Suppose you are climbing a hill whose shape is given by the equation z = 1000 − 0.005x2 − 0.01y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (120, 80, 864). 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? c vertical meters per horizontal meter (b) if you walk northwest, will you start to ascend or descend? ascend descend at what rate? (round your answer to two decimal places.) c vertical meters per horizontal meter (c) in which direction is the slope largest? c what is the rate of ascent in that direction? c vertical meters per horizontal meter at what angle above the horizontal does the path in that direction begin? (round your answer to two decimal places.) c °