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Questions: Algebra BusinessCalculus
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Use the table below to estimate the velocity at \(\displaystyle t=8\) by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to \(\displaystyle (8,19)\)
Using the point to the left gives \(\displaystyle m_1 = \frac{19-10}{8-4} = \frac{9}{4}\). Using the point to the right gives \(\displaystyle m_2 = \frac{19-23}{8-12} = 1\). Taking the average of the slopes gives \(\displaystyle \frac{\frac{9}{4}+1}{2} = \frac{13}{8}\). The estimate of the velocity is \(\displaystyle \frac{13}{8}\) meters per second.
\begin{question}Use the table below to estimate the velocity at $t=8$ by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to $(8,19)$\newline
\begin{tabular}{|c|c|c|c|c|c|}\hline
$t$ seconds & 0 & 4 & 8 & 12 & 16 \\ \hline
$x$ meters & 3 & 10 & 19 & 23 & 27 \\ \hline
\end{tabular}\newline
\soln{9cm}{Using the point to the left gives $m_1 = \frac{19-10}{8-4} = \frac{9}{4}$. Using the point to the right gives $m_2 = \frac{19-23}{8-12} = 1$. Taking the average of the slopes gives $\frac{\frac{9}{4}+1}{2} = \frac{13}{8}$. The estimate of the velocity is $\frac{13}{8}$ meters per second.}
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Use the table below to estimate the velocity at <img class="equation_image" title=" \displaystyle t=8 " src="/equation_images/%20%5Cdisplaystyle%20t%3D8%20" alt="LaTeX: \displaystyle t=8 " data-equation-content=" \displaystyle t=8 " /> by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to <img class="equation_image" title=" \displaystyle (8,19) " src="/equation_images/%20%5Cdisplaystyle%20%288%2C19%29%20" alt="LaTeX: \displaystyle (8,19) " data-equation-content=" \displaystyle (8,19) " /> <br>
</p> </p>
<p> <p>Using the point to the left gives <img class="equation_image" title=" \displaystyle m_1 = \frac{19-10}{8-4} = \frac{9}{4} " src="/equation_images/%20%5Cdisplaystyle%20m_1%20%3D%20%5Cfrac%7B19-10%7D%7B8-4%7D%20%3D%20%5Cfrac%7B9%7D%7B4%7D%20" alt="LaTeX: \displaystyle m_1 = \frac{19-10}{8-4} = \frac{9}{4} " data-equation-content=" \displaystyle m_1 = \frac{19-10}{8-4} = \frac{9}{4} " /> . Using the point to the right gives <img class="equation_image" title=" \displaystyle m_2 = \frac{19-23}{8-12} = 1 " src="/equation_images/%20%5Cdisplaystyle%20m_2%20%3D%20%5Cfrac%7B19-23%7D%7B8-12%7D%20%3D%201%20" alt="LaTeX: \displaystyle m_2 = \frac{19-23}{8-12} = 1 " data-equation-content=" \displaystyle m_2 = \frac{19-23}{8-12} = 1 " /> . Taking the average of the slopes gives <img class="equation_image" title=" \displaystyle \frac{\frac{9}{4}+1}{2} = \frac{13}{8} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B%5Cfrac%7B9%7D%7B4%7D%2B1%7D%7B2%7D%20%3D%20%5Cfrac%7B13%7D%7B8%7D%20" alt="LaTeX: \displaystyle \frac{\frac{9}{4}+1}{2} = \frac{13}{8} " data-equation-content=" \displaystyle \frac{\frac{9}{4}+1}{2} = \frac{13}{8} " /> . The estimate of the velocity is <img class="equation_image" title=" \displaystyle \frac{13}{8} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B13%7D%7B8%7D%20" alt="LaTeX: \displaystyle \frac{13}{8} " data-equation-content=" \displaystyle \frac{13}{8} " /> meters per second.</p> </p>