I am standing on a hillside. Nearby my position, the height of the terrain is de

Question

I am standing on a hillside. Nearby my position, the height of the terrain is described by the equation z = 600 + 0.02x +0.025y. Here, x is the distance from my starting point in the 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 ea distances and heights are measured in feet. (a) By how much does my altitude increase if I walk 200 feet east? (Give an exact answer.) X ft By how much does my altitude increase if I walk 600 feet north? (Give an exact answer.) ft 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.) What is the slope of the terrain in the y direction? In other words, by how much does z increase if y is increased by one, while x is kept constant? (Give an exact answer.)

Explanation / Answer

a)
z = 600 + 0.02x + 0.025y
here chnage in x is 200 feet
increase in z = 0.02*200 = 4 feet
Answer: 4ft

b)
z = 600 + 0.02x + 0.025y
here chnage in x is 600 feet
increase in z = 0.025*600 = 15 feet
Answer: 15 ft

c)
z = 600 + 0.02x + 0.025y
dz/dx = 0.02
Answer: 0.02

d)
z = 600 + 0.02x + 0.025y
dz/dy = 0.025
Answer: 0.025

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