An engineer is building a suspended platform to raise bags of cement. The platform has a mass of 200 kg, and each bag of cement
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Parameterize by the vector function
so that the normal vector to is given by
with magnitude
In this case, the normal vector is
with magnitude . The integral of
over
is then
where is the region in the
plane over which
is defined. In this case, it's the triangle in the plane
which we can capture with
and
, so that we have