content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Decimal Degrees to Degrees-Mins-Secs
GPS tells you where you are in Decimal Degrees (DD), with positive degrees being north latitude or east longitude, and negative degrees being south latitude or west longitude. Most charts (I was a
nautical type before I was an Excel type. Think maps if that’s not you) tell you posit... | 4 | [
0.0888671875,
-0.019287109375,
0.01068115234375,
-0.033203125,
-0.0269775390625,
-0.0269775390625,
-0.07177734375,
0.07763671875,
0.01806640625,
-0.028076171875,
0.041748046875,
-0.056884765625,
0.047119140625,
0.006622314453125,
0.043701171875,
-0.12060546875,
0.07080078125,
0.020... | 4,100 | 4100 | |
an
Conway polynomials for finite fields
Conway polynomials were defined by R. Parker. Their purpose is to provide a standard notation for elements in a finite field GF(p^n) with p^n elements, p being a prime.
This is for example used within computer algebra systems to have data of finite field elements which can easi... | 4 | [
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0.04150390625,
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0.0211181640625,
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0.006195068359375,
0.0107421875,
0.047607421875,
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0.047607421875,
0.046875,
-0.0047607421875,
-0.0595703125,
-0.0341796875,
-0.055419921875,
0.002685546875... | 4,101 | 4101 | |
Initial Value Problems
September 15th 2009, 02:19 PM
Smac
Initial Value Problems
1. y(dy/dx) = (y^3 - 1) (x/y) e^(ax^2) ; y(0) = -1
a > 0 is fixed constant
I solved to split up the x and y components and got:
(y^2)/(y^3 -1) dy = (xe^ax^2) dx
n(y) = m(x) (using equation above i made this one)
... | 5 | [
-0.061279296875,
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-0.007080078125,
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0.0120849609375,
0.033447265625,
0.01190185546875,
-0.04345703125,
-0.02... | 4,102 | 4102 | |
Without Calculator
January 23rd 2007, 05:10 PM #1
Banned
Joined
Jan 2007
Posts
315
Without Calculator
How do I find the appoximation of square roots that are not perfect squares WITHOUT a calculator?
SAMPLES:
(1) sqrt{21} =
(2) sqrt{79} =
DO NOT USE A CALCULATOR.
Thanks!
$\s... | 4 | [
0.072265625,
0.0247802734375,
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0.0306396484375,
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0.0419921875... | 4,103 | 4103 | |
Application of differentiation
March 18th 2007, 03:31 PM
camherokid
Application of differentiation
A baseball diamond is a square with side 90 ft. A batter his the balls and runs toward first base with a speed of 24ft/s.
a. At what rate is his distance from the second base decreasing when he is halfway to fi... | 5 | [
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0.078125,
0.0167236328125,
0.044189453125,
-0.02197265625,
0.038330078125,
-0.0559... | 4,104 | 4104 | |
MathGroup Archive: November 1998 [00082]
[Date Index] [Thread Index] [Author Index]
Re: I have A Problem
• To: mathgroup at smc.vnet.net
• Subject: [mg14656] Re: [mg14621] I have A Problem
• From: Jurgen Tischer <jtischer at col2.tele... | 5 | [
-0.0634765625,
0.007659912109375,
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0.0380859375,
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0.03955078125,
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0.05078125,
0.07275390625,
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0.048828125,
0.032958984375,
0.0198974609375,
-0.14453125,
-0.06298828125,
... | 4,105 | 4105 | |
Compound Angle Formulas
March 28th 2009, 04:06 PM
skeske1234
Compound Angle Formulas
Can someone describe to me clearly, how you would solve these questions:
1. Angles x and y are located in the first quadrant such that sinx=4/5 and cosy=7/25.
a) determine an exact value for cos x
b) determine an ex... | 4 | [
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0.06689453125,
0.095703125,
0.02099609375,
-0.0751953125,
0.0223388671875,
... | 4,106 | 4106 | |
Odd Triangle
August 22nd 2007, 06:02 AM #1
Odd Triangle
I have a triangle HPN with two side lengths HP = 54km and HN = 75km and included angle 15 degrees. Let the angles opposite HP and HN be $\phi$ and $\theta$ respectively. By use of the cosine rule
I get
$PN=\sqrt{54^2+75^2-2(54)(75) \cos {15}}=26.78k... | 4 | [
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0.036621... | 4,107 | 4107 | |
General Solution of a PDE
August 17th 2012, 05:27 PM
princessmath
General Solution of a PDE
Find the general solution of the following PDE.
u[xxyy] = 0
I know I have to go from right to left i.e integrate with respect to y, then y then x and x.
So here it goes :)
u[xxy = ]F(x) Where F(x) is a... | 5 | [
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0.025390625,
-0.09716796875,
-0.0568847656... | 4,108 | 4108 | |
Excel Regression Example
Excel - A Regression Example
Simple linear regression analysis can be easily completed using Excel. The Data Analysis... option of the Tools menu provides what's necessary. If that option is not available in t... | 4 | [
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0.0122070... | 4,109 | 4109 | |
Find the value of Z^69
Write the complex number on the form $z=re^{\theta i}$, and then compute $z^{69}=r^{69}e^{69\theta i}.$
Hello, zorro! $\text{If }z = \frac{\sqrt{3}+1}{2}, \text{ find the value of }z^{69}$ Convert $z$ to polar form: . $z \:=\:\cos\tfrac{\pi}{6} + i\sin\tfrac{\pi}{6}$ Then use DeMoivre's Theorem:... | 5 | [
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0.030029296875,
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Frank Morgan's Math Chat - Rolling a Die Until Every Face Has Appeared
January 7, 1999
OLD CHALLENGE (Steve Jabloner). How many times do you think you need to roll a normal die to be 90% sure that each of the six faces has appeared at least once? Why?
