Solve Static Equilibrium Problem: Get Help Now

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A user seeks assistance with a static equilibrium problem but expresses doubt about the correctness of the problem statement. They have attempted to solve it multiple times but feel stuck. Responses indicate that the submitted work is of poor quality and unreadable, prompting a request for clearer figures and equations. The thread is temporarily closed until the user provides a more legible presentation of their work. Clear communication and quality submissions are essential for effective help in solving such problems.
Emanuel0406
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1. The problem statement, all variabHello. I uploaded a picture with the problem that concerns me. As you can see from my work so far...I have tried to solve the problem but I'm stuck. I have tried a few times and I'm starting to question myself if the problem is correct or not. Please give me a hand with this. Any help is appreciated. Thank you so much
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Homework Equations

The Attempt at a Solution

 

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Your solution is so poor quality as to be unreadable. Please submit neat figures and work. You can upload figures from a graphics app, and you can use LaTex to write equations. I am temporarily closing this thread until a better quality presentation is made available.
 
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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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