300.
Solve the system of equations: {5
�
−2
�
=143
�
+4
�
=11
{
5
x
−2
y
=143
x
+4
y
=11
. - Answer
: �
=2,
�
=3
x
=2,
y
=3
.
301.
Calculate the value of �
x
in the equation log2(
�
+18)−log2(
�
−13)=4log
2
(
x
+18)−log
2
(
x
−13)=4
. - Answer
: �
=19
x
=19
.
302.
Find the area of a regular 180-gon inscribed in a circle with a radius of 88
units. - Answer
: Area = 180×12×8×8×sin(360
∘
180)180×
21
×8×8×sin
(
180360
∘
)
.
303.
Determine the value of �
x
in the equation 8
�
−2
�
=655358
x
−2
x
=65535
. - Answer
: �
=9
x
=9
.
304.
Find the sum of the first 120120
terms of an arithmetic sequence
where the first term is 9090
and the common difference is 3535
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=120
n
=120
,
�
=90
a
=90
, �
=35
d
=35
.
305.
Solve the equation 20
�
−2+23
�
+3=26
�
2−
�
−6
x
−220
+
x
+323
=
x
2
−
x
−626
. - Answer
: �
=26
x
=26
.
306.
Calculate the area enclosed by the curve �
=cos(22
�
)
y
=cos(22
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
44
x
=
44
π
. - Answer
: Area = ∫0
�
44cos(22
�
)
��∫
0
44
π
cos(22
x
)
dx
.
307.
Solve the inequality �
2−46
�
+529<0
x
2
−46
x
+529<0
. - Answer
: �
=23
x
=23
.
308.
Find the derivative of �
(
�
)=24
�
2+18
�
+24
f
(
x
)=
x
2
+18
x
+2424
. - Answer
: �
′(
�
)
f
′
(
x
)
.
309.
Determine the value of �
x
if log30(
�
−12)+log30(
�
)=2log
30
(
x
−12)+log
30
(
x
)=2
. - Answer
: �
=60
x
=60
.
