(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.
Hi,
Equation:

Multiplying two negatives equals a positive.

Now equation looks like:

Hope this helps.
r3t40
Answer:
A. P(n) = 12·2^n
Step-by-step explanation:
From one generation to the next, the population grows by a factor of ...
24/12 = 2
Only one offered expression is an exponential function with a base of 2:
P(n) = 12·2^n
I think the answer to In AQRS OR=7, RS=11 M<=42 IN AUVT VT=26, TU= 44 M is THE TRIANGLES ARE NOT SIMILAR.
<u>0.09</u> = <u>1 </u>
0.9 10
I hope this helps.