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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21738 | Home > Standard Error > Standard Error And Standard Error Of Estimate
# Standard Error And Standard Error Of Estimate
## Contents
If you got this far, why not subscribe for updates from the site? The standard error of the estimate is a measure of the accuracy of predictions. The sample mean will very rarely be equal... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21737 | ## Intermediate Algebra (6th Edition)
$x+3=0$ $x=-3$ This is a vertical line passing through (-3,0). |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_21743 | # Nilpotent group with ascending and descending central series different?
This may turn out to be a bit embarassing, but here it is. It is probably not true that the ascending and descending central series (*) of a nilpotent group have the same terms. (Or at least one of MacLane-Birkhoff, Rotman and Jacobson would hav... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4416 | # Definition:Kronecker Delta
## Definition
Let $\Gamma$ be a set.
Let $R$ be a ring with unity whose zero is $0_R$ and whose unity is $1_R$.
Then $\delta_{\alpha \beta}: \Gamma \times \Gamma \to R$ is the mapping on the cartesian square of $\Gamma$ defined as:
$\forall \tuple {\alpha, \beta} \in \Gamma \times \Gam... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4417 | # Spin and many particle systems
I learned about many particle systems and second quantization recently. The Fock space of distinct particles with single particle Hilbert space $$\mathcal H$$ was defined to be $$\bigoplus_{N=0}^\infty \mathcal H^{\otimes N}$$. Then I learned, that there are two options to find a physi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4418 | # The Unapologetic Mathematician
## Sections of Sets and Functions
Our definitions today are purely set-theoretical. If $E$ is a subset of $X\times Y$, then given a point $x\in X$ we define the “section” of $E$ determined by $x$ to be the set
$\displaystyle E_x=\{y\in Y\vert(x,y)\in E\}$
Similarly, we define the se... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4419 | Feeds:
Posts
## The Origin of Kolmogorov Complexity
A mildly personal post.
The title does not imply that the lines quoted below correspond to the exact origin of Kolmogorov Complexity, though they are related and give away the essence.
Andrey Kolmogorov
Information theory must precede probability theory and not b... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4420 | # Checklist of Rationality Habits
As you may know, the Center for Applied Rationality has run several workshops, each teaching content similar to that in the core sequences, but made more practical, and more into fine-grained habits.
Below is the checklist of rationality habits we have been using in the minicamps' op... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4421 | 2019 Mar 21
(All day)
2019 May 09
(All day)
2018 Nov 15
# Colloquium: Ari Shnidman (Boston College) - Rational points on elliptic curves in twist families
2:30pm to 3:30pm
## Location:
Manchester Building (Hall 2), Hebrew University Jerusalem
The rational solutions on an elliptic curve form a finitely generated... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4423 | Basic Topology
Theorem 2.23
A set $E$ is open if and only if its complement is closed.
Proof
1. $E^c$ is closed implies $E$ is open.
Suppose $E^c$ is closed. This means every limit point of $E^c$ is a point of $E^c$. Equivalently, if $x \notin E^c$, then $x$ is not a limit point of $E^c$.
Choose $x \in E$. Then $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4424 | # . Blast from the Past Find point(s) of intersection 1. 2. 3.4. 5.
## Presentation on theme: ". Blast from the Past Find point(s) of intersection 1. 2. 3.4. 5."— Presentation transcript:
. Blast from the Past Find point(s) of intersection 1. 2. 3.4. 5.
. Blast from the Past Find point(s) of intersection 1. 2. 3.4. ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4425 | # X operation
Applies the Pauli $X$ gate.
\begin{align} \sigma_x \mathrel{:=} \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}. \end{align}
operation X (qubit : Qubit) : Unit
Functors
Adjoint Controlled
## Input
qubit
Qubit
Qubit to which the gate should be applied.
