190.
Solve the system of equations: {3
�
−2
�
=84
�
+3
�
=5
{
3
x
−2
y
=84
x
+3
y
=5
. - Answer
: �
=−1917
x
=−
1719
, Solve the system of equations: {3
�
−2
�
=84
�
+3
�
=5
{
3
x
−2
y
=84
x
+3
y
=5
. - Answer
: �
=−1917
x
=−
1719
, �
=−4617
y
=−
1746
.
191.
Calculate the value of �
x
in the equation log3(
�
+6)−log3(
�
−3)=2log
3
(
x
+6)−log
3
(
x
−3)=2
. - Answer
: �
=12
x
=12
.
192.
Find the area of a regular 20-gon inscribed in a circle with a radius of 1010
units. - Answer
: Area = 20×12×10×10×sin(360
∘
20)20×
21
×10×10×sin
(
20360
∘
)
.
193.
Determine the value of �
x
in the equation 2
�
−3
�
=352
x
−3
x
=35
. - Answer
: �
=4
x
=4
.
194.
Find the sum of the first 4545
terms of an arithmetic sequence where the first term is 1212
and the common difference is 77
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=45
n
=45
, �
=12
a
=12
, �
=7
d
=7
.
195.
Solve the equation 5
�
−1+2
�
+4=7
�
2−
�
−4
x
−15
+
x
+42
=
x
2
−
x
−47
. - Answer
: �
=4
x
=4
.
196.
Calculate the area enclosed by the curve �
=cos(4
�
)
y
=cos(4
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
8
x
=
8
π
. - Answer
: Area = ∫0
�
8cos(4
�
)
��∫
0
8
π
cos(4
x
)
dx
.
197.
Solve the inequality �
2−18
�
+81<0
x
2
−18
x
+81<0
. - Answer
: �
<9
x
<9
.
198.
Find the derivative of �
(
�
)=4
�
2+3
�
+2
f
(
x
)=
x
2
+3
x
+24
. - Answer
: �
′(
�
)
f
′
(
x
)
.
199.
Determine the value of �
x
if log5(
�
−2)+log5(
�
)=3log
5
(
x
−2)+log
5
(
x
)=3
. - Answer
: �
=10
x
=10
.
190.
