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Questions: Algebra BusinessCalculus
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Use the table below to estimate the velocity at \(\displaystyle t=12\) by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to \(\displaystyle (12,35)\)
Using the point to the left gives \(\displaystyle m_1 = \frac{35-25}{12-8} = \frac{5}{2}\). Using the point to the right gives \(\displaystyle m_2 = \frac{35-39}{12-16} = 1\). Taking the average of the slopes gives \(\displaystyle \frac{\frac{5}{2}+1}{2} = \frac{7}{4}\). The estimate of the velocity is \(\displaystyle \frac{7}{4}\) meters per second.
\begin{question}Use the table below to estimate the velocity at $t=12$ by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to $(12,35)$\newline
\begin{tabular}{|c|c|c|c|c|c|}\hline
$t$ seconds & 0 & 4 & 8 & 12 & 16 \\ \hline
$x$ meters & 9 & 16 & 25 & 35 & 39 \\ \hline
\end{tabular}\newline
\soln{9cm}{Using the point to the left gives $m_1 = \frac{35-25}{12-8} = \frac{5}{2}$. Using the point to the right gives $m_2 = \frac{35-39}{12-16} = 1$. Taking the average of the slopes gives $\frac{\frac{5}{2}+1}{2} = \frac{7}{4}$. The estimate of the velocity is $\frac{7}{4}$ 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=12 " src="/equation_images/%20%5Cdisplaystyle%20t%3D12%20" alt="LaTeX: \displaystyle t=12 " data-equation-content=" \displaystyle t=12 " /> by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to <img class="equation_image" title=" \displaystyle (12,35) " src="/equation_images/%20%5Cdisplaystyle%20%2812%2C35%29%20" alt="LaTeX: \displaystyle (12,35) " data-equation-content=" \displaystyle (12,35) " /> <br>
</p> </p>
<p> <p>Using the point to the left gives <img class="equation_image" title=" \displaystyle m_1 = \frac{35-25}{12-8} = \frac{5}{2} " src="/equation_images/%20%5Cdisplaystyle%20m_1%20%3D%20%5Cfrac%7B35-25%7D%7B12-8%7D%20%3D%20%5Cfrac%7B5%7D%7B2%7D%20" alt="LaTeX: \displaystyle m_1 = \frac{35-25}{12-8} = \frac{5}{2} " data-equation-content=" \displaystyle m_1 = \frac{35-25}{12-8} = \frac{5}{2} " /> . Using the point to the right gives <img class="equation_image" title=" \displaystyle m_2 = \frac{35-39}{12-16} = 1 " src="/equation_images/%20%5Cdisplaystyle%20m_2%20%3D%20%5Cfrac%7B35-39%7D%7B12-16%7D%20%3D%201%20" alt="LaTeX: \displaystyle m_2 = \frac{35-39}{12-16} = 1 " data-equation-content=" \displaystyle m_2 = \frac{35-39}{12-16} = 1 " /> . Taking the average of the slopes gives <img class="equation_image" title=" \displaystyle \frac{\frac{5}{2}+1}{2} = \frac{7}{4} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B%5Cfrac%7B5%7D%7B2%7D%2B1%7D%7B2%7D%20%3D%20%5Cfrac%7B7%7D%7B4%7D%20" alt="LaTeX: \displaystyle \frac{\frac{5}{2}+1}{2} = \frac{7}{4} " data-equation-content=" \displaystyle \frac{\frac{5}{2}+1}{2} = \frac{7}{4} " /> . The estimate of the velocity is <img class="equation_image" title=" \displaystyle \frac{7}{4} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B7%7D%7B4%7D%20" alt="LaTeX: \displaystyle \frac{7}{4} " data-equation-content=" \displaystyle \frac{7}{4} " /> meters per second.</p> </p>