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The height of a certain hill (in feet) is given by h(x, y) = 10 (2xy - 3 x^2 - 4y^2 -18x +28y + 12), where y is the distance in miles (north), x the distance east of South Hadley, Massachusetts. a.) Where is the top of the hill located? b.) How high is the hill? c.)How steep is the slope (in feet per mile) at a point 1 mile north and one mile east of South Hadley? In what direction is the slope steepest, at that point? d.) Make a contour map and a 3D plot of the area surrounding South Hadley, from 8 miles west to 4 miles east, and 2 miles south to 8 miles north. Plot only positive heights on the 3D graph; use If to help you out

The height of a certain hill (in feet) is given by h(x, y) = 10 (2xy - 3 x^2 - 4y^2 -18x +28y + 12), where y is the distance in miles (north), x the distance east of South Hadley, Massachusetts. a.) Where is the top of the hill located? b.) How high is the hill? c.)How steep is the slope (in feet per mile) at a point 1 mile north and one mile east of South Hadley? In what direction is the slope steepest, at that point? d.) Make a contour map and a 3D plot of the area surrounding South Hadley, from 8 miles west to 4 miles east, and 2 miles south to 8 miles north. Plot only positive heights on the 3D graph; use If to help you out

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The height of a certain hill (in feet) is given by h(x, y) = 10 (2xy - 3 x^2 - 4y^2 -18x +28y + 12), where y is
the distance in miles (north), x the distance east of South Hadley, Massachusetts.
a.) Where is the top of the hill located?


b.) How high is the hill?

c.)How steep is the slope (in feet per mile) at a point 1 mile north and one mile east of South Hadley? In
what direction is the slope steepest, at that point?


d.) Make a contour map and a 3D plot of the area surrounding South Hadley, from 8 miles west to 4 miles
east, and 2 miles south to 8 miles north. Plot only positive heights on the 3D graph; use If to help you
out

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