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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8220 | Q
# Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
Q : 3 Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
Views
Given: the diagonals of a quadrilateral bisect each other at right angles i.e.BO=OD.
To prov... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8221 | # Computing the Cohomology ring of the torus
I need guidance on finishing off my computation of the cohomology ring of the torus $T$ with coefficients in $\mathbb{Z}_2$.
Consider the following simplicial structure of $T$.
Let $\varphi \in C^0(T, \mathbb{Z}_2)$ be the dual of the vertex $v \in C_0(T, \mathbb{Z}_2)$. ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8222 | American Institute of Mathematical Sciences
ISSN:
1937-5093
eISSN:
1937-5077
All Issues
Kinetic & Related Models
September 2009 , Volume 2 , Issue 3
Select all articles
Export/Reference:
2009, 2(3): 403-424 doi: 10.3934/krm.2009.2.403 +[Abstract](2099) +[PDF](263.3KB)
Abstract:
In a previous work [J. of Hyperbo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8208 | # Which radical expression is larger?
#### Archie
Archie, (in effect) you supported that 2 < $$\displaystyle \ \dfrac{log(10)}{log(3)}, \ \$$ and we know that 2 = 16/8 < 22/8.
But I do not see support as to where you show the relative size of $$\displaystyle \ \dfrac{log(10)}{log(3)} \$$ versus 22/8.
Well $\frac{\lo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8218 | # The Stacks Project
## Tag 015F
Lemma 13.17.9. Let $F : \mathcal{A} \to \mathcal{B}$ be an exact functor of abelian categories. Then
1. every object of $\mathcal{A}$ is right acyclic for $F$,
2. $RF : D^{+}(\mathcal{A}) \to D^{+}(\mathcal{A})$ is everywhere defined,
3. $RF : D(\mathcal{A}) \to D(\mathcal{A})$ is ev... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8223 | Let $\{a_n\}_{n\geq 1}$ be a sequence of real numbers which satisfies the following relation $a_{n+1}=10^n a_n^2.$ a) Prove that if $a_1$ ...
1. Let $\{a_n\}_{n\geq 1}$ be a sequence of real numbers which satisfies the following relation $a_{n+1}=10^n a_n^2.$ a) Prove that if $a_1$ is small enough, then $\displaystyle... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8211 | # Homework Help: Bead on a rotating coil
1. Feb 3, 2014
### nhalford
1. The problem statement, all variables and given/known data
A bead of mass $m$ is threaded around a smooth spiral wire and slides downwards without friction due to gravity. The $z$-axis points upwards vertically. Suppose the spiral wire is rotated... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_22001 | # Help on showing a function is Riemann integrable
Problem Let $(a_k)_{k=1}^\infty$ be the sequence of values of $\mathbb{Q}\cap[0,1]$ (which is countable set). Let $g:\mathbb{R}\rightarrow\mathbb{R}$ by $g=\sum_{k=1}^\infty {1 \over k}\cdot \chi_{a_k}$, that is, $g(x)=0$ if $x\notin\mathbb{Q}\cap[0,1]$ and $g(a_k)={1... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_22002 | Get premium membership and access revision papers with marking schemes, video lessons and live classes.
# Form 3 Mathematics Paper 1 End of Term 3 Exams 2021
Class: Form 3
Subject: Mathematics
Level: High School
Exam Category: Form 3 End Term 3 Exams
Document Type: Pdf
## Exam Summary
Attempt ALL the questions ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_22003 | Browse Questions
# Which one of the following is a correct set?
$\begin {array} {1 1} (1)\;H_2O,sp^3, angular & \quad (2)\;BCl_3,sp^3,angular \\ (3)\;NH_4^+,dsp^2,square\;planar & \quad (4)\;CH_4,dsp^2,tetrahedral \end {array}$
Can you answer this question? |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_22004 | # $\mathbb{R}\cong X\times Y$ (homeomorphic) implies $X$ or $Y$ is a point.
The following is Problem 2.1.1 from Tammo tom Dieck's Algebraic Topology:
Suppose $$\mathbb{R}\cong X\times Y$$ (homeomorphic). Then $$X$$ or $$Y$$ is a point.
