Reviewing old homework sets for a class and I came across this integral:  $$\displaystyle \int_0^1 \int_0^{1-y} \cos\Big( \frac{x-y}{x+y} \Big) \; dx dy,$$  which the question suggests to evaluate using a change of coordinates; however, I haven't a clue where to begin to identify a useful change of coordinates.   I tried $u = x-y$ and $v = x+y$, but then wasn't sure how I'd convert the domain of integration.  After that, I looked to the given limits for inspiration and noticed that $0&lt;x&lt;1-y$ could be rewritten $y &lt; x+y &lt; 1$, so tried $u = x+y$ and $v = y$, which yielded   $$\displaystyle \int_0^1 \int_y^{1} \cos\Big( \frac{ u - 2y }{u} \Big) \; du\,dy,$$  but that doesn't seem any simpler than the original, to me.   Any advice would be appreciated!
Let $D$ be the region bounded by $x+y = 1$, $x= 0$, $y = 0$. Use the result of  to show that $$\iint_D\cos\bigg(\frac{x-y}{x+y}\bigg)~dx~dy = \frac{\sin 1}{2} $$   and graph $D$ on an $xy$ plane and a $uv$ plane, with $u = x-y$ and $v = x+y$.   I got the Jacobian determinant is $\dfrac{1}{2}$, but how do I get the limits of integration for $u$ and $v$?
Cycles in permutations of a given size A positive integer is divisible by $3$ iff 3 divides the sum of its digits I am having trouble proving the two following questions:    If $p|N$, $q|N$ and gcd(p,q)=1, then prove that $pq|N$ If $x$ is non zero positive integer number, then prove that $3|x$ if and only if 3 divides the sum of all digits of $x$.   For both questions I tried to use theorems of discrete mathematics, but I could not find the way to solve them. Can I enter the Schengen area with a German long-term visa through a different country? I am an Indian national. Right now I am staying in Israel. I will be moving to Germany on the last week of this month with german national visa directly from tel aviv. Ticket price of direct flight is high. So I am thinking to buy either Air France or LOT for travelling having layover at Paris or Poland. Am I allowed to do that? I mean is it mandatory to enter in Germany first? May I travel with these airlines with proper transit visa? What's the difference between  and ,  and ? What's the difference between &lt;b&gt; and &lt;strong&gt;, &lt;i&gt; and &lt;em&gt; in HTML/XHTML? When should you use each? A long time ago, I remember hiding some really personal files on my computer. Something that nobody could ever find, so I buried them down pretty darn good.  Now to my problem, I don't remember where.   Do anyone know a way to scan a drive and list all hidden folders and/or files?   I know how to view hidden files in Windows, but as far as I know, there is no way to search for them? I've been looking for a program, but I couldn't find one - and now I'm here, asking the experts. ;)  I'd really appreciate any tips. Story where the main character learns to perceive time out of order from the aliens I read a story several years ago in which aliens come make first contact with Earth, and a bunch of scientists set to work trying to establish communication with them in various fields. The main character is a linguist and her team is working to try to figure out their written language, which doesn't have any sort of linear structure and can be read starting from any place.  It contains some explanation of quantum physics as an analogy for how they view time.  In the end, it turns out that the aliens don't perceive time in a linear fashion, and sort of see the future on equal terms with the past, etc. The main character learns to see time this way by studying their language, and the story is interspersed with her talking about what her child is going to do / is doing / has done.  I think I read it in a science fiction magazine but I'm not sure about this part. How is MSE divided by $\sigma^2$ always a chi-square distribution? How can I give a user one password for normal usage when logging in, and another password for system administration and sudo access? I want one user to have two passwords. If I change the password for the root user is that going to automatically change the password for the user account?   I found this link for root:    How do I change the user account password? Incorrect query filter according to the requirement My requirement wholly depends on the QUERY.  I am filtering my gridview on the basis of three parameters.   Project_name (Always required) Date (Not always) Vehicle_No (Not always)   So, what my requirement is,      With project_name either any one can be used for filtering my gridview.   Currently my debugged query works exactly fine for any two parameters.  