# Ekene Franklin's messageboard.

Feel free to discuss anything here with me friends! We're here to help each other!

Note by Ekene Franklin
1 month ago

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Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

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My country's national olympiads 1st round is to be conducted tomorrow. I will most likely post all of them here for our consumption! I expect them to be pretty easy.

- 3 weeks, 6 days ago

Ok. Thanks and also are you writing that exam.

- 3 weeks, 6 days ago

It is actually meant for students two years older than I am, but I will give it a shot.

- 3 weeks, 6 days ago

Oh !!!

- 3 weeks, 6 days ago

It there a minimum age requirement to be eligible to write your country's olympiads?

- 3 weeks, 6 days ago

Yes, I think it is 13 or 14. People from class 8 or 9 onwards can write the exam.

- 3 weeks, 6 days ago

Are you also writing the olympiads soon?

- 3 weeks, 6 days ago

No. At present I am not interested. The main goal of student student studying in class 11 and 12 in India is to get into IIT (Indian Institute Of Technology)

- 3 weeks, 6 days ago

Oh, so that is what JEE and IIT are all about. I hope you get into it seamlessly. But say, do you hope to write olympiads in the future?

- 3 weeks, 6 days ago

Yes. I may.

- 3 weeks, 6 days ago

This is a marvelous secret and I benefited a lot from this. If you want to write any question for the problems of the week the better option is to write a physics problem rather than maths. Out of 5 problems 3 are allotted for maths and 2 for science. In the maths category there will be a much competition from many users. But in the science category there are only 4 competitors namely Rohit Gupta, Pranshu Gaba, and two staff members Blake Farrow, Danielle Scarano. So, I posted some good physics problems and 3 of them are featured now. But I won't force you to post only physics problems then there will be much competition for science. If you have good problems in maths you can post them (as 3 of my maths problems are also featured although I say that I am basically a physics man).

- 3 weeks, 2 days ago

How do you send questions to them to select for weekly problem??Do they themselves select from your sets?

- 2 weeks, 3 days ago

No. Only staff will select the problems of the week. In general, the notification will be as if I have written the problem of the week.

- 2 weeks, 3 days ago

They themselves select it by seeing your sets or you send them via some forum and then they choose one of the all sent questions??

- 2 weeks, 3 days ago

The community members write problems and post them to community and the staff selects the best 15 questions among all the problems and they will feature them as problems of the week. There is no forum involved in this process.

- 2 weeks, 2 days ago

Where is the show full site option??(from ur mt. Everest Q discussion)

- 2 weeks, 4 days ago

Here is the screenshot of where is it present. Can you find it now ?

- 2 weeks, 3 days ago

Is this screenshot from app?

- 2 weeks, 3 days ago

No. It is from from the main website.

- 2 weeks, 3 days ago

It will be in the main option bar. It is the place where you can find links like "profile", "stats", "search", etc. The "view" full site option will be present there.

- 2 weeks, 3 days ago

Main option bar : Those 3 lines on left corner?? Or in the stats section of taskbar?

- 2 weeks, 3 days ago

Oh so this is on website. Can this be done in app?

- 2 weeks, 3 days ago

Ohh !! You are doing in the app. Sorry, I don't know whether this is possible in app or not. But can't you find any option like this. in the screenshot.

- 2 weeks, 3 days ago

No :-( how can I send screenshot on this chat?

- 2 weeks, 3 days ago

You have to copy the link of the picture and paste it here.

- 2 weeks, 3 days ago

K thnx a lot for helping, and sorry for disturbing..

- 2 weeks, 3 days ago

Mauj Rajpal, from which part of India are you from.

- 2 weeks, 3 days ago

Delhi ;-) and u??

- 2 weeks, 3 days ago

- 2 weeks, 3 days ago

Oh nice. From where do you put your problems in sets(source) and how do you have sets of other people in yours??

- 2 weeks, 3 days ago

Can you suggest me some of your book(especially maths)

- 2 weeks, 3 days ago

It's our college material. It is a collection of all good problems from various books.

- 2 weeks, 3 days ago

In every set there will be a option at the bottom called "save". If you click that, that particular set will be saved into your sets. Some of my problems are original whereas some other are completely taken from books or the problems and the remaining are the problems which I have taken from books and modified them.

