Respuesta :

Trancescient

[tex]\frac{dx}{dt} = 2.5 \: \frac{cm}{sec} [/tex]

Explanation:

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

[tex] \frac{dV}{dt} = 3 {x}^{2} \frac{dx}{dt} [/tex]

or

[tex]\frac{dx}{dt} = \frac{1}{3 {x}^{2}} \frac{dV}{dt} [/tex]

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

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

rvillalta2002

Answer:

Explanation:

[tex]V=x^3\\\\\frac{dV}{dt}=3x^2\frac{dx}{dt}\\\\30\frac{cm^3}{s}=3x^2\frac{dx}{dt}\\\\\frac{dx}{dt}=\frac{30\frac{cm^3}{s}}{3x^2}~at~x=2cm,~\frac{dx}{dt}=\frac{30\frac{cm^3}{s}}{3*(2cm)^2}=\frac{5}{2}\frac{cm}{s}[/tex]

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