Hi.
The instruction: factor by grouping the following quadrinomial.
xz - 4/9x - 9/4yz + y
Now, the problem here is the textbook gives a "weird" solution, which is:
(2/3x - 3/2y) (3/2z - 2/3)
My solution is:
1) I put the monomials coefficients over the common denominator:
36/36xz - 16/36x - 81/36yz + 36/36y
2) I factor out the greatest common factor:
1/36 (36xz - 16x - 81yz + 36y)
3) I factor the expression in parenthesis by grouping:
1/36 [4x (9z - 4) - 9y (9z - 4)]
4) I factor out the greatest common factor from the expression in square brackets:
1/36 (4x - 9y) (9z - 4)
Now, is the textbook solution an actual solution? There is still stuff that can come out of it. But more importantly, how can I arrive at it? I mean, I guess I can play with multiplication properties and multiply each expression in parenthesis by 1/6, but what's the point?
Now, I wouldn't mind if this was a one-off. But there are another two exercises where the same thing happens.
I kind of feel like a dog that doesn't understand why it's being yelled at.

This will be a sort of series analyzing different aspects of Gege's choice of fighting elements and his magic system, with considerations for the anime as well. Though I will be analyzing Jujutsu Kaisen's magic system, I will mostly be focusing on the physical fighting elements, including hand to hand, weapon use, and overall strategic combat. You cannot discuss a jjk fight without mentioning the importance of strategy and deception!
TLDR: Just read the Problem Solver Section for a general idea of what I'm talking about.
I've been reflecting heavily about how to use powerful people in a story all at once. In my mind, in order to have powerful characters, the author will simply have to upscale all others to somewhat match them; that way, an author can avoid a power fantasy or mary sue issue. Upscaling does not always mean bigger blasts. Todo exemplifies a character with a strong ability not reliant on a huge blast.
In effect, Todo uses Goku's Instant Transmission, but limited to an uncertain, wide range relative to himself. I enjoy Gege's ability to take aspects of other manga and effortlessly incorporate them into jjk. Even if Boogie Woogie was not meant to be Goku's IT, there are other direct references to other powers like Yuji's jajanken (Gon from HunterxHunter), and Domain Expansions being similar to bankai (Bleach). Point being, Gege takes pieces of other magic systems and adds to them what he needs to ensure jjkverse maintains its individuality.

Boogie Woogie, The Problem Solver

Boogie Woogie has stood up against two of the most difficult opponents in the entire verse: Kenjaku and Sukuna. Before I delve into breaking down Todo's use as a powerful story mechanism, a small rant. Skip the section below if you don't care about Yuki vs. Kenjaku.

Kenjaku having gravity abilities exists solely so that he can logically survive Yuki's Bombaye and mass-type cursed technique. It makes sense narratively for Yuki to defend Tengen and eventually face Kenjaku, considering they philosophically oppose one another. Yet, with all intents and purposes, Yuki should have killed Kenjaku there. While the fight was entertaining, why go so far as to give Yuki something like a black hole just for it to be countered with a cursed technique reversal? That part specifically was not entertaining, it was disrespectful to both Yuki and the reader who had to see it. 

Rant over.
The difficulties that Kenjaku presents as an opponent in a fight:

• Extremely powerful Simple Domain
• An open Domain Expansion
• 360 antigravity shield
• Any number of useful cursed spirits
• Powerful rct/healing

https://preview.redd.it/cfzfplqq8m1d1.png?width=753&format=png&auto=webp&s=7e8d7b91bdba8b4f4b7b399e315259b3513108a9
https://preview.redd.it/0yzhu56s8m1d1.png?width=900&format=png&auto=webp&s=42cc8902f82b63f8dbe213ac5ef9a4928eed977d
The issue of Kenjaku having arguably the most powerful simple domain and having an open barrier with gravity powers meant that he was practically undefeatable. If someone tried to do a domain battle, he would either easily suffer their domain with SD, or he'd win the clash with an open barrier. If Kenjaku needs to block something, he will just use his antigravity shield. Kenjaku also has multiple cursed spirits with differing beneficial utilities for him to use; this allows Gege to add whatever backdoor or advantage Kenjaku needs at any given moment. If Kenjaku needs to escape, Gege can write in a useful cursed spirit that will allow it.
https://preview.redd.it/7mdvyl9u8m1d1.png?width=900&format=png&auto=webp&s=77510ca3d4ccc8352801006e22a43f9b75c01a9b
In all fairness, in the Lake Gosho colony, Gege used Kenjaku's abilities to their most sensible limits. Why wouldn't Kenjaku have secured surveillance spirits? Of course Kenjaku can track all the resurrected sorcerers. Kenjaku's caution and overall security makes ense for his character, as he's calculating and strategic.
Kenjaku's own capabilities therefore demands a character who does at least one of two things: Gege needs a character that matches his SD, DE, and gravity abilities, and or someone who simply bypasses those factors. Todo, coupled with Yuta, simply bypass all the things that make Kenjaku a difficult opponent. To note, Takaba did his part in weakening and distracting Kenjaku, which allowed Todo and Yuta's attack to work.
From Lightning's Twitter:
https://preview.redd.it/2lz53jfw8m1d1.png?width=2048&format=png&auto=webp&s=9bff5919b9f0ff37fc404f8d436acff251d5076d
https://preview.redd.it/5ht81tex8m1d1.png?width=1071&format=png&auto=webp&s=81c0325e50e1cbfc0f9ec75a75e380f47b0332be
Kenjaku's antigravity shield acts as the ultimate last effort defense. I will avoid saying that Gege wrote himself into a corner, but it does boggle my mind that Gege allowed Kenjaku to have this ability. Regardless of my issues with his gravity powers, Gege masterfully uses Todo to bypass such an overpowered ability.

