9514 1404 393
Answer:
5/48, 5/46, 5/44, 5/42
Step-by-step explanation:
We can choose unit fractions with denominators between 8 and 10, separated by (10-8)/5 = 0.4 units:
1/8.4 = 5/42
1/8.8 = 5/44
1/9.2 = 5/46
1/9.6 = 5/48
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<em>Check</em>
- 1/8 = 0.125
- 5/42 ≈ 0.119
- 5/44 ≈ 0.114
- 5/46 ≈ 0.109
- 5/48 ≈ 0.104
- 1/10 = 0.100
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<em>Additional comment</em>
There are an infinite number of such fractions. We are given unit fractions with different denominators, so it works reasonably well to choose denominators between those given. Then the trick is to convert the fraction to a ratio of integers. In this case, multiplying by (5/5) does the trick.
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Another approach is to write the fractions with a common denominator, then choose numerators between the ones given. For example, 1/10 = 4/40, and 1/8 = 5/40, so you could write some fractions with numerators between 4 and 5. Possibilities are 4.1/40 = 41/400, 4.3/40 = 43/400, 4.7/40 = 47/400, 4.9/40 = 49/400.
Answer: 8n
Let's simplify step-by-step.
(2(n+1)−1)2−(2n−1)2
Distribute:
=4n2+4n+1+−4n2+4n+−1
Combine Like Terms:
=4n2+4n+1+−4n2+4n+−1
=(4n2+−4n2)+(4n+4n)+(1+−1)
=8n
Answer:
46,499 digits
Step-by-step explanation:
Total pages of book = 11,521
9 pages numbered 1 - 9 that need 1 digit each = 9 × 1
= 9 digits
90 pages numbered 10 - 99 that need 2 digits each = 90 × 2
= 180 digits
900 pages numbered 100 - 999 that need 3 digits each = 900 × 3
= 2,700 digits
9000 pages numbered 1000 - 9999 that need 4 digits each = 9000 × 4
= 36,000 digits
1522 pages numbered 1000 - 11521 that need 5 digits each = 1522 × 5
= 7,610 digits
Total digits needed = 9 digits + 180 digits + 2,700 digits + 36,000 digits + 7,610 digits
= 46,499 digits
The correct answer is <span>16666666666/100000000000.</span>
