mild birch
A circular puddle is spreading so that the surface area is increasing at a rate of 1 square foot per minute. How fast is the radius of the puddle increasing when the area of the puddle is
25πft ?
Give you answer in feet per minute, accurate to within one hundredth.
alpine marsh
A circular puddle is spreading so that the surface area is increasing at a rate ...
A'(t) = 1 = 2pi * r(t) * r'(t)
A(t) = pi * r²(t)
r'(t) when A(t) = 25pi is ... ?
25 = pi * r²(t)
r²(t) = 25/pi
r(t) = 5/sqrt(pi)
2pi * (5/sqrt(pi)) * r'(t) = 1
solve for r'(t)
mild birch
A'(t) = 1 = 2pi * r(t) * r'(t)
A(t) = pi * r²(t)
r'(t) when A(t) = 25pi is ... ?...
Would it be the sqrt pi /10pi?