Correcting TCB's Mistake

https://preview.redd.it/buwtfnoz8m1d1.png?width=2048&format=png&auto=webp&s=b94b870cf85deedaf7a8b965bb07a9463b20ed2e
https://preview.redd.it/9ltliuf09m1d1.png?width=1035&format=png&auto=webp&s=c7b1e7d375c7d4a34666b0433fedd5e1f24b4b9e
https://preview.redd.it/zd9fcu519m1d1.png?width=1100&format=png&auto=webp&s=e7bd616e6ef508d8fc2d2c9a6f68e4acca16a8cb
The sound effect on the double spread does not say SLICE, but it instead was Todo's vibraslap onomatopoeia. Kenjaku was standing next to Takaba's body, then after the attack, Yuta now stands in the same place. Yuta and Kenjaku switched places, which allowed Yuta to bypass the antigravity shield. Kenjaku would have been able to use it at least in the direction that Yuta was in, so Todo swapped Yuta to be behind Kenjaku.
https://preview.redd.it/qnnt35039m1d1.png?width=1098&format=png&auto=webp&s=ad6f00b739a4650d3e66036cdffc640941bd4efd
Todo performed BW again here to bring Yuta ans Kenjaku closer so Yuta could stab Kenjaku in the brain.

Just Avoid the Domain Clash

I originally believed that Sukuna would not get his domain back because there's no real way for anyone in the cast to survive it. Again, Sukuna demands the anti-mary sue rules: Gege needs a character that matches his DE and Kamino, and or someone who simply bypasses those factors. Todo does the latter yet again. By expanding his technique, he could successfully save the cast from being oneshotted. I like Gege's execution here, because it allows for the cool moment of Sukuna finally revealing Kamino, and the audience gets to enjoy the calamity that it brings. Gege does all of that while saving the audience from a complete wipeout of the cast. Yet, Gege still understands the give and take of a high stakes narrative and includes a heart wrenching death for good measure.
https://preview.redd.it/ftgaptv59m1d1.png?width=941&format=png&auto=webp&s=111307748c513f7553cf35a3b35deb85fecd92d6
Essentially, Todo and BW allows for Gege to allow powerful characters like Kenjaku and Sukuna to sensibly perform at their best while not being the unbeatable plot devices that Gege made them to be. At the very least, BW enables defeat to a certain degree. Gege's characters' interesting and creative abilities allows for dynamic, somewhat chaotic, but fulfilling fights.
Thank you for reading.
Take Note Please:
I am purposely writing in a way that focuses on Gege's autonomy as an author. Too often, I see people discussing stories generally as if characters have real life autonomy and aren't being controlled by at least one author. Therefore, this isn't about powerscaling, it's about how Gege chooses to tell this story and the choices he makes to do so.

