I just have made an ad banner in photoshop (width 1000px, height 250px) and sent it to the developer, but after an hour he said that the file that I have sent to him opens very slowly because it weights too much (it was saved in PNG and weighed 600KB)  After that I resaved it in JPEG, with medium size and it started weighing 80KB, but the developer said that when he puts it on the web site, it loses the quality and he can see the pixels.  What can be done to resolve this problem?
Web sites can contain JPEG, GIF,PNG, SVG format graphics. Which ones should be used, and when?
Overriding "+=" in Python? (__iadd__() method) I have been told [Warning: I leave this because it's what I asked and allows to understand the dialogues in the comments, but Azad, whom I thank, has pointed that the formula does not hold in general in the form it is expressed] that the angular momentum of and rigid body with respect to any point $P$ can always be expressed as $$\mathbf{L}_{P}=\mathbf{r}_{cm}\times M\mathbf{v}_{cm}+\big(\sum_im_iR_i^2\big)\boldsymbol{\omega}$$ where $\mathbf{r}_{cm}$ is the position of the centre of mass with respect to $P$, $M$ the mass of the body, $R_i$ the distance of the $i$-th point, having mass $m_i$, composing the body, and $\sum_im_iR_i^2=I$ its moment of inertia with respect to the instantaneous axis of the rotation around the centre of mass of angular velocity $\boldsymbol{\omega}$.  I know that the velocity $\mathbf{v}_i$ of each point $P_i$, having mass $m_i$, of a rigid body of mass $M$ can be see as the sum of a translation velocity of one of its points $C$ plus a rotation velocity around that point: $\mathbf{v}_i=\mathbf{v}_{C}+\boldsymbol{\omega}\times\overrightarrow{CP_i}$. If we chose $C$ as the centre of mass I see that $$\mathbf{L}_{cm}=\sum_i \overrightarrow{CP_i}\times m_i\mathbf{v}_{i}=\sum_i \overrightarrow{CP_i}\times m_i\mathbf{v}_{cm}+\sum_i \overrightarrow{CP_i}\times m_i(\boldsymbol{\omega}\times\overrightarrow{CP_i})$$$$=\sum_i \overrightarrow{CP_i}\times m_i(\boldsymbol{\omega}\times\overrightarrow{CP_i}) $$because, if I am not wrong, $\sum_i \overrightarrow{CP_i}\times m_i\mathbf{v}_C=(\sum_i m_i\overrightarrow{CP_i})\times\mathbf{v}_C=\mathbf{0}$ since $\sum_i m_i\overrightarrow{CP_i}$ is the position of the centre of mass with respect to itself, which is $\mathbf{0}$.  How can it be proved that $\sum_i \overrightarrow{CP_i}\times m_i(\boldsymbol{\omega}\times\overrightarrow{CP_i})=(\sum_im_iR_i^2)\boldsymbol{\omega}$? I have searched a lot on the Internet and on books, but I find nothing. To give some background of mine, I have studied nothing of analytical mechanics. I find the formula very, very interesting both in itself and because, if the moment of inertia does not depend upon time, $\forall t\quad I(t)= I(t_0)$, the above expression can be differentiated to get the formula of the resultant torque with respect to the centre of mass $\sum\boldsymbol{\tau}_{cm}=\frac{d\mathbf{L}_{cm}}{dt}=I\boldsymbol{\alpha}_{cm}$ where $\boldsymbol{\alpha}$ is the angular acceleration around the centre of mass. I heartily thank you for any answer!    Some unfruitful trials: by using the "BAC CAB identity" as suggested by Azad, whom I heartily thank, $\mathbf{a}\times(\mathbf{b}\times\mathbf{c})=(\mathbf{a}\cdot\mathbf{c})\mathbf{b}-(\mathbf{a}\cdot\mathbf{b})\mathbf{c}$, I can see that$$\sum_i \overrightarrow{CP_i}\times m_i(\boldsymbol{\omega}\times\overrightarrow{CP_i})=\sum_im_i\|\overrightarrow{CP_i}\|^2\boldsymbol{\omega}-m_i(\overrightarrow{CP_i}\cdot\boldsymbol{\omega})\overrightarrow{CP_i}$$which, by decomposing every $\overrightarrow{CP_i}$ into an axial component $\mathbf{A}_i$ and a radial component $\mathbf{R}_i$, whose norms respectively are $A_i$ and $R_i$, with $R_i$ as the distance from $i$ to the axis of rotation, becomes $$\sum_im_iR_i^2\boldsymbol{\omega}+\sum_i m_i A_i^2\boldsymbol{\omega}-m_i(\mathbf{A}_i\cdot\boldsymbol{\omega})\overrightarrow{CP_i}$$but I cannot prove that $\sum_i m_i A_i^2\boldsymbol{\omega}-m_i(\mathbf{A}_i\cdot\boldsymbol{\omega})\overrightarrow{CP_i}=\mathbf{0}$. How can I determine the current brew package count? I tried to get the number of available brew packages by running  brew search | wc -l   but I don't know how accurate this really is. What do I need to take into account to get a more correct number?  PS: macports lists 19,889 packages online What are the light blue lines on my imported objects Its very easy to prove $p\mid n^p-n$ for p=3,5,7, it fails for p=9 because $$     (n+1)^9-(n+1)= n^9+9n^8+36n^7+84n^6+126n^5+126n^4+84      n^3+36n^2+8n $$ and $84= 2²\times 3\times7$. Is it true for any $p$ prime? I have checked many primes, but have no idea for the general case. In Terraria, is there an order in NPC appearance in addition to the minimum requirements for each one? I noticed a strange thing about Demolitionist that I do not see mentioned on .  Practically on my world I created immediately a good number of houses with  needed to accommodate an NPC.  The first NPC that arrived was the Nurse. Then I found many bombs but Demolitionist never came. He arrived just immediately  Merchant came, when I finally got the 50 silver coin needed for him.  Is this behavior correct? Is there and order in NPC appearance in addition to the minimum requirements for each one? What is glue stretching? I had a question about dynamic vspaces () and there was a hint I should use a stretchable glue. Searching with Google didn't give me a helpful answer.  I would be glad, if someone can explain it and give me a simple example to understand how it works. How can I get debug log in Mavensmate What does this depiction of a black hole in the movie Interstellar mean? Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$ Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$.  