A piece of string 30 inches long has its two ends joined together and is stretched by 3 pegs so as to form a triangle. What is the largest triangular area that can be enclosed by the string?  I took P = a+b+c and Area = 1/2 (b * h) And found h in terms of a and b.Substituting this value to the h in the area equation I differentiated the Area wrt to b and equated to zero.Is this the right way to do it?  Can this be soved only using heron's forumla(not A = 1/2(base*height)?
If perimeter of a triangle is $2d$, what is the length of sides so the triangle has maximal area?    I found some solution using circle and angles, but I think I have to use derivatives.    I need help.
After the therapy, eight children (43%) became able to crawl/move on their back.   Or should I use "on their backs"?   Singular because each child only has one back, or plural because we're dealing with eight backs? Wacom Tablet - Illustrator brush tool I currently got the intuos art wacom tablet so still learning how to use it. I'm currently in illustrator trying to draw out a map and the brush tool is doing something weird and I cannot figure out why. You can see in my image that where there are curves the black slightly spills over and is filling in half the curve with black. Brush setting is set up as a new calligraphic brush and the size is set to pressure, 3pt-3pt. Add time restriction in ArcGIS Network Analyst I would like to know how potential difference is created between two points?Is potential difference created by adding more electrons at one side?If that's the case how to add more electrons at one side?  I'm really looking to know what really constitutes potential difference? Active versus passive transformations I'm trying to install a Matlab R2011a launcher for Unity in Ubuntu 12.04. I've tried  (although I know it's for 11.10 and mentions that even 11.10 is an unsupported OS for Matlab R2011a) but without any satisfactory solution.  This is my launcher file, /usr/share/applications/matlab.desktop:  #!/usr/bin/env xdg-open [Desktop Entry] Type=Application Icon=/usr/share/icons/matlab.png Name=MATLAB R2011a Comment=Start MATLAB - The Language of Technical Computing Exec=matlab -desktop Categories=Development;   I open the dash panel and search for "matlab". This launcher is found among applications. I click it, and Matlab's splash screen shows up, but when it disappears the program doesn't start. (I've verified with htop that no matlab-processes are running in the background either.)  If I add  Terminal=true   to the launcher file, the program starts OK, and opens a terminal as well as Matlab. However, both the terminal and Matlab itself show up in the Launcher area, with the Matlab icon, so it looks like I have two Matlab instances running when really it's only one. (Actually, they show up as two different programs, and not just two instances of the same - the icons are independent, not grouped together.)  This is definitely not optimal. I had hoped to create a launcher I can lock to the launcher area, and then that same icon will be the icon for the active Matlab instance when the program is running.  How do I create a launcher for Matlab that works as expected?  Update: I was apparently a bit unclear on my symptoms, I'll try to clarify a little. I've also tried some suggestions from the answers, and further investigated what happens. My current setup (a launcher file with Terminal=true and Exec=matlab -desktop -nosplash &amp;) renders the following behavior:   I open Dash by pressing the Windows key on my laptop, and search for "matlab". It finds the launcher named "MATLAB R2011a". I click it. A terminal window opens, using the icon I referred to in the launcher file. Almost immediately, MATLAB's splash screen also opens, using the same icon (and thus being grouped with the terminal window in the launcher). The splash screen disappears and, so does one of the icons in the launcher. The MATLAB desktop environment opens, using a different version of the icon which is displayed next to the icon for the terminal window (not grouped with it).   I can lock the terminal window's icon to the launcher and successfully start MATLAB by clicking it, but it doesn't feel optimal that I start the program with one icon, and switch to it with another. I've also tried the following:   Exec without the ampersand &amp; in the launcher command, but it didn't make a difference. Executing matlab -nosplash manually from a terminal still shows the splash screen. (What, then, does the nosplash option really do?) Abnormal behavior with iwlwifi driver: the device is shown as not working Recently I've installed Kubuntu in a newly bought laptop with an Intel WiFi 6 AX200 network card, I can connect to the wifi without apparent problems but when I open the driver manager in the settings I face this weird situation:  Intel Corporation: Wi-Fi 6 AX200 This device is not working.  [ ] Using iwlwifi driver backport in DKMS format from backport-iwlwifi-dkms (open source)  [ ] Continue using a manually installed driver  [x] Do not use the device   Note that "Continue using a manually installed driver" is the only voice selectable in the list.  