Unit |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4426 | # American Institute of Mathematical Sciences
• Previous Article
Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue
• NHM Home
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Numerical study of a domain decomposition method for a two-scale linear transport equation
March 2006, 1(1): 167... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4427 | My Math Forum elements of the subgroup <3,12> of (Z, +)
Abstract Algebra Abstract Algebra Math Forum
June 4th, 2014, 10:03 PM #1 Newbie Joined: May 2014 From: 2219 Posts: 13 Thanks: 2 elements of the subgroup <3,12> of (Z, +) Hi, I'm trying to do this question but im not sure if im doing it right. Find the elemen... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4428 | # Algebraic number
An algebraic number is any complex number (including real numbers) that is a root of a non-zero polynomial (that is, a value which causes the polynomial to equal 0) in one variable with rational coefficients (or equivalently – by clearing denominators – with integer coefficients). All integers and r... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4430 | # Classification of Finite Rings of Order $$p^2$$
by Benjamin Fine (Fairfield University)
Mathematics Magazine
October, 1993
Subject classification(s): Algebra and Number Theory | Abstract Algebra | Rings and Ideals
Applicable Course(s): 4.2 Mod Algebra I & II
Up to isomorphism there are exactly 11 rings of order $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4431 | # Polynomial Relation - Problem 2
Find all polynomials $$p(x)$$ such that for all real numbers $$a,b,c\neq0$$ satisfying $$\frac1a+\frac1b=\frac1c$$,
$\frac1{p(a)}+\frac1{p(b)}=\frac1{p(c)}$
Note by Cody Johnson
4 years, 2 months ago
MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bull... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4422 | 2019
Том 71
№ 6
# Best Approximations and Kolmogorov and Trigonometric Widths of the Classes $B_{p,θ}^{Ω}$ of Periodic Functions of Many Variables
Stasyuk S. A.
Abstract
We obtain estimates exact in order for the best approximations and Kolmogorov and trigonometric widths of the classes $B_{p,θ}^{Ω}$ of periodic fu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4429 | New Titles | FAQ | Keep Informed | Review Cart | Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Ma... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18112 | Lemma 29.46.5. Let $A \subset B$ be a ring extension such that $\mathop{\mathrm{Spec}}(B) \to \mathop{\mathrm{Spec}}(A)$ is a universal homeomorphism inducing isomorphisms on residue fields. If $A \not= B$, then there exists a $b \in B$, $b \not\in A$ with $b^2 \in A$ and $b^3 \in A$.
Proof. Recall that $A \subset B$ ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18113 | ### Forbidden informationForbidden information
Access Restriction
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Author Levin, Leonid A. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2013 Language English
Subject Domain (in DDC) Computer science, information & general ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18114 | # Solving trigonometric equation of a sum of unknowns
1. Sep 11, 2016
### teetar
1. The problem statement, all variables and given/known data
$\sin (x) = \frac{2}{3}$ and $\sec (y) = \frac{5}{4}$, where $x$ and $y$ lie between 0 and $\frac{\pi}{2}$ evaluate $\sin (x + y)$
2. Relevant equations
Looked over some trig... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18115 | # A signed power transformation with application to white noise testing
We show that signed power transforms of some ARCH-type processes give ARCH-type processes. The class of ARCH-type models for which this property holds contains many common ARCH and GARCH models. The results can be useful in testing for white noise... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18116 | # Divisibility Rules L1-1
1. A number $N$ is divided by $D$ resulted in quotient $q$ and remainder $r$. Then $N$ can be written as
a. $Dq - r$
b. $\dfrac{D}{q} - r$
c. $Dq + r$
d. $Dr + q$
2. One to ten numbers are written side by side. If this number is divided by 8 then what is the remainder?
a. 5
b. 6
c. 7
d. 0
3... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18117 | Find all School-related info fast with the new School-Specific MBA Forum
It is currently 25 Aug 2016, 10:50
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
C... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18118 | ## Saturday, 10 September 2011
### Determinants for M2 II: alternative techniques
Determinants
The cyclic determinants are most properly in these forms:
, or , or ANY determinants that can reach these forms via elemental operations. Their symmetricities can be proven by direct expansion so I will skip this.