ANSWER. It takes 23 rolls, as Al Zimmerman discovered in a compute... | 5 | [
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0.0390625,
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0.033935546875,
-0.040283203125,
-0.0698... | 4,111 | 4111 | |
Help with understanding congruence problems
Hello, I am just starting out with Number Theory and am struggling to work out congruence problems. Im sure this one will be easy for most of you, but can you please quickly walk me through it? 3956x
$\equiv$ 7 (mod 2351)
Can anyone actually get the answer for this? Ive been... | 5 | [
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0.006134033203125,
-0.053... | 4,112 | 4112 | |
Errors of numerical approximations
Lecture 1.2:
Errors of numerical approximations
round-off and truncation errors. Inaccuracies of numerical computations due to the errors result in a deviation of a numerical solution from the exact solution, no matter whether the latter is known
explicitly or not. To examine the eff... | 4 | [
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0.0... | 4,113 | 4113 | |
prove that u is open
December 3rd 2011, 06:48 PM #1
Senior Member
Joined
Jan 2010
Posts
273
prove that u is open
Prove that $U \subset M$ is open if and only if whenever $(Xn)^\infty_{n=1}$ is a sequence of elements of M converging to some $x \in U$, then there exists $N \in N$, such that $Xn \in U$for
... | 5 | [
0.0098876953125,
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0.0629... | 4,114 | 4114 | |
[QUIZ] FizzBuzz (#126) [solution #1]
And, here's my second one, written in a subset of Ruby which corresponds
to a pure (though strict) lambda calculus, building up numbers, strings,
and everything else entirely from scratch. (Okay, I cheated a little
bit for actual IO)
Sadly Church numerals are very slow for non-t... | 4 | [
-0.0224609375,
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0.07470703125,
-0.020263671875,
-0.0049743652343... | 4,115 | 4115 | |
Determinant of linear transform with ordered basis is independent of the choice
January 27th 2011, 07:16 PM #1
Determinant of linear transform with ordered basis is independent of the choice
Given a basis $\beta$ for $V$ define $\det(T) = \det([T]_\beta)$. Prove that the definition is independent of choice of an ... | 5 | [
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-0.01263427734375,
-0.0... | 4,116 | 4116 | |
Walking Through the Bolzano-Weierstrass Theorem
(Note: see here for a simpler version of this proof.)
Economic theory relies pretty heavily on a handful of mathematical proofs. One of the most important for proving the existence of equilibria is the Bolzano-Weierstrass theorem.
In this post I'll give a basic explana... | 5 | [
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-0.0... | 4,117 | 4117 | |
Simple 4 equation 4 variable
The main page for solving systems of linear equations on the TI-85 and TI-86.
The previous example page covers a Simple 3 equation 3 variable situation.
The next example page covers a Simple 3 equation 3 v... | 5 | [
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0.046875,
-0.1181640625,
-0.075195312... | 4,118 | 4118 | |
Contraction mapping of a cone, show origin must move.
August 12th 2011, 12:05 PM #1
Newbie
Joined
Aug 2011
Posts
5
Contraction mapping of a cone, show origin must move.
Let Y be the subspace {(x,0)|x $\in$$\mathbb{Q}$, 0 $\leq$ x $\leq$ 1} of $\mathbb{R}^2$ and let X be the cone on Y with vertex (0,1), i... | 5 | [
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-0.039794921875,
-0... | 4,119 | 4119 | |
Proof of intersect between 2 elements of group G
May 19th 2008, 12:57 AM #1
Member
Joined
Jun 2007
Posts
131
Proof of intersect between 2 elements of group G
Hi All
How do I prove the following:
Suppose that G is a group with elements a and b of orders p and q respectively, where p and q are di... | 5 | [
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0.08447265625,
-0.0546875,
... | 4,120 | 4120 | |
Conjugate subgroups.
November 26th 2009, 11:43 AM
platinumpimp68plus1
Conjugate subgroups.
Let H be a subgroup of G, with index p (prime). What are the possible numbers of conjugate subgroups of H?
I'm pretty lost. I think it has something to do with Sylow's Theorems, and the fact that if p=|G|/|H|, so then... | 5 | [
0.0201416015625,
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0.06640625,
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-0.045654296875,
0.025390625,
-0.027099609375,
-0.05419921875,
... | 4,121 | 4121 | |
Numerical integration
From Wikipedia, the free encyclopedia
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to
describe the numerical solution of differential equations. T... | 4 | [
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0.0004673004150390625,
-0.035888671875,
-0.0296630859375,
-0.01831054... | 4,122 | 4122 | |
Today's Puzzle
Written on 3:23 am by Vja Students
You have twelve marbles. Eleven of the marbles are of equal weight, but one is heavier or lighter. You have a balancing scale you can use to find this marble and figure out if it weighs more or less
than the others. What is the minimum number of weighings required to d... | 4 | [
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-0.036376953125,
0.05322265625,
0.125,
... | 4,123 | 4123 | |
Derivative
January 17th 2010, 04:31 AM
Tweety
Derivative
Quote:
Given that $x = sec\frac{y}{2}$
$0 \leq y < \pi$
show that $\frac{dy}{dx} = \frac{2}{x \sqrt{x^{2}-1}}$
$\frac{dx}{dy} = \frac{1}{2} sec\frac{y}{2} tan\frac{y}{2}$
$\frac{dy}{dx} = \frac{1}{ \frac{1}{2} sec\frac{y}{2} tan\fr... | 5 | [
0.02197265625,
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-0.0023345947265625,
0.01226806640625,
-0.003... | 4,124 | 4124 | |
Which distribution would this be?
December 23rd 2009, 10:12 AM #1
Newbie
Joined
Sep 2009
Posts
18
Which distribution would this be?
Someone receives 0,1 or 2 letters to his home per day with Probability 0.2, 0.7, and 0.1 respectively.
