560.
Solve the system of equations: {22
�
−19
�
=6620
�
+21
�
=267
{
22
x
−19
y
=6620
x
+21
y
=267
. - Answer
: �
=9,
�
=6
x
=9,
y
=6
.
561.
Calculate the value of �
x
in the equation log2(
�
+115)−log2(
�
−110)=19log
2
(
x
+115)−log
2
(
x
−110)=19
. - Answer
: �
=111
x
=111
.
562.
Find the area of a regular 780-gon inscribed in a circle with a radius of 4848
units. - Answer
: Area = 780×12×48×48×sin(360
∘
780)780×
21
×48×48×sin
(
780360
∘
)
.
563.
Determine the value of �
x
in the equation 70
�
−2
�
=236118324143482260684770
x
−2
x
=236118324143482260684
7
. - Answer
: �
=26
x
=26
.
564.
Find the sum of the first 670670
terms of an arithmetic sequence
where the first term is 600600
and the common difference is 480480
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=670
n
=670
,
�
=600
a
=600
, �
=480
d
=480
.
565.
Solve the equation 124
�
−2+127
�
+3=130
�
2−
�
−6
x
−2124
+
x
+3127
=
x
2
−
x
−6130
. - Answer
: �
=130
x
=130
.
566.
Calculate the area enclosed by the curve �
=sin(74
�
)
y
=sin(74
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
148
x
=
148
π
. - Answer
: Area = ∫0
�
148sin(74
�
)
��∫
0
148
π
sin(74
x
)
dx
.
567.
Solve the inequality �
2−154
�
+5929<0
x
2
−154
x
+5929<0
. - Answer
: �
=77
x
=77
.
568.
Find the derivative of �
(
�
)=122
�
2+108
�
+122
f
(
x
)=
x
2
+108
x
+122122
. - Answer
: �
′(
�
)
f
′
(
x
)
.
569.
Determine the value of �
x
if log460(
�
−98)+log460(
�
)=2log
460
(
x
−98)+log
460
(
x
)=2
. - Answer
: �
=920
x
=920
.
