Find the value of y. Did I do this problem correct?

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The discussion focuses on solving a problem for the value of y, with an emphasis on unit consistency in the calculations. One participant questions the disappearance of units in the solution, suggesting that the final answer should not lack units. Another participant mentions converting to SI units for clarity and expresses uncertainty about their own calculations. A correction is made regarding the exponent used in the calculations, leading to a revised unit outcome of m²/s². The conversation highlights the importance of maintaining proper units throughout mathematical problem-solving.
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What happened to all the units in line 2?
 
After dividing x by a, you should have gotten rid of the units of mass so your final answer shouldn't have any.

I converted everything to SI units and went on from there, it makes everything easier in my opinion. I'm not sure if I did it right and I probably shouldn't post my answer but I think you should have units of length^(9/2)*time^(9/2) at the end.
 
I get
length2 * time-2

Did you raise each side to the power 3/2 instead of 2/3?
 
Yes, you're right, my mistake. Now I'm getting m2/s2 with SI units.
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
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