MathDB

4

Part of 2013 Stanford Mathematics Tournament

Problems(6)

2013 General Problem 4

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2/4/2013
What is the smallest number over 9000 that is divisible by the first four primes?
SMT 2013 Calculus #4

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2/3/2013
Evaluate ∫04ex dx\int_{0}^{4}e^{\sqrt{x}} \, dx.
calculusintegration
2013 SMT Geometry #4

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11/2/2014
ABCDABCD is a regular tetrahedron with side length 11. Find the area of the cross section of ABCDABCD cut by the plane that passes through the midpoints of ABAB, ACAC, and CDCD.
geometry3D geometrytetrahedronsymmetryrhombus
SMT 2013 Algebra #4

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2/3/2013
Given that f(x)+2f(8−x)=x2f(x)+2f(8-x)=x^2 for all real xx, compute f(2)f(2).
SMT 2013 Team #4

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2/4/2013
For some positive integers aa and bb, (xa+abxa−1+13)b(x3+3bx2+37)a=x42+126x41+⋯(x^a+abx^{a-1}+13)^{b}(x^3+3bx^2+37)^{a}=x^{42}+126x^{41}+\cdots. Find the ordered pair (a,b)(a, b).
SMT 2013 Advanced Topics #4

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12/31/2016
Given the digits 11 through 77, one can form 7!=50407!=5040 numbers by forming different permutations of the 77 digits (for example, 12345671234567 and 63214756321475 are two such permutations). If the 50405040 numbers are then placed in ascending order, what is the 2013th2013^{\text{th}} number?
2013Advanced Topics