PROBLEMS

Question 3.1

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

Question 3.2

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

Question 3.3

Y2Mqpz8XGFaAbtdC4E28ek16Lv+pTseyL7tVf16JJ8gUAiylBi6sJKUO7MALgLfm2b1/cetamUNJoS6nqvb2Ml5/+gdVkQrPYqOYJ3hs6swDTX3yhoY9DHP3W9V3jjp+Sq9OvUlswaS/QEd0sqgJsFILMQUdGZgZrKP7kB+CQzU9kwHuG/5glVMFZBZMU0VBqicHblAMlHlfvalO6c9tcdHz/nE/lFE1Agyf+s2fjuTblEKfYcfT4jVsIHc439zdliCF3uOdhpGp5wvzVciE9rSx7Y6l4mhkB8Rf3eKWRObDTpgEAb+FgQ==

46

Question 3.4

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

Question 3.5

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

Question 3.6

mci7TaZ6WJfLY8up+60ML5ZOPYrwommkHoF8m08BBwRCsT3g93GqnjnAVGVKi9SSpppiI1suXafbbDdPvoSsxSv/nXCk09cog16hUG33dl6QwdN2NxJUVb9BgkJiwpFX/cYH1FcWLyMz3fNQeCUxZktamzZCHtfBMdNvE55F5TXowFagMt0gfKxYpqtH0rRnEgULZvpfZ3pIsa2bGFZ59V+6iZe2EXSeFXVn8AGhCBB0vNFjmL9vhBmYolDk7ub/f5/2U2z+kGkRrUK12i7ppl/TCdy0xIi/

Question 3.7

TabN5SxFipLY1oP/sxBPzRruDX7X6/R309YqBB2Ps0co7T4yY4dBIu2EPMslrbulJPzuXY6b8MTlEPBA5IMMAKPSxtB0aQbQwT6jV3VVJhEB6r0xlp6LNjuhOxloQKlm

Question 3.8

1t9eEsxzV6P4mixwo8qLPFbD67ouHT1htx7Z9CzO1FH321RUSTzqgjJv7kXYsQLT+5tlHfoUcIRbUmgRSHg1O+syKAg4eKR8FyKoTumfG5a4FQAyJWWtkYFBxysn+USsp6OMzgZpZu7yDVJZ3gE6b00OAvhiWC+fpX2rBfEB3pLa1cLRV9GDLL707/ekuhTvgyPuq7101iGiV7hQdDBEfjSZgvceJ5fm6NCJWAPdD9ziv9hb56VCqgNI6DGU68+yPMMw3AfEP2MHSzj+D3iMaQn3k+6NuERSHDKwASTmJ0sMuvQoA+dyNBvm1tp5KN3KUVEeHENF67XG9IfsX/R9nX+XxMS48RNvQ2L9fFst+djLvuQIraPB2ruMLwiVEjGV5XCMW0gp7DNtsgP/fJxB2XcNHc7BgtlreXBnSw==

Question 3.9

7fkdGORSN/6nj7e208/FsqSp038LeacQ12mhsQPTvgyR29v1znUEZRn+ZbbMwmW2OZWCVH5QQIuM7FcF9ULuczIueAZO57ywL9SonPVtmDyYXaph

Question 3.10

VZyyk6fJEG5oQJshbSf7GCliKFy3yGcyah9A1gmZKKbho3yNhCN/RVUPizvqDkicZeeALoEsPrUI6zaRK4pwOrO8NigbZ8P5Fw3WURMhoQQZDv4TqB0VS5kdemmpclh2T0aA4XpFEay70jmq

Question 3.11

WwhIdPNjNhDhDBj04gFJKAjXCp9zWGPOk0isdmROyaJOHRtnkJhu8x7IxwSwzG9HdgBlfwbwHvkwWuCkTPzdFQoginuhhBApC0QFwsN87W7mQI5PM1cRSjW2qgSNmse0In0K5wHa7AGPaI9q/bixQucA7XsyiIJZlhkwovz4x7vaqBOA6Ws9MRTEaK46kq0vLxN1lVmMHwhDgjuI

Question 3.12

wRBjgDAIpVquE/Ufna3EdQH+09Cxw3TBQ8Tq4KHUEx3xDYCywtl1D7BNmzaf7SkAUNjWCZH/SIEm8pISwC9dFsTaC76/ofc6Pt6H5tohSj3hS06dSKRETqRzcmjxJLaabvbUH3KD00zjklqS4GMm4sYSpkdQWBBJ+cGlkM+EmRXF6Xa51Z0dVON3C+H9z50u

