42. The amount of heat (H) in calories generated by an electric current of I amperes flowing through a wire of R ohms resistance, for t seconds is H = 0.24 × I2RT. Find the number of calories of heat generated in a quarter of an hour by a current of 10 amperes passing through a resistance of 2 ohms.

11. An automobile runs 10 miles an hour faster than a bicycle, and it takes the bicycle 10 hours longer to run 144 miles than the automobile. Find the rate of each.

15. The width of a field is of its length. If the width were increased by 5 feet and the length by 10 feet, the area would be increased by 400 square feet. Find the dimensions.

16. Eleven-sixteenths of a certain principle was at interest at 5%, and the balance at 4%. The entire income was $1000. Find the principal.

18. Find the time required for the interest at 5% on a sum of money to be equal to the principal.

23. A man buys lemons for $2. If he had received for that money 50 more lemons, they would have cost him 2 cents less apiece. What was the price per lemon?

24. Find the time in which $75 will amount to $90.75 at 6%?

25. Solve for F in, C

C

= 30.

=

(F - 32). Also find F when

26. At what time between 4 and 5 o'clock are the hands of a clock at right angles to each other?

27. At what depth (h) in fresh water will the pressure (P) on an object having a total area (A) of 4 square feet, be 1000 lbs.? Water weighs 62 lbs. per cubic foot and wAH.

P

=

28. At what time between 5 and 6 o'clock will the hands of a clock be together?

29. A man put out $4330 in two investments. On one of them he gained 12% and on the other he lost 5%. If his net gain was $251, what was the amount of each investment?

CHAPTER XI

GRAPHS

88. If we wish to locate a particular point on the floor of a room, the quickest and simplest method is to measure its distance from each of two walls at right angles to each other. Fig. I.

In the same way, if 2 lines are drawn at right angles to each other, on a piece of paper, any point may be located by stating its distance from each of the two lines. This is most conveniently done by using paper, ruled with horizontal and vertical lines, called graph paper.

FIG. I.

Thus in Fig. II, any point P, may be located if we know its distance from the vertical line or axis, and its distance from the horizontal line or axis.

Here we can see, that the point P is 7 units from the vertical axis and 8 units from the horizontal axis.

The horizontal distance is called the x of the point and as this distance is equal to the distance OA on the horizontal axis, it can be measured along the horizontal axis, which is therefore known as the X axis. Similarly, the vertical distance, called the y of the point, may be measured along the vertical axis and this is the Y axis.

These two distances, which locate any point in a plane surface, or simply a plane, are called the coördinates of the point, and the two axes are called the coördinate axes or axes of reference. As these measurements are usually made from the point O, the intersection of the two axes, this point is called the origin.

The horizontal or x distance of a point is also known as the abscissa and the vertical or y distance, as the ordinate of the point.

If in Fig. III, we imagine a circle drawn from the origin O as a centre, the two axes will divide the circle into 4 equal parts or quadrants. These quadrants are numbered I, II, III and IV, in a direction contrary to the hands of a clock.

In giving the coördinates of a point, the abscissa is always mentioned first. Thus, the point 3, 4, has an abscissa equal to 3 units and an ordinate of 4 units. If we attempted to locate this point, we could find 4 points, each of which

would be 3 units from the vertical axis and 4 units from the horizontal axis, one point in each of the 4 quadrants. To overcome this difficulty, all abscissas measured to the right of the Y axis are called + and abscissas measured to the left, while ordinates measured above the X axis are + and those below the X axis are Then, only one point in the first quadrant will have the coördinates 3, 4, as a point in any other quadrant will have one or both of its

coördinates negative. Thus, in the second quadrant the abscissa is, in the 3d quadrant both coördinates are and in the 4th quadrant, the ordinate is .

Locating a point, when its coördinates are known, is called plotting the point.