I am standing on a hillside. Nearby my position, the height of the terrain is described by the equation z = 400+ 0.05x + 0.015y. Here, x is the distance from my starting point in the east/west direction (positive values of x are east of my starting position) and y is the distance in the north/south direction (positive values of y are north of my starting position). All distances and heights are measured in feet. (a) By how much does my altitude increase if I walk 400 feet east? (Give an exact answer.) ft (b) By how much does my altitude increase if I walk 300 feet north? (Give an exact answer.) ft (c) What is the slope of the terrain in the x direction? In other words, by how much does z increase if x is increased by one, while y is kept constant? (Give an exact answer.) (d) What is the slope of the terrain in the y direction? In other words, by how much does z increase if y increased by one, while x is kept constant? (Give an exact answer.)

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