content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
differential equations
March 2nd 2008, 09:41 AM #1
Newbie
Joined
Mar 2008
Posts
15
differential equations
Can anyone help with this?
x''+9x'+20x=29+20t+6e^(-2t)
i) Obtain the solution x(t) as the sum of the solutions obtained when each component is considered individually in turn.
ii) Solve... | 5 | [
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Section 17.5 Lecture Notes
EQUATIONS OF MOTION: GENERAL PLANE MOTION
(Section 17.5)
Today’s Objectives:
Students will be able to analyze
the planar kinetics of a rigid
In-Class Activities:
body undergoing general plan... | 5 | [
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0.01171875,
... | 36,501 | 36501 | |
Feynman Kac Formula as appears in Krzysztof Gawedzki's Lectures on conformal field theory
up vote 5 down vote favorite
3
The lecture notes appeared in the second volume of "Quantum Fields and Strings, a course for mathematicians". I would like to understand the derivation of (1.3), the 2-point correlation function:
$... | 4 | [
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Proofs of the Theorems on Circumscribable Quadrilaterals
August 17th 2010, 08:42 PM
Vlasev
Observe the following illustration. We have the quadrilateral ABCD. The quadrilateral's incircle's center is pt. O. Then there are the two incircles of the triangles formed by the diagonal. P,Q,R
and S are the points wh... | 4 | [
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Simple proving the inequalities
September 8th 2010, 04:48 PM #1
Member
Joined
Jan 2010
Posts
88
Simple proving the inequalities
|x| ≤ 1 ⇒ |x^2 − x − 2| ≤ 3|x + 1|
im guessing you factor it and cancel out the x+1 then im left with this
|x-2| ≤ 3
What do i do from there?
$|x - 2| = |x + (-... | 4 | [
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How to compute $\mathcal{Ext}^{i}_{X}(\mathcal{O}_{Y_{1}},\mathcal{O}_{Y_{2}})$?
up vote 2 down vote favorite
1
Given a smooth variety $X$ and two smooth subvarieties $Y_{1},Y_{2} \subset X$ with smooth intersection $Z=Y_{1} \cap Y_{2}$, I'd like to compute $\mathcal{Ext}^{i}_{X}(\mathcal{O}_{Y_{1}},\mathcal
{O}_{Y_{2... | 4 | [
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Continuous function problem
November 13th 2006, 01:59 PM #1
Super Member
Joined
Mar 2006
Posts
705
Thanks
2
Continuous function problem
Q: Suppose that f: [0,2] -> [0,4] is continuous. Show that there is an x $\epsilon$[0,2] such that $f(x) = 2x$.
Proof: All I know is use the intermediate value ... | 5 | [
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Identifying $T^* Bun_G$ with Higgs bundles
up vote 1 down vote favorite
1
Let $G$ be a semisimple algebraic group, $C$ be a smooth projective curve, and $\omega$ be canonical line bundle.
The stack $Higgs_{\omega}$ is defined as the stack associating to each $S$ the groupoid consisting of $(E, \phi)$, where $E$ is a ... | 4 | [
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Expected distance between two points with missing coordinates
up vote 3 down vote favorite
What is the expected distance between two points when one of the points has some unknown (or missing) coordinate values?
The two points are in the same finite dimensional real space. Assume that the probability density function... | 5 | [
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Sum of squares of determinants of principal minors
up vote 5 down vote favorite
3
I am interested in computing the sum of squares of determinants of principal minors. Let $A$ be an $n\times n$ positive semidefinite matrix and $A_S$ be a principal minor of $A$ indexed by the set $S
\subseteq \{1,\ldots,n\}$. The classi... | 4 | [
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... | 36,509 | 36509 | |
[SOLVED] finding surface area using parametric equations
March 20th 2010, 06:50 PM #1
Newbie
Joined
Oct 2009
Posts
10
[SOLVED] finding surface area using parametric equations
The question reads
Find the surface area generated by rotating x=e^t -t & y=4e^t for 0 to 1 (this is in terms of t) about the ... | 4 | [
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A. Intervals
>> << Ndx Usr Pri JfC LJ Phr Dic Rel Voc !: wd Help Phrases
4A. Intervals
It is a common need in programming to have to test whether a given number x lies between two other numbers a and b, with a less than b, called the lower boundary and upper boundary. The numbers that
lie between the boundaries are c... | 4 | [
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binomial thm
October 8th 2008, 09:00 AM #1
binomial thm
Write down the first three terms in the expansion, in descending powers of x, of [ax-(b/x^3)]^8. Hence evaluate the term independent of x of [5x-(1/x^3)]^8.
I dunno how to do the Hence part, making use of the terms in the expansion.
In this expansi... | 4 | [
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Prove using set algebra
Prove using set algebra: A U B = (A ∩ B') U (A' ∩ B) U (A ∩ B)
Hello, mathman11! Prove using set algebra: . $A \cup B \;=\; (A \cap B') \cup (A' \cap B) \cup (A \cap B)$ There are two rules for which I do not know the names. I will call them: . $\begin{Bmatrix}S
\cup S' \:=\:U && \text{Property... | 4 | [
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0.0361328125,
-0.0... | 36,513 | 36513 | |
Geometric interpretation of the half-derivative?
up vote 25 down vote favorite
13
For $f(x)=x$, the half-derivative of $f$ is $$\frac{d^{\frac{1}{2}}}{dx^{\frac{1}{2}}} x = 2 \sqrt{\frac{x}{\pi}} \;.$$ Is there some geometric interpretation of (Q1) this specific derivative, and, (
Q2) of the half-derivative more gener... | 5 | [
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Homework Help
Posted by jessica on Saturday, February 16, 2013 at 7:29am.
if log x base a,log y base a and log z base a are three consecutive terms of an AP,show that x,y and z are consecutive terms of a GP
• math - Reiny, Saturday, February 16, 2013 at 8:03am
let A = log[a]x ---> x = a^A
let B = log[a]y -... | 4 | [
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... | 36,515 | 36515 | |
Bearing questions - plz help
May 23rd 2010, 03:50 AM
dee2020
Bearing questions - plz help(SOLVED)
1.A hiker walks due north from A and after 8km reaches B. She then walks a further 8km on a bearing of 120degrees to C. Work out a the distance from A to C and b the bearing of C from A.