FWIW, the section 2.1 is about (path) connected components (i.e., $$\pi_0$$) and ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_22006 | RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB
General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archiv... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_22007 | # Wayne Lewis (University of Hawaiʻi)
When:
August 25, 2020 @ 6:00 am – 8:00 am
2020-08-25T06:00:00-10:00
2020-08-25T08:00:00-10:00
Where:
Lecture held in Elysium
Title: Classification of Periodic LCA Groups of Finite Non-Archimedean Dimension
by Wayne Lewis (University of Hawaiʻi) as part of Topological Groups
Lect... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_22008 | Simple Harmonic Motion – JEE Main Previous Year Questions with Solutions
JEE Main Previous Year Question of Physics with Solutions are available here. Practicing JEE Main Previous Year Papers Questions of Physics will help all the JEE aspirants in realizing the question pattern as well as help in analyzing their weak ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_22009 | # Quantum mechanical measurement
Suppose, a particle has non zero probability to be in any between x = 1 and x = 10. Let, we measure its position with a very low energy photon. It will collapse it’s wave function, since it disturbs the system.
1. What will be the result of such an experiment? Will the position of the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_22010 | # Finding a parametre that satisfies an inequality
For what values of $$k>0$$ does $$a^2+b^2+c^2+d^2+4(\sqrt3 -1)(abcd)^k\geq\sqrt{12(abc+abd+acd+bcd)}$$ hold for all $$a,b,c,d\geq0$$ satisfying $$a+b+c+d=4$$?
On the one hand, I found a lower bound for the LHS by using an equivalent form of Turkevich's inequality : $$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_22011 | Find the equation for the ellipse that satisfies the given conditions : Ends of major axis $(0, \pm \sqrt 5 )$, ends of minor axis $(\pm 1, 0)$
$\begin {array} {1 1} (A)\;\large\frac{x^2}{5}+\large\frac{y^2}{1}=1 & \quad (B)\; \large\frac{x^2}{1}+\large\frac{y^2}{5}=1 \\ (C)\;\large\frac{x^2}{1}-\large\frac{y^2}{5}=1 &... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_22012 | A Comparison with the Density Matrix Master Equation
# Thermodynamics of Maximum Transition Entropy for Quantum Assemblies
## Abstract
This work presents a general unifying theoretical framework for quantum non-equilibrium systems. It is based on a re-statement of the dynamical problem as one of inferring the distri... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_22013 | Iterability of exp(x)-1 bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 08/11/2007, 09:33 PM (This post was last modified: 08/11/2007, 09:45 PM by bo198214.) Hm, this is strange. I just tried numerically the half iterate of $e^x-1$ and it looks quite convergent. However I read in the article of Erdös a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_22014 | # Helmholtz Resonance
One can make a sound by blowing into an empty bottle. The sound is a product of a resonance phenomenon called the Helmholtz resonance. We can determine the resonance frequency by noting the shape and dimension of this cavity, the Helmholtz resonator, where V denotes the volume of the body, S deno... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_22015 | # Solve the equation : $\tan \theta + \tan 2\theta + \tan 3\theta = \tan \theta \tan 2\theta \tan 3\theta$
I've been having some trouble solving this equation. (The solution in my book is given as $\frac {n \pi}{3}, n \in Z$)
Here is what I've done
$$\frac {\sin \theta}{\cos \theta} + \frac {\sin 2\theta} {\cos 2\th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_22000 | # Tag Info
5
In this diagram, the large triangle has sides of $2$ while the four smaller ones have sides of $1$. So place five pandas into those four small triangles. The maximum distance between any two points in any small triangle is clearly just $1$. Use the pigeonhole principle and finish from here.
