390.
Solve the system of equations: {5
�
−2
�
=153
�
+4
�
=25
{
5
x
−2
y
=153
x
+4
y
=25
. - Answer
: �
=3,
�
=2
x
=3,
y
=2
.
391.
Calculate the value of �
x
in the equation log2(
�
+30)−log2(
�
−25)=5log
2
(
x
+30)−log
2
(
x
−25)=5
. - Answer
: �
=26
x
=26
.
392.
Find the area of a regular 400-gon inscribed in a circle with a radius of 1212
units. - Answer
: Area = 400×12×12×12×sin(360
∘
400)400×
21
×12×12×sin
(
400360
∘
)
.
393.
Determine the value of �
x
in the equation 18
�
−2
�
=26214318
x
−2
x
=262143
. - Answer
: �
=9
x
=9
.
394.
Find the sum of the first 310310
terms of an arithmetic sequence
where the first term is 260260
and the common difference is 140140
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=310
n
=310
,
�
=260
a
=260
, �
=140
d
=140
.
395.
Solve the equation 52
�
−2+55
�
+3=58
�
2−
�
−6
x
−252
+
x
+355
=
x
2
−
x
−658
. - Answer
: �
=58
x
=58
.
396.
Calculate the area enclosed by the curve �
=sin(40
�
)
y
=sin(40
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
80
x
=
80
π
. - Answer
: Area = ∫0
�
80sin(40
�
)
��∫
0
80
π
sin(40
x
)
dx
.
397.
Solve the inequality �
2−82
�
+1681<0
x
2
−82
x
+1681<0
. - Answer
: �
=41
x
=41
.
398.
Find the derivative of �
(
�
)=52
�
2+40
�
+52
f
(
x
)=
x
2
+40
x
+5252
. - Answer
: �
′(
�
)
f
′
(
x
)
.
399.
Determine the value of �
x
if log120(
�
−30)+log120(
�
)=2log
120
(
x
−30)+log
120
(
x
)=2
. - Answer
: �
=240
x
=240
.
