content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
An Inequality?
Prove or disproe: For any positive integer n and $x \in [0,\pi], \quad \sum_{k=1}^n \frac{1}{k} \sin kx \geq 0$
Some how I just could not see this clearly before
Say n (>1) is the smallest integer such that for some minimal point $x_0 \in (0,\pi)$, $\sum_{k=1}^n \frac{1}{k} \sin kx_0 \leq 0$, then $\si... | 5 | [
-0.0198974609375,
0.05615234375,
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0.09033203125,
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0.030517578125,
0.00927734375,
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-0.05078125,
0.0732421875,
-0.0230712890625,
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0.1015625,
-0.06201171... | 9,500 | 9500 | |
Finding derivative by first principles?
June 17th 2013, 09:39 AM
misiaizeska
Finding derivative by first principles?
How do I find the derivative of: y = 2/(2-x)
I know that I will have to take the limit of "(f(x+h) - f(x))/h" as h approaches 0, but the algebra is really confusing me. If anyone could help, ... | 4 | [
0.002532958984375,
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0.06591796875,
0.0537109375,
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-0.025146484375,
0.038818359375,
0.055908203125,
-0.01202392578125,
-0.054931... | 9,501 | 9501 | |
Rationalizing Denominators with Cube Roots
Associated Topics || Dr. Math Home || Search Dr. Math
Rationalizing Denominators with Cube Roots
... | 4 | [
0.0107421875,
0.04150390625,
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0.059326171875,
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0.09814453125... | 9,502 | 9502 | |
Distance puzzle
October 2nd 2007, 11:45 AM #1
Newbie
Joined
Oct 2007
Posts
2
Distance puzzle
"Calum was floating down a river on a raft, when, half a mile downstream, his brother duncan set off in a canoe. Duncan paddled downstream as quickly as he could, then turned round and paddles
back again, sti... | 4 | [
0.0218505859375,
0.03564453125,
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0.017822265625,
0.034912109375,
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-0.033203125,
0.08544921875,
0.00933837890625,
0.0380859375,
-0.03857421875,
0.05... | 9,503 | 9503 | |
couple problems i have
April 20th 2009, 05:54 PM #1
Newbie
Joined
Apr 2009
Posts
2
couple problems i have
I need help with a few problems I have left.
1. Given : r = cscΔΞ
how do I find the range of all possible values of r and also how do I find a Cartesian equation without fractions
2. Gi... | 4 | [
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0.0245361328125,
-0.058349... | 9,504 | 9504 | |
Tail bound for $L_2$ norm of top $k$ singular values of a random matrix
up vote 2 down vote favorite
Let $Y=X^\top W$ , with $X, W \in \mathbb{R}^{d \times d}$ are random matrices with standard normal entries. Let $\lambda_j$ be the $j^{th}$ singular value of $Y$. Is there a way to bound the tail
probability of the $L... | 4 | [
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-0.0... | 9,505 | 9505 | |
Least Common Multiple
Date: 3/29/96 at 11:8:1
From: JONATHAN FIELDS
Subject: least common multiples
Hi Dr. Math.
The question I have is about how to find the least common
multiples from a set of numbers.
I know that a multiple of a number has that number as one of its
factors.
What is the least common multiple fo... | 4 | [
0.041015625,
0.017333984375,
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-0.111328125,
0... | 9,506 | 9506 | |
Approximating Natural Log By Hand
March 15, 2012 7:54 AM Subscribe
Calculating/approximating ln(x) 'by hand'?
I've got an application that only has a limited set of mathematical operators: +, -, parens (), multiplication/division, pow() or **, mod, and div.
I've got a request to calculate ln(x). How can I best app... | 5 | [
-0.06494140625,
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0.015625,
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0.03881835... | 9,507 | 9507 | |
math
The other day I described the math textbook that was used in the Soviet Union when I attended school there.Β Β My question was: how could this textbook teach so much in just 220 pages? My tentative
hypothesis was that it eliminated needless βscaffoldingβ (yes, I recognize that the term is problematic) and went right... | 4 | [
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Isosceles Triangle in a Parabola help
September 1st 2007, 08:49 PM #1
Newbie
Joined
Sep 2007
Posts
7
Isosceles Triangle in a Parabola help
Triangle OAB is an isosceles triangle with vertex O at the origin and vertices A and B on the parabola y = 9-x^2
Express the area of the triangle as a function o... | 5 | [
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-0.071289062... | 9,509 | 9509 | |
Math Help
July 5th 2007, 02:31 PM #1
Newbie
Joined
Jun 2007
Posts
18
rate
1. (a) A car traveling at a speed of v can brake to an emergency stop in a distance x. Assuming all other driving conditions arte all similar, if traveling speed of the car doubles, the stopping
distance will be (1) β2x, or (2... | 5 | [
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-0.02307128906... | 9,510 | 9510 | |
Pathological example
September 14th 2009, 10:29 PM #1
Member
Joined
Nov 2008
Posts
76
Pathological example
Will someone help me on this problem?
Let $f(x):R \rightarrow R$ be a continuous but differentiable nowhere ( for example the Weierstrass's function). Define $F(x)=\int_0^x f(r)dr$. Why does F(x... | 5 | [
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Assessing the joint effect of population stratification and sample selection in studies of gene-gene (environment) interactions
Abstract
Background
It is well known that the presence of population stratification (PS) may cause the usual test in case-control studies to produce spurious gene-disease associations. Howev... | 4 | [
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proof for uncorrelated variables X and Y
October 16th 2012, 05:33 PM
shaunoflobe
proof for uncorrelated variables X and Y
Hello :D.
Quick question, how can I show that, for uncorrelated variables X and Y, p(X+Y, X-Y) = (Var(X)-Var(Y)/(Var(X)+Var(Y)) ?