Below is my debugged query:-  SELECT DISTINCT sv.mkey, vehicle_no,                TO_CHAR (date_in, 'dd-MM-yyyy')             || ' &amp; '             || time_in vehicleindate_time,                TO_CHAR (date_out, 'dd-MM-yyyy')             || ' &amp; '             || time_out vehicleoutdate_time,             gate_no_in || ' &amp; ' || gate_no_out ingate_outgateno,             gd.good_type goods_type, net_weight netweight,                TO_CHAR (challan_date, 'dd-MM-yyyy')             || ' &amp; '             || challan_no challandate_no,             remark_in remarkin, NULL receipt_no, date_in        FROM xxcus.xxgid_supinv sv,             xxcus.xx_supinv_goodtype gd,             xxcus.xxacl_xxgid_user_mst ms       WHERE (gd.good_type_code(+) = sv.good_type)         AND (       sv.project_id = '1368'                 AND TO_CHAR (date_in, 'dd-MM-yyyy') = '26-11-2015'              OR vehicle_no = '0'             )         AND sv.delete_flag = 'N'    ORDER BY date_in DESC, vehicle_no   The above query shows me the exact result for project_name and Date which I entered.  But when I add the third parameter say Vehicle_no it doesn't show the data for that exact vehicle_no it still shows me the same data which I looked for 2 parameters.  I am using Oracle for the database.  LATEST UPDATE WHICH IS NOT WORKING  I am confused as how to deal with the query, as Balazs' solution was working fine when I selected, Project_name, Date and then vehicle_no (not necessary). But it was not fetching proper result when I took first as Project_name, and Vehicle_no. Any guesses why?     The issue  is when I only filter with Project_name and Vehicle_no the date_column value comes as 0 so it doesn't show me any row, which is incorrect as I have data for that Project_name and Vehicle_no.   I have used Balaz's second query for the solution which is below  WHERE (gd.good_type_code(+) = sv.good_type)     AND (       sv.project_id = '1368'             AND TO_CHAR (date_in, 'dd-MM-yyyy') = '26-11-2015'          AND vehicle_no = decode(:vehicle_no, '0', vehicle_no, :vehicle_no)         ) Long boot delay on Ubuntu loading/splash screen following regular dist-upgrade on clean SSD install (18.04) I'be been running 18.04 since a clean SSD install on the day of it's official release, without issues. Power on to login was seconds (max 10)  Then, I did a regular upgrade this morning:  $ sudo apt update &amp;&amp; sudo apt dist-upgrade   The packages installed/upgraded were:  Install: linux-headers-4.15.0-24:amd64 (4.15.0-24.26, automatic), linux-headers-4.15.0-24-generic:amd64 (4.15.0-24.26, automatic), linux-modules-extra-4.15.0-24-generic:amd64 (4.15.0-24.26, automatic), linux-modules-4.15.0-24-generic:amd64 (4.15.0-24.26, automatic), linux-image-4.15.0-24-generic:amd64 (4.15.0-24.26, automatic) Upgrade: gnome-control-center-data:amd64 (1:3.28.1-0ubuntu1.18.04.1, 1:3.28.1-0ubuntu1.18.04.2), linux-headers-generic:amd64 (4.15.0.23.25, 4.15.0.24.26), gnome-control-center:amd64 (1:3.28.1-0ubuntu1.18.04.1, 1:3.28.1-0ubuntu1.18.04.2), linux-image-generic:amd64 (4.15.0.23.25, 4.15.0.24.26), linux-signed-generic:amd64 (4.15.0.23.25, 4.15.0.24.26), gnome-control-center-faces:amd64 (1:3.28.1-0ubuntu1.18.04.1, 1:3.28.1-0ubuntu1.18.04.2), linux-generic:amd64 (4.15.0.23.25, 4.15.0.24.26)   I rebooted once the upgrade had completed, and noted a 2-3 minute delay on the Ubuntu loading/splash screen (prior to login) (without any progress/activity indicated on the dots).  I powered off and tried to boot again, but am getting this delay consistently now. Also close down is much slower too.  Update #1 (2018-07-03): Analysis on systemd:  $ sudo systemd-analyze blame 3min 53.073s plymouth-quit-wait.service     2min 20.699s snapd.seeded.service          49.949s snapd.service           6.186s NetworkManager-wait-online.service           1.148s dev-sda2.device           1.098s plymouth-start.service   Showing that plymouth-quit-wait.service (which I now believe is related to the Ubuntu loading/splash screen) and snapd.seeded.service were by far the longest running services to initiate. So I compared the times before the dist-upgrade and after:  $ journalctl -u plymouth-quit-wait.service --since today -- Logs begin at Fri 2018-04-27 13:01:30 BST, end at Tue 2018-07-03 12:38:05 BST. -- Jul 03 04:15:43 user-laptop systemd[1]: Starting Hold until boot process finishes up... Jul 03 04:15:46 user-laptop systemd[1]: Started Hold until boot process finishes up. -- Reboot -- Jul 03 04:21:17 user-laptop systemd[1]: Starting Hold until boot process finishes up... Jul 03 04:24:52 user-laptop systemd[1]: Started Hold until boot process finishes up.   