Sxchen1110

7 Questions
0 Answers

0

1

0

+30

Number Theory

What is the answer?

Sxchen1110 13 nov 2024

0

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2

+30

Geometry

In a right triangle △ABC, ∠ABC=90∘, AB=6, and AC=10. Point D lies on side BC,
and AD is the altitude from vertex A to the hypotenuse BC. Find the length of BD.

Sxchen1110 11 nov 2024

+2

14

1

+30

Combinatorics

Erica and Alan each flip a fair coin 5 times. Suppose that Erica has flipped more heads than Alan after each has flipped the coin 2 times. The probability that Erica has flipped more heads than Alan after each has flipped the coin 5 times is m n , where lee mas ..

Sxchen1110 30 jun 2024

0

24

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+30

Algebra

For every integer n≥1, let P(n) denote the product of the first n odd numbers:
P(n)=1×3×5×⋯×(2n−1)
Prove that for all integers n≥1, P(n)=(2n)!/2^n×n!.

Sxchen1110 18 abr 2024

0

28

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+30

Combinatorics

Let S = {1, 2, . . . , 2021}, and let F denote the set of functions f : S → S. For a function f ∈ F, let Tf = f 2021(s) : s ∈ S , where f 2021(s) denotes f(f(· · ·(f(s))· · ·)) with 2021 copies of f. Compute the remainder when sigma notation f∈F lee mas ..

Sxchen1110 8 abr 2024

0

10

2

+30

Geometry

Let ABTCD be a convex pentagon with area 22 such that AB = CD and the circumcircles of triangles TAB and TCD are internally tangent. Given that ∠ATD = 90◦ , ∠BTC = 120◦ , BT = 4, and CT = 5, compute the area of triangle TAD.

Sxchen1110 8 abr 2024

0

19

1

+30

Geometry

Let the incircle of △ABC be tangent to AB, BC, AC at points M, N, P, respectively. If ∡BAC = 30◦ , find [BP C] [ABC] · [BMC] [ABC] , where [ABC] denotes the area of △ABC.

Sxchen1110 31 mar 2024