If a year consists of 240 days in which he can receive letters, h... | 4 | [
0.03369140625,
0.034423828125,
0.09326171875,
-0.04052734375,
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-0.0263671875,
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0.026611328125,
0.052490234375,
-0.0229492187... | 4,125 | 4125 | |
Find the ANGLE
August 14th 2011, 08:05 AM #20
Member
August 14th 2011, 03:08 AM #19
Super Member
August 13th 2011, 06:06 PM #18
Senior Member
August 13th 2011, 05:03 PM #17
Member
August 13th 2011, 04:51 PM #16
Member
Re: Find the ANGLE
good proof i love it
Re: Find the ANGLE
Hi razemsoft 21,
A... | 4 | [
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-0.046142578125,
-0.0546875,
0.06347656... | 4,126 | 4126 | |
MathGroup Archive: July 2004 [00138]
[Date Index] [Thread Index] [Author Index]
Re: Normal distribtion
• To: mathgroup at smc.vnet.net
• Subject: [mg49224] Re: Normal distribtion
• From: "Roger L. Bagula" <rlbtftn at netscape.net>
•... | 4 | [
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-0.033935546875,
0.0296630859375,
-0... | 4,127 | 4127 | |
Index Law
January 3rd 2011, 06:40 AM #1
Newbie
Joined
Oct 2010
Posts
8
Index Law
I got the answer x^2 + 49 from the question (x+7)^2.
But then i was told the answer was x^2 +14x+49.
could some explain the 14x pleas?
It [I assume you mean 14x not 40x] because $(a+b)^2 eq a^2+b^2$
You ne... | 4 | [
0.000514984130859375,
0.11279296875,
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-0.00048065185546875,
0.044677734375,
-0.03369140625,
-0.004547119140625,
-0.0329589... | 4,128 | 4128 | |
Rational Exponent Equation.
January 17th 2011, 11:43 AM
skoker
Rational Exponent Equation.
I am having some trouble with this one. I think exponentiation would work but i can't seem to get it right. the answer is x=36. could someone show an intermediate step so i can see which form,
radical or fractional exp... | 4 | [
0.01373291015625,
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-0.04638671875,
-0.0180... | 4,129 | 4129 | |
Prove this derivative is continuous
December 6th 2008, 06:20 PM #1
Super Member
Joined
Mar 2006
Posts
705
Thanks
2
Prove this derivative is continuous
Let $U$ be a neighborhood of 0 in $\mathbb {R}$.
Suppose that $f:U \rightarrow \mathbb {R}$ is twice differentiable , f' and f'' are continuous, ... | 5 | [
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0.01104736328125,
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0.035400390625,
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Fraction
Talk0
872pages on
this wiki
A fraction is a number expressed as the quotient of two mathematical expressions, often integers. Fractions come in the form $\frac{a}{b}$, where a is called the numerator and b is called the
denominator.
Sometimes the word "fraction" means the quotient of two integers. Under th... | 4 | [
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Analyzing the Regression Line
Estimating Sigma
The correlation provides us with an estimate of how linear the data is. We would also like to know how close the data are to the regression line. We use a measurement s[e] which is a poi... | 5 | [
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-0... | 4,132 | 4132 | |
Physics! #21: University Physics 3.4
3.4 Motion in a Circle
Uniform Circular Motion
First off, let’s define what we mean.
By “circular” we just mean you’re traveling in a perfect circle. That is, you’re traveling in such a way that one side of your car is always perpendicular to some fixed point. It’s not just any ... | 4 | [
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Secants, Tangents and Derivatives
MTH 207 Lab Lesson 10
Secants, Tangents and Derivatives
Up to M... | 5 | [
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... | 4,134 | 4134 | |
3 more problems
July 30th 2009, 03:22 PM #1
Newbie
Joined
Jul 2009
Posts
24
3 more problems
1. 2ln(3x) = 8
2. Logx + log (x + 15) = 2
3. Ln (x - 4) - ln (x + 1) = ln 6
Thanks just need the last 2
$\underbrace {\ln \left( {x - 4} \right) - \ln \left( {x + 1} \right)}_{\ln a - \ln b = ... | 4 | [
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0.006530761... | 4,135 | 4135 | |
solving complex equation using euler's formula
August 24th 2011, 05:52 PM
snaes
solving complex equation using euler's formula
Not sure where this belonged in the forum, but hopefully I got close.
I need to find values for c and x, that are both real and positive that satisfy this equation. Im pretty sure t... | 4 | [
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0.025634765625,
-... | 4,136 | 4136 | |
Fundamental Theorem of Arithmetic Help
February 23rd 2007, 04:56 PM
jmc1979
Fundamental Theorem of Arithmetic Help
If anyone could help, I will appreciate it!
This are the problem:
1. Show that all of the powers in the prime-power factorization of an integer n are even if and only if n is a perfect squ... | 4 | [
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0.0172... | 4,137 | 4137 | |
Coordinates and Graphs of Lines
Solutions to Equations in Two Variables
Example
Consider the equation
2x + y = 10
We see that when
x = 3 and y = 4
we have
2(3) + 4 = 10
is true. We say that (3,4) is a solution to the equation. ... | 4 | [
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-0.08251953125,
-0.... | 4,138 | 4138 | |
Probabiltiy Question
August 26th 2009, 12:36 PM #1
Newbie
Joined
Aug 2009
Posts
17
Probabiltiy Question
I think I know the answer but would like to hear the forum's answer. What was the logic was in getting at the answer? Also, I copy pasted this from an actual exam so no need to wonder if there
was ... | 4 | [
0.041259765625,
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... | 4,139 | 4139 | |
random variables
January 22nd 2009, 04:18 PM
ashimb9
random variables
Suppose $U_{1}$ and $U_{2}$ are i.i.d. U(0,1) random variables. Let $X=\sqrt{-2.log(U_{1})}.cos(2\Pi.U_{2})$ and $Y=\sqrt{-2.log(U_{1})}.sin(2\Pi.U_{2})$
Show that X and Y are i.i.d. N(0,1)
January 23rd 2009, 04:26 AM
Isomorphism
Q... | 4 | [
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0.0634765625,
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0.1337890625,
0.068359375,
0.053955078125,
0.025390625,
-0.035888671875,
-0.03466796875,
-0.0185546875,
-0.1357421875... | 4,140 | 4140 | |
The Greatest Common Factor
Been here and done this, but we'll go through a couple of examples to jog your memory. Sorry, we know how much your memory despises physical exercise.
