A biologist is comparing the growth of a population of flies per week to the number of flies an iguana will consume per week. He
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Consider the top half of a sphere centered at the origin with radius 
, which can be described by the equation
and consider a plane
with
. Call the region between the two surfaces 
. The volume of is given by the triple integral
Converting to polar coordinates will help make this computation easier. Set
Now, the volume can be computed with the integral
You should get
and consider a plane
with
Converting to polar coordinates will help make this computation easier. Set
Now, the volume can be computed with the integral
You should get
Since Joann receives $10 per hour for the first 35 hours, so she receives $350 (35 times $10) before she starts receiving extra hours.
Since she received $515, we know that she worked extra hours.
Let's use the variable x to represent the number of extra hours worked.
So we can write the following equation for the total payment received:
She worked 11 extra hours. Adding this to the 35 regular hours, so she worked for 46 hours.