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Darya [45]
2 years ago
15

The bottom part of this block is a rectangular prism. The top part is a square

Mathematics
1 answer:
dedylja [7]2 years ago
3 0

Answer:

I think you need 8 papers

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A) Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given cur
Leno4ka [110]

(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]:

\displaystyle 4\pi \int_2^4 y\,\mathrm dy = 2\pi y^2\bigg|_{y=2}^{y=4} = 2\pi (4^2-2^2) = \boxed{24\pi}

(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

\displaystyle 2\pi \int_0^2 (648-144x+8x^2-81x^3+18x^4-x^5)\,\mathrm dx = \boxed{\frac{24296\pi}{15}}

I leave the details of integrating to you.

3 0
2 years ago
The measure of angle A
wariber [46]

Answer:

A. Measure of angle A + measure of angle B

Step-by-step explanation:

Because angle 4 is an exterior angle of given triangle which will be equal to the Measure of angle 2 + measure of angle 3

6 0
3 years ago
Eight toy makers each carved 25 blocks and 15 cars how many toys did they crave in all
Stella [2.4K]

Answer:

320

Step-by-step explanation:

25 + 15 = 40 toys each

Toy makers x number of toys each = total toys carved

8 x 40 = 320 totals carved in all

6 0
3 years ago
Read 2 more answers
-4(x+5)=-4x-30 solution
luda_lava [24]

Answer:

no solution

Step-by-step explanation:

-4(x+5)=-4x-30

-4x-20=-4x+30

no solution

x cancel

7 0
2 years ago
Find the slope of the line that passes through (4, 6) and (2, 3).
Verizon [17]
The slope is 3/2

To find the slope, you have to use the slope formula

y2-y1/x2-x1

6-3/4-2

3/2

So the slope is 3/2
3 0
3 years ago
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