Verify Unit length to y-axis from Tractrix Curve

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The discussion revolves around verifying the unit length to the y-axis from a Tractrix curve, specifically addressing problem number 6. The user expresses confusion about finding the tangent line at a specific point and determining its length. They contemplate whether to subtract the coordinates of the tangent point from the y-axis or to use the integral formula for length. The request for clearer problem statements highlights the need for better communication in problem-solving. Overall, the thread seeks guidance on applying calculus concepts to a geometric problem involving curves.
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Homework Statement


The problem is described in the picture I've attached. It is problem number 6.

Homework Equations


Tangent line of a curve
Length of a curve

The Attempt at a Solution


I don't know why I'm so confused on what seems like it should be a relatively straightforward problem, but I am. I guess I would approach this problem by finding the tangent line at a point (say t=0) (though I forget the procedure to do that exactly) and then basically just show that the tangent line has length 1 from y = 0 basically?
- Also would I just like subtract the two points (i.e., the point on the curve where there is a tangent line and then the y-axis (y = 0)) or would it require the use of the formula for length namely the integral of the absolute value of the derivative of γ(t) from the y-axis to the point on the curve?

Any help with this would be greatly appreciated!
 

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  • 563H_HW1.JPG
    563H_HW1.JPG
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It would help if you would type the statement of the problem instead of posting an illegible image.
 
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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