MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Stanford Mathematics Tournament
2022 Stanford Mathematics Tournament
7
SMT 2022 Calculus #7
SMT 2022 Calculus #7
Source:
March 29, 2023
Problem Statement
Let
A
j
=
{
(
x
,
y
)
:
0
≤
x
sin
(
j
π
3
)
+
y
cos
(
j
π
3
)
≤
6
−
(
x
cos
(
j
π
3
)
−
y
sin
(
j
π
3
)
)
2
}
A_j=\left\{(x,y):0\le x\sin\left(\frac{j\pi}{3}\right)+y\cos\left(\frac{j\pi}{3}\right)\le6-\left(x\cos\left(\frac{j\pi}{3}\right)-y\sin\left(\frac{j\pi}{3}\right)\right)^2\right\}
A
j
=
{
(
x
,
y
)
:
0
≤
x
sin
(
3
jπ
)
+
y
cos
(
3
jπ
)
≤
6
−
(
x
cos
(
3
jπ
)
−
y
sin
(
3
jπ
)
)
2
}
The area of
∪
j
=
0
5
A
j
\cup_{j=0}^5A_j
∪
j
=
0
5
A
j
can be expressed as
m
n
m\sqrt{n}
m
n
. What is the area?
Back to Problems
View on AoPS