1. The problem statement, all variables and given/known data For a hill the elevation in meters is given by z=10 + .5x +.25y + .5xy - .25x^2 -.5y^2, where x is the distance east and y is the distance north of the origin. a.) How steep is the hill at x=y=1 i.e. what is the angle between a vector perpendicular to the hill and the z axis? b.)In which compass direction is the slope at x=y=1 steepest? Indicate whether the angle you provide is the angle measured in the standard way in the counter-clockwise direction from the x axis (east) or whether it is the compass azimuth. 2. Relevant equations 3. The attempt at a solution a.) So I got the gradient to be ∇f(x,y,z)= .5i - .25j...simply by the definition of the gradient. So i figured to figure the angle between the gradient and the z axis i could use the formula cosθ= (A dotted into B)/(lAl*lBl) but wouldn't be the z axis be the unit vector in the k hat direction making the cosθ=0...which can't be right. Any help on what to do? Also, I was given an equation that says ∇f(x,y,z) perpendicular to a 3 dimensional surface f(x,y,z) = constant. But I don't know how to use that equation to generate an answer. b.)The gradient gives you the direction of the quickest altitude ascension (at least for this problem) so how do I use what I calculated for the gradient to answer this part? Thanks for any help!!