430.
- Answer
: �
=5,
�
=6
x
=5,
y
=6
.
431.
Calculate the value of �
x
in the equation log2(
�
+50)−log2(
�
−45)=6log
2
(
x
+50)−log
2
(
x
−45)=6
. - Answer
: �
=46
x
=46
.
432.
Find the area of a regular 500-gon inscribed in a circle with a radius of 2222
units. - Answer
: Area = 500×12×22×22×sin(360
∘
500)500×
21
×22×22×sin
(
500360
∘
)
.
433.
Determine the value of �
x
in the equation 26
�
−2
�
=3355443126
x
−2
x
=33554431
. - Answer
: �
=13
x
=13
.
434.
Find the sum of the first 410410
terms of an arithmetic sequence
where the first term is 340340
and the common difference is 220220
. - Answer
: Sum = �
2(2
�
+(
�
−1)
�
)
2
n
(2
a
+(
n
−1)
d
)
with �
=410
n
=410
,
�
=340
a
=340
, �
=220
d
=220
.
435.
Solve the equation 68
�
−2+71
�
+3=74
�
2−
�
−6
x
−268
+
x
+371
=
x
2
−
x
−674
. - Answer
: �
=74
x
=74
.
436.
Calculate the area enclosed by the curve �
=sin(48
�
)
y
=sin(48
x
)
, the x-axis, and the lines �
=0
x
=0
and �
=
�
96
x
=
96
π
. - Answer
: Area = ∫0
�
96sin(48
�
)
��∫
0
96
π
sin(48
x
)
dx
.
437.
Solve the inequality �
2−98
�
+2401<0
x
2
−98
x
+2401<0
. - Answer
: �
=49
x
=49
.
438.
Find the derivative of �
(
�
)=70
�
2+56
�
+70
f
(
x
)=
x
2
+56
x
+7070
. - Answer
: �
′(
�
)
f
′
(
x
)
.
439.
Determine the value of �
x
if log200(
�
−46)+log200(
�
)=2log
200
(
x
−46)+log
200
(
x
)=2
. - Answer
: �
=400
x
=400
.
