141.
Solve the system of equations: {5
�
+3
�
=194
�
−2
�
=2
{
5
x
+3
y
=194
x
−2
y
=2
. - Answer
: �
=3,
�
=2
x
=3,
y
=2
.
142.
Calculate the value of �
x
in the equation log2(
�
+4)−log2(
�
)=3log
2
(
x
+4)−log
2
(
x
)=3
. - Answer
: �
=4
x
=4
.
143.
Find the area of a regular octagon inscribed in a circle with a radius of 1515
units. - Answer
: Area = 8×12×15×15×sin(360
∘
8)=4208×
21
×15×15×sin
(
8360
∘
)
=420
square units.
144.
Determine the value of �
x
in the equation 3
�
−2
�
=53
x
−2
x
=5
. - Answer
: �
=2
x
=2
.
145.
Find the sum of the first 2020
terms of a geometric series where the first term is 66
and the common ratio is 13
31
. - Answer
: Sum = �
×1−
��
1−
�
a
×
1−
r
1−
r
n
, where �
=6
a
=6
, �
=13
r
=
31
, �
=20
n
=20
. Sum = 6×1−(13)201−13≈8.999956×
1−
31
1−(
31
)
20
≈8.99995
.
146.
Solve the equation 3
�
−2+2
�
+3=1
�
2−
�
−6
x
−23
+
x
+32
=
x
2
−
x
−61
. - Answer
: �
=−1
x
=−1
.
147.
Calculate the area enclosed by the curve �
=
��
y
=
e
x
, the x-
axis, and the lines �
=1
x
=1
and �
=3
x
=3
. - Answer
: Area = ∫13
��
��
=
��
∣
13=
�
3−
�∫
13
e
x
dx
=
e
x
∣
13
=
e
3
−
e
square units.
148.
Solve the inequality �
2−7
�
+10>0
x
2
−7
x
+10>0
. - Answer
: �
<2
x
<2
or �
>5
x
>5
.
149.
Find the derivative of �
(
�
)=ln(
�
2+1)
f
(
x
)=ln(
x
2
+1)
. - Answer
: �
′(
�
)=2
��
2+1
f
′
(
x
)=
x
2
+12
x
.
150.
Determine the value of �
x
if log2(
�
+5)−log2(
�
−3)=2log
2
(
x
+5)−log
2
(
x
−3)=2
. - Answer
: �
=9
x
=9
.