2.A helicopter flies on... | 4 | [
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... | 36,516 | 36516 | |
A Proof that the Natural Numbers Form a pca?
up vote 5 down vote favorite
1
It is known that the set of natural numbers with the operation ab = {a}b, where {a} represents the index of a recursive function, forms a partial combinatory algebra (pca). All the references I have
so far consulted mention the set of natural ... | 5 | [
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Proof of Hartshorne Proposition II 6.8
up vote 5 down vote favorite
1
I would like to ask one question (maybe very simple) about the proof of Proposition II 6.8 in Hartshorne's book Algebraic Geometry page 137. The question is about the proof of the finiteness of
non-trivial morphisms between two projective non-singul... | 4 | [
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Sine integral
$\int_{-\infty}^{+\infty}\frac{\sin x}x\,dx = \int_{-\infty}^0 \frac{\sin x}x\,dx + \int_0^{+\infty} \frac{\sin x}x\,dx$ $= \lim_{a \rightarrow -\infty} \int_a^0 \frac{\sin x}x\,dx + \lim_{b \
rightarrow +\infty} \int_0^b \frac{\sin x}x\,dx$ now, integrate by parts.. continue..
I don't think sin(x)/x is ... | 5 | [
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Solve by finding an inverse for 7
February 28th 2010, 07:46 PM #1
Super Member
Joined
Feb 2008
Posts
535
Solve by finding an inverse for 7
Solve 7x = 11 mod 9 by finding an inverse for 7. (= is congruence not equality)
I'm trying to do this by using the euclidean algorithm:
9 = 1(7) + 2
7 =... | 5 | [
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jan93
Noesis
The Journal of the Mega Society
... | 5 | [
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Aqueeze
I dont understand the idea and proof behind Squeeze Theorem
Hmm, now let me recall the lecture I had myself :D Lets say we want to know what the limit $\lim_{x \rightarrow 0}$ approaches for the function $x \ \sin(x)$ Now we know $\sin(x)$ oscillates between
$1$ and $-1$ So we can say: $-1 < \sin(x) < 1$ (We k... | 4 | [
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Formula for n-th iteration of dx/dt=B(x)
up vote 3 down vote favorite
2
Let B(x) be infinitely differentiable with respect to x. Drop the use of parentheses on B to delimit the argument x and use them instead to hold the order of the derivative with respect to x. i.e. $B
(0) = B$ $B(1) = dB/dx$, etc.
Let parentheses ... | 5 | [
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Very difficult A-level problem from 1971 (UK)
October 16th 2011, 09:42 PM #1
Newbie
Joined
Oct 2011
Posts
3
Very difficult A-level problem from 1971 (UK)
Hi.
I'm having real trouble answering a question posted online as appearing in a 1971 A level exam (as part of a discussion of whether exams have ... | 4 | [
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Divergence of a series
March 20th 2011, 04:01 PM
Bruno J.
Divergence of a series
Here's a challenge problem I just made up:
Let $\{a_n\}$ be a sequence of positive real numbers such that $\sum a_n = \infty$. Show that
$\frac{a_1}{a_0}+\frac{a_2}{a_0+a_1}+\frac{a_3}{a_0 +a_1+a_2}+ \dots = \infty$.
Mar... | 5 | [
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Confidence Interval Review
Chapter 7
Inference for Distributions
1
• The previous chapter emphasized the reasoning
of tests and confidence intervals
• Now we emphasize statistical practice
– we no longer assume that population standard... | 5 | [
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how to dolce this?deviative of exponenetial functions
February 19th 2006, 07:22 AM #1
Newbie
Joined
Feb 2006
Posts
2
how to do this?deviative of exponenetial functions
$<br /> \frac{x^2 -1}{ e^2^x(x+1)}<br /> <br />$
the outcome supposs to be like this
$<br /> \frac{2x-3}{e^2^x}<br /> <br />$
... | 5 | [
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0.007568359375,
-0.1357421875,
0.08935546875,
0.00112152099609375,
0.019775390625,
-0.004486083984375,
0.0106811523437... | 36,527 | 36527 | |
differential systems
April 23rd 2009, 11:39 AM #1
Newbie
Joined
Feb 2009
Posts
17
differential systems
when solving a system of differential equations of the form
dy/dt = Ay
The constant vector lambda is found with
|A - lambda * I| = 0
If lambda is a complex number I have the solution ... | 5 | [
-0.1845703125,
-0.006683349609375,
-0.06982421875,
-0.0174560546875,
0.02685546875,
0.020751953125,
0.08203125,
-0.01092529296875,
0.039306640625,
0.006744384765625,
0.1201171875,
-0.0908203125,
-0.00244140625,
0.05078125,
0.08984375,
-0.0230712890625,
-0.08154296875,
-0.0673828125... | 36,528 | 36528 | |
Statistics
Simple regression
Statistics for dummies
Statistics
Gabriel V. Montes-Rojas
Gabriel Montes-Rojas Statistics
Simple regression
Statistics for dummies
y = β0 + β1x + u
Much of applied e... | 4 | [
0.0012664794921875,
-0.068359375,
0.01141357421875,
0.13671875,
0.064453125,
0.0272216796875,
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0.016357421875,
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0.017822265625,
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0.0654296875,
-0.0302734375,
0.007476806640625,
-0.04150390625,
0.0235595703125,
0.0234... | 36,529 | 36529 | |
Classification of long exact sequences
up vote 12 down vote favorite
3
Let $\mathcal C$ be the category of long exact sequences of finitely generated abelian groups almost all of whose entries vanish.
The category $\mathcal C$ is naturally additive as a subcategory of complexes of abelian groups.