I know how to show that Cov(X+Y, X-Y) = Var(X) - Var... | 4 | [
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0.003051757... | 9,513 | 9513 | |
Is my use of the eigendecomposition correct here?
up vote 2 down vote favorite
I'm exploring different techniques to efficiently solve some matrix equations. My situation is that I have a matrix $\textbf{H} = \textbf{J}^T \textbf{J}$, where $\textbf{J}$ is a matrix with no
special qualities. From this, I first need to... | 5 | [
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The Fundamental Group β A Primer
Being part of the subject of algebraic topology, this post assumes the reader has read our previous primers on both topology and group theory. As a warning to the reader, it is more advanced than
most of the math presented on this blog, and it is woefully incomplete. Nevertheless, the ... | 4 | [
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-0.0033111572... | 9,515 | 9515 | |
Find the derivative
February 5th 2009, 07:23 PM #1
Newbie
Joined
Feb 2009
Posts
11
Find the derivative
Darn professors....wish mine explained things...
How do I find f`(a) for $f(x) = (3x +1)^{1/2}$
Thats the square root of 3x+1, double thanks to someone who shows me how to put that in there.
... | 4 | [
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... | 9,516 | 9516 | |
Converge?
February 11th 2010, 02:51 PM
Henryt999
Converge? any aolternative methods of explaining?
I have this issue about some sums:
$\sum_{k=1}^{\infty} \frac{1}{3^k-2^k}$
It must be divergent because $3^k>2^k$ but I cant show that, any idΓ©as?
Ohh yeah I tried with $3^k=2^{k*ln(3)}$ but that didnΒ΄... | 5 | [
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-0... | 9,517 | 9517 | |
raising complex numbers to complex exponents?
March 25th 2011, 08:14 PM #1
Member
Joined
Jun 2008
Posts
148
raising complex numbers to complex exponents?
Is it possible to calculate something like $(a + bi)^{c+di}$?
I recall reading somewhere that $i^i$ is calculable (I think its a real number), so ... | 5 | [
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0.111816406... | 9,518 | 9518 | |
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Topic: Misner, Thorne and Wheeler: 11.4 Parallel Transpor... | 4 | [
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0.011657714... | 9,519 | 9519 | |
Order statistics: probability random variable is k-th out of n when ordered.
up vote 1 down vote favorite
Given a random variable $X_1$ drawn from a distribution with cdf $F$, and random variables $X_2, \cdots,X_n$ drawn from another distribution with cdf $G$, what is the formula for the probability that
$X_1$ is the ... | 5 | [
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0.08203125,
-0.01574707... | 9,520 | 9520 | |
Find the Laplace transform of each of the following:
August 19th 2009, 07:33 AM
tone999
Find the Laplace transform of each of the following:
(a) e^4t
(b) 4 e^2t + 3 cosh 4t
(c) 2 sin3t + 4 sinh 3t
(d) t^3 + 2t^2 - 4t + 1
August 19th 2009, 07:46 AM
Chris L T521
Quote:
Just apply the formu... | 5 | [
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-0.083984375,
-0.01165771... | 9,521 | 9521 | |
trig substitution
July 26th 2007, 06:02 PM
davecs77
trig substitution
How would you do this
integral of tan^3(x)dx
I broke it down into integral of tan(x)(sec^2(x) - 1)dx
u = tan(x)
du = sec^2(x)
so i got integral of u(du) - integral of (u)
I am not so sure if this is correct so far, and ... | 5 | [
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0.03002929687... | 9,522 | 9522 | |
Congruences, Powers, and Euler's Formula
February 2nd 2009, 08:37 PM
ycsanchez
Congruences, Powers, and Euler's Formula
Hello I can't quite seem how to finish this problem:
The number 3750 satisfies f(3750) = 1000. Find a number a that has the following three properties:
(i) a ΒΊ 7^3003 (mod 3750).
... | 5 | [
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0.0286865234375,
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-0.049560546875,
-0.12109375,
-0... | 9,523 | 9523 | |
another integral reduction
hey i didnot get u!could u show me some of the steps??Like i dunno what identity to use and therefore i dunno wat to add and subtract???
This is what I was thinking but it doesn't really look like a reduction formula. Your integral, by parts $<br /> \int \frac{\sin x}{(a+b \sin x)^{n+1}} dx ... | 5 | [
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0.07958984375,
0... | 9,524 | 9524 | |
Neighboring Cards
Date: 02/18/97 at 13:58:35
From: Christopher K.
Subject: Card probability
Hello,
I have a problem. I found that if you take a deck of cards, name any
two cards, and then look for them in the deck, they will be by each
other or only one card away from each other. I tried to find the
probability of ... | 4 | [
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0.014404296875,
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0.047119140625,
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-0.0022735595703125,
0.0115966796875,
0.0220947265625,
0.029541015625,
-0.008117675... | 9,525 | 9525 | |
Math Forum Discussions
Math Forum
Ask Dr. Math
Discussions
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Search All of the Math Forum:
Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.
Topic: Extended Euclidean Algorithm
Replies: 1 Last Post:... | 4 | [
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0.125,
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0.0177001953125,
0.0228271484375,
0.0634765625,
0.0033721923828125,
-0.058349609375,
... | 9,526 | 9526 | |
The Polynomial van der Waerden Theorem
[Bill Gasarch, known online for his frequent contributions to the Complexity Blog and for his liberal USE of capital LETTERS, has been reading about the "polynomial" and "multi-dimensional" versions
of van der Waerden's theorem (the original theorem being "linear" and "one-dimensi... | 4 | [
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-0.01324462890625,
0.006072998046875,
-0.04736328125,
0.0537109375,
-0.08154296875,
0.0208... | 9,527 | 9527 | |
ifferential
Ordinary differential equation
Book
Ordinary differential equation 1 Ordinary differential equation In mathematics, an ordinary differential equation (or ODE) is a relation that contains functions of
Book
Page 2 of 87 ORDINARY DIFFERENTIAL EQUATIONS DEFINITIONS DefA differential equation is an equati... | 5 | [
-0.1357421875,
-0.058837890625,
0.0498046875,
0.10400390625,
-0.031982421875,
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0.06005859375,
0.056396484375,
0.0260009765625,
0.10498046875,
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0.025146484375,
0.0032806396484375,
0.0216064453125,
-0.12109375,
0.03027343... | 9,528 | 9528 | |
Chain Rule Derivative
You also need to use product rule. The two functions here are, x^3 (2x-4)^4 The respective derivatives are: 3x^2----> Power rule 2*4(2x-4)^3=8(2x-4)^3---->Chain Rule Now apply the product rule,
u'v+uv' We have, [3x^2][(2x-4)^4]+[x^3][8(2x-4)^3] Thus, 3x^2(2x-4)^4+8x^3(2x-4)^3 Factor, x^2(2x-4)^3[3... | 5 | [
0.06298828125,
0.059326171875,
-0.017333984375,
-0.01263427734375,
-0.00555419921875,
0.030517578125,
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-0.0615234375,
-0.01019287109375,
0.0015411376953125,
0.07958984375,
-0.04736328125,
0.0264892578125,
-0.0208740234375,
0.024658203125,
0.0546875,
-0.0849609375,
0.... | 9,529 | 9529 | |
Logarithm Table
From WikiEducator
Created by Paul Tauriki on 02-07-08.
