Question

Really need help with #57!

Answer 1

now, when the candle fully burns, its final height "h" is 0, because, well the candle is not longer standing, it burned completely all you have is a bunch of hot wax on the candle holder, so h = 0.


`\bf r=\sqrt{\cfrac{kt}{\pi (h_o-h)}}\qquad \begin{cases} h=0\\ r=0.875\\ h_o=6.5\\ k=0.04 \end{cases}\implies 0.875=\sqrt{\cfrac{0.04t}{\pi (6.5-0)}} \\\\\\ \textit{now we square both sides}\quad 0.875^2=\cfrac{0.04t}{65\pi }\implies 65\pi \cdot 0.875^2=0.04t \\\\\\ \cfrac{65\pi \cdot 0.875^2}{0.04}=t\implies \stackrel{minutes}{3908.58}\approx t`

which is 65 hours and 8 min and about 35 seconds. Or 2 days and 17 hours and 8 mins and 35 secs.