Question: Can w... | 4 | [
-0.091796875,
-0.03515625,
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-0.00070953369140625,
0.004852294921875,
0.03662109375,
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-0.0034942626953125,
-0.003753662109375,
0.049560546875,
0.029541015625,
0... | 36,530 | 36530 | |
Posts by
Posts by Zach
Total # Posts: 303
Social Studies
What four influences did Greece had on Roman culture?
College Chemistry
1) The concentration of the aluminum ion in a test solution is 0.10M. Using the Ksp for aluminum hydroxide (3. x 10^-34), calculate the concentration of hydroxide needed to precipitate al... | 4 | [
0.04833984375,
-0.018310546875,
-0.0093994140625,
-0.00738525390625,
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-0.011962890625,
0.060791015625,
-0.03515625,
0.01483154296875,
0.04931640625,
-0.0615234375,
-0.01373291015625,
0.004791259765625,
0.040283203125,
0.037841796875,
-0.04443359375,... | 36,531 | 36531 | |
Dedekind-esque sums
up vote 5 down vote favorite
Given real numbers $a, b$, let $f(x)$ be the integer nearest to $ax+b$, let $S_n$ be $\sum_{k=0}^{n} (n-2k) f(n-k) = n f(n) + (n-2) f(n-1) + (n-4) f(n-2) + ... - (n-2) f(1) - n f(0)$, and let $s_n =
an(n+1)(n+2)/6$ (the value you would get if you replaced each term $f(x... | 4 | [
-0.033935546875,
0.0279541015625,
-0.07373046875,
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0.029052734375,
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0.0091552734375,
-0.008544921875,
-0.048828125,
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0.026123046875,
-0.08154296875,
-0.0517578125,
-0.0966796875,
0.1083984375,
-0.00704956054... | 36,532 | 36532 | |
One last exponent question~ Can someone check the answer, please?
September 27th 2011, 06:44 AM #1
Newbie
Joined
Sep 2011
Posts
7
One last exponent question~ Can someone check the answer, please?
With the help of the forum, I've gone through many more exponent exercises. But I have one more questions.
... | 4 | [
-0.01177978515625,
0.0023193359375,
0.013671875,
0.0810546875,
0.0458984375,
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0.07080078125,
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0.008056640625,
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0.07275390625,
0.01806640625,
0.058349609375,
-0.07177734375,
-0.046142578125,
-... | 36,533 | 36533 | |
Homework Help
Posted by Anonymous on Wednesday, January 19, 2011 at 6:23pm.
The price to cover ornaments is a fixed amount plus a percentage of the value of the ornaments.
It costs $32 to insure $1000 worth of jewellery or $44.50 to insure $3500 worth of jewellery.
What is the fixed amount to insure jewellery?
A. $... | 4 | [
0.006378173828125,
0.12109375,
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0.0162353515625,
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-0.0033111572265625,
0.01214599609375,
0.05517578125,
-0.07568359375,
0.05... | 36,534 | 36534 | |
S-unit equation and small sets of places
up vote 7 down vote favorite
Let $K$ be a number field, and let $S_x$ denote the set of primes of norm at most $x$. Is it possible to find a smaller set of places $T_x\subset S_x$ so that a lot of the solutions of the $S_x$-unit
equation $a+b=1$ for $a,b\in S_x$ are solutions o... | 5 | [
-0.02392578125,
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0.12890625,
-0.00982666015625,
0.00390625,
-0.0205078125,
0.06689453125,
-0... | 36,535 | 36535 | |
[SOLVED] tangent sum identity issue
October 21st 2009, 03:05 PM #1
Junior Member
Joined
Sep 2009
Posts
74
[SOLVED] tangent sum identity issue
I've been working through a tanget sum identity problem and I've mostly got it, except I've got the signs reversed. I was curious if someone could point out the mi... | 4 | [
-0.107421875,
0.0654296875,
0.043212890625,
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0.04150390625,
0.003631591796875,
-0.051... | 36,536 | 36536 | |
normal component of accelleration
September 22nd 2010, 10:57 PM #1
Member
Joined
Apr 2009
Posts
87
normal component of accelleration
Iam having issues with this one iff anybody can help?
Given y^2=3x^3+8x
where x and y are in meters and y is positive,what is the normal component of the accellera... | 5 | [
-0.01171875,
-0.06201171875,
0.004486083984375,
0.0218505859375,
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0.0634765625,
-0.040283203125,
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0.158203125,
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0.04052734375,
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0.039306640625,
-0.041259765625,
0.036132... | 36,537 | 36537 | |
diophantine problem
September 4th 2008, 07:20 AM #1
Junior Member
Joined
Aug 2008
Posts
42
diophantine problem
Suppose $n$ is a fixed integer (positive or negative) $eq 0$ and suppose
$x_0^2 - 3y_0^2 = n$
with $x_0 \geq 0,\ y_0 \geq 0$. Let $x_1 = 2x_0 +3y_0,\ y_1=x_0+2y_0$. Show that
$x_1... | 5 | [
-0.06201171875,
0.033447265625,
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-0.0478515625,
-0.017578125,
0.044921875,
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0.0289306640625,
-0.045654296875,
0.01336669921875,
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-0.021484375,
0.0030517578125,
0.03076171875,
0.057861328125,
-0.003448486328125,
-0.084472... | 36,538 | 36538 | |
Quadratic Equation help
April 9th 2013, 08:57 PM #1
Newbie
Joined
Apr 2013
From
Sydney
Posts
17
Thanks
2
Quadratic Equation help
Hi there, I'm having trouble with two of the more challenging problems in my homework.
