$\newenvironment {prompt}{}{} \newcommand {\ungraded }{} \newcommand {\HyperFirstAtBeginDocument }{\AtBeginDocument }$

A rectangle has a constant height of 6 cm, as shown below. The area of the rectangle is given by the formula $A=b h$, where $b$ is the length of the base of the rectangle and $h$ is the height of the rectangle. In order to determine how fast its area is changing at the instant that the base has length 8 cm, which of the following formulas would you use? $\dfrac {dA}{dt} = \dfrac {dA}{db} * \dfrac {db}{dt}$ $\dfrac {dA}{dh} = b$ $\dfrac {dA}{dt} = \dfrac {dA}{dh} * \dfrac {dh}{dt}$ $\dfrac {dA}{db} = h$
A submarine is diving at a rate of 50 feet per minute. As the sub descends, the water temperature outside is falling at a rate of 0.5 degrees per foot. Let D be the depth of the submarine. Let T be the temperature outside the submarine. How quickly is the temperature falling? If your answer is that we need to know the depth and/or temperature, type NEI for not enough information.

$\answer {25}$ degrees per minute

A circle’s radius, $r$, is increasing at a rate of 3 inches per second, as shown below. How quickly is its area increasing? (The formula for the area of a circle is $A = \pi r^2$.) $\answer {6 \pi r}$