Hi can someone plss help me with this I’m really struggling right now and this is due tomorrow. Basically I have to write an essay on how Achilles demonstrates the key qualities (loyalty, strength, intelligence, bravery, and pride) of an epic hero in The Iliad. However right now I have to find 2 examples of each of the key qualities I mentioned and I couldn’t really find anything that makes sense because the information talked about another character from that book.


Strength (2 examples)
Bravery (2 examples)
Loyalty (2 examples)
Pride (2 examples)
Intelligence (2 examples)


Answers

Answer 1

Achilles, having been a famed and valiant soldier, was sought after and loved by all, except his adversary Agamemnon. He was a prominent warrior known for his great strength that actually caused the Acheans to win many battles. But what was it that caused Achilles to be such a hero? Consider the definition for the word, “hero.” A hero is “a person who is admired or idealized for courage, outstanding achievements, or noble qualities.” This gallant warrior is all three of these points in the definition, plus more. Achilles’ honorable attitude for his loved ones, bravery in times of adversity, and as the definition states, “outstanding achievements” make him a hero beyond recognition.

Living in a difficult age full of war and death,

Although Achilles was quite outraged at this, he gave a respectful response, stating that he would drop out of the war because Agamemnon had dishonored him. Later, the Trojans killed Patroclus, Achilles’ dearest and most trusted friend. Achilles was overcome with grief, but realized how stubborn and selfish he was being by dropping out of the war. He decided that he had to join the war once again to honor Patroclus. He told his mother, “Enough. Let bygones be bygones. Done is done. Despite my anguish I will beat it down, the fury mounting inside me, down by force. But now I’ll go and meet that murderer head-on, that Hector who destroyed the dearest life I know.” It is clear that he knew that in those ancient times, a real hero avenged the death of a dear friend, and would sacrifice his own life to save the dead body and give it a proper burial.

The fact that Achilles had bravery in times of adversity shows that he should be given glory as a hero. In spite of the fact that Patroclus had died, and it was immensely hard for him to accept the loss of his friend, Achilles decided that Patroclus would have wanted him to be courageous. Achilles rejoined the war, resolved to kill those that had killed his beloved friend. He was not afraid of dying or being badly wounded, but he wanted to make up for his impulsive absence in the war.  

Achilles had many great accomplishments in the war, proving he showed his venture for arete1. One must not forget how important glory


Related Questions

This random day based on the idiom, "No rhyme or reason," recognizes
words that have no rhyme and encourages activities performed without a
reason. Name another popular idiom and write about what you think it
means.

Answers

Lets begin with the definition of an idiom:

An idiom is a widely used saying or expression that contains a figurative meaning that is different from the phrase's literal meaning. For example, if you say you're feeling “under the weather,” you don't literally mean that you're standing underneath the rain.

To me "under the weather" means not feeling well, my assumption being that the rain is the symbolism for sadness.



1. Which of the following verbs is in its base form (used for simple present
tense?

A. tried
B. swim
C. hopping
D.am

Answers

Answer:

B. swim coz the first answer is in past simple

the third in present continuous

What is an example of direct characterization from the movie frozen

Answers

Answer:

from the movie well sister is scared of losing their family ig, so she ran away in the mountain isn't it??!!

Answer:

Anna demands Kristoff to take her to the mountain. Her demanding him take her shows she determined to find her sister.

Anna wakes up disheveled but calm. This makes you think she's easygoing and unconcerned about her appearance.

WORTH 75 PONITS!!!!CORRECT ANSWERS GET BRAINLIEST!! ANSWER ALL PLEASE IT IS URGENTLY NEEDED!!!!

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Answers

Answer:

vunerable provincal proffessionalibiity occupation

vascuous corpulent

Correct the punctuation and capitalization in the sentences below “When are you going to show me your art project”? “I’m really looking forward to seeing it”! Mom said.

Answers

Answer:

put a period after the question mark

give me brainliest pls pls pls pls pls man come on .....

What punctuation is used to show the division between a word's syllables? apostrophe comma hyphen parentheses quotation marks

Indirect and direct quotations require the same punctuation.

True
False

Answers

1- hyphen
2-true
I think

mice of men Review Chapter 3 pages 51-56 and record 5-10 facts, opinions, or rules related to women.

