111.
Solve the system of equations: {2
�
+3
�
=134
�
−
�
=5
{
2
x
+3
y
=134
x
−
y
=5
. - Answer
: �
=2,
�
=3
x
=2,
y
=3
.
112.
Calculate the value of �
x
in the equation 3
�
+52−4=7
�
−13
23
x
+5
−4=
37
x
−1
. - Answer
: �
=4723
x
=
2347
.
113.
Find the area of a trapezoid with bases 99
units and 1313
units, and height 88
units. - Answer
: Area = 12×(
�
1+
�
2)× =12×(9+13)×8=88
ℎ
21
×(
b
1
+
b
2
)×
h
=
21
×(9+13)×8=88
square units.
114.
Determine the value of �
x
in the equation 2
�
+5=72
x
+5=7
. - Answer
: �
=24
x
=24
.
115.
Find the sum of the first 1010
terms of an arithmetic sequence where the first term is 33
and the common difference is 44
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
, where �
=10
n
=10
, �
=3
a
=3
, �
=4
d
=4
. Sum = 102(2×3+(10−1)×4)=190
210
(2×3+(10−1)×4)=190
.
116.
Solve the equation 2
�
+1=162
x
+1
=16
. - Answer
: �
=3
x
=3
.
117.
Calculate the area bounded by the curve �
=
�
2−3
�
+2
y
=
x
2
−3
x
+2
and the x-axis. - Answer
: Area = ∫02(
�
2−3
�
+2)
��
=[13
�
3−32
�
2+2
�
]02=23
∫
02
(
x
2
−3
x
+2)
dx
=
[
31
x
3
−
23
x
2
+2
x
]
02
=
32
.
118.
Solve the inequality 2
�
2−5
�
−3>02
x
2
−5
x
−3>0
. - Answer
: �
<−12
x
<−
21
or �
>3
x
>3
.
119.
Find the derivative of �
(
�
)=1
�
2
f
(
x
)=
x
2
1
. - Answer
: �
′
(
�
)=−2
�
3
f
′
(
x
)=−
x
3
2
.
120.
Determine the value of �
x
if �
2
�
=10
e
2
x
=10
. - Answer
: �
=ln(10)/2≈0.693
x
=ln(10)/2≈0.693
.
