1. The base is $177.50 and the percentage $11.04. What is the rate? base? Ans. 6,78%. 655 2. The percentage is 17.47 and the rate 7%. What is the Ans. 249.57. 3. A lot of coal was bought for $791. For what must it be sold in order to make 31% ? Ans. $1,036.21. 3. If a wheel has a circumference of 6.75 feet how many times will it revolve in going 74 miles? Ans. 5,671 times. 4. What is the capacity in gallons of a tank that will hold Ans. 234 gallons. 3 hhds. 1 bbl. 13 gals. 3 qts.? EXERCISE V. Change to higher denominations: 1. 34,741 gills. 2. 187,439 pints. 3. Ans. 17 hhds. 14 gals. 2 qts. 1 pt. 1 gi. 84,793,112 ounces. Ans. 2649 T. 15 cwt. 69 lbs. 8 oz. 4. What is the weight of 352 gills of water? EXERCISE VI. Ans. 91.63 lbs. What is the sum of the following? 1. 8° 17' 32" and 6° 14′ 37′′. Ans. 14° 32' 9". 2. 7 mi. 1 rd. 5 yds. 2 ft. 11 ins., 9 mi. 16 rds. 2 yds. 1 ft .7 ins., and 5 mi. 14 rds. 1 yd. 2 ft. 1 in. Ans. 21 mi. 32 rds. 4 yds. 2 ft. 1 in. 3. What are the contents of three barrels which contain respectively 45 gals. 2 qts., 47 gals. 3 qts., and 44 gals.? Ans. 2 hhds. 11 gals. 1 qt. three lots which contain respecA. 145 sq. rds. 2 sq. ft., and Ans. 28 A. 88 sq. rds. 1 sq. yd. 4. How much land is there in tively 7 A. 89 sq. rds. 7 sq. ft., 11 9 A. 14 sq. rds. ? Subtract EXERCISE VII. 1. 18 gals. 3 qts. 1 pt. from 27 gals. 2 qts. Ans. 8 gals. 2 qts. 1 pt. 2. 3 T. 9 cwt. 81 lbs. 13 oz. from 15 T. 7 cwt. 47 lbs. 1 oz. Ans. 11 T. 17 cwt. 65 lbs. 4 oz. 1. 2. 3. 12 gals. 2 qts. 1 pt. 3 gi. by 7. Ans. 1 gal. 3 qts. 24 gi. How long will it take to travel 1 mile, at the rate of 74 miles in 9 hrs. 37 mins.? Ans. 7 mins. 473 secs. 4. How long will it take to pump full a tank which has a capacity of 3700 gals. 3 qts. 1 pt., if the rate of delivery is 19 gals. 1 qt. 1 pt. per second? Ans. 3 mins. 11 secs. (Suggestion.-Reduce both divisor and dividend to pints before dividing.) EXERCISE IX. 1. What is the second power or square of 79? 11,2 55 Ans. 6,241 Ans. 753,571 Ans. -243 16807 Ans. 42,849 Ans. .000000046656 1. What is the difference between involution and evolution? Find the square roots of the following: 2. What is the value of x when b4 and h = 6, 3. If m = 8, n = 6 and e= 3, find the value of x from 4. Multiply 3 a c-9 b c2 + 6 c by 2 a-7 c. 5. Divide 9 m2 x2 + 24 m x y + 16 y2 by 3 mx + 4 y. EXERCISE II. 1. Multiply 3 ab+6c-1 by 2 ca b. 2. 3. Multiply 6 m n − 2 m + 3 n-1 by 4 n-3 m + 4. Divide 12a2 x + 8 a x y + 6ax-6 ay — 4 x y2 — 3 y by 2 ax-y. 4. Divide a3 2 a2 b + 2 ab2 + b3 by a2 + ab + b2. 5. (x2+y3) ( x − y) x2 y2 = ? EXERCISE III. Find the value of x in the following equations. 3. 4. 2 a x = a b 2 a x + 28, when a = 2, and b 16. If m = e in the following equation? 1. If I 14 and R5 what is the value of W from the equation W = 12R. 2. If S9000, E.85, p = 115 and D = 60 find t from the formula 4. If S 887.92 feet and g = 32.16 find the value of t. 1. How many square feet in a square 27 rods on each side? 2. The area of a rectangle is 37.8 square feet, and the base is 7 feet. What is the altitude? 3. The diagonal of a trapezium is 21 feet long, the perpendiculars to this diagonal from the vertices on either side are 9 feet and 8 feet. What is the area? Ans. 178.5 square feet. |