Calendar: 1886-1887 Page 683

GENERAL LITERATURE AND SCIENCE 685 11 Prove that χ χλ χ x2 y2 is the equation to circle described on the straight line join- ing the two points and x2y2 as diameter 024 OCD are two straight lines at right angles to one another BC and AD intersect in Έ prove that the circles on AC BB OB as diameters will all have two points in common 12 Determine the equation to the tangent at any point of the parabola y2 ax If tangents to the parabola at points xYyY and x2y2 intersect in the point prove that a2 χλχ2 md β yx y2 13 One end of cord is fastened to fixed point the other is carried over fixed pulley at Β and fastened to weight what weight must be attached at point midway between and Β that the part AC may rest horizontally AB making an angle with the horizon Find also the tension in AC Divisions III IV -arithmetic an uclfo What is meant by reducing one quantity to fraction of another Reduce 1J yds to the fraction of fur 10 poles Standard gold worth £3 18s an oz is mixed with metal which may be considered valueless until the alloy is worth only £3 10s lOd an oz How much standard gold will there be in oz 12 dwt of the alloy have been making measurements in room with two-foot rule which afterwards discovered to be 37 of an inch too short Determine to five places of decimals in each case the factor by which must multiply my measure- ments of length δ of area in order to make them correct had calculated that should require 112 yds of carpet of yard wide What length shall actually require