2nd Putnam 1939

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Problem B1

The points P(a,b) and Q(0,c) are on the curve y/c = cosh (x/c). The line through Q parallel to the normal at P cuts the x-axis at R. Prove that QR = b.

 

Solution

Trivial. [Let O be the origin. Then OR/OQ = sinh a/c, so QR2 = c2(1 + sinh2a/c), so QR = b.]

 


 

2nd Putnam 1939

© John Scholes
jscholes@kalva.demon.co.uk
4 Sep 1999