I solved this problem using calculus of variations and some help from wolfram-alpha. I used spherical coordinates, with the origin at the cone's peak. This has the advantage of making the phi coordinate (angle from the z axis) constant. The differential arc length on the cone is... L = sqrt((dr/dϑ)^2+(r*sin(φ))^2 )*dϑ where r is a function of theta. You can use the Euler-Lagrange equation (dL/dr - d/dϑ[dL/dr'] =0 )to give you a differential equation, who's solution will minimize the integrated arc length (functional). With the help of a computer-algebra system, I was able to reduce the differential equation to the form... r'' - (2/r)*(r')^2 - r/9 =0. This is where I used Wolfram-Alpha's General Differential Equation Solver for help, as I am pretty clueless when it comes to solving non-linear differential equations. The general solution is... r=C2*sec((9*C1+ϑ)/3) And I used Wolfram-Alpha's systems of equations solver to solve for the integration constants given the boundary conditions (r=60,ϑ=0) and (r=50,ϑ=2pi) C2 = 150*sqrt(3/91) = 27.235239 C1 = (2/3)*atan( (5*sqrt(3)-2*sqrt(91))/17 )= -0.36654527 This gives you the distance from the peak to the points on the track as a function of the angle around the mountain. Here is a plot of the radius. www.wolframalpha.com/input/?i=plot+27.23523897009611*sec((x-3.298907465836848)%2F3)+from+x%3D0+to+2*pi&wal=header And if you want to calculate the altitude below the peak, useful for calculating the elevation the track needs to be at, you can just multiply the radius function by sqrt(1-(20/60)^2) = 2*sqrt(2)/3 = 0.943 From this, you can calculate the grade of the track (rise over run) or (dz/dx). The vertical distance delta_z = (-0.943)*delta_r. dz/dϑ = -0.943*(dr/dϑ). The horizontal distance delta_x = r*sin(φ)*delta_ϑ. You can solve for dϑ/dx from the horizontal distance formula, and use dϑ/dx to change the vertical distance independant variable from ϑ to x. (dz/dϑ)*(dϑ/dx) = dz/dx = -0.943*(dr/dϑ)*(dϑ/dx) now substitute expressions for (dr/dϑ) and (dϑ/dx) into the right hand side of the previous equation... dϑ/dx = 1/(r*sin(φ)) and dr/dϑ = 9.078412*sec((ϑ-3.298907)/3)*tan((ϑ-3.298907)/3) and get a track grade (slope, not a percentage)... dz/dx = -0.333333*2^(3/2)*tan((ϑ-3.298907)/3) www.wolframalpha.com/input/?i=plot+-0.3333333333333332*2%5E(3%2F2)*tan((x-3.298907465836848)%2F3)+from+x%3D0+to+2*pi

Jess Stuart How long and how many pages did it take to get the right answer?

Bill Y. Probably about 4 pages and atleast an hour of trying to solve the Differential Equation, then giving up and using Wolfram Alpha. It was a good excuse to get more practice doing calculus of variations stuff anyway. You would have to do it this way if your surface couldn't be unrolled to a nice flat surface.

Jess Stuart: Thank you for explaining this! I do enjoy when people find "easier" ways to solve the problem, but this is one case I really enjoyed seeing a "harder" way to solve it. Your comment will inspire many to study calculus of variations (and for me to brush up on it and learn more too). Thanks!

I thought about using coordinates to find the shortest distance btw the chord and the arc (on the unfolded cone), then I thought it's multiple choice it can't be that complicated and there has to be a "easier way." Then realize that I can simplify this into solve a triangle with two sides that are 50, 60 and 120 degree angle in btw. sadly I did make some calculation error when applying law of cosine. I like how you just used pythagorean theorem and set up 2 functions and solved for the part directly, I really made the calculation more complicate by trying to solve those angles

This is true, we have about 4 minutes. This question was worth 4 points out of total of 100 points, for which we are given 100 minutes to solve. We have about a minute per point.

Steven McCulloch In Korea you're expected to be able to solve quickly and accurately. This is highschool level stuff here.

MassiveTornado the concepts being applied are, but a good understanding of geometry that they don't teach in schools are needed to figure the entire problem out.

