Recent content by mathisfun1

The centroid of a tetrahedron is the intersection of all line segments that connect each vertex to the centroid of the opposite face.

How to find out the position vector of the centroid of tetrahedron , the position vectors of whose vertices are a,b,c,d respectively. I am familiar with the result, namely a+b+c+d/4 but want to know how to derive it without using the 3:1 ratio property. Any help would be appreciated. Thank you.

Sorry for getting back to you so late, got caught up in school work. Let's just say for some case, r/b=1.7 and at=0.4 then frac (ax) will be 0.7+0.4=1.1 which is not possible. I tried a few cases taking different values of a and b and concluded that this will never happen the sum will always be...

I am much thankful for your reply. However, I am unable to understand how fractional part of ax=fractional part of r/b + at. Also, although I am studying advanced calculus (Relative to XIIth standard, that is I am in XIIth standard but studying a bt ahead for competitive exams, we have never...

I started with taking three cases, 1. a=b since a and b are co primes, both will have to be equal to 1 and then we can easily get lhs = rhs. 2. a>b 3.a<b I have no idea as to how to proceed for the second and third cases. Any help would be greatly appreciated.

If f1(X)>f2(x) doesn't implies that the indefinite integration of f1(x) will be greater than f2(x). This is only applicable when both sides are integrated within limits and thus when integrating from 0 to x, constant gets eliminated.

That f(x) is greater than zero, but that seems to be contradictory as a negative function may also have positive derivative. :(

Wouldn't integrating this inequality conclude the same thing as what we are given, that f is a concave upward function?

Thank you so much! I began with the condition that the secant must lie above the curve at all points if the curve is concave upward but that seem to lead nowhere. I also tried to utilise the fact that the double derivative of f(X) will be positive but to no avail. Any help will be appreciated.

Yes.