Mathematical Questions and Solutions

F. Hodgson., 1891

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Pàgina 136 - The cone intersects the sphere x^ + y^ + z1— <p = 0 in a sphero-conic. Show that the equation of the tubular surface, which is the envelope of a sphere of constant radius k, whose centre moves along this sphero-conic, is had by equating to zero the discriminant of the following cubic in \, 4n2 ain2 qa.'2 4«2 sin2 /3 i/2 P2 + 4\«2cos2a •where P 5448.
Pàgina xxviii - From a point in the circumference of a circular field a projectile is thrown at random with a given velocity which is such that the diameter of the field is equal to the greatest range of the projectile ; find the chance of its falling within the field.
Pàgina xxi - Find the locus of the centre of a circle which touches a given straight line AB at a given point P.
Pàgina 58 - Limax maximus, it was not possible to employ the method described by Miss Henchman ('91) for shelling the eggs. But by inserting two fine cambric needles in one holder, so that the distance between the points is less than the diameter of the unshelled egg, it is possible to hold the egg between these two needles and pierce it by a third. A quick shear-like cut with the third needle against one of the other two tears open one side of the egg and allows the albumen and the ovum to escape from the envelopes....
Pàgina 113 - If a parabola touch the sides of an equilateral triangle, the focal distance of any vertex of the triangle passes through the point of contact of the opposite side. 72. Let RW be the ordinate of R. Then AN...
Pàgina 137 - To find the average distance between two points taken at random in the surface of a sector of a circle.
Pàgina xxv - Prove that the lengths of the perpendiculars from the vertices A, B, C of a triangle on the...

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