An open can of oil is accidentally dropped into a lake; assume the oil spreads over the surface as a circular disk of uniform thickness whose radius increases steadily at the rate 10 cm/sec. At the moment when the radius is 1 meter, the thickness of the oil slick is decreasing at the rate 4 mm/sec; how fast is it decreasing when the radius is 2 meters? (Watch the units!)

−0.0005 m/sec.

Step-by-step explanation:

Let us denote the volume of the can as V

let us denote the radius of the circular disc in lake as r

Let us denote the thickness of the circular disc as h

But we know the volume of the can as πr^2h then we can calculate How fast it is decreasing when the radius is 2 m

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

answer: the proof is mentioned below.

step-by-step explanation:

since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.