# Thread: L@K and Graphs of m?

1. ## L@K and Graphs of m?

Hi, I could use some help on two problems that my teacher gave out. I'm a Sophomore in Algebra II if it helps. My teacher encouraged us to find help anywhere so you don't have to feel like you're helping me cheat or anything like that.

1. What is the largest value of m such that the graph of the equation y=mx meets the graph of the equation (x-10)^2 + (y-5)^2 = 4

2. If L@K = L+(K/L), then find L@(L@K)

My friends and I have worked on these two for awhile now and are stumped, any help is appreciated. Thanks.

2. For number two, L@(L@K)=L@($\displaystyle L+\frac{K}{L}$) since L@K=$\displaystyle L+\frac{K}{L}$ and now

L@B=$\displaystyle L+\frac{B}{L}$
L@(6+B)=$\displaystyle L+\frac{6+B}{L}$ while the notation may be wierd, it just means take whatever is to the very right of the @ sign, and subsitute it for where you see K on the right of the equal sign... L@(something)=$\displaystyle L+\frac{something}{L}$

We do the same thing with normal functions: if f(x)=$\displaystyle x^2+6$ then f(1)=$\displaystyle 1^2+6$, we just put a 1 where the x would be

Similarly, f(triangle) would be $\displaystyle triangle^2+6$

So for this problem, L@($\displaystyle L+\frac{K}{L}$)=$\displaystyle L+\frac{L+\frac{K}{L}}{L}$

We simply took what was to the right of the @ sign,the $\displaystyle L+\frac{K}{L}$, and substituted it for the "K" in the original equation

I'll leave it to you to simplify

the first question is relatively simple with calculus, but given your statement I'm assuming that's a no go

3. Thanks for the help. I think I got L+1+K/(L^2)

I am taking pre-calculus next year so a simple calculus problem is beyond me right not so any help on it would be nice thanks.