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
Solve for r in the first equation:
3(r+300) = 6
Use the distributive property:
3r + 900 = 6
Subtract 900 from both sides:
3r = -894
Divide both sides by 3:
r = -894 / 3
r = -298
Now you have r, replace r in the second equation and solve:
r +300 -2 =
-298 + 300 - 2 = 0
The answer is 0.
3 weeks
Step-by-step explanation:
To find the number of weeks, we have to equate the amount already saved and planned to save by both each week.
So we can write the expression as,
Let w be the number of weeks.
25 + 5w =16 + 8w
Grouping the terms as,
25 - 16 = 8w - 5w
9 = 3w
Dividing both sides by 3, we will get,
3w/3 = 9/3
w = 3
So number of weeks = 3
Step-by-step explanation:
We have got the lines :
Both lines intercept the x-axis in the point :
In all point from x-axis the y-component is equal to 0.
We replace the I point in the lines equations:
From the first equation :
From the second equation :
Then 
Finally :
y = ax + b and y = cx + d have the same x-intercept ⇔ad=bc
Answer:
Mean Absolute Deviation (MAD): 1.6
