121.
Solve the system of equations: {3
�
+2
�
=162
�
−5
�
=−9
{
3
x
+2
y
=162
x
−5
y
=−9
. - Answer
: �
=3,
�
=5
x
=3,
y
=5
.
122.
Calculate the value of �
x
in the equation 2log3(
�
+2)=log3(27)2log
3
(
x
+2)=log
3
(27)
. - Answer
: �
=7
x
=7
.
123.
Find the area of a regular hexagon inscribed in a circle with a radius of 1010
units. - Answer
: Area = 6×12×10×10×sin(360
∘
6)=30036×
21
×10×10×sin
(
6360
∘
)
=3003
square units.
124.
Determine the value of �
x
in the equation 4
�
−4×2
�
+3=04
x
−4×2
x
+3=0
. - Answer
: �
=1
x
=1
or �
=2
x
=2
.
125.
Find the sum of the infinite geometric series 5+2.5+1.25+…
5+2.5+1.25+…
. - Answer
: Sum = �
1−
�
1−
ra
, where �
=5
a
=5
and �
=12
r
=
21
. Sum = 51−12=10
1−
21
5
=10
units.
126.
Solve the equation 1
�
−3+1
�
+2=1
�
2−
�
−6
x
−31
+
x
+21
=
x
2
−
x
−61
. - Answer
: �
=−1
x
=−1
.
127.
Calculate the area enclosed by the curve �
=
�
y
=
x
, the x-axis, and the lines �
=1
x
=1
and �
=4
x
=4
. - Answer
: Area = ∫14
�
��
=[23
�
32]14=103
∫
14
xdx
=
[
32
x
23
]
14
=
310
.
128.
Solve the inequality �
2−4
�
<−4
x
2
−4
x
<−4
. - Answer
: −2<
�
<2−2<
x
<2
.
129.
Find the derivative of �
(
�
)=sin(
�
2)
f
(
x
)=sin(
x
2
)
. - Answer
: �
′
(
�
)=2
�
cos(
�
2)
f
′
(
x
)=2
x
cos(
x
2
)
.
130.
Determine the value of �
x
if log2(
�
)+log2(
�
−4)=3log
2
(
x
)
+log
2
(
x
−4)=3
. - Answer
: �
=8
x
=8
.