- 2 weeks, 3 days ago

It's OK. No problem. I went to brilliant only once in the mobile app so I am not much aware of the options present in it.

- 2 weeks, 3 days ago

The three line aside the option "Premium"

- 2 weeks, 3 days ago

Thanks guys. Keep sending problems and lets discuss!

- 4 weeks, 1 day ago

The multiple choice of a problem brilliant doesn't order them any more you chose on which place is the correct answer.

- 4 days, 8 hours ago

We know that

- 4 days, 8 hours ago

Hello to everyone! I have not been around for some time now on Brilliant. However, I met on my return a delightful change in the method of posting options for multiple choice questions on Brilliant. Kudos to Calvin Lin and the truly brilliant Brilliant team!

- 5 days, 7 hours ago

@Calvin Lin Sir, I am very much happy. But I hope multiple correct answer format will also be soon available for the community.

- 5 days ago

Actually, I sort of did that. So, I made a correct answer then removed it (crossing it with the x) and then the two dummy answers above it, became the correct answers.

- 4 days, 13 hours ago

But after that it says only 1 correct answer must give.

- 4 days, 13 hours ago

OH!

- 4 days, 12 hours ago

See my set: $$\LaTeX$$ Help

- 4 days, 12 hours ago

Good one.

- 4 days, 11 hours ago

I think and hope this change is a step up to the multiple correct answer releasing.

- 4 days, 15 hours ago

Which questions would you handpick for people? (ie. Your favourite questions)

- 5 days, 6 hours ago

DO or DIE

You are lost in a forest on a cold midnight day. The temperature is quite low and it is bitter cold. Now you have only two chances :

• You should lie on the ground and should shrink your body like a tight pack.

• Go and stay in the water in a pond nearby.

There not much time left. Take your decision before cold kills you. So, what wold you choose ?

- 2 weeks, 6 days ago

First option.

- 2 weeks, 6 days ago

But the second one is the correct choice you have to make.

- 2 weeks, 4 days ago

Why? Because of anomaly in expansion and contraction of water.?

- 2 weeks, 3 days ago

And also due to the high specific heat capacity of water. This question is a slight modification of air currents (due to which it is cool during the day and warm during night near coastal areas) and I am going to post this very soon.

- 2 weeks, 3 days ago

I thought as much.

- 2 weeks, 3 days ago

Finally I reached it. I have reached 1 lakh (100 k) solvers in 91 problems.

- 3 weeks ago

Do you know the minimum people to reach?

- 2 weeks, 1 day ago

I didn't get your point !!! Are you asking about minimum people required to get contribution page.

- 2 weeks, 1 day ago

Yes he is.

- 2 weeks, 1 day ago

@X X @X X, I want your help. I am trying to write a new problem but I got struck up at one point. Here is my doubt :

Suppose lets say a man jumps from a building with initial velocity $$u$$. After $$x$$ seconds another man freely falls from the same building and from the same height. Now, we can say that the displacement of both the man's are equal as they both reach the ground simultaneously after they jump from same point, so we can equate their distances. Here is what I did : $ut + \dfrac12 gt^2 = \dfrac12 g(t - x)^2$ where $$t$$ is the time taken by the first person to reach the ground. The main part of my doubt is that whether we should write the time taken by second person as $$(t - x)$$ or $$(t + x)$$.

- 2 weeks, 1 day ago

It should be t+x as he is free falling and the previous one jumped with velocity u

- 2 weeks ago

I'm not good at physics, though. I think the time taken by the second person should be as same as the first one, maybe?

- 2 weeks, 1 day ago

@X X What I think is that as the second person jumps after $$x$$ seconds his time period will be $$(t - x)$$ seconds. Let's ask it to staff.

- 2 weeks, 1 day ago

So, are you caculating " when the first man fell to the ground, what is the distance between the two man"?

- 2 weeks, 1 day ago

@X X No. Both man reach the ground simultaneously so can we write the equation as in my before comment in which we equate displacements.

