290.
Solve the system of equations: {4
�
−3
�
=112
�
+5
�
=8
{
4
x
−3
y
=112
x
+5
y
=8
. - Answer
: �
=2,
�
=−1
x
=2,
y
=−1
.
291.
Calculate the value of �
x
in the equation log5(
�
+17)−log5(
�
−12)=3log
5
(
x
+17)−log
5
(
x
−12)=3
. - Answer
: �
=18
x
=18
.
292.
Find the area of a regular 160-gon inscribed in a circle with a radius of 66
units. - Answer
: Area = 160×12×6×6×sin(360
∘
160)160×
21
×6×6×sin
(
160360
∘
)
.
293.
Determine the value of �
x
in the equation 7
�
−2
�
=327677
x
−2
x
=32767
. - Answer
: �
=8
x
=8
.
294.
Find the sum of the first 110110
terms of an arithmetic sequence
where the first term is 8080
and the common difference is 3030
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=110
n
=110
,
�
=80
a
=80
, �
=30
d
=30
.
295.
Solve the equation 18
�
−2+21
�
+3=24
�
2−
�
−6
x
−218
+
x
+321
=
x
2
−
x
−624
. - Answer
: �
=24
x
=24
.
296.
Calculate the area enclosed by the curve �
=sin(20
�
)
y
=sin(20
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
40
x
=
40
π
. - Answer
: Area = ∫0
�
40sin(20
�
)
��∫
0
40
π
sin(20
x
)
dx
.
297.
Solve the inequality �
2−42
�
+441<0
x
2
−42
x
+441<0
. - Answer
: �
=21
x
=21
.
298.
Find the derivative of �
(
�
)=22
�
2+16
�
+22
f
(
x
)=
x
2
+16
x
+2222
. - Answer
: �
′(
�
)
f
′
(
x
)
.
299.
Determine the value of �
x
if log25(
�
−11)+log25(
�
)=2log
25
(
x
−11)+log
25
(
x
)=2
. - Answer
: �
=50
x
=50
.
