11. x2+12-3x+2=0, 2x2+212-5x-√3y+3=0,

2x2+212-7x+√31 +6 = 0.

7.

The focus is a point 30 ft. below the point from which the ball was dropped; the directrix is a line parallel to the direction of the train 30 ft. above the roof.

8.

10.

(i.) 1200 lbs. ; (ii.) 34800 lbs.
51 inches.

9. (i.) 1:3; (ii.) 1:2e+1.

2. (x-2y)(x2+2xy+4y2), (x−8y)(x − 16y), (x2+xy+y2)(x2−xy+y2).

1.

V. STATICS AND DYNAMICS.

(i.) Equilibrium impossible; (ii.) Parallel to sides of a right-angled triangle.

9.

At height 3520 ft., 11 secs. after the first was fired.

11. Range 7500, velocity 20241 in direction tan-1 to horizontal.

15

10. If the equation to the circle be x2+ y2 + Ax + By + C = 0,

8. B = 54° 56′ 48′′,

C = 83° 3′ 12′′, c = 209 174; or B = 125° 3′ 12",