Steven McCulloch Why do you think Koreans students study outside of school as well

Steven McCulloch Korean education, especially math and English are harder than almost anywhere else in the world

Best comment so far haha😂

U would actually get it correct if u used that method

@@cyanide6954 this method always gets the correct answer it proved itself many many times

What a comment 😂

*UNDERRATTED*

킹정

m/v가왜다름

@@user-qi7rv5bq2f 시행착오가 세기성질이 아닌가보지

그래서 원래 한국애들 유학가면 중고딩까진 우리가 훨씬 ㅈㄴ 더 잘하는데 점점 더 외국 애들이 잘해져서 나중엔 한국 애들이 더 못해짐

한국인이 외국 중고등학교에선 성적이 높은데 대학가선 적응 힘든 이유임

fahad mohamed you cannot bribe God for easy answers with all your flowery duas: God does not reward laziness by giving away easy answers to questions or even giving free scores in exams. God does not grant you easy answers to maths question: otherwise, that would be cheating and unfair.

In this case you should guess #3. It has the same denominator as #4, and the same numerator as #2, so it's the most likely to be correct.

Pink Lady: You cannot bribe God because God exists in your head only.

Logically you should pray first and then guess.

fahad mohamed same

OMG.....so ture

현실이네 시부레

@@djmikecr9284 형님 한국인 이과라면 당연한거 아입니까

@@ys9018 아 수고하세요 저는 6학종..

@@user-tg9uz4ve8w 아따 01년생한테 6학년이라니 거 말이 너무 심한거 아니오! 수학 못해도 드립치는건 내 자유다 이말이야!!

쓸데없는 국뽕이다ㅋㅋㅋㅋ 오히려 독인데 그걸 자랑스럽게 여기는듯한

@@user-kc7ww1tk8k 어떤점에서 독이라는거임

@@jjh4928 이러한 뽕은 필연적으로 다른 나라에 대한 무시와 차별로 이어지죠

@@jjh4928 이미 친 사람들은 모르겠지만 학생이면 개고생 해야되니까. 그리고 수능에 맞춰진 교육방식도 문제가 있고

@@user-pp8bo4jz1c 그게 필연적임? 문화절대주의랑 필연적인 연관성은 없는거 같은데

Isn’t math more difficult and complicated in college ? Or that’s true but still since you’re learning more things it’s becoming more interesting the whole lesson

Math is certainly more fun when you have the time and the context to solve the problems!

americans start hating math in the first grade.

yeah i also usually hate maths but now i love to solve it

@@kdy5617 math before college in S.Korea is more like memorizing problems. Just solving thousands mindlessly.

Lol I wouldn’t be able to solve this either. All these people in the comments saying they could solve this quickly are crazy good at math haha.

*Hannah M* it’s not that hard, if you take out everything i calculator can do for you only a few steps are left -understand it’s a circular cone -put the points st their respective spots -figure out the angle -realize that the right angle line to the path is the highest point That’s the only math involved in this problem, everything else he shows in this video is just boring calculator stuff

Larz B 20 sec? I doubt that any person that ever existed could solve it that fast. I don't even think Terence Tao could solve it that fast and his iq is 200+.

The important part in korean sat you have to solve this at least a minute to maximum 2 minute to solve this because there are like 10 more questions even harder than this. Also you don't use calculator.

Larz B shortest line is not always a straight line. And this took me just 1 second.

Oh, that's a cool thought. I was hung up for a bit on that too, but i unstuck by imagining the more simple question of if the track came back to the same point A, then the downhill would be halfway... noticing that's exactly when the unrolled straight track makes a right angle with the radius.. which i guess is essentially the same thing as parallel to the tangent

탁두둥 i wishnyou luck, you will probably need it based on this video

nice, all the best! xP

>using comedy chevrons on YT >why?

asdmvva 4chan user out of his natural element.

Do you also study all day long till midnight?

Sir

ㄹㅇ 이미 졸라본듯

ㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋ 한국인에게는 그닥 어렵지 않았다...

@UCGBHl99d5_PHk_cl4ZyQlZg 지금은 2021년입니다

전개도면은 누구나알겠지만 내려가는 부분이 어디서 시작하는지 아는 사람은 별로 없을 것 같습니다

여러분 밑댓글중에 중3이 몇초만에 푼다 이런 댓글들 많던데 저는 진짜 개멍청해서 저거 전개도 펼치고 삼각형 만들어서 그 삼각형의 꼭짓점에서 수선 긋고 코사인 법칙쓴 뒤에 넓이 이용해서 수선길이 구하고 개그지같은 루트91로 된 숫자를 피타고라스로 풀어야 하는데 나름 어려운 문제같은데 저만 그런가요

Bravo.

yay! precisely the same solution path I came up with, however, as someone pointed out, "you only have ~10 min to solve this problem", I would have failed. If I were smarter, since it is a multple choice question, I think it is possible to find the right alternative by constructing the path in the 2-d case and just measure the length of the decent part with a ruler. it will be (when I measure) ~42 length units and the correct alternative (400/sqrt(91)=41.9314 lu)

Exactly how I conceived the solution, though I didn't bother doing the grunt work.

