280.
Solve the system of equations: {3
�
−4
�
=102
�
+3
�
=7
{
3
x
−4
y
=102
x
+3
y
=7
. - Answer
: �
=2,
�
=1
x
=2,
y
=1
.
281.
Calculate the value of �
x
in the equation log3(
�
+16)−log3(
�
−11)=2log
3
(
x
+16)−log
3
(
x
−11)=2
. - Answer
: �
=17
x
=17
.
282.
Find the area of a regular 140-gon inscribed in a circle with a radius of 55
units. - Answer
: Area = 140×12×5×5×sin(360
∘
140)140×
21
×5×5×sin
(
140360
∘
)
.
283.
Determine the value of �
x
in the equation 6
�
−2
�
=163836
x
−2
x
=16383
. - Answer
: �
=7
x
=7
.
284.
Find the sum of the first 100100
terms of an arithmetic sequence
where the first term is 7070
and the common difference is 2525
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=100
n
=100
,
�
=70
a
=70
, �
=25
d
=25
.
285.
Solve the equation 16
�
−2+19
�
+3=22
�
2−
�
−6
x
−216
+
x
+319
=
x
2
−
x
−622
. - Answer
: �
=22
x
=22
.
286.
Calculate the area enclosed by the curve �
=cos(18
�
)
y
=cos(18
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
36
x
=
36
π
. - Answer
: Area = ∫0
�
36cos(18
�
)
��∫
0
36
π
cos(18
x
)
dx
.
287.
Solve the inequality �
2−38
�
+361<0
x
2
−38
x
+361<0
. - Answer
: �
=19
x
=19
.
288.
Find the derivative of �
(
�
)=20
�
2+14
�
+20
f
(
x
)=
x
2
+14
x
+2020
. - Answer
: �
′(
�
)
f
′
(
x
)
.
289.
Determine the value of �
x
if log20(
�
−10)+log20(
�
)=2log
20
(
x
−10)+log
20
(
x
)=2
. - Answer
: �
=40
x
=40
.
