(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.
Answer:
B
Step-by-step explanation:
The cube of twice a number =

Decreased by 11 =

Hence, the cube of twice a number decreased by 11 =

Answer:
θ = 83°
Step-by-step explanation:
For acute angles, the sine of an angle is the cosine of its complement, and vice versa.
__
sin(θ) = cos(90° -θ) . . . . relation between sine and cosine
sin(θ) = cos(7°) . . . . . . . . given
90° -θ = 7° . . . . . . . . . matching arguments of cos( )
θ = 83° . . . . . . . . . add θ -7° to both sides
<span>"Give an example of a sound financial decision Maura might make to support this goal. Why is it sound?"
<span>
</span>She could choose to carefully budget her trip and avoid overspending at all costs. This prevents going into debt. She should also save up extra money in the event of an emergency.
</span><span>Then give an example of a poor financial decision Maura might make considering her goal. Why is it a poor decision?</span><span>
Not having a plan would be a poor decision on her part. She could end up spending too much and not realize how much money she has left.
I hope I helped!
</span>
(120x)^1/2 see attached photo for steps