Exercise 98. The literal notation 1. If 3 oranges cost x cents, find the cost of each. If a oranges cost m cents, find the cost of each. 2. Find the altitude of a rectangle whose area is 4ax and whose altitude is a ; whose altitude is 2x. 3. Find the total cost of 3 articles at x cents each, 20 articles at m cents each, and a articles at b cents each. 4. If a man can do a piece of work in 3 days, what part can he do in 1 day? If he can do the work in 6 days, what part can he do in 1 day? What part in 3 days? 5. If a man can do a piece of work in d days, what part can he do in 1 day? What part in 5 days? What part in m days? 6. A salesman begins in a new position at a salary of $600 a year. His salary is increased $50 a year for t years. What is his annual salary at the end of t years? 7. A passenger train is running at the rate of 12 miles an hour, and increases its speed at the rate of 4 miles an hour each minute. Find its rate after 6 minutes. Find its rate at the end of t minutes. 8. Write a formula which gives the number of dollars, N, in d silver dollars, ƒ five-dollar bills, 20 half-dollars, q quarters, s dimes, and 27 pennies. 9. Write a formula for the number, N, of seats in a room with d double desks, n chairs, and 12 settees each seating 4 persons. 10. A piece of sheet-iron weighs 1 pound to the square foot. How many pounds will a rectangular piece (n+2) feet long and w feet wide weigh? 11. Write a formula which gives the number of cents, C, in r dollars, 5 quarters, d dimes, and 12 nickels. 12. How many rectangular blocks x in. by y in. by z in. can be placed in a rectangular box a ft. by b ft. by c ft.? Exercise 100. Equations and Formulas Solve for x and check : 1. 3x-8+2x=x+42. 5. 5x=m. 9. 2x2=50. 13. The volume of a ring (Figure 83) is given by the -R---> FIG. 83 15. If a wrought-iron bar 2 in. deep and 1 in. wide is supported at both ends and loaded in the middle with a weight of W pounds, then the amount the bar is bent, called the de flection, is given by the formula D= where W WL3 32 X29 × 106' = the load in pounds, and L = the length in inches. Find D if W=2 T., and L-6 ft. Find D if W-2 T. and L=4 ft. 16. The resistance of the air to the flight of a bullet is said to be given by the formula F = .0139 d2(v—800), where F is the resistance in pounds, d is the diameter of the bullet in inches, and v is the velocity of the bullet in feet per second. In this formula v is supposed to be greater than 1100. Find the resistance of the air to a bullet which has a diameter of .3 in. and a velocity of 1500 ft. per second. 17. Find the resistance of the air to a bullet .44 in. in diameter and with a velocity of 2000 ft. a second. Exercise 101. Ratio, proportion, and similar figures 1. Define ratio. What are the terms of a ratio called? 2. Define proportion. What are the means? What are the extremes? State a principle that is used in solving a proportion. 3. What is meant by the specific gravity of a substance? Solve the following proportions : 8. A liter of air weighs 1.293 g. A liter of water weighs 1 Kg. Find the specific gravity of air compared to water. 9. Find the weight of air in a room 10 meters by 8 meters by 4.5 meters. 10. Chlorine gas is 2.44 times as heavy as air. What is the specific gravity of chlorine gas compared to air? 11. A legacy of $1200 is divided between two persons in the ratio of 2 to 3. Find how much each receives. 12. The ratio of the cement to the sand in a mixture of concrete is 1 2. How much cement and how much sand in 20 cu. ft. of concrete? 13. Define similar figures. 14. Name the corresponding parts in the similar triangles in Figures 30 and 31, p. 77. 15. In two similar triangles ABC and A'B'C', AB = 12 ft., BC=20 ft., A'B'=8 ft., and A'C' = 12 ft. Find AC and B'C'. 16. Two observers at A and B see an airplane fly over the line AB. From A the angle of elevation of the airplane is 75° and from B, 68°. The distance from A to B is mile. Make a drawing to scale and find, by measuring, the height of the airplane. Exercise 102. Practical measurements 1. What is a board foot? How many cubic inches in a board foot? How many board feet in a cubic foot? 2. If you are given the length of a stick of timber in feet, the width in inches, and the thickness in inches, how do you find the number of board feet the stick contains? 3. In a rain of 1 in. how many barrels of water will fall on 1 acre? 4. A lean-to roof has a span of 12 ft. and a rise of 4 ft. It is 20 ft. long. Find the number of square feet of felt roofing required to cover it. 5. Find the number of gallons of water falling on this roof in a rain of in. 6. How deep will this amount of water fill a cylindrical cistern which is 8 ft. in diameter? 7. A tin pail is 14 in. in diameter at the top and 11 in. at the bottom. How much water will fall into this pail during a rainfall of 1 in.? 8. A bushel of ear corn is commonly taken to be 21 cu. ft. How many bushels are there in a crib 74 ft. long and 12 ft. wide, if the corn is 6 ft. deep? 9. Water is flowing from a pipe which is 12 inches in diameter, at the rate of 10 miles an hour. How many gallons flow out in 10 minutes? 10. A bushel of ear corn weighs 70 lb., and a bushel of shelled corn weighs 56 lb. What per cent of the weight of a bushel of ear corn is cobs? 11. A bushel of shelled corn is 2150.4 cu. in. What per cent of the volume of a bushel of ear corn is cobs? See problem 8. |