151.
Solve the system of equations: {2
�
−5
�
=−43
�
+2
�
=13
{
2
x
−5
y
=−43
x
+2
y
=13
. - Answer
: �
=3,
�
=2
x
=3,
y
=2
.
152.
Calculate the value of �
x
in the equation log3(
�
+1)−log3(
�
−2)=2log
3
(
x
+1)−log
3
(
x
−2)=2
. - Answer
: �
=4
x
=4
.
153.
Find the area of a regular dodecagon inscribed in a circle with a radius of 1010
units. - Answer
: Area = 12×12×10×10×sin(360
∘
12)=300(3+3)12×
21
×10×10×sin
(
12360
∘
)
=300(3+3)
square units.
154.
Determine the value of �
x
in the equation 4
�
−3
�
=134
x
−3
x
=13
. - Answer
: �
=2
x
=2
.
155.
Find the sum of the first 2525
terms of an arithmetic series where the first term is 44
and the common difference is 66
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
, where �
=25
n
=25
, �
=4
a
=4
, �
=6
d
=6
. Sum = 252(2×4+(25−1)×6)=625
225
(2×4+(25−1)×6)=625
units.
156.
Solve the equation 4
�
−3+5
�
+2=2
�
2−
�
−6
x
−34
+
x
+25
=
x
2
−
x
−62
. - Answer
: �
=2
x
=2
.
157.
Calculate the area enclosed by the curve �
=sin(
�
)
y
=sin(
x
)
, the
x-axis, and the lines �
=
�
6
x
=
6
π
and �
=5
�
6
x
=
65
π
. - Answer
: Area =
∫
�
65
�
6sin(
�
)
��
=2
∫
6
π
65
π
sin(
x
)
dx
=2
square units.
158.
Solve the inequality �
2−8
�
+12<0
x
2
−8
x
+12<0
. - Answer
: 2<
�
<62<
x
<6
.
159.
Find the derivative of �
(
�
)=tan2(
�
)
f
(
x
)=tan
2
(
x
)
. - Answer
: �
′
(
�
)=2tan(
�
)sec2(
�
)
f
′
(
x
)=2tan(
x
)sec
2
(
x
)
.
160.
Determine the value of �
x
if log4(
�
+3)−log4(
�
−1)=2log
4
(
x
+3)−log
4
(
x
−1)=2
. - Answer
: �
=7
x
=7
.
