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angelarios
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all edges of a cube are expanding at a rate of 3 centimeters per second. how fast is the volume changing when each edge is (a) 1 cm. (b) 10 cm.
 one year ago
 one year ago
angelarios Group Title
all edges of a cube are expanding at a rate of 3 centimeters per second. how fast is the volume changing when each edge is (a) 1 cm. (b) 10 cm.
 one year ago
 one year ago

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satellite73 Group TitleBest ResponseYou've already chosen the best response.1
looks like a related rate problem fortunately the formula for the volume of a cube is easy, it is \(V(x)=x^3\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
take the derivative with respect to time and get \[V'=3x^2x'\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
you are told \(x'=3\) so this is really \[V'=9x^2\] replace \(x\) by the various values to get \(V'\)
 one year ago

angelarios Group TitleBest ResponseYou've already chosen the best response.0
dV/dt=9x^2dx/dt ?:)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
i used \(V'\) and \(x'\) instead of \(\frac{dV}{dt}\) and \(\frac{dx}{dt}\) because it was easier for me to write also for you it is easier
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
but in your notation, you have \[V=x^3\] so \[\frac{dV}{dt}=3x^2\frac{dx}{dt}\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
this line all edges of a cube are expanding at a rate of 3 centimeters per second tells you that \(\frac{dx}{dt}=3\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
that means \(\frac{dV}{dt}=3x^2\times 3=9x^2\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
let me know if i lost you there
 one year ago

angelarios Group TitleBest ResponseYou've already chosen the best response.0
Ok got it(:
 one year ago

angelarios Group TitleBest ResponseYou've already chosen the best response.0
So dats da answer?:)
 one year ago
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