Answer:
2
−
9
x
Step-by-step explanation:
f
'
(
x
)
=
1
(
x
+
1
)
2
Explanation:
differentiating from first principles
f
'
(
x
)
=
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
f
'
(
x
)
=
lim
h
→
0
x
+
h
x
+
h
+
1
−
x
x
+
1
h
the aim now is to eliminate h from the denominator
f
'
(
x
)
=
lim
h
=0
(
x
+
h
)
(
x
+
1
)−
x
(
x
+
h
+
1)
h
(
x
+
1
)
(
x
+
h
+
1
)
f
'
(
x
)
=
lim
h
→
0
x
2
+
h
x
+
x
+
h
−
x
2
−
h
x
−
x
h
(
x
+
1
)
(
x+h
+
1
)
f
'
(
x
)
=
lim
h
→
0
h
1
h
1
(
x
+
1
)
(
x
+
h
+1
)
f
'
(
x
)
=
1
(
x
+
1
)
2
Answer:
Step-by-step explanation:
From the question, we are informed that Michael and Tyler both ran a half marathon and that Michael finished in 1 hour, 42 minutes and 13 seconds while Tyler finished in 97 minutes and 49 seconds.
First, we should know that 60 minutes makes 1 hour, therefore we need to change Tyler's time taken to finish the marathon appropriately. Since Tyler finished in 97 minutes and 49 seconds, this will be converted to 97 minutes equals 1 hour 37 minutes. Therefore, Tyler used 1 hour, 37 minutes and 49 seconds.
Since Michael finished in 1 hour, 42 minutes and 13 seconds while Tyler finished in 1 hour, 37 minutes and 49 seconds. We can see that Tyler is faster than Michael.
To know how much faster Tyler was, we subtract Tyler's time from Michael's. This will be:
= (1 hour, 42 minutes 13 seconds) - (1 hour, 37 minutes, 49 seconds)
= 4 minutes, 24 seconds.
Tyler was faster by 4 minutes, 24 seconds.
<span>log_9 x + log_9 (x + 12) = log_9 64?
answer is x=4</span>
Eqn (1)*3: 15x + 6y = -9 -> Eqn (3)
Eqn (3) - Eqn (2): 12x = -15
x = -5/4 = -1 1/4
Eqn (2): -15/4 + 6y = 6
6y = 9 3/4
y = 1 5/8
x = -1 1/4
y= 1 5/8
