Search -then-put-in-lowest-terms

# then put in lowest terms

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ooler to fill his water bottle. He then took out 16 plastic cups for his teammates and put the same amount of water in each cup.
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rest. The current unit that our teacher has us on so far is centripetal motion, and I can't recall being taught how to solve this. File attached below shows my work so far, I don't necessarily need the work done for me, but I just want to be put on the right track, such as an equation to start with or what I need to look for. The answer I got was clearly incorrect for part a (which is what I need help with), so please help me get going in the right direction.
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8y and then I solved for y in the area equation and got y=8,000/x then I put that into the other equation and got 20x+64,000/x then took the derivative and got 20-64,000x^-2 and when I solved for the derivative equals 0 I got 40 radical 2 but my teacher said it is supposed to be 20 radical 15, so I do not know where I went wrong.
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