Answer:
Answer is 39
Step-by-step explanation:
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:
2 x 2 x 2 x 5
Step-by-step explanation:
The first few prime numbers: {2, 3, 5, 7, 11, 13, 17, 19}
One way to start is to divide by the first prime until you can't do that any more, then try the next prime and so on until all the numbers in your list are prime.
40 = 2(20) divide 20 by 2 again
40 = 2(2)(10) divide 10 by 2 again
40 = 2(2)(2)(5) stop--all factors are prime.
Answer:
4-3x over x or 4-3x/x
I'm not sure. but I hope it can help you:))
Answer:
It would be helpful if you show me the figure. Thanks :) !!
