Subject: calculus related rates

Name: molly

Who is asking: Student

Level: Secondary

Question:

A tanker spilled 30 ft cubed of chemicals into a river, causing a circular slick whose area is expanding while its thickness is decreasing. If the radius of the slick expands at the rate of 1 foot per hour, how fast is them thickness of the slick decreasing when the area is 100 feet squared?

Thanks!

i figured out a bunch of stuff but i don't know what to do:

Area=(pi)r^{ 2} A=100ft^{ 2} so... r= 5.64ft

Volume=(Area)(height) V=30ft^{ 3} so... h=0.3ft when area is 100ft^{ 2} dr/dt=1ft/hr dA/dt=(pi)2r(dr/dt)

V=(A)x(h) so... h=V/A so... dh/dt= (dV/dt)/(dA/dt)
ummmm.....help?

Hi Molly,
You're on the right track most of the way but look at your last line: you
have h = V/A and then an expression for dh/dt; you're not doing this step
correctly and further you are not using the fact that V is constant.

If f(x) = c/x where c is a constant, what would ^{d}/_{dx}(f(x)) = f'(x) be?

-c/x^{ 2}.
Now what happens if you want ^{d}/_{dt}(f(x))?

Penny