I started off by putting $\gcd(a+b, a-b) = d$. This implies that there are two relatively prime integers $x_1, x_2$, such that   $dx_1 = a+b$   $dx_2 = a -b$  Adding the first equation to the second gives us: $d(x_1 + x_2) = 2a$, and subtracting the second from the first gives us $d(x_1 - x_2) = 2b$. This implies that $d\mid2a, d\mid2b \implies \gcd(2a, 2b) = d \implies d = 2\cdot \gcd(a,b) \implies d = 2$.   This is based on the fact that $\gcd(x_1 + x_2, x_1 - x_2) = 1$, which is in fact the statement of the problem. How do I prove this? Can I somehow use the Euclidean Algorithm for this. Intersecting overlapping polylines using ArcGIS for Desktop? I have 4 multipart polyline shapefiles (download a sample dataset ).   The geometries are identical, except for the length of segments in each shapefile. They represent 4 variables describing an identical shoreline. From these 4 overlapping polylines, I would like to create a resulting polyline that has segments for each unique set of the 4 input lines.    My approach was to use an intersect. This, however, breaks down when I try to run it on 4 huge feature classes.  My question is whether there is a more efficient way to combine polyline attributes stored in separate layers. I thought a union would be good, but it only works on polygons. Spatial Join seems inefficient, as I would end up with many to many joins for a single segment. Turning the segment end points into a point layer, then splitting the line at those points?  I have access to arcpy, PostGIS, and shapely.  Has anyone had experience doing this before on large datasets? Is there a more efficient way to store these variables? I want to start working on a web map at work to map some of our statistics by city.    I have an idea, but I'm not exactly sure where to start.   Are there any definitive resources that provide step by step guidance on how to do this? Any site that I visit can see my local IP (e.g. 192.168.1.102). Is there any reliable way to block this behavior? (browser setting, OS setting, router setting, etc.) I am particularity interested in Google Chrome and Mozilla Firefox, but any modern open source browser will do. If it is a browser plugin, it should be open source with a solid user base.  By reliable I mean, that I do not need to check the leakage again after every software update.  More info / what I have read so far:   There was a Chrome plugin that is not working anymore Local IP is obtained using JavaScript / WebRTC   Live Demo here:  Source code:   Firefox developers is not going to fix the leak (bug is open from 2014):  In Private / Incognito mode does not prevent this leak. If you use static IPs, and have non typical local IP (e.g. 10.66.77.88 or 192.168.212.121), then there is no need for . Your external IP + internal IP is perfect fingerprint.   Update 1: It is not duplicate of  - I want to prevent private / local IP leak, not disable all WebRTC.  Update 2: No, it is not related to header X-Forwarded-For (HTTP_X_FORWARDED_FOR), that is added when user/administrator chooses to do so. In my provided demo it is not your choice... It is Google's and Mozilla's choice to leak your private IP even when using private browsing mode.  Update 3: Ability to determine my local IP allows malicious JavaScript to quickly identify my local subnet and print on my local network printers from any website in the world without me doing anything.  This  finds my LAN printers using JavaScript.  Update 4: It is not a good idea to reveal private IP to every website. By seeing your private IP, for example 192.168.88.101, I can guess with very high probability that you are using MikroTik router. Also, I can track particular user event if user uses different browsers because local and remote IP stays the same for some time (hours or even days). VARCHAR size limit in Excel spreadsheets So, I have about 7 actions users may need in my app, and I have to use text instead of icons because it is a customer requirement.  I can add only 3 actions to my toolbar on iPhone 6. On Android you have the hamburger menu (see image), but I have never seen it in iOS.       So, what is the appropriate concept in iOS to add many actions into a menu? Regular expression to match non-ASCII characters? What is the easiest way to match non-ASCII characters in a regex? I would like to match all words individually in an input string, but the language may not be English, so I will need to match things like ü, ö, ß, and ñ. Also, this is in Javascript/jQuery, so any solution will need to apply to that. Language Options -> Spell Checking in Windows 10 version 1803 su options - running command as another user I was wondering how to run a command as another user from a script.  I have the script's owner set as root. I also have the following command being run within the script to run the command as the hudson user:  su -c command hudson   Is this the correct syntax? Interscholastic Mathematics League Senior B Division #2 In what order do multiple readied actions with the same trigger resolve? My players have been scheming with rapid entry tactics for the megadungeon I've recently started running. Unfortunately, the monsters are aware of the adventurers, and this has lead to a weird question of priority. Given the following situation (which I'm pretty sure is going to happen next session in some form or another) what happens?     Alice the adventurer readies an action; if her teammate Carlos opens   the door, she's going to throw the alchemists fire through the door,   which should do enough damage to kill any goblins hiding there.      Meanwhile, on the other side of the door, Bob the goblin is lying in   wait. He readies an action; if the door opens, he's going to hit the   switch to open the trapdoor in the next room, which should drop any    pesky adventurers into a pit with spikes at the bottom.      Carlos opens the door.   I know what happens when , but what happens when multiple readied actions get triggered at the same time? My guess would be an opposed reflex save or initiative check of some kind to see who goes first, but that's entirely just intuition speaking. The rulebook doesn't seem to speak to the issue.