$200 - $88 = $112
$112 / 32 weeks = $3.50
Brooklyn saved $3.50 each week
To answer this, we need to know the expression for the area of a square which is the square of its side length or:
Area = a²
Solving for the side length,
a = √area
a = √144x²
a = 12x
Therefore, the side length is 12x.
1:2
Similar to the 1/2 fraction, 1:2 is a simplified ratio of a half.
Make a change of coordinates:


The Jacobian for this transformation is

and has a determinant of

Note that we need to use the Jacobian in the other direction; that is, we've computed

but we need the Jacobian determinant for the reverse transformation (from

to

. To do this, notice that

we need to take the reciprocal of the Jacobian above.
The integral then changes to