- 2 weeks, 1 day ago

Yes, I too think the time taken by the second person is $$t-x$$

- 2 weeks, 1 day ago

Oh! Sorry, I misread the problem.

- 2 weeks, 1 day ago

@X X I think you must minimum have 5K people reached. But the main parameter I think is that the contribution page is mostly obtained either by up votes or by solvers to the question (more than 1K). When I got my contribution page I have around 120 upvotes, around 300 solvers, around 30 views for my notes.

- 2 weeks, 1 day ago

OK. Thanks!

- 2 weeks ago

Congratulations!

- 3 weeks ago

Did you know that :

$1 + \omega = \omega \ but \ \omega + 1 \neq \omega$

Freakin' cool right?

P.S. $$\displaystyle \omega \ is \ the \ second \ lowest \ level \ of \ \infty \ after \ \aleph_0$$

- 3 weeks, 2 days ago

DO YOU SERIOUSLY HAVE TO GIVE ME 46 NOTIFICATIONS OVERNIGHT!

- 3 weeks, 2 days ago

Is that bad, Mohmmad? I am usually on Brilliant throughout the night.

- 3 weeks, 2 days ago

Don't call me Mohmmad

- 3 weeks, 2 days ago

Sorry, but why?

- 3 weeks, 2 days ago

See, My brother's name is Farhan but I am Farhat. And Mohmmad is his surname and Mohammad is my surname. (Stupid Passport errors)

- 3 weeks, 2 days ago

- 3 weeks, 2 days ago

YES! FINALLY!

- 3 weeks, 2 days ago

You can change your name in the account settings

- 3 weeks, 2 days ago

@X X I don't bother

- 3 weeks, 2 days ago

I HAVE EXAMS

- 3 weeks, 2 days ago

I see. But you can use Brilliant to prepare.

- 3 weeks, 2 days ago

English EXAMS

- 3 weeks, 2 days ago

Farhat, from which part of India are were from ?

- 3 weeks, 2 days ago

Andhra Pradesh, From Khammam

- 3 weeks, 2 days ago

I am also from Andhra Pradesh. From Visakhapatnam.

- 3 weeks, 2 days ago

I am Telugu. You are Telugu right because you are from Andhra Pradesh right?

- 3 weeks, 2 days ago

Yes. I am born in Visakhapatnam.

- 3 weeks, 2 days ago

Problem 9: How many $$6$$ digit numbers can be formed using only odd digits?

- 3 weeks, 2 days ago

Is it 5^6?

- 3 weeks, 2 days ago

Correct. Nice stuff. What did you do?

- 3 weeks, 2 days ago

There are 1,3,5,7,9 five odd digits. There are six digits, each digit has 5 possibilities, so there are 5^6 possibilities

- 3 weeks, 2 days ago

@X X Bro, u are amazing

- 3 weeks, 2 days ago

Problem 8: A unit square is completely covered by $$3$$ identical circles. Find the smallest possible diameter of the circles.

- 3 weeks, 2 days ago

Problem 7: Simplify $$S = (cot 10^\circ - 3\sqrt{3})(cosec 20^\circ + 2cot 20^\circ)$$

- 3 weeks, 2 days ago

For trigonometric functions, logarithms, limts, etc you must keep a slash before them. Like \cot will be as $$\cot$$ and \log will be as $$\log$$.

- 2 weeks, 6 days ago

Why are you keeping square brackets. For square root you just need to keep flower brackets.

- 3 weeks, 2 days ago

Problem 6: Find all primes which are the sum of two primes and difference of two primes.

- 3 weeks, 2 days ago

5=7-2=3+2,this is the only possibility.

- 3 weeks, 2 days ago

Exactly. Just what I did during the exam, using the logic that if a prime satisfies those conditions, then the only even prime, 2 must be in the sum and difference.

- 3 weeks, 2 days ago

Brilliant DATE OF BIRTH?

- 3 weeks, 3 days ago

B D : Brilliant Date :p

- 3 weeks, 3 days ago

2004?

- 3 weeks, 2 days ago

@B D I think it will be 10 years

- 3 weeks, 2 days ago

X X said it

- 3 weeks, 3 days ago

I have a proof for the existence of infinite dimensions.

