180.
Solve the system of equations: {2
�
−3
�
=74
�
+
�
=1
{
2
x
−3
y
=74
x
+
y
=1
. - Answer
: �
=2,
�
=−7
x
=2,
y
=−7
.
181.
Calculate the value of �
x
in the equation log2(
�
+4)−log2(
�
−1)=3log
2
(
x
+4)−log
2
(
x
−1)=3
. - Answer
: �
=9
x
=9
.
182.
Find the area of a regular 16-gon inscribed in a circle with a radius of 1515
units. - Answer
: Area = 16×12×15×15×sin(360
∘
16)16×
21
×15×15×sin
(
16360
∘
)
.
183.
Determine the value of �
x
in the equation 5
�
−2
�
=535
x
−2
x
=53
. - Answer
: �
=3
x
=3
.
184.
Find the sum of the first 4040
terms of an arithmetic sequence where the first term is 1010
and the common difference is 44
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=40
n
=40
, �
=10
a
=10
, �
=4
d
=4
.
185.
Solve the equation 2
�
−1+3
�
+4=5
�
2−
�
−4
x
−12
+
x
+43
=
x
2
−
x
−45
. - Answer
: �
=4
x
=4
.
186.
Calculate the area enclosed by the curve �
=sin(3
�
)
y
=sin(3
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
6
x
=
6
π
. - Answer
: Area = ∫0
�
6sin(3
�
)
��∫
0
6
π
sin(3
x
)
dx
.
187.
Solve the inequality �
2−16
�
+63<0
x
2
−16
x
+63<0
. - Answer
: 3<
�
<133<
x
<13
.
188.
Find the derivative of �
(
�
)=3
�
2+2
�
+1
f
(
x
)=
x
2
+2
x
+13
. - Answer
: �
′(
�
)
f
′
(
x
)
.
189.
Determine the value of �
x
if log4(
�
−1)+log4(
�
)=2log
4
(
x
−1)+log
4
(
x
)=2
. - Answer
: �
=5
x
=5
.
