A hat is marked down 45% and its new price is $69. What was the original price rounded to the nearest cent?
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In the first octant, the given plane forms a triangle with vertices corresponding to the plane's intercepts along each axis.
Now that we know the vertices of the surface
, we can parameterize it by
where
and 
. The surface element is
With respect to our parameterization, we have
, so the surface integral is
Now that we know the vertices of the surface
where
With respect to our parameterization, we have