If I dropped book and feather from same height. Why book falls first, however book has more windage(air resistance), more area(square) than feather?
We all know that in an idealised world all objects accelerate at the same rate when dropped regardless of their mass.  We also know that in reality (or more accurately, in air) a lead feather falls much faster than a duck's feather with exactly the same dimensions/structure etc.  A loose explanation is that the increased mass of the lead feather somehow defeats the air resistance more effectively than the duck's feather.  Is there a more formal mathematical explanation for why one falls faster than the other?
The coefficient of an explanatory variable in a multiple regression tells us the relationship of that explanatory variable with the dependent variable. All this, while 'controlling' for the other explanatory variables.  How I have viewed it so far:  While each coefficient is being calculated, the other variables are not taken into account, so I consider them to be ignored.   So am I right when I think that the terms 'controlled' and 'ignored' can be used interchangeably? Are common cryptographic hashes bijective when hashing a single block of the same size as the output? Correct usage of will and would True displacement in EEVEE? I have a Blender 2.8 scene with animated true displacement. It is created using material nodes and works fine in Cycles. However, EEVEE doesn't displace my meshes truly, only normals are changed. Is it possible and how to solve the problem now or in the future? How do I configure a new Ubuntu installation to accept ssh connections? Show that Statistic is complete Homeomorphism between the unit disc and the unit square I know that the function that describes the homeomorphism is: $f(x,y) =       \begin{cases}     \frac{x^{2}+y^{2}}{\max(|x|,|y|)}(x,y) &amp;\quad\text{if } (x,y)\ne  (0,0) \\       \text{} (0,0) &amp;\quad\text{if } (x,y) =  (0,0) \\       \end{cases}$  But it's impossible to me to show that $f(x,y)$ is an homeomorphism. Mostly i can't see the injectivity. Is there a difference between single and double quotes in Java? Inequality involving Euler-Mascheroni constant I would like to solve the following problem from 'Real Analysis and Foundations' by S. Krantz.  Let $a_n = 1+\frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{n} - \log{n}$ and $\gamma$ be the Euler-Mascheroni constant. Show that $$\vert a_n - \gamma \vert \le \frac{C}{n}$$ for some universal constant $C&gt;0$.  I have no clue how to solve this problem. From searching various sites it seems that $C=\frac{1}{2}$ but I am not sure with this, too. Thanks in advance. Calculate $\tan9^{\circ}-\tan27^{\circ}-\tan63^{\circ}+\tan81^{\circ}$ Calculate $\tan9^{\circ}-\tan27^{\circ}-\tan63^{\circ}+\tan81^{\circ}$?  The correct answer should be 4. In C#, what is the best way to access a property of the derived class when the generic list contains just the base class.  public class ClassA : BaseClass {    public object PropertyA { get; set; } }  public class ClassB: BaseClass {     public object PropertyB { get; set; } }  public class BaseClass { }  public void Main {     List&lt;BaseClass&gt; MyList = new List&lt;BaseClass&gt;();     ClassA a = new ClassA();     ClassB b = new ClassB();      MyList.Add(a);     MyList.Add(b);      for(int i = 0; i &lt; MyList.Count; i++)     {         //I would like to access PropertyA abd PropertyB from the derived classes             } } How do you delete untracked local files from your current working tree? implicit operator using interfaces I have a generic class that I'm trying to implement implicit type casting for.  While it mostly works, it won't work for interface casting.  Upon further investigation, I found that there is a compiler error: "User-defined conversion from interface" that applies.  While I understand that this should be enforced in some cases, what I'm trying to do does seem like a legitimate case.  