Miscellaneous Problems 1. What is the bank discount of a note of $450, due in 6 months, discounted at a bank at 6% ? 2. What are the proceeds of a note of $240, due in 4 months, discounted at a bank at 41% ? 3. A note due in 3 months was discounted at a bank at 8% and yielded $196 proceeds. What was the face of the note ? The discount is 2% of the face, and the proceeds 98% of the face. Therefore $196 = 98% of the face, and the face = $ 196 - .98. 4. A note due in 9 months was discounted at a bank at 4% and yielded $ 3055.50 proceeds. Find the face of the note. 5. A note due in 2 months was discounted at a bank at 6% and yielded $561.33 proceeds. Find the face of the note. 6. What is the gain per cent in buying a horse for $150 and selling him for $180 ? 7. What is the loss per cent in buying a house for $2000 and selling it for $ 1950 ? 8. On a bill of goods with a list price of $200, is it better to accept trade discounts of 25 and 5, or of 20 and 10, and how much is the difference ? 9. I bought goods, the price of which was $360, at discounts of 20%, and 16%. I sold the goods for $300. What was the gain per cent ? 10. What is the amount of a bill of goods, the list price of which is $425.75, subject to trade discounts of 15% and 12%? 11. I sold goods for $280, at an advance of 12% above the cost. What was the cost ? Problems from Physics 1. The specific gravity of iron is 7.2. What will a cubic foot of it weigh in the air ? 2. What will a cubic foot of iron weigh in water? 3. The specific gravity of marble is 2.8. What will 144 cu. in. of it weigh in the air ? 4. What will 144 cu. in. of marble weigh in water ? 5. If the specific gravity of sea water is 1.026, what is the weight of a cubic foot of sea water? 6. How much less will a cubic foot of any substance weigh in sea water than in air? 7. How much less will a cubic foot of any substance weigh in sea water than in pure water ? 8. If of a cubic foot of silver weighs 4735 ounces when weighed in pure water, what is its specific gravity ? 9. If of a cubic foot of lead weighs 2587 ounces in water, what is its specific gravity ? 10. The specific gravity of milk is 1.03. What is the weight of a cubic foot of milk ? 11. How much less will an object which contains 1 of a cubic foot weigh in milk than in the air ? 12. How much less will it weigh in milk than in pure water ? 13. } of a cubic foot of gold would weigh 3850 ounces in the air. How much would it weigh in water ? 14. What is the specific gravity of gold ? 15. Find how much a cubic inch of gold would weigh in the air. Cones Fig. 1. Fig. 2. See pp. 45, 167. The volume of a cone is of the volume of a cylinder having an equal base and altitude, or of the product of the area of its base and its altitude. 1. What is the volume of a cone, if the area of the base is 13 feet and the altitude 9 feet ? 2. What is the area of the base of a cone whose diameter is 164 inches ? . 3. What is the volume of a cone, if the diameter of the base is 161 in. and the altitude 30 in. ? 4. In Fig. 1, what kind of a triangle is formed by the slant height AB, the altitude AC, and the radius BC? 5. If AB is 25 inches, and BC 15 inches, what is the altitude AC? 6. What is the altitude of a cone the diameter of whose base is 24 ft. and whose slant height is 20 ft.? 7. Find the volume of a cone the circumference of whose base is 31.416 ft. and whose altitude is 12 ft. Find the diameter and area of the base. 8. How many cubic feet are there in a cone whose altitude is 12 ft. and the diameter of whose base is 4 ft. ? 9. Find the convex surface of a cone the circumference of whose base is 37.6992 ft. and whose slant height is 10 ft. Powers and Roots Review p. 118. V4 indicates the square root of 4; $8 the cube root of 8; 516 the fourth root of 16, etc. 32 indicates the square of 3 or the product of 3 and 3. 43 indicates the third power of 4, or the product of 4, 4, and 4. The small figure indicating the power is called the exponent. 1. 52 = ? 6. (1)2 = ? 2. 78 = ? 7. (3)= ? 3. 104 = ? 8. (3)4 = ? 4. 95 = ? 9. .98 = ? 5. 188 = ? 10. .154 = ? 11. V81 = ? 16. V = ? 12. V100 = ? 17. V.64 = ? 13. 64 = ? 18. V.216 = ? 14. 3125 = ? 19. 24 = ? 15. 216 = ? 20. V = ? Find the square root of the following: 21. 169 25. 484 22. 256 26. 784 23. 324 27. 1024 24. 400 28. 1225 Find the cube root of the following: 29. 216 33. 8000 30. 343 34. 13,824 31. 729 35. 19,683 32. 5832 36. 32,768 |