Calendar: 1849-1850 Page 298

29G APPLIED SCIENCES Two dice one having and the otlier 10 faces are marked with the natural numbers beginning from unity tind the number of different throws that can he made If straight line touch circle and from the point of contact straight line be drawn cutting the circle the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the circle If the square root of -f -f ΰ -f can be -f -f expressed by ν χ vy -j- ν then rational hanker borrows money at per cent interest payable annually he lets it out at per cent interest payable quarterly and gains by the transaction 250 what was the amount of the sum lent Let Β be triangle and Β BC produced to £and bisect Ζ Β AC by AG and Ζ CAE by AD meeting BD in and then Β1 is divided harmonically in and Inscribe circle in regular pentagon If cos sin and e- sin then tan w2J tan 10 Α Β Β CD are three unequal lines placed in the same continued straight line find the position of an eye from which they may all appear to be of the same magnitude 11 Kind two numbers whose ratio equals the sum and inverse ratio the difference of their squares 12 Find and when xy 20 XZ 24 yz 38 13 Trove that η cos cos θ -j- See cos "cos