I've been asked by a friend to help him solve this equation, but since we couldn't find the right answer, I thought about posting it here. Firstly, I thought about derivating both sides and get:  $a=be^{bx}$  and from here we could find the answer pretty quickly, but then I noticed that what I did was incorrect because I can't derivate both sides - the functions aren't equal.
A certain physics problem I have been working on has turned into a math problem. Particularly, I want to find the solutions of some equation of the form   $$f(x)=ae^{bx}+cx+d = 0$$  where $a, b, c,$ and $d$ are constant, real numbers that come from the physics problem and $x$ will be a real number. I do not know how to find the solutions of an equation of this form. In the special case where $c=0$, the solution is simply  $$x = \frac{\ln(\frac{-d}{a})}{b}$$  but for other values of $c$, I am stumped. If there is no exact form for the roots, is there a relatively simple way to estimate the roots?
In the ,  can monitor some things like the total traffic on the site. However, it seems to be broken at the moment, all figures are almost zero. This is how it looks for Meta Stack Exchange (other sites show similar pictures): Travelling to Italy without my spouse who is a UK citizen I am India citizen married to a UK national who has been issued a Schengen Visa from the Italian consulate as a spouse of a UK national. My husband was supposed to travel with me but now can’t. We have decided that I should still pursue the trip without him as I will be joining our friends there. Please can someone let me know if I will still be allowed to travel to the Schengen region with a valid Schengen Visa issued as a spouse of a EEA national but without my husband joining me there in person ? I get these weird characters when I try to print out a vector element! Is Design School a Requirement for Graphic Design? Is it required for people to go to design schools to become a Graphic Designer? I've heard many cases where they have started from scratch without previous education in design and are doing fine as freelancers/working in studios.  Would it be better to go to a design school to become a Graphic Designer? How much leverage would it give you if you went to one? Find the value of : $\cos x \cos 2x...\cos 999x$ given that $x=\frac {2\pi}{1999}$ Italian keyboard: entering tilde (~) and backtick (`) characters without changing keyboard layout Here is what the layout of an Italian keyboard looks like:  As you can see, the curly braces, which are absolutely necessary to write code in any of C, C++, JavaScript, Java, Objective-C, and others, appear in purple in this picture. This is because while the other characters can be seen visually as printed characters on most Italian keyboards, these purple characters are actually usually not printed on the keyboard's keys. These characters, found in the upper right corners of the given keys, can usually be generated with the following key combinations: (RIGHT SHIFT or LEFT SHIFT) + (RIGHT CTRL or LEFT CTRL) + (Alt or AltGR) + ([ or ]) (Actually as the MSKLC application shows, SHIFT + AltGr + [ and SHIFT + AltGr + ] are enough to generate the curly braces.) Characters such as the at (@) sign (called 'chiocciola' in Italian) and the hash (#) key (called 'cancelletto' in Italian) found in the lower right hand corner of the keyboard can be generated easily as follows (AltGr + @) or (AltGr + #). Such characters are also fundamental to programming as they can, for instance, be found in CSS, namely with media queries and with selectors referring to the id html attribute. Upon further inspection, we can see that all of the US ASCII keyboard / programmer's keyboard are covered by the keys of the Italian keyboard, except for the following, which are the tilde, which is especially useful on the Linux command line and is used to refer to a user's home directory on such system, as well as the back-tick (`), also known as the back-quote, which is also very useful on the Linux shell when we want to turn the output of a command into a command-line input. So, here comes the question: With all those empty upper-right hand corners of keys, why isn't there a better way of generating these characters, perhaps through a CTRL-ALT-SHIFT modifier key combination? All I've been able to find regarding generation of these characters are the following ALT-codes:  ALT code 96  corresponds to ` ALT code 123 corresponds to { ALT code 125 corresponds to } ALT code 126 corresponds to ~  and to generate a character via an ALT code, you make sure that the NumLock key on your keypad is toggled on, hold down the ALT key, enter the keycode, and release the ALT key. ALT code are documented at:  If someone knows of a better way of inserting these characters from an Italian keyboard without switching the keyboard layout in the Control Panel, then please let me know. Thanks. For a specific package, can I find out why it is installed?  So, can I see or it's manually installed, or that it is installed as a dependency of another package? Or that it is installed as part of the distro? How can phone companies detect tethering (incl. Wifi hotspot) Determining members of local groups via C# I wondered whether anybody knows how to obtain membership of local groups on a remote server programmatically via C#. Would this require administrator permissions? And if so is there any way to confirm the currently logged in user's membership (or not) of these groups? Infinite group with only two conjugacy classes font-not-found error: font "HoeflerText" cannot be found -- LuaLaTex error! I am running this CV/Resume example from :   Here is a relevant fraction of the code:  \documentclass[10pt]{article} %!TEX encoding =  UTF-16 % See geometry.pdf to learn the layout options. There are lots. \usepackage[hmargin=1.25cm, vmargin=1.5cm]{geometry} %symbols - the ones you see on the left of the email and of the phone \usepackage{bbding} \usepackage{amssymb} \usepackage{eurosym} %Colors/Graphics \usepackage{color,graphicx} \usepackage[usenames,dvipsnames]{xcolor}  %Fonts and Tweaks for XeLaTeX \usepackage{fontspec,xltxtra,xunicode} \defaultfontfeatures{Mapping=tex-text} \setromanfont[Mapping=tex-text]{Hoefler Text} ...   