Question 3.13

QJoR/vsAwl6te76fh0vL7IyMIUgwZJQ/Dsbbw0xL9YIwnhNwncl9LuFV+eztT2HqLC/FTU7aQbjL5IInCR6WoVtgotPaD3HwH3nTYo0BIUKuZeLFpTUmyuy8InjYJaLddj4pOFrgv1oIOaY1IbxDy9sNSM6QPSsaxm3aT4+RfaKsOFp9J29K89rnR3uvFpQXLi1qujOWIxFFuxLVUyDKz0Yht9QUMips5vrl/Zwk7IKlWKpFgDq6GbkCRw6wccO049NA47P/PfGCnK64nvBwg7BF/Z6A71FLrqaLE/8TEJvWbvp/E5xhK2SFxyrUsOoQlDGudJABPRk79wa7MtDE3Sx2oa27uU7jcM4WF554T0j6qlSDctqrzR92gAg=

Question 3.14

cNVPlgEXIGm2oFrreXkylHJtAayzHlKiaiXpHl+XdgSc8x+JSqB3PE90GzfQJSmRlMyx+n/pT9lozclJz+W8xsvgFlWg6pyWt6rTYjr5DIZZMU2c1J5Cawh4+aGl+B6tNZkFNgR31J8O5WDHwHWx/WP7Xe10wRZKZoiVsXrdUoG4JcJqzKJ325suD1SsF9YuPSm3nCg6KjlI8kllrvTTyqRr2g91pIcZjs5jmucDUC+Ele55VXpxzv/l2CKgDblq

Question 3.15

5jLpDIG7aYTMPLzJIz14iHkTPN0/fV1VmCX3cGjikWIQeKGO4x0TgEER9EFI6XKNulkSe2iz+cROOeeUAC3G8EjBZcnOjosaIfQJgdbFee94herzeOlqwj/sSRQtN/e6m26kL5bDGMFtqiIGpZ/FiE+UAmruMEkdfPoiFGe+ymlnyJVYb1Xxh4C78ruXTAxwquMj0X7Cv/cFgr3OZmph4NSjWZWsKZTDOPQNf8Ec8R+DgtrxIuEm5Y/SS+Iprto11W0LsH9PHCoKQoNtuQxCHA==

Challenge Problems

Question 3.16

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

Question 3.17

2QPx4ef2aGTT3DPUgQ4sI/HA4kslsrEAFcthk14ssvssor8QgsJDJELGFb9tTwoXtiGnWgJvjuZHN1Fzp+pb9PReVoo9DA8t6uUxIkSweE8HU4qpqElnz0+XuBN4/0cr8Dk8dQSvWZ1Eoc3VR5f8GuLjO29EzuJVLBZ0RM3U/lqTALHXskvhsv6YVGdx6XhoZwhHfonL+HIHeuW1A+Axhs+h7NgxonjucZ6oqLyDIinda5FAxzOzv8pORertiLX9kZSb0h60Uh8C9UxAhtfdulwQgTp0P9bM1Am1UbKjNPRd5U6adrnB4I3ulcnCJRNswECMPWKZJOlEF5XHs/mp24Gh0EC2Wpn6YY6vbNmgQjZJeqZDGCJ9eTvcD4XYw58fAK5WXxpae1zoZ45xhaP3pA==

Question 3.18

EF2nWd3IdTgehn3EgD4/k6j/L7bZtAgM5+dtWg9Du/qLt1kmb9t5wv5HbjgqCCJD8WoJBDH6UVzX24DVRCoqIqQ74Q9arUwwDk+eJLTA3cJwH0XsHQw0c3mGuZUVhKoN2wm43LHZYghZ2AddKAhBAnkQpguNbpz6zfIHPoj+6I+MJ4T7JtZNKjMPHbXjtWfvmzbzgAHgUjUfSjGiLowMriJhdH6pQdr+asd9hfsXFYd4lrG0zOk58g7u82mg6x9utOS6heRuRopqyueiHkj30NrvDMD6rHiGrMrf4ry9FcUgUi6hYHROI6WYPQ4W6bkEWYjqnhGF8afhrvF/KL9kCeL32rCYlsm5I0YM7g==

Question 3.19

kmKY/pc6mIR40cJAB+JEB2jZLSst4NI/lvnZNom/Y+nAAr4tzznlfAdT4xrD4MEJePZlQYBbdiswMjwoLXytFDUgjn0lzVKxTEh7IDj2hJ7L1C4RQHUv9fCtEnNeCTXrRgJvK+uFuH9DnibJ6hx1xejfIoW6bMvuYoGQwveylzkjRmWZWD47ZzGqQcs3QUWEExSFhk+dbCLggxrQaoT0E//m0yMVGFNSQWp14Fk08/Ib+mQ3IIE8z8Gad9iwtcII

Selected Readings for this chapter can be found online at www.whfreeman.com/tymoczko3e.