I mean... MSG is the common salt of amino glutamic acid (which is naturally present in our body), it can be found in many foods/food addictives too so technically... This comment is right.
I tried to multiply in my head some times when I was bored in my "job", I multiplied two numbers of 3 digits, I failed a lot of times, but I had some answers right, but it wasn't instantly, I needed 10 minutes or even more... How can I multiply instantly? it seems fun but I just can't
@@AurA_XTi believe they mean that since that number is more than 30^5 (24,300,000) but less than 40^5 (102,400,000) it makes it easy to solve. If you know your rules for ending digit, you can conclude it must end in a one (rule for any number ending in a digit x raised to odd power is it still ends in x) and the only number that ends with a 1 in that range is 31, so its relatively easy to figure it out. You do still have to know rules for exponents but its not too hard to figure out since they are one simple patterns; 1,5,6,0 all stay no matter the exponent, as long as it is whole and >0. 4 is an alternation between 4 and 6 depending on the parity of the exponent; odd=4, even=6. 9 alternates between 1 and 9, odd exponent is 9, even is 1. 3,7,8 are harder, but still not too hard. 3 is a pattern of 3,9,7,1. 7 is a pattern of 7,9,3,1. 8 is a pattern of 8,4,2,6. This method seems complicated at first, but once you get the gist of it it’s relatively easy to do mentally if you just know the powers of the number 1-9 and can memorize the patterns.
As a Asian, we learned to cook rice from the womb by connecting our vision to the umbilical cord then to our mothers and watch as she presses 3 button on the rice cooker to cook rice
People who ask hard questions like that are not impressive. They always have the look of a giggling idiot on their face while asking those types of questions. Sub par intelligence for the asker. At least 116 IQ for the one who can answer that question like that.
She's also very capable in combat and is very attractive, the woman is probably an equal to Kafka or Himeko but without the intergalactic train or the seer as support.
@@Konpekikaminari i think she just didnt agree with what IPC treat as "Business Ethic" That why she skip those exam. 😂 actually didnt show up to take it.
Not related to the content of the video, but the structural formula of C5H9NO4 is HOOC-CH(NH2)-CH2-CH2-COOH, that chemical is glutamic acid (which has been said in the video), the salt form is monosodium glutamate (MSG) which is used for flavouring foods.
@@archangel7294 Since March 7th can be written as 03/07, going by the IPv6's ignoring 0 at the beginning of a string of four, her value is 307. We can find the value for Pom-Pom by finding the value for "Pom" and then multiply it by 2, giving a value of 323026. So we found our value. We just need to answer our question of March 7th divided by Pom-Pom. 307/232026 is 0.001~.
"I'm impressed with your ability to come up with questions on the spot!" I mean, by this point I think MC has been answering questions for Regin for that one Belobog commission for, like, a while now sooo. xD
0:47 (600-3)(450+14) 6x45 = 270 6x14 = 84 3x45 = 135 3x14 = 42 (I am lazy to multiply hundreds... so I ignore it 😅, just add moar 0 after this) 270. 000 + 8. 400 - 1. 350 -42 = 277. 008 1:04 also for the first question option (fifth root of 28.429.151?) I guess it under 5 second...😅 Answer: Please note that 3^5 = 243 so we know the answer is more than 30 (since 30^5 would be 24.300.000) with the same technique.. we also know the answer is less than 40... now, look at the last digit of that 28 million something... the last digit is 1 ! 👀 this gives us few hint... first our answer last digit cant be even (exclude 32, 34, 36, 38) (why? 2^5 = 3 2 32^5 = [...2]
For the fifth root there are only 8 digit so it must be smaller than 100, it also larger than 10000, thus it has the form xy. The value is abour 280*10^5, so the first digit is 3 The last stays the same. You can prove either by hand or by Fermat's little theorem
Also for FYI 191 is a safe prime since 383 = 191*2+1. Large safe primes are useful in cryptography (they really went hard with the prime factorization problem huh 💀)
She’s that one person (because I’m sure no one is actually like this) who always goes partying until late in the morning when it’s test week yet despite not studying she still gets 100 in every subject.
