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Vector calculus question?
The thickness of the frosting at a point on a rectangular piece of brownie is equal to one
twentieth of the square of the horizontal distance from that point to the bottom left corner of
the brownie when seen from above. If the brownie is three inches wide by two inches across,
what is the average thickness of frosting on the brownie?
Any help would be appreciated
1 Answer
- FredLv 78 years agoFavorite Answer
Choosing coordinates with the bottom left corner of the brownie at the origin, and the 3-in edge going out the x-axis, and the 2-in edge going out the y-axis, the frosting thickness is
f(x,y) = (x² + y²)/20
and the average thickness is
: : : : 2 3
(1/A)∫ ∫ f(x,y) dx dy = ⅙∫∫(x² + y²) dx dy /20
: : : :0 0
= (1/120) ∫(9 + 3y²)dy = (1/120) (18 + 2³) = 26/120
= 13/60