@@weijholtz If the choices are spaced enough to be resolved within your ruler accuracy then it's a great time saver.

Brilliant

그래두 자이스토리 29번인가 30번이었다네용 허헣

Which is the hardest I want to take a crack so if you find that please post a link thank you

@@anmolbaloni every problem numbered 21, 29, 30 in the korean math SAT is difficult

Which is still kinda easy

Bruh this is easy tho😑

ㄹㅇ ㅋㅋㅋㅋㅋㅋㅋㅋㅋ 요즘 수학 가형풀면 기절하겠누 ㅋㅋㅋㅋㅋㅋㅋㅋ 97수능이면 요즘 가형 27번쯤 될 듯

ㄹㅇㅋㅋ

@@user-vr7vm5if4s 17학년도 수능 가형 30번이면ㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋ

@이경훈 솔직히 근데 전체적인 수능 성적으로 따지면 언제가 더 어렵고 쉽고 비교 할 수 있나...? 97수능 문제 구경도 못해보긴 했지만.

@@user-we1dd7kj3u 전반적으로 수준이 올라서 예전이랑은 비교하면 안됨 ㅇㅇ

that case i would choice 2 or 3, 4 so will be given 33% chance

You're genius.

Too easy in 2minutes clear

And now.... we solve that kind of thing for practical qusetion

Just basic question

Lugh Summerson yeah , that is where that formula comes from .

That’s what I did by that does equal 2(pi)/3... am I missing something?

I find it easier to work with revolutions (easy to conceptualize) then convert to degrees or radians when needed. I wish calculators had a 3rd option of revolutions, not just radians and degrees.

@@johndavidalexander6646 (40pi/120pi)*360 or you could shorten it to (1/3)360, using this angle youll get the correct answer, in degrees not radians you either didnt divide both sides by pi or forgot to cancel one out

I always solve like that

How sir

@@narasimharaobejawada2776 Thanks for answering. This was a few months ago. I will have to think about it again and get back to you.

@@Jack_Callcott_AU have you thought about it again?

@@beaclaster I'm sorry to say I haven't. It was very hard for me the first time, so I was loathe to try again. I will have to sit down with pen and paper and try again. I'm sure I'll see the way through. Thanks for the reply.

@@Jack_Callcott_AU did you try again?

SAME...

ㅋㅋㅋㅋㅋㅋ문송쓰

지나가던 문과생입니다. 계속 지나가겠습니다 이거 영어버전인가 ㅋㅋㅋㅋㅋ

문붕잌ㅋㅋㅋㅋ

아 역시 드립의민족

You will never use this once in your life. I guarantee that.

@@LibertyGunsBeerTrump maybe, maybe not.... A lot of things that we eyeball can actually be done using math. We just find it easier to adjust to failure rather than doing some complex calculation and getting it right

ㅋㅋㅋㅋㅋㅋ 저문제 중3때 풀어본거 같은데

@@soobark2 그러게 이거 중3 거 아니냐? ㅋㅋㅋㅋㅋㅋㅋㅋ

그 만큼 헬조선..

@@soobark2 블랙라벨에서 나온거같은데

솔까 수능 이거 못 풀면... 3등급 이하 확정인듯. 곧 마주칠 수능은 범위 달라져서 어떻게 나올지 감은 안오지만 일단 내 시절이라면. 방정식도 그리 복잡하지 않고

So freakin true. Students can solve this problem 3 years before they take KSAT

facts...

i saw this problem in math olympiad book

Too easy for KSAT.

SPayee yea. ksat is harder.

저런 유형들 많이 분석돼서 중딩때 수업 잘 들었고 코사인 법칙만 배웠다면 쉽게 푸는 문제가 되었죠...

ㄹㅇ ㅋㅋ 딱 중3문제인데

@@floccinaucinihiliphilifica5265 ㅇ 맞음 나도 초등학교때 수학학원에서 이 문제 보고 벌벌떨었음 근데 이문제가 정답률이 10퍼센트라고요?

