540.
Solve the system of equations: {20
�
−17
�
=6018
�
+19
�
=237
{
20
x
−17
y
=6018
x
+19
y
=237
. - Answer
: �
=9,
�
=6
x
=9,
y
=6
.
541.
Calculate the value of �
x
in the equation log2(
�
+105)−log2(
�
−100)=17log
2
(
x
+105)−log
2
(
x
−100)=17
. - Answer
: �
=101
x
=101
.
542.
Find the area of a regular 740-gon inscribed in a circle with a radius of 4444
units. - Answer
: Area = 740×12×44×44×sin(360
∘
740)740×
21
×44×44×sin
(
740360
∘
)
.
543.
Determine the value of �
x
in the equation 62
�
−2
�
=236118324143482260684762
x
−2
x
=236118324143482260684
7
. - Answer
: �
=24
x
=24
.
544.
Find the sum of the first 630630
terms of an arithmetic sequence
where the first term is 560560
and the common difference is 440440
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=630
n
=630
,
�
=560
a
=560
, �
=440
d
=440
.
545.
Solve the equation 116
�
−2+119
�
+3=122
�
2−
�
−6
x
−2116
+
x
+3119
=
x
2
−
x
−6122
. - Answer
: �
=122
x
=122
.
546.
Calculate the area enclosed by the curve �
=sin(70
�
)
y
=sin(70
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
140
x
=
140
π
. - Answer
: Area = ∫0
�
140sin(70
�
)
��∫
0
140
π
sin(70
x
)
dx
.
547.
Solve the inequality �
2−142
�
+5041<0
x
2
−142
x
+5041<0
. - Answer
: �
=71
x
=71
.
548.
Find the derivative of �
(
�
)=114
�
2+100
�
+114
f
(
x
)=
x
2
+100
x
+114114
. - Answer
: �
′(
�
)
f
′
(
x
)
.
549.
Determine the value of �
x
if log420(
�
−90)+log420(
�
)=2log
420
(
x
−90)+log
420
(
x
)=2
. - Answer
: �
=840
x
=840
.