On a line (1 Dimension), a number can be represented by a point. On a grid (2 Dimensions), an intersection is represented for the data in a cell. In a cube (3 Dimensions), data can still be represented on a point (where straight lines intersect). Following this pattern, there are infinite dimensions (because there are $$\aleph_0$$ numbers).

- 3 weeks, 3 days ago

You can play a game in brilliant called Word problem Here

- 3 weeks, 3 days ago

# BrilliantForLife

Dare you to toggle $$\LaTeX$$

- 3 weeks, 3 days ago

What courses would you recommend for a 4th grader like me?

- 3 weeks, 3 days ago

You are 4 the grade ????!!!!!

- 3 weeks, 2 days ago

My first trophy was in Grade 1(third)[english], Second in grade 2 (1st)[first scrabble competition] and third in grade 2(Best school player award)[first scrabble competiton]

- 4 days, 11 hours ago

I am going to be 5th grade

- 4 days, 13 hours ago

Oh !!! Good. All the best

- 4 days, 13 hours ago

Actually I am 1 year away from board exam (in 2020)

- 4 days, 11 hours ago

10 years old. I told you

- 3 weeks, 2 days ago

But, I didn't think you are 4 th grade.

- 3 weeks, 2 days ago

I am! REALLY

- 3 weeks, 2 days ago

@X X, @Michael Mendrin, @Chew-Seong Cheong, @Mohmmad Farhan,and the rest of all, Can you please participate in this message-board (as requested by Ekene Franklin)

- 3 weeks, 3 days ago

@Calvin Lin

- 3 weeks, 3 days ago

- 3 weeks, 3 days ago

I think you there is some error in spelling or you have kept a gap between the symbol and name. Once check again. If it is correct then you should get it in blue color link and not just normal text.

For example you should type it as @ _ Ekene Franklin ( _ symbol means no gap) then you will get it as @EKENE FRANKLIN

- 3 weeks, 3 days ago

It is not still working. Do I need to add something like a code or anything, or should I just type it?

- 3 weeks, 3 days ago

You should select from the list which will appear when you type the name. Also the name should be exactly matching with that particular user even capital letters should be taken into consideration.

- 3 weeks, 3 days ago

Which list?

- 3 weeks, 3 days ago

Ok. If you want I will do it on behalf of you.

- 3 weeks, 3 days ago

Of course I want! Thanks!

- 3 weeks, 3 days ago

Tell the names of whom do you want to be called to this note.

- 3 weeks, 3 days ago

@Calvin Lin, @Harsh Shrivastava, @Chew Seong Cheong, @Michael Mendrin, @X X, @Aniket Sanghi.

- 3 weeks, 3 days ago

Hi guys !!! I want to tell you some secret. I think next week would be a week of physics. Because this week I have found six problems which have equal chances in coming to problems of the week. There are Rohit Gupta's Trick Spring Balance and Spring Balance, Pranshu Gaba's Three blocks Sliding and Relative Stuntmen Motion, Danielle Scarano's Thermographic Dog and my Mt. Everest vs Mt. Godwin Austin. I think these question will be featured definitely this week if not possible then next week.

- 3 weeks, 4 days ago

I made the cut for the 2nd round! I scored $$76.70$$ out of a maximum possible 110. Hurray!

- 3 weeks, 4 days ago

Oh !!! Congrats.

- 3 weeks, 4 days ago

Thanks a lot. But no one apart from us is solving the problems. I want to check my solutions and my faulty areas. Please direct the problem solving masters of Brilliant here to help me out.

- 3 weeks, 4 days ago

If you want to direct anyone to this place just keep the symbol @ and type the name of the person. Immediately a notification will be sent to that particular user.

- 3 weeks, 4 days ago

Problem 5: Find the general term of the sequence described by $$a_n = 4a_{n - 1} - 3a_{n - 2}$$ given that $$a_1 = 1$$ and $$a_2 = 9$$.

- 3 weeks, 4 days ago

$$a_n=4\times3^{n-1}-3$$

- 3 weeks, 2 days ago

Great. This was what I got. But do you mind showing your solution so I can clarify mine?

