Math 206 Homework
Author:
Jibri L Kea
Last Updated:
10 yıl önce
License:
Creative Commons CC BY 4.0
Abstract:
Math 206 homework
\begin
Discover why over 20 million people worldwide trust Overleaf with their work.
Math 206 homework
\begin
Discover why over 20 million people worldwide trust Overleaf with their work.
%description: Math 290 HW Template
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\begin{document}
%Identification, Change as necessary!
{\Large Jibri Kea} \hfill
{\large Math 206, Section 2,} %Delete one
\hfill \today
I worked with:
\begin{enumerate}
\item \textbf{Problem 6: Number Systems} Perform D3F02 (hex) + C34D (hex). State your answer in hexadecimal and decimal.
D3F02h + C34Dh
\[ D 3 F 0 2 h\]
\[1101 + 0011 + 1111 + 0000 + 0010 b\]
\[ 13 + 3 + 15 + 0 + 2 d\]
\[13*16^{4} + 3*16^{3} + 15*16^{2} + 0*16^{1} + 2*16^{0}\]
\[851,968 + 12,288 + 3,840 + 0 + 2d\]
\[868,098d\]
\[C34Dh\]
\[1100+0011+0100+1101b\]
\[12+3+4+13d\]
\[12*16^{3} + 3*16^{2} + 4*16^{1} + 13*16^{0}\]
\[49,152+768+64+13d\]
\[49,997d\]
\[D3F02h+C34Dh= 918,095d\]
\[11010011111100000010b\]
\[+1100001101001101b\]
\[11100000001001001111b\]
\[14+0+2+4+15h\]
\[E024Fh = 918,095d\]
\item \textbf{Problem 8: Number Systems} Convert 109 to base 7.
\[109 / 7 = 15 R4\]
\[15 / 7 = 2 R1\]
\[214_{7}\]
\[2*2^{2}*7^{1}+4*7^{0}\]
\[98+7+4 =109d=214_{7}\]
\item \textbf{Problem 19} Find a closed form.
\[1,4,7,10,13,16,19\]
\[a_{n} = c+dn+fn^{2}\]
\[a_{1} = c+d+f=1\]
\[a_{2} = c+2d+4f=4\]
\[a_{3} = c+3d+9f=7\]
\[c=-2\]
\[d=3\]
\[f=0\]
\[a_{n}=-2+3n\]
\item \textbf{Problem 19} Find a closed form.
\[-1,1,3,5,7,9,11\]
For n is greater than/equal to 0.
\[GUESS a_{n}=2_{n-1}\]
\[n=0: True -1=0-1=-1\]
Assume for some n >= 1. a(k) = 2(k) - 1
\[=4n-2-2n+3=2n+1=2(n+1)-1\]
\end{enumerate}
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