It seems that an equation factor must be “squared” as a convenient approximation to balance out some other series of factors invisibly . Might $E=mc^{1.95}$  work as well as $E=mc^2$? Might $A^2+B^2=C^2$ also work if all the factors used the same but different power and be even more accurate? Does anyone know of such a triangle that the current formula comes out to an even number.
I mean, why is $F=ma$? Why not $m^{0.123}$, $a^{1.43}$ or some random non-integers or irrational?  I hope you understand that my question isn't limited just to force, energy, velocity, etc.; it also extends to the area of a square, circle, etc. and all other formulas.  I think the whole thing starts with direct proportionality.  Most of them tell about the area of a circle, $A = πr^2$, where π is 3.14159..... an irrational number! It's not about the constant. I am talking about the power of a physical quantity.  I know why it has pi. It's because we chose the constant for area square to be one. If we chose it to be 1 for the circle then the area of a square will have a constant, 1/pi.   I've edited the question to 'rational exponents' since all are giving me examples of decimal non-integers.
How does the NSAutoreleasePool autorelease pool work? As I understand it, anything created with an alloc, new, or copy needs to be manually released. For example:  int main(void) {     NSString *string;     string = [[NSString alloc] init];     /* use the string */     [string release]; }   My question, though, is wouldn't this be just as valid?:  int main(void) {     NSAutoreleasePool *pool;     pool = [[NSAutoreleasePool alloc] init];     NSString *string;     string = [[[NSString alloc] init] autorelease];     /* use the string */     [pool drain]; } What is the term for the grandson of my aunt? Intuitive Understanding of the constant "$e$" How can I add "Show desktop" to the GNOME dash or Ubuntu Dock? This question is updated to request additional answers and details in light of information now available in the Dungeon Master's Guide. In the released DM basic rules, Lost Mine of Phandelver, Hoard of the Dragon Queen, and the DMG teaser there are wands, staves, and rings that you can use to cast spells.  Do abilities that trigger from casting a spell activate when casting a spell from an item?  Can the character modify the spell using class abilities when casting a spell from an item?   Examples include:  An abjurer Wizard's arcane ward recovering hit points from a Dispel Magic cast from a Ring of Spell Storing  A sorcerer using Twinned Spell on a ray of enfeeblement from a Staff of Power  An evocation wizard using Sculpt Spell on a fireball from a Wand of Fireballs.   Now that the DMG is out we have some clearer rules on casting spells from items (DMG p. 141):  Some magic items allow you to cast a spell from the item.  The spell is cast at the lowest possible spell level, doesn't expend any spell slots, and requires no components, unless the item's description says otherwise  The spell uses its normal casting time, range and duration, and the user of the item must concentrate if the spell requires concentration. A magic item, such as certain staffs, may require you to use your own spellcasting ability when you cast a spell from the item.  Does whether or not you can apply class abilities to the casting of the spell depend whether the item uses the user's own spellcasting ability (such as the Staff of Fire) versus an item that comes with a fixed spellcasting ability built-in (such as the Wand of Fireballs)? Does it matter if it's something that triggers more or less automatically like Arcane Ward, versus something you have to control, like Careful Spell? What is an intuitive explanation of the Expectation Maximization technique? There are several reasons to be looking for a ROM:   Upgrading or downgrading your stock ROM Looking for firmware from a different region/language Flashing a custom ROM for different features, removing bloat, etc.   But where can one find ROMs in the first place?  What sites are likely to have the ROM I need?  ; please add to the wiki answer instead of posting separate answers.  See also: Find examples of two series $\sum a_n$ and $\sum b_n$ both of which diverge but for which $\sum \min(a_n, b_n)$ converges. To make it more challenging, produce examples where $a_n$ and $b_n$ are positive and decreasing.  Edit: This problem is taken verbatim from Exercise 2.7.11 on page 68 of Abbott's Understanding analysis. Why does a Ball bounce back if Forces are Equal and Opposite? When a ball is thrown onto a wall, the ball exerts a force onto the wall. According to Newton's Third Law, the wall will exert an equal and opposite force to the ball. Thus, how would the ball be able to bounce back? Shouldn't it just slide down the wall? Why, microscopically, is the voltage drop across a resistor affected by the current through it? If voltage is a potential difference, describing how much energy will be lost per unit charge as charge carriers pass through the resistor, why would the rate at which charge flows (i.e. current, $=dq/dt$) affect the amount of energy lost per unit charge?  I suppose I am asking why a quasi-"extensive" property of the system (current) would affect a quasi-"intensive" property of the system (voltage drop across the resistor).  