340.
Solve the system of equations: {4
�
−3
�
=102
�
+5
�
=14
{
4
x
−3
y
=102
x
+5
y
=14
. - Answer
: �
=2,
�
=2
x
=2,
y
=2
.
341.
Calculate the value of �
x
in the equation log3(
�
+17)−log3(
�
−12)=2log
3
(
x
+17)−log
3
(
x
−12)=2
. - Answer
: �
=13
x
=13
.
342.
Find the area of a regular 260-gon inscribed in a circle with a radius of 55
units. - Answer
: Area = 260×12×5×5×sin(360
∘
260)260×
21
×5×5×sin
(
260360
∘
)
.
343.
Determine the value of �
x
in the equation 8
�
−2
�
=2621438
x
−2
x
=262143
. - Answer
: �
=9
x
=9
.
344.
Find the sum of the first 210210
terms of an arithmetic sequence
where the first term is 160160
and the common difference is 7070
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=210
n
=210
,
�
=160
a
=160
, �
=70
d
=70
.
345.
Solve the equation 32
�
−2+35
�
+3=38
�
2−
�
−6
x
−232
+
x
+335
=
x
2
−
x
−638
. - Answer
: �
=38
x
=38
.
346.
Calculate the area enclosed by the curve �
=sin(30
�
)
y
=sin(30
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
60
x
=
60
π
. - Answer
: Area = ∫0
�
60sin(30
�
)
��∫
0
60
π
sin(30
x
)
dx
.
347.
Solve the inequality �
2−62
�
+961<0
x
2
−62
x
+961<0
. - Answer
: �
=31
x
=31
.
348.
Find the derivative of �
(
�
)=32
�
2+26
�
+32
f
(
x
)=
x
2
+26
x
+3232
. - Answer
: �
′(
�
)
f
′
(
x
)
.
349.
Determine the value of �
x
if log70(
�
−20)+log70(
�
)=2log
70
(
x
−20)+log
70
(
x
)=2
. - Answer
: �
=140
x
=140
.
