Answer:
2
Step-by-step explanation:
Answer:
The answer is x=3. YOU add the 6 to the zero and then divide the 2x by 6 and you get 3
What we are being asked here is to simply minimize distance. Also, note that we can write
f
(
x
)
=
√
x
as
y
=
√
x
.
Now, what is this "distance?" How do we find it? Well, if you think back to Algebra I or Geometry, you'll remember that the distance between two points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
is given by:
√
(
y
2
−
y
1
)
2
+
(
x
2
−
x
1
)
2
. For example, the distance between the points
(
4
,
0
)
and
(
0
,
3
)
would be:
√
(
3
−
0
)
2
+
(
4
−
0
)
2
=
√
9
+
16
=
√
25
=
5
Ok, so what is
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
in our example?
(
x
1
,
y
1
)
is simple - it's just the point given in the problem,
(
4
,
0
)
. Because we don't know what
x
2
is, we'll just call it
x
for now. As for
y
2
, we don't know that either; and since
y
=
√
x
, we'll call it
√
x
.
Our formula then becomes:
√
(
√
x
−
0
)
2
+
(
x
−
4
)
2
=
√
(
√
x
2
)
+
x
2
−
8
x
+
16
=
√
x
+
x
2
−
8
x
+
16
=
√
x
2
−
7
x
+
16
We are being asked to minimize this distance, which we'll call
s
to make the following calculations easier. To minimize something, we have to take its derivative, so let's start there:
s
=
√
x
2
−
7
x
+
16
=
(
x
2
−
7
x
+
16
)
1
2
d
s
d
x
=
(
2
x
−
7
)
⋅
1
2
(
x
2
−
7
x
+
16
)
1
2
→
Using power rule and chain rule
d
s
d
x
=
2
x
−
7
2
√
x
2
−
7
x
+
16
Now we set this equal to
0
and solve for
x
:
0
=
2
x
−
7
2
√
x
2
−
7
x
+
16
0
=
2
x
−
7
x
=
7
2
This is known as the critical value, and it represents the
x
-value for which the function is minimized. All we need to do now is find the corresponding
y
-value, using the definition of
y
:
y
=
√
x
. Substituing
7
2
for
x
:
y
=
√
7
2
y
≈
1.87
And voila, the
y
-value. We can now say that the minimum distance between
f
(
x
)
=
√
x
and the point
(
4
,
0
)
(the place where these two are closest) occurs at
(
7
2
,
1.87
)
. For a little extra fun, we can use the distance formula to see what the actual distance between the points is:
s
=
√
(
1.87
−
0
)
2
+
(
7
2
−
4
)
2
≈
1.8
units
Tangerine is simply color orange, which is an addition of red and yellow colors. To analyze if the portions written below are reasonable, the given sum must equal to the sum of the individual red and yellow parts.
Total Red + Total Yellow = 5(3/10)
3(9/10) + 2(3/8) ? 5(3/10
3.45 ? 1.5
3.45 ≠ 1.5
<em>Since they are not equal, then it means the portions are unreasonable.</em>
Answer:
there are 12 in a dice and so it is 7/12x2=14/24 or 1/2 and is the same as 18/36
i think
Step-by-step explanation:
