The additive inverse to 2/3 is -2/3 because the additive inverse of a number adds together with the number to get 0. The multiplicative inverse is simply the reciprocal of the number, which is 3/2. The absolute difference is the absolute value of the difference of 2 numbers. So we have |3/2 - (-2/3)|, which is |3/2+2/3|, which gives us our answer of 13/6.

To get around the problem about the order of who orders the dish first, we can do \({10 \choose 2}\). However, as jfan17 said, we can switch the dishes so that Camille has what Yann ordered and Yann has what Camille ordered, so we multiply that by 2. This gives us a total amount of \(\frac{10\cdot9}{2}\cdot2\), which gives us an answer of 90 ways.

Thanks for the help! I got the same answer as you, but I thought I was definitely wrong. Your explanation makes it a lot more clear.

Thank you so much! That makes a lot of sense.

There are an infinite number of unit squares possible in a 4x4 square though, the squares do not have to be on lattice points.

Thanks for the help! I figured out the answer! :)

I multiplied everything by (a+b+c)(a+b)(a+c) and simplified it to where there is only one term on one side that is squared because that is like the cosine rule.

Do the upvotes and downvotes really matter that much??

I am sorry if they do.

So BC is \(\sqrt{19}\).

Then, by the law of sines, sin BCP is \(\frac{\sqrt3}{\sqrt{19}}\).

What now?

Sorry, but this answer is incorrect. Can you show how you got that?

I expanded it to \(a^2-2ab-2ac-b^2-c^2-bc=2a^2\).

I don't know how to compare that to the law of cosines: can I simplify further?

1) How would I find BC?

Taking the square root of 169, you get y = 13.

But we also have to remember that y can be negative, giving us that y = -13.

So our answers are y = 13, and y = -13.

Thank you so much! This makes a lot more sense!