260.
Solve the system of equations: {5
�
−2
�
=133
�
+4
�
=17
{
5
x
−2
y
=133
x
+4
y
=17
. - Answer
: �
=3,
�
=1
x
=3,
y
=1
.
261.
Calculate the value of �
x
in the equation log2(
�
+13)−log2(
�
−8)=3log
2
(
x
+13)−log
2
(
x
−8)=3
. - Answer
: �
=15
x
=15
.
262.
Find the area of a regular 100-gon inscribed in a circle with a radius of 1010
units. - Answer
: Area = 100×12×10×10×sin(360
∘
100)100×
21
×10×10×sin
(
100360
∘
)
.
263.
Determine the value of �
x
in the equation 4
�
−2
�
=40954
x
−2
x
=4095
. - Answer
: �
=6
x
=6
.
264.
Find the sum of the first 8080
terms of an arithmetic sequence where the first term is 5050
and the common difference is 1515
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=80
n
=80
, �
=50
a
=50
, �
=15
d
=15
.
265.
Solve the equation 12
�
−2+15
�
+3=18
�
2−
�
−6
x
−212
+
x
+315
=
x
2
−
x
−618
. - Answer
: �
=18
x
=18
.
266.
Calculate the area enclosed by the curve �
=cos(14
�
)
y
=cos(14
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
28
x
=
28
π
. - Answer
: Area = ∫0
�
28cos(14
�
)
��∫
0
28
π
cos(14
x
)
dx
.
267.
Solve the inequality �
2−32
�
+256<0
x
2
−32
x
+256<0
. - Answer
: �
=16
x
=16
.
268.
Find the derivative of �
(
�
)=16
�
2+10
�
+16
f
(
x
)=
x
2
+10
x
+1616
. - Answer
: �
′(
�
)
f
′
(
x
)
.
269.
Determine the value of �
x
if log15(
�
−8)+log15(
�
)=2log
15
(
x
−8)+log
15
(
x
)=2
. - Answer
: �
=40
x
=40
.
