171.
Solve the system of equations: {4
�
−3
�
=52
�
+5
�
=11
{
4
x
−3
y
=52
x
+5
y
=11
. - Answer
: �
=2,
�
=1
x
=2,
y
=1
.
172.
Calculate the value of �
x
in the equation log4(
�
+2)−log4(
�
)=2log
4
(
x
+2)−log
4
(
x
)=2
. - Answer
: �
=2
x
=2
.
173.
Find the area of a regular 20-sided polygon inscribed in a circle with a radius of 66
units. - Answer
: Area = 20×12×6×6×sin(360
∘
20)=180sin(18
∘
)20×
21
×6×6×sin
(
20360
∘
)
=180sin(18
∘
)
square units.
174.
Determine the value of �
x
in the equation 2
�
−3
�
=52
x
−3
x
=5
. - Answer
: �
=2
x
=2
.
175.
Find the sum of the first 4040
terms of an arithmetic series where the first term is 33
and the common difference is 77
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
, where �
=40
n
=40
, �
=3
a
=3
, �
=7
d
=7
. Sum = 402(2×3+(40−1)×7)=820
240
(2×3+(40−1)×7)=820
units.
176.
Solve the equation 5
�
−2+7
�
+3=3
�
2−
�
−6
x
−25
+
x
+37
=
x
2
−
x
−63
. - Answer
: �
=−1
x
=−1
.
177.
Calculate the area enclosed by the curve �
=sin2(
�
)
y
=sin
2
(
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
x
=
π
. - Answer
: Area = ∫0
�
sin2(
�
)
��
=
�
2
∫
0
π
sin
2
(
x
)
dx
=
2
π
square units.
178.
Solve the inequality �
2−10
�
+21<0
x
2
−10
x
+21<0
. - Answer
: �
<3
x
<3
or �
>7
x
>7
.
179.
Find the derivative of �
(
�
)=cos(
�
)
�
f
(
x
)=
x
cos(
x
)
. - Answer
: �
′
(
�
)=−sin(
�
)
�
−cos(
�
)
�
2
f
′
(
x
)=−
x
sin(
x
)
−
x
2
cos(
x
)
.
180.
Determine the value of �
x
if log3(
�
+1)−log3(
�
−1)=2log
3
(
x
+1)−log
3
(
x
−1)=2
. - Answer
: �
=4
x
=4
.
