Help me to solve problem pless
2 answers:
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By Stokes' theorem, the line integral of over
is given by the surface integral of the curl of
over
, where
is the region of intersection of the plane
and the cylinder
with
having positive/upward orientation.
Parameterize by
with and
.
Take the normal vector to to be
The curl of is
Then the line integral is equivalent to
Let's call a child's ticket and an adult's ticket
. From this, we can say:
,
since 116 tickets are sold in total.
Now, we are going to need to find another equation (the problem asks us to solve a systems of equations). This time, we are not going to base the equation on ticket quantity, but rather ticket price. We know that an adult's ticket is $17,000, and a child's ticket is thus
.
Given these values, we can say:
,
since each adult ticket costs 17,000 and each child's ticket
costs 12,750, and these costs sum to 1,653,250.
Now, we have two equations:
Let's solve:
- Find
on its own, which will allow us to substitute it into the first equation
- Substitute in
for
- Apply the Distributive Property
- Combine like terms
- Subtract 1972000 from both sides of the equation and multiply both sides by -1
We have now found that 75 child's tickets were sold. Thus,
,
41 adult tickets were sold as well.
In sum, 41 adult tickets were sold along with 75 child tickets.