(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.
<h2><u>Graphing</u></h2>
<h3>The graph of this function is shifted 7 units right and shifted 5 units up.</h3>
<h3>f(x) = -2/3(x - 7)² - 5</h3>
<u>Answer:</u>
<u>Explanation:</u>
- Why false? As I noticed, in the equation f(x) = -2/3(x - 7)² - 5, the vertex is (7, -5). The value of a, which is -2/3, is negative. So the graph opens downwards. The graph shifts 7 units to the right, which is correct, but graphing 5 units up is wrong. Why? 5 is negative, so it should be shifted 5 units down.
Wxndy~~
Answer:
2•2²×100+5.
Step-by-step explanation:
Answer:

Step-by-step explanation:
Given
--- interval
Required
The probability density of the volume of the cube
The volume of a cube is:

For a uniform distribution, we have:

and

implies that:

So, we have:

Solve


Recall that:

Make x the subject

So, the cumulative density is:

becomes

The CDF is:

Integrate
![F(x) = [v]\limits^{v^\frac{1}{3}}_9](https://tex.z-dn.net/?f=F%28x%29%20%3D%20%5Bv%5D%5Climits%5E%7Bv%5E%5Cfrac%7B1%7D%7B3%7D%7D_9)
Expand

The density function of the volume F(v) is:

Differentiate F(x) to give:




So:

Answer:
<h2>0</h2>
Step-by-step explanation:
