Pre-Video Questions

$\newenvironment {prompt}{}{} \newcommand {\ungraded }[0]{} \newcommand {\HyperFirstAtBeginDocument }[0]{\AtBeginDocument }$

To go back to the list of video sets, click HERE.

Before watching the videos, think about and answer these questions to the best of your ability.

A right triangle has one leg of constant length 7 cm as shown in the diagram below. The area of the triangle is given by the formula $A=\dfrac {1}{2} b h$ , where $b$ is the length of the base of the triangle and $h$ is the height of the triangle. In order to determine how fast its is area changing at the instant that the other leg has length 10 cm, which of the following formulas would you use?

$\dfrac {dA}{dt} = \dfrac {dA}{dh} * \dfrac {dh}{dt}$ $\dfrac {dA}{dt} = \dfrac {dA}{db} * \dfrac {db}{dt}$ $\dfrac {dA}{dh} = \dfrac {1}{2}b$ $\dfrac {dA}{db} = \dfrac {1}{2}h$ $\dfrac {dA}{dt} = \dfrac {1}{2}$

An airplane is climbing at a rate of 750 feet per minute. As the plane rises, the air temperature outside is falling at a rate of 0.002 degrees per foot. Let A be the altitude of the airplane Let T be the temperature outside the plane. How quickly is the temperature falling per minute?

$0.002+750$ degrees/minute $0.002*750$ degrees/minute $\dfrac {750}{0.002}$ degrees/minute $\dfrac {0.002}{750}$ degrees/minute $0.002-750$ degrees/minute $750-0.002$ degrees/minute You need to know the current altitude of the plane and the current temperature to figure out the answer.

A square’s side length, $x$ , is increasing at a rate of 3 inches per second, as shown below. How quickly is its area increasing?

$9$ in $^2$ /sec $9x$ in $^2$ /sec $6x$ in $^2$ /sec $6$ in $^2$ /sec $1.5$ in $^2$ /sec $1.5x$ in $^2$ /sec