Answers

In "Of Mice and Men," Chapter 3 highlights the patriarchal society where women are considered distractions, objects of desire, deprived of dreams, opportunities, and perceived as weak.

In Chapter 3 of "Of Mice and Men," by John Steinbeck, the author introduces several female characters, including Curley's wife and Aunt Clara. The novel is set in a patriarchal society, where women are often viewed as inferior and their opinions or roles are disregarded. Here are some facts, opinions, or rules related to women in this chapter:1. Women are seen as a distraction and a nuisance to the men working on the ranch.

This is evident when Candy complains about Curley's wife, saying, "You keep away from her, 'cause she's a rattrap if I ever seen one" (p. 53). 2. Women are often treated as objects of sexual desire. Curley's wife is portrayed as a is often referred to as a "tart" or a "tramp" by the men on the ranch. 3. Women are not allowed to have dreams or ambitions of their own. This is demonstrated when Curley's wife tells Lennie, "I coulda been in the movies, an' I coulda been a star" (p. 54), but then reveals that she never pursued her dream because her mother wouldn't let her. 4. Women are not given the same opportunities as men.

This is illustrated when Slim says, "Maybe you better stay here with your wife" (p. 55), implying that a woman's place is in the home. 5. Women are often seen as weak or vulnerable. This is shown when George tells Slim about Lennie's incident with the girl in Weed, saying, "I jus' done it. I didn't mean no harm, George. Honest I didn't. I jus' wanted to pet them mice a little" (p. 56), which implies that Lennie didn't understand the severity of his actions because he has a childlike mentality and women are often seen as innocent or naive.

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a personal _________________ is a statement about ourselves in which we claim our desired qualities as if we already have them in abundance. this statement you would say daily.

Answers

Answer:

Affirmation

Explanation:

An affirmation is something people tell themselves daily to positively view themselves.

Read the following excerpt from benvolio's speech in act 1 of romeo and juliet. "here were the servants of your adversary and yours, close fighting ere i did approach. i drew to part them. in the instant came the fiery tybalt, with his sword prepared;" what can you conclude is the meaning of the word adversary?
question 47 options:

a)

a relative

b)

an enemy

c)

a stranger

d)

a friend

Answers

From the excerpt given above we can conclude the meaning of the word adversary is an enemy. Option B is the correct answer

Early in his career, William Shakespeare wrote the tragedy Romeo and Juliet about two young Italian star-crossed lovers whose demise ultimately brings their warring families together. Along with Hamlet, it was one of Shakespeare's most performed plays during his lifetime and is still played frequently today. The main protagonists are now thought of as typical youthful lovers.

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Before Gremlin became our class pet.
a. Missing a subject
b. Missing a verb
c. Dependent clause
d. -ing fragment

Answers

Answer:

C

Explanation:

The sentnece is incomplete.

Answer:

C. Dependent Clause

Explanation:

Because you don't know what was happening before Gremlin became our class pet.

Find the average rate of change of the function over the given intervals f(x)-2x3+2; a) [5,7], b)I-22] a) The average rate of change of the function f(x)-2x +2 over the interval [5,7] isb) The average rate of change of the function f(x)=2X + 2 over the interval [-22] is

Answers

The average rate of change of the function f(x) = -2x^3 + 2 over the intervals [5,7] and [-2,2] are -218 and 0, respectively.

The average rate of change of a function is defined as the slope of the line connecting two points on the function. It is calculated as the difference in the function values at the two points divided by the difference in the x-values of the two points.
For the function f(x) = -2x^3 + 2, the average rate of change over the interval [5,7] is:
f(7) - f(5) / (7-5) = (-2(7)^3 + 2 - (-2(5)^3 + 2)) / (7-5) = (-686 + 2 + 250 - 2) / 2 = (-436) / 2 = -218
The average rate of change over the interval [5,7] is -218.
For the function f(x) = -2x^3 + 2, the average rate of change over the interval [-2,2] is:
f(2) - f(-2) / (2-(-2)) = (-2(2)^3 + 2 - (-2(-2)^3 + 2)) / (2-(-2)) = (-16 + 2 + 16 - 2) / 4 = 0 / 4 = 0
The average rate of change over the interval [-2,2] is 0.
Therefore, the average rate of change of the function f(x) = -2x^3 + 2 over the intervals [5,7] and [-2,2] are -218 and 0, respectively.

