358 | 37358 | |
partial differential initial value problem
November 17th 2008, 08:19 AM #1
Junior Member
Joined
Nov 2008
Posts
34
partial differential initial value problem
Hi! I am currently trying to find a formula which solves the problem:
$u_t-\triangle u+cu=f$ on $\mathbb{R}^n$ x $(0,\infty)$ and
$u(x,0)=g(... | 4 | [
-0.1533203125,
0.02685546875,
0.043212890625,
0.011474609375,
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-0.033447265625,
0.05322265625,
-0.064453125,
0.0341796875,
-0.099609375,
... | 37,359 | 37359 | |
Uniqueness of Hensel factors of a polynomial (invariant to change of "basepoint")?
up vote 0 down vote favorite
An important component of algorithms for factoring multivariate polynomials over a commutative ring $R$ is Hensel lifting. Here's a brief, concrete example to set the stage for my question:
Let $f \in F[X,... | 5 | [
-0.06689453125,
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-0.05126953125,
0.03515625,
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0.006683349609375,
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0.052001953125,
-0.0400390625,
-0.045654296875,
0.034423828125,
0.123046875,
-0.0771484375,
0.033935546875,
... | 37,360 | 37360 | |
equation rearrange
May 22nd 2008, 07:25 AM #1
Newbie
Joined
Oct 2007
Posts
7
equation rearrange
please help me
wacc=16% kd is 40%,ke is 60% ,t is 30%
required keu?
formula wacc=keu(keu-kd)(1-t)kd/ke.
answer is 14.1% but i dunt know how to calculate it...
I assume $keu$ is one variab... | 4 | [
0.029296875,
0.06494140625,
0.051025390625,
-0.01806640625,
-0.09375,
-0.0279541015625,
0.00531005859375,
-0.02880859375,
-0.0267333984375,
0.068359375,
0.11181640625,
-0.1630859375,
-0.00860595703125,
0.028564453125,
-0.034423828125,
0.045654296875,
-0.0615234375,
0.00970458984375... | 37,361 | 37361 | |
Heron's Formula, Cartesian Coordinate Plane
Date: 11/01/2001 at 07:36:16
From: Jacob Kohl
Subject: Geometry
If a triangle has sides 5, 6, and the square root of thirteen,
what is the area of the triangle?
Thank you for your help.
Date: 11/01/2001 at 12:18:50
From: Doctor Greenie
Subject: Re: Geometry
Hi, Jacob -... | 4 | [
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0.04345703125,
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0.0703125,
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0.0181884765625,
-0.06298828125,
-0.0115356... | 37,362 | 37362 | |
Is arbitrary union of closed balls in R^{N} Lebesgue measurable?
up vote 13 down vote favorite
5
Is an arbitrary union of non-trivial closed balls in the Euclidean space $\mathbb R^{N}$ Lebesgue measurable? If so, is it a Borel set?
@George
I still have two questions concerning your sketch of proof.
First, how can ... | 5 | [
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-0.01324462890625,
-0.0712890625,
0.04443359375,
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0.03125,
-0.000240325927734375,
-0.0289306640625,
0.0615234375,
-0.07958984375,... | 37,363 | 37363 | |
Find fog and its domain and range?
June 25th 2009, 01:15 PM #1
Find fog and its domain and range?
Find $f(g(x))$ if $f(x) = [x] + \{x\}^2$ and $g(x) = [x] + \sqrt{\{x\}}$ and also find the domain and range of f(x).
Answer:
I am not getting a matching answer. Anyone?
NOTE: [x] is floor function/grea... | 4 | [
-0.0223388671875,
0.00701904296875,
0.033203125,
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0.0198974609375,
0.0135498046875,
... | 37,364 | 37364 | |
compound interest
September 24th 2006, 12:19 PM #1
Junior Member
Joined
Sep 2006
Posts
38
compound interest
if $500 was invested at 8%/a, compounded annually, in one account, and $600 was invested at 6%/a, compounded annually, in another account, then when would the amounts in both accounts be equal?
... | 4 | [
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-0.037109375,
-0.0167236328125,
-0.02783203125,
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0.064453125,
0.045654296875,
0.0625,
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0.03076171875,
... | 37,365 | 37365 | |
Properties of the Phi Function
Date: 01/19/99 at 14:06:27
From: Hugo Joyce
Subject: The 'PHI' function.
