Jack has $24 in one-dollar and five- dollar bills. He has a total of 8 bills. How many of each bill does he have?
2 answers:
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Choice A is the answer which is the point (1,-1)
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How I got this answer:
Plug each point into the inequality. If you get a true statement after simplifying, then that point is in the solution set and therefore a solution. Otherwise, it's not a solution.
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checking choice A
plug in (x,y) = (1,-1)
This is true because -3 is equal to itself. So this is the answer.
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checking choice B
plug in (x,y) = (2,4)
This is false because 0 is not to the left of -3, nor is 0 equal to -3. We can cross this off the list.
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checking choice C
plug in (x,y) = (-2,3)
This is false because 7 is not to the left of -3, nor is 7 equal to -3. We can cross this off the list.
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checking choice D
plug in (x,y) = (3,4)
This is false because -2 is not to the left of -3, nor is -2 equal to -3. We can cross this off the list.
Perhaps you mean to find the volume under 
? It seems like you have to rely on calculus otherwise (in the case that you indeed mean 
).
Assuming this, note that describes the top half of a sphere with radius 8, which means the volume below this surface over the disk 
is simply half the volume of the sphere. Thus the volume is
Assuming this, note that