@@floccinaucinihiliphilifica5265 그건 맞지 근데 이게 10퍼센트는 아닌거 같은데 어디 자룐진 모르겠지만 못해도 40퍼정도는 나올듯

@@billykim7179 어디자룐지 모르는게 아니라 당시 수능 정답률인데요ㅋㅋ

맨날 수능 까는애들이 하는말이 "이런거 배워서 어따써먹음?" ㅇㅈㄹ하는데 애초에 수능은 대학교육에 필요한 수학 능력을 측정하는 시험임 이런 댓글보면 한숨만 나온다

@@user-mk5ln8iz7l 그게 한국 한정이니까 그러죠. 수능은 분명 누가누가 수학적 사고가 잘되나 하고 보는건데 현실은 누가누가 더 오랫동안 공부했나를 보는거잖아요. 다른 분들이 말했듯이 이 문제가 기출문제집에 나오고 그러니까 이런걸 풀어본 사람들은 쉽게 풀지만 처음 나왔을때는 정답률 10%잖아요. 같은 유형의 문제만 외워서 뭐해요. 완전히 새로운 유형을 만나면 쩔쩔매는데. 그렇게 대학을 가니까 대학이 취업을 위한게 목적이 되고 말았죠. 취업은 기업에서 그동안 해오던 일을 수행하기 위해 하는거지만 연구는 기존에 없던 새로운 것을 만들어 내는거잖아요. 당연히 자연대나 공대나 상대라면 새로운 수학 문제도 만들테고요. 그런데 문제 유형을 외워서 푼다면 그런 문제를 풀수 있을까요? 흔히 수학 괴물이라고 불리는 천재들이 아니라면 힘들겠죠.

몇년전, 거의 10년전에 하버드 학생들이 한국 고등학교에 와서 고등문제를 못풀었던 적이 있었죠. 그리곤 고등학생들이 풀고서 하는 말이 '이런 문제를 풀어봐서 풀수 있었다.' 였고요. 우리나라 교육과 외국 교육의 차이를 나타내죠.

@Beom Lim저도 님들처럼 딱 그렇게 생각했었음 ㅋㅋ 재수하면서 인강도 많이 봤고 특히 인강 강사들 하는 말이 전부 맞는 말인줄 알았음. 수학 고난이도 문제 풀려면 단순히 공식 외우는게 아니라 개념을 정확히 알아야 풀 수 있는 것이고, 평가원 문제, 특히 수능문제는 정말 교수들이 머리 꽁꽁 싸매서 만든 질 좋은 문제라고 생각했음. 암기가 아니라 정말 개념과 원리를 이해해야 풀 수 있는 아름다운 문제라고 ㅋㅋ 실제로 한국 교육이나 수능 까는 글이나 영상 있으면 공부도 못하는 빡대가리 새기들이 뭣도 모르면서 깐다고 욕도 했었음. 그런 시절을 지나 학부에서 컴퓨터 보안를 전공하고 지금은 대학원에서 인공지능 연구하면서 선형대 통계 해석학 최적화 등등 다양한 분아의 수학을 공부하고 있는 상황인데 지금 생각해보면 입시 교육이 주입식이였다는 생각이 듬. physical한 영역에서의 수학은 정해진 유형도 없고 답도 없음. 외국애들 논문 내는거 보면 정말 창의적인 논문들 많이 내는데 그런것들이 다 어렸을 때 부터 저 유튜버처럼 다양하게 생각하고 고민하는 것에서 부터 발전되는 거임. 한국인들이 창의성이 떨어지고 시키는 것만 잘한다, 한국에서 노벨상이 안나온다 등등의 말이 괜히 나온게 아니구나 라고 생각이 듬. 입시 교육에서 미분을 쓰기 전에 정말 이 상황에서 미분을 사용할 수 있는 조건이라는 생각은 하긴 함? 미분을 사용하기 위해서는 많은 전제조건들이 필요한데 솔직히 대충 그래프 있고 문제에 f' 이런거 있으면 기계적으로 미분 쓰지 않음?

수능의 수학이 그수학인줄아는사람들이있네

May I know what you mean by the angle at the apex being greater than 180 degrees? Does it mean like if the 'net' of the cone turns out to be a sector that has a central angle (subtended by an arc/the circumference of the base of the cone) which is a concave angle?

