In cylindrical coordinates, we have 
, so that
correspond to the upper and lower halves of a sphere with radius 
. In spherical coordinates, this sphere is 
.
means our region is between two cylinders with radius 1 and . In spherical coordinates, the inner cylinder has equation
This cylinder meets the sphere when
which occurs at
where 
. Then 
.
The volume element transforms to
Putting everything together, we have
There are two solutions.
.. (3, 2)
.. (0.2, -3.6)
_____
If you're choosing possibilities from a list, trying them in the equations usually gives quick results.
0.03125 beciase there are 32 people and one ticket make that as a fraction which is 1/32 and make it a decimal
Sophia is more correct in her solution.
Answer:
-81
Step-by-step explanation:
-6(2x² + 5x) - 9
substitute -4 for 'x'
-6[2(-4)² + 5(-4)] - 9
-6[2(16) + (-20) - 9]
-6(32 - 20) - 9
-6(12) - 9
-72 - 9 = -81
