What is the difference between distance and displacement?

Use Venn diagrams to determine whether the following statement are equal for all sets A and B. (A∩B)', A'∪B'

Find the vertical asymptotes (if any) of the graph of the function. $f(x)=\frac{4}{(x-2)^{3}}$

Evaluate teamwork skills, including an analysis of task organization, cooperation, communication, and responsibility.

The water in a river moves south at 5 km/hr. A motorboat travels due east at a speed of 40 km/hr relative to the water. Determine the speed of the boat relative to the shore.

The displacement d (in meters) of an object at time t (in seconds) is given. What is the maximum displacement from its resting position? $d=6+2 \cos (2 \pi t)$

Graphically position the links for the embossing mechanism in the configuration shown. Then reposition the links as the handle is rotated $10^{\circ}$ counterclockwise. Determine the resulting displacement of the stamp and the linear displacement of the handle end.

Read "Mowing" by Robert Frost. Then, answer each question that follows.

There was never a sound beside the wood but one, And that was my long scythe' whispering to the ground. What was it it whispered? I knew not well myself; Perhaps it was something about the heat of the sun, Something, perhaps, about the lack of sound-And that was why it whispered and did not speak. It was no dream of the gift of idle hours, Or easy gold at the hand of fay or elf: Anything more than the truth would have seemed too weak To the earnest love that laid the swale in rows, Not without feeble-pointed spikes of flowers (Pale orchises), and scared a bright green snake. The fact is the sweetest dream that labor knows. My long scythe whispered and left the hay to make.

Reread "Mowing" and write a paraphrase of the poem's first six lines. Then, briefly explain the process you used to develop your paraphrase.

For the following exercise,

State the domain and the vertical asymptote of the function.

$$f(x)=\log _b(x-5)$$

Read "Mowing" by Robert Frost. Then, answer each question that follows.

There was never a sound beside the wood but one, And that was my long scythe' whispering to the ground. What was it it whispered? I knew not well myself; Perhaps it was something about the heat of the sun, Something, perhaps, about the lack of sound-And that was why it whispered and did not speak. It was no dream of the gift of idle hours, Or easy gold at the hand of fay or elf: Anything more than the truth would have seemed too weak To the earnest love that laid the swale in rows, Not without feeble-pointed spikes of flowers (Pale orchises), and scared a bright green snake. The fact is the sweetest dream that labor knows. My long scythe whispered and left the hay to make.

Part B Which aspect of the poem indicates its form?

A. The lines of the poem do not follow a fixed pattern.

B. The poem features repeated lines.

C. The poem contains fourteen lines.

D. The poem has five lines that do not rhyme.

Is displacement the same as distance travelled? Why or why not?

According to the Law of Universal Gravitation, the attractive force F in newtons between any two bodies in the universe is directly proportional to the product of the masses

$$m_1 \ and \ m_2$$

in kilograms of the two bodies and inversely proportional to the square of the distance d in meters between the bodies. That is,

$$F = \frac { G m _ { 1 } m _ { 2 } } { d ^ { 2 } }$$

G is the universal gravitational constant. Its value is

$$6.67 \times 10 ^ { - 11 } \mathrm { Nm } ^ { 2 } / \mathrm { kg } ^ { 2 }$$

Find the gravitational force exerted on each other by two 1000-kilogram iron balls at a distance of 0.1 meter apart.

In each of the preceding examples, our steps in finding $\sqrt[n]{r e^{i \theta}}$ were: (a) Find the polar coordinates of the roots: Take the nth root of r and divide $\theta+2 k \pi$ by n. (b) Make a sketch: Draw a circle of radius $\sqrt[n]{r}$, plot the root with angle $\theta / n$, and then plot the rest of the n roots around the circle equally spaced $2 \pi / n$ apart. Note that we have now essentially solved the problem. From the sketch you can see the approximate rectangular coordinates of the roots and check your answers in (c). Since this sketch is quick and easy to do, it is worthwhile even if you use a computer to do part (c). (c) Find the $x+iy$ coordinates of the roots by one of the methods in the examples. If you are using a computer, you may want to make a computer plot of the roots which should be a perfected copy of your sketch in (b). Follow steps (a), (b), (c) above to find all the values of the indicated roots. $\sqrt[4]{-4}$

If A B C D is similar to K L M N and M N K L, what special type of quadrilateral is K L M N? Justify your reasoning.