Onboard Note

The table below represents the estimated percentage $P$ of the population of cell phone users in Europe. $ \begin{array}{|c|c|c|c|c|c|} \hline \text{Year} & 1998 & 1999 & 2000 & 2001 & 2002 & 2003\\ \hline\\ P & 28 & 39 & 55 & 68 & 77 & 83\\ \hline \end{array} $ a.) Determine the average rate of cell phone growth on the following time frames $ \begin{equation} \begin{aligned} & (i) 1999 \text{ to } 2000 && (ii) 2000 \text{ to } 2001\\ & (iii) 2000 \text{ to } 2002 \end{aligned} \end{equation} $ b.) Estimate the instantaneous rate of growth in 2000 by taking the average of two average rates of change. c.) Estimate the instantaneous rate of growth in 2000 by measuring the slope of a tangent. a.) $(i)$ from 1999 to 2000 $\displaystyle \text{average rate} = \frac{P(2000)-P(1999)}{2000-1999} = \frac{55-39}{2000-1999} = 16 \frac{\%}{\text{year}}$ $(i...

John mentions the eight days on two different occasions. The two times are in consecutive paragraphs, so once you know the general location in the story, it is fairly easy to find the "eight day" information. The first mention of the eight-day journey can be found in the paragraph following the part of the story that has John shooting and killing the panther. John tells readers the following piece of information. It is eight suns' journey to the east and a man passes by many Dead Places. "Eight suns' journey" is presumably counting the number of times the sun is out—sunrise to sunset. John hasn't completed the journey yet, and the eight days' count is confirmed in the following paragraph when John finally arrives at the banks of the great river. Toward the setting of the eighth sun, I came to the banks of the great river. Notice that the sun is setting, and that confirms that it takes eight full days for John to go from his home to the Place of the G...

The showdown between Hamlet and Gertrude in act 3, scene 4 is pretty fraught right from the start. Gertrude starts by confronting Hamlet over his disrespectful behavior towards Claudius. But Hamlet is not in the mood for taking lectures in disrespect from his mother. As far as he's concerned, it is she who has been disrespectful to her late husband, Hamlet's father, by marrying the usurper Claudius and sharing his bed. Hamlet is so infuriated by what he perceives as Gertrude's shameless audacity that he tells her to her face that he wishes she weren't his mother: You are the queen, your husband’s brother’s wife, And—would it were not so!—you are my mother. Gertrude is supposed to be controlling the conversation. Polonius has given her precise instructions that she should give Hamlet a serious dressing down over his recent behavior. Yet it is Hamlet who quickly dominates the brief, acrimonious slanging match that ensues. His language is so violent, his manner so intemper...

It seems that there is a constant struggle over cultural meanings, wherein there is an attempt to change and modernize them. There is resistance to the changing social mores and ideas by certain groups. Cultural meanings are definitely unstable, because throughout history they have changed drastically. For instance, historical masculine and feminine roles were drastically different than they are today. Men, who would work in the fields and hunt, also tended to cook food for the family, while the women would tend to animals and work on the tools that were used in agriculture. The historical period tends to dictate the social and cultural norms. In that regard, cultural meanings are definitely not stable, although many people attempt to impose stability by forcing antiquated meanings on societal customs and norms. "Cultural meanings" are stable or unstable depending upon the technological and social evolution of the individual society being examined. In other words, cultural me...

Antony is Caesar’s ally and supporter. After Caesar's assassination, Antony first pretended to shake hands with the senators, saying that all that he asked for was to give a speech at Caesar's funeral, and he promised not to say anything against the conspirators. However, at the funeral, he uses his oratory skills to stir up fury in the crowd without condemning Brutus and his accomplices directly. In this way, he successfully turns the public against the conspirators to the extent that Brutus and Cassius have no choice but to run away. Then he unites with Octavius, Caesar's son, to prepare for military action and eventually defeated the conspirators in a battle at Philippi. Brutus and Cassius both die at Philippi. Later Antony gradually eliminates the remaining forces of the Republic and resumes the unfinished cause of Caesar.

intsqrt(1+x^2)/xdx Let's evaluate using the trigonometric substitution, Let x=tan(theta) dx=sec^2(theta)d theta =intsqrt(1+tan^2(theta))/(tan(theta))*sec^2(theta) d theta Now use the identity: 1+tan^2(x)=sec^2(x) =intsqrt(sec^2(theta))/tan(theta)*sec^2(theta)d theta =intsec(theta)/tan(theta)*sec^2(theta)d theta =int(sec(theta)(1+tan^2(theta)))/tan(theta) d theta =int((sec(theta))/tan(theta)+(sec(theta)tan^2(theta))/tan(theta))d theta =intsec(theta)/tan(theta)d theta+intsec(theta)tan(theta)d theta =int(1/cos(theta))*(1/(sin(theta)/cos(theta)))d theta+intsec(theta)tan(theta)d theta =int1/sin(theta) d theta+intsec(theta)tan(theta)d theta =intcsc(theta)d theta+intsec(theta)tan(theta)d theta Now using the standard integrals, intcsc(x)dx=ln|csc(x)-cot(x) intsec(x)tan(x)dx=sec(x) =ln|csc(theta)-cot(theta)|+sec(theta) Now substitute back x=tan(theta) =>cot(theta)=1/tan(theta)=1/x 1+tan^2(theta)=sec^2(theta) =>1+x^2=sec^2(theta) =>sec(theta)=sqrt(1+x^2) 1+cot^2(theta)=csc^2(theta) ...

The love described in "Sonnet 75" is undoubtedly extant; while it may not be that love of a poet for his patron as is conveyed in this particular sonnet, the expression of love that is written can also apply in modern times to that between close friends or between lovers. In this particular sonnet, the poet addresses his sponsor, the Earl of Southhampton. While this love for the young man hints at erotic expression, it also conveys feelings shared in any loving relationship. Perhaps the lines that best express these emotions are the following: And for the peace of you I hold such strifeAs 'twixt a miser and his wealth is found;Now proud as an enjoyer, and anonDoubting the filching age will steal his treasure These lines connect to those who are in love during any era. While reveling in the warm and happy sensations of love and cherishing the loved one, there is at the same time a fear of losing this love, just as the miser delights in his gold but then worries that someon...