Dear Dr. Math,
Could you inform me of any possible links between Phi of a number and
the number? For example I know that Phi of any prime number p can be
found by subtracting 1 from the number:
Phi(p) = p - 1... | 4 | [
-0.039306640625,
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0.037353515625,
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0.06787109375,
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0.0966796875,
-0.0137939453125,
0.015869140625,
-0.0289306640625,
-0.0693359375,
-0.078613281... | 37,366 | 37366 | |
Julian Day Number to Julian and Gregorian Date
3.2 Julian Day Number to Julian and Gregorian Date - Algorithm Forms
3.2.1 Julian Day number to Gregorian Date
The previous algorithm development section justifies the following general algorithm forms for converting a Julian Day Number into a Gregorian Date. In this d... | 4 | [
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0.0303955078125,
0.0291748046875,
-0.11474609375,
-0.083984375,
-0.0034790039062... | 37,367 | 37367 | |
Math Help
March 12th 2010, 03:04 PM #1
Member
Joined
Sep 2009
Posts
78
related rates
two cars approach an intersection at a certain time, each car is 5km from it. One car travels west at 90km/h and the other south at 80km/h. How fast is the distance between the two cars
decreasing after 2min?
I... | 5 | [
0.034423828125,
0.026611328125,
0.052001953125,
-0.00946044921875,
-0.034423828125,
0.02294921875,
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0.052978515625,
-0.03173828125,
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0.11474609375,
0.040771484375,
0.03857421875,
0.04736328125,
-0.037353515625,
0.05126953125,
0.00726318359375,
-0.07910... | 37,368 | 37368 | |
The classifying space of a gauge group
up vote 7 down vote favorite
2
Let $G$ be a Lie group and $P \to M$ a principal $G$-bundle over a closed Riemann surface. The gauge group $\mathcal{G}$ is defined by
$$\mathcal{G}=\lbrace f : P \to G \mid f(p \cdot g) = g^{-1}f(p)g\ (\forall g \in G, p \in P) \rbrace.$$
I want ... | 4 | [
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0.0244140625,
0.050048828125,
-0.02734375,
-0.00738525390625... | 37,369 | 37369 | |
Ring theory - radicals.
December 11th 2008, 02:30 PM #1
Member
Joined
May 2008
Posts
86
Ring theory - radicals.
Hello, thank you very much for reading.
I have two homework assignments which I struggle with for quite some time.
1) Let R be a commutative, unitary (R has a unit) Ring, and let I be ... | 4 | [
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-0.015869140625,
0.0064697265625,
0.00946044921875,
0.02880859375... | 37,370 | 37370 | |
Polygon with 13 Sides
The two-dimensional shapes with number of sides at least three are called as polygons. The polygons with 13 sides are called as Tridecagon or other wise called as triskaidecagon. The regular decagon
has 12 equal sides and angles. The Tridecagon cannot be constructed with compass and ruler. In thi... | 4 | [
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0.025146484375,
0.044921875,
-0.11669921875,
-0.0164794921875,
0.011... | 37,371 | 37371 | |
interesting circle problem
April 22nd 2013, 03:04 PM
aaronrpoole
interesting circle problem
I found this the other day online, and its fairly interesting:
a circle is inscribed in a 36 degree sector of a circle with an area of 25(pi) cm squared. What is the circumfrance and area of the smaller circle?
... | 4 | [
0.0302734375,
0.06689453125,
0.009765625,
0.045654296875,
0.00408935546875,
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0.060546875,
0.0693359375,
0.0106201171875,
-0.01513671875,
-0.01550292... | 37,372 | 37372 | |
Has the Lie group preserving a probability distribution been used in Bayesian statistics?
up vote 3 down vote favorite
1
For a (possibly signed) nondegenerate probability measure $\pi$ on $\{1,\dots,n\}$ define $$\langle \pi \rangle := \{R \in \operatorname{STO}(n): \pi R = \pi \}.$$ Here $\operatorname{STO}(n)$
denot... | 4 | [
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0.0228271484375,
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0.03125,
-0.04150390625,
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0.1103515625,
-0.028... | 37,373 | 37373 | |
More fun with Pascal's triangle (Challenge #9)
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
It’s chock-full of amazing patterns (big surprise). I think I’ll spend a post or two (or three?) looking at a few of them.