- 3 weeks, 2 days ago

Solve the equation $$x^2=4x-3$$ and get $$x=3$$ or $$1$$. Let $$b_n=3^n-1^n$$.

The first few terms of $$b_n$$ is $$2,8,26,80...$$ and $$b_n$$ also satisfies the recursion $$b_n=4b_{n-1}-3b_{n-2}$$

Compare the two sequences: $$a_n=\frac43b_n-\frac53=4\times3^{n-1}-3$$

- 3 weeks, 2 days ago

@X X Not exactly what I did, but something similar. Thanks a lot. If I may ask, have you ever participated in an olympiad before, or do you hope to participate in one?

- 3 weeks, 2 days ago

No, I haven't. I knew few things about it, so I'm not sure about participating in one.

- 3 weeks, 2 days ago

@X X Ok. Thanks. By the way, I really admire your problems. They are very cool. One of my major problems here is creating problems. My original problems are too easy(you can check them out). But solving others problems(of course not those extremely hard ones) is not a big problem for me.

- 3 weeks, 2 days ago

@X X I think this is your first problem of the week in easy catogery.

- 3 weeks, 2 days ago

You're right! (Ha, ha! I'm a little jealous of you because your problems are often the first problem in the easy category, and in your contributions page, the number of people are banging up:p)

- 3 weeks, 2 days ago

@X X Don't worry mister !!! You have the skill to post and solve tough questions (level 4 and 5).

- 3 weeks, 2 days ago

@X X But some of your problems came in Intermediate and Advanced catogery.

- 3 weeks, 2 days ago

I know. (Fewer people solves those, that is why I was so happy to see my problem as the second of the basic category)

- 3 weeks, 2 days ago

@X X OH !!! Your problem is featured as the second one in the problems of the week. But my first problem (Thundering Question) is the third one.

- 3 weeks, 2 days ago

How is my new problem, check it here. It is posed by B.D

- 3 weeks, 1 day ago

Cool video!

- 3 weeks, 1 day ago

@X X Yes. I liked that so much that I framed the question based on that.

- 3 weeks, 1 day ago

Oh, I remember that one! (I loved that week because a lot of my solutions appeared in that week. )

- 3 weeks, 2 days ago

@X X It's a Fact :

I have made a hatrick in June 9 - June 29 (3 weeks) as 3 of my problem continuously came in easy part of the POTW. Now again the chance has come for me. Last week and this week too two of my problems are featured. So, if luck favors next week to I can have a problem in POTW. I am thinking very hard on which question should I post the next.

- 3 weeks, 2 days ago

The sequel to the Mt Everest problem about pressure cookers?

- 3 weeks, 2 days ago

Should see about it.

- 3 weeks, 2 days ago

Is it released yet?

- 3 weeks, 2 days ago

No. Still under construction. Before that one I have two more questions, Raising Balloons - 2 and Popping balloons which are yet to be released. After these two the sequel for My. Everest vs Mt K 2 will be released.

- 3 weeks, 2 days ago

OH!

- 3 weeks, 2 days ago

@X X Ram Mohith and X X, both of you are excellent problem contributors, some of the best here. I hope I can reach your level!

- 3 weeks, 2 days ago

@X X Yes, Vamprie Fan Club. It is were I had my first individual century. After that, the next week I had got 150 upvotes for my question Rising Balloons and the next week is a memorable for me, as I had my first double century for the question Counting 0's.

- 3 weeks, 2 days ago

@X X But I am not fully done. I expected that Number + Reciprocal will take me to 1 lakh (100 K) solvers. But it fell short of 7 K. But luckily this week too my question came in one of the problems of week (the first one) so it is confirmed that I will reach the milestone in one or two days.

- 3 weeks, 2 days ago

What is the remainder when $$1^{241} + 2^{241} + 3^{241} + 4^{241}$$ is divided by $$5$$?

- 3 weeks, 5 days ago

$$0$$

- 3 weeks, 3 days ago

Of course that is the answer, but prove it.

