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I don't have a clue what this question wants exactly
interesting okay, so no matter the weird speed he takes the point is he finished both journies in 12 hours
we have to show there is always one point such that the elevation is the same at the same time
ok hang on brb
Just show that E(0) and E(12) have opposite signs and use IVT
Intermediate Value theorem?
How do you know you have to use that tho?
now consider 2 functions h(t)
its bit hard to accept that there exists such a time where the elevations will be equal tho also was wondering what if if the monk knows teleportation..
you see no matter what his function of height is over time
there must be an intersection between h1(t) and h2(t)
1 picture > 1000 words
ya its hard to say in words lol but
you can see, intuitively like no matter what function u can possibly think of, this intersection must exist somewhere
and an intersection means the time and height was the same
And to prove that we gotta use the IVT?
yeah IVT is for mathematical proof that picture is for convincing yourself why IVT works the way it does
E(t) has to change signs from + to - ?
right, that would mean there is an intersection neat trick
we know that h2(0) - h1(0) = Max height and h2(12)-h1(12) = Negative of Max height
hmm... how do you know that again?
that is what is given to us
Ohhh i just realized!! Sorry my bad! >.<
we have 2 functions h1(t) at t=0 , height is 0, t=12 hours height is max h2(t) at t=0, height is max, t=12 hours height is 0
Mhmm I get it now
Another way to visulaize it is... assume that this monk knows magic and duplicated himself - one copy starts frm bottom and the other copy starts from top at the same time; since they both are walking towards each other on the same road, they will meet at some place for sure, no matter what their individual speeds are.
haha i like that
Ahah right that makes sense lol xD nice visualization XD
ikr! everybody likes to duplicate themselves, especially before exams so that more work can be done in less time ;p
*likes the idea of
I think you may also need some help on knowing what exactly IVT is, so suppose f is continuous on [a.b] and let N be in (f(a),f(b)), where f(a) cannot = f(b). Then there exists a number c in (a,b), such that f(c) = N. Looks like bunch of mumbo jumbo so I'll draw a pic won't be as beautiful as dans drawing ;) |dw:1435215756830:dw| also if f(a) is negative and f(b) is positive (vice versa), then the equation f(x) = 0 has at least one root in (a,b). |dw:1435215895403:dw| hope that gives you an idea what is going on and you can relate this with your question now xD
Oh tell me about it!! Hahaha >.< I wish I had an extra week!! Lol might pull an all-nighter tonight :( which is the worst idea ever!!
Good problem though, not too difficult either just needs you to understand IVT really :P
That was a perfect explanation @Astrophysics!!! And beautiful drawings too ;P
I think what ganeshie said would work if the monk was an electron, and haha your welcome :)
Thanks so much @dan815 @ganeshie8 @Astrophysics XD
Hahaha electrons dont duplicate... could be DNA though :P lol
True...but they can be in two places at once! See..at the quantum level nothing makes sense!
Hahaha thats a good point :DDD
Thanks again for all the help! :D
Np, have fun studying xD
Lol thanks... fun tho? XD