360.
Solve the system of equations: {4
�
−3
�
=112
�
+5
�
=17
{
4
x
−3
y
=112
x
+5
y
=17
. - Answer
: �
=4,
�
=1
x
=4,
y
=1
.
361.
Calculate the value of �
x
in the equation log3(
�
+23)−log3(
�
−18)=4log
3
(
x
+23)−log
3
(
x
−18)=4
. - Answer
: �
=19
x
=19
.
362.
Find the area of a regular 300-gon inscribed in a circle with a radius of 1010
units. - Answer
: Area = 300×12×10×10×sin(360
∘
300)300×
21
×10×10×sin
(
300360
∘
)
.
363.
Determine the value of �
x
in the equation 12
�
−2
�
=26214312
x
−2
x
=262143
. - Answer
: �
=9
x
=9
.
364.
Find the sum of the first 250250
terms of an arithmetic sequence
where the first term is 200200
and the common difference is 8080
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=250
n
=250
,
�
=200
a
=200
, �
=80
d
=80
.
365.
Solve the equation 40
�
−2+43
�
+3=46
�
2−
�
−6
x
−240
+
x
+343
=
x
2
−
x
−646
. - Answer
: �
=46
x
=46
.
366.
Calculate the area enclosed by the curve �
=sin(34
�
)
y
=sin(34
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
68
x
=
68
π
. - Answer
: Area = ∫0
�
68sin(34
�
)
��∫
0
68
π
sin(34
x
)
dx
.
367.
Solve the inequality �
2−70
�
+1225<0
x
2
−70
x
+1225<0
. - Answer
: �
=35
x
=35
.
368.
Find the derivative of �
(
�
)=40
�
2+30
�
+40
f
(
x
)=
x
2
+30
x
+4040
. - Answer
: �
′(
�
)
f
′
(
x
)
.
369.
Determine the value of �
x
if log90(
�
−24)+log90(
�
)=2log
90
(
x
−24)+log
90
(
x
)=2
. - Answer
: �
=180
x
=180
.
