MaxWong

Hmm ok. I will do the searching myself.

2) \(\dfrac{12}{13} = \dfrac{923076}{999999} = 0.\overline{923076}\)

If A is fixed, max value occurs when B = C,

If B is fixed, max value occurs when A = C.

If C is fixed, max value occurs when A = B.

So the maximum will occur when A = B = C

Max value = 3 cos (pi / 3) = 3/2

I got the answer, but why does the max value occur when B = C if A is fixed?

1) \(\dfrac{10}{27} = \dfrac{370}{999} = 0.\overline{370} = 0.370\;370\;370\;3...\)

Nope. I am sure it could be greater.

For example. in a 90-45-45 triangle, cos A + cos B + cos C = 2 sqrt (2), which is already greater than sqrt(3)/2.

\(6x^2 +10x = 4-10x-6x^2\\ 12x^2 + 20x - 4 = 0\\ 3x^2 +5x - 1 = 0\\ \)
Then use quadratic formula, simplify, and you get the values of P, Q, and R. Multiply them together and you are done.

Yes. Glad you know these. 

The union of few intervals means that x satisfies any of them, so it means "or".

The intersection of few intervals means that x must satisfy all of them, so it means "and".

https://web2.0calc.com/questions/latex-coding

^ You can learn LaTeX with the links in this post. 

Yes. Solve the inequality 6x < 3, and you get the range of values that are NOT possible to be x. 

You can find what's possible to be x afterwards, as what's NOT impossible to be x, is what's possible to be x.

\(x\in (a, b)\implies a < x < b\\ x \in (a, b] \implies a < x \le b\\ x \in [a, b) \implies a \le x < b\\ x \in [a,b] \implies a \le x \le b\)

\(\cup\text{ means or}\\ \cap\text{ means and}\)