Significant figures
Wikipedia has an article on this subject.
Visit Significant figures for more in depth information
{{Wikipedia|Significant figures}}
Key points
Steps taken to create Logarithm Table.pdf:
1. Created Logarithm Tabl... | 4 | [
0.0361328125,
0.007537841796875,
-0.07666015625,
-0.05517578125,
-0.0498046875,
-0.043701171875,
-0.0164794921875,
0.138671875,
-0.00823974609375,
0.11376953125,
0.01416015625,
-0.060791015625,
0.060791015625,
0.0615234375,
0.0341796875,
-0.02197265625,
-0.12158203125,
0.0771484375... | 9,530 | 9530 | |
Slope of the tangent
November 20th 2008, 06:27 PM #1
Junior Member
Joined
Nov 2008
Posts
66
Slope of the tangent
The slope of the tangent to the curve $y^3x + y^2x^2 = 6$ at (2,1) is:
$-3/2, -1, -5/14, -3/14, 0$
What am I suppose to do? Implicit differentiation? I tried that and I ended up gett... | 5 | [
-0.0947265625,
-0.07275390625,
-0.01104736328125,
0.033447265625,
-0.004364013671875,
0.052978515625,
0.005218505859375,
0.06982421875,
0.060302734375,
-0.00933837890625,
0.134765625,
-0.009765625,
-0.0196533203125,
0.000560760498046875,
-0.01336669921875,
0.05712890625,
-0.103515625... | 9,531 | 9531 | |
[SOLVED] Gmat question...
February 7th 2008, 06:27 PM
aj82da6
[SOLVED] Gmat question...
I need help with this problem from my practice gmat..
(1/5)^m times (1/4)^18 = 1/(2(10)^35)
and we are trying to find m
thank you for your help
February 7th 2008, 07:08 PM
Jhevon
Quote:
$\left( \fr... | 4 | [
0.0089111328125,
0.004058837890625,
0.00131988525390625,
0.0537109375,
-0.04541015625,
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0.0186767578125,
0.06982421875,
-0.0302734375,
0.0654296875,
0.0211181640625,
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0.044189453125,
0.05419921875,
0.0147705078125,
0.1875,
-0.052001953125,
0.049560546875,
... | 9,532 | 9532 | |
Related rates of change involving pythagoras
May 16th 2009, 10:07 PM #1
Newbie
Joined
Mar 2009
Posts
15
Related rates of change involving pythagoras
i have two problems in my book that i cannot solve. They both involve the use of pythagoras. I'll post them here and show my steps, my problem here is findi... | 5 | [
-0.0177001953125,
0.00634765625,
-0.000518798828125,
-0.08203125,
-0.00823974609375,
-0.01544189453125,
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0.09228515625,
-0.000377655029296875,
0.025390625,
0.07958984375,
-0.032470703125,
0.0159912109375,
0.052001953125,
-0.0169677734375,
0.1044921875,
-0.1083984375,
... | 9,533 | 9533 | |
remainder & factor theorem
July 23rd 2009, 04:53 AM #1
Newbie
Joined
Jul 2009
Posts
2
remainder & factor theorem
i understand the concepts and all the theorems for this topic, i am able to do some questions, but have difficulty with others, and also factorising cubic equations from scratch. thanks for
... | 5 | [
-0.0245361328125,
-0.0172119140625,
-0.0028228759765625,
0.08349609375,
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0.0927734375,
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0.0166015625,
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0.072265625,
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-0.049072265625,
-0.04150390625,
0... | 9,534 | 9534 | |
[SOLVED] Function Question
May 2nd 2008, 07:37 AM #1
[SOLVED] Function Question
Question:
The function $f : x \mapsto x^2 + 5x + 8$ is defined for the domain $x \leq a$, where a is a constant.
(i) Express $x^2 + 5x + 8$ in the form $(x + p)^2 + q$.
(ii) Find the smallest value of a for which $f$ has a... | 4 | [
-0.0101318359375,
0.068359375,
0.07568359375,
-0.00933837890625,
-0.00860595703125,
0.029296875,
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0.11474609375,
0.04541015625,
0.0218505859375,
0.07568359375,
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0.0390625,
0.06494140625,
-0.051513671875,
0.035888671875,
0.012939453125,
-0.08203125,
... | 9,535 | 9535 | |
Trig functions
April 29th 2009, 05:53 PM #1
Member
Joined
Oct 2008
Posts
221
1) Find the exact measures of sin2x, cos2x, and tan2x using the double angle formulas, that sinx = -12/13. Show all work.
2) Find the exact value of the trig function given that sinx = 12/13 and cosy = -4/5 and you are in Qu... | 4 | [
-0.049560546875,
0.055908203125,
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0.07080078125,
0.0107421875,
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0.12890625,
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0.034912109375,
0.0223388671875,
-0.037841796875,
-0.01324462890625,
0.02... | 9,536 | 9536 | |
Definition of homotopy limits
up vote 6 down vote favorite
8
Here's a definition for homotopy limits that isn't quite right, but seems salvageable. Does anyone know how to fix it?
