Plotting 2 functions at the same time with Manipulate[]

Here is a code that works well:

f1[x_] := Sqrt[25 - x^2] Manipulate[  Plot[f1[x], {x, from, to}, AspectRatio -> Automatic,    PlotRange -> {{-20, 20}, {-20, 20}},    Epilog -> {Text["From y: " <> ToString[f[from]],       Scaled[{1, 1}], {1, 1}],      Text["To y: " <> ToString[f[to]],       Scaled[{1, 0.96}], {1, 1}]}], {{from, -10, "from x"}, -10, 10,    Appearance -> "Labeled"}, {{to, 10, "to x"}, -10, 10,    Appearance -> "Labeled"}] 

output like:

enter image description here

Now I want to plot 2 functions at the same time. I tryied something like this:

f1[x1_] := Sqrt[25 - x1^2] f2[x2_] := -Sqrt[25 - x2^2] Manipulate[  Plot[{f1[x1_], f2[x2_]}, {x1, from1, to1}, {x2, from2, to2},    AspectRatio -> Automatic, PlotRange -> {{-20, 20}, {-20, 20}},   Epilog -> {Text["From y1: " <> ToString[f[from1]],       Scaled[{1, 1}], {1, 1}],      Text["To y1: " <> ToString[f[to1]], Scaled[{1, 0.96}], {1, 1}]},   Epilog -> {Text["From y2: " <> ToString[f[from2]],       Scaled[{1, 1}], {1, 1}],      Text["To y2: " <> ToString[f[to2]], Scaled[{1, 0.96}], {1, 1}]}],  {{from1, -10, "from1 x"}, -10, 10,    Appearance -> "Labeled"}, {{to1, 10, "to x"}, -10, 10,    Appearance -> "Labeled"},   {{from2, -10, "from2 x"}, -10, 10,    Appearance -> "Labeled"}, {{to2, 10, "to2 x"}, -10, 10,    Appearance -> "Labeled"}] 

But it does not plots anything. How to correct my code above?

Email sent to 2 addresses with shared same organization domain @123abc.com and one bounced back. Was it successfully delivered to the other address?

It is my first time asking questions, so my apologies if there is any mistakes. I sent an email to 2 addresses (2 different departments in same organization with shared @123abc.com), one bounced back from mailer-daemon@googlemail.com due to ‘address not found’. I later found out it was a generated email address. Could someone please tell me if my email was successfully delivered to the other ‘good’ address (the other department)? Thank you very much for your great help in advance.

Can a Circle of the Stars druid fire an arrow from its star form and cast a spell of 1st level or higher during the same turn?

The druid subclass Circle of the Stars from Unearthed Arcana: Subclasses, Part 3 has the 2nd-level feature Starry Form, part of the description of which states:

You gain a bonus action that you can use to make a ranged spell attack, hurling a luminous arrow that targets a creature you can see within 60 feet of you. On a hit, the attack deals radiant damage equal to 1d8 + your Wisdom modifier.

Does “making a ranged spell attack” count as casting a spell and therefore limit your action to a cantrip or can you cast a spell of first level or higher because the arrow is not a spell? Could I cast one of the freely available Guiding Bolts and fire an arrow or do I have to stick with something like frostbite and an arrow?

Can a Readied Action be used multiple times in the same round if you have multiple reactions?

A Marilith picks up a Longbow to use in combat. It walks to a tower window overlooking a large battle with many creatures. It takes the Ready Action with a trigger of "when a creature moves or attacks, I will shoot it".
Mariliths can take a reaction on every turn of combat.

Does the Marilith get to shoot every creature on the battlefield before its next turn?

Can a FOREIGN KEY be referring to the same table as the “source”?

I was sure that I had done this countless times, but I can’t find any previous use of me doing this. But it seems to make perfect sense, so I assume that it must be possible? However, the manual says:

A foreign key constraint specifies that the values in a column (or a group of columns) must match the values appearing in some row of another table.

