Respuesta :
The solution to the problem is as follows:
a cube has sides s
V = s^3 ---> differentiating
dV/dt = 3s^2 * ds/dt
0.5 ft^3 / min = 3 * (12ft)^2 * ds/dt
(1/2) ft^3 / min = 3 * 144 ft^2 * ds/dt
(144/6) ft^3 / ( ft^2 min ) = ds/dt
24 ft / min = ds/dt
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a cube has sides s
V = s^3 ---> differentiating
dV/dt = 3s^2 * ds/dt
0.5 ft^3 / min = 3 * (12ft)^2 * ds/dt
(1/2) ft^3 / min = 3 * 144 ft^2 * ds/dt
(144/6) ft^3 / ( ft^2 min ) = ds/dt
24 ft / min = ds/dt
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Answer:
0.0016 feet per minute
Step-by-step explanation:
Volume =[tex](side)^{3}[/tex]
V= [tex](x)^{3}[/tex]
taking derivative both sides ,we get
[tex]\frac{dV}{dt} = 3x^2\frac{dx}{dt}[/tex]
[tex]\frac{dV}{dt} = 0.5[/tex] [ given ]
[tex]0.5= 3x^2\frac{dx}{dt}[/tex] at x =12
[tex]0.5= 3{(12)}^2\frac{dx}{dt}[/tex]
[tex]\frac{0.5}{3(12)^2}=\frac{dx}{dt}[/tex]
[tex]\frac{dx}{dt}=0.0016 ft per minute[/tex]
