Section 1 | |||
1. 4 + 12i | 2. | 3. | |
4. i3 = –i | 5. –32 – 24i | 6. 32 | |
7. | 8. | 9. | |
10. | 11. | 12. 3x3y | |
Section 2 |
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1. x = 2 | 2. x = –1/2 | 3. x = 28 | |
4. –1/5 ± (i/5)Ö2 | 5. x = –68, 60 | 6. x = 81 | |
7. x = –1/5, 3 | 8. (–¥, –10] È [3,¥) | 9. (–4, –1) È (4,¥) | |
10. (–¥, –5) È [–3, ¥) | 11. (–¥, –7) È (–1, ¥) | 12. x = –9, 3 | |
13. no solution | 14. (–¥, ¥) | 15. 10 lbs. of hazelnuts | |
16. 36/7 hours | 17. 29 and 6 | 18. l = 6 and w = 8 | |
19. The maximum area is 400 cm2 |
20.
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21. approx. 17 years | |
22. 3.2 grams of gold | 23. y = 4000x + 80000 | 24. 11 and 6 | |
Section 3 |
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1. y = –x/2 + 1/2 | 2. y = (5/3)x + 6 | 3. 5 | |
4. | 5. (–6, 8) | 6. (x + 16)2 + (y – 31)2 = 25 | |
7. center is (8, –5) and radius is 7 |
8. | 9. | |
10. | 11. | 12.
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Section 4 |
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1. The domain and range of both f(x) and f -1(x) is (–¥,¥). |
2. f -1(x) = x2 – 3. The domain of f(x) is [–3, ¥), its range is [0, ¥). The domain of f -1(x) is [0, ¥) and its range is [–3, ¥) |
3. f -1(x) = (x + 7)/5. The domain and range of both f(x) and f -1(x) is (–¥,¥). |
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4. The domain of f(x) is (–¥, 4) È (4,¥). |
5. The domain of f(x) is (–¥, –5) È (–5, –3/2) È (–3/2, ¥). |
6. The domain of f(x) is (–¥, ¥). |
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7. The domain of f(x) is [–5, 5]. |
8. The domain of f(x) is (–¥, ¥). |
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Section 5 |
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1. x = (log 37)/(log 4) – 2 | 2. x = 2 | 3. x = (ln 8)/2 | |
4. x = 13 |
5. x = 2 |
6. |
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7. | 8. 5 log2 x + log2 (x + 1) – 2 log2 y – 3 log2 z |
9. Domain (–¥,¥) and Range (3,¥) |
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10. Domain (–¥,0) and Range (–¥,¥) |
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Section 6 |
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1. 5x3 – 4x2 – x + 5 ; R: –6 | 2. x4 – 2x3 + 4x2 + x + 8; R: –1 |
3. 2x2 – x –1; R: –2 | |
4. Yes, x – 2 is a factor. | 5. f(–5) = –365 | 6. –5 multiplicity 2; 5 mulitplicity 1; and –3 mulitplicity 5 |
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7. ±1, ±2, ±4, ±1/5, ±2/5, ±4/5 |