Suppose the category $C$ is some reasonable setting for homotopy theory, say it's enriched over some kind of category of spaces (e.g. chai... | 4 | [
-0.0184326171875,
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0.06884765625,
-0.03271484375,
0.04125976562... | 9,537 | 9537 | |
Analytical Mechanics
ANALYTICAL MECHANICS R = VW+W2
24
and
But since the body is on the point of motion the relation F = /iN holds. Therefore
JL β P cos. ff
: jV~ ^-p sin Β«'
P
j__~~_______ [f
. DISCUSSION. β (a) When a = 0, R = vP2 + H'"2 and ^ ~ .. (b) When a = jj, # = P - 1^... | 5 | [
-0.11083984375,
0.05810546875,
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0.0277099609375,
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-0.02734375,
-0.0947265625,
-0.003463745... | 9,538 | 9538 | |
Even Number of Heads
Associated Topics || Dr. Math Home || Search Dr. Math
Even Number of Heads
Date: 02/12/2002 ... | 5 | [
0.01239013671875,
0.057373046875,
0.044921875,
0.064453125,
-0.0059814453125,
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-0.0244140625,
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0.00118255615234375,
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-0.... | 9,539 | 9539 | |
Converting and Graphing Coordinates
Date: 5/28/96 at 21:25:26
From: Anonymous
Subject:Converting Between Rectangular and Polar Coordinates
I want to know how to convert decimals to polar coordinates, and vice
versa. Also, how would you graph it on a x,y coordinate?
For example, graphing (-1, 3pi/6).
Nanci Echon
D... | 4 | [
-0.025146484375,
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-0.06689453125,
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0.06787109375,
0.0517578125,
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0.038330078125,
-0.0087890625,
-0.09716796875,
-0.0034942626953125,
... | 9,540 | 9540 | |
Binary Sequences of Length 2n
up vote 19 down vote favorite
4
I had posted an urn probability problem that didn't have good motivation. I'd like to try to explain the motivation here, and reintroduce the problem.
Consider binary sequences of length $2n$. Let's say we put a marker in such a sequence as soon as we see ... | 5 | [
-0.0036163330078125,
-0.0267333984375,
0.06591796875,
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0.009521484375,
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0.021240234375,
0.0235595703125,
-0.01531982421875,
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0.005218505859375,
-0.0172119140625,
-0.0537109375,
0.1005859375,
0.031494... | 9,541 | 9541 | |
Calculation of ground resistance and concept of ground resistance
The actual grounding resistance can not be easily calculated. However, the grounding resistance wanted to know whether there is any nature. To assume a uniform soil, I tried to calculate the required
ground resistance. Since this method is my own though... | 4 | [
0.004608154296875,
0.0140380859375,
0.09521484375,
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0.0264892578125,
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0.0966796875,
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0.0067138671875,
0.0390625,
0.02978515625,
-0.06396484375,
-0.052734375,
-0.034423828125,... | 9,542 | 9542 | |
CS145 Lecture Notes (6) -- Relational Database Design
For all but the very simplest database applications, there are many, many different relational database "designs" (schemas) that can be used to store the relevant data.
β’ Q: Can one schema be much better than another?
β’ A: Often, yes
Relational database des... | 5 | [
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0.060791015625,
-0.0361328125,
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0.000881195068359375,
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0.0284423828125,
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0.06396484375,
0.037109375,
-0.002975463867... | 9,543 | 9543 | |
Oblique Asymptotes
Date: 04/03/2002 at 23:47:45
From: Jo
Subject: Oblique limits
Hi,
I'm really stuck on how to calculate oblique limits. Vertical and
horizontal limits are fine, but I don't even know where to start with
oblique ones. For example this question.
x^2 / (x-3)
It seems simple but there is an obliq... | 5 | [
0.0216064453125,
0.0390625,
-0.02783203125,
-0.0014190673828125,
-0.029052734375,
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0.060791015625,
0.0106201171875,
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0.004638671875,
0.01177978515625,
0.08056640625,
-0.00146484375,
0.015380859375,
-... | 9,544 | 9544 | |
Use of Bernoulli's Equation
October 29th 2009, 07:19 AM
danoinferno3
Use of Bernoulli's Equation
I have a problem I am working on:
xy - dy/dx = e^(-3x^2/2) * y^4
If I solve this using the Bernoulli equation then I have n = 4, 1-n = 3.
I make the substitution v = y^3 , y = v^1/3
I'm have a lit... | 4 | [
-0.0179443359375,
-0.012939453125,
0.02197265625,
-0.01513671875,
-0.004852294921875,
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-0.009521484375,
-0.006805419921875,
-0.030517578125,
0.08056640625,
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-0.0230712890625,
0.0064697265625,
0.00750732421875,
0.01806640625,
-0.08740234375... | 9,545 | 9545 | |
Logarithms, Exponentials, Many questions!
November 22nd 2008, 04:19 PM #1
Logarithms, Exponentials, Many questions!
I need help on these questions:
Calculate the exact value of H if:
logH = (log2^1/2) / log2
Also, I scanned these that I don't understand:
If you are having trouble reading th... | 4 | [
0.037841796875,
0.05224609375,
0.009521484375,
0.035400390625,
0.046142578125,
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0.07763671875,
-0.01141357421875,
0.036865234375,
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-0.06640625,
-0.01953125,
-0.0010223388671875,
-0.01446533203125,
0.036376953125,
-0.11669921875,
-0.074... | 9,546 | 9546 | |
How big is the proper class of all sets?
up vote 10 down vote favorite
4
Let $\operatorname{ZFC}^{-}$ be the theory of $\operatorname{ZFC}$ minus the axiom of foundation and define the proper classes $G$ and $V$ as follows:
$G:=$ The proper class of all sets.
