Part 1 out of 2 A patio in the shape of a rectangle , is fenced on all sides with 94 feet of fencing . The patio is 7 feet less
wide than it is long. I feet ( -7 feet What information can be used to solve the problem ? How can you find the information ? You need the select and select of the patio . You can write algebraic expressions for the length and width Use the expressions in the formula for the ( select ) rectangle , and then solve to find the length and the width .
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Under the given transformation, the Jacobian and its determinant are
so that
where is the region
transformed into the
-
plane. The remaining integral is the twice the area of
.
Now, the integral over is
but through the given transformation, the boundary of is the set of equations,
We require that , and the last equation tells us that we would also need
. This means
and
, so that the integral over
is