Over the course of the 100m race, lasting at least 10 seconds, Torty’s average speed on any 5-second interval was less than Harry’s 5-second average speed, and yet Torty won the race!

One year after their first race, Harry decided that he could gain an advantage by hosting a new race. This new footrace would not transpire on flat ground, but instead along a hilly region in the mountains. The hilly region is given in the provided GeoGebra applet.

Harry has become quite adjusted to racing along inclines and declines. Their path in the provided GeoGebra applet is defined by the curve

, for which two laps around the course takes   seconds.

In their rematch, Torty is less adjusted to running along hilly regions, and tires after an initial burst of speed along the hilly regions. Their path in the provided GeoGebra applet is defined by the curve

Both Torty’s and Harry’s curve are depicted in the following GeoGebra application, as is the hilly region over which the track was built. You may alter the “=” slider to view Torty and Harry’s positions, velocities, and accelerations at any time during the race. You may also use the “Show Torty’s Curve” and “Show Harry’s Curve” checkboxes to view either of the racer’s curve in isolation.

Task one:

Answer the following questions about the race depicted in the GeoGebra applet: 

1) How long is the race track? Are we forced to use either Torty’s curve or Harry’s curve to make the measurement? Why?

2) Who wins the race depicted in the GeoGebra application? Justify this

3) In the moments where Torty and Harry meet, who has the greater speed? Who has a greater acceleration?

4) What is the curvature difference between Torty and Harry’s curves in the moments that they meet? Explain this difference. (Note, you’ll need to use a limit to answer this question when Torty’s speed is 0).

Task two:

After the first race on this hilly track, Torty and Harry want a rematch. Define curves for Torty and Harry such that Torty’s average speed is less than Harry’s over any 5-second interval, but Torty wins the race. The race must last at least  seconds, and for simplicity, assume that both Torty and Harry continue to run along the same curves for a whole lap even after the race is concluded.

 

Keep in mind that they need to run the exact same course, so the race track needs to remain unchanged.

 

Task three:

After Harry’s second defeat, they want to look for ways to make the course even more difficult for Torty. After talking to a landscaper, Harry determined that the terrain around the track (considering the center of the track to be the point (0, 0, 0) can be defined by the function f(x, y) = xy2. The race track is determined by taking the points (x, y, f(x, y)), where (x, y) follow the unit circle.

Harry suspects that making the course more difficult within the first quadrant (of the unit circle) will further hinder Torty’s ability to run effectively.

Using only partial derivatives, directional derivatives, and tangent planes, answer the following questions:

• Estimate the current height change along the course between the points and
• How does the current course height change between and compare to the estimated height change if the course had instead moved the same distance directly North or directly West? (Note: Consider the x-axis to be East and the y-axis to be North)
• Because of the topography around the course, Harry can only alter the course after the point by moving Northeast, Northwest, Southeast, or Southwest, and only by the same horizontal distance as the original change from  and  Compare the estimated height changes in each direction to determine the new course that would prove most difficult journey.
  Assignment Details ENG 231 – 1003 FALL 2022
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  2. What is the role of women that demonstrates what is respected and expected of them vs. what is devalued culturally in the female characters in at least three of the readings? Refer to specific characters like Ishtar, Ninsun, Siduri, and/or Shamhat in The Epic of Gilgamesh; Penelope, Athena, Circe, and/or Calypso in The Odyssey, Antigone and Ismene in Antigone; and/or even the female characters who must uphold a social protocol and duties of the courtly life in The Pillow Book.
  3. How is the theme of duty conveyed through the characters in at least three of the readings when you consider the depiction of gods/God depicted in the ancient literature as divine vs. flawed and the type of devotion or defiance expressed to them by the characters?
  o (Note: Consider how Krishna’s portrayal in the Bhagavad-Gita is quite the opposite of the gods like Athena, Poseidon, Calypso, Circe, !no, Hermes, Zeus, and Heracles in The Odysseyor even the gods/goddesses, such as Anu, Aruru, Ea, Siduri, Tammuz, Enlil, Ereshkigal, Ishtar, Ninsun, and Shamash in The Epic of Gilgameshin how they interact with humans. Moreover, in The Bhagavad-Gita, Arjuna learns about duty. The path to God comes with the right action, loving devotion to God, and the way of knowledge. While Antigone may rebel against Creon’s

Directions: You must answer ONE question from the four listed below in essay form and demonstrate how much you have learned by making connections between the readings for the questions you to do.

• You only need to pick ONE question from the four listed below to write just ONE essay. Your essay should have an introduction paragraph with a thesis statement, three body paragraphs (In other words, you should have one separate body paragraph per reading that you cover), and a conclusion paragraph, so a total of FIVE PARAGRAPHS. (Tip: One sentence DOES NOT constitute a paragraph, so aim for 5 sentences or more to have a well-developed discussion per paragraph in your essay.) • Your response should be 500 words or more. Hence, you are encouraged to exceed/write more than 500 words, and please do include the word count after your essay.

• You should use the MLA format for parenthetical citations when you quote, paraphrase, and/or summarize passages because you are required to support yourself with actual examples/passages as evidence from the reading. It would be best if you also had a Works Cited page for the MLA format at the end as it is required to credit sources properly with a parenthesis and Works Cited to avoid plagiarism.

• You should proofread your work carefully for grammar and punctuation so you submit your best

Assignment Details ENG 231 – 1003 FALL 2022
The Epic of Gilgamesh in how they interact with humans. Moreover, in The Bhagavad-Gita, Arjuna learns about duty. The path to God comes with the right action, loving devotion to God, and the way of knowledge. While Antigone may rebel against Creon’s tyrannical laws as civil disobedience, she upholds her duty to the gods to bury her brother as her devotion is to family and the gods. )
4. Consider the theme of a quest/journey in three of the four readings and compare three of the characters for this theme:
o What must Gilgamesh overcome on his quest for immortality, and does he achieve it during his journey in The Epic of Gilgamesh; o What is Arjuna’s spiritual journey and what must be overcome to achieve his quest for enlightenment and the vision of Krishna’s totality in The Bhagavad-Gita; o What are the obstacles that Odysseus must face on his quest/journey to return home, and does he achieve his goal; and/or… o What are the challenges of courtly life, such as obligations, rituals, rules of taste, protocols, and practices, that Sei Shonagon must confront in her quest/journey for love and beauty (aesthetics)?

Assignment Details ENG 231 – 1003 FALL 2022
• You should proofread your work carefully for grammar and punctuation so you submit your best response for the final essay exam. (Note: You are encouraged to submit your work to Smarthinking or use www.Grammarly.com to help you polish your essay responses before posting them in this assignment dropbox.)

Answer ONLY ONE question from the four listed below for your midterm essay exam.
1. Discuss the theme of pride as the fatal flaw in the following three characters: Gilgamesh in The Epic of Gilgamesh, Odysseus in The Odyssey, and Creon in Antigone, bringinga bout their hubris and what they learn from it. Carefully consider their dialogue and actions as evidence to support yourself with passages from the reading.
2. What is the role of women that demonstrates what is respected and expected of them vs. what is devalued culturally in the female characters in at least three of the readings? Refer to specific characters like Ishtar, Ninsun, Siduri, and/or Shamhat in The Epic of Gilgamesh; Penelope, Athena, Circe, and/or Calypso in The Odyssey, Antigone and Ismene in Antigone; and/or even the female characters who must uphold a social protocol and duties of the courtly life in The Pillow
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