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Any cheap, light paper like the sample previously sent you may be used. Do not crowd your work, but arrange it neatly and legibly. Do not copy the answers from the Instruction Paper; use your own words, so that we may be sure you understand the subject. 1. Find the square roots of each of the following: 3. Find the logarithm of 398 4. Find the logarithm of .0062 5. Find the number whose logarithm is 2.4472 6. Find the cube root of 638 by logarithms. 7. In an ingot of brass weighing 105 pounds, if the copper used weighed 20 pounds less and the tin 20 pounds more, the weight of the copper would still be 5 pounds more than the weight of the tin. What is the weight of each? 8. Find the weight of a granite column 22 feet high and 2 feet 6 inches in diameter. (Granite weighs about 156 pounds per cubic foot.) 9. A set of specifications requires that a hole 100 ft. square and 20 ft. deep be blasted in solid rock. If the cost per cubic yard for blasting and labor is $3.00, how much will the excavation cost? How many days will be required to plaster the four walls if 100 sq. yds. can be placed in 1 day of 8 hours? 10. A stand pipe can be emptied by three taps; by the first alone it can be emptied in 80 minutes, by the second in 200 minutes, and by the third in 5 hours. In what time can it be emptied if all the taps are opened? 11. In a certain weight of gunpowder, the saltpeter composed 6 lbs. more than half of the lot, the sulphur 5 lbs. less than a third, and the charcoal 3 lbs. less than a fourth; how many pounds were there of the three ingredients? 12. If 15 masons build a brick wall in 98 days, how long will 36 masons be in doing the same work? 13. Divide 105 into two parts, so that one part diminished by 20 shall be equal to the other diminished by 15. 14. If a locomotive burns 5 tons of coal in running 100 miles, how many pounds will it burn in running 9 miles? 15. The height of a certain conical roof is 20 feet, and the diameter of the circular base is 60 feet. Find the number of square feet of tarred felt that will be required to cover the roof, neglecting laps at seams. 16. A contractor agrees to move a pyramidal marble monument, whose base is 40 square feet, and whose height is 60 feet. If the marble weighs 163 lbs. per cubic foot, and the contractor receives $3.00 per thousand pounds for the moving, how much money does the contractor receive? 17. A cylindrical stand pipe is 100 feet high and 20 feet in diameter. What is its capacity in gallons? 18. A railroad cut has a trapezoidal cross-section. The depth of the cut is 11 ft., the top is 40 ft. wide, and the bottom is 25 ft. wide. If this cut is 200 ft. long, how many cubic yards of earth have been removed? 19. A certain field has the shape of a right triangle, whose hypotenuse is 100 rods; the altitude and base are 60 and 80 rods respectively. Find the area. 20. In a right triangle, whose sides are a and b and whose hypotenuse is c, what relations of a, b, and c represent the sine, the cosine, and the tangent of the angle formed by the sides. b and c? 21. The perimeter of the base of a regular hexagonal prism is 60 feet; the height is 20 feet. Find the volume. Find the lateral area of one side. 22. In the following equation, remove the parentheses and solve for the value of x: 10x = (x −6) — (2x - 8 - 6x-10) -(x-6). |