A model for a power cable suspended between two towers is given.

$y=18+28cosh(\frac{x}{28}),-28x28$

$($a$)$ Graph the model. Then find the heights of the cable at the towers and at the midpoint between the towers. $($Round your answers to three decimal places.$)$ height at towers height at midpoint

$46\mathrm{.}000$

$($b$)$ Find the slope of the model at the point where the cable meets the right$-$hand tower. $($Round your answer to three decimal places.