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Get out six pieces of paper, or create a word processing document with six separate pages. At the top of each page, write down one of the six keys. Then, on each page, write down the questions below, and answer them. Write your answers to these rst three questions as if you are explaining them to your boss so that you can justify the time it takes to plan and manage a project well. If you use this key, what will it do to help the project succeed If you use this key, what problems will you avoid Without blame, describe a past project at work that failed because this key was not used, or was not implemented well.

q = 2t and r = 3t To create the polar graph, we can input various values of t, just as we did before To keep things from getting messy, let s restrict ourselves to values of t such that we see only the part of the graph corresponding to the first full counterclockwise rotation of the direction angle, so 0 q 2p Consider the following cases: When t = 0, we have q = 2 0 = 0 and r = 3 0 = 0 When t = p /4, we have q = 2 p /4 = p /2 and r = 3p /4 When t = p /2, we have q = 2 p /2 = p and r = 3p /2 When t = 3p /4, we have q = 2 3p /4 = 3p /2 and r = 3 3p /4 = 9p /4 When t = p, we have q = 2p and r = 3p

Our graph is a spiral, as shown in Fig 16-2 Its equation can be derived with algebra exactly as we did in the Cartesian plane, substituting q for x and r for y to get r = (3/2)q

Figure 16-2

Write the answers to these questions for yourself, and for a team leader or colleague who wants to learn the keys: What tools do we need to make this key work What are the instructions for using each tool (Write your own, or refer to a page in this book.) On a scale of one to ve, one meaning the tool is new to you and ve meaning you know it well, rate how well you can use this tool now. If your rating is three or lower, write down what you will do to learn the tool better. And put a date on it, so it is an action item.

Heat transfer from one fluid to another through a barrier surface is determined by driving force and resistance: Q = UA AT,,, Control of heat

Polar-coordinate graph of the parametric equations q = 2t and r = 3t Each radial division represents p units For simplicity, we restrict q to the interval [0,2p ]

If you re having trouble understanding the concept of a parameter, imagine the passage of time In science and engineering, elapsed time t is the parameter on which many things depend In the Cartesian situation described above, as time flows from the past (t < 0) through the present moment (t = 0) and into the future (t > 0), a point moves along the line in Fig 16-1, going from the third quadrant (lower left, in the past) through the origin (right now) and into the first quadrant (upper right, in the future) In the polar case, as time flows from the present (t = 0) into the future (t > 0), a point travels along the spiral in Fig 16-2, starting at the center (right now) and going counterclockwise, arriving at the outer end when t = p (a little while from now)

One of the best ways to learn something is to teach it. If you were asked to give a ve-minute presentation to a project team explaining why and how to use this key, what would you say

Here s a challenge!

Find a pair of parametric equations that represent the line shown in Fig 16-3

We re given two points on the line One of them, (0,3), tells us that the y-intercept is 3 We can deduce the slope from the coordinates of the other point When we move 4 units to the right from (0,3), we must go downward by 3 units (or upward by 3 units) to reach (4,0) The rise over run ratio is 3 to 4, so the slope is 3/4 The slope-intercept form of the equation for our line is y = ( 3/4)x + 3