A $0.75\text{~ kg}$ book travels vertically $16$ meters up and then $16$ meters down before returning to its starting point. a) How much of the book's upward movement is caused by gravity? b) How much of the book's downward motion is caused by gravity? c) How much work did gravity complete on the book over the course of the round trip competition? d) On the basis of \syour answer to section (c), would you argue that the gravitational force \sis conservative or non conservative? Why not?

A steady $2.50\,\text{ m/s}$ upward movement is being made by an elevator. A bolt that was tightened in the elevator that was $3.00$ metres above the elevator floor came loose and fell. How long does it take the bolt to reach the elevator floor in question a)? What was the bolt's speed when it struck the elevator floor? b) in the opinion of a bystander in the e leva tor? c) based on an observer positioned on one of the building's floor landings? d) How far did the bolt go between the elevator's ceiling and floor, according to the observer in paragraph (e)?

Pair each rule with the correct translation. A. $(x, y) \rightarrow(x-6, y+2)$

B. $(x, y) \rightarrow(x+3, y)$

C. $(x, y) \rightarrow(x-1, y-5)$

I. $P(4,-1) \rightarrow P^{\prime}(3,-6)$

II. $Q(3,0) \rightarrow Q^{\prime}(-3,2)$

III. $R(-2,4) \rightarrow R^{\prime}(1,4)$

Using the words left or right and up or down state the movement between each point and its image. Be sure to give the number of units each coordinate is translated. Point $P(4,-1)$ to $P^{\prime}(3,-6)$ Point $Q(3,0)$ to $Q^{\prime}(-3,2)$ Point $R(-2,4)$ to $R^{\prime}(1,4)$

The shaft of a stepper motor is directly connected to a leadscrew that drives a worktable in an $x-y$ positioning system. The motor has a step angle $=5^{\circ}$. The pitch of the leadscrew is $6 \mathrm{~mm}$, which means that the worktable moves in the direction of the leadscrew axis by a distance of $6 \mathrm{~mm}$ for each complete revolution of the screw. It is desired to move the worktable a distance of $275 \mathrm{~mm}$ at a top speed of $20 \mathrm{~mm} / \mathrm{sec}$. Determine (a) the number of pulses and (b) the pulse frequency required to achieve this movement. (c) How much time is required to move the table the desired distance at the desired speed, assuming there are no delays due to inertia?

As mentioned earlier, OHaganBooks.com has two main competitors, JungleBooks.com and FarmerBooks.com, and no other competitors of any significance. The following table shows the movement of customers during July. (Thus, for instance, the first row tells us that 80% of OHaganBooks.com’s customers remained loyal, 10% of them went to JungleBooks.com and the remaining 10% to FarmerBooks.com.) $$ \begin{matrix} & \text{} & \text{OHaganBooks} & \text{To JungleBooks} & \text{FarmerBooks}\\ \text{From} & \text{OHaganBooks} & \text{80\\%} & \text{10\\%} & \text{10\\%}\\ & \text{JungleBooks} & \text{40\\%} & \text{60\\%} & \text{0\\%}\\ & \text{FarmerBooks} & \text{20\\%} & \text{0\\%} & \text{80\\%}\\ \end{matrix} $$ At the beginning of July, OHaganBooks.com had an estimated market share of one-fifth of all customers, while its two competitors had two-fifths each. Use this information to answer the exercise. Estimate the market shares each company had at the end of July.

A force of $6$ N makes an angle of $\pi/4$ radian with the $y$ axis, pointing to the right. The force acts against the movement of an object along the straight line connecting $(1, 2)$ to $(5, 4)$.
(a) Find a formula for the force vector $\mathbf{F}$. (b) Find the angle $\theta$ between the displacement direction $\mathbf{D} = (5 − 1)\mathbf{i} + (4 − 2)\mathbf{j}$ and the force direction $\mathbf{F}$.
(c) The work done is $\mathbf{F} \cdot\mathbf{D}$, or, equivalently, $||\mathbf{F}||||\mathbf{D}|| \cos \theta$. Compute the work from both formulas and compare.

