170.
Solve the system of equations: {4
�
−3
�
=112
�
+5
�
=3
{
4
x
−3
y
=112
x
+5
y
=3
. - Answer
: �
=2,
�
=−1
x
=2,
y
=−1
.
171.
Calculate the value of �
x
in the equation log4(
�
+3)−log4(
�
−2)=3log
4
(
x
+3)−log
4
(
x
−2)=3
. - Answer
: �
=5
x
=5
.
172.
Find the area of a regular pentadecagon inscribed in a circle with
a radius of 1212
units. - Answer
: Area = 15×12×12×12×sin(360
∘
15)15×
21
×12×12×sin
(
15360
∘
)
.
173.
Determine the value of �
x
in the equation 3
�
−2
�
=613
x
−2
x
=61
. - Answer
: �
=4
x
=4
.
174.
Find the sum of the first 3535
terms of an arithmetic sequence where the first term is 88
and the common difference is 66
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=35
n
=35
, �
=8
a
=8
, �
=6
d
=6
.
175.
Solve the equation 4
�
−2+5
�
+3=6
�
2−
�
−6
x
−24
+
x
+35
=
x
2
−
x
−66
. - Answer
: �
=6
x
=6
.
176.
Calculate the area enclosed by the curve �
=cos(2
�
)
y
=cos(2
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
4
x
=
4
π
. - Answer
: Area = ∫0
�
4cos(2
�
)
��∫
0
4
π
cos(2
x
)
dx
.
177.
Solve the inequality �
2−14
�
+45<0
x
2
−14
x
+45<0
. - Answer
: 3<
�
<113<
x
<11
.
178.
Find the derivative of �
(
�
)=2
�
2+3
�
+2
f
(
x
)=
x
2
+3
x
+22
. - Answer
: �
′(
�
)
f
′
(
x
)
.
179.
Determine the value of �
x
if log3(
�
−2)+log3(
�
)=3log
3
(
x
−2)+log
3
(
x
)=3
. - Answer
: �
=9
x
=9
.