It is a utopic person type. They usually study secretly if the curriculum of lessons are hard. Because it is impossible to do things nearly perfect without studying
Heres the thing: theres a method for finding perfect 5th roots and its not that hard, you just have to memorize the first 10 5th powers then you can calculate perfect 5th roots up to 10 billion. but whats INSANELY impressive is that trailblazer was able to immediately find such a large perfect 5th root. large digit multiplication is possible but in the millions it takes a few minutes at least btw since ive also been practicing mental maths for the past couple of days, heres how long i took to answer each of the questions(and wether i got them correct) 1.I just assigned march 7th 37 since 3/7 and assigned pom pom 3.7 since its a cute tiny name so i estimated 10(jokishly)(took me around 20 seconds) 2.correct thankfully, but its a harder multiplication problem so it took me 1:30 seconds, idk how she literally did it instantly, either it just skips like 10 seconds-a minute in between dialogue, or topaz is just a literal calculator (im doing all of the dialogue options) 3A i used the method i was talking about and figured out it was 31 in about 10 seconds 3B idk i wouldve used division but i havent really learned much tricks for division till now 3C Damn this is chemistry now, i have a basic knowledge of chemistry since i also like to study it for fun and i have a 7th grade idea of naming compounds so ill just try to name it like its a compound, maybe its carbon-hydrogen nitrate or something? only part im sure of is nitrate o h its glutamic acid(the acid version of monosodium glutmate aka msg the king of flavour) well that was pretty unexpected anyways this was a fun experience. I might actually download HSR since it seems pretty cool. and the characters seem very great and relatable Edit: 1 month later i have actually downloaded hsr and its really fun. also after focusing on mental maths for another week or so ive shifted my focus to calculus one and im currently getting the hang of derivatives.(ill probably start doing integrals soon after practicing derivatives for abit more) Update 2(yes im using this comment as a way to keep track of my progress in math/academics): ive made abit more progress in calc and now im comfortable with most of the differentiation rules i need to know + logarithmic and implicit differentiation, so ive started learning more about limits,related rates, minima and maxima, etc so that i can be knowledgable enough of calc 1 to move on to something else. to be honest however ive also been learning some calc 1 and 2 integration on the side with methods like u sub, ibp, trig sub, etc but im not as comfortable with it as i am with derivatives. regarding the whole mental maths thing its a cool party trick and all but ive stopped doing it(i still can but im not actively practicing anymore) bc you can easily just start setting your expectations too high then always getting dissapointed, like back when i was originally writing this comment i expected to be able to do 3 digit multiplication in 2 secs(like in the video) but ofc that was unrealistic and the best i could get to was 30 secs- a minute.And as for how im doing in school im still in the 7th grade but my finals are in 2 weeks so im studying for them of. btw ive also started learning indonesian(As a 3rd language, i already speak arabic and english since im arab) and learning stuff like languages is really different than stuff like math or science. theyre both still really fun though and im happy with the progress im making on both
The fifth root of 28,629,151 isn’t even too difficult to figure out. 3 to the fifth power is just 81x3=243, which means 30 to the fifth power is 24,300,000. Given that the number in the question ends with a 1, the fifth root can’t end in 2, 3, 4, 5 or 6, and 37 would definitely be too large, so the answer is just 31.
You can limit the last digit even more by asking what each remaining number ^5 would be. Not sure why you narrowed it down to 1, 7, 8 and 9. 8 is even so its obviously out but as it turns out, any integer ^5 will end in the same last digit as that initial integer. If the number ends in a 1 and it has an integer 5th root, so will that root
I really thought when she said its really a chemistry problem, we gonna get an option to rizz her up like "but its not gonna affect our chemistry" or something 💀
I pick option 3 because she want most hard question, sasuga mc aureum manager, kafka taught too well, i know majority here self immerse but stelle caelus smart you know thanks to kafka
Oh, well, that's very cool, Topaz. Can you please solve for the indefinite integral of a particle moving along the curve of the function f(x)=e^(2x)× sin(x) (x represents time), knowing that the velocity of the given particle at a random point is given by V(x)=f'(x), and the acceleration of the particle is given by a(x)=V'(x)? (Yes I'm salty that somebody is smarter than me, even though they're a fictional character.)
