Type II error hypothesis question

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The discussion centers on confusion regarding part b of a Type II error hypothesis question. The user disagrees with the professor's provided solution and questions the origin of the formula used. They calculated a beta value of 0.4825 using class methods and intuition. The user seeks validation for their approach and asks for input from others on the correctness of both their work and the professor's solution. Clarification on the calculation methods and the formula's derivation is requested.
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Homework Statement


Here is the question (I am only confused about part b):
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Here is the solution given by my professor:
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The Attempt at a Solution


However, I do not agree with part b and honestly have no clue where they got that formula from. I used the method taught in my class along with a bit of intuition and came up with a beta value of 0.4825. Does anyone agree with me work or is the solution from the professor actually correct?
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Anyone got an idea? :O
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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