Answer
(a) $\frac{1}{3}$
(b) $10\sqrt{10}$
Work Step by Step
(a) The slope can be found by dividing the rise by the run. The rise is 1 and the run is 3, so the slope is $\frac{1}{3}$
(b) Before finding the length of the conveyor, find the horizontal and vertical distance. The vertical distance is 10 feet. The horizontal distance can be found using the equation:
$slope=\frac{vertical}{horizontal}$
$\frac{1}{3}=\frac{10}{horizontal}$
$horizontal=30$
Now the length of the conveyor can be found using the Pythagorean Theorem:
$horizontal^2+vertical^2=length^2$
$30^2+10^2=length^2$
$1000=length^2$
$length=\sqrt{1000}$
$length=10\sqrt{10}$
