Mathematics, 22.06.2019 14:00 kevinh2683
Assume there is a cube with all sides equal to x. the change in x with respect to t is x(t)=2t. what is the formula for the rate of change of the volume of the cube?
Answers: 1
![\bf \textit{volume of a cube}\\\\ V=x^3~~ \begin{cases} x=length~of\\ \qquad a~side\\[-0.5em] \hrulefill\\ x(t)=2t\\ x=2t \end{cases}\implies V=[x(t)]^3\implies V=[2t]^3 \\\\\\ V=[2^3t^3]\implies V=8t^3\implies \boxed{\cfrac{dV}{dt}=24t^2}](/tpl/images/0004/3376/ca663.png)
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