Question

Hi there! I'm not quite sure on how to solve this....

Answer 1

Step-by-step explanation:

`V=x^3\\\\(dV)/(dt)=3x^2(dx)/(dt)\\\\30(cm^3)/(s)=3x^2(dx)/(dt)\\\\(dx)/(dt)=(30(cm^3)/(s))/(3x^2)~at~x=2cm,~(dx)/(dt)=(30(cm^3)/(s))/(3*(2cm)^2)=(5)/(2)(cm)/(s)`

Answer 2

`(dx)/(dt) = 2.5 \: (cm)/(sec)`

Step-by-step explanation:

The volume of a cube is V = x^3. Taking the time derivative of this expression, we get

`(dV)/(dt) = 3 {x}^(2) (dx)/(dt)`

or

`(dx)/(dt) = \frac{1}{3 {x}^(2)} (dV)/(dt)`

We know that dV/dt = 30 cm^3/sec so the value of dx/dt when x = 2 cm is

`(dx)/(dt) = \frac{1}{3 {(2 \: cm)}^(2)}(30 \: \frac{ {cm}^(3) }{sec} ) = 2.5 \: (cm)/(sec)`