Un helicóptero sobrevuela una bahía a 304.6 m de altura mien- tras un submarino se encuentra a 451.5 m bajo el nivel del mar (- 451.5 m ). ¿Cuál es la distancia entre ambos artefactos cuando el helicóptero pasa por encima del submarino?

29. Let \[ A=\left[\begin{array}{rrrr}1 & 1 & 1 & 1 \\ 0 & 1 & 0 & 0 \\ 1 & -1 & 1 & 1\end{array}\right] \] We wish to determine all \( 4 \times 3 \) matrices \( X \) for which \( A X A=A \) Observe that \[ P A Q=\left[\begin{array}{rrrr}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0\end{array}\right] \] where \( P \) and \( Q \) are the invertible matrices \[ P=\left[\begin{array}{rrr}1 & 0 & 0 \\ 0 & 1 & 0 \\ -1 & 2 & 1\end{array}\right] \text { and } Q=\left[\begin{array}{rrrr}1 & -1 & -1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & -1 \\ 0 & 0 & 0 & 1\end{array}\right] \] (a) Explain how you can use this to convert the problem of finding all \( X \) so that \( A X A=A \) to finding all \( 4 \times 3 \) matrices \( Y \) so that \( B Y B=B \), where \( B=P A Q \). Make sure to indicate how \( X \) and \( Y \) are related. (b) Find all \( Y \) so that \( B Y B=B \). (c) Use your answer in (b) to find all \( X \) so that \( A X A=A \). (d) Give 2 explicit \( X \) with \( A X A=A \).

\( 54 \times 740 m \ell = \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \)

Question 8 Solve the following quadratic inequality: \( 2 x^{2}+1 x-1 \geq 0 \) Write your answer in interval notation. Enter DNE if there is no solution. Question Help: Video Submit Question

Given the rational function, \( f(x)=\frac{x^{2}-5 x+6}{x+3} \) sketch the graph on your paper then determine the oblique asymptote and range. A. \( O A: y=-3 \); range: \( (-\infty,-3) \cup(-3, \infty) \) B. \( O A: y=0 ; \) range: \( (-\infty, 0) \cup(0, \infty) \) C. \( O A: y=x-8 ; \) range \( :(-\infty,-21.954] \cup[-.046, \infty) \) D. \( O A: y=x-8 ; \) range: \( (-\infty,-8.477] \cup[2.477, \infty) \)

Solve the inequality. \( 2(4+2 x) \geq 5 x+5 \) \( x \leq-2 \) \( x \geq-2 \) \( x \leq 3 \) \( x \geq 3 \)