Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

13. What will be the amount in the last problem if the bank pays 41% per annum?

14. What should be paid to-day for an annuity of $500 a year, for 12 years, if money is worth 31%, compound interest?

NOTE. First find the sum of the payments and interest at the end of the 12 yrs., and then the present worth of that sum.

15. What should be paid to-day for an annuity of $300 a year, for 10 years, if money is worth 4%, compound

interest?

16. What should be paid to-day for the assurance that 5 yrs. hence I shall begin to receive $500 a year, for 8 yrs., if money is worth 44%, compound interest?

NOTE. Find what should be paid, if paid all at once, 5 yrs. hence; then find the present worth of that sum.

17. If interest is reckoned at 6%, what sum of money must be paid annually, beginning a year hence, to clear off a debt of $10,000 in 5 equal payments?

18. If interest is reckoned at 6%, what is the amount of each of 12 equal semi-annual payments, the first to be paid 6 mos. hence, required to clear off a debt of $24,000?

CHAPTER XXV.

MISCELLANEOUS PROBLEMS.

1. Make six different numbers with the digits 1, 2, 3, and find their sum.

2. Make six different numbers with the digits 2, 3, 5, and find, by logarithms, their continued product.

3. Make six different numbers with the digits 8, 7, 3, and find, by logarithms, their continued product.

4. Find, by logarithms, the missing term in each of the following proportions:

(i.) 7.133.57 4.18:? (iii.) 7.37 :? :: 86.1: 43.7. (ii.) 5.89 76.3: ?: 38.7. (iv.) ?: 69.7:: 3.79: 29.4. 5. Find, by logarithms, the values of .08; 2734; 21.97*.

73.6.

6. Find, by logarithms, the values of 9.71; 7.935.

NOTE. In solving the following problems use logarithms whenever they can be used with advantage.

7. What is the horizontal distance between two points, when the air-line distance is 1534 ft., and the difference of level 34 ft.?

8. Find the horizontal distance when the road distance is 1 mile, and the rise 347 ft.

9. If the road distance is half a mile, and the horizontal distance 2513 ft., find the difference of level.

10. The diagonal of a rectangular floor is 34.6 ft., and the width is 17.8 ft. Find the length of the floor.

11. The height of a tower on a river's bank is 55 ft., the length of a line from the top to the opposite bank is 78 ft. Find the breadth of the river.

12. The number of seamen at Portsmouth is 800, at Charlestown 404, and at Brooklyn 756. A ship is commissioned whose complement is 490 seamen. Determine the number to be drafted from each place in order to obtain a proportionate number from each.

13. Show, without division, that 36,432 contains 8, 9, 11 as factors.

14. Find the smallest multiplier that will make 47,250 a perfect cube.

15. Find the proper fraction which, when reduced to a continued fraction, has for quotients 1, 3, 5, 7, 2, 4. 16. If the meter is equal to 1.09362 yds. find a series of four fractions that will express more and more nearly the true ratio of the meter to the yard.

17. Find the square factors contained in 33,075.

18. The top of St. Peter's, Rome, is of a mile above the ground, and that of St. Paul's, London, is

of a

mile. By how many feet does the height of St. Peter's exceed that of St. Paul's?

19. How many days elapsed between the annular eclipse of May 15, 1836, and that of March 15, 1858?

20. In a gale, a flag-staff 60 ft. high snaps 28.8 ft. from the bottom; and, not being wholly broken off, the top touches the ground. If the ground is level, how far is the top from the bottom?

21. Seventeen trees are standing in a line, 20 yds. apart from each other; a person walks from the first to the

second and back, then to the third and back, and so on to the end. How far does he walk?

22. A level reach in a canal is 14 mi. long and 48 ft. broad. At one end is a lock 80 ft. long, 12 ft. broad, and with a fall of 8 ft. 6 in. How many barges can pass through the lock before the water in the canal is lowered 1 in.?

23. Find the capacity, in liters and in bushels, of a box 1.7m long, 87cm wide, and 31cm deep.

24. Find the number of kilograms of olive oil, specific gravity .915, to fill a vessel 2.3m long, 1.8m wide, and 74cm

deep.

25. How many tons in a block of marble 4 ft. long, 34 in. wide, 17.3 in. thick, if its specific gravity is 2.73?

26. Find the surface of a sphere 18.3 in. in diameter.

NOTE. The area of a circle is 3.1416 times the square of the radius; and the surface of a sphere is 4 times the area of a circle of the same radius as the sphere.

27. Find the number of acres in a circular field 213 yds. 2 ft. across.

28. How many cubic inches in a 10-inch globe? in a 20

inch globe? What is the ratio of their volumes? 29. How many balls 3 in. in diameter can be cast from a pig of iron 7 ft. long, 6.7 in. wide, 3.8 in. thick, if the waste in melting and casting is reckoned at 31% ? 30. Find the difference in length, at 80° F., of a glass and a steel rod, each 3 ft. long at freezing point, if the expansion at 100° C. is .00085 for glass and .0012 for steel.

31. A grain of gold is beaten out in leaf to cover 56 sq. in. What weight will be required for gilding the faces of a cube whose edge is 3 ft.?

32. What premium must be paid, at the rate of 13%, for insuring a vessel worth $117,750, in order that in

the event of loss the owner may receive both the value of the ship and the premium?

33. By selling goods at 60 cts. a pound, 8% on the cost is lost; what advance must be made in the price in order to gain 15% on the cost?

34. Divide $27.12 among three persons, giving the second $5 less than the first, and twice as much as the third.

35. The population of a city in 1880 was 12,298, showing a

decrease of 81% on its population in 1870; in 1870

there was an increase of 71% on the census of 1860. What was its population in 1860 ?

36. Find the increase of income obtained by transferring $2500 from 3% stocks at 94 to 4% stocks at 105.

37. Each person breathing in a closed room spoils the air at the rate of about 8 cu. ft. a minute. A congregation of 400 persons enter a closed room 70 ft. by 40 ft. and 20 ft. high. How long will it take them to spoil the air?

38. How long can the windows and doors of a school-room be safely kept closed when occupied by 50 children, if the room is 25 ft. by 20 ft. and 10 ft. high? 39. Find the square root, to four decimal places, of the reciprocal of .0043.

40. A pays B $230 as the present value of $300 due in 5 yrs. Which gains by the payment, and how much, if interest is reckoned at 5%?

41. Find the quantity of coal required by a steamer for a voyage of 4043 mi., if her rate per hour is 14.04 knots, and her consumption of coal 87 t. per day.

Reckon 2240 lbs. to the ton, and a knot 6086 ft.

42. Find the area of a circular ring of which the inner and outer diameters are 7.36 and 10.64 in.

43. A and B can do a piece of work in 13 dys., A and C in 10 dys., A, B, and C in 71 dys. In how many days can A do it alone?

44. If 3 men working 11 hrs. a day can reap 20 A. in 11

dys., how many men working 12 hrs. a day can reap

a field 360 yds. long and 320 yds. broad in 4 dys.? 45. Find the area of a triangle whose sides are 12, 5, and

13 in.

« ΠροηγούμενηΣυνέχεια »