Is "kind", as a noun, singular, or plural? People nearly always say "these/those kind of (things)" rather than "this/that kind of (things)" makes more sense.
I have a question about the following text:     Last week Alex Knapp at Forbes published an article criticizing my Nikola Tesla comic. I don't normally respond to these kinds of thing, but since it's' Forbes I figured a proper response was in order.    I would rather say "this kind of things" rather than the version in the text above.
I want to show that  $$\int_{0}^{\frac{\pi}{2}}\frac{d\theta}{a + \sin^2(\theta)} = \frac{\pi}{2\sqrt{a(a+1)}}$$  for $a &gt; 0$.  I try several methods   Substitutions to rationalize The famous $U = \tan(\frac{\theta}{2})$ Multiplying by conjugates   and other calculus techniques and still, I can not prove the equality.   Anyone can give me a hint of how should I begin to work this integral?  I'm very ashamed that I can not solve this problem. Using Mosfet with seperate Logic Converter and Arduino Solve $x^2$ $mod$ $23 = 7^2$ What is the procedure to solving $x^2$ $mod$ $23 = 7^2$? According to WolframAlpha, there is no integer solution but I am completely confused as to what steps was taken to determine that.  Before asking the question, I did try to solve this using brute force by plugging in some arbitrary numbers to see whether the square of that number mod $23$ gave me a remainder of $49$ but the procedure was quite tedious. Hence the reason I turned to WolframAlpha.   Going back to the question, I want to know how WoflramAlpha determined that there was no integer solution to solving for $x$. There are 100 ropes in a bag. In each step, two rope ends are picked at random, tied together and put back into a bag. The process is repeated until there are no free ends. What is the expected number of loops at the end of the process? Background - I am doing my PhD in atmospheric physics/photobiology.  Here is a scenario:   The experiments are complete - the results are far better than expected  Successfully got the computer program to work properly and have developed another Papers are published Much of the thesis is drafted   The light at the end of the tunnel is most definitely no longer an oncoming train.  But, at this stage, you just don't feel like working on the thesis, you do other things like cleaning, reading, watching movies - procrastination gets worse, and worse despite the submission deadline coming closer.     The procrastination resulting in more apathy towards the project, despite being fully aware of how much work has been put into the project, how much has been achieved and how little, comparatively, needs to be done.  What strategies are there to overcome this academic-apathy, particularly in this late stage of the thesis? Preventing brute force attacks against ssh? What tool or technique do you use to prevent brute force attacks against your ssh port. I noticed in my Security logs, that I have millions of attempts to login as various users through ssh.  This is on a FreeBSD box, but I imagine it would be applicable anywhere. Prove that even + odd is odd. Prove that a even number + odd number = odd number  Let $x$ be the even number, let $y$ be the odd number.   From the definition of odd numbers, $y + 1$ is even.   Let:  $$x + y = z$$  Suppose $z$ is even.   $$x + y = z$$  It follows that:  $$x = x + y - y = z - y$$  But I cant think of any other contradiction here. The issue is with the assumption I suppose. Any help is appreciated! Installing Cygwin packages from the command-line queries with db_select don't respect integers MacBook Pro: How to disable discrete GPU permanently from EFI? I want to do:  cat update_via_sed.sh | sed 's/old_name/new_name/' &gt; new_update_via_sed.sh   in my program.  But I want to use variables, e.g.  old_run='old_name_952' new_run='old_name_953'   I have tried using them but the substitution doesn't happen (no error). I have tried:  cat update_via_sed.sh | sed 's/old_run/new_run/' cat update_via_sed.sh | sed 's/$old_run/$new_run/' cat update_via_sed.sh | sed 's/${old_run}/${new_run}/' I am reading through a directory with some pictures and such using a pretty simple implementation of readdir() like the following:  if ($handle = opendir($path)) {     while (false !== ($szFilename = readdir($handle))) {     if ($szFilename[0] !== '.') {         if (is_file($path.$szFilename)) {                 // do stuff             }         }      }  }   The problem that I am having is that the files are not being read in alphabetical order as the docs for readdir() state:     Returns the filename of the next file   from the directory. The filenames are   returned in the order in which they   are stored by the filesystem.   Another weird thing is that, on the local testing server, the same code works great.  This is running on a server using the LAMP stack in both cases.  I know that I can build an array and just sort it, but I was wondering if I was missing something in what I was doing. How to disable Windows 10 memory compression? my former wrong assumption: it drains my notebook battery and I've no shortage of RAM. In Task manager you see ntoskrnl.exe is eating more CPU time than any other process. this feature does not appear to be optional and came 2 days ago with the 1st Win10 Update (Win10Pro in my case).  Edit:  I want to disable it, at least to exclude it as a culprit for my (unproven) assumptions. That process never came to my attention in the last 2 months and in task manager's long name it's called "system memory and compressed memory". Setting constraints causes the location of the constrained objects/bodies not be accessible I set up 2 bodies manually &amp; assigned Copy Location constraint to one with respect to another body. Then I set up the keyframe for the guiding body &amp; then I started to view the change in the location of the constrained body. What I noticed in the 3D viewport was the constrained object moves, but when I look into its real position the values are stagnant. Why is that? I was unable to find my answer in previously asked questions by other people !! How to prove for each positive integer $n$, the sum of the first $n$ odd positive integers is $n^2$? I'm new to induction so please bear with me. How can I prove using induction that, for each positive integer $n$, the sum of the first $n$ odd positive integers is $n^2$?  I think $9$ can be an example since the sum of the first $9$ positive odd numbers is $1,3,5,7,9,11,13,15,17 = 81 = 9^2$, but where do I go from here. Looping through array and removing items, without breaking for loop In the Avengers movie, was Thor going to kill Captain America during his woods battle with Iron Man? I can't seem to find a story related to mine so here it is.  I am 25 and a German citizen. In 1998 when I was 7 years old my family moved to the states and we stayed until early 2002 and left voluntarily. Basically we overstayed. I am aware that my parents had the ten year ban and since I was a minor at the time of our overstay I did not receive such ban.  Ever since 2002 I have not attempted to go back to the USA for any reason. However now that I am older I would like to go back for vacation and stay for a short period of time (one month) during my christmas break.  I've lived in Germany since leaving, have a great job, enough money in the bank account. My whole life is here and I have no intention on moving anywhere else.  After reading a bunch of stories online I have decided to apply for a B2 visa to be on the safe side but I was curious about the ESTA approval. For the last question. 8) Have you ever stayed in the United States longer than the admission period granted to you by the U.S. government?   I should put yes but is it a no if I stayed when I was a minor? And what are my chances on getting the B2 Visa? How to re-index the values of an array in PHP? I recently upgraded from QGIS 3.2 to 3.4 using the standalone installer (Windows 64 bit), and uninstalling 3.2 beforehand.  When I open 3.4 it goes the background behind all my other open programs and clicking its icon on the taskbar does nothing, nor does Alt-Tab.  To use QGIS I have to minimize all my other open programs.    Is this a Windows issue, a QGIS issue, or something else entirely?