The Student Room Group

Girls vs boys maths challenge

Ok, so here's how I think it should work. Someone asks a maths question ( that they know the answer to) and the first person to answer it correctly scores a point for their genders team.

So who's gonna win?

First question : Work out the mean of these three numbers : √75, √75 and 6 divided by √3.

Come on girls!

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Original post by Bluebubbles123
Ok, so here's how I think it should work. Someone asks a maths question ( that they know the answer to) and the first person to answer it correctly scores a point for their genders team.

So who's gonna win?

First question : Work out the mean of these three numbers : √75, √75 and 6 divided by √3.

Come on girls!


434 \sqrt 3

Can I answer any more or am I frozen out of the game?
Reply 2
What level of maths are we talking? A2? AS? GCSE? this looks like AS-level to me but I wan't to know what is viable to post. Can there also be proof questions?. Longer juicier proof questions would be more entertaining then small surd questions imo, as some would be clueless but others would be racing to find the fastest method
(edited 10 years ago)
Original post by Mr M


am I frozen out of the game?


Seems unfair. Perhaps a 10 post cooldown period to allow brian cells to recover (and others to have a chance!).
(edited 10 years ago)
Original post by Robbie242
...


OP flagged it as "secondary school".

Is it fair for anyone beyond that level to post? Oops!
Reply 5
Original post by ghostwalker
OP flagged it as "secondary school".

Is it fair for anyone beyond that level to post? Oops!


I was wondering because I wanted to do some quotient rule and trig identities and maybe complex numbers but this would probably cause a meltdown from secondary school students :redface:.

''Ok, so here's how I think it should work. Someone asks a maths question ( that they know the answer to) and the first person to answer it correctly scores a point for their genders team.'' this suggests you can post literally anything but the threads flag suggests otherwise
(edited 10 years ago)
I think the winner of the previous round should set the next question. This is secondary school level but reasonably difficult. You won't find it anywhere on the internet as I made it up so there is no point Googling. I do have a worked solution.

Question 2

A scalene right-angled triangle with perimeter x cm and area x cm^2 contains a pair of congruent semicircles of radius y cm that do not overlap.

Given that xy2\displaystyle \frac{x}{y^2} is a minimum, find the exact value of y.
Reply 7
Original post by Mr M
I think the winner of the previous round should set the next question. This is secondary school level but reasonably difficult. You won't find it anywhere on the internet as I made it up so there is no point Googling. I do have a worked solution.

Question 2

A scalene right-angled triangle with perimeter x cm and area x cm^2 contains a pair of congruent semicircles of radius y cm that do not overlap.

Given that xy2\displaystyle \frac{x}{y^2} is a minimum, find the exact value of y.


Is it bad that I can't attempt this question at all as an a-level student lol, I just don't know where to even start I've got 1 length but the other 2 are missing, I know the definition of scalene and had to look up congruent but I'm getting nowhere haha, I want a-level questions I feel so stupid with these :tongue:. Also when you mention minimum all I can think off is differentiation now xd. I think I need a quadratic in y and then take the highest value so its minimum but how haha, not a very good question to ask on a competitive thread like this though
(edited 10 years ago)
Reply 8
Oh no, I was wondering how long it'd be until a geometry question was asked :lol:
Original post by Mr M
I think the winner of the previous round should set the next question. This is secondary school level but reasonably difficult. You won't find it anywhere on the internet as I made it up so there is no point Googling. I do have a worked solution.

Question 2

A scalene right-angled triangle with perimeter x cm and area x cm^2 contains a pair of congruent semicircles of radius y cm that do not overlap.

Given that xy2\displaystyle \frac{x}{y^2} is a minimum, find the exact value of y.


Your question seems flawed. What position are the semicircles in? Are they just within the triangle or do they touch the sides?

Posted from TSR Mobile
Reply 10
Original post by Irish-Cailin
Your question seems flawed. What position are the semicircles in? Are they just within the triangle or do they touch the sides?

Posted from TSR Mobile


Given that xy2\dfrac{x}{y^2} is a minimum you know exactly where the centre of the two circles will be.
Original post by Noble.
Given that xy2\dfrac{x}{y^2} is a minimum you know exactly where the centre of the two circles will be.


Wtf is the smiley face?

Posted from TSR Mobile
Original post by Irish-Cailin
Wtf is the smiley face?

Posted from TSR Mobile

It seems you're on the app. The smiley face is something written using tex.
Original post by keromedic
It seems you're on the app. The smiley face is something written using tex.


Ohh right, so what exactly is a minimum?

Posted from TSR Mobile
Original post by Irish-Cailin
Ohh right, so what exactly is a minimum?

Posted from TSR Mobile

On a graph, it's a stationary point.
Original post by keromedic
On a graph, it's a stationary point.


Yeah I get what minimum means but what is a stationary point lol, the centre point of the circle?

I don't want you to explain stationary point, just when you say 'it is' what is the it

Posted from TSR Mobile
(edited 10 years ago)
Original post by Irish-Cailin
Yeah I get what minimum means but what is a stationary point lol, the centre point of the circle?

Posted from TSR Mobile

I don't really understand the problem so I'm probably not the best person to ask.
When I looked at it, I didn't think the minimum referred to a particular point, but perhaps I'm wrong!
Original post by keromedic
I don't really understand the problem so I'm probably not the best person to ask.
When I looked at it, I didn't think the minimum referred to a particular point, but perhaps I'm wrong!


Okay never mind haha, thanks, the smiley face is just really offputting for me :tongue:

Posted from TSR Mobile
Anyone up for some calculus here? :P

Posted from TSR Mobile
Reply 19
Original post by Irish-Cailin
Yeah I get what minimum means but what is a stationary point lol, the centre point of the circle?

I don't want you to explain stationary point, just when you say 'it is' what is the it


Original post by keromedic
I don't really understand the problem so I'm probably not the best person to ask.
When I looked at it, I didn't think the minimum referred to a particular point, but perhaps I'm wrong!


The question is:
Given a right-angled scalene triangle of perimeter = area = x, with two of the same semicircle positioned entirely inside with no overlap, where the semicircle is of radius y, find the value of y such that x/y^2 is minimised. That is, find the radius of the semicircle so as to make x/y^2 as small as possible.
In practice, I hope this means "maximise the radius" - I very much don't want to have to optimise over x and y at the same time…
There's an easy but very weak upper bound on y, by the way:

Spoiler

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