Additionally, can you prove that the topological space a is finite, given the conditions that a satisfies the properties of a compact space, a connected space and a Hausdorff space? (Yes, I'm still salty, and yes, I'm extremely insecure about my intelligence, since it's lower than the highest point of a bell curve.)
Btw, the solution to the second problem is actually pretty easy. A is a finite space since...well, that's literally one of the properties of a finite space. An infinite space cannot be connected, compact and Hausdorff at the same time, so it must be finite. There's a complete proof for why that's true, but it's too long for me to type out, and I don't really understand some parts of the proof anyways. As for the integration problem... *the answer is trivial and is left as an exercise for the reader.*
I’m surprised she was able to crack that molecular formula in mere seconds… I had to think for a bit, as it has N there must be an amine group attached an O4 could indicate two Carboxylic acid groups which makes it an α-amino acid which IS glutamic acid.
The 5th root of 28,629,151 isn't that hard if you think about it. It ends in 1, so you can immediately figure out its something like 11, 21, 31, etc. And you can probably rule out 41+, because its obviously too large. and it starts with 28, checking the Plus/Minus One leads to 27. Which can be gotten via 3. so 31. ...oh fuck I'm out of school and learning math on my own now
I'm not surprised that she is that smart, they are literally some thousands years ahead from us and they are probably also type 3 or even type 4 civilizations. Not to mention that they may surpass the 'singularity' of science. We probably look like children compare to them. 😩😩😩
If anyone is curious I did abit of quick math myself and used a calculator to check, the answer for the first question is 31. And to show my work, the way I came to this conclusion was I first started with a simple number of 10 and multiplied it to the fifth power and just incrementally increased it. Such as 10^5 then went to 20^5 and then 30^5 each time using a calculator to speed up the multiplying process. Once I noticed that 30^5 was really close to the base value i increased it to 32^5 but found that was to high so lowered it to 31 and found it equaled it exactly. Honestly thought I was gonna need to go into decimals. Personally I find, finding powers and roots easy but just taking simple whole numbers and multiplying it to see how close it is to the supposed answer and work from there till i need to find decimals if needed.
i can do the first two in my head, but i wouldn't be happy about it, I'm saying this as someone who has a serious problem in calculus of not writing things out and doing it in my head instead
Now I want Topaz, as someone who also really likes math, and do mental math for "fun". But is she still available? or I'm too late now? I don't have hsr rn cuz of storage issue.
Tbh the 5th root of 28629151 just sounds hard but it's really quite simple. Assuming we know it has a whole number as it's 5th root, then we know that the last digit is 1 because it's the only single digit when powered to 5 that results in 1. Since 28629151 has 8 digits, we know that the possibility of the range is definitely above 10 and below 100. That leaves 11, 21, 31, 41, 51, 61, 71, 81, and 91. We can approximate 28629151 to 2.86*10^7. We use 10^5 as a baseline. And we'll divide each of the possible answers by 10 (1.1, 2.1, 3.1, etc). The 5th power of the numbers will need to approximately be equal to 2.86*10^7 divided by 10^5 or around 286. The only whole number which nears that when put to the power of 5 is 3. So we then know that the answer is 31. The key isn't to actually calculate the answer, it's to approximate.
Bruh, who the fuck are you actually. Not that hard he says, comes out with a whole ass formula. You're the guy teachers use when they demand students "show their answer."
Nah, that's indeterminate. Undefined is any number not equal to 0 being divided by 0. The 0 divided by 0 can have many results depending on the function.
Yeah, fair enough. It is more accurate to say Indeterminate (it's been a while since I've taken math proof classes). So March 7th divided by Pom-Pom is really indeterminate.
I’m not even thinking about the fact that she can answer such hard questions on the spot, I’m still on the fact that she called March 7th cute, cute enough to make her doubt between her or Pom-Pom Topaz I know what you are
-TOPAZ answer for 2nd question:
Glutamic Acid = MSG (King of Flavour)
But there's no sodium (Na) in glutamic acid.
Its NO not Na
I mean... MSG is the common salt of amino glutamic acid (which is naturally present in our body), it can be found in many foods/food addictives too so technically... This comment is right.