1) 2x^2 - 3x + 2a = 0 , this needs to be solved using complete the square me... | 4 | [
-0.01519775390625,
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0.09375,
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0.0255126953125,
0.044921875,
-0.06005859375,
0.0419921875,
0.047119140625,
0.0041... | 36,539 | 36539 | |
Jumping Jack
March 22, 2013
We have a fun little programming puzzle today; I found it here, but don’t know the original source of the puzzle:
Jack starts at 0 on the number line and jumps one unit in either direction. Each successive jump he makes is longer than the previous by 1 unit, and can be made in either ... | 5 | [
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0.045654296875,
-0.06201171875,
0.047... | 36,540 | 36540 | |
non-abelian groups of prescribed order
up vote 2 down vote favorite
2
Is there a construction that will give a non-abelian group of order $p^mr$ where $p$ is a prime, $r$ and $p$ are relatively prime and $m$ is an arbitrary non-negative integer? I suspect in this
generality there is no simple construction so feel free... | 4 | [
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-0.005706787109375,
0.0971... | 36,541 | 36541 | |
Please need help with direct proof
November 9th 2006, 09:24 PM #1
Junior Member
Joined
Nov 2006
Posts
48
Please need help with direct proof
Hi, I have a few problems which i can't solve
1) need to prove (m+dk)mod d = m mod d (where m, d and k are integers and d does not equal to zero)
2) if r i... | 4 | [
-0.054443359375,
0.025390625,
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-0.08203125,
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0.04638671875,
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0.04150390625,
0.09375,... | 36,542 | 36542 | |
Exponential form - Math Central
Hi Kent.
"Exponential form" simply means a numeric form involving exponents.
One way to write such a number is by recognizing that each position represents a power (exponent) of 10. So you can first break it up into separate pieces.
I will use my own number 5 625 702:
5 625 702 = 5 00... | 4 | [
-0.0478515625,
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0.0252685546875,
-0.091796875,
0.021... | 36,543 | 36543 | |
Question about second/third derivative
March 18th 2011, 07:05 AM
HAL9000
Question about second/third derivative
Hello!
I've got a somewhat dumb question.
What is the second and third derivative of a composition of two functions in Leibniz notation?
March 18th 2011, 07:17 AM
HallsofIvy
Not a dumb... | 5 | [
-0.0230712890625,
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0.08398... | 36,544 | 36544 | |
Dimensions of cylinder of a constant surface area but changing volume
December 28th 2012, 11:20 AM
taursaw62
Dimensions of cylinder of a constant surface area but changing volume
Hi there! I'm new around so please feel free to correct me on forum ettiquete here!
I am modelling a cylinder that changes volume... | 4 | [
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0.02490234375,
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-0.0174560546875,
-0.0419921875,
0.088... | 36,545 | 36545 | |
Solving the Beltrami Equation for a very simple Beltrami Coefficient
up vote 7 down vote favorite
3
Let $\mu$ be a function on the complex plane with the property $\mu(z) = \overline{\mu(\bar{z})}$, such that $\mu(z) = \epsilon e^{-2\pi i \bar{z}}$ on the upper-half plane, where $\epsilon$ is a
complex number such tha... | 5 | [
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0.05859375,
-0.044189453125,
-0.0439453125,
0.07421875,
-0.0986328125,
0.052001953125,
-0.00006771087646484375,
0.04638671875,
-0.052490234375,
0.00531005859375,
-0.065917... | 36,546 | 36546 | |
Projective plane conics over
Returns True if and only if self has a point defined over \(\QQ\).
If point and obstruction are both False (default), then the output is a boolean out saying whether self has a rational point.
If point or obstruction is True, then the output is a pair (out, S), where out is a... | 5 | [
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0.0400390625,
0.006683349609375,
-0.0101318359375,
0.01031494140625,
-0.052001953125,
... | 36,547 | 36547 | |
Markov chains
Talk0
34,136pages on
this wiki
Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Individual differences | Personality | Philosophy | Social |
Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology |
Statistics: Scientific meth... | 4 | [
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0.051025390625,
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-0.046630859375,
-... | 36,548 | 36548 | |
E.W.Dijkstra Archive: Primes once more (re Kac & Ulam) (EWD 1203)
The plurals are defined as the integers ≥ 2. The plurals come in two sorts, the composite numbers, i.e. the plurals divisible by a smaller plural, and the prime numbers, i.e. the plurals not
divisible by a smaller plural.
Lemma 0 Each plural has a prime... | 4 | [
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-0.0244140625,
-0.003753662109375,
0.02... | 36,549 | 36549 | |
Math Help
June 28th 2011, 07:23 AM #1
MHF Contributor
Joined
Mar 2010
From
Florida
Posts
3,093
Thanks
5
Subsequences
Suppose $\{x_n\}\to x_0$ and $\{y_n\}\to x_0$. Define a sequence $\{z_n\}$ as follows: $z_{2n}=x_n$ and $z_{2n-1}=y_n$. Prove that $\{z_n\}$ converges to $x_0$.
Let $\epsilon... | 4 | [
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0.000637054443359375,
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0.0189208984375,
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0.04833984375,
-0.0076904296875,
0.09033203125,
0.0390625,
0.001953125,
0.0... | 36,550 | 36550 | |
Solving of Trigonometry equation
January 2nd 2011, 06:10 PM #1
Junior Member
Joined
Aug 2010
Posts
37
Solving of Trigonometry equation
Hi Guys !
Am Currently stuck with this question :
If sin(x+y) = 1 and if tanx = 9tany , find the value of tanx.
Need help guys thanks !
have you playe... | 4 | [
-0.05029296875,
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0.08056640625,
0.09814453125,
-0.04052734375,
-0.0242919921875,
0.... | 36,551 | 36551 | |
M. L. BAKER
GG.
An angel came down for a meeting of the American Philosophical Association. Greeting the assembled philosophers, the angel offered to answer a single question for them. Immediately the philosophers
set to arguing about what they should ask. So the angel said, “Alright, you figure out what you want to a... | 4 | [
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0.037841796875,
-0.031494140625,
... | 36,552 | 36552 | |
[SOLVED] Equivalence Relations
October 22nd 2008, 08:54 AM #1
Junior Member
Joined
Sep 2008
From
Indiana
Posts
26
[SOLVED] Equivalence Relations
Prove that if R is a symmetric, transitive relation on A and the domain of R is A, then R is reflexive on A.
