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anonymous
 one year ago
A Tibetan monk leaves the monastery at 7:00 am and takes his usual path to the top of the mountain, arriving at 7:00 pm. The following morning, he starts at 7:00 am at the top and takes another path back to the monastery, arriving at 7:00 pm. Show that there is some elevation that he reaches at the exact same time on both days. Hint: Let h1(t) be the monk’s elevation on the first day and h2(t) his elevation on the following day. Consider the function E(t) = h1(t) − h2(t).
anonymous
 one year ago
A Tibetan monk leaves the monastery at 7:00 am and takes his usual path to the top of the mountain, arriving at 7:00 pm. The following morning, he starts at 7:00 am at the top and takes another path back to the monastery, arriving at 7:00 pm. Show that there is some elevation that he reaches at the exact same time on both days. Hint: Let h1(t) be the monk’s elevation on the first day and h2(t) his elevation on the following day. Consider the function E(t) = h1(t) − h2(t).

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't have a clue what this question wants exactly

dan815
 one year ago
Best ResponseYou've already chosen the best response.2interesting okay, so no matter the weird speed he takes the point is he finished both journies in 12 hours

dan815
 one year ago
Best ResponseYou've already chosen the best response.2we have to show there is always one point such that the elevation is the same at the same time

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Just show that E(0) and E(12) have opposite signs and use IVT

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Intermediate Value theorem?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How do you know you have to use that tho?

dan815
 one year ago
Best ResponseYou've already chosen the best response.2now consider 2 functions h(t)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2its 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..

dan815
 one year ago
Best ResponseYou've already chosen the best response.2you see no matter what his function of height is over time

dan815
 one year ago
Best ResponseYou've already chosen the best response.2there must be an intersection between h1(t) and h2(t)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.21 picture > 1000 words

dan815
 one year ago
Best ResponseYou've already chosen the best response.2ya its hard to say in words lol but

dan815
 one year ago
Best ResponseYou've already chosen the best response.2you can see, intuitively like no matter what function u can possibly think of, this intersection must exist somewhere

dan815
 one year ago
Best ResponseYou've already chosen the best response.2and an intersection means the time and height was the same

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And to prove that we gotta use the IVT?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2yeah IVT is for mathematical proof that picture is for convincing yourself why IVT works the way it does

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0E(t) has to change signs from + to  ?

dan815
 one year ago
Best ResponseYou've already chosen the best response.2right, that would mean there is an intersection neat trick

dan815
 one year ago
Best ResponseYou've already chosen the best response.2we know that h2(0)  h1(0) = Max height and h2(12)h1(12) = Negative of Max height

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmm... how do you know that again?

dan815
 one year ago
Best ResponseYou've already chosen the best response.2that is what is given to us

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohhh i just realized!! Sorry my bad! >.<

dan815
 one year ago
Best ResponseYou've already chosen the best response.2we 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

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Another 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ahah right that makes sense lol xD nice visualization XD

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2ikr! everybody likes to duplicate themselves, especially before exams so that more work can be done in less time ;p

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1I 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh tell me about it!! Hahaha >.< I wish I had an extra week!! Lol might pull an allnighter tonight :( which is the worst idea ever!!

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Good problem though, not too difficult either just needs you to understand IVT really :P

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That was a perfect explanation @Astrophysics!!! And beautiful drawings too ;P

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1I think what ganeshie said would work if the monk was an electron, and haha your welcome :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks so much @dan815 @ganeshie8 @Astrophysics XD

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hahaha electrons dont duplicate... could be DNA though :P lol

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1True...but they can be in two places at once! See..at the quantum level nothing makes sense!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hahaha thats a good point :DDD

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks again for all the help! :D

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Np, have fun studying xD

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Lol thanks... fun tho? XD
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