"what is genshin impact + phone?"
@@specificallytherandom C7H5N3O6?
If someone says they're practicing mental math "for fun", best believe they're going to get the right answers.
You should run when you see one, they're psychopaths
@@bounds.astroeexcuse me?
@@kaithedoge5861pretty sure its a joke lol
@@justarandompersonontheinte5119 I'm aware lol
I tried to multiply in my head some times when I was bored in my "job", I multiplied two numbers of 3 digits, I failed a lot of times, but I had some answers right, but it wasn't instantly, I needed 10 minutes or even more...
How can I multiply instantly? it seems fun but I just can't
What’s really impressive is the trailblazer knowing that 28,629,151 is the fifth power to begin with.
Nvm she's just found that question popped up in her braincell
Best way to find the answer to this type of questions is to find a range then it will become very easy
@@SUNGJINWOOTHESHADOWMONARCH0what range are you talking about
@@AurA_XTi believe they mean that since that number is more than 30^5 (24,300,000) but less than 40^5 (102,400,000) it makes it easy to solve. If you know your rules for ending digit, you can conclude it must end in a one (rule for any number ending in a digit x raised to odd power is it still ends in x) and the only number that ends with a 1 in that range is 31, so its relatively easy to figure it out. You do still have to know rules for exponents but its not too hard to figure out since they are one simple patterns; 1,5,6,0 all stay no matter the exponent, as long as it is whole and >0. 4 is an alternation between 4 and 6 depending on the parity of the exponent; odd=4, even=6. 9 alternates between 1 and 9, odd exponent is 9, even is 1. 3,7,8 are harder, but still not too hard. 3 is a pattern of 3,9,7,1. 7 is a pattern of 7,9,3,1. 8 is a pattern of 8,4,2,6. This method seems complicated at first, but once you get the gist of it it’s relatively easy to do mentally if you just know the powers of the number 1-9 and can memorize the patterns.
@@ShadowPhoenix4798 I feel like I'm back in 8th grade wtf😭
Stelle isn't even a year old and she's already dropping Arithmetic and Chemistry problems
Chinese game, Chinese child
As a Asian, we learned to cook rice from the womb by connecting our vision to the umbilical cord then to our mothers and watch as she presses 3 button on the rice cooker to cook rice
Seems like someone didn't do the Kafka story quest yet
I'm Asian and I'm dumb as fvck
SW DNA
i don't know which one is more impressive. topaz that could answer it on the spot or trailblazer who could think of such hard questions on the spot
@@Twentizz who asked about being funny???
Probably trailblazer asking hard questions on the spot
The fact that Trailblazer even knows the answers of such questions
People who ask hard questions like that are not impressive. They always have the look of a giggling idiot on their face while asking those types of questions. Sub par intelligence for the asker. At least 116 IQ for the one who can answer that question like that.
And Trailblazer isn't even a year old.
So she’s multilingual, excessively good at her job, and also can perform multi-digit operations on a dime… I can see why the IRS hired her
She's also very capable in combat and is very attractive, the woman is probably an equal to Kafka or Himeko but without the intergalactic train or the seer as support.
IIRC. She ace all her exam at IPC
Except "Business Ethics" 😆
Read it from her story info.
@@tiartiz ironic because so far she's the most ethical IPC employee we've met
Wait............IRS?
@@Konpekikaminari i think she just didnt agree with what IPC treat as "Business Ethic"
That why she skip those exam. 😂 actually didnt show up to take it.
Not related to the content of the video, but the structural formula of C5H9NO4 is HOOC-CH(NH2)-CH2-CH2-COOH, that chemical is glutamic acid (which has been said in the video), the salt form is monosodium glutamate (MSG) which is used for flavouring foods.
you know, i didn't memorized them, so i guessed Nitroglycerin
C3H5N3O9 is not that far from C5H9NO4 tho, cmon, i was almost there LMAO
FUIYOOHHHH
King of Flavor
Uncle Roger would be proud
EMESJEE
I find it fun that she calls Pom-pom and March 7th so cute that she can’t easily equate the values
If we'll consider their names as string variables, we can't divide them either.
