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
The factors of 33 are <u>1</u>, 3, <u>11</u>, and 33 .
The factors of 55 are <u>1</u>, 5, <u>11</u>, and 55 .
The <u>common</u> factors of 33 and 55 are 1 and 11 .
The<u> greatest</u> one is <em>11</em> .
Answer:
y because its y i really dont no
Answer:
Since there are 60 seconds in one minute, we can write this as 146,000 inches per minute. Since there are 60 * 60 = 3600 minutes in one day, we can write it as 525,600,000 inches per day. Since there are about 63360 inches in one mile, the answer is about 8295 miles per day.
I'm pretty sure 10/63 is simplified.
