other 7 gallons per minute. How long will it take each to empty the tank? How long will it take both together? 12. A parlor is 18 feet long, 15 feet wide. Make a diagram. showing how carpet 27 inches wide can be laid without cutting the carpet lengthwise. Which would be the better way to lay carpet 30 inches wide in the above room? 13. Calculate the number of running yards of carpet 30 in. wide needed for the floor of the above room, including 4 yards wasted in matching the pattern. Find the cost of carpeting the room at 95 cents per running yard for carpet, 5 cents per square yard for lining, and 10 cents per running yard for sewing and laying. 14. A rug 18 feet long, 15 feet wide, is placed in the centre of the floor of a room 21 feet long, 18 feet wide. What is the width of the strip left uncovered? Find the area of the uncovered space? 15. A room is 18 feet wide, 24 feet long, 9 feet high. There are two doors 4 feet wide, 74 feet high; two windows 4 feet wide, 6 feet high; and a fire-place 5 feet square. How many square feet of plastering will there be on the walls and ceiling, deducting for a baseboard 12 inches wide? How many running feet of baseboard will be needed? Draw "development" of the above room, showing the four walls and the ceiling, and locating the doors, the windows, and the baseboard. Do not use baseboard where it is not required. 16. At the rate of $1,400 for a pile of lumber 25 ft. long, 20 ft. wide, 10 ft. high, what is the value of a pile 50 ft. long, 40 ft. wide, 20 ft. high? 17. If it costs $14 to paint the walls and the ceiling of a room 25 ft. long, 20 ft. wide, and 10 ft. high, what will it cost to paint the walls and the ceiling of a room 50 ft. long, 40 ft. wide. and 20 ft. high? SQUARE ROOT. 1029. Squaring a number is multiplying the number by itself. The square of 8 = 8 x8 = 64. 1030. The square of a number is indicated by writing a small 2 a little to the right of the upper part of the number. 52 25, 122 = 144. What is the square of 4? Of 6? Of 7? Of 9? Of 10? Of 11? Square 13. 15. 21. 16. 19. 14'? 17? 242=? 332=? 1031. The square of 25 = (20+5) × (20+5). 202 + 2(20 × 5) + 52 = 400 + 200 + 25 = 625. of the sum of two numbers is equal to the twice the product of the first by the second the square of the second. 1032. The square of the first square = 13 (103)2= 102+2 (10 × 3)+32=? 18 = = (108)2= 100+ 160+64 =? 27' (20+7)2 400 +280+49=? 1033. Oral Exercises. 1034. The square root of 4 is 2; of 9 is 3; of 16 is 4; of 25 is 5. 1035. Give the square root of 36. Of 64. Of 81. Of 121. Of 49. Of 100. Of 144. 1036. The sign of square root is v √81=9. √121 = ? √25=? √49=? 1037. Find the square root of 169. 102 = 100. 202 = 400. The square root is between 10 and 20; it is, therefore, 10+ a second number. 169 = 102 + 2(10 x second) + second 2. 169 100+ 20 x second + second 2. 20 x second + second2 = 69. From this it appears that the second number is 3, since 20 × 3 + 32 = 69. 40 × 280, trial divisor) 516(6 second number) Ans. 46. 480 1040. Instead of multiplying the trial divisor by the second number, and then ascertaining whether the remainder is the square of the second number, the second number is added to the trial divisor and this sum is multiplied by the second number. 40 (first number) 2,116 1,600 (2 × 40) + 6 = 86) 516(6 second number) 516 Ans. 46. 4 6 Ans. 21'16 16 1041. In practice, the work is shortened by omitting the ciphers. First, point off in periods of two figures, commencing at the right. Find the greatest square in the first period, and place the root in the quotient. Subtract the square from the first period. Bring down the next period. Multiply the first quotient figure by 2, and use it as a trial divisor. Place the second figure in the quotient. Affix it also to the trial divisor. Multiply the two figures in the trial divisor by the second quotient figure. 1042. Slate Exercises. 86) 516 516 1044. An Invoice (English). Invoice of 3 bales Linen Goods forwarded by rail to Glasgow, for shipment thence per S.S. Anchoria to New York, to order, and for account and risk of Messrs. Robinson & Co. 1. Find the duty in U. S. money at 50% ad valorem. £= $4.8665. 2. What is the cost in English money of crockery amounting to £166 13s. 4d. less a discount of 5 and 5% ? RATIO. 1045. Ratio is the relation which one number has to another of the same kind. 1046. The first term of the ratio is called the antecedent; the second, the consequent. The ratio of 3 to 6, $9 to $18, 15 cows to 30 cows may be expressed 8, 1, 15. They are each equal to §. |