3
This is a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_22005 | Courses
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# Let ABCD be a parallelogram and let E be the mid point of side AB. If EC is perpendicular to ED, then(a) $ED=EC$ (b) $EB=BC$ (c) $EA=ED$ (d) $EC+ED=2BC$
Last updated date: 25th Mar 2023
Total views: 308.7k
Views today: 6.85k
Ans... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16064 | # Tag Info
23
The main likely reasons why barter is not more common are: The inconvenience of having to find another party who both offers what you want and wants what you offer. Even if such a party can be found, the possible complexity of negotiating a "fair" transaction (eg I'll do your electrical job if you'll cl... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16065 | # point to point topology is also known as
Tree Topology. Offers the easiest method for error detecting and troubleshooting, Highly effective and flexible networking topology, It is scalable so you can increase your network size. There are methods which employ one more backup ring. of a computer network. Every communi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16066 | # How is the formula for the base current value derived in a three-phase per-unit system
currentpower
When analysing a power system using the per-unit system for a three phase system, why is \$S_b = \sqrt{3}*V_b*I_b\$, where as shown in the link, \$S_b\$ is the base power value, \$V_b\$ is the base voltage value and ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16067 | # Separating populations and estimating line-fit parameters
Given a dataset containing two populations, each of which can be described by a linear relationship between two variables in each sample with high R$^2$, how does one separate the two populations (and incidentally compute the line-fit)?
This is fairly easy t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16068 | # If sinA = -2/5 and tan θ > 0, then what are the five other trigonometric ratios?
Apr 12, 2016
$\cos A = - \frac{\sqrt{21}}{5}$
#### Explanation:
$\sin A = - \frac{2}{5}$. Find cos A by the identity:
${\cos}^{2} A = 1 - {\sin}^{2} A$
${\cos}^{2} A = 1 - \frac{4}{25} = \frac{21}{25}$ ---> $\cos A = \pm \frac{\sqrt{... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16070 | ## Workshop on Complex Analytic Geometry
### Organizers G. Marinescu, N. Savale, V.-D. Vu
##### Dienstag, 12.07.22, 09:30 -16:00, Raum 313 und Raum 314 des Department Mathematik
ANR-DFG project QuaSiDy
"Quantization, Singularities,
and Holomorphic Dynamics".
09:30-10:30 im Raum 313 Masanori Adachi (Shizuoka ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16071 | Question 80
Consider three mixtures — the first having water and liquid A in the ratio 1:2, the second having water and liquid B in the ratio 1:3, and the third having water and liquid C in the ratio 1:4. These three mixtures of A, B, and C, respectively, are further mixed in the proportion 4: 3: 2. Then the resulting... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16073 | ## iluvvyyhu Group Title Can someone explain to me how i would solve this problem thanks <3 "Estimate graphically the local maximum and local minimum of f(x)=((1/4)x^5)+(x^2)-4x"? one year ago one year ago
1. iluvvyyhu Group Title
o-o i have a graphing calculator since the review worksheet said i needed one x.x but i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16074 | # Difference of Compound Interest and Simple Interest | Simple Interest Vs. Compound Interest
The Difference of Compound Interest and Simple Interest is explained based on the principal amount. The simple interest depends on the principal amount and compound interest depends on the principal amount and the interest co... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16075 | Functions!
Algebra Level 3
Let $$F(x) = x - \lfloor x \rfloor$$. Find the number of solutions to the equation $$F(x) + \dfrac1{F(x)} = 1$$.
Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16076 | # The subbase theorem for total boundedness
The uniform space analogue of Alexander's subbase lemma on compact subbase is (As we know, Alexander subbase lemma can be used to prove Tychonoff's theorem) :
Let $(X,\mathcal{U})$ be a uniform space such that for each member $U$ of some subbase for $\mathcal{U}$ there is a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16069 | # A torus splits over a finite Galois extension
Let $k$ be a field. A torus $T$ is an affine group scheme over $k$ such that $T \times_k \overline{k}$ is isomorphic as $\overline{k}$-schemes to $\textrm{Spec }\overline{k}[T_1^{\pm1}, ... , T_n^{\pm1}]$. If $E$ is a field containing $k$, we say that $T$ splits over $E$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16072 | ## Why do mathematicians always confuse Halloween and Christmas?
Posted: October 30, 2012 in Mathematics
Tags: , ,
Why, why, why?
Since Halloween is coming soon, I will answer the question.
Proof of Halloween = Christmas
Halloween = 31 Oct = 3×8+1 = 25 Dec = Christmas 🙂
## special technique on definite integral
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16077 | A function being “finite” over a point on non-normal schemes?
I recently came across a remark about Cartier divisors in a textbook on algebraic geometry. I'm not sure how to interpret the remark. I've attached the previous paragraph as well for context.
