## Calculus 10th Edition

(a) $\frac{1}{3}$ (b) $10\sqrt{10}$
(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: $horizontal^2+vertical^2=length^2$ $30^2+10^2=length^2$ $1000=length^2$ $length=\sqrt{1000}$ $length=10\sqrt{10}$