15. A degree of longitude in latitude 45° is about 70% of the length of a degree on the equator. Calling the latter length 69 miles, how long is a degree of longitude in latitude 45°? 16. At $44 per acre, how much land can be bought for $968? 17. A number of marbles divided among 29 boys gives each 16 marbles, and leaves a remainder of 26. How many marbles are there? 18. What is the monthly salary of a clerk who receives $1,500 per year? 19. How many revolutions in a mile, 5,280 ft., are made by a locomotive wheel 16 ft. in circumference? 20. How many feet of fence are there around a lot 49 ft. wide, 87 ft. long? 21. How many bricks 8 in. by 4 in. by 2 in. would make a cubic foot? 22. 13 is one factor of 1,001. Find the other two prime factors. 23. What are the three equal factors of 343? 24. What is the square root of 1,225? 25. At 4 miles per hour, how long will it take a man to walk 371⁄2 miles? 26. What will be the cost of 9 dozen hats at $1.331 each? MEASUREMENTS. 1137. Find the area of each of the following triangles and its altitude. When the area of a triangle is known and the length of the base, how can its altitude be calculated? 1. Base, 51 ft.; other sides, 20 ft. and 37 ft. 2. Base, 21 yd.; other sides, 13 yd. and 20 yd. 3. Base, 148 rods; other sides, 39 rods and 113 rods. 4. Base, 28 chains; other sides, 17 chains and 25 chains. 5. Base, 75 inches; other sides, 20 inches and 65 inches. 1. A and B rented a field for a year for $175. A put in 6 horses for the whole time, B put in 5 horses for 11 months and 3 horses for 5 months. How much of the rent had each to pay? 2. A bankrupt surrenders property worth $1,287 for the benefit of three creditors to whom he owes $750, $1,125, and $1,245, respectively. How much should each creditor receive? 3. Four persons rented a pasture for 26 weeks. K put in 50 sheep and L 60 sheep for the whole time, M put in 70 sheep for 20 weeks, and N 90 sheep for 22 weeks. How much of the rent, $130, had each to pay? 4. A employs a capital of $2,500 in business, and at the end of 3 years takes into partnership B, who furnishes $4,000. Four years later they are joined by C, with a capital of $5,000. At the end of 12 years from the commencement of the business, the profits, amounting to $15,000, are divided. What amount should each receive? A's money is in the business how many years? B's, how many years? C's, how many? 5. Four butchers rent a field, and pay for 6 months' rent $152.50. The first puts in 20 oxen for 10 weeks and 50 sheep for 8 weeks; the second, 25 oxen for 8 weeks and 30 sheep for 7 weeks; the third, 18 oxen for 10 weeks and 10 sheep for 12 weeks; the fourth, 30 oxen for 12 weeks. What share will each have to pay, counting 3 sheep equal to 1 ox? 6. A wall 700 yards long was to be built in 29 days. At the end of 11 days, 18 men had built 220 yards of it. How many extra men had then to be put to work, so that the wall might be completed in the given time? 7. If 5 needlewomen can do a piece of work in 11 days of 9 hours each, how long will it take 3 needlewomen to do two such pieces, supposing them to work 10 hours each day? 8. If 14 men can mow 168 acres in 12 days of 8 hours 15 minutes each, how many acres can 20 men mow in 11 days of 7 hours 48 minutes each? 9. If 12 men can do a piece of work in 20 days, what number of men will be required to do four times as much work in a fifth part of the time? 10. A ship sailed with a crew of 60 men, and provisions for 34 days, and 10 days afterwards, 12 persons were received on board from a sinking vessel. How long would the provisions last the 72 persons then on board? How long would the provisions last the 60 persons at the time the sinking vessel was met? 11. If 76 boards, each 14 feet long and 10 inches wide, are worth $19.76, how much would 50 such boards be worth? 12. If 7 men receive $126 for 5 weeks' work, how much should they receive for 9 weeks' work? 13. If for 7s. 6d. I can buy 9 lb. of raisins, how many pounds can I buy for £56 16s.? 14. A field of grain was to be cut down by 40 men in 10 days. Eight of the men, however, failed to come. How long did it take the others to do the work? 1884 317,853,850 733,669 1,323,861 6,287,462 7,180,990 8,266,643 1,682,120 8,503,581 Average Tax Rate per $1,000 of Valuation. 1891 466,914,249 589,178 2,159,879 9,241,130 483,738,129 888,297 2,240,613 10,324,617 1892 Av. of 10 yr. Find for each year the total tax levy, and the tax rate in dollars, cents, and mills per $1,000 of assessed value. Find the average assessment per year; the average tax levy for state, county, and city purposes; and the average tax rate. SURFACES OF PRISMS AND CYLINDERS. 1141. Slate Exercises. NOTE. The pupils should be encouraged to make cardboard models of the forms studied. 1. Find the convex surface of a square prism, one side of its base being 4 inches and its height 6 inches. Draw the development. NOTE. The convex surface is the surface exclusive of the bases. 2. Find the convex surface of a triangular prism, each side of whose base measures 4 inches and whose altitude is 6 inches. Draw the development. 3. Find the convex surface of an hexagonal prism, each side of its base being 4 inches and its altitude 6 inches. Draw the development. 4. Can you show that the convex surface of a prism is found by multiplying the perimeter of the base by its altitude (height)? 5. Find the convex surface of a cylinder, the diameter of its base being 4 inches and its height 6 inches. 6. How do you find the entire surface of a prism or cylinder? 7. What is the entire surface of a cube whose side is 7 inches? Of a cube whose side is x inches? 8. The entire surface of a cube is 216 sq. in. What is the length of one side? 9. The convex surface of a cube is 144 sq. in. Find the entire surface. |