45 lines
1.3 KiB
TeX
45 lines
1.3 KiB
TeX
\documentclass{report}
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\input{preamble}
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\input{macros}
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\input{letterfonts}
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\title{\Huge{Calculus III}\\Homework \# 1}
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\author{\huge{Krishna Ayyalasomayajula}}
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\date{}
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\begin{document}
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\maketitle
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\newpage% or \cleardoublepage
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% \pdfbookmark[<level>]{<title>}{<dest>}
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\pdfbookmark[section]{\contentsname}{toc}
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\tableofcontents
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\pagebreak
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\chapter{Lab 2 - 13.1 Apps}
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\section{Work}
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\qs{}{
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Let $\vec{T_1}$ represent the tension of the leftmost cable, while $\vec{T_2}$ encodes the tension force experienced by the rightmost cable. Our coordinate system will originate at the intersection of the two cables.
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\begin{align*}
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\vec{T_1} \coloneqq \langle \|\vec{T_1}\| ; 135\degree \rangle \\
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\vec{T_2} \coloneqq \langle \|\vec{T_2}|\| ; 15\degree \rangle \\
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500=\|\vec{T_1}\|\sin{135\degree} + \|\vec{T_2}\|\sin{15} \\
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0 = \|\vec{T_1}\|\cos{135\degree} + \|\vec{T_2}\|\cos{15} \\
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\implies 500=\|\vec{T_1}\|\tfrac{\sqrt{2}}{2} + \|\vec{T_2}\|\cdot0.258819045103 \\
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\implies0 = \|\vec{T_1}\|\tfrac{-\sqrt{2}}{2} + \|\vec{T_2}\|\cdot0.965925826289 \\
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\text{Solving the system numerically yields: }\\
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\|\vec{T_1}\| \Rightarrow 557.677\, \mathrm{lb}\\
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\|\vec{T_2}\| \Rightarrow 408.248\,\mathrm{lb} \\
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\text{This corresponds to answer choice A}
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\end{align*}
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}
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\qs{}{
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}
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\end{document}
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