anonymous
  • anonymous
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).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I don't have a clue what this question wants exactly
dan815
  • dan815
okay
dan815
  • dan815
interesting okay, so no matter the weird speed he takes the point is he finished both journies in 12 hours

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More answers

anonymous
  • anonymous
Right lol
dan815
  • dan815
we have to show there is always one point such that the elevation is the same at the same time
dan815
  • dan815
ok hang on brb
anonymous
  • anonymous
Yeah np
Astrophysics
  • Astrophysics
IVT
ganeshie8
  • ganeshie8
Just show that E(0) and E(12) have opposite signs and use IVT
anonymous
  • anonymous
Intermediate Value theorem?
Astrophysics
  • Astrophysics
Yup
anonymous
  • anonymous
How do you know you have to use that tho?
dan815
  • dan815
ok back
dan815
  • dan815
now consider 2 functions h(t)
ganeshie8
  • ganeshie8
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..
dan815
  • dan815
|dw:1435215072294:dw|
dan815
  • dan815
you see no matter what his function of height is over time
dan815
  • dan815
there must be an intersection between h1(t) and h2(t)
dan815
  • dan815
|dw:1435215133891:dw|
ganeshie8
  • ganeshie8
1 picture > 1000 words
anonymous
  • anonymous
Right...
anonymous
  • anonymous
LOL @ganeshie8
dan815
  • dan815
|dw:1435215224870:dw|
dan815
  • dan815
ya its hard to say in words lol but
dan815
  • dan815
you can see, intuitively like no matter what function u can possibly think of, this intersection must exist somewhere
dan815
  • dan815
and an intersection means the time and height was the same
anonymous
  • anonymous
Correct
anonymous
  • anonymous
And to prove that we gotta use the IVT?
ganeshie8
  • ganeshie8
yeah IVT is for mathematical proof that picture is for convincing yourself why IVT works the way it does
anonymous
  • anonymous
E(t) has to change signs from + to - ?
dan815
  • dan815
right, that would mean there is an intersection neat trick
dan815
  • dan815
we know that h2(0) - h1(0) = Max height and h2(12)-h1(12) = Negative of Max height
anonymous
  • anonymous
hmm... how do you know that again?
dan815
  • dan815
that is what is given to us
anonymous
  • anonymous
Ohhh i just realized!! Sorry my bad! >.<
dan815
  • dan815
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
anonymous
  • anonymous
Mhmm I get it now
ganeshie8
  • ganeshie8
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.
dan815
  • dan815
haha i like that
anonymous
  • anonymous
Ahah right that makes sense lol xD nice visualization XD
ganeshie8
  • ganeshie8
ikr! everybody likes to duplicate themselves, especially before exams so that more work can be done in less time ;p
ganeshie8
  • ganeshie8
*likes the idea of
Astrophysics
  • Astrophysics
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
anonymous
  • anonymous
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!!
Astrophysics
  • Astrophysics
Good problem though, not too difficult either just needs you to understand IVT really :P
anonymous
  • anonymous
That was a perfect explanation @Astrophysics!!! And beautiful drawings too ;P
Astrophysics
  • Astrophysics
I think what ganeshie said would work if the monk was an electron, and haha your welcome :)
anonymous
  • anonymous
Thanks so much @dan815 @ganeshie8 @Astrophysics XD
anonymous
  • anonymous
Hahaha electrons dont duplicate... could be DNA though :P lol
Astrophysics
  • Astrophysics
True...but they can be in two places at once! See..at the quantum level nothing makes sense!
anonymous
  • anonymous
Hahaha thats a good point :DDD
anonymous
  • anonymous
Thanks again for all the help! :D
Astrophysics
  • Astrophysics
Np, have fun studying xD
anonymous
  • anonymous
Lol thanks... fun tho? XD

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