410.
Solve the system of equations: {7
�
−4
�
=215
�
+6
�
=47
{
7
x
−4
y
=215
x
+6
y
=47
. - Answer
: �
=5,
�
=7
x
=5,
y
=7
.
411.
Calculate the value of �
x
in the equation log2(
�
+40)−log2(
�
−35)=5log
2
(
x
+40)−log
2
(
x
−35)=5
. - Answer
: �
=36
x
=36
.
412.
Find the area of a regular 450-gon inscribed in a circle with a radius of 1818
units. - Answer
: Area = 450×12×18×18×sin(360
∘
450)450×
21
×18×18×sin
(
450360
∘
)
.
413.
Determine the value of �
x
in the equation 22
�
−2
�
=419430322
x
−2
x
=4194303
. - Answer
: �
=11
x
=11
.
414.
Find the sum of the first 370370
terms of an arithmetic sequence
where the first term is 300300
and the common difference is 180180
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=370
n
=370
,
�
=300
a
=300
, �
=180
d
=180
.
415.
Solve the equation 60
�
−2+63
�
+3=66
�
2−
�
−6
x
−260
+
x
+363
=
x
2
−
x
−666
. - Answer
: �
=66
x
=66
.
416.
Calculate the area enclosed by the curve �
=sin(44
�
)
y
=sin(44
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
88
x
=
88
π
. - Answer
: Area = ∫0
�
88sin(44
�
)
��∫
0
88
π
sin(44
x
)
dx
.
417.
Solve the inequality �
2−90
�
+2025<0
x
2
−90
x
+2025<0
. - Answer
: �
=45
x
=45
.
418.
Find the derivative of �
(
�
)=62
�
2+48
�
+62
f
(
x
)=
x
2
+48
x
+6262
. - Answer
: �
′(
�
)
f
′
(
x
)
.
419.
Determine the value of �
x
if log160(
�
−38)+log160(
�
)=2log
160
(
x
−38)+log
160
(
x
)=2
. - Answer
: �
=320
x
=320
.
