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Questions: Algebra BusinessCalculus
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Use the table below to estimate the velocity at \(\displaystyle t=2\) by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to \(\displaystyle (2,11)\)
Using the point to the left gives \(\displaystyle m_1 = \frac{11-3}{2-0} = 4\). Using the point to the right gives \(\displaystyle m_2 = \frac{11-19}{2-4} = 4\). Taking the average of the slopes gives \(\displaystyle \frac{4+4}{2} = 4\). The estimate of the velocity is \(\displaystyle 4\) meters per second.
\begin{question}Use the table below to estimate the velocity at $t=2$ by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to $(2,11)$\newline
\begin{tabular}{|c|c|c|c|c|c|}\hline
$t$ seconds & 0 & 2 & 4 & 6 & 8 \\ \hline
$x$ meters & 3 & 11 & 19 & 28 & 34 \\ \hline
\end{tabular}\newline
\soln{9cm}{Using the point to the left gives $m_1 = \frac{11-3}{2-0} = 4$. Using the point to the right gives $m_2 = \frac{11-19}{2-4} = 4$. Taking the average of the slopes gives $\frac{4+4}{2} = 4$. The estimate of the velocity is $4$ 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=2 " src="/equation_images/%20%5Cdisplaystyle%20t%3D2%20" alt="LaTeX: \displaystyle t=2 " data-equation-content=" \displaystyle t=2 " /> by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to <img class="equation_image" title=" \displaystyle (2,11) " src="/equation_images/%20%5Cdisplaystyle%20%282%2C11%29%20" alt="LaTeX: \displaystyle (2,11) " data-equation-content=" \displaystyle (2,11) " /> <br>
</p> </p>
<p> <p>Using the point to the left gives <img class="equation_image" title=" \displaystyle m_1 = \frac{11-3}{2-0} = 4 " src="/equation_images/%20%5Cdisplaystyle%20m_1%20%3D%20%5Cfrac%7B11-3%7D%7B2-0%7D%20%3D%204%20" alt="LaTeX: \displaystyle m_1 = \frac{11-3}{2-0} = 4 " data-equation-content=" \displaystyle m_1 = \frac{11-3}{2-0} = 4 " /> . Using the point to the right gives <img class="equation_image" title=" \displaystyle m_2 = \frac{11-19}{2-4} = 4 " src="/equation_images/%20%5Cdisplaystyle%20m_2%20%3D%20%5Cfrac%7B11-19%7D%7B2-4%7D%20%3D%204%20" alt="LaTeX: \displaystyle m_2 = \frac{11-19}{2-4} = 4 " data-equation-content=" \displaystyle m_2 = \frac{11-19}{2-4} = 4 " /> . Taking the average of the slopes gives <img class="equation_image" title=" \displaystyle \frac{4+4}{2} = 4 " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B4%2B4%7D%7B2%7D%20%3D%204%20" alt="LaTeX: \displaystyle \frac{4+4}{2} = 4 " data-equation-content=" \displaystyle \frac{4+4}{2} = 4 " /> . The estimate of the velocity is <img class="equation_image" title=" \displaystyle 4 " src="/equation_images/%20%5Cdisplaystyle%204%20" alt="LaTeX: \displaystyle 4 " data-equation-content=" \displaystyle 4 " /> meters per second.</p> </p>