200.
Solve the system of equations: {5
�
−3
�
=122
�
+4
�
=8
{
5
x
−3
y
=122
x
+4
y
=8
. - Answer
: �
=2,
�
=2
x
=2,
y
=2
.
201.
Calculate the value of �
x
in the equation log2(
�
+7)−log2(
�
−2)=4log
2
(
x
+7)−log
2
(
x
−2)=4
. - Answer
: �
=9
x
=9
.
202.
Find the area of a regular 24-gon inscribed in a circle with a radius of 66
units. - Answer
: Area = 24×12×6×6×sin(360
∘
24)24×
21
×6×6×sin
(
24360
∘
)
.
203.
Determine the value of �
x
in the equation 4
�
−3
�
=614
x
−3
x
=61
. - Answer
: �
=3
x
=3
.
204.
Find the sum of the first 5050
terms of an arithmetic sequence where the first term is 1515
and the common difference is 66
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=50
n
=50
, �
=15
a
=15
, �
=6
d
=6
.
205.
Solve the equation 3
�
−2+4
�
+3=5
�
2−
�
−6
x
−23
+
x
+34
=
x
2
−
x
−65
. - Answer
: �
=6
x
=6
.
206.
Calculate the area enclosed by the curve �
=sin(5
�
)
y
=sin(5
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
10
x
=
10
π
. - Answer
: Area = ∫0
�
10sin(5
�
)
��∫
0
10
π
sin(5
x
)
dx
.
207.
Solve the inequality �
2−20
�
+99<0
x
2
−20
x
+99<0
. - Answer
: 3<
�
<173<
x
<17
.
208.
Find the derivative of �
(
�
)=5
�
2+4
�
+3
f
(
x
)=
x
2
+4
x
+35
. - Answer
: �
′(
�
)
f
′
(
x
)
.
209.
Determine the value of �
x
if log6(
�
−2)+log6(
�
)=3log
6
(
x
−2)+log
6
(
x
)=3
. - Answer
: �
=12
x
=12
.
