- #1
noblegas
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Homework Statement
the height of a certain hill is given by
h(x,y)=10(2xy-3x^2-4y^2-18x+28y+12)
wher y is the distance north and x is the distance east of south hadley
a)Where is the top of the hill
b) how high is the hill
c) how steep is the hill at a point 1 mile north
Homework Equations
The Attempt at a Solution
dh/dx=y-3x-9=0
dh/dy=x-4y+14=0
using linear system of algebra I find that my coordinates on top of the hill are
(x=-26,y=-3)
b) just plug in the coordinates you got in part a, into the h function; answer: h(x=-26,y=-3)
c) the slope would just be the gradient of h , which is: [tex]\nabla[/tex]h=(dh/dx)x-hat+(dh/dy)y-hat=-7x-hat+11y-hat
|[tex]\nabla[/tex]h|=sqrt(49+196)
direction is just: cos(theta)=[tex]\nabla[/tex]h dot dl/(
|[tex]\nabla[/tex]h||dl|), you take the inverse of cos(theta)