I have a doubt on taking pad dimensions in this below picture what is the pad width and height.any body kindly clear my doubt
What is the size of this microcontroller? Having trouble reading a data sheet
Inequality involving sides of a triangle How can one show that for triangles of sides $a,b,c$ that   $$\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b} &lt; 2$$  My proof is long winded, which is why I am posting the problem here.   Step 1: let $a=x+y$, $b=y+z$, $c=x+z$, and let $x+y+z=1$ to get   $\frac{1-x}{1+x}+\frac{1-y}{1+y}+\frac{1-z}{1+z}&lt;2$  Step 2: consider the function $f(x)=\frac{1-x}{1+x}$, and note that it is convex on the interval (0,1), so the minimum of   $\frac{1-x}{1+x}+\frac{1-y}{1+y}+\frac{1-z}{1+z}$  is reached when the function takes the extreme points. i.e. $x=y=0, z=1$.    But going back to the fact that this is a triangle, we note that $x=y=0 \implies a=0$ which is not possible, so the inequality is strict. LIGO flawed by the identical expansion of laser wavelength and arms in presence of a gravitational wave? , Laser Interferometer Gravitational-Wave Observatory, is a large-scale physics experiment aiming to directly detect gravitational waves. The device measures the phase shift laser beams.  If I understand this well, the measurement assumes that a suitable gravitational wave reduces and prolongs one of the tubes and the extension will take effect in the phase-shifting laser beams.  But I think if there's a gravitational wave that passes through it, it will affect everything, even the laser beam. This means that when the wave lengthens or shortens the tube, it also lengthens or shortens the wavelength of the laser beam.  In my opinion, therefore, this device does not work. Or am I wrong? Is there a preferred way to return multiple values from a C++ function?  For example, imagine a function that divides two integers and returns both the quotient and the remainder.  One way I commonly see is to use reference parameters:  void divide(int dividend, int divisor, int&amp; quotient, int&amp; remainder);   A variation is to return one value and pass the other through a reference parameter:  int divide(int dividend, int divisor, int&amp; remainder);   Another way would be to declare a struct to contain all of the results and return that:  struct divide_result {     int quotient;     int remainder; };  divide_result divide(int dividend, int divisor);   Is one of these ways generally preferred, or are there other suggestions?  Edit: In the real-world code, there may be more than two results.  They may also be of different types. C# Regular Expressions with \Uxxxxxxxx characters in the pattern A few years ago Umber Ferrule wrote that the toolbars in the taskbar are defined in   HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\Streams.   This looks very plausible but cannot be the entire story.  Deleting this key will in no way affect the taskbar and on rebooting the system the key magically reappears.  Why do I want to know?  Simple.  I would like to export the key to a reg. file as a convenient backup. Can the present perfect continuous construct be used in passive voice? Can the passive voice be used for sentences in the present perfect continuous?  I understand the present perfect and its passive voice (have/has built, has been built). However, the passive voice of present perfect continuous is unclear:   Active: They have been building this house for years. Passive: ???   I have seen suggestions of “This house has been being built for years,” but it sounds awkward and I don't recall anywhere else where two be verbs follow one another. Is this the right form to use? Do we really need reals? It seems to me that the set of all numbers really used by mathematics and physics is countable, because they are defined by means of a finite set of symbols and, eventually, by computable functions.  Since almost all real numbers are not computable, it seems that real numbers are a set too big and most of them are unnecessary.  So why do mathematicians love this plethoric set of numbers so much? Should an image carousel on a mobile site automatically rotate? Or should the user have complete control? The intention is to have a slider/carousel that shows 6 or 7 images which the user can look through by clicking arrow buttons left or right. But the question has also come up if the user has not started looking through the images, should the carousel start automatically rotating the images. Since this is for a mobile site, I'm uncertain... Group of order $p^2$ is abelian. Yes, I know that there are tons of solutions of this up here, but I, essentially, wanted to try it a different way and ah, well.  Let $|G| = p^2$ for some prime $p$.  Consider $x \in G$. So, $|x| = p, $ or $ p^2$. If it is the latter, then, we are done.  So, if $|x|= p$, then, let, $H = [h|  h=x^i, i \in Z] \Rightarrow |H|= p$.  As $p$ is the smallest prime dividing $|G|$, $H$ is a normal subgroup.  Now, consider some $y \in G$, but not in $H \Rightarrow y^p= e$. Then, its easy to show that $G = \langle x,y \rangle$.  Now, consider a homomorphism $f:G \rightarrow \operatorname{Aut}(H), g \to c_g $, wherein $c_g$ represents conjugacy by $g$. So, for example, $c_g(x) = gx g^{-1}$.  Then, it is clear that, $H \subset \operatorname{Ker}(f) $, as it is cyclic and therefore abelian. So, we need only look at $G/H$.  