First up: as noted by Steve Gilberg, ... | 4 | [
-0.0888671875,
0.0142822265625,
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0.0498046875,
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-0.0322265625,
0.0164794921875,
-0.0603027343... | 37,374 | 37374 | |
Linear Transformation & Invariant subpsce Question
October 26th 2008, 11:09 AM #1
Member
Joined
Jan 2008
Posts
78
Linear Transformation & Invariant subpsce Question
The matrix A given below represents a linear transformation L : R2 --> R2 in
the standard basis. Argue that this linear transformation o... | 5 | [
-0.08056640625,
-0.037109375,
-0.01092529296875,
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0.06884765625,
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0.02099609375,
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0.029052734375,
-0.004180908203125,
-0.030029296875,
0.0054931640625,
-0.040771484375,
-0.... | 37,375 | 37375 | |
Trig Identities
1. December 3rd 2009, 03:17 AM #1
2. December 3rd 2009, 04:12 AM #2
By letting $x=cos\theta$, differentiating to get $\frac{dx}{d\theta}=-sin\theta$, which becomes $dx=-sin\theta{d\theta}$
Substituting into the integral, you get
$\frac{-sin\theta{d\theta}}{(1+cos^2\theta)... | 5 | [
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0.047119140625,
0.046630859375,
-0.050... | 37,376 | 37376 | |
3 points of a triangle, 21 bits to find
March 16th 2009, 04:12 PM
Knoll318
3 points of a triangle, 21 bits to find
Okay, the title may not have made it very clear, but I have 3 vertexes of a triangle.
$A= (3,2)$
$B= (1,-2)$
$C= (-2,1)$
I need to find a bunch of stuff, all in Standard Form (Ax+B... | 4 | [
-0.06884765625,
0.024169921875,
0.0184326171875,
-0.046875,
0.0274658203125,
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0.0286865234375,
-0.05615234375,
-0.0... | 37,377 | 37377 | |
Finding cos and sin from tan?
April 5th 2010, 06:49 PM #1
Member
Joined
Mar 2010
Posts
133
Give the expression for one of the three functions sin θ, cos θ, or tan θ, with θ in the first quadrant. Find expressions for the other two functions. Your answer will be algebraic expressions in
terms of x.
... | 4 | [
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-0.02783203125,
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0.0322265625,
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0.02294921875,
-0.07958984375,
0.0284423828125,
... | 37,378 | 37378 | |
Inverse Functions
March 11th 2007, 09:00 PM #1
Junior Member
Joined
Mar 2007
Posts
56
Inverse Functions
So, I need to find (F^-1)'(a) of
f(x) = 3 x^2 + tan(πx/2) , -1< x < 1, a=3
I have worked the problem to this point
(f^-1)'(3) = 1/2x + sec^2(πx/2)π/2
= 1/2(0) + sec^2(π(0)/2)π/2
... | 5 | [
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0.046142578125,
-0.027587890625,
-0.018310546875,
-0.03759765625,
0.01708984375,
-0.07568359375,... | 37,379 | 37379 | |
Linear factors with complex numbers.
April 29th 2013, 01:14 PM
FatimaA
Linear factors with complex numbers.
I went through my completed pretest with a classmate and came across this problem:
Factor x^4-4x^2-45 into linear factors allowing complex numbers. If you use your graphing calculator, be sure to expl... | 4 | [
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-0.007476806640625,
-0.0230712890625,
-0.0634765625,
... | 37,380 | 37380 | |
Norm convergence of multiple ergodic averages for commuting transformations
I’ve just uploaded to the ArXiV my paper “Norm convergence of multiple ergodic averages for commuting transformations“, submitted to
Ergodic Theory and Dynamical Systems. This paper settles in full generality the norm convergence problem for s... | 4 | [
0.048828125,
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-0.01202392578125,
-0.033203125,
-0.0118408203125,
0.0120849609375,
0.03... | 37,381 | 37381 | |
Directional derivative
February 4th 2011, 04:07 PM #1
Junior Member
Joined
Feb 2011
Posts
30
Directional derivative
Find $a,b,c$ constants so that the directional derivative of $f(x,y,z)=axy^2+byz+cz^2x^3$ on $(1,2,-1)$ has a maximum value of $64$ on a parallel direction to the $z$ axis.
I think we ... | 5 | [
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... | 37,382 | 37382 | |
FX Derivatives
SWAPS
Types and Valuation
INTEREST RATE AND
CURRENCY SWAPS
Definition
A swap is a contract between two parties to deliver one sum of money
against another sum of money at periodic intervals.
• Obviously, the sums exchanged should be ... | 5 | [
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On reducible polynomials with positive coefficients, $1$ as constant coefficient and certain bounds on coefficients
up vote 0 down vote favorite
Given $a \in \mathbb{Z}$ with $a > 1$. Let $g(x) \in \mathbb{Z}[x]$ be a polynomial with $g(a)=\pm 1$. Let $h(x) \in \mathbb{Z}[x]$ be a polynomial with $h(a)= p$, a prime. L... | 5 | [
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Sunday FunctionSunday Function
There’s an interesting book I’m working on called The Fall of Rome: And the End of Civilization
You can make a similar argument in a positive direction about the history of mathematics. Math has existed more or less forever, but I’d say there’s a definite new era that started at roughly ... | 4 | [
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Arithmetic Sequences - T5 = 3T2 and S6= 36, find the first three terms.