Here co... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18120 | # Connexions
You are here: Home » Content » Trigonometry: Revision of grade 11
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# Trigonometry: Revision of grade 11
Module by: Pinelands High School. E-mail the author
## Trigonometry Summary
### Basic knowledge and skills required for Grade 12
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18121 | Wolfram Alpha:
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18123 | # Lagrangian for a bead on a wire
## Homework Statement
A bead of mass ##m## slides (without friction) on a wire in the shape, ##y=b\cosh{\frac{x}{b}}.##
1. Write the Lagrangian for the bead.
2. Use the Lagrangian method to generate an equation of motion.
3. For small oscillations, approximate the differential equat... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18124 | A quick recap of last time. We are trying to make sense of affine varieties over the elusive field with one element $\mathbb{F}_1$, which by Grothendieck’s scheme-philosophy should determine a functor
$\mathbf{nano}(N)~:~\mathbf{abelian} \rightarrow \mathbf{sets} \qquad A \mapsto N(A)$
from finite Abelian groups to s... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18125 | The role of definitions in mathematics and theory
Alfonso Bedoya was not a theoretician, but an actor. He is perhaps most famous for uttering the lines:
He played Gold Hat, in the The Treasure of the Sierra Madre.
Today I want to talk about definitions.
We all think mostly about theorems and proofs. We try to under... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18126 | MathSciNet bibliographic data MR2321376 11A25 (11E25) Alaca, Şaban; Williams, Kenneth S. Evaluation of the convolution sums $\sum\sb {l+6m=n}\sigma(l)\sigma(m)$$\sum\sb {l+6m=n}\sigma(l)\sigma(m)$ and $\sum\sb {2l+3m=n}\sigma(l)\sigma(m)$$\sum\sb {2l+3m=n}\sigma(l)\sigma(m)$. J. Number Theory 124 (2007), no. 2, 491–510... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18127 | # Mean of losses of k bets
I'm trying to solve the following problem :
There is man in a casino that players makes a bet on the number $13$ at the roulette ( roulette has numbers between $1$ and $36$ ). He continues to make this bet until he finally wins; After he wins he then makes the same numbers of bets as he mad... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18119 | Server Error
Server Not Reachable.
This may be due to your internet connection or the nubtrek server is offline.
Thought-Process to Discover Knowledge
Welcome to nubtrek.
Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.
In ea... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18122 | New Zealand
Level 8 - NCEA Level 3
# Applications of Linear Systems in 3 (or more) unknowns
Lesson
We've now covered how to solve linear systems of equations in three unknowns. We can solve by elimination where we can multiply/divide any equation and add/subtract equations. Or also solve by substitution where we sub... |
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12354 | 5 views
Consider a square pulse $g(t)$ of height $1$ and width $1$ centred at $1 / 2$. Define $f_{n}(t)=\frac{1}{n}\left(g(t) *^{n} g(t)\right),$ where $*^{n}$ stands for $n$-fold convolution. Let $f(t)=\lim _{n \rightarrow \infty} f_{n}(t)$. Then, which of the following is TRUE?
1. The area under the curve of $f(t)$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12356 | # www.consciousness.arizona.edu April 25-30 - StudyLib
Publikationer 2003 - Institutionen för informationsteknologi
The snowflake model was created in 1904 by Helen von Koch. This snowflake appeared to be one of the earliest fractal curves. The fractal is built by starting with an equilateral triangle. One must remov... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12358 | Théorie des singularités
Contact unimodal map germs from the plane to the plane
Comptes Rendus. Mathématique, Tome 358 (2020) no. 8, pp. 923-930.
