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Mathematics
Mathematics
Problem
Consider the family of regions
S
(
k
)
S(k)
S
(
k
)
,
0
<
k
<
3
0 < k < 3
0
<
k
<
3
, each bounded above by
y
=
9
−
x
2
y = 9 - x^2
y
=
9
−
x
2
, below by
y
=
k
x
y = kx
y
=
k
x
, and between
x
=
0
x = 0
x
=
0
and
x
=
k
x = k
x
=
k
. For which value of
k
k
k
does the area of
S
(
k
)
S(k)
S
(
k
)
attain its maximum? a)
k
=
3
2
k=\dfrac{3}{\sqrt{2}}
k
=
2
3
b)
k
=
6
5
k=\sqrt{\dfrac{6}{5}}
k
=
5
6
c)
k
=
18
5
k=\sqrt{\dfrac{18}{5}}
k
=
5
18
d)
k
=
9
5
k=\sqrt{\dfrac{9}{5}}
k
=
5
9
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