- 3 weeks, 3 days ago

Since the divisibility rule of 5 only concerns the last digit, we have to find the last digits of the values. $$1^{124}$$ is obviously 1. Since the repetition in the last digit is (for 2): 2, 4, 8, 6 then $$241 \div 4 = k (\text{Remainder}1$$) the first number is 2 (in this set). Apply this to the other powers. Summing the last digits, we get 10 and $$10 \div 5 = k (\text{Remainder}0)$$

- 3 weeks, 3 days ago

Excellent

- 3 weeks, 3 days ago

Great job. I did modular arithmetic during the examination.

- 3 weeks, 3 days ago

Me too

- 3 weeks, 2 days ago

Problem 3: $$20$$ lines are drawn in a plane. What is the maximum number of parts into which the plane can be divided by the $$20$$ straight lines?

- 3 weeks, 5 days ago

There is a trick. First, take the 20th triangular number. $$\displaystyle\frac{20(20+1)}{2} = 210$$ Add 1. $$210+1=211$$ These numbers are known as pizza numbers and are always one more than a triangular number.

P.S. @EKENE FRANKLIN did you use this method?

- 3 weeks, 3 days ago

Great! Just what I wanted, and what I used during the examination!

- 3 weeks, 2 days ago

Thumbs Up!

- 3 weeks, 2 days ago

I think it is $$211$$

- 3 weeks, 3 days ago

Problem 2: What is the maximum possible area of a quadrilateral of sides $$1, 4, 7, 8$$?

- 3 weeks, 5 days ago

Looks similar to:

https://brilliant.org/problems/hexagon-octagon-in-a-rectangle/?ref_id=1538063

Maybe a harder version perhaps! :D

- 1 week, 6 days ago

I think we should use the concept of maxima and minima.

- 3 weeks, 5 days ago

Perhaps you should solve it. I used the maximality condition of Bretschneider's formula. My answer was $$18$$.

- 3 weeks, 5 days ago

What is that?

- 1 week, 6 days ago

Yes I too got like that.

- 3 weeks, 5 days ago

Problem 1: A password consists of $$4$$ distinct digits such that their sum is $$19$$ and exactly two of its digits are prime, e.g. $$0397$$. How many possible such passwords exist?

- 3 weeks, 5 days ago

2,3: (2,3,6,8)

2,5: (2,5,4,8)

2,7: (2,7,4,6),(2,7,1,9)

3,5: x

3,7: (3,7,1,8),(3,7,0,9)

5,7: (5,7,1,6)

There are $$7\times4!=168$$ possibilities

- 3 weeks, 2 days ago

How did you get all possibilities?

- 3 weeks, 2 days ago

Find the 7 possibilities one by one, then times 24

- 3 weeks, 2 days ago

Gearing up for today's 1st round olympiads!

- 3 weeks, 5 days ago

Good luck!

- 3 weeks, 5 days ago

Thanks. The results will be uploaded online in about 1.5 hours. Meanwhile I am posting them here for our consumption. Solve some, post solutions and invite others to do same!

- 3 weeks, 4 days ago

Maybe you can post them like problems.

- 3 weeks, 4 days ago

@B D Ok.

- 3 weeks, 4 days ago

How do I post numerical answer problems on Brilliant?

- 3 weeks, 6 days ago

I think you have posted many problems in brilliant. However, when you are writng a question there will be two options, either Number or Multiple choice. You can select whatever you wish.

- 3 weeks, 6 days ago

@Mohmmad Farhan why can't you come here. I think this is a best place for a student like you. You can post your quires here.

- 3 weeks, 6 days ago

Sorry! I am not really active these days because of exams

- 3 weeks, 3 days ago

Ok. No problem !!!

- 3 weeks, 3 days ago

Does anyone know how to post a solution of a problem that doesn't have a posted solution yet?

- 4 weeks ago

If you got it correct you click the button "No solution" under Continue and write. And if you got it wrong you can't.

- 4 weeks ago

Thanks a lot, bro!

- 4 weeks ago

You are welcome!

- 4 weeks ago

Explain the Bohr theory of atoms, combining both mathematics and physics in your explanations.

- 4 weeks, 1 day ago

Hi guys! For sure we all have noticed that the derivative of kinetic energy is momentum. Is there a physical explanation for this?

