By Robert Milne

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**Additional resources for A theory of programming language semantics, part B**

**Sample text**

If yl9 y2, j>3, . . , y2n+1 are an odd number of ordinates which are at equal distances h apart, then the area bounded by the curve, the x-axis, yx and j>2«+i *s given by A % \h{y1+y2n+i+2(y2+ys+ . . 4-^n-i) Example. The table gives corresponding values of the velocity in metres per second and the time in seconds from the beginning of the motion of a particle moving along a straight line. The particle starts from a point O in the line. (a) Draw a v, t graph of the motion and use your graph to estimate the acceleration of the particle at time / = 30 second.

E. ^ + Γ χ έ " Γ Χ ^ = 0· (b) The sum of the vertical components of the forces is zero. e. Tx ^+TX 17Γ A-=^- -^-OOlg = 0. «sO-0055^. The horizontal force is 5-5 X 10~8 g N and the tension in the string is 8 X10""8 g N. 7. In each of Exercises 1-6 find, correct to two significant figures, the magnitude of the resultant of the forces shown in the figure (Fig. 14) and in each case calculate, correct to the nearest degree, the angle which the resultant makes with the largest force. In each case, also, obtain an approximation to the magnitude and direction of the resultant by drawing a polygon of forces.

1. A uniform rod AB is 8 m long and of mass 10 kg. The rod rests inclined at 30° to the horizontal with the upper end A against a smooth vertical wall. The lower end B is fastened to a string, the other end of which is attached to the wall at C, vertically above A. Find the tension in the string. 2. A uniform beam 12 m long is hinged at A to a wall and is of mass 40 kg. It is held at 40° with the upward vertical by means of a chain 8 m long making an angle of 30° with the downward vertical, and attached to a point on the wall vertically above A.