(a) See the attached sketch. Each shell will have a radius <em>y</em> chosen from the interval [2, 4], a height of <em>x</em> = 2/<em>y</em>, and thickness ∆<em>y</em>. For infinitely many shells, we have ∆<em>y</em> converging to 0, and each super-thin shell contributes an infinitesimal volume of
2<em>π</em> (radius)² (height) = 4<em>πy</em>
Then the volume of the solid is obtained by integrating over [2, 4]:

(b) See the other attached sketch. (The text is a bit cluttered, but hopefully you'll understand what is drawn.) Each shell has a radius 9 - <em>x</em> (this is the distance between a given <em>x</em> value in the orange shaded region to the axis of revolution) and a height of 8 - <em>x</em> ³ (and this is the distance between the line <em>y</em> = 8 and the curve <em>y</em> = <em>x</em> ³). Then each shell has a volume of
2<em>π</em> (9 - <em>x</em>)² (8 - <em>x</em> ³) = 2<em>π</em> (648 - 144<em>x</em> + 8<em>x</em> ² - 81<em>x</em> ³ + 18<em>x</em> ⁴ - <em>x</em> ⁵)
so that the overall volume of the solid would be

I leave the details of integrating to you.
We just need to find the multiples of 9 that are greater than 20.
9*1 = 9
9*2 = 18
9*3 = 27
9*4 = 36
9*5 = 45
We can use 27,36, 45, .....
Your final answer should be any multiple of nine greater than 20. I recommend using 27, 36, and 45. Hope this helps!<span />
Answer:
The pattern is + 10.
Step-by-step explanation:
13 + 10 = 23
23 + 10 = 33
33 + 10 = 43
...and so on.
I hope this helped! :-)
Answer:
Step-by-step explanation:
<u>Solve the inequality:</u>
- - a + 1/3 > 1/4
- a < 1/3 - 1/4
- a < 4/12 - 3/12
- a < 1/12
Correct choice is B