Oil tanker at (0,0) starts to leak oil in a circulat pattern.?

If the radius of the circle of the oil increses steadily at 3m/min what equation would representthe perimeter of the oil slick exacly 5 minutes after the rupture b) how long does it take for the oil slick to reach a seagull swinmming at (-12,25)? ThanksOil tanker at (0,0) starts to leak oil in a circulat pattern.?
Ooh, calculus... well, maybe.





Actually not. The radius five minutes after is 15meters, right? So the perimeter is 2蟺r = 30蟺





If the seagull is swimming at (-12, 25) then the radius is determined by the Pythogorean theorem, which is:





r = 鈭?x虏 + y虏) = 鈭?144 + 625) = 27.73 meters





How long does it take for the radius to get to 27.73 meters? Divide by 3 ... so about 9.24 minutes.





Here I thought you were asking for the equation of the ship's motion if it's moving steadily in a circular pattern where the radius increases at 3m/minute. That would have been an interesting problem.Oil tanker at (0,0) starts to leak oil in a circulat pattern.?
actually, the oil slick doesn't have an initial perimeter of 3m, so the equation should probably be





2蟺(t x 3m/min) = 30蟺.


where t = time in minutes





Much too lazy to solve the second part %26gt;_%26lt; Sorry!
the rate of change of the radius of oil spill, dr/dt = 3.


Therefore, integrating that eqn, r=3t.


When t=5mins, the radius, r=3x5 = 15m.


The equation for perimeter is given as p=2(pi)(r).


Therefore, at t=5 mins, the eqn is p=2(pi)(15) = 30(pi).