Here's an example:  public class Foo&lt;T&gt; where T : IBar {     private readonly T instance;      public Foo(T instance)     {         this.instance = instance;     }     public T Instance     {         get { return instance; }     }     public static implicit operator Foo&lt;T&gt;(T instance)     {         return new Foo&lt;T&gt;(instance);     } }   Code to use it:  var concreteReferenceToBar = new ConcreteBar(); IBar intefaceReferenceToBar = concreteReferenceToBar; Foo&lt;ConcreteBar&gt; concreteFooFromConcreteBar = concreteReferenceToBar; Foo&lt;IBar&gt; fooFromConcreteBar = concreteReferenceToBar; Foo&lt;IBar&gt; fooFromInterfaceBar = intefaceReferenceToBar; // doesn't work   Does anyone know a workaround, or can anyone explain in a satisfactory way why I shuouldn't be able to cast interfaceReferenceToBar implicitly to Foo&lt;IBar&gt;, since in my case it is not being converted, but only contained within Foo?  EDIT: It looks like covariance might offer salvation.  Let's hope the C# 4.0 specification allows for implicit casting of interface types using covariance. Weight Painting Won't Get Rid of Weird Protrusions How to check if jQuery.ajax() request header Status is "304 Not Modified"? How do I install Chromium from the command line? I have already tried using the Ubuntu Software Center, but it won't install the Chromium browser. How can I install it using the terminal? Position of "only" in “We 𝒐𝒏𝒍𝒚 have two possibilities” Is there any difference in meaning between the three following sentences?   We only have two possibilities. We have only two possibilities. We have two possibilities only.   I have already read  and I know that the position of only and the emphasis (written or oral) may change the meaning of some sentences, but I am not sure if it does here.  Note: It is clear that “only we have two possibilities” has a different meaning. My question is restricted to the sentences I’ve listed above. I was wondering how to create a theorem environment similar to the following example:   Specifically, the environment should resemble the box that contains "Claim -- The function g is linear".  This comes from a , who has his style files uploaded  I have tried to mimic what I believed to be the relevant code (as there's a lot of stuff there that isn't related to this), to no avail. I have attached my attempt below, but it may be better to ignore it.  \usepackage{amsmath} \usepackage{amsthm} \usepackage{mdframed} \usepackage{thmtools} \usepackage{tikz} \usepackage{xcolor} \usepackage[framemethod=TikZ]{mdframed}     \mdfdefinestyle{mdgreenbox}{%         linewidth=0.5pt,         skipabove=12pt,         frametitleaboveskip=5pt,         frametitlebelowskip=0pt,         skipbelow=2pt,         frametitlefont=\bfseries,         innertopmargin=4pt,         innerbottommargin=8pt,         nobreak=true,         backgroundcolor=SpringGreen!15,         rightline=false,         leftline=false,         topline=false,         bottomline=false,         linecolor=green,     }     \declaretheoremstyle[         headfont=\bfseries\color{OliveGreen},         mdframed={style=mdgreenbox},         headpunct={\\[3pt]},         postheadspace={0pt},     ]{thmgreenbox} \declaretheorem[style=thmgreenbox]{thrm1}   This returns an error, one for xcolor not recognizing the colors, and the following.  l.17        \mdfdefinestyle                       {mdgreenbox}{% The package mdframed has already been loaded with options:   [] There has now been an attempt to load it with options   [framemethod=TikZ] Adding the global options:   ,framemethod=TikZ to your \documentclass declaration may fix this. Try typing  &lt;return&gt;  to proceed.  Package thmtools Info: Key `mdframed' (with value `style=mdgreenbox') (thmtools)             is not a known style key. (thmtools)             Will pass this to every \declaretheorem (thmtools)             that uses `style=thmgreenbox' on input line 39. Package thmtools Info: Automatically pulling in `thmdef-mdframed' on input line 40. (/usr/local/texlive/2017/texmf-dist/tex/latex/thmtools/thmdef-mdframed.sty Package: thmdef-mdframed 2014/04/21 v66 ) \c@thrm1=\count282 (/compile/output.aux) \openout1 = `output.aux'.   I am looking for a way to mimic the environment more than to fix my methods.  Thank you in advance! How can I repair grub? (How to get Ubuntu back after installing Windows?) How can I run a program on startup, minimized? I just want Telegram to be run and I have added it to startup apps. The point is that I need it to be minimized. Any commands?