OK, what I said was elliptical, but I think you get what I mean. But more carefully now: We unrolled one cone, and we mapped the apex of the cone to a particular point on the plane. I called that point the apex also. The circular sector subtends a particular angle at that point - I called that angle theta. Then I multiplied theta by N, the number of windings. Then I called N times theta the angle at the apex. That's the angle which we test for being greater than 180 degrees. So yes, sounds like you got it.

Whoa! I didn't think about "unrolling N times." It's a strange concept (strange for 3D to 2D anyway). Can I unroll something a fraction/ negative number/ irrational number/ complex number Number of times?!?

Well, unrolling a negative number of times is the easy one. It just corresponding to negative winding numbers, which are just going around the cone the opposite way. So we'd just unroll the cone the other way. Zero makes sense in this picture too: when you unroll the cone zero times, you just have the line segment from the base of the cone to the apex. Zero area, zero angle at the point corresponding to the apex, and the path corresponds to the solution of zero windings. Fractional - we can say that it corresponds to placing the target point a fraction of the way around the circle at that latitude of the cone. That should cover irrational too. Complex winding numbers would get a lot messier. We'd like to say such a path "winds around in it the imaginary direction", but that doesn't make sense on a real-valued cone. Maybe we embed the cone and the whole problem in complex 3d space, but then it's not a cone any more. We could generalize the cone - like, the base of it is not a circle but any solution to x^2 + y^2 = c and similarly for other latitudes, so x^2 + y^2 = c * z. Then in imaginary space it has this hyperbolic cross-section, and there are solutions that make the path length zero. That's if we're looking to minimize its absolute value - if we're looking to minimize its natural value, we can find paths of negative infinite length, which is a fair bit shorter than 400/sqrt(91). Like I said, it gets messy.

The cone with a vertex angle V >180 is geometrically identical to one with vertex angle (180-V). After you unroll it you can't tell the difference. To see this in practice make a sector out of paper and draw on it the railway then roll it in to a cone. Roll it into a cone by curving the paper the other way: all that is different is that the track is on the inner surface instead of the outer: the shape in 3D is the mirror image but all the lengths are the same

가연이 남친있노

Hello. I.m a viewer of this channel too and i.m from Indonesia:)

e-z

Geometry dash

Fact

umm.. it was hard but not hardest.

ez 4 me

1. Make an actual model out of the sheet the question is on. 2. Take a rubber band. 3. Mark the points A and B by pins. 4. Connect them by the rubber band. 5. Take a marble and let it roll from the highest point of the trajectory towards B. 6. Measure the path the marble took. There you go.

N○OO◦◦oo....༼;´༎ຶ ۝ ༎ຶ༽

Just chose the one nearest to ur answer

푸아송 What grade is this for?

@@acutepenguin3577SAT for hight school grade 3 students. This is last grade in Korea.

It isn't going to be that hard since lots of Korean students get familiarized with similar types of problems throughout their math courses at Hak-won prior to taking the CSAT.

How much time you have for this one depends on how fast you are on the easier problems. :)

But isn’t the math section 100 minutes for 30 questions? 현재 한국 고등학생으로서 이렇게 알고 있습니다

Is reply 1996 relatable for you?

I was the one who made this question.

LOL

@@chinmayh2745 I was the one who made u

@@jjraga 😂 😂 badass

true

panulli4 He most probably meant editing the Korean dude's English, since Korea is the Asian country that is least able use it.

Mitko Gospodinov dude the joke flew right over your head holy fook

@@m.g.6081 whoosh

probably fixing grammar and spelling?

i guess he made the problem easier by editing it

He probably meant there is a specific formula for this type of question, which is totally useless outside of solving this question. It is the art of test taking(not saying it is a good thing tho).

Are you a student yourself taking this exam? If so, can you please teach me this so called ‘specific formula’? As a korean student studying for csat this year, I would be grateful to know if there is a such formula to solving these type of questions. Because as far as I know, there is no such thing as ‘specific formula’ for this problem and all the other problems asked on csat.

That's not true There's no specific formula

That’s not truth guys.. the KICE which is making questions in the CSAT never intend to solve it by simple formula..I think Junho is not Korean lol 평가원 기출 5년만 풀어봐도 진짜 문제 잘만들었다고 느껴지는데 준호님은 평가원이랑 교육청이랑 헷갈리셨나보네요

They're many questions using 'cone' and 'shortest path', maybe occured after this question. Actually, Korean students, including me, are well trained to this kind of questions. So many of ours can approach like that easily. I think Junho Son said like that in this aspect.