October 26th 2008, 05:37 AM #1
Newbie
Joined
Oct 2008
Posts
1
Arithmetic Sequences - T5 = 3T2 and S6= 36, find the first three terms.
Yo, some questions.
As in how do u do these. Thanks.
T5 = 3T2 and S6= 36, find the first ... | 4 | [
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Calculus/parametric problem. I can't figure this out : (
January 19th 2009, 09:32 PM #1
Newbie
Joined
Jan 2009
Posts
2
Calculus/parametric problem. I can't figure this out : (
Hey all, here's the problem I've been struggling with:
Cameron is located 2 miles due East of an intersection between two co... | 5 | [
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Beyond the Ariel - Page 714 - diyAudio
Here you go Elias, enjoy.
The Tale of the Transfer Function
Let’s revisit the “sinusoidal steady state” course notes and stick with the same notation: lower case for time domain signals, upper case for frequency domain; a system of impulse response h(t),
transfer function (Frequ... | 4 | [
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Proof/derivation of the trapezium rule error estimate
November 16th 2012, 07:17 AM #1
Newbie
Joined
Nov 2012
From
United Kingdom
Posts
4
Proof/derivation of the trapezium rule error estimate
Hi, I'm trying to derive the error estimate in the trapezium rule but can't find any derivations on the intern... | 4 | [
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Integral of Rational Function
September 29th 2010, 08:17 AM
centenial
Integral of Rational Function
I got this question on an exam this morning and I didn't know how to answer it. I've been working on it the past hour trying to figure it out. Usually with rational functions, I factor to get it
in a from that... | 5 | [
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Fourier transform and spectrum of PDOs in $L^p$
up vote 2 down vote favorite
1
Let $K$ be a compact subset in $\mathbb{R}^n$ with $m(K)=0$, Suppose $supp\hat{u}\subset K$ for some $u\in L^p$,where $2\leq p\leq \frac{2n}{n-1}$,can we get $u\equiv 0$ ?
Motivation: If $K$ is a compact non-degenerate hypersurface,then it... | 4 | [
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Program to Convert Number Bases
Date: 07/12/99 at 11:02:43
From: Mike Manson
Subject: Easier way to convert base systems of numbers
Hi,
I've learned that you can convert the base system of a number using
the following method:
12461 base 10 --> base 4
4|12461
3115 r 1
778 r 3
194 r 2... | 4 | [
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Proof Adj characteristic
Hi, How can I proof that adj(AB)=adj(B)*adj(A)? I tried to use with the characteristic of A*adj(A)=|A|*I Thanks.
If A,B are invertible matrices the proof is very easy and short, but in the general case it is, imo, a very involved, long proof which uses, if I remember correctly, exterior produc... | 5 | [
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help with work
May 2nd 2007, 03:17 PM
^_^Engineer_Adam^_^
help with work: Integral applications
A hemispherical tank, placed so that the top is a circular region of radius 6ft, is filled with water to a depth of 4 ft. Find the work done in pumping the water to the top of the tank.
Ans. 50,185 lb-ft
October... | 5 | [
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Math Help
March 15th 2011, 07:10 PM #1
ordered bases
Let $S={\vec v_1, \vec v_2}$ and $T={\vec w_1, \vec w_2}$ be bases for $P_1$ where $\vec w_1 = t-1$ and $\vec w_2 = t+1$. If the transition matrix from T to S is $\left[ {\begin{array}{cc}<br />
1 & 2 \\<br /> 2 & 3 \\<br /> \end{array} } \right]<br />$ de... | 4 | [
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... | 37,395 | 37395 | |
1980
1980 Applied Maths Higher Level Questions
1.
A boat has to travel by the shortest route to the point 4.25 j km and then return immediately to its starting
point at the origin.
... | 4 | [
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Please help with Composite Rule
Part2.doc Can someone please help as I have tried this and have gone without sleep for 2 nights. Thank you.
The composite rule is also known as the chain rule. Put simply, the derivative of the inside times the derivative of the outside. $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$ W... | 5 | [
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Functionn of two random variables.
Could anyone help me with this question please?
Given X and Y are continuous random variables with the following joint probability density function:
$<br /> <br /> f(x,y) =<br /> \begin{cases}<br /> {\theta}^2 e^{-{\theta} y} & 0 < x < y \\<br /> 0 & \text{otherwise}<br ... | 4 | [
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Radians. how to solve problem.
September 29th 2009, 07:45 PM #1
Junior Member
Joined
Sep 2009
Posts
27
Radians. how to solve problem.
1) Give the exact value of the following: 4cos(π/4)
2) Evaluate the following expression when x is π/4. Use the exact value:
5cos(2x)
3) For the following e... | 4 | [
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