Sample Problem
Factor the polynomial x^2 + x.
Since each term has a common factor of x, we can pull out the x and factor the polynomial as ... | 4 | [
0.0029754638671875,
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0.0595703125,
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0.0610... | 4,141 | 4141 | |
Additional maths O level (chapter polynomial)
Moderator
Registered: 2010-06-20
Posts: 6,092
Re: Additional maths O level (chapter polynomial)
righen
Guest
Additional maths O level (chapter polynomial)
Hi everyone,
Can someone help me solve this problem?
Solve this equation:
X^2 (x+3)=10x+24
Hence u... | 4 | [
-0.0625,
0.021240234375,
0.03271484375,
-0.01806640625,
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0.0303955078125,
0.04736328125,
0.12060546875,
-0.054443359375,
0.033203125,
-0.... | 4,142 | 4142 | |
The encircled goat puzzle
Yes, this one is going to be wickedly hard!
A field has the shape of a circle of radius 100m and is enclosed by a circular fence. A goat is attached by a rope to a hook, at a fixed point on the fence. To stop the goat from getting too fat,
the farmer wants to make sure that it can on... | 5 | [
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0.0859375,
-0.0595703125,
-0.01696777343... | 4,143 | 4143 | |
Challenge Problem
July 12th 2010, 08:43 AM #1
Member
Joined
Sep 2009
Posts
177
Thanks
1
Challenge Problem
This is a challenge problem. It has been approved by Mr Fantastic.
This problem is from some putnam comptition. I got the problem out of a book that I have. It's fun.
Problem:
let ... | 5 | [
-0.0830078125,
0.04736328125,
-0.005859375,
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-0.05810546875,
0.06640625,
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0.0279541015625,
0.038330078125,
-0.035888671875,
-0.0615234375,
0.064453125,
0.05419921875,
0.02880859375,
0.048583984375,
0.00604248046875,
-0.000728607177734... | 4,144 | 4144 | |
Introduction: PID Controller Design
In this tutorial we will introduce a simple yet versatile feedback compensator structure, the Proportional-Integral-Derivative (PID) controller. We will discuss the effect of each of the pid
parameters on the closed-loop dynamics and demonstrate how to use a PID controller to improv... | 5 | [
-0.0849609375,
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0.0751953125,
0.06640625,
0.0673828125,
0.0458984375,
0.05615234375,
0.08251953125,
-0.09375,
-0.07275390625,
-0.0047607421875,
0.0208740234375,
0.05322265625,
-0.03466796... | 4,145 | 4145 | |
Dimensional Analysis and Gradient Descent
Consider learning a linear predictor according to a loss function $l$, \[
\begin{aligned}
p^{(t)} &= w^{(t) \top} x^{(t)}, \\
w^{(t+1)} &= w^{(t)} - \eta \frac{\partial l}{\partial p} x^{(t)}.
\end{aligned}
\] Suppose the optimal weight vector is $w^*$. If all the inputs a... | 4 | [
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0.09228515625,
-0.0260009765625,
0.08447265625,
0.004547119140625,
0.07910... | 4,146 | 4146 | |
Thermodynamic equations
From Wikipedia, the free encyclopedia
For a quick reference table of these equations, see: Table of thermodynamic equations
In thermodynamics, there are a large number of equations relating the various thermodynamic quantities. In chemical thermodynamics, which is a sub-branch of thermodyn... | 4 | [
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0.016845703125,
0.0025634765625,
0.01153564453125,
-0.042724609375,
-0.0422363281... | 4,147 | 4147 | |
Torque Speed Characteristics of Induction Motor - The Engineering Projects
Hello friends, hope you all are fine and enjoying good health In the previous posts we have seen the basic concepts and introduction of Induction motor, we did few calculations as well and now I am
gonna discuss the torque speed characteristi... | 4 | [
-0.09375,
-0.00933837890625,
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-0.0732421875,
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0.056640625,
0.06396484375,
0.01226806640625,
-0... | 4,148 | 4148 | |
Proof inequality
June 22nd 2007, 09:52 AM #1
Member
Joined
Sep 2006
Posts
221
Proof inequality
For all real numbers a, b, c, prove that:
a(a - b) + b(b - c) + c(c - a) >= 0.
Thanks!
Open paranthesis,
$a^2 - ab + b^2 - bc + c^2 - ac \geq 0$
Iff,
$a^2+b^2+c^2 \geq ab+bc+ac$
... | 5 | [
-0.072265625,
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0.038330078125,
0.0302734375,
-0.017... | 4,149 | 4149 | |
Verify my answers on (system/solutions)
April 4th 2012, 04:07 PM #1
Junior Member
Joined
Mar 2012
From
United States
Posts
43
Verify my answers on (system/solutions)
Could someone verify my answers in the following problems?
1. An aircraft can fly 912 miles with the wind in three hours, while i... | 4 | [
-0.022216796875,
0.0140380859375,
-0.0220947265625,
-0.0162353515625,
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0.0654296875,
0.0830078125,
0.01348876953125,
0.01324462890625,
-0.00799560546875,
0.0224609375,
0.109375,
-0.10302734375,
-0.... | 4,150 | 4150 | |
Math Forum Discussions
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Topic: Smash Product
Replies: 1 Last Post: May 29, 2011 1... | 4 | [
-0.10400390625,
-0.051025390625,
-0.004364013671875,
-0.034912109375,
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0.0927734375,
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0.02490234375,
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0.06640625,
0.0869140625,
0.1455078125,
-0.045654296875,
-0.0093994... | 4,151 | 4151 | |
MathGroup Archive: June 2007 [01232]
[Date Index] [Thread Index] [Author Index]
Re: Maximize with Integer constraints
• To: mathgroup at smc.vnet.net
• Subject: [mg78263] Re: [mg78227] Maximize with Integer constraints
• From: Adam St... | 4 | [
-0.0167236328125,
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0.033203125,
0.04931640625,
-0.0546875,
0.035888671875,
0.09521484375,
0.025878... | 4,152 | 4152 | |
The Learning Curve or
Introduction
The theory of the learning curve or experience
^1
curve is based on the simple idea that the time required to perform a task decreases as a worker gains experience. The basic concept is that the time, or cost, of performing a task (e.g., producing a
unit of output) decreases at a ... | 5 | [
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0.07763671875,
-0.06640625,
-0.01531982421875,
-0.037841796875,
-0.0006... | 4,153 | 4153 | |
Heisenberg group and Lewy operator.