When he started drawing the lines from the vertex to the radius... I also facepalmed.

Peter Geras 😂😂😂

Makes sense, but using intuition to solve math questions like this, because they give you multiple choices and just one makes sense feels like cheating. Doesn't feel like you're doing actual math

@@IDyn4m1CI Hi Vinicius Thanks for the comment. Please let me explain my rational. My intuition is based on many years doing and checking engineering drawings so it is a bit different from the average person. In an examination you have to use every tool available. The question was select the correct answer ....not calculate the answer from first principals. If this was the intention it would not have been multiple choice. Make your choice... be morally correct and fail the exam or use all your tools and pass. Exams don't reflect reality. Also from past experience the smartest person does not make the best employee. I will always employ the person with the best imagination. I am an engineer and we never do important calculations in a hurry unlike an exam. We do them slowly and check then recheck. For important structures we often employ an independent party to check our calculations and assumptions. Often in engineering I select a member size based on experience then do my calculations and code checks to prove it is correct. If they don't align then alarm bells ring. In this problem I did do a manual calculation to verify my assumption. Sorry for this long winder reply. Cheers John

@@johnspathonis1078 Thanks for the reply man. Although that still doesn't quite sit right with me. If the exam is meant to evaluate your math knowledge, than you should have to use every bit of knowledge you have to calculate the answer, and not make educated guesses based on intuition. I had to do a similar exam (ENEM, here in Brazil) to get selected to study in my current uni (I'm an undergrad physics student) and it sucks, you have to develop a whole new set of skills to pass that thing because you simply don't have time to read some of the questions or do the math required to solve them. The exam is divided in 2 days, in each day you have to answer 90 questions, and in the second day you also have to write a 24-30 line text about a selected theme, elaborating about it and proposing a solution. Some of the questions are so large you can't bother to read the text, and in the Math part of the test, there are questions ranging from easy (trivial), medium and hard difficulty, the hard ones you simply have to skip or make educated guesses, and then take your time after the exam to solve them to find out if your guess was correct.

@@IDyn4m1CI Hi Vinicius. Agreed exams really suck. They do not reflect reality but I am unsure what the practical alternative is. I think in a way we are saying the same thing. I used the word intuition and you said educated guess. I think they are the same. They are both based on our knowledge and understanding of the subject matter. It has been interesting discussing this with you. I am in Australia and am currently in lockdown due to a Covid outbreak new me. Cheers and stay safe. John

Are you two just good at math from the beginning? The reason I chose med school was because I could never survive this exams. All we need is just read and read no calculations. Most of my friends who became specialist surgeon etc are rather average but they’re all diligent. I bet they’ll have a stroke trying to pass this exam. The irony is there was this junior who was a math freak but after 4 semester he quit and moved back to his habitat: engineering school. Last time I heard he was in Japan pursuing PhD in fields I can’t even remember, still in the realm of physics & math.

High school questions won’t get more difficult than this. This is an example of a high school question at the absolute highest level

I saw this type of question in my class 9th reference book ....not exactly this question but this type of question. And I am form india ....there are some similarities between us ...

Still working on this problem, huh haha

This is a very reasonable problem to solve in 2-3 min... just the calculations are a bit cumbersome definitely NOT A HARD problem

​@@Mike-rw1jw Altough there are problems that are harder this one is difficult.

Nice! Yes, a bit more convoluted, but more systematic, straightforward and relentlessly working solution :)

@Helloo There lmao

ㅋㅋㅋㅋㅋㅋㅋ

? 저만 이해 못한겅가요? 혹시 이거 왜 웃긴지? 알려주실분!

@궁예 아 ㅋㅋㅋㅋㅋ 감사합니다 ㅋㅋㅋ

UNDERRATED

하 근데 수능문제는 다시봐도 모르겄네… +아! 문제만 다시 보니까 어떻게 푸는 지는 대강 알 것 같네.

이거 우리나라식 알고리즘 드립이잖앜ㅋㅋㅋㅋㅋㅋㅋㅋㅋ

@@HwanyPlayz 외국도 많이 그런답니다

@@andrewjung2218 오 그렇군요

@@HwanyPlayz 한국인이 쓴거임

And Karren Brady didn't even understand the problem. 😉

And by its solution, if given on a silver plate.