Here is some additional information:  $ lspci -nnk | grep 0280 -A3 02:00.0 Network controller [0280]: Intel Corporation Wi-Fi 6 AX200 [8086:2723] (rev 1a)         Subsystem: Intel Corporation Wi-Fi 6 AX200 [8086:0084]         Kernel driver in use: iwlwifi         Kernel modules: iwlwifi  $ rfkill list all 0: hci0: Bluetooth         Soft blocked: yes         Hard blocked: no 1: phy0: Wireless LAN         Soft blocked: no         Hard blocked: no  $ dmesg | grep iwl [    2.888227] iwlwifi 0000:02:00.0: enabling device (0000 -&gt; 0002) [    2.945179] iwlwifi 0000:02:00.0: Direct firmware load for iwlwifi-cc-a0-50.ucode failed with error -2 [    2.945217] iwlwifi 0000:02:00.0: Direct firmware load for iwlwifi-cc-a0-49.ucode failed with error -2 [    2.947244] iwlwifi 0000:02:00.0: TLV_FW_FSEQ_VERSION: FSEQ Version: 43.2.23.17 [    2.947250] iwlwifi 0000:02:00.0: Found debug destination: EXTERNAL_DRAM [    2.947252] iwlwifi 0000:02:00.0: Found debug configuration: 0 [    2.947697] iwlwifi 0000:02:00.0: loaded firmware version 48.4fa0041f.0 op_mode iwlmvm [    3.145585] iwlwifi 0000:02:00.0: Detected Intel(R) Wi-Fi 6 AX200 160MHz, REV=0x340 [    3.159226] iwlwifi 0000:02:00.0: Applying debug destination EXTERNAL_DRAM [    3.160060] iwlwifi 0000:02:00.0: Allocated 0x00400000 bytes for firmware monitor. [    3.336456] iwlwifi 0000:02:00.0: base HW address: 50:eb:71:d7:0b:40 [    3.353553] iwlwifi 0000:02:00.0 wlp2s0: renamed from wlan0 [    4.457920] iwlwifi 0000:02:00.0: Applying debug destination EXTERNAL_DRAM [    4.621843] iwlwifi 0000:02:00.0: FW already configured (0) - re-configuring [    4.629999] iwlwifi 0000:02:00.0: BIOS contains WGDS but no WRDS   Someone have idea why this happened? I'm trying to prove that if $A\neq 0$ is a commutative ring and there is an injective $A$-module homomorphism $A^m\hookrightarrow A^n$ then $m\leq n$ must necessarily hold.    This is exercise 2.11 from Atiyah and MacDonald's Introduction to Commutative Algebra, but unfortunately all the solutions available online are either very sparse with regard to this question or seem to use (to my surprise) a generalized version of Cramer's rule. Is there perhaps some other "cleaner" approach to solving this problem? Pluralization issue on new question statistics underneath title, with views It looks like the new question statistics underneath the question title introduced a pluralization issue with views:        To be clear here, this was not an issue with the old sidebar-based question statistics; that used to properly say "viewed 1 time". Why is it called Area 51? According to : "We like the little aliens."  This seems well targeted to appeal to the Stack Overflow / Server Fault / Super User audience, but way off the mark if the goal is to "make the Internet a better place to get expert answers to your questions."    There are experts who aren't interested in or focused on technology oriented topics.  Little aliens are unlikely to be something that someone interested in organizing a site on gardening would gravitate too.  No, I'm not suggesting that no one interested in gardening would be bother to look at a site with little aliens, but won't it be likely that the sort of mass appeal to to a very broad cross section of the internet will be lacking? Which is correct?   Sheila and Angie are wearing the same shirt today.  Sheila and Angie are wearing the same shirts today. Sheila and Angie are wearing same shirts today. There are lots of questions tagged  that don't have a  response.  How do we interpret this? Is it because they are declined by default? We just have to wait for a response (the team is very busy)? Is Jeff the only one that reviews this questions?  I suppose the ones that have negative votes may (or may not) be declined by default, but there are quite a few with some to a lot upvotes that should have an official answer. How to import a jar in Eclipse Give moderators the ability to mark reviews as "bad" From what I've seen, many SO moderators trawl completed reviews and watch out for robo reviewers; and manual banning them when they see enough (>= 3?) bad reviews. This is inefficient because:   It doesn't integrate into the audit system. There's no "memory" to it. If mod A finds that user X has made two (any number less than the threshhold) bad reviews, he may make a mental note but there probably won't be any permanent/shared memory of this. If moderator B finds this user at a later date, he will have to look through the entire history, including stuff that mod A has already checked.    What I propose is that moderators get the ability to mark individual reviews as "invalid" from the completed review page. This is only to be used for reviews where any reviewer who is paying attention (and knows the rules) would choose the opposite reason (spam and other low quality stuff).   These bad review flags are treated like audits for a user -- if the number of failed audits and bad reviews is enough, the user gets autobanned. The nice thing is that this system should (probably) easily be able to , fixing the "Why was I manual banned?" problem.  This could also be integrated well with . Starting digits of $2^n$. Which side of wave-particle duality to choose in a given situation How does one know whether, in treating a certain problem, one should consider particles as waves or as point-like objects? Are there certain guidelines regarding this? How do you greet multiple recipients in an e-mail? How do you greet multiple recipients in an e-mail?  Assuming they're both male, I just use "Sirs", but it seems a bit informal. How to create a Customized Ubuntu Server ISO? Is there any differences between      Try to do   And     Try doing   Thank you in advence. Where can I install ubuntu if I have 4 primary partitions? I want to triple boot Windows 7, Backtrack, and Ubuntu. Windows and Backtrack are already installed. The problem is that both of them take 4 partitions: 3 for Windows, and 1 for Backtrack. When I try to make another partition, it says I can't have over 4. How can I install Ubuntu with this problem? Note: The 3 Windows partitions are PQSERVICE, SYSTEM RESERVED, and eMachines. I don't really know if I can delete one.