1. Introduction
The existence theorems,
elliptic el·lip·tic or el·lip·ti·cal
adj.
1. Of, relating to, or having the shape of an ellipse.
2. Containing or characterized by ellipsis.
3.
a.
boundary problems and boundary value problems in the theory of differential operators (wi... | 4 | [
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0.005767822... | 4,154 | 4154 | |
Cramér–Rao Lower Bound for a Function of a Parameter
March 26th 2010, 06:36 AM
alan4cult
Cramér–Rao Lower Bound for a Function of a Parameter
I'm trying to compute the Cramér–Rao Lower Bound for a function of the parameter $\lambda$ of a Poisson distribution.
The function is $g (\lambda) = e^{-\lambda}$.
... | 5 | [
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0.116699... | 4,155 | 4155 | |
mathschallenge.net
Consecutive Composites
Problem
Although there are infinitely many primes it is a most remarkable fact that there can always be found a sequence of $n$ consecutive composite numbers. For example, there are thirteen consecutive
composite numbers between the primes 113 and 127.
Prove that there exist... | 4 | [
-0.07275390625,
-0.01611328125,
-0.032470703125,
-0.09765625,
0.011474609375,
0.07763671875,
0.029541015625,
0.0400390625,
-0.09912109375,
0.0233154296875,
-0.06005859375,
0.035400390625,
0.044677734375,
-0.021484375,
-0.01397705078125,
-0.091796875,
-0.006988525390625,
-0.00396728... | 4,156 | 4156 | |
Stuff... again... :)
November 9th 2007, 08:07 PM #1
Member
Joined
Apr 2006
Posts
85
Stuff... again... :)
1. Frank and Ernest start jogging on a 110m circular track. They begin at the same time and from the same point but jog in opposite directions, one at $\frac{8}{3}m$ per second and the other at $
... | 4 | [
0.056884765625,
0.0390625,
0.0078125,
0.06298828125,
-0.02392578125,
0.03955078125,
-0.06982421875,
-0.00628662109375,
0.031982421875,
-0.038330078125,
-0.0201416015625,
-0.035400390625,
-0.023193359375,
0.0478515625,
0.054931640625,
0.04833984375,
-0.103515625,
0.0242919921875,
... | 4,157 | 4157 | |
trigonometry
October 25th 2009, 01:58 AM #1
Super Member
Joined
Aug 2009
Posts
639
trigonometry
hi!
Can someone teach me how to solce arccos(cos(7Pi/ 6))?
i tried to change 7pi/ 6 into the principal angle but what i thought of was:
cos (7pi/6)= -cos (pi/6)
although it is in the princip... | 4 | [
-0.09765625,
-0.0057373046875,
0.032958984375,
0.06396484375,
-0.048095703125,
-0.033203125,
-0.01446533203125,
0.03564453125,
0.041015625,
0.04931640625,
0.08544921875,
-0.0308837890625,
-0.0250244140625,
0.025390625,
-0.00946044921875,
-0.0478515625,
-0.0098876953125,
0.018676757... | 4,158 | 4158 | |
Kelvin Wave Pattern
When we look at ducks, boats, ships and other objects moving through calm water we can see that they produce a characteristic surface pattern. The envelope of these waves stands at a fixed angle of
19.5 degrees and the wake has a characteristic feathered pattern. These patterns are named after Lord... | 4 | [
-0.08935546875,
0.08203125,
0.0089111328125,
-0.0264892578125,
0.03857421875,
0.032958984375,
0.0096435546875,
-0.029052734375,
-0.057373046875,
-0.033935546875,
-0.0185546875,
-0.046142578125,
-0.00909423828125,
0.015380859375,
0.043212890625,
-0.032470703125,
-0.109375,
-0.061279... | 4,159 | 4159 | |
Treatise On Analysis Vol-Ii
3 SPECTRUM OF A COMMUTATIVE BANACH ALGEBRA 329
veE(p) and \u(x)\ — 1 almost everywhere. Deduce that we !(//,) and then use (f).)
(i) Let /e K(p) be such that (fu dp = 0 for all u e I(/i) for which f u dp, ^ 0. Show
that/is /x-negligible. (By applying the canonical decomposition o... | 4 | [
-0.04345703125,
0.0673828125,
0.040283203125,
0.03857421875,
0.0576171875,
0.01177978515625,
0.1748046875,
0.00372314453125,
-0.05419921875,
-0.043212890625,
0.0166015625,
-0.046142578125,
0.022705078125,
-0.030029296875,
-0.01171875,
-0.06640625,
0.01708984375,
-0.01129150390625,
... | 4,160 | 4160 | |
ntroducing
10 Apr 2006 - 04:14
introducing the absolute value
Ben is encountering absolute value now, in Saxon 8/7, for the first time (he's in 6th grade, which I think is an appropriate place to see it for the first time -- and of course to master it at the
appropriate level). Absolute value should be on the all-tim... | 4 | [
0.0101318359375,
0.060791015625,
-0.007232666015625,
-0.09033203125,
-0.021728515625,
-0.0673828125,
-0.049560546875,
0.05517578125,
-0.0225830078125,
0.021728515625,
0.031982421875,
-0.01434326171875,
0.06982421875,
0.08984375,
-0.0157470703125,
0.0439453125,
0.053466796875,
-0.05... | 4,161 | 4161 | |
SparkNotes
Factors
A factor is a number that evenly divides the given number. A factor need not be a constant. In fact, any integer, variable, or polynomial that can be multiplied by an integer, a variable, or a
polynomial to produce the given expression is a factor of the given expression.
