Could someone give some guidance on how to solve c and d?
As you mention only about the 3rd and 4th one, i'll go briefly for the first and 2nd one.
We can write , where is the proportionality constant. And .
So we get the differential equation as
.
After solving this we get as,
, where r is the radius of the cylinder and C is the unknown arbitrary number, yet to find out.
Now we have to unknown in the equation k and C, to find these we need to two equation. This conditions are given the 3rd problem. Initially the filter was full i.e ate t=0, h=12 cm and when t=2.2 min, h=0 as filtration process was over.
Now inputting the 1st condition in the previous equation we get
,
and putting the 2nd condition we get,
, rearranging this equation and putting the value of we get cm/min.
So cm/min.
Getting k a -ve number was quite normal because becomes a -ve number which means as time increase volume will decrease.
For thew fourth part, as rate of volume is constant the filter tube will maintain a height of .
Could someone give some guidance on how to solve c and d? 1. During the last...
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