The phrasing I am confused about is "thus the function $$f$$ may... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16079 | College Algebra (6th Edition)
False, $\ln(x\cdot 1)=\ln x+\ln 1$
On the RHS, the term ln1 equals zero, (a basic logarithmic property, so the equation of the problem statement is equivalent to ln(x+1)=lnx, which is false. A property for expanding $\log_{b}(...sum...)$ does not exist. There is, however, The Product Rule... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_16078 | # Homework Help: Expected r^2 for the 2s wavefunction of hydrogen atom
1. Sep 6, 2010
### chall
1. The problem statement, all variables and given/known data
Calculate the expected value for r^2 for the 2s wavefunction of the hydrogen atom (only the radial part of the function is needed for l=0). If you choose to sol... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9344 | # Good Boy
In 1919, engineer James Cowan Smith bequeathed £55,000 to the National Gallery of Scotland.
He set two conditions. One was that the gallery provide for his dog Fury.
The other was that this picture of his previous dog Callum, by painter John Emms, always be hung in the gallery.
Both conditions were fulfi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9347 | zbMATH — the first resource for mathematics
On the recovery of a curve isometrically immersed in $$\mathbb E^n$$. (English) Zbl 1080.53003
The $$n-1$$ curvature functions of a curve in Euclidean $$n$$-space are assumed to belong to suitable Sobolev spaces, the first $$n-2$$ to have positive values. The derivatives in ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9349 | Electronic Communications in Probability
On recurrence and transience of multivariate near-critical stochastic processes
Götz Kersting
Abstract
We obtain complementary recurrence/transience criteria for processes $X=(X_n)_{n \ge 0}$ with values in $\mathbb R^d_+$ fulfilling a non-linear equation $X_{n+1}=MX_n+g(X_n... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9350 | ### Width(element)
Line width for a Plot element
#### Description:
This attribute determines the line width used when drawing each element of graphical output produced by a Plot. It takes a separate value for each graphical element so that, for instance, the setting " Width(border)=2.0" causes the Plot border to be ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9353 | Dilogarithm
The dilogarithm function $\mathrm{Li}_2$ is defined for $|z| \leq 1$ by $$\mathrm{Li}_2(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{z^k}{k^2},$$ which is a special case of the polylogarithm. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9355 | # Class 9 Maths Important Questions for Heron Formula Mensuration
Given below are the Class 9 Maths Important Questions for Heron Formula Mensuration
(a) Concepts questions
(b) Calculation problems
(c) Multiple choice questions
(e) Fill in the blank's
Question 1
Calculate the area in each case
1. Triangle have sides ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9358 | # Expository Writings, Notes, Problem Solutions, etc.
The following are (expository) papers I wrote as an undergrad to satisfy various course and degree requirements.
• Fourier Analysis on the Torus – An introduction to Fourier analysis on the Torus, which includes Kolmogorov’s construction of an $L^{1}$ function who... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9359 | # Problem 2-9: Differentiating Polynomial and Rational Functions
Differentiate
a) $f\left(x\right)= 1+ 2x$
b) $f\left(x\right)= 1 - 2x + 2x^2$
c) $f\left(x\right)= 1- x^2 +\frac{1}{x}$
d) $f\left(x\right)= 1 - x +\frac{1}{1-x}$
Solution
The following rules can be used:
I) $\displaystyle\frac{d}{dx}ax^n=anx^{n-1}$
II)... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9345 | # Quick question on notation
Gold Member
## Main Question or Discussion Point
I was wondering how to express "x is a real number and not 1". What's the best way to express this? Right now I'm using...
$$x \epsilon \mathbb{R} \wedge x \neq 1$$
But I'm sure there's a better way.
