A right circular cone is undergoing a transformation in such a way that the radius of the cone is increasing at a rate of 1/2 inches per minute while the height of the cone is decreasing at a rate of 1/3 inches per minute. At the moment the radius of the cone is 2 in and the height of the cone is 1/3 in, find the rate of change of the volume of the cone. Simplify your answer and be sure to include units with your answer.

The volume is decreasing at the rate of 1.396 cubic inches per minute

Step-by-step explanation:

Given

Shape: Cone

--- rate of the radius

--- rate of the height

Required

Determine the rate of change of the cone volume

The volume of a cone is:

Differentiate with respect to time (t)

Substitute values for the known variables

The volume is decreasing at the rate of 1.396 cubic inches per minute

a = 11 : 4

b = 38

c = 1 for every 6

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: