Asking for help in problem 4 of section 2.5 of David Burton book
How to find solutions of linear Diophantine ax + by = c?
macOS Catalina File Structure: Cannot remove &gt; sudo rmdir /sw rmdir: /sw: Read-only file system  &gt; mount | grep read /dev/disk1s5 on / (apfs, local, read-only, journaled)  &gt; sudo mount -o rw / &gt; mount /dev/disk1s5 on / (apfs, local, journaled) &gt; sudo rmdir /sw rmdir: /sw: Operation not permitted     root /&gt;$ mkdir a root /&gt;$ rmdir a root /&gt;$ rmdir sw &lt;b&gt;rmdir: sw: Operation not permitted&lt;/b&gt; root /&gt;$ rmdir opt &lt;b&gt;rmdir: opt: Operation not permitted&lt;/b&gt; root /&gt;$ rmdir mnt &lt;b&gt;rmdir: mnt: Operation not permitted&lt;/b&gt; root /&gt;$ rmdir home &lt;b&gt;rmdir: home: Operation not permitted&lt;/b&gt;   What exactly is preventing me from removing these directories even with SIP disabled? Force MacBook to drain the battery while connected to charger I leave my MacBook Pro on my desk nearly all the time, connected to the charger with the lid closed, connected to an external display.  I've heard this is bad for the battery health, and everyone in my office have to replace swollen batteries every couple of years. I want to regularly discharge the battery, per , but I don't want to physically unplug it because that temporarily turns off the external monitor, and then I have to reconnect the monitor.  So I am looking for a software method of disabling the power input, to force the laptop to discharge its battery to 20% and then re-enable the power input. Why doesn't running "sudo shutdown now" shut down? I need to know what the original account was for my Clash of Clans is so I may transfer to another device. Any suggestions? I have tried multiple times trying to find through my emails with no luck. Can Game Center email a list of my CoC account? Executing a certain action for all elements in an Enumerable static_assert fails compilation even though template function is called nowhere Is there a C++ decompiler? Recommended books for advanced undergraduate electrodynamics What books are recommended for an advanced undergraduate course in electrodynamics? Typesetting UML class diagrams What's the best way to draw UML class diagrams in LaTeX? SQL Server Linked Server to Microsoft Access Number of equivalence relations on a set If a set has $n$ elements then what are maximum number of equivalence classes and equivalence relations possible on it? I've got a project where I'm looking to tweak the standard lead conversion process.   Triggers and lead conversion has always been funky in past projects so I was hoping to start the design off by reviewing the order of execution, but after a long google search I'm coming up empty handed.   Anyone out there know the specific trigger order for lead conversion?    Edit: I'm not asking about trigger execution order for any object, but all the objects created in the lead conversion process.  I'd think it would be something like this:        Lead Before Update Triggers (isConverted = false, convertedAccountId = null, convertContactId = null, convertedOpportunityId = null)         Account Before Insert Triggers (not fired if merged with existing account)   Account After Insert Triggers (not fired if merged with existing account)   Contact Before Insert Triggers (not fired if merged with existing contact)   Contact After Insert Triggers (not fired if merged with existing contact)   Opportunity Before Insert Triggers (not fired if no opportunity) (OpportunityContactRoles null)   Opportunity After Insert Triggers (not fired if no opportunity) (OpportunityContactRoles = convertedContactId)   Lead After Update Triggers (isConverted = true, convertedAccountId = XXX, convertedContactId = XXX, convertedOpportunityId = XXX) Duplicate:                      The number of residents has grown.    The number of residents have grown.      Which of the above sentences is grammatical? Since has should stick with singular nouns and have with plural ones, I guess (2) should be correct, but I'm not sure. I'm not quite sure how the total attack bonus interacts with BAB.   Can you make more attacks than shown by your BAB (e.g. +11/+6/+1 BAB allows you to make 3 attacks) by having a high enough DEX, STR or other attack bonus modifiers? Assuming I have +11/+6/+1 BAB, and a spell gives me +6 attack bonus, would that make me able to attack as if I had +17/+12/+7/+2 BAB, giving me an extra attack?)   Can you make multiple attacks even if you have one of your stats drained, making your attack bonus negative, or less than 5?      It says in the SRD that the formula for attack bonus in melee is this:       Base attack bonus + Strength modifier + size modifier   I've also been told that you can make multiple attacks in one turn, but each attack gains a -5 penalty to attack bonus. Limit of $n$th root of $n$! I am asked to determine if a series converges or not:  $$\displaystyle\sum\limits_{n=1}^{\infty} \frac{(2^n)n!}{(n^n)}$$  So I'm using the $n$th root test and came up with $\lim_{n \to {\infty}}\frac{2}{n}\times(\sqrt[n]{n!})$ I know that the limit of $\frac{2}{n}$ goes to $0$ when $n$ goes to infinity but what about the $(\sqrt[n]{n!})$? "In a party people shake hands with one another" Combine rows / concatenate rows Which serial protocol or encoding scheme does this scoreboard use? I am trying to decode a signal stream coming from a Nevco scoreboard controller:    Packets like this are sent every ~2.7 ms.  I suspect it is some sort of UART signal because it is on the RX line of a ATMEGA48, but I cannot identify the finer protocol details like parity and stop bits. All the combinations I have tried returns junk data, so it may be another encoding scheme.  What's unusual is that the same signal is also sent to the MOSI pin of the microcontroller, but there is no clock signal anywhere.  A .vcd file is .   The shortest pulses (both high and low) are always 8us in length.    This is what two packets look like. Anyone got ideas? There's another question on physics.SE whose , if I have understood it correctly, explains that the farther the points are in space the faster they are moving away from each other.     Actually, the apparent speed with which two of the points on the   circle in a distance $D$ of each other would move relative to each   other will be $v = H_0 D$ where $H_0$ is the speed the balloon itself   is expanding.   This means that even the ruler sitting on my desk is expanding, just that the expansion is very very slow owing to the ruler's small size relative to the cosmic scales. However, if everything is scaling then everything should apparently be of the same size to an observer in such an expanding space. The  quote from the show "The Big Bang Theory" comes to mind.   To be able to counter that, there're some phenomena that we can observe which are scale invariant. Red-shift would be one such phenomenon. But is red-shift the only way we can tell that the space is expanding? Is there a logical flaw in my thinking? I know that red-shift is a result of the Doppler effect - there's bound to be a decrease in the frequency of a signal, as perceived by an observer, emitted by a source which is moving away relative to the observer. Simple chessboard exercise