Solutions of Weekly Problem Papers

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■ _f cosar — cosy cosz ^ , , /. if xy'i! are in the given proportion, -. ^ = B, and by sm y sinz adding numerator and denominator, each is evidently = A.
3. l-i + J-i + ---= log. (1 + 1) = logs 2 = -6931471 . . .
4. The points A, B are supposed to he fixed. Draw the tangent BH.
Then the angle BFG = EOD = EAB, and .-. the triangles FBO, EBA are similar. .-. BG : BF :: BE : BA. ,: BO.BA = BH\ .: ff is a fixed point.
5. Let P he the point on the ellipse such that FP is a minimum.
Take a point P' o
...n the curve indefinitely near to P. Then PP = FP'.
,: the angle FPP' = PFP, and each ultimately = 1 right angle.
But PP" is the direction of the tangent at P. .: FP is the normal.
.-. SF : SP :: SA : AX, .: SP = 1. SF e 6. Suppose the weight of the triangle to he represented by « + J + e.
Then \ of this is supported at each angular point, and at these points we have remaining the pressures represented by a, b, c. Divide AB WEEKLY PROBLEM PAPERS. 159 at D so that AB : BB :: b : a :: AC : CB.


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