Find the value 9-2(--6-4)
1 answer:
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<em>x</em> ^2 + <em>y</em> ^2 = 9 => <em>y</em> = <em>y(x)</em> = ± √(9 - <em>x</em> ^2)
Each cross section would be a square with side length equal to the vertical distance between the upper and lower semicircles defined by <em>y(x)</em>, which is
√(9 - <em>x</em> ^2) - (- √(9 - <em>x</em> ^2)) = 2 √(9 - <em>x</em> ^2)
The area of each square section is the square of this length,
(2 √(9 - <em>x</em> ^2)) = 4 (9 - <em>x</em> ^2) = 36 - 4<em>x</em> ^2
We get the whole solid for -3 ≤ <em>x</em> ≤ 3, so integrating gives a volume of
[ Answer ]
[ Explanation ]
- Simplify: 5(x + 3)(x + 2) - 3(x2 + 2x + 1)
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- Add Similar Elements: 2x + 2x = 4x
5(x + 3)(x + 2) - 3(4x + 1)
- Expand: 5(x + 3)(x + 2) - 3(4x + 1):
+ 25x + 30
+ 25x + 30 - 3(4x + 1)
- Expand: - 3(4x + 1): -12x - 3
+ 25x + 30 - 12x - 3
- Simplify:
= + 13x + 27