#83: KAZUO TENGAN
And so we begin at the bottom, with a character I don’t think will cause any controversy being down here at bedrock. Kazuo Tengan of Danganronpa 3 is possibly the perfect example of every single thing in the series that can go badly, going badly.
A massively overcomplicated plan that ultimately makes no sense at all? Check. Confused motivation that, again, really just makes no sense at all if you think about it for a moment? Double check.
It’s not like there’s zero positives to him- he’s a character with potential, and he does take part in the singular best fight scene in the series. But I just don’t care in the slightest about him. And that’s because his character just seems to exist so that there can be a mastermind. Unlike the other big bads of the series, he isn’t even given a chance to explain himself in detail, so all we’re left with is crumbs of stupidity in a recorded video, because the writers knew that if he had survived to explain himself, it would be a pretty stupid explanation.
Anyway, let’s move onto better things.
#82: DAISAKU BANDAI
Honestly, if you have Daisaku Bandai as your favorite character in the series, I harbor massive respect for you. And also feel really sorry for you because of how crap a deal he gets.
Unfortunately, I can’t say I see it that way. Daisaku is very clearly meant to be a showing-off-the-threat character, a way to show the game means business. But unlike other examples from before (Mukuro, Monomi, etc), he gets absolutely nothing else… besides a disastrous character design.
Seventy-nine times out of eighty, Danganronpa hits it out of the park with their designs, or at the very least lands nicely. But it’s like they looked at this empty slot for the killing game and thought ”…I’m gonna make some weird shit…”
…and it didn’t work out. Bandai’s bizarre design, contrasted with his helium-tank voice and weird (but not interesting) way of speaking made it very, very clear that this was never going to be more than a lab rat for this game’s rules.
#81: ULTIMATE IMPOSTER
…I’m not saying it. Anyway, here we are with our first mainline game character, with ol’ Twogami. And, uh, this one might get some flack.
For what it’s worth, I do genuinely enjoy the character for the… half a chapter or so that he’s alive, and he’s nice enough in UTDP/DRS/etc. Unfortunately, that aspect’s not really the problem.
The problems lie in his concept. Personally, I spent most of Goodbye Despair debating and theorizing about what he could possibly be, why Byakuya was here and what had happened to him, both in body and in mind… only to find out that he was completely separate from anything else in the story, a different character we cannot learn about at all in the main game.
You might think that in a series where a high school girl can destroy the world, a group of children can bring an entire city to its knees, and you can have a person as clueless as Tenko (we’ll get to you, don’t worry), someone constantly posing as different individuals all their life, despite having a very specific… shape, isn’t really a step too far. But for me, it is. The more I think about it, the more silly it seems, and not in a good way. Especially when he reveals his “true” identity in DR3, to absolutely zero fanfare or reaction.
It also doesn’t help that he’s one of two overweight characters in the games… and an enormous chunk of his personality comes down to food. Like… really?
#80-79: KUROKUMA/SHIROKUMA
If I had a nickel every time a possessed animatronic bear said “It’s Me” as a massive lore implication in a series I liked, I’d have two nickels. Which isn’t much, but it’s weird that it happened twice, right?
These two are ranked together not because they’re technically the same character, but simply because I rank them about equally.
These two… aren’t great. They have very little story presence, and anything they do add (such as Shiro’s sacrifice) is entirely negated by the plot twist. It’s a pretty good plot twist, honestly, and I wish it could have been done without sacrificing character.
Kurokuma specifically used to occupy my singular least favourite spot, but I’ve warmed up to him. Knowing that it’s Junko essentially trolling the Warriors and Nagito with everything “he” says does make his lines much funnier. Still wish he had a better voice.
#78: MONOPHANIE
I admit, I do have a soft spot for the Monokub troupe. As a group, I find them funnier than most, and they don’t overstay their welcome for me besides some select moments.
…but even I have to admit that Monophanie is just terrible. She has a couple of funny moments, but that’s really all it is. She’s the girl of the group, because it would seem they designed four Kubs, realized they were all male, and decided they needed a girl. Her personality consists of: “Nice” and “Girly”. Her voice is grating. And do I even need to go into detail about what happens with her and Monotaro? No. No I do not. And neither did the game.
I’m not going to go into any more detail with her at all, because nobody will complain about her being down this low. Except maybe saying that Monokid should be even lower, but… we’ll get to him.
#77: JIN KIRIGIRI
Who? Oh, right, Kirigiri’s pops. Has a small cameo in Trigger Happy Havoc as the first onscreen kill- can we talk about that for a moment, actually? I honestly believe the game would be better off without that little intro cutscene. Having Sayaka and Junko being the first kills, and Leon being the first execution seen, is much more satisfying, I feel, than some random character whose death doesn’t really have a purpose in being shown.
Anyway, part of the reason I said all that is because I feel like there’s nothing at all to say here with Jin. He’s Kirigiri’s motivation, and that’s all the story lets him be. Appearing in the flesh in DR3 does nothing at all to change that.
Tsumugi and Makoto wish they were as bland and plain as this guy.
#76: SONOSUKE IZAYOI
Ah, speaking of characters with no real distinct personality. It’s a shame, because he has a decently cool character design, but you could quite literally change Izayoi from a dude connected at the hip with Ruraka to a particularly loyal dog (WITHOUT the romance aspect), and absolutely nothing would change story-wise or with Sonosuke’s character.
Ruraka’s character would be changed, actually, but we’ll get to her when we get to her. I’ve got a lot to say on that one.
I think they were trying to go for something like the danger of complete obedience/passiveness with him, but they just did not have the time to fit it in the Future Arc along with everything else. Maybe if he was a game character, but, alas.
Izayoi is basically Jin again: A blank prop for another character. But at least this time he has a pretty cool design.
#75: SATO She… doesn’t even have a first name? Really??
Sato completes the holy trilogy down at the bottom of the list of “characters who exist to be props”. In her case, that prop is a dead body. However, at the very least, she’s given a personality before she’s hoisted off to her death. She’s given a motivation, a reason for being. Is it a particularly great motivation, considering what she does because of it? …you know what, it works well enough. Better than our other options here.
At the very least, I can say that I would want to see more of her, that I’d want to find out more about her because I feel there’s something there to discover. Something I can’t say for most of the others this low.
#68: KYOSUKE MUNAKATA
Going from three characters with little to no impact, we get mister Munakata of Danganronpa 3. And… yikes, what a mess we have going on here. You’ll learn going on that I don’t dislike asshole characters simply because they’re assholes. But Munakata? He’s an utterly confusing compound of a “character” that the series quite clearly doesn’t know what to do with.
And it’s in part, I’d argue, because he’s a little bit right. Naegi is too soft. If Junko hadn’t been so suicidal by the end, she’d probably just be out continuing the war right now. But instead of providing any legitimate back-and-forth with Naegi, Munakata is reduced to spouting the word “platitude” a million times over and making his plans so ridiculous and over-the-top (planning to wipe out all traces of despair even if he is the “last human alive”) just so Makoto can easily counter him. It doesn’t strike me as a good man driven mad by hatred, it strikes me as the writers needing an easy way out.
He’s not closer to the bottom because he does have things going for him- a smooth design, taking part in some very cool fights, and all in all a good amount of potential… but good lord, it was heavily squandered by DR3.
And you can bet your right hand that that’s not the last time you’re going to hear me say that last part.
He’s yet another example of why DR3, or at the very least the Future Arc, needed to be a game. At least there we could break down why he thinks that way, and/or other parts of his personality. But as it stands, he’s a dark reflection of Makoto in the barest sense, that just makes me incredibly bored to watch.
#72: NATSUMI KUZURYU
Now we move from characters I’m just not fond of to… characters I’m just meh on. Or those who had soured potential. Natsumi? She falls squarely in the middle of those two categories. Due to the nature of her character (a guaranteed death), she only has so long to shine before being swept away by the Twilight Syndrome case.
And it’s a shame, because she does have aspects of her that I’d like to see more. She’s a good example of the violent jealousy that Hope’s Peak, deliberately or not, stokes within those who don’t make it to the course. She has a pretty good character design, and her motivations and personality are understandable.
But… well, that’s about it. She does the bare minimum she can, and before anything more than that can be done, her fate is already resigned. It’s a shame, but there’s very little that can be done about it, and that’s what lands her here. She does the best she can, and I think that’s shown by how she still has a decent number of fans (or at the very least number of fans shipping her with Hajime. Like, come on, guys, the man’s harem is big enough as is.)
#69: MONOSUKE
What can I even say for Monosuke? What can anyone say about Monosuke?
He’s the equivalent of the second-chapter victim that gets neither the development of future deaths, nor the shock factor of chapter ones. And he’s a Monokub. Pretty screwed either way.
Still, it’s not like he has nothing going for him. He’s funny, funny enough that it bumps him up several spots, and probably has my second favorite design out of the Kubs. Yellow tiger style stripes suits the look very well. And it’s his death, not Monokid’s, that fully establishes the reign of terror that Monodam is bringing to the V3 cast.
… Yeah, that’s about all I can say. He really doesn’t have much to him, but he’s entertaining enough to worm his way up here, and he doesn’t overstay his welcome.
#70: TAICHI FUJISAKI Spike, we need the rest of the Ultra Despair Girls’ cast in DRS. Otherwise, poor Taichi might have been bumped up a few spots. We got Shirokuma and Kurokuma, for god’s sake!
Anyway, moving on. Taichi is a character with very little screentime, perhaps only ten or fifteen minutes of game time. But hey, it’s not like you can’t do a lot with that, Darth Vader only has twelve minutes of screentime in the original Star Wars!
Obviously, that’s not exactly a fair comparison, but Fujisaki Senior does well in the time he is given. You can clearly see where the family timidity comes from, yes, but he’s also steadfast enough to be looking for a way to thwart the Warriors of Hope before they can continue much longer. His relationship with Komaru and Toko is sweet, but tinged with a huge amount of bitterness because you know it can’t end well. Unlike Yuta, he’s going to find out that Chihiro didn’t make it… or he’s going to die.
Unfortunately, fate and Kodaka chose the latter. And I can’t say it’s really a surprising twist, especially considering what happens earlier. He’s not exactly a fascinating character by any sense, but he’s very good with what he’s got to work with.
#74: MONOKID
Okay, real talk. I honestly don’t get how Monokid is always ranked the lowest of all the Monokubs. The only time, in my opinion, where he does something genuinely frustrating as a player is his death. It does take away from Kaede’s horrific and incredible execution, but… until then? He’s honestly pretty damn funny, and dying in Chapter 1 means that he doesn’t even get a chance to overstay his welcome.
Is he still one of the weakest Monokubs/characters of the franchise? Oh, of course. I’m far from proclaiming he’s well-written, the writers clearly just took a LOT of psychedelics and used their best writings from that particular day for this particular bear’s “personality”. But hey, those crazed scrawls can be pretty funny if you embrace the balls-to-the-wall energy.
#71: RANTARO AMAMI
And… here might be the first controversial pick XD
Okay, so, Rantaro. I can’t deny he has some level of merit. He has a very nice design, a buttery smooth voice, and he has a decent mystery behind him. For the third time in the series, a character is presented as the “Ultimate ???”, and it’s our job to figure out what’s going on.
That being said, there’s a reason he’s so low down here. Rantaro exists to be a mystery, that is how I see the extent of his character. It’s not as offensive as Twogami and not as well-done as Kirigiri (who we’ll get to soon), but his missing talent plays no part in any of V3’s plot twists, not even coming up once in its gigantic grand finale.
Rantaro just doesn’t really pose much interest to me, personally, because it’s very clear he is here for the shock value. Combining the most intriguing aspects of Nagito and Kirigiri into one, then taking him out before the first trial, to get players invested. And, unfortunately, despite the best efforts of the writers, he loses most of his intrigue after that, at least to me.
We find out nothing about his game, nothing about his talent, nothing about his relationship with Team Danganronpa or Tsumugi or anything. It’s a shame, that’s all I can say on this one.
Oh, and I guess I should mention his FTEs as well- simply put, they don’t really do anything for me. I don’t… dislike them? But they certainly don’t add much to the character, at least in my opinion. I know he has his fans, and to those, I apologise. But I’ve never been a fan of avocados, and it seems that trend continues even here.
——————————————
Really hope you enjoyed reading! Expect a new part every day or two. :)

