Answer:
10 water stations are needed
Step-by-step explanation:
To get the number of water- station needed, we simply divide the total length of the half marathon by the distance where we can find a water station
mathematically,
that would be 13.1 divided by 1 1/3
= 13.1 divided by 4/3
= 13.1 * 3/4 = 9.825 which is approximately 10
Answer:
see below
Step-by-step explanation:
![x^{\frac{p}{r}}=\sqrt[r]{x^{p}}](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7Bp%7D%7Br%7D%7D%3D%5Csqrt%5Br%5D%7Bx%5E%7Bp%7D%7D)
![3a^\frac{5}{3} =\sqrt[3]{3a^5}](https://tex.z-dn.net/?f=3a%5E%5Cfrac%7B5%7D%7B3%7D%20%3D%5Csqrt%5B3%5D%7B3a%5E5%7D)
Answer:4x
Step-by-step explanation:
Answer:
4x+2h
Step-by-step explanation:
The average rate of change of a continuous function,
f
(
x
)
, on a closed interval
[
a
,
b
]
is given by
f
(
b
)
−
f
(
a
)
b
−
a
So the average rate of change of the function
f
(
x
)
=
2
x
2
+
1
on
[
x
,
x
+
h
]
is:
A
r
o
c
=
f
(
x
+
h
)
−
f
(
x
)
(
x
+
h
)
−
(
x
)
=
f
(
x
+
h
)
−
f
(
x
)
h
...
.
.
[
1
]
=
2
(
x
+
h
)
2
+
1
−
(
2
x
2
+
1
)
h
=
2
(
x
2
+
2
x
h
+
h
2
)
+
1
−
2
x
2
−
1
h
=
2
x
2
+
4
x
h
+
2
h
2
−
2
x
2
h
=
4
x
h
+
2
h
2
h
=
4
x
+
2
h
Which is the required answer.
Additional Notes:
Note that this question is steered towards deriving the derivative
f
'
(
x
)
from first principles, as the definition of the derivative is:
f
'
(
x
)
=
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
This is the function we had in [1], so as we take the limit as
h
→
0
we get the derivative
f
'
(
x
)
for any
x
, This:
f
'
(
x
)
=
lim
h
→
0
4
x
+
2
h
=
4
x
