# Catherinekem

Members

4

• Lepton

10

1. ## Another Lonely Valentine's Day

Dude (hereme3), Have you ever read any autobiographies or biographies of some the greatest or successful people (If not I strongly recommend)? Most of them went through such moronic events and found something that sticks in their brain and they work hard on it and come out as successful people. You have one such great opportunity. I can show you one such opportunity in your reply. You said, " I'm sorry to hear that. Valentine's Day seems like a time when bad things happen. I hope your dad will get better soon". Here is the project. Call it hereme3 conjecture, and it goes like this: "Valentine's Day seems like a time when bad things happen." Prove or disprove (I mean scientifically or mathematically) this and you will be famous. You see that you are lucky dude to have such a conjecture on your name. I am just hinting you to see the real world and appreciate the constraints. These constraints give shape to life. And thats the beauty. Most of the great mathematicians went through finite number of times of more pain than we do yet they saw the beauty in their pain. One may use simple logic theory or discrete mathematics to solve the hereme3 conjecture. Good luck. Luck prefers the prepared mind.
2. ## x^n

Take logarithm on both sides, and simplify.
3. ## linear transformation

Proof of uniqueness of a linear transformation: We can assume that {e1,e2,...} is the basis of the vector space V. Suppose T and T' two linear transformations such that T(e1) = u1 and T'(e1) = u1 T(e2) = u2 and T'(e2) = u2 T(e3) = u3 and T'(e3) = u3, etc. Then, for each v in V T(v) = T(k.e1+l.e2+m.e3+...) = k.u1 + l.u2 + m.u3 + ... for some real k,l,m, ... and T'(v)= T'(k.e1 + l.e2 + m.e3+ ...) = T'(k.e1) + T'(l.e2) + T'(m.e3) + ... = k.T'(e1) + l.T'(e2) + m.T'(e3) + ... = k.u1 + l.u2 + m.u3 + ... Hence, T = T' Hope this answers your problem.
4. ## Quartiles

There are two ways that one can compute quartiles. The standard way uses interpolation approach to evaluate a quartile, which is typical with a continuous data; But one can avoid using interpolation and find the quartiles; the later approach is used in nominal or discrete data. Both the answers are correct in the above problem.
×