Removing Common Factors
W... | 4 | [
0.047119140625,
0.04345703125,
0.005523681640625,
0.00164794921875,
0.0458984375,
0.036865234375,
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-0.013671875,
-0.06982421875,
0.0380859375,
0.0145263671875,
0.042236328125,
0.0133056640625,
0.0390625,
0.0179443359375,
-0.00970458984375,
-0.10546875,
0.0791015625... | 4,162 | 4162 | |
Inequality
June 19th 2012, 12:53 PM #1
Junior Member
Joined
Apr 2012
From
planet earth
Posts
31
Thanks
1
Inequality
I have the following inequality
$-1 \leq \frac{p2R\cos(\phi)+R^2-p-2R\cos(\phi)}{1-pR^2} \leq 3$
where $p\in(-\infty,\infty)$, $R\in(0,\infty)$ and $\phi\in(0,\pi)$.
... | 5 | [
-0.0732421875,
-0.0078125,
0.007354736328125,
0.0206298828125,
0.005645751953125,
0.000850677490234375,
-0.050537109375,
0.08642578125,
-0.01251220703125,
0.038330078125,
-0.04296875,
0.035888671875,
-0.01422119140625,
0.04052734375,
0.04931640625,
-0.057373046875,
0.04052734375,
-... | 4,163 | 4163 | |
Example 7.2.12(a): Integrating Rational Functions
The polynomial
p(x)
can be factored into
p(x) = 1 - x^2 = (1 + x) (1 - x)
By the partial fraction decomposition theorem we know that:
^1 / [p(x)] = ^A / [1 + x] + ^B / [1 - x]
for some constants
A
and
B
. To find these constants, we combine the two ra... | 5 | [
0.006317138671875,
-0.01007080078125,
0.07275390625,
0.08154296875,
0.03955078125,
-0.0277099609375,
0.009765625,
-0.026611328125,
0.00347900390625,
-0.0028533935546875,
0.01171875,
-0.030029296875,
0.09814453125,
0.0294189453125,
-0.08935546875,
0.0098876953125,
-0.07275390625,
0.... | 4,164 | 4164 | |
biharmonic equation
May 16th 2011, 03:19 AM #1
Member
Joined
Mar 2010
Posts
122
biharmonic equation
verify that the following is a solution to the biharmonic equation
F(x,y)=(Acosbx+Bsinbc+Cxcosbx+Dxsinbx)(Ecoshby+Fsi nhby)
i have tried taking the derivates and have gotten up to the laplacian b... | 4 | [
-0.021728515625,
0.0179443359375,
0.033203125,
-0.036865234375,
-0.0084228515625,
0.0712890625,
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-0.05419921875,
-0.0247802734375,
0.0303955078125,
0.03955078125,
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-0.0299072265625,
-0.0189208984375,
0.017333984375,
0.0576171875,
-0.047607421875,
-0.0... | 4,165 | 4165 | |
Economic Analysis of the New York Times Paywall
After the New York Times announced its metered paywall last week there has been a lot of empty blather. Standing out from all the noise are two very good analyses. The first was by Felix Salmon for
Reuters, analyzing a consumers decision of whether or not to pay. The seco... | 4 | [
-0.0150146484375,
0.01116943359375,
-0.025634765625,
0.000171661376953125,
0.0185546875,
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0.0234375,
-0.006439208984375,
0.0673828125,
0.0308837890625,
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0.06982421875,
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0.0458984375,
0.028076171875,
-0.0458984375,
0.072265625,
-0.03686... | 4,166 | 4166 | |
MathGroup Archive: March 1995 [00038]
[Date Index] [Thread Index] [Author Index]
Re: Numerical evaluation of HypergeometricPFQ[{a,b,c},{d,e},1]
• To: mathgroup at christensen.cybernetics.net
• Subject: [mg512] Re: [mg497] Numerical eval... | 5 | [
-0.0272216796875,
0.080078125,
0.0283203125,
0.011962890625,
0.01123046875,
-0.022705078125,
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-0.03271484375,
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0.0286865234375,
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0.01470947265625,
-0.02978515... | 4,167 | 4167 | |
word problem
March 30th 2009, 05:53 AM #1
Junior Member
Joined
Feb 2009
Posts
31
word problem
A jet flies twice as fast as a propeller plane. On a trip 1500 miles, the propeller plane took 3 hours longer than the jet. Find the speed of each plane.
If the propeller plane is twice as slow and it took ... | 4 | [
0.0137939453125,
0.0211181640625,
-0.01904296875,
-0.043701171875,
0.0234375,
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0.014892578125,
0.0216064453125,
0.064453125,
0.10693359375,
-0.013427734375,
-0.03173828125,
-0.004119873046875,
-0.0157470703125,
0.064453125,
-0.0260009765625,
0.0180... | 4,168 | 4168 | |
The Gordon Growth Model and the income approach to value.
Link/Page Citation
The idea that property has a value directly proportional to its earning ability has been around sinc... | 4 | [
0.003936767578125,
0.0380859375,
-0.007415771484375,
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0.009765625,
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0.00775146484375,
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0.0233154296875,
-0.0263671875,
0.... | 4,169 | 4169 | |
Is the Hessian of Hamilton's function positive-definite?
up vote 2 down vote favorite
1
Background
Consider an electron with mass $1$ moving in $\mathbb R^n$ in under the influence of a static electromagnetic field. Up to identifying vector fields with differential forms, Maxwell's equations state
that the electric f... | 4 | [
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0.11279296875,
0.00885009765... | 4,170 | 4170 | |
T
2
LIMITS
Section 2: Theorems on limits
Limits of polynomials
Back to Section 1
We will now prove that a certain limit exists, namely the limit of f (x) = x as x approaches any value c. (That f(x) also approaches c should be obvious.)
