A particle is in the first excited ( $n=2)$ state of a onedimensional box that has length $L$. (The box has one end at the origin and the other end on the positive $x$ axis.) . Find \left\langle x^2\right\rangle$.

Write the symbol for the element: iron

Use trigonometric identities to find the below indicated value(s). $\newline$ If $\cos \theta=\frac{7}{25}$ and the terminal side of $\theta$ lies in QIV, find $\cot \theta$.

Determine whether the following statements are true and give an explanation or counterexample.

$| \mathbf { u } \times \mathbf { v } |$ is less than both $|u|$ and $|v|$.

Find all horizontal and vertical asymptotes. $f(x)=\frac{3 x+2}{x-4}$

A point on the terminal side of an angle $\theta$ is given. Find the exact value of each of the six trigonometric functions of $\theta$.

$$(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2})$$

Explain why fluid pressure on a surface is calculated using horizontal representative

A uniform solid cylinder of mass ($M$) is supported on a ramp that rises at an angle $\theta$ above the horizontal by a wire that is wrapped around its rim and pulls on it tangentially parallel to the ramp (a) Show that there must be friction on the surface for the cylinder to balance this way. (b) Show that the tension in the wire must be equal to the friction force, and find this tension.

Some people with a deficit of IgA exhibit recurrent paranasal sinus and respiratory tract infections. Explain these symptoms.

Determine whether the statement is true or false. $\\$ The horizontal asymptote of$y=2^x$is$y=0$.

If imports exceed exports, is it a trade deficit or a trade surplus? What about if exports exceed imports?

A box of snack-size cracker packs weighs $28 \frac{1}{2}$ ounces. Each snack pack weighs $4 \frac{3}{4}$ ounces. How many snack packs are in the box?

A wall has inner and outer surface temperatures of 16 and $6^{\circ} \mathrm{C}$, respectively. The interior and exterior air temperatures are 20 and $5^{\circ} \mathrm{C}$, respectively. The inner and outer convection heat transfer coefficients are 5 and $20 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$, respectively. Calculate the heat flux from the interior air to the wall, from the wall to the exterior air, and from the wall to the interior air. Is the wall under steady-state conditions?

A point on the terminal side of an angle $\theta$ is given. Find the exact value of each of the six trigonometric functions of $\theta$.

$$(\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2})$$