chiro
I was wondering how to express... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9346 | # quantum mechanics in multiple dimensions
by aaaa202
Tags: dimensions, mechanics, multiple, quantum
P: 960 Suppose we have a 2d problem (for instance a 2d box). You look for separable solutions in x and y. But it seems to me that the solutions are in a way determined by how we choose the separation constant. Do we k... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9352 | # Basics of Fractions / Percentages
In mathematics, fractions and percentages are both rational numbers. These numbers are called “rational”, not because they’re more reasonable than other numbers, but because they are formed as the ratio of two integers. For example, 2/5, 25/8, -4/3, and 0 are all rational numbers. E... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9354 | # Tag Info
## New answers tagged amsmath
0
A solution with blkarray and eqparbox: \documentclass{article} \usepackage{mathtools, blkarray} \usepackage{eqparbox} \begin{document} \begin{blockarray}{lc@{{}={}}c} \begin{block}{\BAmultirow{\eqboxwidth{T}}\{c@{{}={}}c} \eqparbox{T}{Text text 1:} & a &b+c\\ & d &e+f \\ \e... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9356 | Free Version
Moderate
# Term in Arithmetic Sequence
ACTMAT-FVRERN
For the sequence 3, 7, 11, 15, …, where 3 is the value of the first term, which of the following represents the value of the 63th term?
A
$16$
B
$67$
C
$247$
D
$251$
E
$255$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9357 | Question
# For the following exercises, find the domain of the rational functions. f(x)=\frac{x^{2}+4x-3}{x^{4}-5x^{2}+4}
Rational functions
For the following exercises, find the domain of the rational functions.
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}^{{{2}}}+{4}{x}-{3}}}{{{x}^{{{4}}}-{5}{x}^{{{2}}}+{4}}}... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9348 | # Solving x'=Ax+g using undetermined coefficients
1. May 8, 2010
### Jamin2112
1. The problem statement, all variables and given/known data
Problem #4 from here: http://www.math.washington.edu/~jtittelf/ExtraCredit.pdf
2. Relevant equations
?
3. The attempt at a solution
There's only one example of using undete... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9351 | # Magnetic susceptibility (Ising model)
Hi,
I'm slightly confused about how to prove that:
$$\chi$$=$$\vartheta$$<M>/$$\vartheta$$H
is equal to...
$$\chi$$=(<M2>-<M>2 )/ T
I've expressed <M> as $$\sum$$Msexp(-E/kBT) /
$$\sum$$exp(-E/kBT)
and know that E=-J$$\sum$$SiSj-H$$\sum$$Si
But seem to get lost in the dif... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24192 | # What is the length of the hypotenuse of a right triangle whose legs have lengths of 5 and 12?
May 7, 2018
The length of the hypotenuse is 13 units.
#### Explanation:
Pythagorean Theorem:
${a}^{2} + {b}^{2} = {c}^{2}$
${5}^{2} + {12}^{2} = {c}^{2}$
$25 + 144 = {c}^{2}$
$169 = {c}^{2}$
$\sqrt{169}$ = c
c = 13 |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24193 | # The $p$-Weak Gradient Depends on $p$
created by dimarino on 18 Nov 2013
modified by speight on 16 May 2017
[BibTeX]
Published Paper
Inserted: 18 nov 2013
Last Updated: 16 may 2017
Journal: Proceedings of the American Mathematical Society
Volume: 143
Number: 5239-5252
Year: 2014
Notes:
The new version generalize... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24194 | # For the given fraction and decimals we have to write its equivalent percent. Given fractions are a)frac{3}{25} b) frac{1}{5} c) frac{2}{5} And the decimals are, d) 0.01, e) 4.06, f) 0.6 We have to find its equivalent percent.
For the given fraction and decimals we have to write its equivalent percent. Given fraction... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24195 | # Guided proof to the isomorphism theorems.
1. Apr 4, 2007
### *melinda*
1. The problem statement, all variables and given/known data
Let $G_1$ and $G_2$ be groups with normal subgroups $H_1$ and $H_2$, respectively. Further, we let $\iota_1 : H_1 \rightarrow G_1$ and $\iota_2 : H_2 \rightarrow G_2$ be the injection... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24197 | # Coordinate geometry - circles.
1. Aug 11, 2004
### Gaz031
I'm just introducing myself to coordinate geometry in the xy plane of cirlces.
