What are the formulas in this physics document and how can they be decoded?

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The document contains essential formulas related to Mechanics and Thermodynamics. Users are encouraged to reference their lecture notes for additional context on these formulas. If specific formulas are unclear, asking for clarification is recommended. A list of common physics notations may also assist in decoding the formulas. Understanding these concepts is crucial for mastering physics topics.
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Welcome to PF, Kevin! You certainly study Physics. The sheet contains all formulas you learn when studying Mechanics and Thermodynamics. Look after them in your lecture book or notes. And ask the one you can not find.
 

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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