In this article, we correct the classification of unimodal map germs from the plane to the plane of Boardman symbol $\left(2,2\right)$ given by Dimca and Gibson. Also, we ch... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12359 | This is a problem by Lewis Carroll and it revolves around some of the many interesting properties of sums of squares of integers. Is it always true that if you double the sum of two squares you get the sum of two squares? If so can you prove it? Here are some examples.
$2(5^2 + 3^2) = 2(25 + 9) = 68 = 64 + 4 = 8^2 + 2... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12360 | # Definition:General Solution
## Definition
Let $E$ be an equation in which $x$ is the independent variable.
The general solution of $E$ is the set of all $x$ that make $E$ a true statement.
### General Solution to Differential Equation
Let $\Phi$ be a differential equation.
The general solution of $\Phi$ is the ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12361 | # Chapter 1 - Tools of Geometry - 1-7 Midpoint and Distance in the Coordinate Plane - Practice and Problem-Solving Exercises - Page 56: 70
504 in
#### Work Step by Step
One yard is 36 inches. $14\ yd\times\frac{36\ in}{1\ yd}=504\ in$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12362 | # How do you solve log_5(3x^2 - 1) = log_5 2x?
May 19, 2016
x = 1.
#### Explanation:
Logarithm is a single-valued function.
So, $3 {x}^{2} - 1 = 2 x$. Solving this quadratic equation
$3 {x}^{2} - 2 x - 1 = 0 , x = 1. - \frac{1}{2}$
Negative root is inadmissible for #log_5(2x).
So, x = 1. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12363 | # 9.5: Uniform Plane Waves - Characteristics
In Section 9.4, expressions for the electric and magnetic fields are determined for a uniform plane wave in lossless media. If the planar phasefront is perpendicular to the $$z$$ axis, then waves may propagate in either the $$+\hat{\bf z}$$ direction of the $$-\hat{\bf z}$$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12364 | ## Tuesday, January 24, 2006
### Just Try and Reduce It. Topic: Number Theory. Level: AIME/Olympiad.
Problem: (1959 IMO - #1) Prove that the fraction $\frac{21n+4}{14n+3}$ is irreducible for every natural number $n$.
Solution: First, we're going to prove a very useful lemma.
**Lemma: For positive integers $a,b$, if... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12366 | ## Before You Watch
This video shows you how to interpret a linear equation and graph it on a Cartesian plane. So, it will refresh your memory of how to use a Cartesian plane and develop your understanding of what the graph of a linear equation means.
This topic also builds on the fundamental concepts of algebra cove... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12367 | To do so, we can take the dot product of the inverse of matrix A, and the matrix B as shown below: If you are not familiar with how to find the inverse of a matrix, take a look at this link to understand how to manually find the inverse of a matrix. $$Numerical Analysis EMT can solve non-linear equations and systems, o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12357 | # Mathspp Blog
### A blog dedicated to mathematics and programming!
As of now, my blog is being migrated here. You can find all the old content over here.
231
##### My two cents on the 2020 APL competition
The 2020 APL programming competition was tough! In this post I share a couple of thoughts and my solutions.
3... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12352 | If you find any mistakes, please make a comment! Thank you.
## Exhibit an element in the center of a group ring of finite group
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.2 Exercise 7.2.12
Let $R$ be a ring with $1 \neq 0$, and let $G = \{g_1, \ldots, g_n \}$ be a finite group. Prove that t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12355 | < Back to Blog
# Camera Modeling: Focal Length & Collinearity
###### June 10, 2021
Tutorial
Camera calibration is a deep topic that can be pretty hard to get into. While the geometry of how a single camera system works and the physics describing lens behavior is well-known, camera calibration continues to be mystify... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12365 | # Converse of Banach fixed-point theorem
Banach fixed-point theorem states that:
If $(X,d)$ - complete metric space and $f:X\to X$ is contraction mapping. Then exists unique point $x_0$ such that $f(x_0)=x_0.$
And I have the following question:
Is there incomplete metric space in which every contraction mapping has... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5408 | # What was the speed of the projectile when it left the cannon?
