Radio receivers can comfortably pick up a broadcasting station's signal when the electric field strength of the signal is about $10.0 \mathrm{mV} / \mathrm{m}$. If a radio station broadcasts in all directions with an average power of $50.0 \mathrm{~kW}$, what would be the maximum distance at which you could easily pick up its transmissions? (Atmospheric conditions can have major effects on this distance.)

Would the maximum-shear-stress theory of failure predict failure (yielding) if the components of plane stress at a point in a member with yield stress $\sigma_Y$ were to reach the values shown in Fig. Would failure be predicted by the maximum-distortion-energy theory?

Why are the sharp transitions at the Fermi energy "smoothed out" by increasing the temperature?

What are the vertices of the region that is the solution of $y \leq-x+1, y \leq 3 x+5$, and $y \geq \frac{1}{3}(x-1)$ ? Give a point in the region that is not on the boundary.

Use the limit process to find the area of the region between the graph of the function and the x-axis over the indicated interval. Sketch the region.
$y=\dfrac{1}{4} x^3, \quad[2,4]$

Write an abbreviated orbital diagram and determine the number of unpaired electrons in each species in Question 32 .

A square matrix $A$ is said to be antisymmetric if $A=-A^t$.

(a) Give an example of an antisymmetric matrix. (b) Prove that the diagonal elements of an antisymmetric matrix are zero. (c) Prove that the sum of two antisymmetric matrices of the same size is an antisymmetric matrix. (d) Prove that the scalar multiple of an antisymmetric matrix is antisymmetric.

Pipe A, which is 1.20 m long and open at both ends, oscillates at its third lowest harmonic frequency. It is filled with air for which the speed of sound is 343 m/s. Pipe B, which is closed at one end, oscillates at its second lowest harmonic frequency. This frequency of B happens to match the frequency of A. An x-axis extends along the interior of B, with x = 0 at the closed end. What is the second smallest value of x locating those nodes?

You work at a restaurant as a host and a server. You earn $9.45 for each hour you work as a host and$3.78 for each hour you work as a server. a. Write an equation in standard form that models your earnings. b. Graph the equation.

$$\begin{matrix} \text{Basic Information} & \text{ }\\ \text{Number of hours worked as host:} & \text{x}\\ \text{Number of hours worked as server:} & \text{y}\\ \text{Earnings for this pay period:} & \text{\$113.40}\\ \end{matrix}$$

Describe what king of study you would conduct to answer each statistical question. Is the lifespan of giraffes affected by the number of offspring they produce?

Match the suffix on the left to its meaning on the right.

Is there an association between the percent of adult birds in a colony that return from the previous year and the number of new adults that join the colony? Research on 13 colonies of sparrowhawks produced the following data.

$$\begin{array}{|l|c|c|c|c|c|c|c|} \hline \text { Percent return } & 74 & 66 & 81 & 52 & 73 & 62 & 52 \\ \hline \text { New adults } & 5 & 6 & 8 & 11 & 12 & 15 & 16 \\ \hline \text { Percent return } & 45 & 62 & 46 & 60 & 46 & 38 & \\ \hline \text { New adults } & 17 & 18 & 18 & 19 & 20 & 20 & \\ \hline \end{array}$$

Sketch a scatterplot of these data, using percent return as the explanatory variable.

Explain why the rotational inertia of a hollow ball is greater than that of a uniform solid ball with the same mass and radius.

Solve. -4a - 2a + 11 = 6a - 13