So far, for this video, 👍 : 👎 = 810 : 10 = 81 : 1 For last video, 👍 : 👎 = 566 : 442 = 1.28 : 1 Presh, you are back on the right track.

Likes and dislikes don't matter to the success of a video. Advertisers only care about the number of views. Liking is only to help the algorithms build up a profile of you.

머염쿤KZfaq 난 수능도 안보는데 왜 추천해주누 ㅋㅋㅋㅋ

어떻게 사람이 문과냐

I completely agree man you guys are nuts. In a good way.

@@ab-bo5hq 문들문들;

well but there are ways u can follow to solve ODE, so it's easier for some ppl

It really looked like a calculus problem. Should be no problem for students in differential equation.

Diff Eqs in high school sounds unusual

@@pierrecurie welcome to Asia

Korean SAT or Korean high school math doesn't deal with differential equation. The trickiest part is calculus(excluding differential "equation") related to analysis(like a transcendental functions graph). As that person said, ODE has specific way to solve. Most of tricky part in Korean SAT isn't solved by memorizing. It demands creativity. (Sorry for my poor English. I'm just pure Korean)

너가 머리가 안좋아서 그럼ㅋㅋㅋㅋ

@@user-oe9sg5rn5v 진짜 역겹네

@@user-oe9sg5rn5v 이런애들 특) 영어독해 저사람보다 못함

@@YUUUUUUUUUUUUUUUUUUUUUUUN 아니 저사람은 원어민이자너ㅋㅋ

Agree! try to solve some interesting Math Olympic question here!

kzfaq.info/get/bejne/hdGdgbuqnMvWaGg.html

the question is literally: "what is the probability that this tetrahedron contains the spheres center?"...

if ur talking of that tetrahedral one I agree that was too difficult for me i spent 4 hrs working on it but finally had to look towards the answer

this one didnt need calculus

YH C true lol

RIGHT... It's not actually really hard question.

I find it pretty hard. I mean u dont have all the time in the world to solve it, if u can figure it out in 5 minutes or so you have my congratiolations

Lol

@@yuno7825 koreans can cuz they study math in a different way... they study math by memorizing, not understanding. imo this is not a good way to learn math.

Good for you. I only understood it when he unraveled the cone into a circular arc, then it became easy from there. I didn’t even realize that there’ll be a downhill at first until I realized that the line should be parabolic for it to have no downhill. Facepalm*

이게 우리나라에서 0.08% 맞췄다구요??? ㅎㄷㄷ. 지금보면 쉬운문제중 1개인데

And it freaking worked for me .........question done in 1st attempt ....

nah, 45~50min. it was on my test actually.

Yes, but the persistence mentioned should be applied to thousands of problems before this test, making every new problem easier. It is impossible to be persistent only during tests!

박상현 22 ㅋㅋㅋㅋㅋㅋ

박상현 hahahahah Kim jong un

This is easy for japanese students. They have to more difficult questions. It's why Japan have a lots of Nobel prize unlike S.korea. Another levels of brain

@@guozhou8114 中国人だとおもいますが、確かに認めざるを得ない部分もありますね.でも、動画に関係ない話で他国を批判することはお止めください.

김도현 translate please. I dont know so much. And why can you use complexed japanese language?

어억... 루트가 중3에 나올텐데 중2 문제집에 이게 나온다구요..?

중2때 블랙라벨에서 본 것 같기도 하네요

@@user-dj5qg2zv3w 저도 왜인지 모르겠는데 2015 개정교육과정 중2 쎈 Cstep에 있습니다;;

@@user-dj5qg2zv3w 음 예전수학이랑 지금수학이랑 배우는 것이 달라지지않았을까요

지금 곧 고1인데 요즘은 중학교 3학년 때 삼각비 파트 나옴 이런 문제는 중3 때 난이도 상짜리로 나올 수도 있을 듯

Incorrect answer means deducted points, n/a means nothing. Still willing to take that chance?

what is enie minie minie mo?

@@piyushashinde2189 a way to select anything.

@@freddelgado wdym?

@@freddelgado hey thanks

jagmarz exactly..but at first I thought that the shortest distance is a curved line even after spending the 3d cone to 2d..really silly isn't it?.otherwise it's not that tough..but to get it right at first attempt ina short time is the real challenge

We should solve that at 3~4 minutes😭