For
to be a proper density function, we need to have the integral over its support
to equal 1.
Now,
Answer:
13.5 meters
Step-by-step explanation:
lets take width as w
l=24
and length is 3 meters less than twice the width
so
l+3=2w
24+3=2w
27=2w
divide both sides by "2"
27/2=13.5
13.5=w
x
4
−
12
x
2
=
64
x
4
-
12
x
2
=
64
Move
64
64
to the left side of the equation by subtracting it from both sides.
x
4
−
12
x
2
−
64
=
0
x
4
-
12
x
2
-
64
=
0
Rewrite
x
4
x
4
as
(
x
2
)
2
(
x
2
)
2
.
(
x
2
)
2
−
12
x
2
−
64
=
0
(
x
2
)
2
-
12
x
2
-
64
=
0
Let
u
=
x
2
u
=
x
2
. Substitute
u
u
for all occurrences of
x
2
x
2
.
u
2
−
12
u
−
64
=
0
u
2
-
12
u
-
64
=
0
Factor
u
2
−
12
u
−
64
u
2
-
12
u
-
64
using the AC method.
Tap for fewer steps...
Consider the form
x
2
+
b
x
+
c
x
2
+
b
x
+
c
. Find a pair of integers whose product is
c
c
and whose sum is
b
b
. In this case, whose product is
−
64
-
64
and whose sum is
−
12
-
12
.
−
16
,
4
-
16
,
4
Write the factored form using these integers.
(
u
−
16
)
(
u
+
4
)
=
0
(
u
-
16
)
(
u
+
4
)
=
0
Replace all occurrences of
u
u
with
x
2
x
2
.
(
x
2
−
16
)
(
x
2
+
4
)
=
0
(
x
2
-
16
)
(
x
2
+
4
)
=
0
Rewrite
16
16
as
4
2
4
2
.
(
x
2
−
4
2
)
(
x
2
+
4
)
=
0
(
x
2
-
4
2
)
(
x
2
+
4
)
=
0
Since both terms are perfect squares, factor using the difference of squares formula,
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
a
2
-
b
2
=
(
a
+
b
)
(
a
-
b
)
where
a
=
x
a
=
x
and
b
=
4
b
=
4
.
(
x
+
4
)
(
x
−
4
)
(
x
2
+
4
)
=
0
(
x
+
4
)
(
x
-
4
)
(
x
2
+
4
)
=
0
If any individual factor on the left side of the equation is equal to
0
0
, the entire expression will be equal to
0
0
.
x
+
4
=
0
x
+
4
=
0
x
−
4
=
0
x
-
4
=
0
x
2
+
4
=
0
x
2
+
4
=
0
Set the first factor equal to
0
0
and solve.
Tap for fewer steps...
Set the first factor equal to
0
0
.
x
+
4
=
0
x
+
4
=
0
Subtract
4
4
from both sides of the equation.
x
=
−
4
x
=
-
4
Set the next factor equal to
0
0
and solve.
Tap for more steps...
x
=
4
x
=
4
Set the next factor equal to
0
0
and solve.
Tap for more steps...
x
=
2
i
,
−
2
i
x
=
2
i
,
-
2
i
The final solution is all the values that make
(
x
+
4
)
(
x
−
4
)
(
x
2
+
4
)
=
0
(
x
+
4
)
(
x
-
4
)
(
x
2
+
4
)
=
0
true.
x
=
−
4
,
4
,
2
i
,
−
2
i
x
=
-
4
,
4
,
2
i
,
-
2
i
x
4
−
1
2
x
2
=
6
4
x
4
-
1
2
x
2
=
6
4
The easiest way to find answers for questions like these is to convert them to improper fractions, solve, and then convert them back to mixed numbers (if the question required it). When we convert these to improper fractions, we have 7/4 and 19/8. We can then find the least common denominator of the 2 so that we can solve. The least common denominator is 8, and since we are multiplying the 4 by 2 to get it there, we must also multiply the 7 by 2. Now we have 19/8-14/8. At this point, we can use simple subtraction to subtract the numerators and get 5/8.
To summarize, Cameron used 5/8 more acid in the second experiment.