250.
Solve the system of equations: {4
�
−3
�
=102
�
+5
�
=14
{
4
x
−3
y
=102
x
+5
y
=14
. - Answer
: �
=2,
�
=2
x
=2,
y
=2
.
251.
Calculate the value of �
x
in the equation log4(
�
+12)−log4(
�
−7)=2log
4
(
x
+12)−log
4
(
x
−7)=2
. - Answer
: �
=13
x
=13
.
252.
Find the area of a regular 80-gon inscribed in a circle with a radius of 99
units. - Answer
: Area = 80×12×9×9×sin(360
∘
80)80×
21
×9×9×sin
(
80360
∘
)
.
253.
Determine the value of �
x
in the equation 3
�
−2
�
=10233
x
−2
x
=1023
. - Answer
: �
=5
x
=5
.
254.
Find the sum of the first 7575
terms of an arithmetic sequence where the first term is 4040
and the common difference is 1212
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=75
n
=75
, �
=40
a
=40
, �
=12
d
=12
.
255.
Solve the equation 10
�
−2+13
�
+3=15
�
2−
�
−6
x
−210
+
x
+313
=
x
2
−
x
−615
. - Answer
: �
=15
x
=15
.
256.
Calculate the area enclosed by the curve �
=sin(12
�
)
y
=sin(12
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
24
x
=
24
π
. - Answer
: Area = ∫0
�
24sin(12
�
)
��∫
0
24
π
sin(12
x
)
dx
.
257.
Solve the inequality �
2−30
�
+225<0
x
2
−30
x
+225<0
. - Answer
: �
=15
x
=15
.
258.
Find the derivative of �
(
�
)=14
�
2+9
�
+14
f
(
x
)=
x
2
+9
x
+1414
. - Answer
: �
′(
�
)
f
′
(
x
)
.
259.
Determine the value of �
x
if log12(
�
−7)+log12(
�
)=2log
12
(
x
−7)+log
12
(
x
)=2
. - Answer
: �
=42
x
=42
.
