490.
Solve the system of equations: {15
�
−12
�
=4513
�
+14
�
=162
{
15
x
−12
y
=4513
x
+14
y
=162
. - Answer
: �
=9,
�
=6
x
=9,
y
=6
.
491.
Calculate the value of �
x
in the equation log2(
�
+80)−log2(
�
−75)=12log
2
(
x
+80)−log
2
(
x
−75)=12
. - Answer
: �
=76
x
=76
.
492.
Find the area of a regular 640-gon inscribed in a circle with a radius of 3434
units. - Answer
: Area = 640×12×34×34×sin(360
∘
640)640×
21
×34×34×sin
(
640360
∘
)
.
493.
Determine the value of �
x
in the equation 42
�
−2
�
=439804651110342
x
−2
x
=4398046511103
. - Answer
: �
=19
x
=19
.
494.
Find the sum of the first 530530
terms of an arithmetic sequence
where the first term is 460460
and the common difference is 340340
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=530
n
=530
,
�
=460
a
=460
, �
=340
d
=340
.
495.
Solve the equation 92
�
−2+95
�
+3=98
�
2−
�
−6
x
−292
+
x
+395
=
x
2
−
x
−698
. - Answer
: �
=98
x
=98
.
496.
Calculate the area enclosed by the curve �
=sin(60
�
)
y
=sin(60
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
120
x
=
120
π
. - Answer
: Area = ∫0
�
120sin(60
�
)
��∫
0
120
π
sin(60
x
)
dx
.
497.
Solve the inequality �
2−122
�
+3721<0
x
2
−122
x
+3721<0
. - Answer
: �
=61
x
=61
.
498.
Find the derivative of �
(
�
)=94
�
2+80
�
+94
f
(
x
)=
x
2
+80
x
+9494
. - Answer
: �
′(
�
)
f
′
(
x
)
.
499.
Determine the value of �
x
if log320(
�
−70)+log320(
�
)=2log
320
(
x
−70)+log
320
(
x
)=2
. - Answer
: �
=640
x
=640
.