THEOREM. If f (x) = x, then for any value c that we might name:
For, if a seq... | 4 | [
-0.2216796875,
0.0150146484375,
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0.00567626953125,
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-0.033203125,
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-0.04052734375,
... | 4,171 | 4171 | |
Relative Minimum
What is the relative minimum for y = x + 1/x
Quote: Originally Posted by nath_quam A local minimum of a function can be found by differentiating the function and solving for the zeros of the derivative. These zeros comprise local maxima, minima
and points of inflection, so you will need to confirm whi... | 4 | [
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0.08056640625,
-0.05029296875,
0.033447265625,
0.1064453125,
-0.094238281... | 4,172 | 4172 | |
scid.linalg
This module contains functions related to linear algebra.
For the time being these functions are just a user-friendly interface to the corresponding LAPACK functions. Hence, one can only use matrices and vectors where the elements are of FORTRAN-compatible
types, namely:
float
double
cfloat
... | 5 | [
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0.01904296875,
-0.023193359375,
-0.044189453125,
0.0771484375,... | 4,173 | 4173 | |
High School Mathematics-Physics SMILE Meeting
07 May 2002
Notes Prepared by Porter Johnson
Fred Schaal (Lane Tech HS, Mathematics) -- Hexcode Digital Numbers
Fred presented an extension of the the lesson on Digital Numbers by Monica Seelman at the 23 April 2002 (last) SMILE meeting. Monica converted multiplication tab... | 4 | [
-0.044189453125,
0.00015354156494140625,
-0.048828125,
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0.10302734375,
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0.04541015625,
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0.02490234375,
0.01007080078125,
0.03515625,
-0.0289306640625,
-0.0634765625,
-0.1513671875,
0.05346... | 4,174 | 4174 | |
Use the definition of a parabola and the distance
April 20th 2010, 02:21 AM #1
Senior Member
Joined
Oct 2009
Posts
290
Use the definition of a parabola and the distance
Hi all
Use the definition of a parabola and the distance formula to find the equation of a parabola with
a ) directix x = -4 a... | 4 | [
0.08642578125,
-0.0306396484375,
-0.04931640625,
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0.10302734375,
-0.058837890625,
-0.0966796875,
... | 4,175 | 4175 | |
Integration by parts
September 3rd 2007, 01:45 PM #1
Junior Member
Joined
Aug 2007
Posts
45
Integration by parts
I am half way stuck with this integral, any help would be appreciated.
Integral (p^5)ln(p) dp
u = ln p, du = 1/p
dv = p^5, v = p^6/6
Integral (p^5)ln(p) dp = p^6/6 ln(p) - I... | 5 | [
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0.022216796875,
0.031982421875,
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0.05126953125,
0.00872802734375,
-0.0693359375... | 4,176 | 4176 | |
elementary number theory: sum of digits
October 17th 2009, 03:23 AM #1
Member
Joined
Oct 2008
Posts
130
elementary number theory: sum of digits
let x be an integer and let j be the sum of the digits of x. Subtract j from x and get x-j=y. Let k be the sum of the digits of y. Show that y-77,778j cannot equ... | 5 | [
-0.068359375,
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0.0634765625,
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-0.0225830078125,
0.059326171875... | 4,177 | 4177 | |
Find a set of vectors spanning the solution space, stuck at last step
February 27th 2011, 12:35 PM
Jskid
Find a set of vectors spanning the solution space, stuck at last step
Find a set of vectors spanning the solution space of Ax=0 where $<br /> \[<br /> A =<br /> \left[ {\begin{array}{cccc}<br /> 1 & 0 & 1 & 0... | 4 | [
-0.08056640625,
-0.06494140625,
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0.0478515625,
0.007110595703125,
0.0546875,
-0.064453125,
0.03662109375,
0.01123046875,
0.03662109375,
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0.027099609375,
-0.064453125,
-0.06787109375,
0.005584716796875,
-0.08349609375,
-0.0986328125,
0... | 4,178 | 4178 | |
Trisection of an Angle
September 1st 2010, 08:49 PM #1
Newbie
Joined
Sep 2010
Posts
1
Trisection of an Angle
Given:
<XOY is a given angle which has to be trisected.
Construction:
Draw a circle "O" intersecting OX and OY at A and B respectively.
Joi A, B. Draw a semi circle on AB... | 4 | [
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0.0732421875,
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0.029052734375,
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0.05810546875,
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0.06591796875,
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0.05712890625,
0.01318359375,
0.04345703125,
0.02099609375,
-0.06689453125,
-0.0185546875... | 4,179 | 4179 | |
PDPOCON
Section: LAPACK routine (version 1.5) (l) Updated: 12 May 1997 Local index Up
NAME
PDPOCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite distributed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed
by PDPOTRF
SYNOPSIS
SUBROU... | 4 | [
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-0.057373046875,
-0.024169921875,
0.07421875,... | 4,180 | 4180 | |
Convergent Subsequences....
December 19th 2009, 08:58 AM #1
Senior Member
Joined
Jan 2009
Posts
296
Convergent Subsequences....
I am reviewing my analysis midterm to study for the final, and I can't seem to remember how to get the correct solution to one of the problems.
It says: consider the seque... | 5 | [
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0.043212890625,
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0.02880859375,
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0.09814453125,
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0.017333984375,
0.006988525390625,... | 4,181 | 4181 | |
Binomal Expansion
(1+ax)/(1+bx) = 1+(a-b)x+(b^2-ab)x^2 is this correct upto x^2 terms? thanks
$\frac{(1+ax)}{(1+bx)}=$ $=(1+ax) * (1+bx)^{-1}$ Now we expand $=(1+bx)^{-1}$ $=1+\frac{-1}{1} * (bx)^1 + \frac{(-1) * (-2)}{1 * 2} * (bx)^2$ $=1-bx + b^2 * x^2$ Hence, your initial expression will
be: $=(1+ax) * (1-bx + b^2 ... | 5 | [
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0.017578125,
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0.11181640625,
0.005462646484375,
... | 4,182 | 4182 | |
Math-Intensive Reports with GNU Emacs and Calc, Part 2
Using Calc for vector, matrix and complex operations.
