310.
Solve the system of equations: {3
�
−2
�
=82
�
+3
�
=5
{
3
x
−2
y
=82
x
+3
y
=5
. - Answer
: �
=−1,
�
=−2
x
=−1,
y
=−2
.
311.
Calculate the value of �
x
in the equation log4(
�
+20)−log4(
�
−15)=3log
4
(
x
+20)−log
4
(
x
−15)=3
. - Answer
: �
=21
x
=21
.
312.
Find the area of a regular 200-gon inscribed in a circle with a radius of 1010
units. - Answer
: Area = 200×12×10×10×sin(360
∘
200)200×
21
×10×10×sin
(
200360
∘
)
.
313.
Determine the value of �
x
in the equation 9
�
−2
�
=1310719
x
−2
x
=131071
. - Answer
: �
=17
x
=17
.
314.
Find the sum of the first 150150
terms of an arithmetic sequence
where the first term is 100100
and the common difference is 4040
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=150
n
=150
,
�
=100
a
=100
, �
=40
d
=40
.
315.
Solve the equation 24
�
−2+27
�
+3=30
�
2−
�
−6
x
−224
+
x
+327
=
x
2
−
x
−630
. - Answer
: �
=30
x
=30
.
316.
Calculate the area enclosed by the curve �
=sin(24
�
)
y
=sin(24
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
48
x
=
48
π
. - Answer
: Area = ∫0
�
48sin(24
�
)
��∫
0
48
π
sin(24
x
)
dx
.
317.
Solve the inequality �
2−50
�
+625<0
x
2
−50
x
+625<0
. - Answer
: �
=25
x
=25
.
318.
Find the derivative of �
(
�
)=26
�
2+20
�
+26
f
(
x
)=
x
2
+20
x
+2626
. - Answer
: �
′(
�
)
f
′
(
x
)
.
319.
Determine the value of �
x
if log40(
�
−14)+log40(
�
)=2log
40
(
x
−14)+log
40
(
x
)=2
. - Answer
: �
=80
x
=80
.
