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Deadly_king:

--- Quote from: ashish on October 08, 2010, 05:43:56 am ---+ rep  yeah thanks  my doubt is clear !

hey do you have  Imran Amiran A/AS level pure mathematics book?

--- End quote ---

You're welcome :)

Hmm.....nopes. Never used that book though I heard a lot about its author who seems to be an extremely strict teacher :P

ashish:
 
here is another question

there are 2 cylinders A and B , A has base area of 60cm² and cylinder B has a base area of 40cm²
both of them are on the same level, and are connected by a tube at their bases. initially the water in A has a height of 120 cm while B has a height of 20cm. the rate of flow of water is proportional to the root of the height difference, h between the two cylinders.... show that dh/dt= -(k(h)^0.5)/24.....

can anyone show me how can i get this
i know that we should start by
dv/dt is proportional to (h)^0.5

ashish:
hey deadly king i managed to work it  ;D

let say that  cylinder A lost a volume V

new volume of water would be 7200(initial volume)- V
new height would be 120-(V/60)

on the other hand cylinder B has gained a volume V
new volume would be 800(initial volume)+ V
the new height would be 20+(V/40)

height difference h would be (20+(V/40))-(120-(V/60))
h=(V/24)-100

by making V subject of formula we obtain
V=24h+2400

now
as i said
dV/dt is proportional to root of h

since V= 24h+2400
d(24h+2400)/dt = -k(h)^0.5

since differential of a number is zero
24dh/dt=-k(h)^0.5

dh/dt=(-k/24)(h)^0.5

phew it was quite lengthy....

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