What in The Ride Together: A Brother and Sister's Memoir of Autism in the Family engaged you intellectually and emotionally, thereby contributing to your understanding of how a person experiences impairment and disability in contrast with how society frequently views a person who has a disability? Distinguish between impairment and disability as appropriate.

There are so many images and ideas in the book that you might find affecting, emotionally and intellectually. For example, Paul Karasik does a very touching job of portraying the way in which his brother, David, sees the world, particularly when David, shown as a child in the graphic parts of the book, is being menaced by nonsense words that appear in front of his face and by all the noise coming at him from the television. These images help the reader understand a bit of what it's like to have autism and to be unable to make sense of the world around one. Judy Karasik's description of David's response to his father's death is also affecting. After he comes home from the institution where he's living, David responds to the situation in an agitated way and keeps asking what he's going to be doing during all his upcoming vacations over the next several months. He becomes fixated on who's going to cut his hair, and he keeps mentioning people who long ago worked at the local barber shop (and who might not work there anymore). David keeps responding, "I forbid it!" (page 167), when Judy and their mother mention that there might be new people at the barber shop.
These portraits of David help the reader understand how David sees the world. Rather than focusing on his disability, the authors of the book (David's brother and sister) explain how David sees the world differently. For example, after his father dies, David yearns for order, and his means of getting order is to figure out who will cut his hair. While much of society views people with disabilities as frightening, foreign, or stupid, the authors of this book provide David with a sense of dignity, individuality, and humor that show he is human and relatable.
Impairment refers to a loss of function or an abnormality, while disability refers to a person's restriction or lack of capability to perform an activity. In David's case, he has an impairment in understanding the social, sensory, and psychological world around him, and his disability is that he can't work a normal job or lead an independent life. However, the authors of the book do not define David by his disability.  

Single Variable Calculus, Chapter 3, 3.8, Section 3.8, Problem 35

At what rate is the length of the third side increasing when the angle between the sides of fixed length is $60^\circ$

$
\begin{equation}
\begin{aligned}
\text{Given: } L_1 &= 12 m\\
L_2 &= 15m\\
\\
\frac{d \theta}{dt} &= 2\frac{^\circ}{\text{min}} \left( \frac{\pi}{180} \right) = \frac{2\pi}{180} /\text{min}
\end{aligned}
\end{equation}
$

Required: $\displaystyle \frac{dx}{dt}$ when $\theta = 60^{\circ}$




We will use cosine law for triangles to solve $x$ at $\theta = 60^\circ$

$
\begin{equation}
\begin{aligned}
x^2 &= L_1^2 + L_2^2 - 2(L_1)(L_2) \cos \theta && \Longleftarrow \text{ Equation 1}\\
\\
x &= \sqrt{12^2 + 15^2 - 2(12)(15) \cos 60^{\circ}}\\
\\
x &= 3\sqrt{21}
\end{aligned}
\end{equation}
$

We will derive the Equation 1 to solve for $\displaystyle \frac{dx}{dt}$, given that $L_1$ and $L_2$ are constants

$
\begin{equation}
\begin{aligned}
\cancel{2}\frac{dx}{dt} &= \cancel{2}(L_1)(L_2) \sin \theta \left( \frac{d \theta}{dt} \right)\\
\\
\frac{dx}{dt} &= \frac{(L_1)(L_2)\sin \theta \left( \frac{d \theta}{dt}\right)}{x}\\
\\
\frac{dx}{dt} &= \frac{(12)(15)\sin 60\left( \frac{2\pi}{180}\right)}{3\sqrt{21}}
\end{aligned}
\end{equation}\\
\quad\boxed{\displaystyle \frac{dx}{dt} = 0.396 \frac{m}{\text{min}}}
$

Does Odysseus believe that his destination is more important than the journey?

Yes, I think it's safe to say that Odysseus cares more about reaching his destination than he does about the journey to it. He isn't traveling for adventure or glory: he just wants to get home to the wife and son he left behind in Ithaca some twenty years prior. Odysseus originally left home to fight in the Trojan War, and he expected to be home a long time ago. Everyone else who'd fought in and survived the ten-years-long war has come home. However, Odysseus's return journey gets off to a bad start, and things never really improve. His men are attacked at Ismarus (after they've plundered and looted); several are eaten by the Cyclops, Polyphemus; they are again attacked by the Laestrygonians; they are delayed by a stop at the Land of the Lotus-Eaters as well as by a stop at Circe's island; Odysseus travels to the Underworld; several men die when they are eaten by Scylla; and all but Odysseus die after eating the cattle that belong to the sun god at Thrinacia. Finally, Odysseus is detained by Calypso for several years, and she keeps him captive on her island. All along, however, Odysseus dreams of reaching his home. He worries for his wife and son, and getting back to them is his number one priority.

