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2 Figure A-8 is a plot of the point (q,r,h) = (3p /4,6,8) in cylindrical coordinates 3 We want to find the (x,y,z) representation of the point (q,r,h) = (p /4,0,1) Let s use the conversion formulas we learned Here are the formulas again: x = r cos q y = r sin q z=h Plugging in the values, we get x = 0 cos p /4 = 0 y = 0 sin p /4 = 0 z=h=1 Therefore, the Cartesian equivalent point is (x,y,z) = (0,0,1) 4 We want to convert the xyz space point ( 4,1,0) to cylindrical coordinates In this situation, we have x = 4 and y = 1 To find the angle, we should use the formula q = p + Arctan ( y /x) because x < 0 and y > 0 When we plug in the values for x and y, we get q = p + Arctan [1/( 4)] = p + Arctan ( 1/4)

Heat transfer rate ran be normalized by dividing by its maximum possible value, which would occur with both streams at infinite flow such that THY = THY a n d Tcz = Tel:

9

A project is a process that creates a product Therefore, the rst ve stages are the project life cycle stages At that point, the project is over, and the product or service is in production Operations and maintenance supports the relatively stable, mature production stage Products and services have a stage beyond maturity, where they are bringing in less value or revenue This is more of a concern for marketing than it is for project management Therefore, we will focus our attention on the project stages However, we will address the entire life cycle, even though the project ends with transition to production and project close There is real value in this If we do not think about and understand production and maintenance, then we will design products and services that do not work.

When we input the values for x and y to the formula for r, we get r = [( 4)2 + 12]1/2 = (16 + 1)1/2 = 171/2 Because z = 0, we know that h=z=0 The exact cylindrical equivalent point is (q,r,h) = {[p + Arctan ( 1/4)],171/2,0} Using a calculator set for radians to approximate the angle coordinate to four decimal places, we get q = p + Arctan ( 1/4) 31416 + ( 02450) 28966 When we approximate the radius coordinate to four decimal places, we obtain r = 171/2 41231 The approximate ordered triple representing our point in cylindrical coordinates is therefore (q,r,h) (28966,41231,0) The first coordinate represents an angle in radians The second and third coordinates represent linear displacements in space 5 We want to find the (x,y,z) equivalent of (q,r,h) = (p /4,21/2,1) First, let s find x Using the cylindrical-to-Cartesian conversion equation, we get x = r cos q = 21/2 cos (p /4) = 21/2 21/2/2 = 2/2 = 1 The cylindrical-to-Cartesian conversion equation for y tells us that y = r sin q = 21/2 sin (p /4) = 21/2 21/2/2 = 2/2 = 1 Finding z involves no conversion at all We have simply z=h=1 Therefore, the Cartesian equivalent point of the cylindrical (q,r,h) = (p /4,21/2,1) is (x,y,z) = (1,1,1) That s what we began with when we worked out the example in the chapter text

510 Worked-Out Solutions to Exercises: 1-9