Hey everyone.
I'm the person you all hate. Or I suppose I'm one of the few, about 3 main individuals including myself operate 3 seperate leaker groups. I have info and know each of these individuals by their online, anonymous profiles; let me summarise their personalities: Revisionvillage archived founder: Quick witted, and good at communicating. IBDP Vaults (now known as PL Vaults): Generous, Greedless & Surprisingly Kind. PirateIB's lead team: Lacking conscientiousness, Abundant in achievement and speed; extremely competent; as is evident in their incredibly organised and accurate leaks.[Looking at you, solvers for M24 P3 Math AAHL(inside joke)] Jacob99 (Most prominent guilded seller): Looking to make some money; but helpful and kind nonetheless. SATLeaks(summary of the 2 competing sellers on telegram): Playful, lacking conscientiousness, but empathetic to students with no money to spend.
Some of us knew Ivan, I did not. I'm sure he was a great guy, and not really the brightest. PirateIB wasn't directly operated by Ivan but he did have influence over some aspects of it to the best of my knowledge. An admin of sorts if you will. Regardless, I've created this thread to answer the one question: Why? Why do we want to increase all of your grade boundaries and ruin the fun of natural attainment? We don't.
Here, let me explain:
I personally started leaking papers to first increase my grades in M23 when I graduated from the IB. Then, slowly, over time, I had come to realise that the IB did not exactly prepare me for college, at all. I currently do a mechanical major involving completopology, algebraic geometry, and number theory. Most engineering and science-based majors cover some of these topics. All I know is that we were never sufficiently prepared. The IB exams determined what colleges we got into, with no real correlation to what we could achieve in college, and no direction correlation or representation to what we would cover in college. This is why I think that scoring well in the IB is a binary factor to every students' academic success. I don't believe that your grades should define your future. I feel for these students that have to live with the regret of not studying before the exams, or sometimes being forced to not study due to emergencies like surprise surgeries, hospital stays, hard family passings, and much more. I don't believe that a teenager in hs should have to deal with the academic decline associated with majorly traumatic events, and while the amount of students that experience these sorts of events are low, they're most of what form the failing group of IB students that don't qualify for their diploma. I aim to reduce this number. I aim to not limit a student based off of their grades, and rather, their abilities. While most of you may think that these leaks prohibit you from achieving your naturally earned grades, they don't. You'll see a maximum bump of 5% for a 7, reducing your likelihood of achieving a 6 by very slight amounts. That's assuming the IBO doesn't automatically adjust the boundaries for these leaks. Keep In mind, M23 had leaks too; they were simply not as widely available; but available nonetheless if you looked for it.
Hope this clears up the invisible confusion as to why; we do not want to bring down the IBO; you're already doing it by messaging these news companies and expecting them to defame and bring down the reputability of the very diploma you'll be applying to colleges with; we simply want to help students that need it the most.
I'll end with saying that no student is ever limited if they simply know that their limits are boundless.

