Square root of $x^2$ equal to $|x|.$  Does $|x|$ qualify as rational expression?  Why |x| is not a polynomial?
Why is absolute value  function   not a polynomial?   I need  a clear  answer to this question please,?  Why couldn't we consider absolute value function as a polynomial?
Why are there so many places to put a binary in Linux? There are at least these five:   /bin/ /sbin/ /usr/bin/ /usr/local/bin/ /usr/local/sbin/   And on my office box, I do not have write permissions to some of these.  What type of binary goes into which of these bins? Auto mount a disk drive in ubuntu 14.04 LTS (Bookmark directory not found) What really allows airplanes to fly? What aerodynamic effects actually contribute to producing the lift on an airplane?  I know there's a common belief that lift comes from the Bernoulli effect, where air moving over the wings is at reduced pressure because it's forced to travel further than air flowing under the wings. But I also know that this is wrong, or at best a minor contribution to the actual lift. The thing is, none of the many sources I've seen that discredit the Bernoulli effect explain what's actually going on, so I'm left wondering. Why do airplanes actually fly? Is this something that can be explained or summarized at a level appropriate for someone who isn't trained in fluid dynamics?  (Links to further reading for more detail would also be much appreciated) Why can't I find the Karin Kuruma? I am trying to slice up my models using the Boolean modifier.  After applying the modifier on my smooth mesh, I get the expected result, a flat dissection to separate my mesh into two.  The problem lies in how I can resolve the visual "jaggered" edge that separates my (smooth) mesh exterior from the flat dissection face.    Is it possible to achieve a smooth-to-flat variation without this artifact?   I tried to alter a mixture of the two but end up with artifacts, or unwanted blocky flat mesh faces around the dissection edge of my mesh. Here is my player code.  Rigidbody rb;  Vector3 currMovement; public float jumpSpeed = 10; public float moveSpeed = 10; public float rotSpeed = 180;  float distToGround;  public float posSmoothTime = 0.5f; float currPos; float targetPos; float posVel;  public float rotSmoothTime = 0.5f; float currRot; float targetRot; float rotVel;  void Start() {     rb = GetComponent&lt;Rigidbody&gt;();     distToGround = GetComponent&lt;Collider&gt;().bounds.extents.y; }  bool isGrounded() { return Physics.Raycast(transform.position, Vector3.down, distToGround + 0.1f); }  void Update() {     Move(); }  void Move() {     // Rotation smoothing.     targetRot = Input.GetAxisRaw("Horizontal") * rotSpeed * Time.smoothDeltaTime;      if (targetRot &gt; 360)         targetRot -= 360;     if (targetRot &lt; 0)         targetRot += 360;     currRot = Mathf.SmoothDampAngle(currRot, targetRot, ref rotVel, rotSmoothTime * Time.smoothDeltaTime);      transform.eulerAngles += new Vector3(0, currRot, 0);      // Movement smoothing.     targetPos = Input.GetAxisRaw("Vertical") * moveSpeed;      currPos = Mathf.SmoothDamp(currPos, targetPos, ref posVel, posSmoothTime * Time.smoothDeltaTime);     currMovement = new Vector3(0, 0, currPos);     currMovement = transform.rotation * currMovement;      if (isGrounded())     {         if (Input.GetButtonDown("Jump"))             rb.velocity += Vector3.up * jumpSpeed;     }      rb.position += currMovement * Time.smoothDeltaTime; }   I have a Rigidbody attached to my player. I think the problem is with my camera script. Here is my camera script.  public Transform player; Quaternion targetLook; Vector3 targetMove; public float smoothLook = 0.5f; public float smoothMove = 0.5f; public float distFromPlayer = 5, heightFromPlayer = 3; Vector3 moveVel;  void LateUpdate() {     CameraMove(); }  void CameraMove() {     targetMove = player.position + (player.rotation * new Vector3(0, heightFromPlayer, -distFromPlayer));     transform.position = Vector3.SmoothDamp(transform.position, targetMove, ref moveVel, smoothMove);      targetLook = Quaternion.LookRotation(player.position - transform.position);     transform.rotation = Quaternion.Slerp(transform.rotation, targetLook, smoothLook); }   }  The player is not an parent of my camera. When I parent the player to my camera the shake stops. But I want a custom smooth camera movement with my custom scirpt, so I can't make the player a parent of the camera. I started to work with EEVEE short time ago and I was amazed by the capabilities of this engine. However, I noticed something strange when I was rendering some tests. Some objects/reflections/shadows dissapear when they're off canvas. I imagine that maybe this is for save memory data, but it can be not suitable to some projects. To make my point graphical, I made a simple scene with simple objects. The main object is the sphere with a mirror-like shader. Out of focus there are different objects with different shaders. A yellow cone, a blue cylinder and a white cube light. But surprisingly, those objects dissapear when the composition is rendered. See the rendered animation below:  Notice that the blue cylinder is not even showing at all in the final render. And the blooming effect from the light cube also dies. I would like to improve this bahaviour and render the objects that are still out of canvas using