150.
Solve the system of equations: {2
�
−3
�
=54
�
+5
�
=7
{
2
x
−3
y
=54
x
+5
y
=7
. - Answer
: �
=2,
�
=−1
x
=2,
y
=−1
.
151.
Calculate the value of �
x
in the equation log3(
�
+1)−log3(
�
−2)=2log
3
(
x
+1)−log
3
(
x
−2)=2
. - Answer
: �
=5
x
=5
.
152.
Find the area of a regular decagon inscribed in a circle with a radius of 1010
units. - Answer
: Area = 10×12×10×10×sin(360
∘
10)=250(5+25)10×
21
×10×10×sin
(
10360
∘
)
=250(5+25)
square units.
153.
Determine the value of �
x
in the equation 5
�
−2
�
=335
x
−2
x
=33
. - Answer
: �
=3
x
=3
.
154.
Find the sum of the first 2525
terms of an arithmetic sequence where the first term is 66
and the common difference is 33
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
, where �
=25
n
=25
, �
=6
a
=6
, �
=3
d
=3
. Sum = 252(2×6+(25−1)×3)=975
225
(2×6+(25−1)×3)=975
units.
155.
Solve the equation 3
�
−2+4
�
+3=5
�
2−
�
−6
x
−23
+
x
+34
=
x
2
−
x
−65
. - Answer
: �
=3
x
=3
.
156.
Calculate the area enclosed by the curve �
=cos(
�
)
y
=cos(
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
x
=
π
. - Answer
: Area = ∫0
�
cos(
�
)
��
=[sin(
�
)]0
�
=0
∫
0
π
cos(
x
)
dx
=[sin(
x
)]
0
π
=0
square units.
157.
Solve the inequality �
2−10
�
+21>0
x
2
−10
x
+21>0
. - Answer
: �
<1
x
<1
or �
>9
x
>9
.
158.
Find the derivative of �
(
�
)=2
�
+1
f
(
x
)=2
x
+1
. - Answer
: �
′
(
�
)=12
�
+1
f
′
(
x
)=
2
x
+11
.
159.
Determine the value of �
x
if log4(
�
−2)+log4(
�
)=2log
4
(
x
−2)+log
4
(
x
)=2
. - Answer
: �
=4
x
=4
.