1. Aurorai (January)
2. Nebulon (February)
3. Solarix (March)
4. Lunara (April)
5. Stellara (May)
6. Quantus (June)
7. Galaxia (July)
8. Cosmion (August)
9. Aetherius (September)
10. Vortexa (October)
11. Meteoron (November)
12. Voiden (December)
    Here are some additional signs based on the lunar cycle:
    
13. Crescentus - For those born during the waxing crescent moon, symbolizing growth and creativity.
    
14. Gibbosa - For those born during the waxing gibbous moon, representing refinement and adjustment.
    
15. Pleniluna - For those born on a full moon, embodying completion and illumination.
    
16. Balsamica - For those born during the waning balsamic moon, signifying wisdom and introspection.
    

These lunar-based signs can be interwoven with the birthdate signs to create a multi-layered astrological profile in FutureSigns. Each lunar sign could provide additional insights into a person’s character and potential life path. 🌙✨
Here are some traits for each of the signs we’ve created:

1. Aurorai - Innovative, visionary, and charismatic. Aurorai are natural leaders who inspire change.
2. Nebulon - Intuitive, empathetic, and mysterious. Nebulons have a deep understanding of emotions and human connections.
3. Solarix - Energetic, passionate, and bright. Solarix individuals shine in creative endeavors and are always full of life.
4. Lunara - Reflective, calm, and adaptive. Lunaras are in tune with their inner selves and the world around them.
5. Stellara - Ambitious, determined, and resilient. Stellaras aim high and work hard to achieve their goals.
6. Quantus - Intellectual, curious, and analytical. Quantus thinkers are great problem solvers and love to learn.
7. Galaxia - Adventurous, daring, and spirited. Galaxians are always ready to explore new horizons and take risks.
8. Cosmion - Innovative, universal, and forward-thinking. Cosmions are always ahead of their time and embrace change.
9. Aetherius - Spiritual, wise, and serene. Aetherians seek harmony and have a profound sense of the bigger picture.
10. Vortexa - Dynamic, powerful, and transformative. Vortexans are agents of change and thrive in chaos.
11. Meteoron - Lively, spontaneous, and impactful. Meteorons leave a lasting impression and are the life of the party.
12. Voiden - Deep, mysterious, and introspective. Voidens are thoughtful and often have a unique perspective on life.

And for the lunar-based signs:

• Crescentus - Creative, growth-oriented, and expressive. Crescentus individuals are always looking to improve and innovate.
• Gibbosa - Detail-oriented, perfectionist, and nurturing. Gibbosans focus on the finer things and care deeply for others.
• Pleniluna - Complete, illuminating, and influential. Plenilunans have a full range of qualities that can light the way for others.
• Balsamica - Wise, introspective, and philosophical. Balsamicans value knowledge and the lessons from the past.

These traits can be mixed and matched with the birth month signs to create a complex and personalized astrological profile for each individual in the FutureSigns system. Enjoy crafting the narratives for your modern astrology! ✨
Solar Intensity: Factor in the intensity and duration of sunlight the location receives, which could affect one’s temperament.
Subdividing solar intensity into signs can add a fascinating layer to FutureSigns. Here’s how we might categorize it based on the intensity and duration of sunlight during the birth month:
​

1. Solarae - Born in months with the longest days and highest solar intensity, these individuals are vibrant, energetic, and often natural leaders.
2. Luminae - Born in months with moderate sunlight, these people tend to be balanced, harmonious, and adaptable to different situations.
3. Umbrae - Born in months with shorter days and lower solar intensity, they are introspective, intuitive, and deeply connected with their inner world.
4. Aurorae - Born in months with the most significant variations in daylight, such as near the poles, these individuals are dynamic, innovative, and embrace change.

Each category reflects the solar qualities present at the time of birth, influencing personality traits and life paths in the FutureSigns system. 🌞✨
Interstellar Stones
Here’s a list of interstellar stones, each associated with a sign in the FutureSigns system, along with their believed properties:

1. Aurorai - Opal: Inspires creativity and attracts positive energy.
2. Nebulon - Amethyst: Enhances intuition and offers emotional balance.
3. Solarix - Ruby: Encourages passion and provides protection.
4. Lunara - Moonstone: Promotes inner growth and strength.
5. Stellara - Topaz: Brings success and good fortune.
6. Quantus - Sapphire: Stimulates wisdom and spiritual insight.
7. Galaxia - Garnet: Boosts energy and revitalizes feelings.
8. Cosmion - Aquamarine: Calms the mind and eases fears.
9. Aetherius - Lapis Lazuli: Reveals inner truth and promotes self-awareness.
10. Vortexa - Obsidian: Provides grounding and removes negativity.
11. Meteoron - Peridot: Attracts abundance and enhances well-being.
12. Voiden - Onyx: Offers strength and promotes vigor.

For the lunar signs:

• Crescentus - Pearl: Symbolizes purity and brings tranquility.
• Gibbosa - Jade: Represents harmony and encourages prosperity.
• Pleniluna - Diamond: Signifies invincibility and pure energy.
• Balsamica - Labradorite: Aids in transformation and imparts strength.

These stones can be used as personal talismans or incorporated into rituals to enhance the traits of the signs. They add another layer of personalization and mystique to the FutureSigns system. ✨
The Cusps
In the FutureSigns system, we can introduce special aberrations for individuals born at the cusp of two signs. These aberrations can blend the traits of both signs, creating a unique profile. Here’s how we might name and describe them:

1. Aurorai-Nebulon Cusp - “The Enlightened Visionaries”: These individuals combine Aurorai’s innovative spirit with Nebulon’s intuitive depth, making them insightful leaders.
2. Solarix-Lunara Cusp - “The Radiant Reflectors”: A blend of Solarix’s bright energy and Lunara’s calm introspection, they are both creative and thoughtful.
3. Stellara-Quantus Cusp - “The Ambitious Scholars”: Merging Stellara’s ambition with Quantus’s intellect, they are driven to achieve and learn.
4. Galaxia-Cosmion Cusp - “The Adventurous Innovators”: Integrating Galaxia’s adventurousness with Cosmion’s forward-thinking, they are fearless in exploring new ideas.
5. Aetherius-Vortexa Cusp - “The Serene Storms”: Combining Aetherius’s wisdom with Vortexa’s transformative power, they are calm yet capable of profound change.
6. Meteoron-Voiden Cusp - “The Impactful Mystics”: A mix of Meteoron’s lively spirit and Voiden’s depth, they leave a lasting impression with their mysterious aura.

These cusp aberrations provide a nuanced interpretation for those born on the edges of the monthly cycles, offering a more personalized astrological reading in the FutureSigns system. 🌟✨

Hello! I have not fully played the game, so some of my questions here may have super obvious answers. I also haven’t found any posts addressing these specific questions, but I may have missed them while searching. Apologies if either is the case.
Long story short, I am writing a fanfic and I’d like to have a better understanding of how Monokuma's rules work. It’s intended to follow the English translation, so any situation where the Japanese rules are more clear would not be relevant (but I would be interested in knowing!). My questions are mostly minute, nitpicky, detail-oriented, as I think I have a good general understanding. If I need to be corrected, my understanding is as follows:

• Monokuma cannot change rules, only add new ones
• Rules are only enforced once broken (as an example, a student would not be stopped from killing more than 2 students, they’d be executed for doing so AFTER the third student’s already dead)
• Monokuma can choose NOT to enforce rules (RE: Ch.3 Akane, Ch. 5 Nagito w/ Rules #1, #2, #3, #10)
• The simulation does NOT stop Monokuma from trying to break rules (RE: Ch. 3 Nekomaru is allowed to be injured despite Rule #4 even being referenced in the scene)

So, with regards to my list of questions, if people wanna discuss the intent and speculate, go for it. I would just like 'canon' answers to be differentiated from theories. Also, it is assumed that I am overthinking this and the game may not have answers because, in context of the narrative, these questions do not matter. Again, this is just for the sake of a writing project, I am not critiquing the game’s plot and please do not take it as that. I just NEED the things to make sense to me, if you get my vibe.
List of rules: https://danganronpa.fandom.com/wiki/Killing_School_Trip#List_of_Rules
1. This is the main one: Genuinely what is Rule #4 supposed to mean?
Rule #4: The lead teacher cannot directly interfere with the students. An exception to this rule is made if any student violates a rule.
What does directly interfere mean? There’s no clause on how/to what extent they can interfere.
Hypothetically, could Monokuma have just killed Hiyoko for being inconsiderate to Mikan per Rule #2 (since killing everyone is Junko’s stated goal)? Kill a litterer? Or would something limit that?
Additionally, Hajime got cut by shrapnel (not addressed as interfering by the narrative), Fuyuhiko is injured while trying to stop an execution (addressed as interfering by the narrative, and Monokuma is forced to undo this action) and Nekomaru is essentially killed for stepping in the way of a punishment (same as previous). So it appears he is only forced to undo lethal damage, which would mean there's SOME sort of when he breaks the rule too much (it would make more sense from a software engineering perspective for him to not be allowed to break the rules at all, but that would remove all stakes).
In both of the cases where his damage is undone, it was a student stepping into another person’s punishment after they broke a rule. Which brings me to the next question. Given that Rules #6 - #9 & #11 aren’t written as rules that can be broken by anyone but Monokuma (they’re more like protocols), it’s valid to assume Rule #1 enables the trials. I think.
So, does that entail that one person breaking a rule means the lead teacher can kill EVERYONE (thus Rule #7 is permitted)? I think so, given the 'any' in Rule #4. This would mean the Fuyuhiko is saved by Rule #6 (albeit I feel as if Monokuma's intent - NOT executing him - should factor in), but what saves Nekomaru?
Alternatively, are ‘if x, then y’ rules valid (Rule #7 again)? The latter implies he could write an ‘if she breathes, she’s dead’ rule and kill everyone (as there’s no established limit to directly interfering). I think it’s in character for him not to do that, but could he? If not, that raises the possibility that he actually straight up cannot execute the students upon a wrong vote. The concept is backed up by him being forced to save Nekomaru when Akane broke a rule. I am assuming this is NOT intended by the narrative, although I think it'd be an interesting spin on things.
Finally, is there a reason the Monobeasts, the Funhouse, the Despair Disease, or anything enforcing the Killing Game that isn’t a rule, are distinctly NOT considered interfering compared to other stunts he’s pulled? Monomi turned a chicken into a cow, and. Nothing else that could imply interfering. So is there any point at which the extent of allowed direct interfering is defined?
2. Don’t the Monobeasts break Rule #11?
Rule #11: You are free to investigate this island at your own discretion. Your actions in this regard are not limited.
They quite literally limit movement. Could the Monobeasts legally (according to how the simulation is code) do anything if a student walked onto a blocked island? Or would they maim the student, only for Monokuma to be forced to heal them? Which then goes back around to the Rule #4 question. The Funhouse seems more valid as it’s a structure, not Monokuma actively limiting movement with threats of violence. Abeit, I am assuming this island refers to all the islands, right, not just the central one?
3. Would Monokuma be forced to help a potential third victim?
Rule #12: The blackened may only kill a maximum of two people during any single "killing game".
I’m leaning to no, he wouldn’t be, but I’m not certain because he’s forced to save Fuyuhiko and Nekomaru who essentially stepped into his line of fire (albeit, again, Rule #6’s phrasing may be forcing him in Fuyuhiko's case). If two students are killed and a third is bleeding out, but salvageable, would he be able to just wait it out and kill the blackened? This would be an ideal move for killing more people, not what he’d do in character (as I assume he’d prefer the trial).
I may come up with more later, these are just thoughts that occurred to me while trying to make sense of how I’d enforce the rules myself in different scenarios. Again, apologies if there are answers in the text and please point me to previous discussions if needed. Thank you.