@@archangel7294 Since March 7th can be written as 03/07, going by the IPv6's ignoring 0 at the beginning of a string of four, her value is 307. We can find the value for Pom-Pom by finding the value for "Pom" and then multiply it by 2, giving a value of 323026. So we found our value. We just need to answer our question of March 7th divided by Pom-Pom. 307/232026 is 0.001~.
Topaz is a freaking mathematical genius
Normal on a astral scale
She uses math to calculate how to get as thicc as she is.
But what about a Steven He scale
No it's a fckn programm
Fun fact: John Von Neumann could divide two 8-digit numbers perfectly in his head, at the age of 6. Sometimes, reality is stranger than fiction.
"I'm impressed with your ability to come up with questions on the spot!"
I mean, by this point I think MC has been answering questions for Regin for that one Belobog commission for, like, a while now sooo. xD
Ah yes, the old guy who’s "retired" 157 times by now.
0:47
(600-3)(450+14)
6x45 = 270
6x14 = 84
3x45 = 135
3x14 = 42
(I am lazy to multiply hundreds...
so I ignore it 😅,
just add moar 0 after this)
270. 000
+ 8. 400
- 1. 350
-42
= 277. 008
1:04
also for the first question option
(fifth root of 28.429.151?)
I guess it under 5 second...😅
Answer:
Please note that 3^5 = 243
so we know the answer is more than 30
(since 30^5 would be 24.300.000)
with the same technique..
we also know the answer is less than 40...
now, look at the last digit of that 28 million something...
the last digit is 1 ! 👀
this gives us few hint...
first
our answer last digit cant be even
(exclude 32, 34, 36, 38)
(why?
2^5 = 3 2
32^5 = [...2]
Why would you multiply like that? Is this even helpful mentally?
🤓🤓🤓🤓🤓🤓🤓🤓🤓🤓🤓🤓🤓🤓🤓🤓🤓🤓🤓🤓🤓🤓
For the fifth root there are only 8 digit so it must be smaller than 100, it also larger than 10000, thus it has the form xy. The value is abour 280*10^5, so the first digit is 3
The last stays the same. You can prove either by hand or by Fermat's little theorem
Also for FYI 191 is a safe prime since 383 = 191*2+1. Large safe primes are useful in cryptography (they really went hard with the prime factorization problem huh 💀)
Can I go to a timeline where America had a better schooling system and I actually understand what's being said here?
What in the... She's definitely a human calculator
I'd like to believe that with interstellar travel being on the table, math at this level is the standard rather than the exception.
Nah, she herself admits some people think of her as human calculator in her voicelines
@@FrenchDinosauryeah it's basic maths but the way she answered those questions in no time makes her a human calculator.
We have the walking dictionary, and the human calculator, now we just need the translator
@@rianluka6900 It's a sinestesia beacon, also, whos the human dictionary?
She’s that one person (because I’m sure no one is actually like this) who always goes partying until late in the morning when it’s test week yet despite not studying she still gets 100 in every subject.
It is a utopic person type. They usually study secretly if the curriculum of lessons are hard. Because it is impossible to do things nearly perfect without studying
And sometimes study at the party
Yeah, they study, dont worry
@@slvfarvet2626Im one of them. Work hard play hard
Consistent literal100s probably not, but there are almost certainly people who can get straight A's without studying.
