How Do I Rearrange Variables in Equations for Homework?

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The discussion revolves around a student seeking help with rearranging variables in equations for a homework assignment. The student specifically mentions difficulty with four equations and expresses a desire to learn the procedure. Respondents encourage the student to share their attempts to facilitate better assistance. They also suggest techniques such as completing the square and using trigonometric identities to solve the equations. Overall, the focus is on collaborative problem-solving and understanding the methods involved in rearranging variables.
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Hello, the teacher gave us this assignment in which we had to separate some variables from equations. (example: E=mc^2 for m -> m=E/c^2). I had trouble with 4 of them (the ones in the attachment), I would appreciate some help, The procedure is really important since I want to learn how to solve them.
 

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Hi woz,

While we're waiting for the attachment to get approved...

Why don't you go ahaid and post what you've tried / where you're stuck on them. It'll help us help you.
 
9. Do you know how to complete the square?

10. Can you get thins in terms of \cos \theta and apply \arccos to both sides?

11. Simmilar to 10

15. This seems to be a trick question, the equation isn't dependent on m at all :confused:
 
the solution in a word doc

regards
marlon
 
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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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