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Whenever flowing streams are joined, heat transfer is governed by mixing. hIost heat transfer operations, however, are limited by the necessity of maintaining isolation between the flowing streams; in these cases, the boundary conditions at the heat transfer surfaces control its flow. Radiation is important where temperatures are sufliciently high to promote incandescence, typically in the combustion of a fuel. Each of these situations will be examined individually.

and b = (7p /6,5) The coordinate values are qa = p, qb = 7p /6, ra = 8, and rb = 5 In this situation, we have qb qa = 7p /6 p = p /6 That s smaller than p, so the cross product vector points directly toward us as we look down on the polar plane and imagine going counterclockwise from a to b To find the magnitude ra b, we use the formula for situations in which 0 < qb qa < p, getting ra b = rarb sin (qb qa) = 8 5 sin (p /6) = 8 5 1/2 = 20 so we know that the magnitude of a b is 20

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1 We know that j 2 = 1 by definition, and we derived the fact that ( j )2 = 1 in the chapter text We might think that j = j Let s suppose, for the sake of argument, that the above equation is true Multiplying each side by j gives us j j = j j which can be rewritten as 1 j j = j j Because j j = j 2 = 1 by definition, we can rewrite the above as 1 ( 1) = 1 and finally simplify it to 1 = 1 This statement is obviously false By reductio ad absurdum, we must conclude that our original assumption, j = j, is also false Therefore j j

The deliverable, or output, of each task becomes the input for another task or tasks In creating the WBS, we use several di erent methods to ensure that we de ne each task and deliverable precisely In this way, the WBS becomes a linked series of steps Each task, like a stepping stone, gets us one step closer to the other shore When we nish each step, our feet are planted solidly, and we can take the next step When a set of tasks are completed, we have a set of deliverables that make up a milestone The tasks and deliverables and intermediate milestones are organized into the phases of the system development life cycle, and each phase ends with a major milestone One of the keys to a successful work breakdown structuring process is to make it a team e ort.

6

2 The quantity j 1 can also be written as 1/j It s an unknown, so let s call it x and then set up the simple equation 1/j = x We can multiply through by j to get j/j = jx Because any nonzero quantity divided by itself is equal to 1, we can simplify to 1 = jx Multiplying through by j gives us j = jjx which can be rewritten as j = j 2x We know that j 2 = 1, so the above equation becomes j = ( 1)x which simplifies to j = x Our unknown quantity is equal to j We have just demonstrated that j 1 = j The multiplicative inverse (reciprocal) of j is the same as its additive inverse (negative) No real number behaves like that! 3 First, let s add 3 + j4 and 1 + j5 When we add the real parts, we get 3 + 1 = 2 When we add the imaginary parts, we get j4 + j5 = j9 The sum can be expressed directly as ( 3 + j4) + (1 + j5) = 2 + j9