Posted by **sam** on Monday, May 19, 2008 at 3:00am.

oil is leaking from a pipeline on the surface of a lake and forms an oil slick whose volume increases at a constant rate of 2000 cubic centimeters per minute. The oil slick takes the form of a right circular cylinder with both its radius r and height changing h is given by V= pie times r to the second power times h)

b) a recovery device arrives on the scene and begins removing oil. The rate at which oil is removed is R(t)=400 times square root of t cubics per min, where t is the time in min since the device began working.oil continues to leak at the rate of 2000 cubic cm per min. Find t when oil slick reaches its max volume.

c) By the time the recovery device began removing oil 60000 cubic cm of oil had already leaked. write but not evauate and expression involving an integral that gives the volume of oil at the time found in part (b)

help please start them

- calc -
**Damon**, Monday, May 19, 2008 at 1:24pm
V = pi r^2 h

dV/dt = 2000 - 400 t^.5

b) when is dV/dt = 0?

400 t^.5 = 2000

sqrt t = 5

t = 25 min

c) V at t=0 = 60,000

dV/dt = 2000 -400 t^.5

V = 60,000 + integral from t = 0 to t = 25 of (2000 - 400 t^.5) dt

## Answer this Question

## Related Questions

- calculus - oil is leaking from a pipeline on the surface of a lake and forms an ...
- Calculus - An ocean oil well is leaking oil into the ocean at a rate of 1 m3/hr ...
- Calculus - An ocean oil well is leaking oil into the ocean at a rate of 1 m3/hr ...
- Calculus - An ocean oil well is leaking oil into the ocean at a rate of 1 m3/hr ...
- CAL-Help on dr/dt - A circular oil slick of uniform thickness is caused by a ...
- MATH-CALC - 3.A ruptured oil tanker causes a circular oil slick on the surface ...
- CALCULUS - A ruptured oil tanker causes a circular oil slick on the surface of ...
- math please help - A ruptured oil tanker causes a circular oil slick on the ...
- physics - one liter (1000cm3) of oil is spiled onto a smooth lake. if the oil ...
- Calc - We assume that an oil spill is being cleaned up by deploying bacteria ...

More Related Questions