Before the upgrade plymouth-quit-wait.service took 3 seconds. After the upgrade it took 3 minutes 35 seconds  $ journalctl -u snapd.seeded.service --since today -- Logs begin at Fri 2018-04-27 13:01:30 BST, end at Tue 2018-07-03 12:42:14 BST. -- Jul 03 04:15:43 user-laptop systemd[1]: Starting Wait until snapd is fully seeded... Jul 03 04:15:43 user-laptop systemd[1]: Started Wait until snapd is fully seeded. -- Reboot -- Jul 03 04:22:47 user-laptop systemd[1]: Starting Wait until snapd is fully seeded... Jul 03 04:24:49 user-laptop systemd[1]: Started Wait until snapd is fully seeded.   Before the upgrade snapd.seeded.service took 0 seconds. After the upgrade it took 2 minutes 2 seconds.  Update #2 (2018-07-06): This morning's boot saw the return of the delay. So I guess we're still waiting for the kernel/plymouth/snapd update.  Update #3 (2018-07-12): The problem seems to be resolved, but I didn't see any update to snap or plymouth, and I'm still running 4.15.0-24 kernel. So I'm not sure which package update fixed the problem, or if it just resolved itself somehow. Reading the bug updates on launchpad it's unclear to me what was done (or is being done) to what package/s. If anyone can clarify that would be very useful. Intuition behind the Definition of Conditional Probability (for 2 Events) What to do about rep inflation? Overall reputation scores are headed nowhere but up.  Pretty soon there will be thousands of mods.  What to do?  Thoughts on possibilities:   Thousands of mods is fine.  Carry on. Adjust the threshold values for high-level SO privileges. Do a straight-up inflation adjustment.  You had x rep, then at the turn of the year we applied the Consumer Rep Index to all scores, now you have (x / inflation) rep. Implement a rep decay mechanism, so that inactivity sheds some of the overall rep that's built up. How do you configure email notifications in Cognito Forms? I'm fairly new to LaTeX and I want to know how to change the way sections are numbered by default. I use LyX, and there it is relatively simple to change the way an enumeration is numbered, i.e.  1 foo  a bar    i baz   But I want to know if there is a way to do this by default for sections and subsections. $\operatorname{gcd}(ab,a+b)=1$ if $a$ and $b$ are relatively prime Hi currently Nagios sends notifications from nagios@server.domain.com, How do I go about configuring this? Thanks Connecting desktop computer to the internet through laptop wifi Due to some home network complications I have had to move my router to a seperate part of the house, therefore the wired network I had set up can no longer work. Before I find the time to go out and buy a Wifi adapter for my desktop PC, I have a laptop that uses a built in Wifi card to connect to my router and this can connect to the internet, and I was wondering if I could somehow access the internet on my desktop PC via my laptop.  I'm hoping for a not-so-complex solution as this will only be set up for a few days, but it is quite vital that my desktop computer gets internet access.  Does anyone have experience in this sort of thing and can help me out? Thanks. Is gcc 4.8 or earlier buggy about regular expressions? How does a USB 2.0 Wall Charger negotiate current output? I'm trying to use a mobile phone charger for my projects, and want a high current output. I have read , however my measurements show something else.  is a link to the Battery Charging Specification Rev. 1.2.  1.4.7 Dedicated Charging Port A Dedicated Charging Port (DCP) is a downstream port on a device that outputs power through a USB connector, but is not capable of enumerating a downstream device. A DCP shall source \$I_{DCP}\$ at an average voltage of \$V_{CHG}\$. A DCP shall short the D+ line to the D- line.   I verified on three different chargers, and all read \$R_{DCP\_DAT}\$ as ~1.5 Ohms. Now, if there is a short between the D+ and D-, there is no detection on the charging port side, and the charger should always output \$I_{DCP}\$ {0.5 - 5.0A max} on the VBUS line - is this correct? I tested the current output of three chargers, but they are all completely different. Charger 1 - Nokia Rated current output: 1.3A Measured current output: 1.34A Charger 2 - Asus Rated current output: 2.0A Measured current output: 0.7A - 1.1A (unstable) Charger 3 - HTC Rated current output: 1A Measurent current output: 0.1A If all these dedicated charging ports have no current negotiation, how come only one charger is showing it's rated output? N.B All three chargers can charge a mobile phone in a reasonable amount of time.