370.
Solve the system of equations: {5
�
−2
�
=163
�
+4
�
=23
{
5
x
−2
y
=163
x
+4
y
=23
. - Answer
: �
=3,
�
=2
x
=3,
y
=2
.
371.
Calculate the value of �
x
in the equation log2(
�
+25)−log2(
�
−20)=4log
2
(
x
+25)−log
2
(
x
−20)=4
. - Answer
: �
=21
x
=21
.
372.
Find the area of a regular 320-gon inscribed in a circle with a radius of 99
units. - Answer
: Area = 320×12×9×9×sin(360
∘
320)320×
21
×9×9×sin
(
320360
∘
)
.
373.
Determine the value of �
x
in the equation 14
�
−2
�
=52428714
x
−2
x
=524287
. - Answer
: �
=10
x
=10
.
374.
Find the sum of the first 270270
terms of an arithmetic sequence
where the first term is 220220
and the common difference is 100100
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=270
n
=270
,
�
=220
a
=220
, �
=100
d
=100
.
375.
Solve the equation 44
�
−2+47
�
+3=50
�
2−
�
−6
x
−244
+
x
+347
=
x
2
−
x
−650
. - Answer
: �
=50
x
=50
.
376.
Calculate the area enclosed by the curve �
=sin(36
�
)
y
=sin(36
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
72
x
=
72
π
. - Answer
: Area = ∫0
�
72sin(36
�
)
��∫
0
72
π
sin(36
x
)
dx
.
377.
Solve the inequality �
2−74
�
+1369<0
x
2
−74
x
+1369<0
. - Answer
: �
=37
x
=37
.
378.
Find the derivative of �
(
�
)=48
�
2+32
�
+48
f
(
x
)=
x
2
+32
x
+4848
. - Answer
: �
′(
�
)
f
′
(
x
)
.
379.
Determine the value of �
x
if log100(
�
−26)+log100(
�
)=2log
100
(
x
−26)+log
100
(
x
)=2
. - Answer
: �
=200
x
=200
.