topaz's voice is so soothing and calming to hear
Heres the thing: theres a method for finding perfect 5th roots and its not that hard, you just have to memorize the first 10 5th powers then you can calculate perfect 5th roots up to 10 billion. but whats INSANELY impressive is that trailblazer was able to immediately find such a large perfect 5th root. large digit multiplication is possible but in the millions it takes a few minutes at least
btw since ive also been practicing mental maths for the past couple of days, heres how long i took to answer each of the questions(and wether i got them correct)
1.I just assigned march 7th 37 since 3/7 and assigned pom pom 3.7 since its a cute tiny name so i estimated 10(jokishly)(took me around 20 seconds)
2.correct thankfully, but its a harder multiplication problem so it took me 1:30 seconds, idk how she literally did it instantly, either it just skips like 10 seconds-a minute in between dialogue, or topaz is just a literal calculator
(im doing all of the dialogue options)
3A i used the method i was talking about and figured out it was 31 in about 10 seconds
3B idk i wouldve used division but i havent really learned much tricks for division till now
3C Damn this is chemistry now, i have a basic knowledge of chemistry since i also like to study it for fun and i have a 7th grade idea of naming compounds so ill just try to name it like its a compound, maybe its carbon-hydrogen nitrate or something? only part im sure of is nitrate
o h its glutamic acid(the acid version of monosodium glutmate aka msg the king of flavour) well that was pretty unexpected
anyways this was a fun experience. I might actually download HSR since it seems pretty cool. and the characters seem very great and relatable
Edit: 1 month later i have actually downloaded hsr and its really fun. also after focusing on mental maths for another week or so ive shifted my focus to calculus one and im currently getting the hang of derivatives.(ill probably start doing integrals soon after practicing derivatives for abit more)
Update 2(yes im using this comment as a way to keep track of my progress in math/academics):
ive made abit more progress in calc and now im comfortable with most of the differentiation rules i need to know + logarithmic and implicit differentiation, so ive started learning more about limits,related rates, minima and maxima, etc so that i can be knowledgable enough of calc 1 to move on to something else. to be honest however ive also been learning some calc 1 and 2 integration on the side with methods like u sub, ibp, trig sub, etc but im not as comfortable with it as i am with derivatives. regarding the whole mental maths thing its a cool party trick and all but ive stopped doing it(i still can but im not actively practicing anymore) bc you can easily just start setting your expectations too high then always getting dissapointed, like back when i was originally writing this comment i expected to be able to do 3 digit multiplication in 2 secs(like in the video) but ofc that was unrealistic and the best i could get to was 30 secs- a minute.And as for how im doing in school im still in the 7th grade but my finals are in 2 weeks so im studying for them of. btw ive also started learning indonesian(As a 3rd language, i already speak arabic and english since im arab) and learning stuff like languages is really different than stuff like math or science. theyre both still really fun though and im happy with the progress im making on both
Topaz is so goofy.
Topaz is such silly so goofy so cutie patootie
Ofc our mc has good ability with questions formed on the spot. Our mc was trained by mommy Kafka
Nah he/she already train in reign daily missions countless time😂
Now that we have a math person in star rail now we just need a language person and a type of student that excels in P.E
Dude in Star rail almost every person is peak performance
I think Topaz talks in diferent languages in one of her idle animations
@@ragnarokgamer7476yep she does
@@ragnarokgamer7476all four major dubbed languages, each of her VAs speak all four. For JP it goes, JP then CN then KR then EN. She's built different
luka
The fifth root of 28,629,151 isn’t even too difficult to figure out. 3 to the fifth power is just 81x3=243, which means 30 to the fifth power is 24,300,000. Given that the number in the question ends with a 1, the fifth root can’t end in 2, 3, 4, 5 or 6, and 37 would definitely be too large, so the answer is just 31.
You can limit the last digit even more by asking what each remaining number ^5 would be. Not sure why you narrowed it down to 1, 7, 8 and 9. 8 is even so its obviously out but as it turns out, any integer ^5 will end in the same last digit as that initial integer. If the number ends in a 1 and it has an integer 5th root, so will that root
The implication that Stelle is able to quiz Topaz with these questions is that she must know the answers as well
Who knows she is a receptacle after all maybe she got some implanted knowledge
They should have had her object that C5H9NO4 could be any number of isomers. Could just as easily be methylated aspartic acid or acetylated serine.
Kafka: "That's my girl"
Dr Ratio to Topaz: “That’s my girl!”
Trailblazer: Little did this woman know, I am the enlightened one. Wait you aren't supposed to know I used to be an accountant!
top-Ass and top mind, truly one of the waifu of all time
I really thought when she said its really a chemistry problem, we gonna get an option to rizz her up like "but its not gonna affect our chemistry" or something 💀
“March divided by Pom Pom”
I dunno, reminds me of someone else dividing a supposed honoured one…
Literal Chinese education
sis called me stupid in 3 ways ;
I pick option 3 because she want most hard question, sasuga mc aureum manager, kafka taught too well, i know majority here self immerse but stelle caelus smart you know thanks to kafka
Oh, well, that's very cool, Topaz.
