Math IP 5 Essay Example | Topics and Well Written Essays - 750 words

Math IP 5 - Essay Example Answer: 3 Show work in this space. 27 9 =3 9 3 = 3 3 1 = 3 b) Using the formula for the nth term of a geometric sequence, what is the 10th term Answer: 19683 Show work in this space. a10 = a1 rn-1 a10 = (1) (3) 10-1 = (1) (19683) = 19683 c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms Answer: 29524 Show work in this space. Sn = a1 (1- rn) / 1-r = 1 (1-310) / 1-3 = 1 (1-59049) / -2 = -59048 / -2 = 29524 3) Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27 to find the following: a) What is r, the ratio between 2 consecutive terms Answer: 1/3 Show work in this space. 1/27 1/9 = 1/3 1/9 1/3 = 1/3 1/3 1 = 1/3 b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms Carry all calculations to 6 decimals on all assignments. Answer: 1.499976 Show work in this space. Sn = a1 (1- rn) / 1-r = 1 (1-(1/3)10) / 1-1/3 = 1 (1- 1.693508-5) / 2/3 = 1. 49976 c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms Carry all calculations to 6 decimals on all assignments. Answer: 1.499998 Show work in this space. Sn = a1 (1- rn) / 1-r = 1 (1-1/312) 1-1/3 = 1 (1-1.881676-6) 1-2/3 = 1.499998 d) What observation can make about the successive partial sums of this series In particular, what number does it appear that the sum will always be smaller than Answer: When plotted in a graph, it is expected that the partial sum of the series is a graph which grows flatter over time. This is because the partial sums grow slower over each value. The sum will always be smaller than 3....He rushed over and pulled a young lady out of the flaming truck. Farmer Crane came out and gratefully thanked the traveling salesman for saving his daughter's life. Mr. Crane insisted on giving the man an award for his heroism. So, the salesman said, "If you insist, I do not want much. Get your checkerboard and place one grain of wheat on the first square. Then place two grains of wheat on the next square. Then place four grains on the third square. Continue this until all 64 squares are covered with grains of wheat." As he had just harvested his wheat, Mr. Crane did not consider this much of an award, but he soon realized he made a miscalculation on the amount of wheat involved. c) Calculate the amount of wheat necessary to fill the whole checkerboard (64 squares). How much wheat would the farmer need to give the salesman Please provide the answer in either scientific notation, or calculate and show all 20 digits.

Using Humor to Survive Tragedy Essay Example | Topics and Well Written Essays - 500 words

Using Humor to Survive Tragedy - Essay Example Not a single character in the play profits from propriety. The not so serious characters are the ones who  benefit  in the end; and it is because of their  frivolous  behavior all through the play. This indicates that there is little, if any,  benefit  to being modest. In bill Cosby’s words, when one finds laughter, they can survive some of the worst moments in life.  By using humor, one can  stand  up to the challenges that life brings, no matter tragic they may be.  Situations in life are always changing; once one finds an  intriguing  way to survive a  dark  session, they will make it to the happy parts. In The Importance of Being Earnest, Oscar puts the conventions in the Victorian times aside and presents us the absurdity of such an  ardent  attachment  to seriousness. The  play  presents two young men, Algernon and Jack. Algernon is the symbol of un-earnestness, and Jack is his  ward  in jocularity and deceit. Marriage is of utmost significance in The Importance of Being Earnest. This is because it is what drives the  plot  and is the  primary  subject  for  philosophical  debate and speculation. We  are introduced  to the nature of marriage for the first time when Algernon is talking to his butler, Lane. The subject of marriage stays on for the most part of the  play  as it develops. Jack and Algernon talk about the important things in marriage, and what matters in it. They  talk  of it as either a matter of â€Å"pleasure† or â€Å"business†. During Victorian times, there were conventions on marriage; with  regard  to its  purpose  and  nature. These include such things as the social position of a person, the  income  the person had as well as the person’s  character. Algernon and jack are remarkably in the know of these assumptions, as well. Society expects them to follow these conventions, but they do not. They ridicule th ese customs, and, in situations where they cannot, they assume the