Answer:
Step-by-step explanation:
Given:
'w' represents inches of water left after 't' minutes of time.
The dripping out of water is a linear function.
At time 't' equal to 0, the bucket was empty.
After 14 minutes, there are 7 inches of water in the bucket.
A linear function model is of the form: 
Now, at 
At 
Therefore, plugging these values in the above linear model and solving the system of linear equations. This gives,
Therefore, the values of 'm' and 'b' are 0.5 and 0 respectively.
Thus, the linear model is given as:
Answer:
2x+5=31 is the most common correct answer
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:
d = √(x²~x¹)² + (y²-y1)²
Step-by-step explanation:
√(1--3)² + (7-2)²
the square root covers everything
then put this answer on the calculator
The standard equation of a parabola is:
(y-k) = a(x - h)² , where h and k are the coordinates of the Vertex
Since the vertex is ( - 5 , -7), then :
(y +7) = a (x + 5)².
It's given that the vertex is a minimum, that means the coefficient a>0 and the parabola is open upward.
Depending on the value of a (always a>0) , the equation :
y = a(x-5)² + 7 is a parabola
