Answer:
The volume of the solid is 19.
unit³
Step-by-step explanation:
The given function is y = x³
The solid is created by revolving R about the line y = 1
We have that when y = 1, x = 1
Taking the end point as x = 2, we have the volume given by the washer method as follows;
![V = \pi \cdot \int\limits^a_b {\left( [f(x)]^2 - [g(x)]^2 \right)} \, dx](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%5Ccdot%20%5Cint%5Climits%5Ea_b%20%7B%5Cleft%28%20%5Bf%28x%29%5D%5E2%20-%20%5Bg%28x%29%5D%5E2%20%5Cright%29%7D%20%5C%2C%20dx)
Where;
a = 1, and b = 2, we have;
g(x) = 1
![V = \pi \cdot \int\limits^{2}_1 {\left( [x^3]^2 - [1]^2 \right)} \, dx = \pi \cdot \left[\dfrac{x^7}{7} + x \right]_1^{2} = \pi \cdot \left[\dfrac{2^7}{7} +2 -\left( \dfrac{1^7}{7} + 1\right)\right] =19\dfrac{1}{7}](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%5Ccdot%20%5Cint%5Climits%5E%7B2%7D_1%20%7B%5Cleft%28%20%5Bx%5E3%5D%5E2%20-%20%5B1%5D%5E2%20%5Cright%29%7D%20%5C%2C%20dx%20%20%3D%20%5Cpi%20%5Ccdot%20%5Cleft%5B%5Cdfrac%7Bx%5E7%7D%7B7%7D%20%2B%20x%20%5Cright%5D_1%5E%7B2%7D%20%3D%20%5Cpi%20%5Ccdot%20%5Cleft%5B%5Cdfrac%7B2%5E7%7D%7B7%7D%20%2B2%20-%5Cleft%28%20%5Cdfrac%7B1%5E7%7D%7B7%7D%20%2B%201%5Cright%29%5Cright%5D%20%3D19%5Cdfrac%7B1%7D%7B7%7D)
The volume of the solid, V = 
unit³ = 19. unit³
Answer:
A). Farmers refused to move to new territories
Step-by-step explanation:
hope this helps :) :)
Answer:
√
8
≈
3
Explanation:
Note that:
2
2
=
4
<
8
<
9
=
3
2
Hence the (positive) square root of
8
is somewhere between
2
and
3
. Since
8
is much closer to
9
=
3
2
than
4
=
2
2
, we can deduce that the closest integer to the square root is
3
.
We can use this proximity of the square root of
8
to
3
to derive an efficient method for finding approximations.
Consider a quadratic with zeros
3
+
√
8
and
3
−
√
8
:
(
x
−
3
−
√
8
)
(
x
−
3
+
√
8
)
=
(
x
−
3
)
2
−
8
=
x
2
−
6
x
+
1
From this quadratic, we can define a sequence of integers recursively as follows:
⎧
⎪
⎨
⎪
⎩
a
0
=
0
a
1
=
1
a
n
+
2
=
6
a
n
+
1
−
a
n
The first few terms are:
0
,
1
,
6
,
35
,
204
,
1189
,
6930
,
...
The ratio between successive terms will tend very quickly towards
3
+
√
8
.
So:
√
8
≈
6930
1189
−
3
=
3363
1189
≈
2.828427
Answer:
What two consecutive odd integers have a sum of 88? x + x + 2 = 88 • 2x + 2 = 88 • 2x = 86 • x = 43, x + 2 = 45 • 43 + 45 = 88 • Ans: 43, 45 • They equal 88 and are both odd.
2 and 9 thousandths. That is in word form