Here's a question i'm having trouble with:
Q11: The line with equation y=mx is a tangent to the circle with equation x^2 + y^2 - 6x - 6y + 17 = 0. Find the possible values of m.... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24199 | # In a single throw of two dice, find
Question:
In a single throw of two dice, find P (a total of 9 or 11)
Solution:
We know that,
Probability of occurrence of an event
$=\frac{\text { Total no.of Desired outcomes }}{\text { Total no.of outcomes }}$
Total outcomes are $(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)$, $(2,1... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24200 | # zbMATH — the first resource for mathematics
Hyperstability of the Jensen functional equation. (English) Zbl 1299.39022
S.-M. Jung, M. S. Moslehian and P. K. Sahoo [J. Math. Inequal. 4, No. 2, 191–206 (2010; Zbl 1219.39016)] investigated the conditional stability of the generalized Jensen functional equation $$f(ax+b... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24202 | quantum mechanics variational theory
In this limit the model is translation invariant. The Variational Method is a mathematical method that is used to approximately calculate the energy levels of difficult quantum systems. ), to assume that the state minimising, is itself translation invariant. An arbitrary element of... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24203 | # Count The Squares
Probability Level 4
Consider the following $8\times8$ grid. Count the total number of squares that do not contain the square with the red star.
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24205 | Quasiregular Polyhedron
Get Quasiregular Polyhedron essential facts below. View Videos or join the Quasiregular Polyhedron discussion. Add Quasiregular Polyhedron to your PopFlock.com topic list for future reference or share this resource on social media.
Quasiregular Polyhedron
Quasiregular figures
Right triangle doma... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24206 | 1-646-564-2231
# Fractions and Division
## Key Concepts
• Fractions
• Divisions
• Relating fractions and divisions
## Division
Division is one the four basic mathematical operations, the other three being addition, subtraction, and multiplication. In simpler words, division can be defined as the splitting of a la... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24207 | # Wavelength of Light
Have you ever thought about the reason how humans are capable of seeing colours? The reason is, colours are nothing but electromagnetic radiations with a different wavelength of light. In the electromagnetic spectrum, the visible region is otherwise called visible light.
## What is Visible Spect... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24196 | # Show that the determinant of a given matrix is equal to the product of the difference between all of its entries
Let $\alpha_1, \alpha_2, \dots, \alpha_n \in \mathbb{R}$, where $n\ge 2$. Show that
$$\left|\begin{matrix} 1& \alpha_1 & \alpha_1^2 & \dots & \alpha_1^{n-1} \\ 1 & \alpha_2 & \alpha_2^2 & \dots & \alpha_... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24198 | Limited access
Consider the following demand curve for shoes:
$$P = 50 - 3Q_d$$
At which of the following quantities is the price elasticity of demand for shoes the most elastic?
(For an extra challenge, try finding the answer without doing any calculations!)
A
$Q_d=10$
B
$Q_d=11$
C
$Q_d=12.5$
D
$Q_d=15$
S... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24204 | ## Introduction
Brzezniak (2000) is a great book because it approaches conditional expectation through a sequence of exercises, which is what we are trying to do here. The main difference is that Brzezniak takes a more abstract measure-theoretic approach to the same problems. Note that you do need to grasp the measure... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24201 | # An implementation plan to annually re-weight the Australian CPI
The ABS maintains a program of periodic reviews of the Consumer Price Index (CPI) which examines CPI concepts, methodologies and data sources
Release date and time
## Preface
The Australian Bureau of Statistics (ABS) maintains a program of periodic r... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2288 | 1. ## Minimizing
Hard Math Question?
Minimize Z=9x1 + 4x2 + 12x3
The 1,2, and 3 are superscript.
Subject to the constraints:
3x1+x2+4x3 larger or equal to 24
3x1 + x2 + 2x3 larger or equal to 18
x1 >= 0, x2 >=0, x3 larger or equal to 0
What is Z, x1, x2, and x3?
All numbers after letter are superscript. Thanks!
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2289 | # Math Help - partial derivatives
1. ## partial derivatives
1. If it's given that A: R2 -> R is defined by A(x, y)={1, if xy greater than or equal to 0.
and 0, if xy < 0.
(a) how do i show that the partial derivatives Ax(0) and Ay(0) exist? (Note that Ax and Ay doesn't mean A*x and A*y. I just mean the first order de... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2290 | ## Generalizations of pseudo MV-algebras and generalized pseudo effect algebras.(English)Zbl 1174.06330
Summary: We deal with unbounded dually residuated lattices that generalize pseudo MV-algebras in such a way that every principal order-ideal is a pseudo MV-algebra. We describe the connections of these generalized p... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2291 | Can a hypothetical universe have more than 2 types of dimensions: spatial and temporal?