College Algebra, Chapter 5, 5.1, Section 5.1, Problem 48

a.) Compose the rates of growth of the functions $f(x) = 3^x$ and $g(x) = x^4$ by drawing the graphs of both functions in the following viewing rectangle.
$(i) [-4,4] \text{ by } [0,20] \qquad (ii) [0,10] \text{ by } [0,5000] \qquad (iii) [0,20] \text{ by } [0,105]$
b.) Determine the solutions of the equation $3^x = x^4$

a.)
$(i) [-4,4]$ by $[0,20]$



$(ii) [0,10]$ by $[0,5000]$



$(iii) [0,20]$ by $[0,105]$


It shows from the graph that the growth rate of the function $f(x) = 3^x$ is greater than the growth rate of the function
$g(x) = x^4$ as the values of $x$ becomes larger.

b.) Based from the graphs, both functions are equal when $x$ is approximately $1.55$ and $7.30$

How did the doctor feel

"In Another Country" is a short story by Ernest Hemingway about wounded soldiers undergoing treatment at an Italian hospital during World War I. It is somewhat autobiographical because Hemingway was treated at an Italian hospital after a wound he received as an ambulance driver for the Italian Army. The doctor in the story is enthusiastic about the hospital's new therapeutic machines and feels they will work well to help his patients recover strength and flexibility. He promises the narrator, "You will be able to play football again better than ever."
The doctor is symbolic of the rapid advancement of technology during the twentieth century and the optimistic feeling that new gadgets would lead the world to a better place. Unfortunately, some of the new technology proved instrumental in making World War I the bloodiest war in the history of the world. The Italian major is a symbol of the resistance to this new world and its "machines." He scoffs at the doctor and frankly admits that he has no confidence the new procedures will heal his injured hand.

How might the pigs' appearance at the end of the novel be symbolic?

At the end of Animal Farm, the pigs start to walk on their hind legs. This is significant because the animals have gone from saying "Four legs good, two legs bad" to the chant "Four legs good, two legs BETTER." Napoleon begins carrying a whip, and soon all the supervisor pigs are carrying whips. Napoleon also is seen with a pipe in his mouth. The pigs literally wear the clothes straight from Mr. Jones's closet:

Napoleon himself appearing in a black coat, ratcatcher breeches, and leather leggings, while his favourite sow appeared in the watered silk dress which Mrs. Jones had been used to wearing on Sundays.

When Mr. Pilkington joins the pigs, he talks of how the pigs dealing with lower animals is similar to how humans must deal with lower classes. The other animals observe:

The creatures outside looked from pig to man, and from man to pig, and from pig to man again; but already it was impossible to say which was which.

The appearance of the pigs show how they have become the oppressors. They wear the humans' clothes, walk on two legs like humans, and use pipes and whips like humans. The whip further signifies oppression and the control the pigs have over others. The specific clothing is reflective of the upper class, as Mr. Pilkington suggests. The fact that the sow wear the best Sunday dress shows that the clothing is not worn for warmth or protection—it is worn to make a statement.
It is also important to remember that Napoleon the pig is reflective of Joseph Stalin and Napoleon Bonaparte.

In Chapter 10, Napoleon walks around Animal Farm carrying a whip and wearing a black coat, ratcatcher breeches, and leather leggings. Napoleon's appearance is symbolic of his tyrannical rule and represents his proximity to the animal's original oppressor, Mr. Jones. The fact that Napoleon is wearing Mr. Jones' old clothes symbolically represents the way in which Napoleon treats the animals the same way Mr. Jones once did. Napoleon's whip is also a symbol of oppression and violence. Similar to Joseph Stalin's political purges, Napoleon violently executes animals who present a challenge to his authority. Napoleon's black coat, ratcatcher breeches, and leather leggings are symbolic of his social status. In Victorian England, ratcatcher attire was worn by aristocrats who participated in fox hunts. Napoleon and the other pigs occupy the upper class and are part of the aristocracy on Animal Farm. Napoleon does not consider himself equal to the other animals and is essentially a megalomaniac who takes advantage of the socially lower ranked animals on the farm.

How would you describe Bryant's understanding of death as expressed in "Thanatopsis"?

William Cullen Bryant expressed his views about death most clearly in two of his poems: "Thanatopsis" and "To a Waterfowl."  Often associated with the English Romantic poets, Bryant, like them, turned to nature for an understanding of death.  In nature, Bryant saw a way of accepting the inevitability of death.  Let's start with "Thanatopsis," whose title literally means "a view of death." 
This poem begins with praising nature, which has the ability to comfort us with its beauty and vastness:

When thoughts
Of the last bitter hour come like a blight
Over thy spirit . . .
Go forth under the open sky

But in our contemplation of nature, we are also reminded that we will return to Earth and in our death "mix forever with the elements."  The consolation comes from the idea that the earth is a wonderful eternal resting place where we will lie down with all the great people of the past and be surrounded by the rivers, woods, and meadows.  It is the place to which all must eventually go, and because of this fact we will not be alone:

The speechless babe, and the gray-headed man--
Shall one by one be gathered to thy side
By those, who in their turn shall follow them.

We, then, should not be afraid of death but go to our graves as if we are lying down to begin "pleasant dreams."  In this poem, Bryant stresses the fact that becoming one with nature and with all past living things is our solace for death. He does not refer to the afterlife, except obliquely, when he connects dreams and death.  
In "To a Waterfowl," Byrant uses the flight of a bird to explain how we should feel about death.  This poem has a more religious tone that "Thanatopsis."  In the latter poem, Bryant mentions a "Power" that guides the waterfowl to its "summer home, and rest."  As he watches the bird's "certain flight" through "the cold, thin atmosphere" until it disappears in the "abyss of heaven," he applies this journey metaphorically to himself.  As he walks the long way alone, he knows that there is a power that guides him, that 

Will lead my steps aright.

The two poems express similar ideas about death.  Nature is a way of understanding and accepting our own mortality.  In the first, nature becomes our final peaceful resting place; in the second, nature becomes more of a metaphor that teaches us how we should view death. The second has more religious overtones than the first in its mention of a supernatural power that guides both the bird and the speaker to the heavens.
I have posted two links below that should provide more ideas about Bryant's understanding of death.