Suppose you are climbing a hill whose shape is given by the equation $z=1,700-0\mathrm{.}005x^2-0\mathrm{.}01y^2,$ where $x,y,$ and $z$ are measured in meters, and you are standing at a point with coordinates $(160,160,1316).$ The positive $x-$axis points east and the positive $y-$axis points north.

$($a$)$ If you walk due south, will you start to ascend or descend?

ascend

descend

At what rate $($in vertical meters per horizontal meter$)?$

$$ vertical meters per horizontal meter

$($b$)$ If you walk northwest, will you start to ascend or descend?

ascend

descend

At what rate $($in vertical meters per horizontal meter$)?($Round your answer to two decimal places.$)$

$$ vertical meters per horizontal meter

$($c$)$ In which direction is the slope largest?

$$

What is the rate of ascent $($in vertical meters per horizontal meter$)$ in that direction? $($Round your answer to two decimal places.$)$

$3\mathrm{.}5$ vertical meters per horizontal meter

At what angle $($in degrees$)$ above the horizontal does the path in that direction begin? $($Round your answer to two decimal places.$)$

$7$