$V:=$ The proper class of Von neumann cumulative heirachy... | 5 | [
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0.01239013671875,
0.02978515625,
0.0859375,
-0.03295... | 9,547 | 9547 | |
Need help please ! [urgent]
November 25th 2007, 04:51 PM #1
Newbie
Joined
Nov 2007
Posts
13
Hi there
Please help me solve these problems. I tried, but I can't figure them out.
1) If $y$ is a differentiable function of $x$ then the slope of the tangent to the curve $xy-2y+4y^2=6$ at the point whe... | 5 | [
-0.03759765625,
-0.047119140625,
0.025634765625,
-0.07421875,
0.015869140625,
0.019287109375,
0.0264892578125,
0.08203125,
-0.03076171875,
-0.0244140625,
0.06982421875,
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0.0257568359375,
-0.038330078125,
-0.0164794921875,
0.06640625,
-0.1142578125,
-0.013671875,
-... | 9,548 | 9548 | |
Catenary differential equation (suspension bridge)
July 13th 2011, 05:31 PM #1
Newbie
Joined
Jul 2011
Posts
1
Catenary differential equation (suspension bridge)
So I am getting stuck trying to solve this. pgA and Tx are constants
d^2h/dx^2 = (pgA/Tx)*sqrt(1+(dh/dx)^2)
I substitute dh/dx = sinh(u... | 4 | [
-0.037109375,
0.04248046875,
0.10498046875,
0.005584716796875,
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0.048583984375,
-0.056640625,
-0.0133056640625,
-0.007080078125,
0.06... | 9,549 | 9549 | |
mathschallenge.net
Prime Partner
Problem
Given that $p$ is an odd prime and $n$ is a positive integer, prove that there always exists a value of $n$ for which the expression $n^2 + np$ is a perfect square.
For example, when $p = 7$, $9^2 + 9 \times 7 = 144 = 12^2$.
Furthermore, prove that this value of $n$ is uniqu... | 5 | [
-0.007232666015625,
0.0673828125,
0.043701171875,
0.0478515625,
-0.0294189453125,
0.15234375,
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0.002044677734375,
0.0225830078125,
-0.049560546875,
0.011474609375,
0.06884765625,
-0.02685546875,
0.08154296875,
-0.039794921875,
-0.1064453125,
-0.028076171875,
0.02319335... | 9,550 | 9550 | |
Transformation about a line other than an axis
June 9th 2009, 08:45 AM #1
Member
Joined
Mar 2009
From
Alberta
Posts
173
Transformation about a line other than an axis
Hey, I'm sorry if this is in the wrong place, I wasn't too sure where to put a transformation question. No idea what I'm doing wrong, ... | 4 | [
-0.03173828125,
-0.03173828125,
-0.057861328125,
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0.04296875,
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-0.035400390625,
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0.0654296875,
-0.0263671875,
0.0005912780... | 9,551 | 9551 | |
Algebra writing equations
July 13th 2007, 01:57 AM #1
Sean.A.C
Guest
Algebra writing equations
Taken from practise exam:
QUESTION SIX
Peter has more than twice as many CDs as Mary.
Altogether they have 97 CDs.
Write a relevant equation, and use it to find the least number of CDs that Peter coul... | 4 | [
0.029541015625,
0.050048828125,
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0.080078125,
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0.072265625,
0.021240234375,
0.07666015625,
0.0673828125,
-0.02392578125,
0.03051757812... | 9,552 | 9552 | |
Posts by
Posts by GG
Total # Posts: 60
the cell
Which of these is the smallest structure? A. Dipeptide B. Amino acid C. Protein D. Polypeptide
gg
if company 2 lease/lease maintenance totals $125,000 for the year and the company 1 spends 27% for the least maintenance how much is company 1 paying for their lease/main... | 5 | [
-0.061767578125,
0.006317138671875,
-0.026123046875,
-0.0849609375,
-0.01385498046875,
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0.019775390625,
-0.032958984375,
0.0390625,
0.051513671875,
0.00152587890625,
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0.0220947265625,
-0.0478515625,
0.1337890625,
-0.038330078125,
0.00... | 9,553 | 9553 | |
Enumerating tree-like chemical graphs with given upper and lower bounds on path frequencies
Abstract
Background
Enumeration of chemical graphs satisfying given constraints is one of the fundamental problems in chemoinformatics and bioinformatics since it leads to a variety of useful applications including
structure d... | 4 | [
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0.019775390625,
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0.04638671875,
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0.044189453125,
-0.0224609375,
0.09619140625,
-0.018310546875,
0.01879882... | 9,554 | 9554 | |
Paper Patterns for Building Cones
Date: 11/03/2003 at 16:23:29
From: mike
Subject: how do I make a pattern for building a cone
I am building a cone shaped fish trap for teaching kids about fish
living in the salt marsh. The mouth will be 26" in diameter and the
overall length will be 72". Is there a way to make a p... | 4 | [
-0.031494140625,
0.111328125,
-0.005889892578125,
-0.050048828125,
-0.1240234375,
-0.01202392578125,
-0.0390625,
0.060302734375,
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0.040283203125,
-0.0206298828125,
-0.002105712890625,
-0.03515625,
0.0927734375,
-0.03076171875,
-0.0296630859375,
-0.146484375,
0.07177... | 9,555 | 9555 | |
Chain of Sine and Cosine
March 20th 2009, 11:55 PM #1
Chain of Sine and Cosine
As I was messing around in Maple (yes I'm a nerd), I noticed something.
It appears as if the infinite chain $\sin(\cos(\sin(\cos(\sin(\cos(.....(\sin(\cos(x))) ))))))$ converges for all x.
It appears to be converging to a num... | 4 | [
-0.08447265625,
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Homework Help
Posted by livy on Tuesday, May 8, 2012 at 8:02pm.
( egyptian fractions are fractions where the numerator can only be one) find two egyptian fractions where when added together it equalls 11/32
β’ math!!!!!!!!!!!!!!! - Reiny, Tuesday, May 8, 2012 at 8:46pm
let them be 1/a and 1/b
we are given
... | 4 | [
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0.0595703125,
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-0.03759765625,... | 9,557 | 9557 | |
Answer to criticism of my treatment of nonscattering of sound by
ASA 127th Meeting M.I.T. 1994 June 6-10
2pPA12. Answer to criticism of my treatment of nonscattering of sound by sound.
