530.
Solve the system of equations: {19
�
−16
�
=5717
�
+18
�
=222
{
19
x
−16
y
=5717
x
+18
y
=222
. - Answer
: �
=9,
�
=6
x
=9,
y
=6
.
531.
Calculate the value of �
x
in the equation log2(
�
+100)−log2(
�
−95)=16log
2
(
x
+100)−log
2
(
x
−95)=16
. - Answer
: �
=96
x
=96
.
532.
Find the area of a regular 720-gon inscribed in a circle with a radius of 4242
units. - Answer
: Area = 720×12×42×42×sin(360
∘
720)720×
21
×42×42×sin
(
720360
∘
)
.
533.
Determine the value of �
x
in the equation 58
�
−2
�
=28823037615171174358
x
−2
x
=288230376151711743
. - Answer
: �
=23
x
=23
.
534.
Find the sum of the first 610610
terms of an arithmetic sequence
where the first term is 540540
and the common difference is 420420
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=610
n
=610
,
�
=540
a
=540
, �
=420
d
=420
.
535.
Solve the equation 108
�
−2+111
�
+3=114
�
2−
�
−6
x
−2108
+
x
+3111
=
x
2
−
x
−6114
. - Answer
: �
=114
x
=114
.
536.
Calculate the area enclosed by the curve �
=sin(68
�
)
y
=sin(68
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
136
x
=
136
π
. - Answer
: Area = ∫0
�
136sin(68
�
)
��∫
0
136
π
sin(68
x
)
dx
.
537.
Solve the inequality �
2−138
�
+4761<0
x
2
−138
x
+4761<0
. - Answer
: �
=69
x
=69
.
538.
Find the derivative of �
(
�
)=110
�
2+96
�
+110
f
(
x
)=
x
2
+96
x
+110110
.
- Answer
: �
′(
�
)
f
′
(
x
)
.
539.
Determine the value of �
x
if log400(
�
−86)+log400(
�
)=2log
400
(
x
−86)+log
400
(
x
)=2
. - Answer
: �
=800
x
=800
.
