Question

Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 3m/s, how fast is the area of the spill increasing when the radius is 40m?
Rate of change of area = m^2/s

Answer 1

\[A(r)=\pi r^2\\
{dA\over dt}=2\pi r{dr\over dt}\\
\quad=2\pi\times 40{\rm m}\times 3{\rm m/s}\\
\quad=240\pi\, {\rm m^2/s}
\]

Answer 2

so its the same thing as yesterday, just with less information given?

Answer 3

what yesterday?

Answer 4

things like this

Suppose that x=x(t) and y=y(t) are both functions of t. If
x2+y2=25,
and dx/dt=2 when x=3 and y=4, what is dy/dt?

dy/dt =

Answer 5

right.
parametric equations.

Answer 6

ok, il see what i can do on these other ones, thank you