F(x) = 1 x g(x) = 1 x − 1 − 1

Volumes of the solids with disk or shell method?

lina2011 [118]

The answer to the questions of volumes are given as follows

a) $v=128 \pi$

b) $v=\frac{128}{3} \pi$

c) $v=\frac{1024}{5} \pi$

d) $V=\frac{13568}{15} \pi$

Generally, the questions are mathematically solved below

$y=\sqrt{x}, y=4, x=0$

a) x-axis

if $y=4, x=16, x=0$

Using disk method

$} v=\pi \int_{0}^{16}(\sqrt{x})^{2} d x \\$

$v=\pi\left(\frac{x^{2}}{2}\right)_{0}^{16} \\$

$v=\frac{\pi}{2} \times 16 \times 16 \\$

$v=128 \pi$

b) line y=4

if x=0, y=0 ;

$y=\sqrt{x} \Rightarrow x=y^{2}$

Using shell method

$v = \int_{0}^{4} 2 \pi(4-y) \cdot y^{2} d y \\$

$v=2 \pi \int_{0}^{4}\left(4 y^{2}-y^{3}\right) d y$

$v=2 \pi\left[\frac{4 y^{3}}{3}-\frac{y^{4}}{4}\right]_{0}^{4} \\$

$v=\frac{2 \pi}{12}[1024-768] \\$

$v=\frac{512 \pi}{12} \\$

$v=\frac{128}{3} \pi$

c) y-axis

0 ≤ y ≤ 4

x=y^2

Using disk method

volume

$v=\pi \int_{0}^{4} y^{4} d y$$

$v=\pi\left(\frac{y 5}{5}\right)_{0}^{4} \\$

$v=\frac{1024}{5} \pi$

d) line x=-1

y=√x, y=4, x=0

0 ≤ x ≤ 6

Using shell method

volume is

$V=\int_{0}^{16} 2 \pi(1+x) \sqrt{x} d x$$

$V=2 \pi\int_{0}^{16}(x^{1 / 2}+x^{3 / 2}\right) )d x\right. \\$

$V=2 \pi\left[\frac{x^{3 / 2}}{3 / 2}+\frac{x^{5 / 2}}{5 / 2}\right]_{0}^{16} \\$

$V=2 \pi\left[2 / 3 \cdot\left(4^{2}\right)^{3 / 2}+2 / 5\left(4^{2}\right)^{5 / 2}\right] \\$

$V=4 \pi / 3 \cdot 4^{3}+4 \pi / 5 \cdot 4^{5} \\$

$V=4 \pi\left(\frac{1}{3}+\frac{4^{2}}{5}\right)$

$V=\frac{256}{15}(5+48) \pi \\$

$V=\frac{256 \times 53}{15} \pi \\$

$V=\frac{13568}{15} \pi$

Read more about volumes

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8 0

2 years ago

Please help on both questions. I would appreciate it.

ohaa [14]

Answer:

first one is 4.5 second one is 45

Step-by-step explanation:

8 0

3 years ago

Please help with math!!!!!!!

iVinArrow [24]

Answer:

Step-by-step explanation:

5a. 7 < x

b. 2< 2x

c. 8 > x

d. 3 > x/29

joe = j

christina = c

Aaron = a

j = 3a , c = a-6 total ages is 149

149 = j + c+ a

149 = 3a + a-6 + a

149 = 5a-6

add 6 to both sides

149 + 6 = 5a-6+6

155 = 5a

a = 155/5

a = 31

c = a - 6

c = 31 - 6

c = 25

7 0

2 years ago

How do I am write an inequality?

elena-14-01-66 [18.8K]

How do you? easy = is an inequality

3 0

4 years ago

Read 2 more answers

Give the diagram below find the value of x

Aleks [24]

Answer:

Well this is Same side interior angles which would mean that its supplementary or 180.

So we can just,

4x-2+17x+14=180

Combine like terms

21x+12=180

Perform inverse

21x=168

Divide/isolate

x=8

So the value of (x) is 8

Step-by-step explanation:

Well here’s a little tip that might help

So in order to identify interior/exterior angles you have to find the location. The two lines are whats separates the inner and the outter.

The Outter are outside the two parralel lines, their not in between. There are 4 exterior angles.

The inner are the 4 angles between the two parralel lines. There are 4 interior angles.

So there are 5 different ways you would usually hear them.

Alternate interior angle

Alternate exterior angle

Same side exterior (or better known as Converese of the same side exterior)

Same side interior (better known as the converse of the same side interior)

Corresponding

Alternate is basically different sides, but they gotta be only one angle choice, exterior or interior, if correct it makes this slash or back slash if you connect the points.

Same side is basically same side and they have to be the right type (exterior/ interior)

Corresponing has to be the same side also but they have to have.One interior and one exterior.

Corresponing angles are congruent (equal)

Alternate exterior/interior are congruent (equal)

Same side exterior/interior Are supplemenaty (they equal 180)

5 0

3 years ago