I think therapy is highly misunderstood and one of the reasons why it is a taboo topic is because of how calculate the effectiveness of therapy.
We usually look at the split between how many people benefited vs people who didn’t from therapy.
I think this is a highly unfair way to calculate the effectiveness of therapy because unlike a product or a service, therapy doesn’t work in blacks and whites. There aren’t many measurable metrics to understand the effects.
Additionally, there are many factors which contribute towards how therapy works, one of it could literally even be how the room makes you feel like. When given so many affecting variables, it is unfair to study the effectiveness of therapy in a liner manner.
There are two most important aspect in a therapy which can be a bug hurdle between you and therapy to work for you:

1. The Therapist

A therapist is a human being who has his/her ideas and belief systems formed due to his/her experiences. Therapy is highly labour dependent which means the effectiveness of therapy is directly proportional to the quality of labour, quality of therapist. Now the quality doesn’t mean by the standards only but also if the quality matches you. Emotions do not look at credibility, they look at comparability. If there is not compatibility, sharing can take long time because willingness needs comfort.

1. Seeker

One of the key aspect for therapy to work for the seeker is the seeker itself. For therapy to work for you, you have to have the willingness to change and overcome. We are so habitual to denial and dishonesty that the willingness to change has to go through an ocean of biases and self doubt. The response to which is being ignorant. If there is no willingness and a constant pessimism about it not working for you, it will never work for you. Its like finding food that suits you, is healthy and also tastes good. At least a taste which is acceptable to you. Hence for willingness to come, there has to be an unbiased effort to solve the problem.
A problem solver relies on insights. The problem is that there is so much of unapplied self help knowledge fed in all our brains which makes us think we know and this brings up a very popular argument, “I already know what the therapist is going to say”. A problem solver looks for insights, insights can be taken by observation and not blaming. Problem solver optimises doesn’t cancel. The unapplied self help knowledge makes us think we know but we are not even in a fair position to judge because we haven’t applied.
This is what makes a therapist different. A therapist doesn’t just bombard you with self help knowledge but also gives you an actionable plan to be able to apply it. This is what you need. Knowledge without application is utterly useless and only remains in memory sitting there to be forgotten eventually.
Hence I think the better way to judge the effectiveness of therapy is to highlight the people who have benefited from it and optimise it for the ones who haven’t benefited. This is not an individual effort but an effort that has to be taken by the seeker and the therapist.

Need Attention 1. Solver tool mandatory for every solving procedure if available then should be used. If not available then solve the task manually. 2. By similar or Pervious procedure is not allowed in options, if given 4 options all options check by complete method. By similar procedure is allowed like factors 100, 88 and also allowed in graphing. 3. Table must be according new table feature. If table made by other source except ( latex command table) should be flagged for visual bonus fruad. 4. All simple calculations should be done by Solver tool like ( 2+1, 3>4 etc) 5. Substitute values like as V=2bh Substitute b=6 and h=10 into the equation V=2(6)(10)_✅ Is allowed and tasks should be approved. Not mandatory like as: V=2bh;b=6;h=10 ✅ In both cases task 🆗👍 (if solver tool not solved) 7. Solver toll not solver the high power values like solver mentioned that _solved by calculator the answer is, should be approved.

https://preview.redd.it/j2gulp6gc7yc1.png?width=1524&format=png&auto=webp&s=9019ce76aeeedc2b265cde0414b865aafe149d13
Hello Populli and photomath team! I m here to discuss issues and confusions on behalf of the whole photomath community. This post is all about new rules that are introduced by Photomath yesterday.
In the given scenario depicted in screenshot 1, some experts are opting to utilise the equation solver for determining the equation of the line, subsequently extracting the slope from the intermediate steps. However, considering the task at hand specifically calls for determining only the slope, this approach may potentially cause confusion for the end user. It is essential to adhere to the newly introduced guidelines and compute the fractional slope manually, ensuring clarity and alignment with the user's requirements. Our question here is, what should we do according o the new rule? Is it OK to select solver for equation of line for just slope requirements or should we find slope manually for these type of tasks? Similarly, there are many other examples, like finding the median only, but selecting the solver for the box and whisker plot.
https://portal.photomath.net/job/QJZMRK8N Check out this example now. What should we do if the number is any other number, such as 250 or 100? Should we search for each factor separately? or write as it is stated in step 9, applying the same process that the other factors are using? Kindly elucidate as there are numerous comparable instances where we are encountering this problem following the implementation of new regulations.
https://portal.photomath.net/job/QJZMG61N Check out this example now. The solver did it manually but in the screenshot below you can see that there is a method which can be used here. But many experts are saying that both methods are good to go. What are the actual guidelines from the team.
https://preview.redd.it/fstzynnb18yc1.png?width=1692&format=png&auto=webp&s=3c222cefb8cfbd7a1f5d633494bdfba41e4c82c9
These are some examples from a few experts in the community. I hope u/JessieDFord, and our other moderators will help us regarding these issues.