1. Homework Statement
A projectile is shot from the surface of te Earth by means of a very powerful cannon. If the projectile reaches a height of 35,000 m above Earth's surface, what was the speed of the projectile when it left the cannon?
a. 355 m/s
b.... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5409 | ## College Algebra 7th Edition
$714$ runs.
Let the amount of home runs Babe Ruth hit during his career be $x$. Therefore Hank Aaron hit $x+41$ runs. In total, they hit $(x)+(x+41)$ runs, which the problem stated was $1469$ runs. Set up the equation of $2x+41=1469$ and solve for $x=\frac{(1469-41)}{2}=714$ runs. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5410 | null pointer
Ideas expressed here are nobody’s.
On Leibniz's Truth
Let a statement be any sentence of form
$\mathcal S + \phi$
Where $$\mathcal S$$ is a subject and $$\phi$$ is a predicate. The sentences "Spinoza died in the Hague", and "Grey is grey", for example, qualify as statements. In the first, we have "Spi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5411 | # How come such different methods result in the same number, $e$?
I guess the proof of the identity $$\sum_{n = 0}^{\infty} \frac{1}{n!} \equiv \lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x$$ explains the connection between such different calculations. How is it done?
-
This is usually done by restricting $x$ to... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5412 | # Problem with \bordermatrix
I need to write a complicated determinant of matrix, that has a structure as in the attached picture.
• Welcome to TeX.SX! You like to pose difficult questions, don't you? :-D – egreg Oct 9 '16 at 11:39
Some manual work is still needed, but I hope you don't have so many objects like thes... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5413 | # Fixed Point on Perpendicular Bisector
### Problem
Let two circles $(C_{1}),$ $(C_{2})$ intersect at two points $A$ and $B$ and a variable line through $A$ cut circle $(C_{1})$ in $P_1$ and circle $(C_{2})$ in $P_2.$
Prove that the perpendicular bisector of line $P_{1}P_{2}$ passes through a fixed point.
### Solut... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5414 | ## Basic College Mathematics (10th Edition)
Sphere. $V\approx 15.0~m^3$
The solid shown is a sphere. We know that the volume of a sphere is given by: $\displaystyle V=\frac{4}{3}\pi r^3$ $V=\frac{4}{3}*3.14*1.53^3$ $V\approx 15.0~m^3$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5416 | # If Spec Z is like a Riemann surface, what's the analogue of integration along a contour?
Rings of functions on a nonsingular algebraic curve (which, over $\mathbb{C}$, are holomorphic functions on a compact Riemann surface) and rings of integers in number fields are both examples of Dedekind domains, and I've been t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5417 | # Order Isomorphism is Equivalence Relation
## Theorem
Order isomorphism between ordered sets is an equivalence relation.
So any given family of ordered sets can be partitioned into disjoint classes of isomorphic sets.
## Proof 1
Follows directly from Identity Mapping is Order Isomorphism.
Follows directly from I... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5418 | # Quasilinear integrodifferential Bernoulli-type equations
Результат исследования: Научные публикации в периодических изданияхстатья по материалам конференциирецензирование
## Аннотация
The equations considered in this article have the form in which the time derivative of the unknown function is expressed as a doubl... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5420 | ## Emerging thoughts on the Poisson as a limit of the Binomial
I am trying to set down some thoughts on the relationship between the Binomial and the Poisson. The specific problem emerges from modelling data where I assume $Y_{i1} \sim Poisson(\lambda_i)$ and $Y_{i2} | n_i \sim Binomial(n_i, p_i)$. The specific proble... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5421 | mscroggs.co.uk
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# Puzzles
## Archive
Show me a Random Puzzle
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## x to the Power of x Again
Permanent link to this puzzle: mscroggs.co.uk/puzzles/13
Let $$y=x^{x^{x^{x^{...}}}}$$ [$$x$$ to the power of ($$x$$ to the power of ($$x$$ to the power of ($$x$$ to the power of ...))) with ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5422 | 1. ## Factorising
Express x^4 - x in its fully factorise form.
