Answer:
2 1/6
Step-by-step explanation:
Answer:
- r1 +4×r3 ⇒ r1
- r2 -3×r3 ⇒ r2
Step-by-step explanation:
We note that the coefficient of y in equation (iii) is 1, so it is convenient to use that equation to eliminate y from the others.
__
<em>To eliminate the y-variable from equation (i), four times equation (iii) can be added to equation (i).</em>
<em>To eliminate the y-variable from equation (ii), three times equation (iii) can be subtracted from equation (i).</em>
_____
The result of these operations would be ...
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:
Step-by-step explanation:
The surface area of the cone shaped roof is:
The cost of roofing per square feet is: (USD stands for US dollar)
