thickhead wrote:

multiply the slopes of OA and BC and set it to -1

What exactly does this mean?

Also, from what the rest of thickhead's method is, how exactly should I find the coordinates of (h, k). Sorry, I just didn't really understand what you wrote.

Lastly,

bob bundy (moderator) wrote:

I called the points (a,1/a); (b,1/b); and (c,1/c) and worked out the equation of the line perpendicular to AB through C. Once you have the form for that line, you can write down a similar equation for the line perpendicular to BC through A.

How did you work the equation for the line perpendicular to Ab through C?

Thanks,

ET ag

P.S. I only need a specification, since I see the method that you guys used, which was quite smart.

]]>I use capital letters for the point location and small letters for position vector. that always gives a disciplined approach rather than using free vectors.the origin acts as anchor so that you won't go astray.]]>

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Welcome to the forum.

The forum LaTex doesn't support your draw commands so you won't get an image that way. Most members use Geogebra to construct their diagrams; save them to an on-line site; and then link from there using bcCode. A recent post has addressed this.

Bob

]]>Since you use AoPS, you should be familiar with the AoPS Honor Code. Specifically, you should know that you should try to look up answers but rather try them. Remember, the teachers of your course are happy to help you on the Page Feed.

Also, the answer 0 is correct given Bob's reason.

]]>Not that I know of. What would be the advantage of such a thing?

]]>f(x) o f(x)^-1 = f(x)^-1 o f(x) = identity operation (same as if no operation was performed) = x]]>

hi Maroon900

Welcome to the forum.

At first I thought this was a use of the triangle inequality and, after a bit of manipulating, I got AD < AB + AC. Nearly there I thought. Then I tried a fresh approach:

Rotate the triangle about point D to create a new triangle A'BC below the first. The resulting shape ABA'C is a parallelogram (can you prove this?) and the diagonal is 2AD. You'll get the required result from this.

Bob

Brilliant. Creating parallelogram was the trick.

Maroon900, Hint, SSS and 2AD < AC+ A'C

]]>"Jayne has 3 quarters, 2 dimes, a nickel, and 2 pennies in her pocket. How many different amounts can she make using some or all of these coins?" Please solve this and show me how you got the answer step-by-step.

Use generating functions:

But we need to use some of the coins so 0 is out. There are 71 ways to give change using these coins but only 62 of them are different amounts so that is the answer.

]]>JaneFairfax wrote:

Twenty-three. Thats one name for the number 23.it is numbers not STUPID LETTERS

13kayduz wrote:

Shurrik wrote:二十三 = 23 (in Chinese)

Thank you oh so very much:D

Those are letters too. --'

]]>Sorry, but I can't answer your ranking question. Maybe someone else here can.

I googled around a bit and came across quite a range of coverage about this topic on the net. Here are some search suggestions:

"Sports teams' ranking"

"Sports rating system methods"

"Sports power ranking"

Hopefully a ready-made system exists for your model!

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