We can compute the integral directly: we have

Then the integral is



You could also take advantage of Stokes' theorem, which says the line integral of a vector field
along a closed curve
is equal to the surface integral of the curl of
over any surface
that has
as its boundary.
In this case, the underlying field is

which has curl

We can parameterize
by

with
and
.
Note that when viewed from above,
has negative orientation (a particle traveling on this path moves in a clockwise direction). Take the normal vector to
to be pointing downward, given by

Then the integral is



Both integrals are kind of tedious to compute, but personally I prefer the latter method. Either way, you end up with a value of
.
The value of x from the given equation is -4/3
<h3>Factorization</h3>
Given the quadratic equation x^2 – 3x – 4 = x^2 – 6x + 8
x^2 – 3x – 4 - x^2 + 6x - 8 = 0
-3x + 6x - 4 + 8 = 0
3x + 4 = 0
- Subtrcat 4 from both sides
3x + 4 - 4 = 0 - 4
3x = -4
3x/3 = -4/3
x = -4/3
Hence the value of x from the given equation is -4/3
Learn more on equations here: brainly.com/question/2972832
Answer:
- 197 popcorn bags
- 202 food trays
Step-by-step explanation:
Since the numbers are split evenly 5 ways, each stand gets 1/5 of the total:
(985 bags)/5 = 197 bags
(1010 trays)/5 = 202 trays
Each concession stand receives 197 popcorn bags and 202 food trays.