Write the symbol for the element: platinum

In the following spaces, indicate the movement of air associated with high- and low-pressure cells in each hemisphere. Write one of the two choices given in italics for each blank.

$$\begin{matrix} \text{ } & \text{Northern Hemisphere}\\ \text{ } & \text{High} & \text{Low}\\ \text{Surface air moves into or out of} & \text{\_\_\_\_\_} & \text{\_\_\_\_}\\ \text{Surface air motion is clockwise or counterclockwise} & \text{\_\_\_\_\_} & \text{\_\_\_\_}\\ \text{ } & \text{Southern hemisphere}\\ \text{ } & \text{High} & \text{Low}\\ \text{Surface air moves into or out of} & \text{\_\_\_\_\_} & \text{\_\_\_\_\_}\\ \text{Surface air motion is clockwise or counterclockwise} & \text{\_\_\_\_\_} & \text{\_\_\_\_\_}\\ \end{matrix}$$

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?

Prove each of the given statements by mathematical induction.

$(2 n) !<(n !)^2 4^{n-1}$ for every integer $n \geq 5$.

Find any vertical and horizontal asymptotes. $f(x)=\frac{-3}{2 x^{2}}$

The graph of y = sin (x- sin x) appears to have horizontal tangents at the x-axis. Does it?

Determine all vertical, horizontal and slant asymptotes. $f(x)=2 e^{1 / x}$

Sketch the level curve z=k for the specified values of k. z=y csc x; k=-2, -1, 0, 1, 2

A $0.04-\mathrm{m}^{3}$ tank initially contains air at ambient conditions of 100 kPa and $22^{\circ} \mathrm{C}.$ Now, a 15-L tank containing liquid water at $85^{\circ} \mathrm{C}$ is placed into the tank without causing any air to escape. After some heat transfer from the water to the air and the surroundings, both the air and water are measured to be at $44^{\circ} \mathrm{C}.$ Determine (a) the amount of heat lost to the surroundings and (b) the exergy destruction during this process.

Determine convergence or divergence of the series. $\sum_{k=3}^{\infty} \frac{k+1}{k^{2}+2}$

Compute the partial sums

$$S_2, S_4,$$

and

$$S_6.$$

$$\sum _ { k = 1 } ^ { \infty } ( - 1 ) ^ { k } k ^ { - 1 }$$

You want to heat the air in your house with natural gas $\left(\mathrm{CH}_4\right)$. Assume your house has $275 \mathrm{~m}^2$ (about $2800 \mathrm{ft}^2$ ) of floor area and that the ceilings are $2.50 \mathrm{~m}$ from the floors. The air in the house has a molar heat capacity of $29.1 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}$. (The number of moles of air in the house can be found by assuming that the average molar mass of air is $28.9 \mathrm{~g} / \mathrm{mol}$ and that the density of air at these temperatures is $1.22 \mathrm{~g} / \mathrm{L}$.) What mass of methane do you have to burn to heat the air from $15.0^{\circ} \mathrm{C}$ to $22.0^{\circ} \mathrm{C}$?

Repeat previous problem for a circular horizontal duct of diameter $4 \mathrm{~in}$.

Find all horizontal and vertical asymptotes. $f(x)=\frac{x^{3}}{x^{2}+6}$