Can you please solve for the indefinite integral of a particle moving along the curve of the function f(x)=e^(2x)× sin(x) (x represents time), knowing that the velocity of the given particle at a random point is given by V(x)=f'(x), and the acceleration of the particle is given by a(x)=V'(x)?
(Yes I'm salty that somebody is smarter than me, even though they're a fictional character.)
Additionally, can you prove that the topological space a is finite, given the conditions that a satisfies the properties of a compact space, a connected space and a Hausdorff space?
(Yes, I'm still salty, and yes, I'm extremely insecure about my intelligence, since it's lower than the highest point of a bell curve.)
This is immense nerd fight club vibe and im loving it
Topaz be like: Finally ! a worthy opponent!
If im allowed to try the first question i'd say:
2/5[e^(2x)×sin(x)] - 1/5[e^(2x)×cos(x)] + C
Btw, the solution to the second problem is actually pretty easy. A is a finite space since...well, that's literally one of the properties of a finite space. An infinite space cannot be connected, compact and Hausdorff at the same time, so it must be finite. There's a complete proof for why that's true, but it's too long for me to type out, and I don't really understand some parts of the proof anyways. As for the integration problem...
*the answer is trivial and is left as an exercise for the reader.*
Never mess with the IRS
For anyone wondering: its 31
The 5th root of 28 629 151 is 31
My brain's arithmetic register is only 8-bit wide 😐
Debt collector always crazy at math
Trailblazer: “I’m not gonna check if that’s really correct or not but okay.”
xD
Nice, but it would be even better, if we could talk to Numby.
....no doubt she in the high position in IPC
F. Even myself cant thinking of that question (also answer) so fast
Never knew Senku has a sister who works at intergalactic company
And she's smart? here I was thinking she couldn't get any better
Bro say us dumb in every possible language in the universe 💀
These are otherworldly math questions..
her cornerstone form is just a calculator
Great, now solve the collatz conjuncture
Math is really needed for her to do the work, that's why she's so good in math
As expected of the Cute and Clever Elichika.
(another character voiced by her)
Ok, I definitely want her now
the reverse of millenium treasurer relationship story 6
As expected from our beloved Elichika (Eli Ayase from Love Live, Yoshino Nanjo's favorite role).
💀
Wait until she gets some questions from my teachers
She obviously stalled that third question for a bit
I’m surprised she was able to crack that molecular formula in mere seconds… I had to think for a bit, as it has N there must be an amine group attached an O4 could indicate two Carboxylic acid groups which makes it an α-amino acid which IS glutamic acid.
first yuuka, now topaz. why i always land on ~~thicc thighs~~ calculator waifu😂
I somehow got the question right but it took me a few minutes. Wouldn’t have been able to do it without the number right in front of me though.
And this is why I love Topaz.
we need to pit Topaz and Dr Ratio against each other for a math exam
Topaz really said "FUIYOOOHHH"
when shes smart too
The 5th root of 28,629,151 isn't that hard if you think about it.
It ends in 1, so you can immediately figure out its something like 11, 21, 31, etc. And you can probably rule out 41+, because its obviously too large.
and it starts with 28, checking the Plus/Minus One leads to 27. Which can be gotten via 3.
so 31.
...oh fuck I'm out of school and learning math on my own now
I feel mad in love and stupidly stupid at the same time. Thanks topaz 😊
"why don't you test me?" "make it Hard"
Bro just ask her to divide by zero
Shes smarter than the same topaz in henry stickman
I'm not surprised that she is that smart, they are literally some thousands years ahead from us and they are probably also type 3 or even type 4 civilizations. Not to mention that they may surpass the 'singularity' of science. We probably look like children compare to them. 😩😩😩
chill it just a fictional character.
If anyone is curious I did abit of quick math myself and used a calculator to check, the answer for the first question is 31.
