220.
Solve the system of equations: {4
�
−2
�
=93
�
+3
�
=12
{
4
x
−2
y
=93
x
+3
y
=12
. - Answer
: �
=3,
�
=1
x
=3,
y
=1
.
221.
Calculate the value of �
x
in the equation log2(
�
+9)−log2(
�
−4)=4log
2
(
x
+9)−log
2
(
x
−4)=4
. - Answer
: �
=13
x
=13
.
222.
Find the area of a regular 40-gon inscribed in a circle with a radius of 77
units. - Answer
: Area = 40×12×7×7×sin(360
∘
40)40×
21
×7×7×sin
(
40360
∘
)
.
223.
Determine the value of �
x
in the equation 4
�
−2
�
=2554
x
−2
x
=255
. - Answer
: �
=5
x
=5
.
224.
Find the sum of the first 6060
terms of an arithmetic sequence where the first term is 2525
and the common difference is 99
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=60
n
=60
, �
=25
a
=25
, �
=9
d
=9
.
225.
Solve the equation 7
�
−2+8
�
+3=9
�
2−
�
−6
x
−27
+
x
+38
=
x
2
−
x
−69
. - Answer
: �
=9
x
=9
.
226.
Calculate the area enclosed by the curve �
=sin(7
�
)
y
=sin(7
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
14
x
=
14
π
. - Answer
: Area = ∫0
�
14sin(7
�
)
��∫
0
14
π
sin(7
x
)
dx
.
227.
Solve the inequality �
2−24
�
+144<0
x
2
−24
x
+144<0
. - Answer
: �
=12
x
=12
.
228.
Find the derivative of �
(
�
)=8
�
2+6
�
+8
f
(
x
)=
x
2
+6
x
+88
. - Answer
: �
′(
�
)
f
′
(
x
)
.
229.
Determine the value of �
x
if log8(
�
−4)+log8(
�
)=3log
8
(
x
−4)+log
8
(
x
)=3
. - Answer
: �
=32
x
=32
.