The Doppler effect (named after Christian Doppler) is the change in the pitch (frequency) of the sound from a source as heard by an observer when one or both are in motion. If we assume both the source and the observer are moving in the same direction, the relationship is $f^{\prime}=f_{a}\left(\frac{v-v_{o}}{v-v_{s}}\right)$ where f' = perceived pitch by the observer, $f_{a}=$ actual pitch of the source, v = speed of sound in air (assume 772.4 mph), $v_{o}=$ speed of the observer, $v_{s}=$ speed of the source. Suppose that you are traveling down the road at 45 mph and you hear an ambulance (with siren) coming toward you from the rear. The actual pitch of the siren is 600 hertz (Hz). If f' = 620 Hz, find the speed of the ambulance.

A psychologist compares the mean amount of time of rapid-eye movement (REM) sleep for subjects under three conditions. She randomly assigns 12 subjects to the three groups, four per group. The sample means for the three groups were 18, 15, and 12. The table shows the ANOVA table from SPSS.

REM sleep

Source	DF	SS	MS	F	P
Group	2	72.00	36.00	0.79	0.481
Error	9	408.00	45.33
Total	11	480.00

For the Tukey 95% multiple comparison confidence intervals comparing each pair of means, the margin of error for each interval is 13.3. Is it true or false that since all the confidence intervals contain 0, it is plausible that all three population means equal 0.

In earlier Section, the twos complement operation is defined as follows. To find the twos complement of X, take the Boolean complement of each bit of X, and then add 1.

a. Show that the following is an equivalent definition. For an n-bit integer X, the twos complement of X is formed by treating X as an unsigned integer and calculating

(2$_n$ - X).

b. Demonstrate that Figure 10.5 can be used to support graphically the claim in part (a), by showing how a clockwise movement is used to achieve subtraction.

What was an effect of the movement of foods like corn and potatoes from the western hemisphere to the eastern hemisphere?

a) foods from the Americas contributed to population growth around the world

b) foods from the Americas contributed to a rise in food prices around the world

c) foods from Europe did not grow well in the old world and famine resulted

d) foods from the Americas became widely grown in Africa

Using a chart like the one below, identify a possible symbolic meaning for each character or place. Include details from the story to support your interpretation. Based on your answers, what lesson about temptation does Bunyan's allegory convey?

$$\begin{array}{|l|l|l|} \hline \text{ } & \text{Possible Meaning} & \text{Supporting Details}\\ \hline \text{Christian} & \text{all people} & \text{ }\\ \hline \text{Faithful} & \text{ } & \text{ }\\ \hline \text{Vanity Fair} & \text{ } & \text{ }\\ \hline \text{Jury Members} & \text{ } & \text{ }\\ \hline \text{Celestial City} & \text{ } & \text{ }\\ \hline \end{array}$$

Let

$$A=\left[\begin{array}{rr}-1 & 0 \\ 0 & 1\end{array}\right]$$

and

$$B=\left[\begin{array}{rr}1 & 0 \\ 0 & -1\end{array}\right]$$

. Matrix

$$Q=\left[\begin{array}{rrrr}-3 & 3 & 3 & -2 \\ 3 & 2 & -2 & -1\end{array}\right]$$

Represents the vertices of quadrilateral $J K L M$ at left.

Make and verify a conjecture about the effect of matrix $A$ on a geometric figure in the plane. (Hint: Describe the movement of the vertices from $J K L M$ to $J^{\prime} K^{\prime} L^{\prime} M^{\prime}$.)

To help predict eruptions from the volcano Mauna Loa on the island of Hawaii, scientists keep track of the volcano's movement by using a "super triangle" with vertices on the three volcanoes .

(For example, in one year, Mauna Loa moved $6$ in., a result of increasing internal pres- Hualaai sure.)

$A B=22.47928 \mathrm{mi}, A C=28.14276 \mathrm{mi}$, $A=58.56989^{\circ} ; \quad$ find $B C$

Consider a simple metapopulation in which subpopulation A grows at a per capita rate of $r_A = 1$ and subpopulation B declines at a per capita rate of $r_B = -1.$ Suppose the per capita rate of movement between subpopulation patches is m in both directions. This gives

$$\begin{aligned} &\frac{d x_{\mathrm{A}}}{d t}=(1-m) x_{\mathrm{A}}+m x_{\mathrm{B}}\\ &\frac{d x_{\mathrm{B}}}{d t}=-(1+m) x_{\mathrm{B}}+m x_{\mathrm{A}} \end{aligned}$$

where $x_A$ and $x_B$ are the numbers of individuals in patches A and B, respectively. Classify the equilibrium at the origin.