So, the answer is that there is no locus or the locus contains just one point and the contact points with the curve are at infinity as I initially proposed (?).
If it is so, I must play lottery. :rolleyes:
Thank you for your time.
I see your point but there is always a but ... :frown:
No matter how hard I try, I cannot figure out an equation by eliminating x',x'',y' and y''.
Maybe there is another way of solving the problem.
I don't know. What do you think ?
Yes, I do mean rectangular hyperbola.
When it comes to geometry it is all Greek to me ... :confused:
I'm not sure whether we should say "conducted tangent from a given point" or "subtended tangent".
As far as I understand two tangent lines start from a point on the locus and touch the...
Hello all,
I would like beforehand to inform you that the translation of the following geometric problem is not very good and consequently you will have to use your mathematical intuition just a little bit. I encountered it while giving admission exams in a Mathematics department to pursue a...
if we add an element to the set which previously had k elements (that is now has k+1 elements) the new subsets that include the new element will be :
(k+1)k/2 - k(k-1)/2 = k
So, how can we argue that this will solve the problem ?
I would very much like some help to the following problem.
Homework Statement
Using mathematical induction, prove that a finite set A of n elements has n(n-1)/2 subsets of two elements.
The Attempt at a Solution
* Base step n=2: 2(2-1)/2= 1 subset of two elements.
* Inductive step: assuming...
Thanks for the answer,
Okay, here is my solution. I thought that at the problem defintion "is divisible by" and "is a multiple of" makes a huge difference.
The base case is obvious.
Let that the statement holds for n=k, that is,
k^3+(k+1)^3+(k+2)^3 is a multiple of 9.
We will then show that...
Hello everybody,
I am doing my reading lately to prepare for some exams to join a mathematics department.
And I would very much like, if anyone could help, the solution (or a hint) to the following induction proof.
" Show that n^3 + (n+1)^3 + (n+2)^3 is a multiple of 9 "
:smile:
I...
Thanks for the reply,
Indeed the "vice-versa" does not hold for every function F(x) as it has also been discussed https://www.physicsforums.com/showthread.php?t=515616&highlight=bounded+function+derivative".
How can we argue that F(x) is bounded ? :confused: By intuition the statement is...
Hello everybody,
A few years ago i tried to join a mathematics department and in the relevant exams
i came up against the following problem. I apologise beforehand if the statement of the problem is a little bit ambiguous because i do not remember it exactly. However, I am sure you will get...