A jogger runs around a circular track of radius 45 ff . Let \( (x, y) \) be her coordinates where the origin is the center of the track. When the jogger's coordinates are ( 27 36), her \( x \)-coordinate is changing at a rate of \( 16 \mathrm{ft} / \mathrm{s} \). Find \( d y / d t \). \( d y / d t= \) Submit answer

4. Si el discriminante de la función es mayor que cero, significa que: A) La parábola intersecta una vez en el eje de las abscisas B) La parábola intersecta dos veces en el eje de las ordenadas C) La parábola no intersecta en el eje de las abscisas D) La parábola intersecta dos veces en el eje de las abscisas E) La parábola no intersecta porque no existe parábola

1) \( 5 x^{2}+13 x-6= \)

3. Determine o valor real de \( y \) para que as expressões \( \frac{3 y}{y-4} \) e \( 3+\frac{2}{y} \) sejam iguais, sabendo que \( y \neq 0 \) e \( y \neq 4 \)

4. Considere a função definida por: \[ g(x)=\left[\begin{array}{l}x^{2}+2 \text { se } x<0 \\ 3 x-1 \text { se } 0 \leq x \leq 2 \\ 4 x-3 \text { se } x>2\end{array}\right. \] \( \begin{array}{lll}\text { a) } g(1) & \text { b) } g(2) & \text { calcule: } \\ g(3)\end{array} \)

Write the system of equations corresponding to the augmented matrix. Then perform the row operations \( R_{2}=-3 r_{1}+r_{2} \) and \( R_{3}=9 r_{1}+r_{3} \) on the given augmented matrix. Perform the row operations \( R_{2}=-3 r_{1}+r_{2} \) and \( R_{3}=9 r_{1}+r_{3} \) on the original matrix given in the problem, and enter the resulting matrix below. \begin{tabular}{rrr|r}1 & -3 & 3 & -7 \\ 3 & -4 & 8 & -7 \\ -9 & -6 & 5 & 3\end{tabular} \( \square \) \( \square \)