460.
Solve the system of equations: {12
�
−9
�
=3610
�
+11
�
=117
{
12
x
−9
y
=3610
x
+11
y
=117
. - Answer
: �
=7,
�
=6
x
=7,
y
=6
.
461.
Calculate the value of �
x
in the equation log2(
�
+65)−log2(
�
−60)=9log
2
(
x
+65)−log
2
(
x
−60)=9
. - Answer
: �
=61
x
=61
.
462.
Find the area of a regular 560-gon inscribed in a circle with a radius of 2828
units. - Answer
: Area = 560×12×28×28×sin(360
∘
560)560×
21
×28×28×sin
(
560360
∘
)
.
463.
Determine the value of �
x
in the equation 32
�
−2
�
=429496729532
x
−2
x
=4294967295
. - Answer
: �
=16
x
=16
.
464.
Find the sum of the first 470470
terms of an arithmetic sequence
where the first term is 400400
and the common difference is 280280
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=470
n
=470
,
�
=400
a
=400
, �
=280
d
=280
.
465.
Solve the equation 80
�
−2+83
�
+3=86
�
2−
�
−6
x
−280
+
x
+383
=
x
2
−
x
−686
. - Answer
: �
=86
x
=86
.
466.
Calculate the area enclosed by the curve �
=sin(54
�
)
y
=sin(54
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
108
x
=
108
π
. - Answer
: Area = ∫0
�
108sin(54
�
)
��∫
0
108
π
sin(54
x
)
dx
.
467.
Solve the inequality �
2−110
�
+3025<0
x
2
−110
x
+3025<0
. - Answer
: �
=55
x
=55
.
468.
Find the derivative of �
(
�
)=82
�
2+68
�
+82
f
(
x
)=
x
2
+68
x
+8282
. - Answer
: �
′(
�
)
f
′
(
x
)
.
469.
Determine the value of �
x
if log260(
�
−58)+log260(
�
)=2log
260
(
x
−58)+log
260
(
x
)=2
. - Answer
: �
=520
x
=520
.