I'm not really sure where to start.
I... | 4 | [
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0.0751953125,
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-0.00860595703125,
0.054443359375,
-0.0... | 36,553 | 36553 | |
Trivial canonical bundle
up vote 1 down vote favorite
Let $X$ be a complex compact Kähler minimal surface with zero algebraic dimension and $H^2(X,\mathcal{O}_X) \ne 0$. We know that according to Enriques–Kodaira classification, $X$ is either a torus or
a K3 surface. In particular, its canonical bundle is trivial.
My... | 4 | [
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0.0546875,
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0.0128784179687... | 36,554 | 36554 | |
ISDA® - PDF
ISDA®
Alternative compounding methods for over-the-counter derivative transactions
David Mengle, ISDA Head of Research
February 5, 2009
Summary
• There are two methods for compou... | 5 | [
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0.02587890625,
0.0035552978515625,
-0.08935546875,
0.003326416015625,
-0.002716064453125,
-0.02587890625,
-0.03369140625,
... | 36,555 | 36555 | |
Help with this Calculus Problem
May 30th 2006, 01:42 PM
Susie38
Help with this Calculus Problem
This is a piecewise function
Let f(x) = 2/pi*x when [0,pi/2]
2sinx when (pi/2, 3pi/2]
1 when (3pi/2, 2pi]
a. find a continuous function, F(x), satisfying F(x) = the integral f(t) dt from 0 to x, on [... | 5 | [
-0.004852294921875,
0.01007080078125,
-0.005340576171875,
-0.017822265625,
-0.0003986358642578125,
0.01385498046875,
-0.01434326171875,
0.058837890625,
-0.07421875,
0.00628662109375,
0.058837890625,
-0.04248046875,
0.00762939453125,
-0.0341796875,
0.0220947265625,
-0.006561279296875,
... | 36,556 | 36556 | |
Statistics Question
February 21st 2008, 07:47 AM #1
Member
Joined
Dec 2006
Posts
79
Statistics Question
I'm given this problem. σ²(t) = V((1-t)X + tY) = at² + 2bt+c where
a=? b=? c=?
E(X) = 2
E(Y) = 3
E(X^2) = 53
E(Y^2) = 45
E(XY) = -21
Can someone please explain what σ²(t... | 4 | [
-0.0174560546875,
0.00433349609375,
0.078125,
0.048828125,
-0.002593994140625,
0.11474609375,
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0.017578125,
0.0135498046875,
0.06005859375,
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-0.041259765625,
0.0157470703125,
-0.0211181640625,
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-0.07... | 36,557 | 36557 | |
The mathematics of blackjack: Probabilities
We first present the probabilities attached to card dealing and initial predictions. In making this calculus, circumstantial information such as fraudulent dealing is not taken into account (as in
all situations corresponding to card games). All probabilities are calculated ... | 5 | [
-0.0263671875,
0.01385498046875,
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0.002685546875,
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0.09228515625,
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0.0059814453125,
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0.0284423828125,
-0.0247802734375,
-0.06982421875,
0.033935546875,
0.0198974609375,
... | 36,558 | 36558 | |
Cutting Elbows
Let's cut one of these 90° elbows into smaller 45° elbows.
A quick division of 90° /45° shows that two 45° elbows can be created from one 90° elbow. Below you will find three different ways to calculate measurements to mark 45° elbows.
The first method is: Measuring or calculating the insid... | 4 | [
0.03271484375,
0.05419921875,
0.02294921875,
-0.0157470703125,
0.01141357421875,
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0.10205078125,
0.004669189453125,
-0.0252685546875,
-0.0126953125,
-0.056884765625,
-0.0108642578125,
0.055908203125,
0.01361083984375,
-0.048095703125,
-0.047119140625,
0.... | 36,559 | 36559 | |
Formulas and Missing Quantities
Date: 10/09/2004 at 04:45:34
From: Pilar
Subject: Drinking a swimming pool
Could you drink enough water in a life time to empty a pool? My math
teacher told us to solve this problem and I understand it but I really
don't get how we have to solve it!
I thought of using a pool that is ... | 4 | [
0.01953125,
0.068359375,
0.0625,
0.031982421875,
-0.046630859375,
-0.0247802734375,
-0.0107421875,
0.052001953125,
-0.0216064453125,
-0.021728515625,
-0.01507568359375,
-0.09033203125,
0.01434326171875,
0.146484375,
-0.0380859375,
0.0147705078125,
-0.1025390625,
0.003662109375,
-... | 36,560 | 36560 | |
Pascal Triangle
If the computational board fields are used for the numbers from the above binomial expressions, the following number triangle is formed :
There are some proofs that this number triangle was familiar to the Arab astronomer, poet and mathematician Omar Khayyam as early as the XI century. Most probably th... | 4 | [
-0.038330078125,
0.05615234375,
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-0.02294921875,
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0.016845703125,
0.0634765625,
0.049072265625,
-0.020263671875,
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0.033203125,
0.00677490234375,
0.01556396484375,
0.0167236328125,
-0.1005859375,
-0.0067... | 36,561 | 36561 | |
Monotone sequences and Cauchy sequences
March 19th 2009, 11:35 AM #1
Member
Joined
Oct 2008
Posts
124
Monotone sequences and Cauchy sequences
Suppose that x>0. Define a sequence (s_n) by s_1=k, and s_(n+1) = (((s_n)^2)+x)/(2s_n) for n elements in N. Prove that for any k>0, lim s_n = sqrt(x).
I've go... | 5 | [
0.0213623046875,
-0.038330078125,
0.07568359375,
-0.04296875,
-0.04541015625,
0.076171875,
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0.00469970703125,
0.004302978515625,
-0.01806640625,
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0.06103515625,
-0.004974365234375,
-0.053955078125,
-0.040283203125,
0.09228515625,
0.04... | 36,562 | 36562 | |
Differential equation with switched parameters and boundary conditions in integral form
up vote 0 down vote favorite
1
Sorry for the title, I didn't find a better description (showing that I have no idea for the solution). Feel free to put in a better title and change the tags if you can grasp a view on the problem.
