MaxWong

\(\dfrac{10}{3}=3.\underbrace{333333333333333333333333333........}_\infty\)

Yes there is no end.

\(\dfrac{2\frac{1}{4}\text{ inches}}{\frac{1}{4}\text{ inches}}=\dfrac{60 \text{ inches}}{\text{what}}\)LOL xD

\((2\frac{1}{4}\text{ inches})(\text{what})=(60\text{ inches})(\frac{1}{4}\text{ inches})\)

\(\text{what} = \dfrac{15\text{ inches}^2}{2\frac{1}{4}\text{ inches}}=\color{red}6\frac{2}{3}\text{ inches}\)

2²⁰¹⁴ is so big that our calculator on this page can't calculate. And it's good to know that the unit digit of this number is 4.

\(2014\pmod4 \equiv 2\\ \therefore \text{Unit digit of }2^{2014} = \text{Unit digit of }2^2 = 4\)

Divide 52 by 50.

\(\dfrac{52 \text{ hours}}{50\text{ day}}=1.04 \text{ hours per day}\)

\(u^2+33.405u-2360.582=0\)

\(u = {-33.405 \pm \sqrt{33.405^2-4(1)(-2360.582)} \over 2(1)}\) Quadratic Formula.

Use your calculator for the answer. Probably same answer as Guest #1

\(\begin{array}{rl}&\dfrac{2}{3}+\dfrac{4}{5}\\=&\dfrac{10}{15}+\dfrac{12}{15}\\=&\dfrac{22}{15}\\=&1\dfrac{7}{15}\end{array}\)

Example:

\(\color{aqua}e^x\cdot e^{-x}= 1\)

Uh sorry that holds for every values of x XDDDDD

\(\color{blue}e^x=e^{-x}\)

\(\color{blue}\ln e^x = \ln e^{-x}\)

\(\color{blue}x=-x\) \(\color{red}\leftarrow \color{}\boxed{\color{red}\ln x = \log_e x}\\\color{}\boxed{\color{red}\ln e^x=x}\)

\(\color{blue}2x=0\)

\(\color{blue}x=0\)

\(\color{aqua}\left(\dfrac{3}{9x^2}-\dfrac{5}{6x}-14\right)-\left(\dfrac{7}{9x^2}-\dfrac{5}{6x}+1\right)\)

\(\color{aqua}=\dfrac{3}{9x^2}-\dfrac{5}{6x}-14 - \dfrac{7}{9x^2}+\dfrac{5}{6x}-1\\ \color{aqua}=\dfrac{3}{9x^2}-\dfrac{7}{9x^2}-14-1\\\color{aqua} =-\dfrac{4}{9x^2}-15\)

Same as Mellie's answer, only difference is the steps.

\(\begin{array}{rll}\dfrac{3}{12}&=&\dfrac{5}{x}\\\dfrac{1}{4}&=&\dfrac{5}{x}\\\dfrac{5}{20}&=&\dfrac{5}{x}\\x&=&20\end{array}\)