Apologies if the answer is obvious; I was having trouble understanding why the rate of charge flow would factor into voltage drop whilst trying to rationalize Ohm's law for myself. I have installed nodeJS on Ubuntu with following code   sudo apt-get install nodejs   Since I am a new user for ubuntu I also ran this code too  sudo apt-get install npm   Now when I type    nodejs --version   It shows   v0.6.19   I checked and saw latest nodeJS version is 0.10.26   How can I update my version of nodeJS to 0.10.26?  I tried with    sudo apt-get install &lt;packagename&gt;  sudo apt-get install --only-upgrade &lt;packagename&gt;   but no luck. How do I install the latest version of gcc and g++?  I am using a variety of C++11 and C++1y features; which is why I need this. banner set interval Beamer: \nonumber equivalent for slides? Is there an equivalent command to \nonumber when one doesn't want to include certain slides in the numbering? I would like to leave outline and title slides out of my numbering, and instead just number slides with actual content. Other workarounds would be nice to know about as well.  Edit: Since a MWE example was requested, here is one. Suppose I have a title page and two other slides. The code below gives a slide counter that goes up to 3, and the title slide is slide 1. I would prefer to have the title slide not be numbered, the counter go up to 2, and the the numbering start at the slide after the title. Here is some code.  \documentclass{beamer}  \mode&lt;presentation&gt;  {    \usetheme{Dresden}  }   \setbeamertemplate  {footline}{\quad\hfill\insertframenumber/\inserttotalframenumber\strut\quad}    \begin{document}  \begin{frame}  \titlepage \end{frame}  \begin{frame} Some actual content here \end{frame}  \begin{frame} Some more actual content here \end{frame}  \end{document} How can I break an align environment for a paragraph? I would like to have two displayed equations, broken by a short paragraph, but with aligned equal signs (as if using the align environment).  Is there some way to "break" the align environment temporarily? Storable Action - System.LimitException: Too many DML statements: 1 @AuraEnabled(cacheable=true) public static String  deleteContacts(List&lt;String&gt; contactIds) {     List&lt;Contact&gt; returnList = new List&lt;Contact&gt; ();     String query = ' SELECT Id,Name, LastName,Department,MobilePhone, Email FROM Contact WHERE id IN : contactIds ';     for (Contact thisContact:  Database.Query(query)) {          returnList.add(thisContact);     }     try {       delete returnList;       return'deleted successfully';     }     catch(Exception ex){        return 'Problem occoured';     }  }  JS Method deleteSelected(){     deleteContacts({         contactIds :this.selectedIds     })      .then(result =&gt; {         this.dispatchEvent(             new ShowToastEvent({                 title: 'Success',                 message: result,                 variant: 'success',             }),         );         return refreshApex(this.getContactList, { searchKeyWord: '$searchKeyWord' });     })     .catch(error =&gt; {         this.error = error;     }); I am interested in displaying some things (e.g.: title page) in full color on screen, while having the same object/page display in a black and white friendly form when printed.  According to , there is built-in functionality in the PDF specification for Screen-Only objects and Screen-And-Print objects.  There may also be a way to add a layer on top of the B&amp;W page that only displays the full color page on screen via the PDF 1.5 Optional Content Groups feature.  Similarly,  demonstrates the selective printing of text via ocg-p.  But it is not clear how I can use this package in the way that I need to.  My scenario is compounded by the fact that my color page text is white on a dark background.  MWE:  This code presents the way I am currently switching back and forth between color and b&amp;w.  I change the printincolor bool variable to make the change.  \documentclass[11pt]{article}  \usepackage[demo]{graphicx} \usepackage{etoolbox}  \providebool{printincolor} % Will set color title page and section headings \setbool{printincolor}{false}  % Setup color if needed \ifbool{printincolor}{% \usepackage[pagecolor=none]{pagecolor}% \definecolor{MyBlue}{HTML}{1b3667}% \usepackage{afterpage}}{}  \begin{document}  % Begin Title Page {  \thispagestyle{empty}   \ifbool{printincolor}{%   \pagecolor{MyBlue}%   \afterpage{\nopagecolor}}{}   \begin{center}   {\ifbool{printincolor}{\color{white}\sffamily}{\sffamily}%  Set text color white or leave [default] black   \ifbool{printincolor}{\includegraphics[width=1.5in]{logo-gold}}{\includegraphics{logo-blue}}% put logo gold or blue   \\ \vskip 1in   \begin{huge}         \textbf{Title}         \vskip 0.1ex\rule{0.5\textwidth}{0.8pt}\vskip 1ex         Subtitle         \\         \end{huge}   \vfill\vfill   \begin{large}    Authors:\\   John Doe and Jane Doe\\   \end{large}   }   \end{center} }  \end{document}   How can I layer (or otherwise display) two versions of the title page in a way that color displays on screen, but black and white is printed? Root of continuous function using Rolle's Theorem $$f(x)= 1 + e^x\cos(x)$$   $$g(x)= 1 + e^x\sin(x)$$      Show that there is at least one root of $g$ between two roots of $f$   How do I start to answer this question and do I need to use Intermediate Value Theorem? Finding $ \int^1_0 \frac{\ln(1+x)}{x}dx$ Why does Stack Overflow only allow one @User per comment?  This restriction lead me to a non-comment like :     @MiMo - seem my previous comment (Only one @ user per comment)   Which left me wondering why Stack Overflow is blocking me from notifying two users of a response.  I am sure there is a reason for this, can some one share it with me?