Calendar: 1893-1894 Page 847

FACULTY OF SCIENCE cxxv brass wire 83 cm in length 0423 cm in diameter and of density 838 stretched with weight of 16 kilogrammes vibrates 191 times second find the number of vibrations per second of steel wire metre long 053 cm diameter and of density 7'8 stretched with weight of 25 kilogrammes &naI1 ttcat &tomttvv YEAR II Prove that the points whose rectangular coordinates are V3-1 V3-1 and form an equilateral triangle Find the distance of the circum-centre of this triangle from the origin The line 5x Yly 60 cuts the rectangular axes in Ρ and φ and the line 6x 48 48 cuts them in and find the lengths of their intercepts on the axes the tangents of the angles of their inclinations to the axis of the length of the perpendicular from the origin on PQ the distance of the mid-point of PQ from the mid- point of RS the coordinates of the point of intersection of PQ and RS 10 Find κ in order that 9x2 4y2 4y may represent two straight lines 11 Prove that in an equation of the second degree no transformation of rectangular axes with the same origin can alter the sum of the goefficients of x2 and y2 Mention another function that is unaltered If 6x2 j- xy 3y2 be transformed into Ax2 By2 find the values of and 12 Find the coordinates of the centre and the radius of 2x2 2y2 4x by Obtain the length of the tangent to this circle from th point Η