Ejercicio: Aceleraciones media e instantánea Supongamos que la velocidad \( v_{z} \) de una bicideta en función del tiempo \( t \) está dada por la ccusción: \[ v_{z}=40 \mathrm{~m} / \mathrm{s}+\left(0.80 \mathrm{~m} / \mathrm{s}^{3}\right) t^{2} \] a) Calcula el cambio de velocidad de la bicicleta en el intervalo entre \( t_{1}=1.5 \mathrm{~s} \) y \( t_{2}=4.5 \mathrm{~s} \). b) Calcula la aceleración media en este intervalo. c) Obtén la aceleración instantánea en \( t_{t}=1.5 \mathrm{~s} \) tomando \( \Delta t \) primero como 0.1 s , luego como 0.01 s , y finalmente como 0.001 s . d) Deduce una expresión para la aceleración instantánea en cualquier instante \( t \) y úsala para obtener la aceleración en \( t=1.5 \mathrm{~s} \) y \( t=4.5 \mathrm{~s} \).

Solve by Substitution \( \left\{\begin{array}{c}-6 x-3 y=-45 \\ -4 x+y=-27\end{array}\right. \)

How to Measure Technological Progress One of the most common methods used to measure technological progress is through the Solow Residual. The Solow Residual method works under the assumption that all changes in output that can't be explained by changes in the capital stock or changes in the number of workers must be due to technological progress. The method uses a simple linear regression to estimate growth. - Regress output on capital and labor using simple linear regression. - The regression residuals are TFP growth. (Total Factor Productivity - the ratio of aggregate output (e.g., GDP) to aggregate inputs) of Distanco Eduration Iniversitv of Calicut

A local college student will be randomly selected to attend a leadership conference in Washington, D.C. There are 2020 local college students, of which \( 40 \% \) are male. 480 of the college students are graduate students, and half of the graduate students are female. Which of the following best represents the probability that the selected college student will be a male student or a graduate student?

\begin{tabular}{l} 10) Eló los valores de \( m \in \Re \) para que \( S=\{(0 ; 1 ; 1),(-m ; 3 ;-1),(1 ; 0 ; m)\} \) constituya una base \( \Re^{3} \) son: \\ \( \begin{array}{ll}\text { a) } \nexists m \in \Re & \text { b) } m \neq-2 \wedge m \neq 2 \\ \square \text { c) } \forall m \in \Re & \square \text { d) } m=-2 \wedge m=2\end{array} \) \\ \hline\end{tabular}

8 Choose problem 4, 5, or 6. Explain how you could check your answer.