In part 1 of this article, I explained some of the evolving and complicated requirements of math calculations in certain types of reporting. As part 1 outlined, Emacs and the Calc application offer
many types ... | 5 | [
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-0.04931640625,
0.061279296... | 4,183 | 4183 | |
work problem
May 25th 2008, 06:26 PM #1
Newbie
Joined
May 2008
Posts
22
work problem
A is twice as good a workman as B and together they finish a piece of work in 18 days.in how many days will A alone finish this work?
Lets suppose that worker A works finishes a job in A days
and worker B finis... | 4 | [
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Finding a constant to make a perfect square trinomial
find a constant to add to the binomial so that it becomes a perfect square trinomial. x^2-15x
Divide the coefficient of the linear term by 2 (ie divide b by 2) $(x+7.5)^2 + k = x^2 - 15x + 0$ $k = -(7.5^2)$ ----------------------------------------------------------... | 4 | [
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-0.0088... | 4,185 | 4185 | |
T-Test in Hypothesis Testing help!
November 30th 2009, 09:15 AM #1
T-Test in Hypothesis Testing help!
A brewery claims that the consumers are getting a mean volume equal to 32 ounces of beer in their quart bottles. The Bureau of Weights and Measures randomly selects 36 bottles. Test the claim of
the brewery a... | 5 | [
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Cartesian product
August 27th 2009, 02:50 AM #1
Newbie
Joined
Aug 2009
From
Malmö-Linköping
Posts
6
My teatcher wasn't able to explain this for me in a clear way. See if you guys can help.
Let A and B be two random sets. Prove that A $<span style=$\times" alt="\times" /> B (B $<span style=$\cap" a... | 4 | [
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Vector algebra question(s)
December 9th 2012, 12:36 PM
willsor
Vector algebra question(s)
Hi MHF
This is my first post, I'm faaaairly certain this is in the right subforum, sorry if it isn't.
Anyway, I'm having difficulty with vector algebra, more specifically, proving one expression equals another
... | 4 | [
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MathGroup Archive: June 2008 [00308]
[Date Index] [Thread Index] [Author Index]
Re: DiffMaps package
• To: mathgroup at smc.vnet.net
• Subject: [mg89544] Re: DiffMaps package
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
... | 5 | [
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... | 4,189 | 4189 | |
Find number of values of x satisfying the given equation.
March 14th 2011, 12:05 AM #1
Find number of values of x satisfying the given equation.
limit 0 to 2[x+14] $\int [\frac{t}{2}].dt$=limit 0 to {x} $\int [t+14] dt$
where {.} is fractional part of x and [.] is integer number less than or equal to x.
... | 5 | [
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-0.023193359375,
... | 4,190 | 4190 | |
True muzzle velocity
#
1
09-14-2010, 11:19 AM
Join Date: Sep 2009
Junior Member
Posts: 9
True muzzle velocity
Hello everybody!does anybody know the equation which permits you to calculate the real muzzle velocity from a recorded velocity in a chronograph which is set at a certain d... | 4 | [
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A-level Physics (Advancing Physics)/Gravitational Potential
Gravitational potential is the gravitational potential energy given to objects per unit mass:
$V_{grav} = \frac{E_{grav}}{m} = \frac{-\frac{GMm}{r}}{m} = \frac{-GM}{r}$
For short changes in distance Δh (Δh << r), gravitational potential energy is given by:
... | 4 | [
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... | 4,192 | 4192 | |
Finding ŷ from a Regression on TI-89/92
with a Note on Finding Residuals
Copyright © 2001–2014 by Stan Brown, Oak Road Systems
Summary: The regression line represents the model that best fits the data. One important reason for doing the regression in the first place is to answer the question, what average y value doe... | 4 | [
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MATLAB
Create six bins, numbered 0 through 5, to use for data pooling.
bins = 0:5;
Create a vector containing the observed counts for each bin and compute the total number of observations.
obsCounts = [6 16 10 12 4 2];
n = sum(obsCounts);
Fit a Poisson probability distribution object to the data and compute the ex... | 5 | [
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-0.10595703... | 4,194 | 4194 | |
Find all pairs of positive integers whose squares differ by 400?
I have pairs, but I need to find an organzied method for finding them?
$<br /> m^2 - n^2 = 400\quad m,n \in Z^ +$ $\left( {m - n} \right)\left( {m + n} \right) = 400$ thus m-n, or m+n must equal one of the divisors of 400, to satisfy the equation, and so... | 4 | [
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0.0267333984375,... | 4,195 | 4195 | |
Applications of Calculus - maximum height
August 24th 2010, 02:34 AM #1
Member
Joined
Dec 2008
From
Australia
Posts
161
A body is projected vertically upwards from the ground in a medium that produces a resistance force per unit mass of $kv^2$, where v is the velocity and k is a positive constant. Giv... | 5 | [
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Why is the greenhouse effect logarithmic?
Steve McIntyre at climateaudit.org is trying to locate the provenance ;-) of the logarithmic formula for the greenhouse effect. Instead of joining him, let me post my explanation why I personally
think that the idealized greenhouse warming is a logarithmic function of the conce... | 4 | [
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-0.0... | 4,197 | 4197 | |
complex analysis question
May 11th 2008, 06:25 PM #1
Member
Joined
Apr 2008
From
Seoul, South Korea
Posts
128
complex analysis question
p is the radius of convergence of Σa_n*z^n (n≥0) and let r be a real number less than p. prove that the series converges normally on the disc abs (z)<r and diverges ... | 5 | [
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0... | 4,198 | 4198 | |
On the eigenfunctions of the finite Hankel transform.
Abstract
In this paper, we study the properties of the eigenfunctions of the finite
Hankel transform
Besides the meaning discussed in this article, the Hankel transform may also refer to the determinant of the Hankel matrix of a sequence.
In mathematics, ... | 4 | [
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