550.
Solve the system of equations: {21
�
−18
�
=6319
�
+20
�
=252
{
21
x
−18
y
=6319
x
+20
y
=252
. - Answer
: �
=9,
�
=6
x
=9,
y
=6
.
551.
Calculate the value of �
x
in the equation log2(
�
+110)−log2(
�
−105)=18log
2
(
x
+110)−log
2
(
x
−105)=18
. - Answer
: �
=106
x
=106
.
552.
Find the area of a regular 760-gon inscribed in a circle with a radius of 4646
units. - Answer
: Area = 760×12×46×46×sin(360
∘
760)760×
21
×46×46×sin
(
760360
∘
)
.
553.
Determine the value of �
x
in the equation 66
�
−2
�
=7555786372591432341913566
x
−2
x
=75557863725914323419
135
. - Answer
: �
=25
x
=25
.
554.
Find the sum of the first 650650
terms of an arithmetic sequence
where the first term is 580580
and the common difference is 460460
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=650
n
=650
,
�
=580
a
=580
, �
=460
d
=460
.
555.
Solve the equation 120
�
−2+123
�
+3=126
�
2−
�
−6
x
−2120
+
x
+3123
=
x
2
−
x
−6126
. - Answer
: �
=126
x
=126
.
556.
Calculate the area enclosed by the curve �
=sin(72
�
)
y
=sin(72
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
144
x
=
144
π
. - Answer
: Area = ∫0
�
144sin(72
�
)
��∫
0
144
π
sin(72
x
)
dx
.
557.
Solve the inequality �
2−150
�
+5625<0
x
2
−150
x
+5625<0
. - Answer
: �
=75
x
=75
.
558.
Find the derivative of �
(
�
)=118
�
2+104
�
+118
f
(
x
)=
x
2
+104
x
+118118
. - Answer
: �
′(
�
)
f
′
(
x
)
.
559.
Determine the value of �
x
if log440(
�
−94)+log440(
�
)=2log
440
(
x
−94)+log
440
(
x
)=2
. - Answer
: �
=880
x
=880
.