Our universe is often described as having 3 space-like dimensions and 1 time-like dimension.
Can hypothetical universe exist with more than space- and time-like dimensions?
If so how would these dimensions appear like?
• possibl... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2292 | ## Precalculus (6th Edition)
Published by Pearson
# Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.1 Inverse Functions - 4.1 Exercises - Page 416: 7
#### Answer
$x^{1/3}$ or $\sqrt[3]{x}$
#### Work Step by Step
To find the equation for $f^{-1}$, replace $f(x)$ with $y$, interchange $x$ and $y$, a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2295 | # 1.64: Wigner Distribution for the Double Slit Experiment
The quantum mechanical interpretation of the double‐slit experiment is that position is measured at the slit screen and momentum is measured at the detection screen. Position and momentum are conjugate observables connected by a Fourier transform and governed... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2296 | # UGC-NET | UGC NET CS 2015 Dec – III | Question 65
Consider a standard additive model consisting of rules of the form of If x is Ai AND y is Bi THEN z is Ci.
Given crisp inputs x = x0, y = y0, the output of the model is:
My Personal Notes arrow_drop_up
Article Tags :
Be the First to upvote.
Please write to us at ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2297 | ## Course Catalogue
#### Prerequisite courses for Undegraduates: UM 204
Functions on $R^n$ , directional derivatives, total derivative, higher order derivatives and Taylor series.The inverse and implicit function theorem, Integration on $R^n$ , differential forms on $R^n$ , closed and exact forms. Green’s theorem, St... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2300 | # The Precession of the Perihelion of Mercury via Legendre Polynomials
## Introduction
The planet Mercury has a highly elliptical orbit with a perihelion of about 0.31 AU and an aphelion of about 0.47 AU. This ellipse is not stationary but itself rotates about the Sun, a phenomenon known as the precession of the peri... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2302 | Solve by Factoring x-3x^(1/2)-4=0
Rewrite as .
Let . Substitute for all occurrences of .
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Replace all occurrences of... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2303 | • ### High harmonic imaging of ultrafast many-body dynamics in strongly correlated systems(1704.08471)
April 27, 2017 cond-mat.str-el
This Letter brings together two topics that, until now, have been the focus of intense but non-overlapping research efforts. The first concerns high harmonic generation in solids, which... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2293 | # Equivalence of Definitions of Generalized Ordered Space/Definition 3 implies Definition 1
## Theorem
Let $\left({S, \preceq, \tau}\right)$ be a generalized ordered space by Definition 3:
$\left({S, \preceq, \tau}\right)$ is a generalized ordered space if and only if:
$(1): \quad \left({S, \tau}\right)$ is a Hausd... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2298 | # How do you differentiate y^2-x^3cos(x) = x^2-y?
Jun 1, 2018
$y ' = \frac{2 x + 3 {x}^{2} \cos \left(x\right) - {x}^{3} \sin \left(x\right)}{2 y + 1}$
#### Explanation:
Using the chain and the product rule
we get
$2 y y ' - 3 {x}^{2} c 9 s \left(x\right) + {x}^{3} \sin \left(x\right) = 2 x - y$
solving for $y '$
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2299 | Chapter 10 - Area - 10-2 Areas of Trapezoids, Rhombuses, and Kites - Lesson Check - Page 625: 8
No. You only need to know the lengths of the bases and the height.
Work Step by Step
If you know the height, then you only need to know the lengths of the bases. The formula to find the area of a trapezoid is A=$\frac{1}{... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2301 | # Edwards curve
In mathematics, the Edwards curves are a family of elliptic curves studied by Harold Edwards in 2007. The concept of elliptic curves over finite fields is widely used in elliptic curve cryptography. Applications of Edwards curves to cryptography were developed by Bernstein and Lange: they pointed out s... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_2294 | Where am I supposed to go? Where was I supposed to know?get lost in questionsmore quotes
# pi: exciting
EMBO Practical Course: Bioinformatics and Genome Analysis, 5–17 June 2017.
