240.
Solve the system of equations: {3
�
−2
�
=72
�
+3
�
=11
{
3
x
−2
y
=72
x
+3
y
=11
. - Answer
: �
=3,
�
=2
x
=3,
y
=2
.
241.
Calculate the value of �
x
in the equation log2(
�
+11)−log2(
�
−6)=3log
2
(
x
+11)−log
2
(
x
−6)=3
. - Answer
: �
=13
x
=13
.
242.
Find the area of a regular 60-gon inscribed in a circle with a radius of 66
units. - Answer
: Area = 60×12×6×6×sin(360
∘
60)60×
21
×6×6×sin
(
60360
∘
)
.
243.
Determine the value of �
x
in the equation 2
�
−3
�
=8192
x
−3
x
=819
. - Answer
: �
=6
x
=6
.
244.
Find the sum of the first 7070
terms of an arithmetic sequence where the first term is 3535
and the common difference is 1010
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=70
n
=70
, �
=35
a
=35
, �
=10
d
=10
.
245.
Solve the equation 9
�
−2+11
�
+3=12
�
2−
�
−6
x
−29
+
x
+311
=
x
2
−
x
−612
. - Answer
: �
=12
x
=12
.
246.
Calculate the area enclosed by the curve �
=sin(10
�
)
y
=sin(10
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
20
x
=
20
π
. - Answer
: Area = ∫0
�
20sin(10
�
)
��∫
0
20
π
sin(10
x
)
dx
.
247.
Solve the inequality �
2−28
�
+196<0
x
2
−28
x
+196<0
. - Answer
: �
=14
x
=14
.
248.
Find the derivative of �
(
�
)=12
�
2+8
�
+12
f
(
x
)=
x
2
+8
x
+1212
. - Answer
: �
′(
�
)
f
′
(
x
)
.
249.
Determine the value of �
x
if log10(
�
−6)+log10(
�
)=2log
10
(
x
−6)+log
10
(
x
)=2
. - Answer
: �
=30
x
=30
.
