Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 8, Problem 3A
To determine
The dimensions
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1.
2.
Show that the following are not logically equivalent by finding a counterexample:
(p^q) →r and
(db) V (d←d)
Show that the following is not a contradiction by finding a counterexample:
(pV-q) AqA (pv¬q Vr)
3.
Here is a purported proof that (pq) ^ (q → p) = F:
(db) v (bd) = (db) v (bd)
=(qVp) A (g→p)
= (¬¬q V ¬p) ^ (q→ p)
(db) V (db) =
=¬(a→p)^(a→p)
= (gp) ^¬(a → p)
=F
(a) Show that (pq) ^ (q→p) and F are not logically equivalent by finding a counterex-
ample.
(b) Identify the error(s) in this proof and justify why they are errors. Justify the other steps
with their corresponding laws of propositional logic.
5
Show by multiplying matrices that the following equation represents an ellipse:
5
-
-7
I
(x)(3)()=30.
y)
7
7)
Chapter 8 Solutions
Mathematics for Machine Technology
Ch. 8 - Prob. 1ACh. 8 - Use Figure 8-4 to answer exercises 1-6. All...Ch. 8 - Prob. 3ACh. 8 - Prob. 4ACh. 8 - Prob. 5ACh. 8 - Prob. 6ACh. 8 - Prob. 7ACh. 8 - Prob. 8ACh. 8 - Prob. 9ACh. 8 - In each of the following exercises, the value on...
Ch. 8 - In each of the following exercises, the value on...Ch. 8 - In each of the following exercises, the value on...Ch. 8 - In each of the following exercises, the value on...Ch. 8 - In each of the following exercises, the value on...Ch. 8 - In each of the following exercises, the value on...Ch. 8 - In each of the following exercises, the value on...Ch. 8 - In each of the following exercises, the value on...Ch. 8 - In each of the following exercises, the value on...Ch. 8 - In each of the following exercises, the value on...Ch. 8 - Write these numbers as words. 20. 0.064Ch. 8 - Write these numbers as words. 21. 0.007Ch. 8 - Write these numbers as words. 22. 0.132Ch. 8 - Write these numbers as words. 23. 0.0035Ch. 8 - Write these numbers as words. 24. 0.108Ch. 8 - Write these numbers as words. 25. 1.5Ch. 8 - Write these numbers as words. 26. 10.37Ch. 8 - Write these numbers as words. 27. 16.0007Ch. 8 - Write these numbers as words. 28. 4.0012Ch. 8 - Write these numbers as words. 29. 13.103Ch. 8 - Write these words as numbers. 30. eighty-four...Ch. 8 - Write these words as numbers. 31. three tenthsCh. 8 - Write these words as numbers. 32. forty-three and...Ch. 8 - Write these words as numbers. 33. four and five...Ch. 8 - Write these words as numbers. 34. thirty-five...Ch. 8 - Write these words as numbers. 35. ten and two...Ch. 8 - Write these words as numbers. 36. five and one...Ch. 8 - Write these words as numbers. 37. twenty and...Ch. 8 - Write these numbers as words using the alternative...Ch. 8 - Write these numbers as words using the alternative...Ch. 8 - Write these numbers as words using the alternative...Ch. 8 - Write these numbers as words using the alternative...Ch. 8 - Write these numbers as words using the alternative...Ch. 8 - Write these numbers as words using the alternative...Ch. 8 - Write these numbers as words using the alternative...Ch. 8 - Write these numbers as words using the alternative...Ch. 8 - Write these words as numbers. 46. forty-three and...Ch. 8 - Write these words as numbers. 47. fourteen and...Ch. 8 - Write these words as numbers. 48. thirty-seven and...Ch. 8 - Write these words as numbers. 49. one hundred six...Ch. 8 - Write these words as numbers. 50. seventy-six...Ch. 8 - Write these words as numbers. 51. four and one...Ch. 8 - Each of the following common fractions has a...Ch. 8 - Each of the following common fractions has a...Ch. 8 - Each of the following common fractions has a...Ch. 8 - Each of the following common fractions has a...Ch. 8 - Each of the following common fractions has a...Ch. 8 - Each of the following common fractions has a...Ch. 8 - Each of the following common fractions has a...Ch. 8 - Each of the following common fractions has a...Ch. 8 - Each of the following common fractions has a...
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