5. A coffeepot has the shape of a cylinder with radius 5 inches, as shown in the figure above. Let $h$ be the depth of the coffee in the pot, measured in inches, where $h$ is a function of time $t$, measured in seconds. The volume $V$ of coffee in the pot is changing at the rate of $- 5 \pi \sqrt { h }$ cubic inches per second. (The volume $V$ of a cylinder with radius $r$ and height $h$ is $V = \pi r ^ { 2 } h$.) (a) Show that $\frac { d h } { d t } = - \frac { \sqrt { h } } { 5 }$. (b) Given that $h = 17$ at time $t = 0$, solve the differential equation $\frac { d h } { d t } = - \frac { \sqrt { h } } { 5 }$ for $h$ as a function of $t$. (c) At what time $t$ is the coffeepot empty?
5. A coffeepot has the shape of a cylinder with radius 5 inches, as shown in the figure above. Let $h$ be the depth of the coffee in the pot, measured in inches, where $h$ is a function of time $t$, measured in seconds. The volume $V$ of coffee in the pot is changing at the rate of $- 5 \pi \sqrt { h }$ cubic inches per second. (The volume $V$ of a cylinder with radius $r$ and height $h$ is $V = \pi r ^ { 2 } h$.)\\
(a) Show that $\frac { d h } { d t } = - \frac { \sqrt { h } } { 5 }$.\\
(b) Given that $h = 17$ at time $t = 0$, solve the differential equation $\frac { d h } { d t } = - \frac { \sqrt { h } } { 5 }$ for $h$ as a function of $t$.\\
(c) At what time $t$ is the coffeepot empty?\\