... | 4 | [
-0.02099609375,
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0.04052734375,
-0.09765625,
0.01123046875,
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0.0166015625,
0.052001953125,
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0.061279296875,
0.0654296875,
0.12158203125,
-0.12255859375,
-0.05004882... | 36,563 | 36563 | |
A direct proof that minimal primes are associated
up vote 0 down vote favorite
2
It is a well-known theorem that, for a Noetherian ring $A$, the minimal primes of $A$ are among the associated primes of $A$; i.e., for every minimal prime $\mathfrak{p}$ of $A$, there is an element
$f \in A$ such that $Ann(f) = \mathfrak... | 5 | [
-0.00274658203125,
0.0771484375,
0.00347900390625,
-0.0179443359375,
0.09228515625,
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0.08642578125,
0.029052734375,
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0.0230712890625,
-0.004974365234375,
0.0184326171875,
0.00396728515625,
-0.0178222... | 36,564 | 36564 | |
Is the evaluation of polynomial functors appropriately continuous?
up vote 7 down vote favorite
1
I'd like a nice proof of the following fact.
Let $C$ and $D$ be categories, and let $\mathbf{Cat}/(C\times D)$ be the usual (1-categorical) slice category whose objects are triples $(X,F\colon X\to C, G\colon X\to D)$, $... | 4 | [
0.004638671875,
0.029296875,
-0.0203857421875,
-0.049560546875,
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0.0118408203125,
-0.0040283203125,
-0.03857421875,
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0.037841796875,
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0.03515625,
0.07666015625,
0.055419921875,
0.00506591796875,
0.04321289... | 36,565 | 36565 | |
What is the lower bound for highly composite numbers?
Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
I will start off with the simplest type, $$ d(n) \leq \sqrt{3 n} $$ and $$ d(n) \leq 24 \left(\frac{n}{315}\right)^{1/3}... | 4 | [
0.01904296875,
-0.08935546875,
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0.04736328125,
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0.0306396484375,
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0.04052734375,
-0.00518798828125,
-... | 36,566 | 36566 | |
How to solve this System of Second Order Differential Equations (DE) with Initial Value Problem (IVP)
up vote 3 down vote favorite
1
Hello, I'm trying to figure out how solve the below for varying time and/or corresponding theta. I'm stumped.. any insight is greatly appreciated. Thank you
$\ddot{R} = −\alpha|v|\dot{R... | 4 | [
-0.10302734375,
-0.0322265625,
0.0018310546875,
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-0.00421142578125,
-0.03662109375,
0.05908203125,
0.0032653808593... | 36,567 | 36567 | |
Torsors and the fpqc topology
up vote 4 down vote favorite
Fix a scheme $S$, a group scheme $G/S$ (let us say smooth, maybe even affine with some finiteness conditions if you like), and suppose I have some other $S$-scheme $P$ with a right $G$-action. We
want to investigate the question of whether $P$ is a $G$-torsor ... | 4 | [
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0.0107421875,
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-0.0032806396484375,
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0.0712890625,
-0.0019683837890625,
0.09130859375,
-0.056396484375,
0.09375,
0.009... | 36,568 | 36568 | |
Preduals of B(E)
up vote 7 down vote favorite
1
For a Hilbert space $H$ it is well known that the algebra $B(H)$ has a unique predual; the Banach space of trace class operators.
If $E$ is a Banach space then is it known whether
1. $B(E)$ is always a dual Banach algebra?
2. The predual is always unique?
I'm aware... | 4 | [
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-0.06396484375,
-0.0052490234375,
-0.0595703125,
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0.0908203125,
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-0.046630859375,
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0.01446533203125,
-0.033203125,
0.0927734375,
0.09228515625,
0.00616455078125,
0.0219... | 36,569 | 36569 | |
Irrationality of pi: the unpossible function
Recall from my last post what we are trying to accomplish: by assuming that $\pi$ is a rational number, we are going to define an unpossible function! So, without further ado:
Suppose $\pi = \frac{a}{b}$, where $a$ and $b$ are positive integers. Define the function $f$ lik... | 5 | [
-0.04931640625,
-0.0201416015625,
-0.0830078125,
0.06689453125,
-0.076171875,
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0.036865234375,
-0.0255126953125,
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0.03271484375,
0.0279541015625,
-0.0615234375,
0.045166015625,
-0.0112... | 36,570 | 36570 | |
Symmetries of a Cube
Date: 10/09/2003 at 02:27:34
From: Johny
Subject: symmetries of cube
Prove that the group of symmetries of a cube is isomorphic to S_4.
Date: 10/09/2003 at 07:10:14
From: Doctor Jacques
Subject: Re: symmetries of cube
Hi Johny,
Note that we must consider the group of rotations of the cube (i.... | 5 | [
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-0.0732421875,
... | 36,571 | 36571 | |
Question about the Hardy-Littlewood method (quite basic)
up vote 7 down vote favorite
3
Hi, I have a question about the Hardy-Littlewood method.
