9. A B-52 bomber jet flies at a horizontal velocity of \( 286.2 \mathrm{~m} / \mathrm{s} \) and at an altitude of 7500 m above the ground. How far away horizontally should a payload be dropped to land on a target?

Jack paid back the money as soon as he could, because did not like being in \( \begin{array}{ll}\text { (1) credit } & \text { (2) trouble }\end{array} \)

If \( s(\vec{x})=x^{2}+y^{2}+(z-1)^{2} \) where \( \vec{x}=\left(\begin{array}{l}x \\ y \\ z\end{array}\right) \), then colculate \( \frac{\partial s}{\partial \vec{x}} \)

9. Suppose the joint pdf of \( (X, Y) \) is \[ f(x, y)=\left\{\begin{array}{cc}x^{2} y, & x^{2} \leqslant y \leqslant 1 \\ 0, & \text { otherwise }\end{array}\right. \] (1) Find the constant \( c \); (2) Find the marginal probability density functions of \( X \) and \( Y \).

Given the vector field \( \vec{u}\left(u_{x}, u_{y}, u_{z}\right)=\left(x^{2} y^{2}, y^{2} z, x z^{2}\right) \) calculate the Iaplacion of \( \vec{u}, \vec{\nabla}^{2} \vec{u} \) that is : \( \vec{\nabla}^{2} \vec{u}=\left(\vec{\nabla}^{2} u_{x}\right) \vec{z}+\left(\vec{\nabla}^{2} u_{y}\right) \vec{j}+\left(\vec{\nabla}^{2} u_{z}\right) \vec{k} \)

11 Resuelve cada triángulo si es posible. De no ser así, explica la razón. a. \( \triangle A B C \), rectángulo en \( B ; c=4 \mathrm{~cm}, A=32^{\circ} \) b. \( \triangle M N P \), rectángulo en \( N ; n=6 \mathrm{~cm}, p=10 \mathrm{~cm} \) c. \( \triangle X Y Z \), rectángulo en \( Y ; x=5 \mathrm{~cm}, y=5 \sqrt{2} \mathrm{~cm} \) d. \( \triangle H I J \), rectángulo en \( H ; h=8 \mathrm{~cm}, j=10 \mathrm{~cm} \) e. \( \triangle P Q R \), rectángulo en \( R ; P=58^{\circ}, q=6 \mathrm{~cm} \)