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© 20�� by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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c01.qxd 1/27/09 1:00 PM Page 1
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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c01.qxd 1/27/09 1:00 PM Page 4
© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
© 20�� by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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c01.qxd 1/27/09 1:00 PM Page 12
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
1
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
c02.qxd 1/30/09 11:11 AM Page 1
© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
c02.qxd 1/30/09 11:11 AM Page 3
© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
c02.qxd 1/30/09 11:11 AM Page 5
© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
c02.qxd 1/30/09 11:11 AM Page 7
© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
9
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
c02.qxd 1/30/09 11:11 AM Page 9
© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
c02.qxd 1/30/09 11:11 AM Page 17
© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
c02.qxd 1/30/09 11:11 AM Page 25
© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
c02.qxd 1/30/09 11:11 AM Page 27
© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
c02.qxd 1/30/09 11:11 AM Page 29
© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
c02.qxd 1/30/09 11:11 AM Page 31
© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
c02.qxd 1/30/09 11:12 AM Page 33
© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
c02.qxd 1/30/09 11:12 AM Page 35
© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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©2014 by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
c02.qxd 1/30/09 11:12 AM Page 43
© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
c02.qxd 1/30/09 11:12 AM Page 45
© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
1
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
c03.qxd 1/27/09 1:10 PM Page 5
© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20��
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by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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Problem 8.23 Solution Given: A blast wave traveling at 1000=sU m/s at standard sea-level conditions. As shown in Fig. P8.23 (and reproduced below), the moving blast wave can be transformed into an equivalent steady flow with 10001 =U m/s.
For standard sea-level conditions from Table 1.2A:
51 1001325.1 !== ppSL N/m2
150.2881 == TTSL K
29.3401 == aaSL m/s
The Mach number of the flow is:
939.229.340
10001
11 ===
aUM
For flow through a normal shock wave at this Mach number:
47886.02 =M
( )( ) 652 1000423.11001325.1911.9 !=!=p N/m2
( )( ) 50.751150.288608.22 ==T K
( )( )( ) 55.54950.75105.2874.122 === RTa ! m/s
( )( ) 16.26355.54947886.0222 === aMU m/s
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However, this is the velocity of the shock in the shock-wave-fixed coordinate system. The actual velocity of the air behind the shock the shock wave is determined by returning to the ground-based coordinate system:
84.73616.26310001000 2 =!=!= Uuds m/s and the Mach number of the shock-induced motion is:
341.155.54984.736
2
===auM ds
ds
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© 20�� by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.
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© 20�� by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.
All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of thismaterial may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20�� by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.
All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of thismaterial may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20�� by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.
All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of thismaterial may be reproduced, in any form or by any means, without permission in writing from the publisher.
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© 20�� by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.
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c13.qxd 1/27/09 2:02 PM Page 1
by John J. Bertin and Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.© 20��
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by John J. Bertin and Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.© 20��
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c13.qxd 1/27/09 2:02 PM Page 3
by John J. Bertin and Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.© 20��
Problem 13.4 Solution Winglets would be desirable for a transport aircraft that operates for long periods of time in cruise flight, since the reduction of induced drag would be an important consideration. The maneuvers of a stunt airplane would be at large angles of attack. In addition, a stunt airplane typically only flies for fairly short periods of time, making induced drag reduction only marginally important for performance and fuel efficiency.
© 20�� by John J. Bertin, Russ Cummings. Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ.All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this
material may be reproduced, in any form or by any means, without permission in writing from the publisher.
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