Math 206 Homework
Forfatter:
Jibri L Kea
Sidst opdateret:
9 år siden
Licens:
Creative Commons CC BY 4.0
Resumé:
Math 206 homework
\begin
Opdag hvorfor 18 millioner mennesker verden rundt stoler på Overleaf med deres arbejde.
Math 206 homework
\begin
Opdag hvorfor 18 millioner mennesker verden rundt stoler på Overleaf med deres arbejde.
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%Identification, Change as necessary!
{\Large Jibri Kea} \hfill
{\large Math 206, Section 2,} %Delete one
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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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