I went through factorising methods:
common factor
difference of two squares X
breaking brackets X
polynomial ?
I would say answer = x(x^3 - 1)
But that is way to simple for the level i'm taking, so im asking if polynomials are involved here? If not, wha... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5423 | # Dependency of vectors in eigenspace corresponding with eigenvalue zero
The eigenspace corresponding with the eigenvalue zero is the same as the null space of the original matrix. All vectors in the null space are linearly independent so the eigenvectors of zero are also independent.
Is this conclusion right?
-
Yo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5419 | NZ Level 7 (NZC) Level 2 (NCEA)
Solve Equations with Rational Expressions
Lesson
We've learnt a lot about solving equations including how to solve one step, two step and three step equations, as well as equations that include fractions. We've also looked at how to group pronumerals (ie. algebraic letters) when they ar... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5415 | # Solid state physics: From nonequilibrium distribution function to Boltzmann equation
1. Jan 24, 2013
### Denver Dang
1. The problem statement, all variables and given/known data
Hi.
I have a course where I am supposed to show how to get to the Boltzmann equation from a nonequilibrium distrubution function.
At the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2722 | ### Show Posts
This section allows you to view all posts made by this member. Note that you can only see posts made in areas you currently have access to.
### Topics - Min Gyu Woo
Pages: [1]
1
##### MAT334--Lectures & Home Assignments / Sample Final Solutions
« on: December 11, 2018, 08:38:32 PM »
Could the prof go ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2723 | ## G-Engine #7: Vectors
We have added a basic math library to the 3D engine, but we’re still missing several fundamental mathematical building blocks to move forward and build full-fledged 3D environments. In particular, I want to implement Vectors, Matrices, and Quaternions. This post will cover Vectors, which enable... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2724 | # Tag Info
A rng is an associative ring without necessarily having a multiplicative identity (rng = ring - $i$dentity). |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2725 | Question
# Internal bisector of $$\angle \mathrm{A}$$ of triangle ABC meets side BC at D. A line drawn through $$\mathrm{D}$$ perpendicular to AD intersects the side AC at $$\mathrm{E}$$ and the side AB at F. If $$\mathrm{a},\ \mathrm{b},\ \mathrm{c}$$ represent sides of $$\Delta \mathrm{A}\mathrm{B}\mathrm{C}$$ then
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2726 | # Existence of closed form for indefinite integral
During calculus studies, I tried to find a primitive for the following indefinite integral, in a simple form using standard functions:
$\int \sqrt{\sin x} \mathrm{d}x$
I always failed. It may be possible to prove that the primitive exists, or even to find an infinit... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2727 | # Inverse function of $x-\lfloor x \rfloor$ and $(x-\lfloor x \rfloor)^2$
I need to find the inverse of these two functions if they exist:
$$f_1 = x-⌊x⌋, 1\leq x<2, 0\leq f_1<1$$ and $$f_2 = (x-⌊x⌋)^2, 1\leq x<2, 0\leq f_2<1$$
I worked through it and I think they are both bijective functions, but I am not exactly su... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2728 | # The Convenient Setting for Quasianalytic Denjoy-Carleman Differentiable Mappings - Mathematics > Functional Analysis
Abstract: For quasianalytic Denjoy-Carleman differentiable function classes $C^Q$where the weight sequence $Q=Q k$ is log-convex, stable under derivations, ofmoderate growth and also an $\mathcal L$-i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2730 | # Math Help - Law of Sine and Cosine Question
1. ## Law of Sine and Cosine Question
C----35----A
--\---------/
---\------/
---28--17
-----\--/
------\/
------B
This is what the triangle is suppose to be like.
