Solving $(x^2+4x+3)^x+(2x+4)^x=(x^2+4x+5)^x$ with $x\in(-1,\infty)$
Find $x$ such that $(x^2 + 4x + 3)^x + (2x + 4)^x = (x^2 + 4x + 5)^x$
Is it true that a dihedral group is nonabelian? Is it true that a dihedral group is nonabelian?  I'm not sure if the result is true. I checked it for some lower order and I think the result may correct.   But I failed to prove/disprove the result. Assign multiple colors to features within a single vector layer jQuery/JavaScript to replace broken images I have a web page that includes a bunch of images. Sometimes the image isn't available, so a broken image is displayed in the client's browser.  How do I use jQuery to get the set of images, filter it to broken images then replace the src?    --I thought it would be easier to do this with jQuery, but it turned out much easier to just use a pure JavaScript solution, that is, the one provided by Prestaul. Dual Booting win 10 and Ubuntu 18.04 on two separate physical ssds I have gotten as far as to create the bootable usb, booting into that bootable usb and getting to the install options however i quit because I had some concerns.  I currently have a Samsung 850 evo 1tb that has win 10ninstalled. I want to dual boot with Ubuntu 18.04 by installing it on a brand new unformatted uninitialized Samsung 860bevo 250gb. Should i format the brand new ssd as a new volume in win 10 and then proceed with the Ubuntu install on this volume. What else should i do? Im a first time Ubuntu user and installer.  Any and all help is appreciated. How to make a curve path from scratch given a list of (x, y, z) points? How do I add a .sty file to my MacTeX/TeXShop installation? I have been using the Copy Attributes add-on to copy some properties from active object to selected objects. This add-on is not enabled by default and must be explicitly enabled. But its a very useful workflow enhancing tool.    There is a limitation though. Not all properties can be copied and even those that can be copied are copied in groups (Its hard-coded in to the add-on).  My question is if there is a built-in feature or any another other way to copy any property from the active object to the selected objects? How can I install Ubuntu on a headless machine? I have a headless storage server with preconfigured Windows Home Server. How can I install Ubuntu without a display?  Do I have to build a custom install flash drive? If so, what would be the basic procedure? Is there a program (like unetbootin) to do this? Why, logically, is proof by contradiction valid? I have an external sound card which mostly works fine, except that when its first plugged in, or when I turn on my laptop, the volume gets set to 100%. That is, the overall system volume, as shown in the sound indicator.  What I'm looking for is a terminal command that will set that volume to 50%, so that I can run it on login and not have to worry that the first audio I play is going to blare out at me if I forget to turn the volume down. What commands allow you to change that volume, i.e. the one in the sound indicator?  I've poked around in gsettings and dbus, but have been unable to find anything that would let me set the system volume like that. I do know about alsamixer, but that's not the solution I'm looking for, since that doesn't allow me to change the volume using the sound indicator or my laptop's multimedia keys. I'm trying to get through my first SalesForce mod and it's definitely been a rocky path. I have one task I'm trying to do, but this section is holding me back.  I have two custom fields.  One a pick list and the other a text box. I have added them to the Approve/Reject Approval Request section in the Opportunity page. I added the fields through the Select Fields to Display on Approval Page Layout and they DO show up on the Approve/Reject Approval Request section. I added them in like ().  However, just the label for the fields show, the field itself is nowhere to be found and can't be used.    You can see and even use the fields when you open the Opportunity page itself, but when you go to use the Approve/Reject, you can't do anything with them or see any values.  I was never a SalesForce user and got this tossed in my lap and really don't know my way around yet. I appreciate any help on this!!  Thanks!!  Kurt Series prove or disprove statement Let $a_n$ be a sequence. $\lim_{n\to\infty} a_n =0 $ then the series: $\sum_{n=1}^\infty a_n, \ \sum_{n=1}^\infty (a_n+a_{n+1}) $ converge and diverge together.  It doesn't seem right, there are no convergence tests that fit this question yet every counterexample I try does not seem to work. Is this how I should see the sum? $\sum_{n=1}^\infty (a_n+a_{n+1})=2\sum_{n=1}^\infty a_n +a_{n+1}$ If so then there's no real difference between the two series since you multiply it by a constant and add just one more value. Play a short sound in iOS Why do we use the base form of verbs instead of the past form in past tense questions? In regard to this , my question is similar but that answer is not clear. I want to know why we use base form of verb, e.g. 'go' to form the past tense instead of past form such as 'went'?     Question: Did you go to a bank?  (Why we use 'go' here, rather than 'went'?)   Answer: I went to a bank.   Am I confusing verb forms with tenses? Please note that I'm not a native speaker so some clarification or reference on this would be helpful. Collapsible fieldsets error for previous dates Do electrons move around a circuit? We could imagine a simple electronic circuit composed by a power source and a resistor.   It is usual find descriptions as "The moving charged particles in an electric current are called charge carriers. In metals, one or more electrons from each atom are loosely bound to the atom, and can move freely about within the metal. These conduction electrons are the charge carriers in metal conductors." (wikipedia ). That made me imagine electrons going from power -, running by the wires, crossing the resistor and returning to power +, where they suffer a new kick to power -. All that at near the speed of light.  In this model, it is easy to define "electrical current intensity" as proportional to the number of electrons per second that cross one specific point of the circuit.  However, looking for the physics of resistivity, I can read the phrase "The actual drift velocity of electrons is very small, in the order of magnitude of a meter per hour." (wikipedia ). This is a complete different point of view, where electrons are more or less fixed around a fixed position (or moving very slowly), an electricity is a wave of "collisions" or "jumps" of electrons, like in a Newton's cradle (or "do the wave" as public in a football match). Obviously, we do not need severals hours from the switch on to the light on.  So, the question is, do electrons move around a circuit ? References to band theory are welcome.  A related question is: if electrons doesn't moves along the circuit, what is "electrical current intensity"?  Note: I known there are similar questions already posted, but answers of the ones I've read are not very detailed (could be I've not found the best ones). Please, be a few patient before "close vote". I have been thinking a bit about Morita equivalence   and I would like to know whether it also applies to subrings such as right or left ideals.  And, if so, how specifically? Could you illustrate if with the example of 2x2 matrices with zero entries in the bottom row? Since Morita equivalence concerns non-commutative rings, I am assuming it should apply, but I am just guessing.  Thanks in advance. How to match all occurrences of a regex Is there a quick way to find every match of a regular expression in Ruby? I've looked through the Regex object in the Ruby STL and searched on Google to no avail. How can I install Whatsapp web app on Ubuntu? I found a similar question , but here I am asking for the WhatsApp desktop webapp so that I can directly access the application without opening a browser. Mouse gestures for Unity desktop