- 4 weeks, 1 day ago

Quantitatively speaking, momentum is the product of mass of a body and its velocity. It is denoted by $$\overline{P}$$. $\large \overline{P} = m \overline{v}$ But the above definition is valid only when velocity of the body is constant. If the velocity of the body is variable we cannot use this formula and we should go by calculus. Physically speaking, momentum is the rate of change of kinetic energy with respect to its velocity. So, you ca say it as kinetic energy at that instance. Here is how we get $$\overline{P} = m \overline{v}$$ from kinetic energy. $K.E = \dfrac12 m (\overline{v})^2$ Now, differentiate both side with respect to velocity. We get : $\dfrac{d}{dx} K.E = \dfrac{d}{dx} \left ( \dfrac12 m (\overline{v})^2 \right )$ As, we know $$\dfrac{d}{dx} K.E = \overline{P}$$, we get : $\overline{P} = \dfrac12 \cdot m \cdot 2 \overline{v}$ So, we get : $\large \boxed{\color{blue} \overline{P} = m \overline{v}}$

- 4 weeks, 1 day ago

Perfect bro!

- 4 weeks, 1 day ago

Thanks. But what I should say you, brother or sister

- 4 weeks ago

I am a young boy:)

- 4 weeks ago

Ok

- 4 weeks ago

$$I\ accidentally\ dropped\ the\ milk\ box\ (from\ paper)\ and\ it\ fell\ on\ cap\ even\ when\ I\ dropped\ with\ the\ bottom\ to\ the\ ground.$$

- 1 month ago

Wow, that's funny. What did you mean?:)

- 4 weeks, 1 day ago

Because I dropped it with the bottom to the ground I was wondering why it fell on cap.

- 4 weeks ago

@B D Are you inviting physics?

- 4 weeks ago

Yes it is physics.

- 4 weeks ago

@B D Can you give a shot at explaining it?

- 4 weeks ago

No. That's why I ask here.

- 4 weeks ago

@B D The air in the box initiates a couple, whose direction depends on the side that has greater aerial density. Thus the block may either fall with its top or its bottom.:)

- 4 weeks ago

$$\text{Doubt : 4}$$

In $$(Si_4O_{12})^{8-}$$, how many $$Si - O - Si$$ linkages are there ?

- 1 month ago

What is the answer bro?:)

- 4 weeks ago

It is 4.

- 4 weeks ago

I was actually sure of 4 linkages, but I was not sure of one more. Thanks anyways.

- 4 weeks ago

It's OK.

- 4 weeks ago

You are a great guy, Ram.

- 4 weeks ago

That's my quality quantitatively speaking.

- 4 weeks ago

My goal in many interactions is to make them frictionless. Trivially speaking, I resist every enmity and conduct friendliness. I have even successfully transmuted people from an angry ground state, to a happy excited state!

- 3 weeks, 6 days ago

Oh !!! That's good.

- 3 weeks, 6 days ago

Thanks. Ask if you want more!

- 3 weeks, 6 days ago

I have an answer, but I am not totally sure it is correct. Coordination structure chemistry of silicates and silicones is my weakest point in chemistry. Perhaps I need to practise more!:)

- 1 month ago

$$\text{Doubt : 3}$$

Uncertainty in position and momentum are equal. Then what will be the Uncertainty in velocity ?

- 1 month ago

I don't think uncertainty in position and momentum are relativistically equal. However, if a non-relativistic assumption is to be made, then from Heisenberg's, and taking p=mv, then uncertainty in velocity>=(h/2pi)X(1/(uncertainty in position X mass)). Sorry for the math ambiguity. My device doesn't type LaTeX.

- 1 month ago

Yes you are correct. You got the correct answer. Regarding the latex you can keep it in \ (...\ ).

- 1 month ago

The LaTeX is not still working. It prevents me from posting some reeeeeeallly cool problems.;(

- 4 weeks ago

$$\text{Doubt : 2}$$

In the following reaction : $\large aNO_3^- + bCl^- + cH^+ \rightarrow dNO + eCl_2 + fH_2O$ find the value of $$\dfrac{a^2(b + c)}{d \times f}$$

- 1 month ago

Did you tried it. What is the answer you got.

