Day 5: More Problems

We had our non-stop 4 hour math class today, and I accumulated lots of problems, so today's post is purely dedicated to problems:

1. Two charges q and -2q are kept a distance d apart. Assuming the origin at the 'q' charge and '-2q' at x=d, draw a graph of electric field intensity(E) versus position(x).

2. 9 lattice points ( 3 dimensional points whose x,y,z coordinates are all integers) are joined by 9C2=36 lines. Prove that at least one point exists on one of these lines which is an integer.

3. Solve sinx + cosx + |sinx-cosx| > √2

4. Draw the graph of 1/x+1/y=1/k, where k is a constant.

5. Find the angle at which the curve of sinx,cosx and tanx intersect the x-axis

And if nobody gets the equilateral triangle proof anomaly, then I declare it tomorrow..

Today's Formula:

If x, y and z are three sides of a triangle, then |x|+|y|<|z|

"If you sit to study for 2 minutes, it seems like 2 hours, but if you sit with a nice girl for 2 hours, it seems like 2 minutes. This is the theory of relativity." -Albert Einstein