Peter J. Westervelt
Dept. of Phys., Brown Univ., Providence, RI 02912
Following a suggestion by Professor M. Korman, the transient... | 4 | [
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0.0... | 9,558 | 9558 | |
Inverse of x/(xΛ2-4)
July 28th 2011, 04:15 PM
nicksbyman
Inverse of x/(xΛ2-4)
Attempted solution:
y=x/(xΛ2-4)
let y = inverse of y
x=y/(yΛ2-4)
xyΛ2-4x = y
xyΛ2-y-4x = 0
a = x, b = -1, c = -4x
y = (1 +/- sqrt(1-(4x)(-4x)))/(2x)
= (1+/- sqrt(1+16xΛ2))/2x, which is my solutio... | 5 | [
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... | 9,559 | 9559 | |
non-commutative finite rings
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
This is probably simple. Is there a finite non-commutative ring $R$ with identity in which all of its ideals are two-sided !?
up vote 5 down v... | 5 | [
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[SOLVED] Proof divisible by 64
April 12th 2005, 06:41 PM
Tatanka
[SOLVED] Proof divisible by 64
Can someone point me in the right direction of solving the following problem:
Prove that for any postive integer n, the value of the expression 3^(2n+2)-8n-9 is divisible by 64.
April 19th 2005, 04:32 AM
hpe
... | 4 | [
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... | 9,561 | 9561 | |
Math Forum Discussions - Re: Building an Equation to find (Maximum Y) ie Highest Point on a curve!
Date: Sep 12, 2013 3:03 AM
Author: quasi
Subject: Re: Building an Equation to find (Maximum Y) ie Highest Point on a curve!
mervynmccrabbe@gmail.com wrote:
>
>x^4 + y^4 + a(x^2) - a(y^2) + 2(x^2)(y^2) - bxy + c = 0
>
>If... | 4 | [
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0.01068115234375,
-... | 9,562 | 9562 | |
Maximum Likelihood Estimate
July 17th 2008, 03:55 AM
dagmary
Maximum Likelihood Estimate
I need help with this question :( :
Suppose a town has bicycles with license numbers 1, . . . , N . You observe
5 bicycles and the highest number you observe is 60. What is the MAximum Likelihood Estimate(MLE) for ... | 5 | [
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0.04150390625,
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-0.... | 9,563 | 9563 | |
EQUIVALENT CONDUCTANCE
ELECTROCHEMISTRY
Electrochemistry deals with the study of electrochemical processes and their applications which involve:
i) the conversion of electrical energy into chemical energy and
ii) the conversion of chemical energy into electrical energy.
It is possible to carry out a non spontaneou... | 4 | [
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0.0510253... | 9,564 | 9564 | |
Standard Error of a Binomial Distribution
March 31st 2011, 06:21 AM
ProphetofProfit
Standard Error of a Binomial Distribution
Checked the FAQ and there is nothing that says 'no gambling problems' so this question might be ok. I am trying to create a soccer model using shots on target and 'conversion rate' (CR) w... | 5 | [
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0.037353515625,
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-0.0771484375,... | 9,565 | 9565 | |
Mostly linear problems i had trouble with
December 28th 2007, 11:17 PM
chaneliman
Mostly linear problems i had trouble with
Okay, so i did all the questions in the chapter and these are the questions i had trouble with. If u don't might could u show ur working becos i know wot the answes r, i just don't know how... | 4 | [
-0.0810546875,
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0.07421875,
-0.125,
-0.0712890625,
-0.049072265625... | 9,566 | 9566 | |
Debt Concepts
Understanding the concept of Modified Duration
"Modified Duration" is a widely used measure for evaluating interest rate risk associated with bonds or bond portfolios. While it is an important and useful tool in investment decision making, it is
often not well understood by retail investors. In this edit... | 4 | [
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0.01269... | 9,567 | 9567 | |
prove using integration by parts
February 12th 2009, 12:25 PM
valkyrie
prove using integration by parts
I tried doing this, but ended up at a dead end.
Use integration by parts to show that the integral from 0 to 1 of f''(x)g(x)dx = the integral from 0 to 1 of f(x)g''(x)dx.
suppose f(0)=g(0)=0 and f(1)... | 4 | [
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... | 9,568 | 9568 | |
Homework Help
Posted by amaa on Friday, November 30, 2012 at 9:19pm.
Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer.
tan ΞΈ = β sqrt 3/3
β’ precalculus - Reiny, Friday, November 30, 2012 at 11:05pm
tanΓ = -β3/3
from the 30-60-90 triangle, you should recognize ... | 4 | [
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0.0118408203125,
-0.08154296875,
-0.03100585... | 9,569 | 9569 | |
solve the system:
1.) y= 2/3x-3 , y=-5/6x+7
- Homework Help - eNotes.com
solve the system:
1.) y= 2/3x-3Β Β ,Β Β y=-5/6x+7
Β
Given:
y = 2/3x - 3
And:
y = -5/6x + 7
Since left hand side of both equation is same, the right hands side of these equation will be equal. Thus:
2/3x - 3 = -5/6x + 7
==> 2/3x + 5/... | 4 | [
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0.02001953125,
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-0.0810546... | 9,570 | 9570 | |
Cut-distance between two Erdos-Renyi random graphs
up vote 4 down vote favorite
Consider two Erdos-Renyi random graphs $G_1,G_2$ on $n$ nodes, with the edges in each graph generated independently at random with probability $1/2$. My question is about the cut-distance between
these two graphs. Recall that the cut-dista... | 5 | [
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0.099609375,
... | 9,571 | 9571 | |
Problem of a function
January 26th 2007, 09:39 AM #1
Super Member
Joined
Mar 2006
Posts
705
Thanks
2
Problem of a function
Suppose that $f:\mathbb{R}\mapsto\mathbb{R}$ is a continuous, bounded, strictly increasing function.
