Ellis's backyard has a 6.256.256, point, 25 by 6.25\,\text{m}6.25m6, point, 25, space, m patio. She would like to build a 1.5\,\
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Split into two component segments,
and
, parameterized by
respectively, with , where
.
We have
where
so the line integral becomes
We have been given that Sterre charges $35 to file tax returns, but files for free if she only needs the easiest form. Also, she donates $2 to clean water projects per tax return she files.
Further we know that Sterre charged $7,245 and made a donation of $1,242 this year for the tax returns she filed.
Let x be the number of free income tax returns and y be the number of $35 income tax returns.
Therefore, we can set up:
Since she donates $2 for each return that she files, therefore, we can set up:
Therefore,
Sterre filed 414 tax returns for free and filed 207 tax returns for $35.