At time t is greater than or equal to zero, a cube has volume V (t) and edges of length x (t). If the volume of the cube decreases at a rate proportional to its surface area, which of the following differential equations could describe the rate at which the volume of the cube decreases?

A) dV/dt=-1.2x^2

B) dV/dt=-1.2x^3

C) dV/dt=-1.2x^2 (t)

D) dV/dt=-1.2t^2

E) fav/dt=-1.2V^2

Question

Mathematics

Izabelle Herman

23 July, 17:04

At time t is greater than or equal to zero, a cube has volume V (t) and edges of length x (t). If the volume of the cube decreases at a rate proportional to its surface area, which of the following differential equations could describe the rate at which the volume of the cube decreases?

A) dV/dt=-1.2x^2

B) dV/dt=-1.2x^3

C) dV/dt=-1.2x^2 (t)

D) dV/dt=-1.2t^2

E) fav/dt=-1.2V^2

+5

Answers (2)

Know the Answer?

Matias Harrison · Answer 1

C

Step-by-step explanation:

V (t) = [x (t) ]³

A (t) = 6[x (t) ]²

dV/dt = k * 6[x (t) ]²

Where k < 0

From the options,

taking k = - 0.2

dV/dt = - 1.2[x (t) ]²

Myles Malone · Answer 2

A) dV/dt=-1.2x^2

Step-by-step explanation:

The rate of change of volume is given by dV/dt. Surface area is proportional to x^2. Since the volume is decreasing, the constant of proportionality between surface area and rate of volume change will be negative. Hence a possible equation might be ...

dV/dt = - 1.2x^2