Law of sine: (sinA/a)=(sinB/b)=(sinC/c)
Law of cosines: a2=b2+c2-2bc(cosA)
b2=a2+c2-2ac(cosB)
c2=a2+b2-2ab(co... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2731 |
Definition 4.32.9. Let $\mathcal{C}$ be a category. The $2$-category of fibred categories over $\mathcal{C}$ is the sub $2$-category of the $2$-category of categories over $\mathcal{C}$ (see Definition 4.31.1) defined as follows:
1. Its objects will be fibred categories $p : \mathcal{S} \to \mathcal{C}$.
2. Its $1$-... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2733 | # Solutions To Mathematics Textbooks
Solutions To Mathematics Textbooks
This wikibook aims to provide many solutions and explanations to questions and assignments posed in mathematics textbooks. Few mathematics textbooks (especially towards university / college level mathematics) have the complete set of solutions av... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2735 | # Congruence of all integers n, 4^n and 1 +3n mod(9)?
by mgiddy911
Tags: congruence, integers, mod9
P: 332 I just took a number theory midterm, the professor had a question the that said "Show by induction that for all integers n, 4$$^{n}$$ is congruent to 1 +3n mod(9). Now am I crazy or did the professor probably me... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2720 | $\frac{n+3}{n-1} = \frac{n-1}{n-1} + \frac{4}{n-1} = 1 + \frac{4}{n-1}$. Thus $\frac{n+3}{n-1}$ is an integer if and only if $n-1$ divides exactly into $4$. The values of $n$ for which this is true are $-3, -1, 0,2,3,5$. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2732 | Math Help - Finding the area of this region
1. Finding the area of this region
I've attached a picture of the problem I'm working on. First I set each equation equal to y so I have y=x+a and y=-x+b which would make the points of intersection (0,0) and (-2,-5) so I then subtracted -x+b from x+a (substituting in the co... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2734 | # Math Help - Need some derivatives guidance
1. ## Need some derivatives guidance
Finding the derivatives of
f(x)=e^(1-x^2)
f(x)=ln(x^3-1)
f(x)=3xe^2x
Anything will be greatly appreciated, I am just trying to figure out exactly how to solve these, I understand using the different rules..but, I am still having tro... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2721 | # [Solution] Maximum Crossings (Hard Version) solution codeforces – What is the maximum number of crossings there can be if you place the wires optimally?
Maximum Crossings (Hard Version) solution codeforces – The only difference between the two versions is that in this version 𝑛2105n≤2⋅105 and the sum of 𝑛n over al... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2729 | ## Elementary Technical Mathematics
$$\frac{ 43 }{9 \ x y^2}.$$
We divide by the monomial as follows: $$\frac{215x^2y^3}{45x^3y^5}=\frac{5\cdot 43 }{5\cdot 9 \ x y^2}=\frac{ 43 }{9 \ x y^2}.$$ Note that we can not simplify any further, because "$9$" does not go into "$43$" evenly. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6320 | # Impredicative Encodings of (Higher) Inductive Types
Postulating an impredicative universe in dependent type theory allows System F style encodings of finitary inductive types, but these fail to satisfy the relevant η-equalities and consequently do not admit dependent eliminators. To recover η and dependent eliminati... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6321 | # Lie algebra question
1. Aug 19, 2007
### Fredrik
Staff Emeritus
I'm reading about gauge theory and the text goes through some stuff about Lie groups and algebras rather quickly. I tried to prove one of the things they state without proof and got stuck.
Suppose that M and N are manifolds and $\phi:M\rightarrow N$ ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6322 | ## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
Published by Pearson
# Chapter R - Elementary Algebra Review - R.4 Polynomials - R.4 Exercise Set - Page 961: 38
#### Answer
$8x^5+\dfrac{3}{10}x+\dfrac{2}{3}$
#### Work Step by Step
By combining like terms, the given expression, $8x^5-... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6324 | pt Consider the series n 1 8 n 2 9 n Determine whether the series converges and
# Pt consider the series n 1 8 n 2 9 n determine
• Homework Help
• 2
• 100% (2) 2 out of 2 people found this document helpful
This preview shows page 1 - 2 out of 2 pages.
3.(1 pt)Consider the seriesn=18n+29nDetermine whether the series... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6325 | # Amount of Cl- needed to precipitate AgCl given Ksp and [Ag+]
Why is $0.25 \ \mathrm{mL}$ the correct answer in this problem?
I used the Ksp to find the molarity of Chlorine to be $3.47 \times 10^{-2} \ \mathrm{M}$.
Then I used the formula
$$\text{Molarity}_{\text{initial}} \times \text{Volume}_{\text{initial}} = ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6326 | The Law of Sines defines the relationships between the angles and sides of any triangle.
Law of Sines |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6327 | Area Index
# Area of a Scalene Triangle Formulas & Calculator
The area of a scalene triangle can be calculated using the following formula: if you know the length of the base side and the height.
## Formula Knowing the base and the height
If you know the length of the base and height, you can calculate its area usi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6328 | # Multiplicative Group of Reals is Subgroup of Complex
## Theorem
Let $\struct {\R_{\ne 0}, \times}$ be the multiplicative group of real numbers.
Let $\struct {\C_{\ne 0}, \times}$ be the multiplicative group of complex numbers.
Then $\struct {\R_{\ne 0}, \times}$ is a normal subgroup of $\struct {\C_{\ne 0}, \time... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6329 | # Continued Fraction Identities/First/Infinite
It has been suggested that this article or section be renamed. One may discuss this suggestion on the talk page.
## Theorem
Let $\left[{a_0, a_1, a_2, \ldots}\right]$ be a simple infinite continued fraction.
Then:
$\left[{a_1, a_2, a_3, \ldots}\right] = a_1 + \dfrac ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6330 | 💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!
# Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.$y = x^{\frac{3}{2}}$ , $y = 8$ , $x = 0$
## $V=192 \pi$
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6331 | The Journal of Advanced Studies in Topology (JAST) is dedicated to rapid publication of the highest quality short papers, regular papers, and expository papers. JAST is a peer-reviewed international journal, which publishes original research papers and survey articles in all aspects of topology and its applications.
V... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6333 | # Cochleoid
Figure 1. The cochleoid (pdf)
A plane transcendental curve whose equation in polar coordinates is $$\rho = a\frac{\sin\varphi}{\varphi}.$$
The cochleoid has infinitely many spirals, passing through its pole and touching the polar axis (see Fig.). The pole is a singular point of infinite multiplicity. Any... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6334 | Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles an... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6335 | # Prove that two congruences by modulo are equivalent
Given $a \equiv a'\pmod m$ and $b \equiv b' \pmod m$.
Prove that $ax \equiv b \pmod m$ and $a'x \equiv b' \pmod m$ are equivalent.
I understand I have to show that this modulo congruences have the same set of solutions. But what is solution?
• You do not have to... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6332 | # B How come this natural logarithm approximation works?
1. Dec 1, 2016
### Andreas C
I came across a guy claiming that the "best approximation" for the natural logarithm of a number is this:
ln x=2^n*(x^(2^-n)-1)
Oddly enough, it seems to work rather well! I don't really get why it does... I also don't know if it ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6323 | # Thread: Prove using epsilon - delta definition of a limit?
1. ## Prove using epsilon - delta definition of a limit?
How can I prove lim x->1 (x^2 + 4x) = 5 and lim x->2 (1/x^2) = 1/4 using the epsilon - delta definition of a limit?
2. For example:
$\displaystyle |x^2+4x-5|<\epsilon \Leftrightarrow \ldots \Leftrig... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16736 | # no. of non-singular matrices
If $A$ is a $3 \times 3$ matrix with entries from the set $\left\{-1,1\right\}$. Then Total no. of non-singular matrices $A$ is |
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