And to show my work, the way I came to this conclusion was I first started with a simple number of 10 and multiplied it to the fifth power and just incrementally increased it. Such as 10^5 then went to 20^5 and then 30^5 each time using a calculator to speed up the multiplying process. Once I noticed that 30^5 was really close to the base value i increased it to 32^5 but found that was to high so lowered it to 31 and found it equaled it exactly. Honestly thought I was gonna need to go into decimals. Personally I find, finding powers and roots easy but just taking simple whole numbers and multiplying it to see how close it is to the supposed answer and work from there till i need to find decimals if needed.
Shes a Walking bakery and human calculator
Give her the Three Bodies problem :)
Stella make me thinking that she learn how to play piano when she in womb. Steven
Bruh, how would you do mental fifth roots and prime factors, that's nuts
i can do the first two in my head, but i wouldn't be happy about it, I'm saying this as someone who has a serious problem in calculus of not writing things out and doing it in my head instead
Can you prove that no three positive integers a, b, and c satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2?
When you challange Topaz with how to create PTO(Π1,3-CA0)
Topaz:...
i'm taking high school chemistry this year. i was told acids always start with hydrogen. apparently, i was lied to lol.
If I had a brain like hers, I wouldn’t be eating instant noodles everyday smh
you have that as your train cabin ost??? omg why??? i thought this was a hack or glitch or something lol
how to challenge topaz: ask her algebraic expressions: n - 3 =?
WAKARAN!!!!!! I DON'T THINK EVEN THE MC KNOW THE ANSWER INSTANTLY LIKE THAT!!!! 😂😂😂😂
She definitely needs to touch some grass
ugh topaz so cute im gonna pull her
She's giving me highschool ptsd
topaz would be good at maths given that perfect 4/3πr³ topass
100% planned to skip but my nerdiness compels me to try and get her
she didnt even pay the taxes (staller jade)
I don’t even know my 8x properly 😊
Now I want Topaz, as someone who also really likes math, and do mental math for "fun". But is she still available? or I'm too late now? I don't have hsr rn cuz of storage issue.
You still have about a week
I will be pulling
Tbh the 5th root of 28629151 just sounds hard but it's really quite simple. Assuming we know it has a whole number as it's 5th root, then we know that the last digit is 1 because it's the only single digit when powered to 5 that results in 1. Since 28629151 has 8 digits, we know that the possibility of the range is definitely above 10 and below 100. That leaves 11, 21, 31, 41, 51, 61, 71, 81, and 91. We can approximate 28629151 to 2.86*10^7. We use 10^5 as a baseline. And we'll divide each of the possible answers by 10 (1.1, 2.1, 3.1, etc). The 5th power of the numbers will need to approximately be equal to 2.86*10^7 divided by 10^5 or around 286. The only whole number which nears that when put to the power of 5 is 3. So we then know that the answer is 31. The key isn't to actually calculate the answer, it's to approximate.
Bruh, who the fuck are you actually. Not that hard he says, comes out with a whole ass formula.
You're the guy teachers use when they demand students "show their answer."
If possible i want ask her:you travel to 6 planet and each have 5 Lightyear long so how many total milimeter you travel
Pov: 10 Stellar Jades
That 5th root thing is answered by 31 BTW, you mostly just eliminate impossible solutions and see it from the characteristics
big brain top ass woooo!!!
I just want my 10 jades man......
0 divided by 0 is undefined.
Nah, that's indeterminate. Undefined is any number not equal to 0 being divided by 0.
The 0 divided by 0 can have many results depending on the function.
Yeah, fair enough. It is more accurate to say Indeterminate (it's been a while since I've taken math proof classes).
So March 7th divided by Pom-Pom is really indeterminate.
Woah she so smart while me over here keeps forgetting 11 x 11 isn't 111 :(
3 semesters of organic chemistry and I can't tell the formula of glutamic acid on spot, meanwhile topaz does it like it's nothing.
31 is the fifth root btw I manually experimented with numbers and skipped a few until I can finally get 28,629,151
March 7th: HOW THE FU-
Kafka taught her welll
I’m not even thinking about the fact that she can answer such hard questions on the spot, I’m still on the fact that she called March 7th cute, cute enough to make her doubt between her or Pom-Pom
Topaz I know what you are
Gomen Topaz coming soon
DAMMMNNNN GURLLL