440.
Solve the system of equations: {10
�
−7
�
=308
�
+9
�
=87
{
10
x
−7
y
=308
x
+9
y
=87
. - Answer
: �
=7,
�
=6
x
=7,
y
=6
.
441.
Calculate the value of �
x
in the equation log2(
�
+55)−log2(
�
−50)=7log
2
(
x
+55)−log
2
(
x
−50)=7
. - Answer
: �
=51
x
=51
.
442.
Find the area of a regular 520-gon inscribed in a circle with a radius of 2424
units. - Answer
: Area = 520×12×24×24×sin(360
∘
520)520×
21
×24×24×sin
(
520360
∘
)
.
443.
Determine the value of �
x
in the equation 28
�
−2
�
=6710886328
x
−2
x
=67108863
. - Answer
: �
=14
x
=14
.
444.
Find the sum of the first 430430
terms of an arithmetic sequence
where the first term is 360360
and the common difference is 240240
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=430
n
=430
,
�
=360
a
=360
, �
=240
d
=240
.
445.
Solve the equation 72
�
−2+75
�
+3=78
�
2−
�
−6
x
−272
+
x
+375
=
x
2
−
x
−678
. - Answer
: �
=78
x
=78
.
446.
Calculate the area enclosed by the curve �
=sin(50
�
)
y
=sin(50
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
100
x
=
100
π
. - Answer
: Area = ∫0
�
100sin(50
�
)
��∫
0
100
π
sin(50
x
)
dx
.
447.
Solve the inequality �
2−102
�
+2601<0
x
2
−102
x
+2601<0
. - Answer
: �
=51
x
=51
.
448.
Find the derivative of �
(
�
)=74
�
2+60
�
+74
f
(
x
)=
x
2
+60
x
+7474
. - Answer
: �
′(
�
)
f
′
(
x
)
.
449.
Determine the value of �
x
if log220(
�
−50)+log220(
�
)=2log
220
(
x
−50)+log
220
(
x
)=2
. - Answer
: �
=440
x
=440
.
