+2354

Well obviously you have a picture with that indicating the quadrants.

But it's the quadrant on the left-bottom since that's where x<0 and y<0.

Think for yourself if you also know which quadrant gives x>0 y<0, x<0 y>0 and x>0 y>0

reinout-gJun 19, 2014

+26400

$${\frac{{\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{15}}{\mathtt{\,\times\,}}{\mathtt{15}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{20}}}{{\mathtt{15}}}}\right)}}{{\mathtt{360}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{20}}{\mathtt{\,\times\,}}{\mathtt{20}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{15}}}{{\mathtt{20}}}}\right)}}{{\mathtt{360}}}}{\mathtt{\,-\,}}{\mathtt{15}}{\mathtt{\,\times\,}}{\mathtt{20}} = {\mathtt{166.041\: \!867\: \!567\: \!676\: \!442}}$$

$$\tan^{-1} ( \frac{15}{20} )
= \tan^{-1}( \frac {1}{\frac{20}{15}} )
=\cot^{-1} ( \frac{20}{15} )
=\frac{180}{2}-\tan^{-1} ( \frac{20}{15} )\\
\Rightarrow$$

$$\left({\frac{{\mathtt{\pi}}}{{\mathtt{180}}}}\right){\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{20}}}{{\mathtt{15}}}}\right)}{\mathtt{\,\times\,}}\left({\mathtt{15}}{\mathtt{\,\times\,}}{\mathtt{15}}{\mathtt{\,-\,}}{\mathtt{20}}{\mathtt{\,\times\,}}{\mathtt{20}}\right){\mathtt{\,\small\textbf+\,}}{\frac{\left({\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{20}}{\mathtt{\,\times\,}}{\mathtt{20}}\right)}{{\mathtt{2}}}}{\mathtt{\,-\,}}{\mathtt{15}}{\mathtt{\,\times\,}}{\mathtt{20}} = {\mathtt{166.041\: \!867\: \!567\: \!676\: \!442}}$$

heurekaJun 19, 2014

#147

+346

Nevermind

DragonJun 19, 2014

+2354

The value of leela's account can be calculated in the following way;

$$\begin{array}{lcl}
\mbox{At the beginning (year 0) }VI = 500\\
\mbox{After 1 year }VI = 500 \times 1.045\\
\mbox{After 2 years } VI = 500 \times 1.045 \times 1.045= 500 \times 1.045^2\\
\mbox{After t years } VI=500 \times 1.045^t\\
\mbox{Adele started 2 years earlier so by the time Leela started saving she already had }500*1.045^2 \mbox{ in her account}\\
\mbox{Therefore at year t Adele has }500*1.045^2*1.045^t = 500*1.045^{t+2} \mbox{ in her account}\\
\mbox{Therefore the percentage of value of Adele's account compared to Leela's account can be given by}\\
\frac{500*1.045^{t+2}}{500*1.045^t} \times 100\%= 1.045^2 \times 100\% = 1.092025 \times 100\% = 109.2025 \% \approx 109.20 \%
\end{array}$$

Reinout