160.
Solve the system of equations: {3
�
−2
�
=104
�
+3
�
=5
{
3
x
−2
y
=104
x
+3
y
=5
. - Answer
: �
=−711
x
=−
117
, �
=−111
y
=−
111
.
161.
Calculate the value of �
x
in the equation log2(
�
+5)−log2(
�
−2)=4log
2
(
x
+5)−log
2
(
x
−2)=4
. - Answer
: �
=17
x
=17
.
162.
Find the area of a regular dodecagon inscribed in a circle with a radius of 88
units. - Answer
: Area = 12×12×8×8×sin(360
∘
12)=192(3+3)12×
21
×8×8×sin
(
12360
∘
)
=192(3+3)
square units.
163.
Determine the value of �
x
in the equation 2
�
−3
�
=232
x
−3
x
=23
. - Answer
: �
=3
x
=3
.
164.
Find the sum of the first 3030
terms of a geometric sequence where the first term is 44
and the common ratio is 13
31
. - Answer
: Sum = �
×1−
��
1−
�
a
×
1−
r
1−
r
n
, where �
=30
n
=30
, �
=4
a
=4
, �
=13
r
=
31
. Sum = 4×1−(13)301−134×
1−
31
1−(
31
)
30
.
165.
Solve the equation 2
�
−1+3
�
+4=4
�
2−
�
−4
x
−12
+
x
+43
=
x
2
−
x
−44
. - Answer
: �
=4
x
=4
.
166.
Calculate the area enclosed by the curve �
=sin(
�
)
y
=sin(
x
)
, the
x-axis, and the lines �
=0
x
=0
and �
=
�
2
x
=
2
π
. - Answer
: Area = ∫0
�
2sin(
�
)
��
=1
∫
0
2
π
sin(
x
)
dx
=1
square unit.
167.
Solve the inequality �
2−12
�
+35<0
x
2
−12
x
+35<0
. - Answer
: 5<
�
<75<
x
<7
.
168.
Find the derivative of �
(
�
)=1
�
2+1
f
(
x
)=
x
2
+11
. - Answer
: �
′
(
�
)=−2
�
(
�
2+1)2
f
′
(
x
)=−
(
x
2
+1)
2
2
x
.
169.
Determine the value of �
x
if log5(
�
−3)+log5(
�
)=2log
5
(
x
−3)+log
5
(
x
)=2
. - Answer
: �
=8
x
=8
.