Writing $R_s(n)$ for the number of ways to write $n$ as a sum of $s$ $k$-th powers and $f(\alpha )$ for the sum $\sum _{m=1}^Ne(\alpha m^k)$, we have
$R_s(n)=\int _\mathfra... | 5 | [
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0.01025390625,
0.057861328125,
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0.0308837890625,
-0... | 36,572 | 36572 | |
Is displacement controled by stable norm?
up vote 4 down vote favorite
1
Let $T^n$ be the $n$-dimensional torus and $g$ be a Riemannian metric on $T^n$. Let $\tilde g$ be the induced metric on the universal covering; using suitable coordinates, $\tilde g$ is therefore a $
\mathbb{Z}^n$-periodic metric on $\mathbb{R}^n... | 5 | [
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-0.0908203125,
-0.107421875,
0.0281982421875,
0.07373046875,
-0.... | 36,573 | 36573 | |
Expected value and variance
March 9th 2010, 12:52 AM #1
Member
Joined
Oct 2009
Posts
195
Thanks
1
Expected value and variance
An electronic system has two components X and Y, and works if just one or both components are functioning. Their lifespan function is written as:
f(x,y) = 2^e−(x+2y), x >... | 5 | [
0.04736328125,
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0.05126953125,
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0.0208740234375,
0.072265625,
0.0250244140625,
-0.0634765625,
-0.1098... | 36,574 | 36574 | |
Question about WHY something must be done
September 16th 2010, 04:35 PM #1
Junior Member
Joined
Aug 2008
Posts
40
Question about WHY something must be done
Hi, I've been away from math for a few years now and coming back to it with an algebra review I've run into a problem.
I was answering a questio... | 4 | [
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0.033935546875,
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0.00946044921875,
-0.08984375,
0.00958251... | 36,575 | 36575 | |
Laplace Transforms
January 28th 2009, 07:03 PM #1
Member
Joined
Jan 2009
Posts
91
Laplace Transforms
find the laplace transform F(s) of f(t) = sin wt
the w is actually supposed to be omega
what i got was
integeral from 0 to infinity of: (sin wt)*(e^-st) dt
then i integrated by parts a... | 5 | [
-0.07958984375,
0.1044921875,
0.0203857421875,
0.0419921875,
0.1484375,
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0.0091552734375,
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0.00040435791015625,
-0.0166015625,
-0.038330078125,
-0.00970458984375,
0.0... | 36,576 | 36576 | |
Volume of body obtained by rotating around the x axis and y axis.
May 3rd 2012, 03:14 PM #1
Newbie
Joined
Feb 2011
Posts
18
Volume of body obtained by rotating around the x axis and y axis.
Hi,
If y= 4x^3+3x^2-4x-3, calculate the volume of the body obtained by rotating y around 1) the x axis 2) the ... | 5 | [
0.039306640625,
-0.01324462890625,
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-0.0849609375,
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0.038330078125,
0.0673828125,
-0.046875,
0.025146484375,
0.01171875,
0.03955078125,
0.01275634765625,
0.0189208984375,
0.026123046875,
-0.0250244140625,
0.052001953125,
-0... | 36,577 | 36577 | |
Math Forum Discussions - Re: Definitions missing
Date: Jun 4, 2013 5:58 AM
Author: Andrzej Kozlowski
Subject: Re: Definitions missing
In most cases exact definitions can be found in the various relevant
tutorials. For example, StandardDeviation for discrete data (list) is
defined in tutorial/BasicStatistics:
The vari... | 4 | [
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0.03857421875,
-0.053955078125,
-0.00396728515625,
-0.037841796875,
0.023681640625,
0.008178710... | 36,578 | 36578 | |
COnverting rectangular equations to polar (and vice versa)
April 27th 2008, 11:28 PM #1
Junior Member
Joined
Oct 2007
Posts
31
COnverting rectangular equations to polar (and vice versa)
i understand the concepts of converting single coordinates, however im confused on how and why on some these parts.... ... | 4 | [
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0.061279296875,
0.0517578125,
0.00689697265625,
-0.044921875,
0.0036315... | 36,579 | 36579 | |
Does the tangent bundle of this fiber product split?
up vote 1 down vote favorite
1
Let $\mathcal X \to S$ be the local universal family of an elliptic curve, and let $E \to S$ be a vector bundle over $S$. Then we can form the fiber product $\mathcal Y = \mathcal X \times_S E$,
which will be a smooth complex manifold ... | 4 | [
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0.0208740234375,
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0.07421875,
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0.1259765625,
-0.059814453125,
-0.03662109375,
0.01361083984375,
-0.0... | 36,580 | 36580 | |
dy
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Here's the question you clicked on:
9 Group Title
Suppose a forest fire spread... | 4 | [
-0.05029296875,
0.01513671875,
0.0047607421875,
0.001373291015625,
0.05224609375,
-0.02294921875,
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0.08251953125,
-0.00701904296875,
0.0272216796875,
0.0101318359375,
-0.0478515625,
0.0040283203125,
0.06201171875,
-0.0201416015625,
0.031494140625,
-0.026123046875,
... | 36,581 | 36581 | |
how many distinguishable words
December 23rd 2010, 12:09 PM
bigwave
how many distinguishable words
How many distinguishable words can be formed from the letters of the word "casserole" if each letter is used exactly once? answer is 90,720
December 23rd 2010, 12:16 PM
Plato
If the same question were asked ... | 4 | [
0.060791015625,
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0.03564453125,
-0.0069580078125,
-0.01104736328125,
0.10986328125,
0.035888671875,
0.017333984375,
-0.034423828125,
0.029052734375,
-0.006011962890625,
-0.076171875,
0.0010528564453125,
-0.00439453125,
-0.02294921875,
-0.05859375,
-0.00665283203125,
... | 36,582 | 36582 | |
Inverse Functions: Arcsec(x)
Date: 02/11/99 at 20:15:09
From: Knote
Subject: Calculus
If y = arcsec(x) then what does x equal?
Date: 02/22/99 at 15:53:11
From: Doctor Elizabeth
Subject: Re: Calculus
Hi, Knote.
Good question! Let's take a closer look at that.
First, what does the notation "arcsec()" stand for? W... | 4 | [
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0.02734375,
0.05859375,
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0.033203125,
-0.06396484375,
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0.032958984375,
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Software Sales
Date: 02/01/97 at 11:07:47
From: frank kreager
Subject: Software Sales
Hi,
I am doing word problems and am having a lot of trouble putting them
into mathematical equations. Once I get the mathematical equation, I
don't have any difficulties.
