00:01
Hi, from the question given that suppose in calm water the oil spilled from the reputed well of a grounded tanker forms an oil slick that is in the circular shape.
00:15
If the radius of the circle is increasing at the rate of r dash of t is equal to 30 over under root of 2t plus 4 feet per minute.
00:29
So, here find an expression for the radius at any t.
00:36
So, r of t is the thing we need to find and also we need to find how large is the filled area 16 minute after the rupture occurred.
00:47
So, if t is equal to 16 then we need to find r of 16.
00:55
So, here first we need to find r of t.
00:59
So, for that first we need to integrate on both side.
01:01
So, integral of r dash of t is equal to r dash of t dt is equal to integral of 30 divided by square root of 2t plus 4 dt.
01:14
So, here r of t is equal to 30 times of integral 2t plus 4 to the power of 1 over 2 negative 1 over 2 dt.
01:27
So, here let u is equal to 2t plus 4.
01:32
So, du is equal to 2 dt.
01:36
So, dt is equal to du by so on substituting.
01:43
So, we have r of t is equal to 30 times of integral for 2t plus 4 substitute u to the power of minus half for dt substitute du by 2.
01:56
So, 15 times of integral u to the power of minus half du.
02:03
So, when we integrate this we obtain 15 times of u to the power of minus half plus 1 divided by minus half plus 1 plus integrating constant c...