So... when compiling with LuaLaTeX (part of MiKTeX on Windwos XP x64), I am getting the following error:  ... luaotfload | Font names database loaded: C:/Documents and Settings/Ampleforth/L ocal Settings/Application Data/MiKTeX/2.9/luatex-cache/generic/names/otfl-names .lua luaotfload | Updating the font names database: luaotfload | Scanning TEXMF and OS fonts... luaotfload | Font names database saved: %s  : C:/Documents and Settings/Ampleforth/Local Settings/Application Data/MiKTeX/2 .9/luatex-cache/generic/names/otfl-names.lua  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !  ! fontspec error: "font-not-found" !  ! The font "HoeflerText" cannot be found. !  ! See the fontspec documentation for further information. ! For immediate help type H &lt;return&gt;. !...............................................    l.28 \setromanfont[Mapping=tex-text]{Hoefler Text}   What is wrong? How can I install this font so LuaLaTeX is picking it up? Where to download? Any other thoughts about this? High Voltage Powerlines - clarification of energy loss Windows 10 update broke my MBR / GRUB Adding word 'Table' before each entry in list of tables I need to prefix each entry in list of tables and figures with appropriate text - table or figure for each. Also I need to remove chapter numbers from list, because tables are numbered consequently through the whole report.  I managed to do everyting I need with this simple commands:  \renewcommand{\thetable}{\arabic{table}} \renewcommand{\thefigure}{\arabic{figure}}  \makeatletter \providecommand\phantomsection{}% for hyperref  \newcommand\listoftablesandfigures{%     \chapter*{List of Tables and Figures}%     \phantomsection %\addcontentsline{toc}{chapter}{List of Illustrations}% %\section*{Figures}% %\phantomsection %\addcontentsline{toc}{section}{\protect\numberline{}Figures}% \@starttoc{lof}% \bigskip %\section*{Tables}% %\phantomsection %\addcontentsline{toc}{section}{\protect\numberline{}Tables}% \@starttoc{lot}} \makeatother   Now only one thing remains: to be consistent with text in list of tables and figures. Where such a term would reference the location/time of an object, almost like it was of a property of the object. That is to say, if a duck is red, blue, yellow etc, we describe it has having a certain colour. If it's a nanometre, or 10km big, then it's property of size.  Now I know that where/when an object exists an object isn't a property of an object, but it is something unique to that object, so I think it would be useful to have a shorthand for 'geographical location', and 'time of existence'.  There are terms describing both time and location, such an event, or rendezvous (which I think is used to describe the when and where of a meeting between two humans) but I wan't a term that just describes one of each. Is there something I can add to the preamble of my document such that multiple letters without spacing in a Math environment (such as $NP$) do not have extra spacing between them and are not considered multiple distinct variables? Right now, I have to use $\mathit{NP}$ to prevent any extra spacing, but I feel that it is more natural to add a space between the letters if they are a different variable ($N P$). For example, if I want the multi-letter variable NP, I want to be able to say $NP$ which would automatically be replaced by $\mathit{NP}$. If I want N and P to have the proper inter-variable spacing, I want to do that only when they are separated by a space, like so: $N P$. Is there a way to achieve this? Would it break something that I'm unaware of? Edit: Here's a screenshot that shows what I mean:  So basically, is it possible for line 1 to automatically give me line 3 and for line 2 to give me line 2? Induction Proof that $x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1})$ Non-interleaved vertex buffers DirectX11 Just recently, the right-click context menus in Windows 7 have been acting in a kind of left-handed way. That is, when possible, the initial menu appears to the left of the mouse pointer. When I hover over a submenu option, the next level of context menu appears to the left of the first and so-on.  Basically, what normally happens when you're right at the right-hand edge of the screen is happening all the time - except when I'm at the left-hand edge. Perhaps it's some kind of left-handed users option, but that doesn't seem likely - more like a right-to-left language option, except that I've never even tried to use a right-to-left language.  I haven't checked every app. for the issue - probably only Windows Explorer, definitely not in Firefox, for the moment that's as far as I've checked.  Scratch that - this affects menu bars as well as context menus. The menus dangle down to the left of the menu-bar item instead of the right, and submenus open to the left too. This seems to apply to most applications, but not too Firefox or Thunderbird.  I find this extremely annoying.  I have no idea how this occurred, though it isn't the only weird glitch I've had in Windows 7 in the last few days - see   I assume there's a setting somewhere that has got changed, but I can't find anything. There's also a chance that I've suffered some kind of registry corruption, so I might need to apply a fix in the registry - not something that scares me, but I need to know what to fix and how.  So - does anyone know what setting has been changed, and how I can fix it?  Also, beyond CCleaner (which I already have), are there any tips on making sure that the registry stays clean and sane?  Finally, both Microsoft Security Essentials and Malwarebytes Antimalware seem happy that I don't have a malware problem. Should my recent glitches make me doubt that? Choosing variables to include in a multiple linear regression model I am currently working to build a model using a multiple linear regression. After fiddling around with my model, I am unsure how to best determine which variables to keep and which to remove.  My model started with 10 predictors for the DV. When using all 10 predictors, four were considered significant. If I remove only some of the obviously-incorrect predictors, some of my predictors that were not initially significant become significant. Which leads me to my question: How does one go about determining which predictors to include in their model? It seemed to me you should run the model once with all predictors, remove those that are not significant, and then rerun. But if removing only some of those predictors makes others significant, I am left wondering if I am taking the wrong approach to all this.  I believe that  thread is similar to my question, but I am unsure I am interpreting the discussion correctly. Perhaps this is more of an experimental design topic, but maybe someone has some experience they can share.