Viewing page 62 of 91

This transcription has been completed. Contact us with corrections.

35-36        ARMY AIR FORCES

8) The velocity of sound in air depends on the temperature of the air. By use of the following data, draw a graph showing how the velocity varies with the temperature.
 
[[8 column table]]
| Velocity (ft per sec.)__| 1,030 | 1,040 | 1,060 | 1,080 | 1,110 | 1,140 | 1,170 | 
| Temperature (F.)_____|  -30° |  -20° |   0°  |  20°  |  50°  |  80°  | 110°  |


From the graph, find the velocity if the temperature is 35[[degree]]; 10.5[[degree]]; -25[[degree]]; 120[[degree]].

1095; 1070.5; 1035; 1180      Answers.

(9) The effective disk area of a propeller depends on the diameter of the propeller. By use of the table below, draw a graph showing how the effective area A in square feet varies with the diameter in feet.

[[7 column table]] 
| A (sq.ft)____________| 4.2 | 6.5 | 9.4 | 12.7 | 16.6 | 21 |
| D (ft)_______________|  8  |  10 |  12 |  14  |  16  | 18 |

From the graph, find the area if the diameter is 9 feet; 12.5 feet; 14 3/4 feet.

36. Graphic solution of algebraic equations containing two unknowns.-a. It is sometimes necessary to find a pair of numbers that will satisfy two equations at the same time. One method of doing this is to graph each equation on one set of coordinate axes and find the intersection of the curves.

Example: Find the values of x and y which will satisfy the following two equations simultaneously:

2x-y=3
3x+2y=8

Solution: By graphing each equation separately on the same pair of coordinate axes, the line AB is obtained, every point of which has coordinates satisfying the equation 2x-y=3; and the line CD is obtained, every point of which has coordinates satisfying the equation 3x+2y=8.

The intersection of CD and AB is the point P the coordinates of which (2,1) are the only ones satisfying both of the given equations. 

b. This graphical method usually gives approximate results only, because of errors in measuring line segments when determining certain coordinates.

c. If the lines are parallel, it is obvious that no coordinate values will satisfy both of the given equations.
     
60