MaxWong

Example: \(\text{Hi}\)

In this example I just typed \(

and then \text{Hi}

then \).

I didn't even click LaTeX button :)

Also I have found a way to use LaTeX without even clicking the LaTeX button.

Type '\(' 

and then type '\)'

and then type your LaTeX commands between the 2 notations.

Thank you :)

That is the Quadratic Equation and we don't need it for finding the value of \(\pi\) . 

\(\pi \approx 3.1415926\)

And that's a quite good approximation already.

Very simple way #1:Use a calculator!! :)

Very simple way #2:

If the number can be simplified to x^2 times y, this will be simple, you get a multiple of the square root of a prime number.

Example: \(\sqrt8 = \sqrt{2^2 \times 2}=2\sqrt{2}\)

\(\sqrt{175}=\sqrt{5^2\times 7}=5\sqrt7\)

The middle step is just for visualization, I can compute these 2 in 1 step in mind because I practise it over and over.

X+y = X+y.

It can't be further simplified, please come back with a sensible question.

2(-6)+4(-5)2: Do you mean 2(-6)+4(-5)²?

\(\begin{array}{rl}&2(-6)+4(-5)^2\\=&-12+4(25)\\=&100-12\\=&88\end{array}\)

Volume of water: \(\dfrac{1}{2}\left(\dfrac{4\pi(6)^3}{3}\right)\times\dfrac{2}{5}=144\pi \times\dfrac{2}{5}=\dfrac{288\pi}{5}\)cm³

If the cone is inverted, the shape that the water formed in the cone is still a cone:

\(\dfrac{1}{3}\pi r^2(12)=\dfrac{288\pi}{5}\\ 60\pi r^2=864\pi\\ r^2=\dfrac{864}{60}=\dfrac{72}{5}\\ r=\dfrac{6\sqrt{10}}{5}\)

ANS: r = 6/5 x sqrt(10)

If the cone is not inverted, the shape that the water formed in the cone is a fructum(or something like that?) and the surface area can't be worked out without the exact height of the hollow cone.

Therefore ANS = 6sqrt(10)/5

2/3 + 1/7

= 14/21 + 3/21

= 17/21

Do you mean 3.(285714)repeated?

\(3.\bar{2}8571\bar{4}\\ = 3 + \dfrac{2}{7}\\ =3\dfrac{2}{7}\\ =\dfrac{23}{7}\)