physics
One day I decide I want to see how high I can throw a rock. I throw a rock straight up in the air and it has a speed of 30 m/s when it leaves my hand. I then realize this was foolish, as I need to get out of the way before the rock comes back down and hits me on the head. How ...
physics
Two point charges +q=1 μC and −q=−1 μC with mass m=1 g are fixed at the positions ±r⃗ 0 with |r0|=1 m. The charges are released from rest at t=0. Find the time τ in seconds at which they collide. Hint: Can you do it without integrating b...
MATHS
Find the largest possible integer n such that there exists a non-constant quadratic polynomial f(x) with integer coefficients satisfying f(1)∣f(2),f(2)∣f(3),…f(n−1)∣f(n). Details and assumptions For (possibly negative or zero) integers m and k the ...
MATHS
How many positive integers n are there such that 10^n≤n^10?
MATHS
Find the number of real solutions of the system of equations. x^2−y^2=z y^2−z^2=x z^2−x^2=y
MATHS
A simple graph G has 200000 edges and for any 3 vertices v,w,x, at least one of the edges vw,wx,xv is not present in G. What is the least number of vertices that G can have? Details and assumptions A simple graph does not have multiple edges between vertices, or self loops.
MATHS
THANKS:D
MATHS
ABC is a triangle with a right angle at A. M and N are points on BC such that AM is the altitude, and AN is the angle bisector of ∠BAC. If CN/NB=21, what is CM/MB?
MATHS
For a set of numbers T, we say that T has distinct subset sums if all distinct subsets of T have distinct sums. How many subsets of {1,2,3,4,5,6,7,8} have distinct subset sums? Details and assumptions The empty set (the set of no elements) has a sum of 0 by convention.
MATHS
A national math contest consisted of 11 multiple choice questions, each having 11 possible choices, of which only 1 of the choices is correct. Suppose that 111 students actually wrote the exam, and no two students have more than one answer in common. The highest possible avera...
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