# visualization + design
The 2017 Pi Day art imagines the digits of Pi as a star catalogue with constellations of extinct animals and pla... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3345 | # Real number between Two Unequal Real Numbers
We will learn here ‘how to find a real number between two unequal real numbers?’.
If x, y are two real numbers,$$\frac{x + y}{2}$$ is a real number lying between x and y.
If x, y are two positive real numbers, $$\sqrt{xy}$$ is a real number lying between x and y.
If x,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3346 | # Formal Semantics of Model Fields in Annotation-based Specifications
#### Reviewed Paper In Proceedings
Author(s):Bernhard Beckert and Daniel Bruns
In:KI 2012: Advances in Artificial Intelligence
Publisher:Springer-Verlag
Series:Lecture Notes in Computer Science
Volume:7526
Year:2012
Pages:13-24
## Abstract
It is ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3347 | # Sequence puzzling - what is the next number?
As stated, what's the next number?
71,82,94,94,53,43,62,?
1) hints are already given somewhere in this question!
2) operators aren't necessary involved
• I notice you've attracted a lot of downvotes with no explanation so I figure I'll state this just to help you out: ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3349 | If you're seeing this message, it means we're having trouble loading external resources on our website.
If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.
# Congruence & transformations
## Problem
Jerome was curious if triangle, A, B, C was congruent t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3350 | Contents
Partial differential equation
In mathematics, and in particular calculus, a partial differential equation (PDE) is an equation involving partial derivatives of an unknown function.
Partial differential equations are ubiquitous in science, as they describe phenonena such as fluid flow, gravitational fields, ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3351 | definite integral of piecewise function
This is going to be equal equal to one over pi. Suppose we have a function $$y=f(x)$$ that is bounded and piecewise continuous on an interval $$(a,b)$$ ($$a \lt b$$). So this first part was 1/2, this second part right So this first part right over here is positive 1/2. And then ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3352 | ## a very occasional diary.
nondescript
## 2010-01-12
### The Hunt for Addi(c)tive Monster
This is another spurious post about mathematics that happened instead of something more useful. Let's talk about one of the most common mathematical objects: a function that maps real numbers () to real numbers. We shall cal... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3353 | ## ISC Computer Science Previous Year Question Paper 2013 Solved for Class 12
Maximum Marks: 70
Time allowed: 3 hours
Part – I
While answering questions in this Part, indicate briefly your working and reasoning, wherever required.
Question 1.
(a) State the Principle of Duality. Write the dual of: [2]
(P + Q’).R.1 =... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3356 | # Has the equation $p^3-q^2+2=2^3\cdot q$ infinitely many solutions for $p$ and $q$ prime? [closed]
Consider the equation:
$$p^3-q^2+2=8\cdot q$$
Has this equation infinitely many solutions for $$p$$ and $$q$$ prime?
• No, every Mordell curve has only finitely many integral points. – probably destiny function Mar 2... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3357 | # Thread: quotient rule differentiation check !!
1. ## quotient rule differentiation check !!
$
f(x) = \frac{sinx}{x^2+1}
$
differentiation is:
$
f '(x) = \frac{(x^2+1)(cosx)-(sinx)(2x)}{(x^2+1)^2}
$
$
f '(x) = \frac{(cosx)-(sinx)(2x)}{x^2+1}
$
is this correct? thank u
2. Originally Posted by jvignacio
$
f(x)... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3359 | Electric Field distance
Homework Statement
A proton enters a parallel-plate capacitor traveling to the right at a speed of 1.276 x 10-5 m/s. The distance between the two plates is 1.59 cm. The proton enters the capacitor halfway between the top plate and the bottom plate; that is, a distance r = 0.795 cm from each pl... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3344 | #### Thank you for registering.
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_3348 | Question
# Let $$f(x)$$ be a polynomial of degree 6, which satisfies $$\displaystyle \lim_{x\rightarrow 0}\left ( 1+\frac{f\left ( x \right )}{x^{3}} \right )^{1/x}={e^{2}}$$ and local maximum at $$x= 1$$ and local minimum at $$x= 0$$ and $$2$$, then $$5f(3)$$ is equal to
Solution
## $$\displaystyle \lim_{x\rightarr... |
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