A small object is placed $20 \ \mathrm{cm}$ from the first of a train of three lenses with focal lengths, in order, of $10$, $15$, and $20\ \mathrm{cm}$.. The first two lenses are separated by $30 \ \mathrm{cm}$ and the last two by $20 \ \mathrm{cm}$ . Calculate the final image position relative to the last lens and its linear magnification relative to the original object when (a) all three lenses are positive, (b) the middle lens is negative, (c) the first and last lenses are negative. Provide ray diagrams for each case.

The 2-kg bar rotates in the horizontal plane about the smooth pin. The 6-kg collar $A$ slides on the smooth bar. At the instant shown, $r=1.2 \mathrm{~m}, \omega=0.4 \mathrm{rad} / \mathrm{s}$, and the collar is sliding outward at $0.5 \mathrm{~m} / \mathrm{s}$ relative to the bar. If you neglect the moment of inertia of the collar (that is, treat the collar as a particle), what is the bar's angular acceleration?

Strategy: Draw individual free-body diagrams of the bar and the collar, and write Newton's second law for the collar in polar coordinates.

Presented with recordings of a pair of people of the same sex speaking the same phrase, can a listener determine which speaker is taller simply from the sound of their voice? Twenty four young adults at Washington University listened to 100 pairs of speakers, and within each pair were asked to indicate which of the two speakers was the taller. Here are the number correct (out of 100) for each of the 24 participants:

$$\begin{array}{llllllllllll} 65 & 61 & 67 & 59 & 58 & 62 & 56 & 67 & 61 & 67 & 63 & 53 \\ 68 & 49 & 66 & 58 & 69 & 70 & 65 & 56 & 68 & 56 & 58 & 70 \end{array}$$

Researchers believe that the key to correct discrimination is contained in a particular type of sound produced in the lower airways or the lungs, known as subglottal resonances, whose frequency is lower for taller people. Despite the masking of these resonances by other voice sounds, researchers wondered whether the information they contained could still be heard by listeners and used to identify the taller person.

(a) Make two stemplots, with and without splitting the stems. Which plot do you prefer and why?

(b) Describe the shape, center, and variability of the distribution. Are there any outliers?

(c) If the experimental subjects are just guessing which speaker is taller, they should correctly identify the taller person about 50% of the time. Does this data support the researchers, conjecture that there is information in a person's voice to help identify the taller person? Why or why not?

Distance In Exercises $75-80$, find the distance between the point and line, or between the lines, using the formula for the distance between the point $\left(x_1, y_1\right)$ and the line $A x+B y+$ $C=0$

$$\text { Distance }=\frac{\left|A x_1+B y_1+C\right|}{\sqrt{A^2+B^2}}$$

Point: $(-2,1)$ Line: $x-y-2=0$

The circuit consists of three resistors and one battery with no internal resistance.
(a) Find the current in the $5.00-\Omega$ resistor.
(b) Find the power delivered to the $5.00-\Omega$ resistor.
(c) In each of the circuits an additional $15.0-\mathrm{V}$ battery has been inserted into the circuit. Which diagram or diagrams represent a circuit that requires the use of Kirchhoff's rules to find the currents? Explain why. In which of these three circuits is the smallest amount of power delivered to the $10.0-\Omega$ resistor? You need not calculate the power in each circuit if you explain your answer.

We frequently must solve equations of the form f(x) = 0. When f is a continuous function on [a, b] and f(a) and f(b) have opposite signs, the intermediate-value theorem guarantees that there exists at least one solution of the equation f(x) = 0 in [a, b]. (a) Explain in words why there exists exactly one solution in (a, b) if, in addition, f is differentiable in (a, b) and $f^{\prime}(x)<0$ is either strictly positive or strictly negative throughout (a, b). (b) Use the result in (a) to show that $x^{3}-4 x+1=0$ has exactly one solution in [−1, 1].

Write a program to solve the general case of following problem , in which the initial state and the expansion ratio are input variables. The power stroke in an internal combustion engine can be approximated with a polytropic expansion. Consider air in a cylinder volume of $0.2 \mathrm{~L}$ at 7 $\mathrm{MPa}, 1800 \mathrm{~K}$, shown in figure. It now expands in a reversible polytropic process with exponent $n$ $=1.5$, through a volume ratio of $8: 1$. Show this process on $P-v$ and $T-s$ diagrams, and calculate the work and heat transfer for the process.

In an elementary chemical reaction, single molecules of two reactants $A$ and $B$ form a molecule of the product $C$: $A + B \rightarrow C$. The law of mass action states that the rate of reaction is proportional to the product of the concentrations of $A$ and $B$:

$$\dfrac{d[C]}{dt} = k[A][B]$$

Thus, if the initial concentrations are $[A] = a \text{ moles/L}$ and $[B] = b \text{ moles/L}$ and we write $x = [C]$, then we have

$$\dfrac{dx}{dt} = k(a - x)(b - x)$$

Find $x(t)$ assuming that $a = b$. How does this expression for $x(t)$ simplify if it is known that $[C] = \frac{1}{2}a$ after 20 seconds?

Johnstown Foundry, Inc., with several major plants, is one of the largest makers of cast-iron water and sewer pipes in the U.S. In one of the nation's most dangerous industries, Johnstown is perhaps one of the most unsafe, with four times the injury rate of its six competitors combined. Its worker death rate is six times the industry average. In a recent 7-year period, Johnstown's plants were also found to be in violation of pollution and emission limits 450 times.

Workers who protest dangerous work conditions claim they are "bull's-eyed"-marked for termination. Supervisors have bullied injured workers and intimidated union leaders. Line workers who fail to make daily quotas get disciplinary actions. Managers have put up safety signs after a worker was injured to make it appear that the worker ignored posted policies. They doctor safety records and alter machines to cover up hazards. When the government investigated one worker's death recently, inspectors found the Johnstown policy "was not to correct anything until OSHA found it."

Johnstown plants have also been repeatedly fined for failing to stop production to repair broken pollution controls. Three plants have been designated "high-priority" violators by the EPA. Inside the plants, workers have repeatedly complained of blurred vision, severe headaches, and respiratory problems after being exposed, without training or protection, to chemicals used in the production process. Near one Pennsylvania plant, school crossing guards have had to wear gas masks; that location alone has averaged over a violation every month for 7 years. Johnstown's "standard procedure," according to a former plant manager, is to illegally dump industrial contaminants into local rivers and creeks. Workers wait for night or heavy rainstorms before flushing thousands of gallons from their sump pumps.

Given the following scenarios, what is your position, and what action should you take?

You are Johnstown's banker.

Using the story earlier, answer the questions below:

(a) Cite two memories Brave Orchid has while waiting at the airport.

(b) Are these memories typical features of a memoir? Why or why not?

Add commas where necessary. Cross out commas used incorrectly by using the delete symbol. Some sentences may be correct. This year Emily will be attending cheerleading camp from July 28 to August 2.

True or False: If a random variable has mean $\mu$, then one of its values must be $\mu$.

Why do you think businesses offer discounts if the invoice is paid early? Do you think it is always to the purchaser's advantage to pay early?

• Explain your reasoning.
• Show your understanding of mathematics in an organized manner.
• Use charts, graphs, and diagrams in your explanation.
• Show the solution in more than one way or relate it to other situations.
• Investigate beyond the requirements of the problem.

Why did the U.S. government decide to reopen the long-running trade dispute between Boeing and Airbus in 2004? Do you think the U.S. position is reasonable? What about the EU’s countercharges? Are they reasonable?