350.
Solve the system of equations: {5
�
−2
�
=133
�
+4
�
=19
{
5
x
−2
y
=133
x
+4
y
=19
. - Answer
: �
=3,
�
=2
x
=3,
y
=2
.
351.
Calculate the value of �
x
in the equation log2(
�
+20)−log2(
�
−15)=3log
2
(
x
+20)−log
2
(
x
−15)=3
. - Answer
: �
=21
x
=21
.
352.
Find the area of a regular 280-gon inscribed in a circle with a radius of 88
units. - Answer
: Area = 280×12×8×8×sin(360
∘
280)280×
21
×8×8×sin
(
280360
∘
)
.
353.
Determine the value of �
x
in the equation 10
�
−2
�
=52428710
x
−2
x
=524287
. - Answer
: �
=10
x
=10
.
354.
Find the sum of the first 230230
terms of an arithmetic sequence
where the first term is 180180
and the common difference is 9090
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=230
n
=230
,
�
=180
a
=180
, �
=90
d
=90
.
355.
Solve the equation 36
�
−2+39
�
+3=42
�
2−
�
−6
x
−236
+
x
+339
=
x
2
−
x
−642
. - Answer
: �
=42
x
=42
.
356.
Calculate the area enclosed by the curve �
=sin(32
�
)
y
=sin(32
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
64
x
=
64
π
. - Answer
: Area = ∫0
�
64sin(32
�
)
��∫
0
64
π
sin(32
x
)
dx
.
357.
Solve the inequality �
2−66
�
+1089<0
x
2
−66
x
+1089<0
. - Answer
: �
=33
x
=33
.
358.
Find the derivative of �
(
�
)=36
�
2+28
�
+36
f
(
x
)=
x
2
+28
x
+3636
. - Answer
: �
′(
�
)
f
′
(
x
)
.
359.
Determine the value of �
x
if log80(
�
−22)+log80(
�
)=2log
80
(
x
−22)+log
80
(
x
)=2
. - Answer
: �
=160
x
=160
.
