How do I find the value of r?
(r - 2)^2 + (r - 4)^2 = r^2
I know what r is, coincidentally, (it's 10)
But how would I go about finding it if I didn't know?
Wasn't sure where to post this, it's not homework, I got it from a brain teaser (finding the radius of a circle which is inside a square with a 2x4 rectangle in the corner, the radius is r as seen above)
Ahh yes. I didn't quite understand at first, how to arrive at
is what trips me up I think. I can grasp everything you just wrote, I was able to test it... but I just don't get my head around the workings of it heh.
I think I'm a lot closer to understanding it than I was before though.
Mind you, I never went much past basic math and some algebra in school, I just do these kinds of things for fun and learning.
I also think my understanding is "contaminated" by knowing the value of r.
What you guys have shown me is useful information though for learning how to do this.
2. Because (when you have parentheses up against eachother as we will, it is understood that they are to be multiplied) you can rewrite the initial equation like this:
3. Using the technique called FOIL: first, outer, inner, last. Which basically boils down to (a+b)(c+d)=ac+ad+bc+bd.
So which can be simplified to which can again be simplified to
and using the same technique:
4. So applying what we just went over:
5. combine like terms such as and so on
6. Subtract from both sides (you must do it to both sides, because if you only did it to one side they would no longer be equal. For example, 5=5, if you subtract 1 from either side, you must subtract it from the other, so 4=4, if you do not do it to both sides, they will no longer be equal)
That is how you get to this step.
edit: I can break it down a little more if you are really struggling with any given step here, let me know.
Oh wow, I actually got it!! Thank you!
I was thinking I was a bit dumb there for a while but I actually understand it now.
Haha, I went back to the same brain teaser, and it happened to have different values this time but I was actually able to figure it out.
in this case however, it didn't make life much simpler, so i see no harm in sticking with the straight forward approach...not that Jane was saying anything different
The reason for the substitution is that the equation is symmetrical about . For other similar problems, you make similar substitutions involving whatever the equation is symmetrical about. For example …
<screams in terror and gives up>
The equation is symmetrical about so let . Then
You see the difference between your method and mine? Therefore my method is not a one-trick pony! Next time think before making another similar comment.