470.
Solve the system of equations: {13
�
−10
�
=3911
�
+12
�
=132
{
13
x
−10
y
=3911
x
+12
y
=132
. - Answer
: �
=8,
�
=6
x
=8,
y
=6
.
471.
Calculate the value of �
x
in the equation log2(
�
+70)−log2(
�
−65)=10log
2
(
x
+70)−log
2
(
x
−65)=10
. - Answer
: �
=66
x
=66
.
472.
Find the area of a regular 600-gon inscribed in a circle with a radius of 3030
units. - Answer
: Area = 600×12×30×30×sin(360
∘
600)600×
21
×30×30×sin
(
600360
∘
)
.
473.
Determine the value of �
x
in the equation 34
�
−2
�
=1717986918334
x
−2
x
=17179869183
. - Answer
: �
=17
x
=17
.
474.
Find the sum of the first 490490
terms of an arithmetic sequence
where the first term is 420420
and the common difference is 300300
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=490
n
=490
,
�
=420
a
=420
, �
=300
d
=300
.
475.
Solve the equation 84
�
−2+87
�
+3=90
�
2−
�
−6
x
−284
+
x
+387
=
x
2
−
x
−690
. - Answer
: �
=90
x
=90
.
476.
Calculate the area enclosed by the curve �
=sin(56
�
)
y
=sin(56
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
112
x
=
112
π
. - Answer
: Area = ∫0
�
112sin(56
�
)
��∫
0
112
π
sin(56
x
)
dx
.
477.
Solve the inequality �
2−114
�
+3249<0
x
2
−114
x
+3249<0
. - Answer
: �
=57
x
=57
.
478.
Find the derivative of �
(
�
)=86
�
2+72
�
+86
f
(
x
)=
x
2
+72
x
+8686
. - Answer
: �
′(
�
)
f
′
(
x
)
.
479.
Determine the value of �
x
if log280(
�
−62)+log280(
�
)=2log
280
(
x
−62)+log
280
(
x
)=2
. - Answer
: �
=560
x
=560
.