Questions:
(a) Show that there is a point $a_{1}\epsilon\mathbb{R}$... | 5 | [
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0.0286865234375,
0.01806640625,
-0.056... | 9,572 | 9572 | |
Confirm My Answers? (Varied Problems)
May 8th 2008, 12:47 AM #1
Newbie
Joined
Feb 2008
Posts
13
Confirm My Answers? (Varied Problems)
UPDATE: Thanks for the help but since I didn't get the confirmation in the time needed I went for tutoring instead.
Last edited by riker; May 8th 2008 at 05:40 PM.
... | 4 | [
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0.08251953125,
-0.0927734375,
-0.01306... | 9,573 | 9573 | |
Unitary Matrix problem
October 28th 2010, 12:01 PM #1
Junior Member
Joined
Oct 2010
From
Zulu-5
Posts
60
Unitary Matrix problem
I've been strugling with the following for a while. Will appreciate any direction.
If U is a unitary matrix and (U+iI) is hermitian, prove that U=-iI. (U is obviously s... | 5 | [
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0.05810546875,
-0.04980... | 9,574 | 9574 | |
Deriviative of function
August 14th 2009, 11:22 AM #1
Senior Member
Joined
Nov 2008
Posts
425
Deriviative of function
If a force F is defined by F=k(e^(-s) -6e^(-2s)), where S is the distance between two objects, then prove (d^(2)F)/(d(S)^2)=F-18ke^(-25).
I'm not sure what d^2 is supposed to mean..... | 5 | [
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0.08837890... | 9,575 | 9575 | |
number theory
Prove that if gcd(a,b)=1 and if c divides b, then gcd(a,c)=1.
Suppose gcd(a,b) = 1. That is, b=1k and a = 1m for some integers k,m. Suppose b|c that is, c = bx for some integers x. Then c = (1k)x where 1k is an integer. I think now you need to show that k = 1
because a = 1m (and so 1 is the largest divis... | 4 | [
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0.051513671875,
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0.049560546875,
0.00089645385742187... | 9,576 | 9576 | |
Finding the Dimensions of a Room
Date: 12/5/95 at 20:54:44
From: Anonymous
Subject: Fariba's Nightclub - High School word problem
My daughter's Algebra I teacher gave her students this word problem
as a challenge:
Mrs. Fariba Suarez has decided to use the profits from her
swimwear company to open a night club. Aft... | 4 | [
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0.020751953125,
-0.0556640625,
0.0213623046... | 9,577 | 9577 | |
Proving limits
November 29th 2010, 06:20 AM
chr91
Proving limits
Prove (from the definition) that if f(x) tends to L as x tends to a then 2f(x) tends to 2L as x tends to a
Now we can suppose (For all epsilon>0) (There exists delta >0) (For all x E X)
0<|x-a|<delta implies |f(x) - L| < epsilon.
Now ... | 4 | [
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0.029052734375,
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0.01348876953125,
0.0157470703125,
-... | 9,578 | 9578 | |
Vector - straight lines
November 12th 2008, 07:56 AM
geton
Vector - straight lines
The straight lines $l_1$ and $l_2$ have vector equations r = (i + 4j + 2k) + t(8i + 5j + k) and r = (i + 4j + 2k) + s(3i + j) respectively. P is the point with coordinate (1, 4, 2) & Q is the
point with coordinate (9, 9, 3).
... | 4 | [
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0.0006103515625... | 9,579 | 9579 | |
Categorifying Quantum Mechanics
John Baez
January 29, 2003
These are some notes for the first of three talks I gave at the Australian Category Theory Seminar. They are very rough; the actual talk was of course infinitely clearer and more entertaining. For
more details, see my paper with James Dolan, From Finite Sets... | 4 | [
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... | 9,580 | 9580 | |
Mach-Zehnder Modulators Serve Radio Over Fiber
By using several Mach-Zehnder modulators and an optical delay line, it is possible to provide the frequency multiplication needed for creating millimeter-wave frequencies.
See sidebar: What Is Radio Over Fiber?
Millimeter-wave wireless communications networks can take ad... | 4 | [
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0.044921... | 9,581 | 9581 | |
Change of basis?
March 11th 2010, 12:25 PM
chickeneaterguy
Change of basis?
Let B = {(1, -4), (-2, 9) and notice that B is a basis for R2. Therefore each (x,y) in R2 can be written as a linear combination of the vectors in B. If (x,y) = a(1,-4) + b(-2,9) then the
coordinates of (x,y) relative to the basis B ... | 5 | [
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0.032470703125,
0.0419921875,
0.06201171875,
-0.0966796875,
0.02197265625,
... | 9,582 | 9582 | |
inner product spaces
October 18th 2008, 10:24 PM
bamby
inner product spaces
Can you please, help me with this
Suppose V and W are finite dimensional inner product spaces with orthogonal bases B1 and B2, respectively. Let T: V->W is linear, so we know that T*: V->W (linear) exists and is unique. Prove
tha... | 4 | [
-0.0859375,
0.01116943359375,
0.01458740234375,
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0.00628662109375,
0.09521484375,
-0.0341796875,
-0.035888671875,
-0.0390625,
-0.08642578125,
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-0.07177734375,
0.0189208984375,
0.1142578125,
-0.005645751953125,
-0.00... | 9,583 | 9583 | |
Applied Linear Equations: Distance Problem - Concept
Brightstorm is like having a personal tutor for every subject
See what all the buzz is about
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Applied Linear Equations: Distance Problem - Concept 12,548 views
To solve rate word problems, knowledge of solving systems of equations is necessary. Rate w... | 4 | [
0.05126953125,
0.047607421875,
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Math Help
October 8th 2007, 07:42 PM #1
new puzzle
You are equipped with two 2's, three 3's, and the ability to combine them using addition, subtraction, multiplication, division, and exponentiation.
Create all of the integers from 37 to 67 (inclusive).
