-------------------------------------- / (6-2/7 - 4-3/9) x 8-7/16 / ------------------------ x 67873.367, and show your work. \/ 4-4/12 5. The population of a certain town in 1880 was 7,095; it having increased 25 per cent. in ten years, what was it in 1870? Show your work. 6. How many feet, board measure, in the flooring of a room 20 feet by 30 feet and 21/2 inches thick? 7. Find value of x and y in the following equations: 2 x + 3 y = 33 4 x - y = 17. 8. Find value of x in equation x squared - x - 40 = 170. 9. Find value of x in equation -------- a / a squared - x squared x - + / ------- = - b \/ x squared b 10. Explain the meaning of the expression a1/2 x b3/4. 11. What is a logarithm? 12. What is the base of the common system? 13. In making what calculations are logarithms useful? 14. How do you find the logarithm of a number in a table of logarithms? 15. What are similar triangles? 16. How are similar triangles proportioned to each other? 17. The sides of a polygon being prolonged, what is the sum of all the exterior angles equal to? 18. How do you pass the circumference of a circle through three given points not in the same straight line? 19. How do you describe a square in a circle? [Illustration] 20. In the triangle, b being a right angle, what proportion does d b bear to a d and d c? 21. How do you inscribe a regular hexagon in a circle? 22. What proportion do circumference and areas of circles bear to their radii? 23. How do you find the area of a regular polygon? 24. Of an irregular polygon? 25. Of a circle? 26. How do you find the solid contents of a cylinder? 27. Of a wedge? 28. Of a pyramid? 29. Find the contents of the wedge, base 20 feet by 30 feet, height 10 feet, edge 15 feet. 30. State the prismoidal formula; would you use it in calculating earthwork? 31. Is a simple question in calculating areas.--Ed. _Eng. News_. 32. How many and what parts of a plane triangle must be given to find the rest? 33. Define the terms sine, co-sine, tangent, and co-tangent. 34. What are natural sines, co-sines, etc.? 35. What is a table of logarithmic sines, co-sines, etc.? 30. Two sides and two angles of a plane triangle being given, how do you find the other parts? 37. When two sides of a plane triangle and their included angles are given, how do you find the other parts? 38. In the right-angled triangle, A B H express algebraically the value of the sine, co-sine, tangent, and co-tangent of angle A in terms of a, b, and h, they being the altitude, base, and hypothenuse of the triangle. 39. What is the law of gravitation? 40. Do you understand that there is any difference in the meaning of the terms gravitation and gravity? 41. What is the law of falling bodies? 42. Express algebraically this law, taking v = velocity of falling body; g = acceleration of gravity; and h = height. 43. What is the center of gravity of a body?