Bruce B. answered • 01/16/14

Mathematics and Physics; Calculus and Mechanics Specialty

Actually, the only point where 0.5x

^{2}and 2x^{2}are evenly spaced from x^{2}is at x = 0.This is found by taking the difference between x

^{2}and the other equation at any given point

|2x

And then setting them equal to each other.

|2x

^{2}- x^{2}| and |0.5x^{2}- x^{2}|And then setting them equal to each other.

|2x

^{2}- x^{2}| = |0.5x^{2}- x^{2}| → x^{2}= 0.5x^{2}→ x = 0.5xBut that isn't your question. Numbers always have patterns, so let's see if we can find this one. :)

Using the same functions, we can make a table to look at how things are spaced. I'll be going up in increments of 1, starting at 0.

0.5x

Using the same functions, we can make a table to look at how things are spaced. I'll be going up in increments of 1, starting at 0.

0.5x

^{2}| x^{2}| 2x^{2}| 2x^{2}- x^{2}| x^{2}- 0.5x^{2}0 | 0 | 0 | 0 | 0

0.5 | 1 | 2 | 1 | 0.5

2 | 4 | 8 | 4 | 2

4.5 | 9 | 18 | 9 | 4.5

8 | 16 | 32 | 16 | 8

So there's our pattern. Comparing just the last two columns, we see that for each increment the difference is doubled. This makes sense because the difference between 2x

I hope that helped!

^{2}and x^{2}is twice as large as the difference between 0.5x^{2}and x^{2}.I hope that helped!

George H.

01/18/14