400.
Solve the system of equations: {6
�
−3
�
=184
�
+5
�
=32
{
6
x
−3
y
=184
x
+5
y
=32
. - Answer
: �
=5,
�
=4
x
=5,
y
=4
.
401.
Calculate the value of �
x
in the equation log2(
�
+35)−log2(
�
−30)=5log
2
(
x
+35)−log
2
(
x
−30)=5
. - Answer
: �
=31
x
=31
.
402.
Find the area of a regular 420-gon inscribed in a circle with a radius of 1515
units. - Answer
: Area = 420×12×15×15×sin(360
∘
420)420×
21
×15×15×sin
(
420360
∘
)
.
403.
Determine the value of �
x
in the equation 20
�
−2
�
=104857520
x
−2
x
=1048575
. - Answer
: �
=10
x
=10
.
404.
Find the sum of the first 330330
terms of an arithmetic sequence
where the first term is 280280
and the common difference is 160160
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=330
n
=330
,
�
=280
a
=280
, �
=160
d
=160
.
405.
Solve the equation 56
�
−2+59
�
+3=62
�
2−
�
−6
x
−256
+
x
+359
=
x
2
−
x
−662
. - Answer
: �
=62
x
=62
.
406.
Calculate the area enclosed by the curve �
=sin(42
�
)
y
=sin(42
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
84
x
=
84
π
. - Answer
: Area = ∫0
�
84sin(42
�
)
��∫
0
84
π
sin(42
x
)
dx
.
407.
Solve the inequality �
2−86
�
+1849<0
x
2
−86
x
+1849<0
. - Answer
: �
=43
x
=43
.
408.
Find the derivative of �
(
�
)=58
�
2+44
�
+58
f
(
x
)=
x
2
+44
x
+5858
. - Answer
: �
′(
�
)
f
′
(
x
)
.
409.
Determine the value of �
x
if log140(
�
−34)+log140(
�
)=2log
140
(
x
−34)+log
140
(
x
)=2
. - Answer
: �
=280
x
=280
.