Hi! Everyone whos making money on their stores-What is your winning product criteria?🏆 Where do you look for products? As far as ive heard its: -Problem solver -Wow factor -Passion product (pet niche for ex) -Has demand -Has competitors that you could win over potentially
If a product is over a year old and its not seasonal is it worth trying to sell it?

Ahoy treasured veterans and esteemed newcomers! I'm level 84, mostly built around Cold Shoulder because it's the first gun I got that's dependably lethal with ammo to spare. I mained it for a bit but its gunplay fun factor is pretty low so I'm trying to see if I can hold onto it as a emergency problem solver while exploring other gun types.
I'd like help understanding how the game is balanced as far as how many weapon types can be part of an effective build. Do I have to build for only one or is it balanced for multiple?
I don't want to use just one gun type in an FPS. In previous Fallouts I would like to carry a shotgun for rapid close quarters resolution, an automatic rifle for medium range engagement, a sniper rifle for long distance takedowns, some throwable explosives bc idk I've been playing shooters that way for years (toss a grenade before duck/cover to reload) i like playing that way, I like explosions in my firefights, that little "tink" sound of the pin being pulled... ha anywho, uh.. yea and a melee weapon because sometimes it just feels better, and a heavy weapon to go toe-to-toe with the big boys.
As far as gunplay I'm currently enjoying an auto .45 Fixer, an auto silenced long scoped 5.56mm Handmade and a .308 LMG. I really enjoyed VATS in previous Fallouts but I don't much care for this one so far. I'd rather build toward fun gunplay than VATS unless I'm missing something.
Grenades: I collect all that I find and stash them; when one type reaches 10+ I bring them out for use.
I'm not hitting any walls yet as far as difficulty I'm just curious how specialized one "must be" and how to proceed accordingly :) Any insight is appreciated. Cheers!

Why are dolls wounds suddenly not healing anymore? We can see in the first pic that the native solvers glyph appears right at the wound site, did the solver straight up disable her healing factor?

The emergency shutdown systems market is anticipated to grow at 7.2% CAGR during the forecast period. The emergency shutdown system is largely deployed in the oil & gas industry, power generating sector, manufacturing industry, and various other industries. The emergency shutdown system market consists of standardized software and hardware systems. The software-based technologies have extensive safety functions that are important for personnel and machinery safety. Software-based technologies offer high flexibility for the modification and maintenance of systems. The growing demand for safety and shutdown systems in the oil & gas industry is a major factor propels the growth of the emerging shutdown systems market. This system supports in reducing the consequences of emergency conditions that include uncontrolled flooding, escape of hydrocarbons and outbreak of fire in hydrocarbon areas.
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The global emergency shutdown systems market is segmented on the basis of component and application. Based on component, the market is segmented into safety switches, safety sensors, safety valves, actuators, emergency stop devices, safety controllers and programmable safety systems. The programmable safety system is expected to grow at a considerable growth rate during the forecast period. It is the backbone of an entire safety system and reliable logic solvers offer fail-safe and fault-tolerant operations. They are flexible to design, highly efficient, highly reliable, highly secure and easy to install. These benefits of programmable safety systems have boosted the growth of programmable safety systems in the emergency shutdown system market.
full report of Emergency Shutdown Systems Market available @ https://www.omrglobal.com/industry-reports/emergency-shutdown-systems-market
· Market Coverage
· Market number available for – 2024-2030
· Base year- 2023
· Forecast period- 2024-2030
· Segment Covered- By Source, By Product Type, By Applications
· Competitive Landscape- Archer Daniels Midland Co., Ingredion Inc., Kerry Group Plc, Cargill
· Inc., and others
Market Segmentation
Global Emergency Shutdown Systems Market by Component
o Safety Switches
o Safety Sensors
o Safety Valves
o Actuators
o Emergency Stop Devices
o Safety Controllers
o Programmable Safety Systems
Global Emergency Shutdown Systems Market by Application
o Oil & Gas
o Pharmaceutical
o Power Generation
o Chemical
o Food & Beverages
o Metal & Mining
o Others
Regional Analysis
o North America
o US
o Canada
o Europe
o UK
o Germany
o Italy
o Spain
o France
o Rest of Europe
o Asia-Pacific
o China
o India
o Japan
o Rest of Asia-Pacific
o Rest of the World
Company Profiles
o ABB, Ltd.
o Emerson Electric Co.
o Esoteric Automation & Control Technologies
o General Electric Co.
o HIMA Paul Hildebrandt GmbH
o Honeywell International, Inc.
o IMI Norgren, Ltd.
o Johnson Controls, Inc.
o Kongsberg Gruppen ASA
o Nidec Corp.
o Proserv UK, Ltd.
o Rockwell Automation
o Schneider Electric SE
o SELLA CONTROLS
o Siemens AG
o Yokogawa Electric Corp.
The Report Covers
· Market value data analysis of 2018 and forecast to 2025.
​

• Annualized market revenues ($ million) for each market segment.
• Country-wise analysis of major geographical regions.
• Key companies operating in the global emergency shutdown systems market. Based on the availability of data, information related to pipeline products, and relevant news is also available in the report.
• Analysis of business strategies by identifying the key market segments positioned for strong growth in the future.
• Analysis of market-entry and market expansion strategies.
• Competitive strategies by identifying ‘who-stands-where’ in the market.

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