For instance: The three best selling software applications... | 4 | [
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0.12353515625,
-0.003631591796875,
0.051025390625,
0.09716796875,
-0.052734... | 36,584 | 36584 | |
When does "splits" imply "cosplits"?
up vote 7 down vote favorite
4
In the category of groups, there are lots of "exact sequences", e.g. 4 → H → 2, that neither split nor cosplit, where H is the eight-element group of quaternions, and lots of sequences like 4 → D → 2
that split but do not cosplit, where D is the eight... | 4 | [
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0.023681640625,
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-0.08251953125,
-0.013671875,
... | 36,585 | 36585 | |
Prove an inequality
Hello, could someone help with proving this inequality: $a^2+b^2+1 \ge ab + a + b$ Thanks in advance
One way is to consider a line b = k * a for some number k and to prove that the inequality holds for all points (a, b) on this line. (For completeness, one should consider the line a = 0, but the
in... | 5 | [
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0.030517578125,
-0.030... | 36,586 | 36586 | |
O-Level Questions
O-Level Practice Question 2: A helium balloon has a volume of 621 cm3 at ground level where the atmospheric pressure is 101,000 Pa. The balloon rises and expands to 636 cm3. At this point, what is
the height of the balloon above ground ? Take the density of air to be 1.25 kg/m3 and constant over the h... | 4 | [
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-0.0260009765... | 36,587 | 36587 | |
Folding a piece of paper in half
A few weeks ago, I asked the following question:
“If you fold a (humungous) piece of paper in half 50 times, how thick would the pile be? 1cm, 1m, 1km, 1,000km, 1,000,000km…?”
Here I discuss the possibilities of folding paper in half 50, 25, 15 and then 9 times.
50 folds
How thick?... | 5 | [
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0.06298828125,
-0.10107421875,
0.015869140625... | 36,588 | 36588 | |
Does Weyl's Inequality prove equidistribution?
up vote 10 down vote favorite
3
Let $f(n) = \theta n^d + a_{d-1} n^{d-1} + \cdots a_1 n + a_0$ be a polynomial with real coefficients, and $\theta$ irrational. Let $S_N = \sum_{n=1}^N e^{2 \pi i f(n)}$. Weyl's Equidistribution
theorem for polynomials is equivalent to the ... | 4 | [
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-0.06982421875,
-0.049560546875,
0.056640625,
-0... | 36,589 | 36589 | |
Discounted Cash Flow Questions & Answers - Basic
1. Walk me through a DCF.
"A DCF values a company based on the Present Value of its Cash Flows and the Present Value of its Terminal Value.
First, you project out a company's financials using assumptions for revenue growth, expenses and Working Capital; then y... | 4 | [
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0.0498046875... | 36,590 | 36590 | |
Intersection of 2 Planes help
July 20th 2008, 08:12 AM #1
Junior Member
Joined
Sep 2007
Posts
55
Intersection of 2 Planes help
Hello everyone! I truly hope someone can explain this question out to help me out! It's been 2 hours and still no luck! Any help is truly appreciated!
----------------------... | 4 | [
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Integration Question
May 21st 2008, 06:21 AM
looi76
Integration Question
Question
A curve is such that $\frac{dy}{dx} = \frac{4}{\sqrt(6 - 2x)}$, and $P(1,8)$ is a point on the curve. Find the equation of the curve.
Attempt:
$\frac{dy}{dx} = \frac{4}{\sqrt(6 - 2x)}$
$\int 4(6-2x)^{-\frac{1}{2}... | 4 | [
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-0.06835... | 36,592 | 36592 | |
Given 2 towers of fields, when are these fields isomorphic?
up vote 5 down vote favorite
Let $F_0 \subset F_1 \subset F_2 \subset \cdots$ and $K_0 \subset K_1 \subset K_2 \subset \cdots$ be two towers of fields. Also, let $F = \cup_{i=0}^\infty F_i$ and $K = \cup_{i=0}^\infty K_i$.
Now suppose for each $i$ we have in... | 5 | [
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-0.044189453125,
0.0732... | 36,593 | 36593 | |
dy
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Here's the question you clicked on:
agentx5 Group Title
Check my work on this ... | 5 | [
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0.12890625,
-0.0551757812... | 36,594 | 36594 | |
Confusion with respect to a general angle
September 14th 2012, 01:38 AM #1
Confusion with respect to a general angle
Hello,
I shall post the problem with the answer (s) as a given, but it's more of an explanation on what's just happened from which I'm after.
Anyway:
$-540 < 3x < 540$
$tan\ 3x ... | 4 | [
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... | 36,595 | 36595 | |
A problem about Determinant of sum of permutation matrices
up vote 3 down vote favorite
Let $w_1$ and $w_2$ be two permutations of $\{1, \cdots , k\}$ such that for all $1\leq i \leq k$, $w_1(i)\neq w_2(i)$. Let $m$ and $n$ be two relatively prime integers. Then is there exist two
diagonal matrices $D_1, D_2 \in M_k(\... | 5 | [
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... | 36,596 | 36596 | |
Modeling
April 9th 2007, 07:17 PM
pakman
Modeling
The problem states that a tank originally contains 100 gal of fresh water. Then water containg 1/2 lb of salt per gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed
to leave at the same rate. After 10 min the process is stopped,... | 5 | [
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0.024658203125,... | 36,597 | 36597 | |
Equivalence Relations
April 29th 2010, 02:44 PM #1
MHF Contributor
Joined
Mar 2010
From
Florida
Posts
3,093
Thanks
5
Equivalence Relations
$x,y,z\in\mathbb{R}$
$x\sim y$ iff. $x-y\in\mathbb{Q}$
Prove this is an equivalence relation.
Reflexive:
$a\sim a$
$a-a=0$; however, doe... | 4 | [
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Very tricky and interesting modular question
July 9th 2010, 12:29 PM
elemental
Very tricky and interesting modular question
This is a very tricky question:
Find the last three digits of
2008^2007^2006^2005^...^1
If you're having trouble thinking about how the exponents are arranged, just imagine eve... | 5 | [
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