You may use any number of parentheses to control ... | 4 | [
-0.021728515625,
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-0.140625,
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0.0... | 9,585 | 9585 | |
Jacobs Physics
We're just now finishing with electricity concepts -- fields, potentials, resistors, capacitors. Coincidentally for me, we have a couple days off for "long winter weekend" starting tomorrow. This is
the perfect time to attempt to cement the tough-to-remember rules we've learned over the past month.
On M... | 5 | [
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Integral of Trigonometric Functions
August 15th 2010, 03:57 AM #1
Newbie
Joined
Aug 2010
Posts
9
Integral of Trigonometric Functions
Hi, sorry for not fixing my profile but I'll get right on it after posting this problem. I'm sure there is a rule about Latex here but forgive me if I will post the problem... | 5 | [
-0.040771484375,
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0.016845703125,
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0.08447265625,
0.03015136718... | 9,587 | 9587 | |
Measuring similarities between transcription factor binding sites
Abstract
Background
Collections of transcription factor binding profiles (Transfac, Jaspar) are essential to identify regulatory elements in DNA sequences. Subsets of highly similar profiles complicate large scale
analysis of transcription factor bindi... | 4 | [
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0.... | 9,588 | 9588 | |
Gauss-Elimination Problems
September 17th 2012, 07:30 AM #1
Junior Member
Joined
Sep 2012
From
NY
Posts
32
Gauss-Elimination Problems
I stuck with these 2 problems for a long time
Question 1: Give all solutions, if any, of
x + y =1
sin(x - y) =1/2
with 0 less than or equal to X and... | 5 | [
-0.046630859375,
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0.0390625,
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0.031494140625,
-0.03466796875,
-0.01397705078125,
-0.0849609375,
-0.... | 9,589 | 9589 | |
[SOLVED] Absolute Values and Inequalities
February 2nd 2009, 05:11 PM #1
Junior Member
[SOLVED] Absolute Values and Inequalities
My Answer
greater than or equal to 0
x can be any real number, because the absolute value of any number is bigger or equal to 0.
greater than or equal to 0
x can be any... | 4 | [
0.03662109375,
0.029541015625,
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0.08203125,
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0.11572265625,
0.045654296875,
0.0101318359375,
0.0157470703125,
0.0810546875,
-0.0927... | 9,590 | 9590 | |
Using Properties to determine derivative and original equation
March 1st 2009, 09:30 AM #1
Junior Member
Joined
Feb 2009
Posts
36
Using Properties to determine derivative and original equation
A function f is defined for all real numbers and has the following properties.
(i) f(1)=5
(ii) f(3)=21
... | 5 | [
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0.01123046875,
0.03466796875,
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0.0284423828125... | 9,591 | 9591 | |
Proving limit exists
November 2nd 2009, 04:12 PM #1
Proving limit exists
Well the problem reads: Suppose $f: (a, b) \rightarrow R$ and $\lim_{x\to\infty}f(x_n)$ exists for every sequence $x_n$ (where n goes from $1 \to \infty$) in $(a, b)$ such that $\lim_{x\to\infty}
x_n = a$. Prove that $\lim_{x\to a^+}f(x_... | 4 | [
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0.0234375,
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0.04736328125,
0.004486083984375,
-0.0262... | 9,592 | 9592 | |
Math Help
January 10th 2009, 04:59 AM #1
Member
Joined
Jan 2008
Posts
132
Vectors
Q1: If a = i + 2j - k and b = j + k, find a unit vector perpendicular to both a and b.
===
Q2: The points P and Q have position vectors a + b and 3a - 2b respectively when referred from the origin O. Given that O... | 4 | [
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0.0869140625,
0.004638671875,
0.0032653808593... | 9,593 | 9593 | |
quadratic word problem
November 14th 2008, 05:55 AM
euclid2
quadratic word problem
a stone is tossed from a bridge into the river below. its path is represented by h=-2t^2+7t+9 where h is height(in metres) and t is time (in seconds)
a) what is the maximum height and how many seconds does it take to reach th... | 4 | [
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0.0234375,
-0.00244140625,
... | 9,594 | 9594 | |
Chapter 7
In section 3-5 we used the GDP deflator to calculate real GDP. We then computed the percentage change in real GDP for each pair of consecutive years and used the Descriptives routine to compute
the average percentage growth in real GDP. For the period 1930-1996, the average annual change in real GDP ... | 4 | [
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... | 9,595 | 9595 | |
Precise definition of a limit question
September 18th 2011, 10:09 AM #1
Newbie
Joined
Sep 2011
Posts
10
Precise definition of a limit question
For the limit
lim
x β 2
(x^3 β 4x + 7) = 7
illustrate the definition by finding the largest possible values of Ξ΄ that correspond to Ξ΅ = 0.2 and Ξ΅... | 5 | [
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0.0191650390625,
... | 9,596 | 9596 | |
Minimal polynomial
October 7th 2009, 02:57 PM #1
Newbie
Joined
Oct 2009
Posts
6
Minimal polynomial
Find the minimal polynomial given $T:\mathbb R^2\to\mathbb R^2$ where $T(x,y)=(x+y,x-y).$
I found the associated matrix, which is $A=\left[\begin{array}{rr}1&1\\1&-1\end{array}\right].$
Now I need... | 4 | [
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0.051513671875,
0.00445556640625,
0.01544189453125,
-0.02880859375... | 9,597 | 9597 | |
Finding standard matrix for T
July 31st 2008, 09:51 AM #1
Newbie
Joined
Jul 2008
Posts
1
Finding standard matrix for T
This problem was on one of my tests, but I can't find any similar problems in the book or in HW to help me figure it out, and I'm crap at using the book to help solve problems
Let t... | 4 | [
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-0.002227783203125,
0.00372314453125,
... | 9,598 | 9598 | |
Analytical Mechanics
298 ANALYTICAL MECHANICS
Putting equation (II) in the form
and integrating we obtain
"1
sn"β = u+d,
VQ
or x = β sin (ut + 5)
CO
J+S), (III)
where <5 is the constant of integration and a = ~ β’
CO
227. Displacement. β The d... | 4 | [
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0.011... | 9,599 | 9599 |