4. Show that the area of Figure 2 is given by the formula A=a2-4 b2. In making tinplates of this form how many square feet of tin are required to make 1000 of each of the following sizes, no allowance being made for waste? Copy and fill out this table. 5. Make a formula for finding the perimeter of Figure 2. Find the perimeter for the values of a and b given in the preceding exercise. 6. Use the formula s=16.12 for finding the number of feet that a body starting from rest falls in 3 sec.; in 15 sec. ; in 30 sec. 7. Show that a body starting from rest will fall nearly one mile in 18 sec. 8. Use the percentage formulas for finding the missing numbers in the following table: 9. Use the interest formulas for finding the missing numbers in the following table: 10. Find the value of 3x+6 when x=4; when x=3.5. 11. Find the value of 5x+2 when x=98; when x=34.1; when x=11. 12. Find the value of 4x-3 when x has each of the following values: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. 13. Find the value of 6n+1 when n has each of the following values: 0, .2, .4, .6, .8, 1, 1.2. 14. Find the value of 2x2-x+2 when x has each of the following values: 0, .1, .5, 1, 1.5, 2. 15. Find the value of 3a2+a-4 when a has each of the following values: 1, 1.1, 1.6, 2. 16. Find the area of a trapezoid whose altitude is 20 in., and bases 36 in. and 40 in. D C 18. Find the area of this plate, Figure 4, if the radius of the plate is 2 ft. 6 in. and the radius of each of the holes is 4 in. 19. The area of a circle of radius 12 in. is how many times the area of a circle of radius 4 in.? Estimate the answer and then compute it. O О FIG. 4 ་ 20. In the formula d=rt, d represents the distance traveled by a moving object, r the rate of motion, and t the time. Use this formula to find (a) The distance a train travels in 18 hr. at the rate of 27 mi. per hour. (b) The number of hours it takes an airplane to travel 640 mi. at the rate of 75 mi. per hour. (c) The rate a bird flies if it flies 720 mi. in 121⁄2 hr. 21. Make a formula that states that p is the product of the factors f and f'. How can you find ƒ if you know p and f'? How can you find f' if you know p and ƒ? 22. Find ƒ if p=954 and ƒ'=24. 25. The load that may be safely attached to an iron chain is given by the formula, L=7.11d2, where L is the load in tons, and d is the diameter of the chain iron in inches. Find the safe load when the chain iron has the following diameters: † in. ; † in.; 1.3 in. 13 26. The number of pounds of blasting powder, p, used to blow a hole in a wall of thickness t feet is given by the formula How many pounds must be used to blow a hole 80 through a wall 3 ft. thick? 4 ft. thick? 6 ft. thick? Ρ 27. The total surface, T, of a cylinder is found by the formula T=2′′ r (r+h), in which r is the radius of the cylinder and h is its altitude. Find the total surface of a cylinder whose radius is 3 in. and height 7 in. Find the total surface of a cylinder whose radius is ft. and height .7 ft. 28. The amount, A, of a certain principal, p, in t years at rate, r, is given by the formula A=p(1+rt). Find A when p is $450, r is 5%, and t is 2 yr. 3 mo.; also find A when p=$5460, r=7%, and t=1 yr. 4 mo. 29. The beam in Figure 5 is supported at one end and supports a load at the other end. The heaviest load that a steel beam in such a position will support without breaking is given by FIG. 5 is the load in pounds, b the width, d the supported at the end Find the heaviest load that can be 30. The horsepower of certain types of gasoline automobile engines is given by the formula H.P.= where H. P. ND2 is the number of horsepower, N is the number of cylinders, and D is the diameter of the cylinders. Find the number of horsepower of the engine in each of the following kinds of automobiles : 1 CHAPTER II FUNDAMENTAL OPERATIONS AND EQUATIONS 6. Addition and subtraction. Such sums as 7.8+3·8 are usually found in arithmetic by first multiplying and then adding. Thus, 7.8+38-56+24=80. Since these two terms contain a common factor the sum may be found by first adding and then multiplying. Thus, 7.8+3.8=10.8=80. When terms to be added have a common factor the second way is generally used. Thus in finding the sum, 7x+3x= 10x, the 7 and 3 are first added and x is multiplied by their sum. What has been said about sums applies also to finding the difference of two numbers. Thus 7.8-3.8=4·8=32, and 7x-3x=4x. Since ax+bx means x taken a times added to ≈ taken b times, the sum is x taken a+b times. This is written, ax+bx=(a+b)x. Exercise 5 Find the following sums and differences. First add or subtract, then multiply. 1. 5.7+8.7. 2. 25.6+19.6. 3. 12.9+4.9. 4. 15.7+3. 7. 5. 15.3-7.3. 6. 37.7-27.7. 7. 84.17-64. 17. 8. 246.359-239.359. |