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:
if we simplify then the answer is 7k
Step-by-step explanation:
can someone please answer my question from my profile.
The answer is (x,y) = (-2, 16)
do you need an explanation as well?
Using the equation of the circle, it is found that since it reaches an identity, the point (√5, 12) is on the circle.
<h3>What is the equation of a circle?</h3>
The equation of a circle of center 
and radius r is given by:
In this problem, the circle is centered at the origin, hence 
.
The circle contains the point (-13,0), hence the radius is found as follows:
Hence the equation is:
Then, we test if point (√5, 12) is on the circle:
25 + 144 = 169
Which is an identity, hence point (√5, 12) is on the circle.
More can be learned about the equation of a circle at brainly.com/question/24307696
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