- 1 month ago

Yeah, I solved it. My answer is 7.

- 4 weeks, 1 day ago

That's correct answer. Can you atleast keep the values of a,b,cd,e,f.

- 4 weeks, 1 day ago

a=2, b=6, c=8, d=2, e=3 and f=4

- 4 weeks, 1 day ago

Ok. Thanks i will check with mine.

- 4 weeks, 1 day ago

Simply balance the redox equation and substitute the stoichiometric coefficients of the balanced reaction into your expression.( I would have posted a solution if only my device could type LaTeX.)

- 1 month ago

Ok. Try now after keeping it in \ (....) without spaces which will give you $$...$$

- 1 month ago

$$\text{Doubt : 1}$$

If the mole fraction of a solute is changed from $$\dfrac14$$ to $$\dfrac12$$ by adding some solute in the $$800~g$$ of $$H_2O$$ solvent, then what will be the ratio of molarity of the two solutions ?

- 1 month ago

I really like this note that is why I saved it!

- 1 week, 6 days ago

Pls see my problem 'The Strange Angle' and also how to use latex

- 2 weeks ago

Here is a note how to use $$LaTeX$$.

- 2 weeks ago

Anyone knows some app for drawing geometry figures??

- 2 weeks ago

I want your help. I am trying to write a new problem but I got struck up at one point. Here is my doubt :

Suppose lets say a man jumps from a building with initial velocity $$u$$. After $$x$$ seconds another man freely falls from the same building and from the same height. Now, we can say that the displacement of both the man's are equal as they both reach the ground simultaneously after they jump from same point, so we can equate their distances. Here is what I did : $ut + \dfrac12 gt^2 = \dfrac12 g(t - x)^2$ where $$t$$ is the time taken by the first person to reach the ground. The main part of my doubt is that whether we should write the time taken by second person as $$(t - x)$$ or $$(t + x)$$.

What do you think @Blake Farrow , @Calvin Lin , @Danielle Scarano , @Brilliant Physics , @Pranshu Gaba, @Rohit Gupta and others ??

- 2 weeks, 1 day ago

It should be 't+a' as 1st man had jumped with velocity u so he will reach earlier than the freely falling man and it isn't necessary that the extra time 2nd man takes is equal to 'x'

- 2 weeks ago

Doesn't really matter, as long as you're clear on what the definition of "positive x" is. IE If you used $$t+x$$ and then solved for $$x$$ and got that it is negative, what is the interpretation?

In a similar manner, if we say that gravity acts downwards in the positive direction, then the "height at which the ball is thrown upwards" will (likely) be negative. Or vice versa.

Staff - 2 weeks ago

Yes. You are correct. I understood it now. Thanks for clarifying.

- 2 weeks ago

Hi guys !!! How is my note Square Root Of a Complex Number. It is a quite interesting and good technique to find square root of a complex number.

- 2 weeks, 1 day ago

Pls see my problem 'the blue one' and tell how I can make it look better.

- 2 weeks, 2 days ago

At the end of the question where you have kept Bonus there is a latex mistake I think. If you want it to be in bold letters you should keep in in between two * such that there is no space between * and the next letter or the previous one.

- 2 weeks, 2 days ago

How can I draw a figure for my question (on website in phone)?

- 2 weeks, 2 days ago

But if you want you can draw the figures in Microsoft, Paint or any other drawing apps and keep that picture.

- 2 weeks, 2 days ago

kk

- 2 weeks, 2 days ago

Any mobile app you know??

- 2 weeks, 1 day ago

We cannot draw a figure. We can only keep pictures or gif's.

- 2 weeks, 2 days ago

Do you know that brilliant staff has been removed the leader board from all the sets?

- 2 weeks, 4 days ago

Really.

- 2 weeks, 4 days ago

Comment deleted 3 weeks ago

The slashes your are using are wrong. It should be in the reverse direction like this \ (Exam) with no spaces between slash and bracket. You will get it as $$Exam$$.

- 3 weeks, 5 days ago

Thanks a lot bro! You're awesome!

- 3 weeks, 5 days ago

$$Ok$$

- 3 weeks, 5 days ago