d) Calculate the least squares line. Put the equation in the form of: \( \hat{y}=a+b x \). e) Find the correlation coefficient. Is the decrease in times significant? f) Find the estimated gold medal time for 1932. Find the estimated time for 1984 . g) Why are the answers from part f different from the chart values? h) Does it appear that a line is the best way to fit the data? Why or why not? i) Use the least-squares line to estimate the gold

d) Calculate the least squares line. Put the equation in the form of: \( \hat{y}=a+b x \). e) Find the correlation coefficient. Is the decrease in times significant? f) Find the estimated gold medal time for 1932 . Find the estimated time for 1984 . g) Why are the answers from part f different from the chart values? h) Does it appear that a line is the best way to fit the data? Why or why not?

14. (a) Verificar que \( [\operatorname{senh}(x)]^{\prime}=\cosh (x) \) y que \( [\cosh (x)]^{\prime}=\operatorname{senh}(x) \).

Given the functions \( p(x) \) and \( q(x) \), use long division to find \( \frac{p(x)}{q(x)} \) \( p(x)=2 x^{3}-9 x^{2}+7 x+9 \), and \( q(x)=x-2 \)

Cuál de los siguientes es el conjunto \( X \backslash Y \) ?

Calcule los eigenvalores (o valores propios de la siguiente matriz) \[ \begin{array}{lll}A=\left(\begin{array}{ccc}1 & 1 & -2 \\ -1 & 2 & 1 \\ 0 & 1 & -1\end{array}\right) \\ \lambda \text { Respuesta. } & E(2)=\left\{\left(\begin{array}{l}1 \\ 3 \\ 1\end{array}\right)\right\} \\ \lambda=-1, E(-1)=\left\{\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right)\right\} \\ \lambda=1, & E(1)=\left\{\left(\begin{array}{l}3 \\ 2 \\ 1\end{array}\right)\right\}\end{array} \]