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HACTEHA [7]
3 years ago
11

Find the largest prime divisor of $15^6 - 7^6$.

Mathematics
1 answer:
lilavasa [31]3 years ago
6 0

ANS : 11,272,976 = 2^4 * 11 * 13^2 * 379

Step by step :

[7 + b]^6 - 7^6

b^6 + 42 b^5 + 735 b^4 + 6860 b^3 + 36015 b^2 + 100842 b + 117649 -7^6

Sub 8 for b

262,144 + 1,376,256 + 3,010,560 + 3,512,320 + 2,304,960 + 806,736

11,272,976 = 2^4 * 11 * 13^2 * 379

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Answer:

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the volume of a cylinder is base area times height.

Vc = pi×r²×h = pi×15²×20 = pi×225×20 = pi×4500 cm³

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similar to volume, the side "mantle" area of the cylinder is the circumference of the base area times height.

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for this we need now to do the multiplication with pi and then convert the cm³ to liters.

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pi×4500 = 14137.17 cm³ = 14.13717 liters or rounded 14 liters

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