Emphasis mine. Source: https://www.postgresql.org/docs/current/ddl-constraints.html#DDL-CONSTRAINTS-FK

I have a table for bookkeeping, and whenever a transaction "corrects" or "updates" a previous one, I have a column called "corrects id" which is a bigint and, to me, makes perfect sense to have as a FOREIGN KEY as such:

..., FOREIGN KEY ("corrects id") REFERENCES bookkeeping (id) 

Note: "corrects id" is a column in the "bookkeeping" table, and id is the primary key (bigserial) of the same table.

Surely this is correct? So why does the manual say that it has to be another table? And why is the name "FOREIGN" keys if you can refer to the same table?

What happens when allies occupy the same space?

According to “Moving Around Other Creatures” (PH p. 191 / SRD p. 92):

You can move through a nonhostile creature’s space. […] another creature’s space is difficult terrain for you. Whether a creature is a friend or an enemy, you can’t willingly end your move in its space.

So it’s possible for Alice to move into an ally’s space, attack from there, then move out, the only penalty being that the ally’s space counts as difficult terrain to enter.

If an enemy adjacent to the ally’s space has readied a grapple against Alice and is successful, then Alice (unwillingly) ends her move in her ally’s space.

Do allied characters in the same space suffer any negative effect?

Now the rest of Alice’s allies do the same thing.

Is there a limit to the number of characters that can be stacked on a space?

What if Alice’s ally was the one with the readied grapple?

Can you stack an ally on your space by readying a grapple to prevent them from leaving?

Why developers put the installer/executable and the file checksum on the same server? [duplicate]

On https://exiftool.org/ , there is a link to https://exiftool.org/exiftool-12.01.zip and https://exiftool.org/checksums.txt .

Both the ZIP archive and the checksum hash are hosted on the same machine. This means that an attacker who has compromised the server also will have replaced checksums.txt with a fake one matching the malware-infected ZIP archive. And thus there is no point in checking this checksum?

Maybe the answer is "they can’t afford a separate server", which explains it and is understandable. However, what is the point?

One idea I had was that maybe it’s implied that I should store these hashes "for the next time", and thus be reasonably sure (at least slightly less unsure) that somebody hasn’t compromised the server since the last check. However, the checksums are very specific to the current file! They are not some kind of general "author’s signature" which I can use to verify that it’s the real author who has signed the new binaries. So that idea goes out of the window as well.

Since the security hashes are very specific for the current files, there is no value in "pre-fetching" and storing these locally to compare them the next time, since they always correspond to the current version of the binaries.

I refuse to believe that a person smart enough to make such a project would not have thought of this, so I assume that I must be missing something.

(Also, this is far from the only project where I’ve seen this, so this is not specifically about ExifTool. I just used it as an example since I’m trying to code a secure update mechanism for this program.)

What happens if a sender changes the TCP window size over multiple packets that have the same ACK number?

I’m currently doing research on evasion attacks that seek to bypass a Deep-learning based Network Intrusion Detection System.

In order to achieve this, I need to know what the constraints are for the TCP window size field in the TCP packet header. Imagine a client has just sent the last TCP-ACK packet to a server in order to complete the 3-way handshake. He then immediately proceeds to send a GET request to the server (these 2 packets are thus sent one after the other, and contain the same ACK-number).

What happens if the TCP window size in the TCP-ACK packet does not match the window size in the TCP packet containing the GET request? Will the receiver simply observe the last value for the window size that he obtained? Or will there be a violation in the TCP protocol in any way? You can assume that the change in window size is very small, and will not cause the buffer to be full.

More generally, if the client sends N uninterrupted packets (e.g. a heavy-load POST request), can he change the window size in each packet header without repercussions?

Does PGP passphrase necessary if I store private key and passphrase in the same place?

I’m building a system that generates PGP key and store private key in secret vault. One thing I’m not fully understanding is the need for passphrase.

I can generate a random passphrase during the key generation and then store it in the secret vault along side with the private key, but I’m wondering if it has any benefit. If I store both passphrase and private key in the same place and that place can be considered secure, is there any additional benefit of using the passphrase? Or just storing the private key securely is enough?