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BMT Problems
2014 BMT Spring
11
11
Part of
2014 BMT Spring
Problems
(2)
2014 BMT Team 11
Source:
1/6/2022
Suppose that
x
10
+
x
+
1
=
0
x^{10} + x + 1 = 0
x
10
+
x
+
1
=
0
and
x
1
00
=
a
0
+
a
1
x
+
.
.
.
+
a
9
x
9
x^100 = a_0 + a_1x +... + a_9x^9
x
1
00
=
a
0
+
a
1
x
+
...
+
a
9
x
9
. Find
a
5
a_5
a
5
.
algebra
BMT 2014 Spring - Individual 11
Source:
1/22/2022
Suppose
x
,
y
x, y
x
,
y
, and
1
1
1
are side lengths of a triangle
T
T
T
such that
x
<
1
x < 1
x
<
1
and
y
<
1
y < 1
y
<
1
. Given
x
x
x
and
y
y
y
are chosen uniformly at random from all possible pairs
(
x
,
y
)
(x, y)
(
x
,
y
)
, determine the probability that
T
T
T
is obtuse.
geometry