Answer:
<em>Both lights will blink at the same time 12 times in 3 minutes</em>
Step-by-step explanation:
<u>Greatest Common Factor (GCF)
</u>
The greatest common factor of a set of numbers is the largest positive integer that divides exactly into all numbers. For example, 24 is the GCF of 6 and 8 because there is no smaller number who divides both numbers with zero-remainder.
We know two neon lights blink every 6 seconds and 8 seconds respectively. It means they coincide every 24 seconds. Thus it's only a matter of know how many times we can count 24 seconds in 300 seconds. We can easily find it by dividing 300/24=12.5
So both lights will blink at the same time 12 times in 3 minutes
Start: 21.5
After Tacos: 21.5*(1-1/4)=21.5*(3/4)=16.125
Used For Burgers: 16.125*(2/3)=10.75
Burgers: 10.75/(1/4)=10.75*4=43
89 divided by 21 is 4.23 then add a notation bar above the 3
We will use integration by substitution, as well as the integrals
∫
1
x
d
x
=
ln
|
x
|
+
C
and
∫
1
d
x
=
x
+
C
∫
x
3
x
2
+
1
d
x
=
∫
x
2
x
2
+
1
x
d
x
=
1
2
∫
(
x
2
+
1
)
−
1
x
2
+
1
2
x
d
x
Let
u
=
x
2
+
1
⇒
d
u
=
2
x
d
x
. Then
1
2
∫
(
x
2
+
1
)
−
1
x
2
+
1
2
x
d
x
=
1
2
∫
u
−
1
u
d
u
=
1
2
∫
(
1
−
1
u
)
d
u
=
1
2
(
u
−
ln
|
u
|
)
+
C
=
x
2
+
1
2
−
ln
(
x
2
+
1
)
2
+
C
=
x
2
2
−
ln
(
x
2
+
1
)
2
+
1
2
+
C
=
x
2
−
ln
(
x
2
+
1
)
2
+
C
Final answer