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How did the early Spanish and Portuguese expeditions change the world?

HURRY GIVING 100!!!! POINTS

Answers

Answer:

Explanation:The Spanish colonization of the Americas began under the Crown of Castile and spearheaded  In the early 19th century, the Spanish American wars of independence  Spain and Portugal formalized a division of the world between them in the 1494 Treaty Five hundred Spaniards did not topple the Aztec Empire alone.

if you could travel to any time,past or future,what year would you go to what would you learn about

Answers

Answer:

Personally for me I would go to the moon landing on July 20th, 1969. There are so many accusations and conspiracies about if it was real or not. And I would like to find out for myself.

Explanation:

In addition to writing your draft, you must respond to at least one counterclaim. This
response may appear in one of the body paragraphs you already planned out in
Lesson 1, or it may appear in a new body paragraph. Your assignment should show
good judgment about where best to address counterclaims.
Your essay should include the following elements:
A claim, supporting reasons, and evidence from at least five sources
An introduction paragraph, body paragraphs, and a conclusion paragraph
• A counterclaim, followed by a response that supports your argument
• Transitions to show how the claim, reasons, evidence, and counterclaim are
related
You should have completed a draft of this assignment in the activity before this one.
If you haven't done so, go back and complete that activity now.
Tips for SUCCESS
Ask yourself these questions as you revise:
• Is my claim arguable and defensible? Do my supporting reasons back up my
claim? Does my evidence back up both my claim and my supporting reasons?
• Does my introduction paragraph get the reader's attention? Does it present my
claim clearly? Does it give the reader enough information about my topic to
understand my position?
Do my body paragraphs present both reasons and evidence? Does the evidence
come from credible sources? Do my body paragraphs include an appropriate
amount of content? Do I provide a topic sentence for each paragraph that clearly
explains what it's about?
• Do I address at least one counterclaim? Do I respond to it fairly and
professionally? Is my response located in an appropriate place in my essay?

Answers

The text units known as body paragraphs provide evidence to back up the thesis statement of an essay, report, or tale. The theme sentence (or key sentence), pertinent supporting sentences, and a concluding (or transitional) sentence are the three primary parts of a strong body paragraph.

What is a body paragraph example?

The last sentence of each body paragraph will highlight the significance of the examples used to support it or assess how they relate to one another.

How are body paragraphs used?

The reader's evidence that has been gathered to support the main argument is presented in the body paragraphs. Before starting to use evidence from many sources to support the issue in the body paragraphs, authors should gather information to do so.

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The Great Gatsby
Describe Nick Carraway's family background. Which category does he fit into? Old money or New money?

Answers

The History of Nick Carraway family is that Nick was said to have been  raised in an affluent family that was said to be a clan seen in the middle West.

His grandfather's brother was known to be one that started a wholesale hardware company that provided income for his family after sending a stand-in to fight for him in the Civil War.

The category is people with new money.

Nick Carraway has either new or old money.

For those with new money, West Egg is where Jay Gatsby and Nick Carraway reside. They are despised because they have only recently become wealthy.

In East Egg, wealthy residents like Daisy and Tom Buchanan reside. Since their riches has persisted down the centuries, they are seen as belonging to the upper class.

Hence, based on the above description, the answers given are correct.

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"Why, why now? Child of Zeus with the shield of thunder, why come now? To witness the outrage Agamemnon just committed? I tell you this, and so help me it's the truth-he'll soon pay for his arrogance!"

Answers

When Agamemnon commits some sort of offense, the speaker seems to be wondering why this person has decided to show up at this specific time. The speaker gives the impression of thunder that Agamemnon will soon pay for his conceit and that his deeds would have repercussions.

I am able to offer a thunder thorough analysis without any Agamemnon information regarding for any context of all remark. The speaker appears to be addressing someone who has just arrived to witness Agamemnon's atrocity based on the statement.

The speaker seems to be inquiring as to the reason for this person's decision to show up at this particular moment, suggesting that they could be involved in the activities that are taking place.

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Which supporting detail from The Great Fire conveys the main idea that firefighters alone were not able to contain the fire?

Answers

Answer:

Firefighters asked spectators to help, and many did.

Explanation:

According to the text of the "Great Fire", there was an outbreak of fire which overwhelmed firefighters because of the winds which made the flames to be fierce and uncontrollable.

Fires were common in those days and people were used to seeing fires so they were not in panic and when the fire overwhelmed the firefighters, they enlisted the help of spectators and they obliged.

Answer:

A

Explanation:

in "52," derek walcott’s lines "because we serve english, like a two-headed sentry / guarding its borders? no language is neutral" contain

Answers

In “52,"Derek Walcott's lines "because we serve English, like a two-headed sentry/ guarding its borders? No language is neutral;" contain irony. So the option C is correct.

An inanimate object or an abstract concept is given human traits through the literary device of personification. It is frequently used to increase the amount of description in a poem or story and to increase the reader engagement.

Words that rhyme within a line of a poem, as opposed to at the end, are known as internal rhymes. A poem with this kind of rhyme can be more engaging and dynamic for the reader by adding rhythm and meter.

Irony is a literary technique when a circumstance or occurrence is not what it first appears to be. It is frequently employed to highlight the disparity between what is anticipated and what actually transpires in a scenario.

Caesuras are pauses in poetry lines that are used to highlight specific passages or to evoke a sense of suspense. They can be utilized to make the poem appear more organized and official.

So the option C is correct.

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The complete question is:

In “52,"Derek Walcott's lines "because we serve English, like a two-headed sentry/ guarding its borders? No language is neutral;" contain (A) personification (B) internal rhymes (C) irony (D) caesuras.

In a work of fiction, which plot stage introduces main characters, setting, and initial conflicts? A. exposition B. rising action C. climax D. falling action

Answers

Answer:

A. exposition

Explanation:

the exposition is the beggining to the story and is when we learn about the main character(s), setting(s), and initial conflict(s).

The plot stage where the main characters are introduced is known as the A. exposition

What is a Plot?

This refers to the sequence in which storytelling has to follow, from start to finish, to introduce the characters and resolve the conflict.

Hence, we can note that the exposition is the start of a story and this would help to give background information about the characters and also to introduce the main characters.

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The fact that language learning is achieved by typically developing infants across the globe indicates that language is?

Answers

Answer: The first signs of communication occur when an infant learns that a cry will bring food, comfort, and companionship. Newborns also begin to recognize important sounds in their environment, such as the voice of their mother or primary caretaker. As they grow, babies begin to sort out the speech sounds that compose the words of their language. By 6 months of age, most babies recognize the basic sounds of their native language.

Children vary in their development of speech and language skills. However, they follow a natural progression or timetable for mastering the skills of language. A checklist of milestones for the normal development of speech and language skills in children from birth to 5 years of age is included below. These milestones help doctors and other health professionals determine if a child is on track or if he or she may need extra help. Sometimes a delay may be caused by hearing loss, while other times it may be due to a speech or language disorder.

Explanation:

as children grow,their languge skills develope so that they may acquire a larger and more complex

Answers

vocabulary sorry if not
1. lexicon
2. Verbose
3.Epilogue
4. Scribbling
5.Bibliophile
Explanation:
Plato :)



Exercise 2 Complete each sentence by writing the form of the verb listed in parentheses.

Sousa _____________ many famous marches, including "Washington Post March" and "Stars and Stripes Forever." (present perfect tense/compose)

Answers

Sousa has composed numerous famous marches, including "Washington Post March" and "Stars and Stripes Forever." The present perfect tense highlights the enduring significance of his compositions, showcasing their ongoing popularity and impact in contemporary music.

Sousa has composed many famous marches, including "Washington Post March" and "Stars and Stripes Forever." The present perfect tense is used here to indicate an action that started in the past and has a connection to the present.

In this case, the action of composing the marches began in the past, when Sousa was actively creating these musical pieces, and it has relevance to the present because these marches continue to be widely recognized and performed.

John Philip Sousa, an American composer, and conductor, is renowned for his significant contributions to the genre of military marches. Throughout his career, Sousa has demonstrated exceptional musical talent and creativity, which is evident in the numerous renowned compositions he has crafted.

Among his notable works are the "Washington Post March" and the "Stars and Stripes Forever," both of which have become iconic and synonymous with American patriotism.

