00:01
Hello students, it is given that tank with base square equal to 5 meter and water enter at rate 20 liter per minutes and depth equal to 2 meter.
00:12
Now water at a time is w of t equal to 5 into 5 into 2 meter square plus 20 t minus 3 of t plus 1 divided by 2.
00:24
Now multiply these three terms we get 50 ,000 plus 20 t minus t square plus t minus t divided by 2.
00:33
Therefore, w of t equal to minus t square minus 39 t divided by 2 plus 50 ,000.
00:40
Now consider w of t equal to 0.
00:44
So, now equating this equation equal to 0, we get t square minus 39 t plus 100 equal to 0.
00:52
By using, now use quadratic formula that is x equal to minus b plus or minus root of b square minus 4ac divided by 2a.
01:05
So, here a equal to 1, b equal to minus 39 and c equal to 1 lakh.
01:15
So, substitute these three value into this formula, so we get t equal to 39 plus or minus root of 39 square plus 4 into 1 into 1 lakh divided by 2.
01:27
Now solve this formula, so we get t equal to 336 .33 minutes.
01:35
Now coming to part b, here at t equal to 0, the depth of water equal to 5 meter that is h of 0 equal to 5 meter and it is given that d of v divided by dt equal to 1 plus t divided by 2 into m cube divided by r.
01:53
Now find the volume, so volume v equal to area of base in the height.
01:59
So, here area of base equal to 2 into 5, the height 5.
02:03
So, we get volume equal to 10 h, here height is h.
02:12
So, we get volume 10 h.
02:14
Now differentiate this term, we get dv divided by dt equal to 10 into dh divided by dt.
02:21
Now substitute dv divided by dt equal to 1 plus t divided by 2...