Basically, I am asking for a hint as to why $c_y(x) = yxy^{-1} = x = c_e(x)$, where $x$ and $y$ are the generators of $H$ and $G/H$, respectively?  Because, if I establish it for the generators, then it follows that it applies for for all elements, i.e, that $\operatorname{Im}(f)$ is trivial and therefore that $G$ is abelian.  Thank You! What's optimal hardness for a kitchen knife blade? Many knife manufacturers provide the hardness value for the knife blade in the specifications - like 53HRC or 57 HRC.  What's the optimal hardness for kitchen knives? Do I always prefer the ones with higher hardness all else being equal? Relationship between balloon size and pressure I see numerous websites talking about how a small balloon is at higher pressure than a big balloon. This is a fun counter-intuitive factoid... unless it isn't a fact at all.  Young-Laplace gives  $$T = \Delta p \frac R2 $$  Which means that for a given tension, increasing the radius does decrease the pressure. But why would the tension be constant? A latex balloon is like a 2D spring, right? So the tension in a inflated spherical balloon should be proportional to the surface area, correct?  $$T \propto R^2 $$  But this gives  $$\Delta p \propto R$$  Which means the bigger the balloon, the higher the internal pressure. Which, again, would be the normal intuition - but it would burst the bubble of some simplified explanations. (har har) How do "pet" Walkers help ward off other Walkers? In both the comics and the show, Michonne first appears with two walkers that she essentially keeps as pets.    The comics sort of half-explain this - as per :     She notices walkers don't attack one another and hacks off the arms and lower jaws of Mike and Terry. She chains them up by their necks to use them as escorts for an escape that was successful.   In , we see that even if they still sort of smell like Walkers, the Walkers can smell/detect the living and will attack.  In ,      We see Andrea effectively making a new "pet" so that she can use to deter the Walkers that she comes across on her trip to the prison. Along the trip, she is shown to come within close range of Walkers, but they give her space when she points the "pets" in the right direction.   Why would the Walkers not just attempt to go around the "pets"? What about them creates an effective protective barrier? I have just bought a Nikon 50mm f/1.8D prime lens.  I took this picture (leg of my glasses frame on a mouse, and a LED desk lamp is on top of it) : f1.8, 1/80s, ISO 200   The purple fringing is right in the middle of the picture. Does it happen very often to this lens? Why constructors will always have same name as of class and how they are invoked implicitly? Why am I getting shopping trolley notifications about local store savings? I am getting "Shopping Trolley" notifications appearing regularly. The notification looks like this:   The notification is about "Store savings" at a local supermarket and that is it!   Is this notification from Google Maps or another application like Google Assistant? I'm struggling to find the specific setting to disable the notification.  I am also interested to know if this notification could in any way be targeted advertising generated by the store. My marketing preferences with the store are opt-out and this strikes me as very dumb advertising. Surely Google isn't doing this? Is there a means that a store can generate notifications like this? Could it be targeted if they have my email address?  These are pain and I want to understand why they are spamming me and disable them without disabling everything else.  I can see various options under Google Maps, settings, notifications. Which setting would apply? Could it be "New on maps, Get occasional updates about new features in your area"? I can't see what setting to suppress!  Thanks for all help. This has been a old live-action movie from Asia, most likely Japan. I've seen it some time in the late 80's and I think it's been black/white only.  Earth is invaded by UFOs (small and round, like flying balls), coming from Mars.  Japan (I think) built some kind of super spaceship, initially hidden within some secret port in some kind of island/mountain.  The spaceship looks similar to a classic battleship, but with an added drill below the front.  In the movie's finale it's revealed that this is some kind of   super weapon/bomb that has to be manually piloted by someone. When launched it starts rotating and flies (formed like a bullet but with the drill/corkscrew head).   To defend Earth, the ship is sent on a mission to Venus, where the UFOs seem to originate. I don't remember the specific reason or conclusion here.  The ship starts underwater or launches from the mountain on the island, then taking off and fighting UFOs while leaving Earth's atmosphere. Video editing. Audio and Video strip have different length General way to determine $\mathbb{Q}(\gamma) = \mathbb{Q}(\alpha,\beta)$ given $\alpha$ and $\beta$ Handle application exit I typed up an assignment with a lot of numbers in LaTeX and turned it in to my adviser.  When he returned it to me with some corrections, one of which was a lot of $ around my numbers.  I understand that $ are necessary around some mathematical formulas, but I was just using numbers like -2 and 4.  I did not see any change in the font of the numbers when I added the $ either.  Since my adviser did not want to give me an explanation, what is the rationale?