EEVEE. Do I missing something like memory configuration or reflection/shadow tweaks? Is this caused by the EEVEE engine or by my GPU config (GTX1060)? Thank you in advance! Accelerating electrons via microwaves In Synchrotrons I think they use microwaves to accelerate the electrons bundles that fly through-how does putting a microwave through a cavity accelerate an electron? I know that the Electric and Magnetic fields could and do have an effect on the electron, but if the radiation is moving parallel to the electron, wouldn't the force be perpendicular? Also, how exactly does the microwave radiation look in the vacuum chamber? Are the two ends constant nodes? Proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where $l=\mathrm{lcm}(m,n)$ and $d=\gcd(m,n)$ How would one go about proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where  $l=\mathrm{lcm}(m,n)$ and $d=\gcd(m,n)$?    I am attempting to use the fundamental theorem of finitely generated abelian groups but am struggling. In the interest of honesty, this is a past exam question that I am attempting for which the solutions are not available. EDIT: As the question was asked in the paper, the Chinese Remainder Theorem would not be permitted since this is only proved in the follow-up course. How do I report a bug? How do I split a string so I can access item x? Using SQL Server, how do I split a string so I can access item x?  Take a string "Hello John Smith". How can I split the string by space and access the item at index 1 which should return "John"? Why is Android File Transfer necessary? Apparently newer versions of Android require the use of Android File Transfer. I have an older machine that doesn't require this, and just mounts as a USB mass storage device. I can't see a technical reason why Android File Transfer is now required when it used not to be.  What changed in order to make this necessary? Why is it necessary? What to call the attitude of pursuing something How to copy files into /usr/local/? (permission denied) I'm still a little new to Ubuntu and was wondering how I can copy files, in this case Aptana Studio, to /usr/local/ without being denied.   Is there a way to do it in terminal? Or a way to allow myself permission?  I should add that I am using 10.10 Desktop edition, not server. In C# how do I get the list of local computer names like what one gets viewing the Network in windows explorer How to use the Bevel node in 2.79b I'd like to know how exactly to use the new bevel node in Blender 2.79b. It's in the manual now, but I've not yet been able to even locate it. How exactly do you use it? Is there a difference between copy initialization and direct initialization? Run 32bit applications on Windows 10 64 Bit I've got a Windows 10 Computer (home edition), which has 4GB of Ram and an i5 processor. I need to run an old 32 bit accounting programme. The vendor said it won't release a 64 bit version (although a 64bit version exists, it's missing key features from the older version).  The programme installs fine, but when I click on the programme icon, it says the programme won't work on a 64 bit system.   What options do I have?    I've done a fair bit of research, but it seems to run up dead ends.   1) WoW64     Apparently, this is supposed to let you run 32 bits on 64 bit Windows. However, I am not sure how to install it. I think it's for web servers only. However,  says it can work on Windows 7, but doesn't explain how to set it up (or if it will work on Windows 10).  2) XP mode     A 32bit Windows XP emulator. However, it seems to be for Windows 7 only. Also according to this , you need Windows Professional.   3) Virtual Box Machine    Let's you emulate Windows. Seems overkill for my purposes. Plus I would need to buy a 32 bit Windows license. I think it would run slowly with 4GB of Ram.  4) Partition drive into 32bit and 64 bit versions Apparently, you can use the free tool  to split the drive into two and then install separate 32bit and 64 bit versions.   Again, seems overkill and it looks like I would need buy a 32 bit Windows 10 license.   Are these my only options?     Images  Installation    First run (From the error message I guess it's a 16-bit program)   Clicking on programme Mixing plural and singular list items with a single verb A friend wants to write,   There is no hardware to purchase, no additional software to install and no key fobs to worry about.   This is awkward because the verb "is" doesn't match up with the third item, which is plural and demands "There are" as the subject. However,    There is no hardware to purchase, no additional software to install and there are no key fobs to worry about.   sounds awkward as well.  Is there a good workaround for this problem where some list items are singular and some are plural, so they don't share a common verb? Run python script when a file has been added to a folder? Is it possible to run a Python script when a file has been added to a folder?  In my scenario I have a folder that contains movies and the Python script gets the details (name, year, plot, rating, etc) from OMDb and puts them into a file, which MySQL uses.   Every time I add a movie I have to run the Python script.  I want to know if it is possible to automatically run the Python script when a file has been added to the folder?  Thanks in advance.