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An angle is the figure formed by two rays with a common end point. The rays are the sides of the angle, while the end point is itsSvertex. The symbol for angle is / or ]; the plural is . S Thus, AB and AC are the sides of the angle shown in Fig. 1-8(a), and A is its vertex.



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An angle may be named in any of the following ways: 1. With the vertex letter, if there is only one angle having this vertex, as /B in Fig. 1-8(b). 2. With a small letter or a number placed between the sides of the angle and near the vertex, as /a or /1 in Fig. 1-8(c). 3. With three capital letters, such that the vertex letter is between two others, one from each side of the angle. In Fig. 1-8(d), /E may be named /DEG or /GED.

federal unemployment tax rate is 6.2 percent. As long as the employer is up to date on the state tax, the employer is allowed an automatic credit of 5.4 percent no matter what rate the employer actually pays. The effective federal unemployment rate is therefore 0.8 percent.

Fig. 1-8





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This creates 254 new networks available to be assigned to address 216.182.123.0, reserving 216.182.123.255 as the broadcast address (which sends packets to all hosts on the network) and 216.182.123.0 for the network. NOTE: If there aren t eight binary digits in any section of the IP address, 0s need to be padded to the left of the digits to make eight. You do not have to use 255.255.255.0 for the subnet mask; it is only speci ed as the default value. However, it is the most common value. Using the conversion from binary to decimal (and back) and the bitwise AND operation allows most of the calculations needed for determining network scale and resources, as well as assigning IP addresses within a network. By following some simple rules (for example, the proper mask for each class network), you can be reasonably secure in knowing that there will not be addressing con icts with other networks. Keep in mind that IP or network addresses cannot be assigned at random. It is advisable to consult a good reference text on TCP/IP and networking before embarking on a project such as this. There are a few simple rules for subnetting: All hosts in the network must agree on the mask used. No two di erent subnets can use the same host address. The rst (*.*.*.0) and last (*.*.*.255) numbers are reserved. The subnet cannot be all 1s in binary form. For much more detailed information, see the relevant RFCs: RFC 917: Internet Subnets RFC 950: Internet Standard Subnetting Procedure RFC 1517: Applicability Statement for the Implementation of Classless InterDomain Routing (CIDR) RFC 1518: An Architecture for IP Address Allocation with CIDR

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Fig. 18-8

Only (b), (e), and (f) have reflectional symmetry. Note that when (d) is flipped, it will look like Fig. 18-9, which is different from the original in that the upper-left-hand crossing is horizontal instead of vertical.

Fig. 18-9

If a pin were pushed through the origin on a graph and the paper were to be turned, the result would be a rotation about the origin. A rotation is described by the number of degrees by which the paper is turned. The 90 clockwise rotation (or 270 counter-clockwise) about the origin is given by P(x, y) A P (y, x). The 180 rotation about the origin is given by P(x, y) A P (x, y). The 270 clockwise (or 90 counter-clockwise) rotation about the origin is given by P(x, y) A P ( y, x). In general, the clockwise rotation about the origin of is given by P(x, y) A P (x cos y sin , y cos x sin )

Performing rotations Let triangle ABC be given by A(2, 1), B(3, 1), and C(3, 4). Graph the image of ^ABC as rotated about the origin by (a) 90 clockwise, (b) 180 , and (c) 270 clockwise.

See Fig. 18-10.

Summary

Fig. 18-10

(a) Ar(1, 2), Br(1, 3), and Cr(4, 3) (b) As( 2, 1), Bs( 3, 1), Cs( 3, 4) (c) A-( 1, 2), B-( 1, 3), C-( 4, 3)

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