The use of the present perfect tense emphasizes the lasting impact of Sousa's compositions. By employing this tense, we acknowledge that Sousa's creative output endures and remains influential even in the present day. The marches he composed continue to be cherished and performed by bands and orchestras worldwide.

Sousa's ability to capture the spirit of American pride and nationalism through his compositions has solidified his place as one of the most celebrated composers in American music history.

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i need help pls
Select the two adverbs.
Act fast and take advantage of the amazingly low prices at our fabulous Labor Day sale.

Answers

Answer:

amazingly and fabulous

Answer: Check out quizlet. Search Ixl Adverbs Quizlet. They have like all the answers

There seems to be too much standardized testing in public schools fact or opinion

Answers

Answer:fact

Explanation:

Even teachers agree

Answer:fact

Explanation:

What’s the main expression of a poem

Answers

The overarching sentiment or concept that the poet intends to get over to the reader is the poem's principal expression. The poet's feelings, experiences, and thoughts are reflected in this expression.

The poet strives to convey to the reader both a feeling and a message. A poem's fundamental idea can be expressed in a variety of ways, including through imagery, symbolism, and metaphor. Additionally, it may be expressed through the poet's word choice, the poem's organisation, and the use of rhyme and rhythm.

The title, the introduction, the body, and the conclusion all include the major statement, which is the poem's overarching topic. The overarching message of a poem is its major message.

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What does the passage reveal about Old Major's
character? Select three options.
-He is decisive.
-He is naive.
-He is a persuasive speaker.
-He is firm in his beliefs.
-He is cowardly

What does the passage reveal about Old Major'scharacter? Select three options.-He is decisive.-He is

Answers

Answer:

The answers are A,C,D

Explanation:

The passage reveal about Old Major's character is that he is decisive and he is a persuasive speaker and he is firm in his beliefs. Thus, option A, C and D are correct.

What is the significance of Old Major?

The Old Major is perceived as a character who speaks too much, and always wants the people around him to get persuaded by the things that he says or mentions. The second-nature of Old Major is decisive, i.e., he wants to be the one who takes all the decisions.

Apart from being a decisive and persuasive speaker, the Old Major is also childlike in his nature, where he wants the things to take place or happen in a particular way. His behavior throughout the passage can be described as naive.

Therefore, the options A, B and C hold true and state regarding the significance of the Old Major.

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The common valid forms that we have encountered so far (go ahead and use whatever letters you prefer):

Modus Ponens (e.g., If A, then B, A, B)

Modus Tollens (e.g., If A, then B, ~B,~A)

Disjunctive Syllogism (e.g., A v B, ~A, B)

Hypothetical Syllogism (e.g., if A, then B, if B, then C, If A, then C)

Answers

In propositional logic, the types you mentioned are instances of legitimate argument forms.

An expanded description of each form is provided below:

1. Modus Ponens:

  - Form: If A, then B. A. Therefore, B.

  - Explanation: We can infer that B must also be true if we have a conditional statement that says if A is true, then B is true and we also have the premise that A is true.

2. Modus Tollens:

  - Form: If A, then B. Not B. Therefore, not A.

  - Explanation: We can deduce that A must also be false if we have a conditional statement that says if A is true, then B is true and we also have the premise that B is false.

3. Disjunctive Syllogism:

  - Form: A or B. Not A. Therefore, B.

  - Explanation: If one of the alternatives in a disjunction (A or B) is known to be false, we can infer that the other option (B) must be true.

4. Hypothetical Syllogism:

  - Form: If A, then B. If B, then C. Therefore, if A, then C.

  - Explanation: If two conditional propositions, such as if A implies B and B implies C, produce a chain of implications, then logically speaking, if A is true, then C must also be true.

In propositional logic, these forms indicate legitimate logical deductions from provided premises that can be utilised to deduce conclusions. They offer a methodical framework for debating and assessing ideas.

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Help meeeeeeeeeeeeeeee

Help meeeeeeeeeeeeeeee

Answers

Well, what's a hobby of yours?

based on question 3, events a and b are exhaustive.

Answers

Based on question 3, events A and B are exhaustive because they cover all possible outcomes of the experiment.

Exhaustive events are those that include all possible outcomes of an experiment or situation. If events A and B are exhaustive, it means that there are no other possible outcomes besides those included in events A and B. In other words, the probability of either event A or event B occurring is equal to 1.

For example, if we are rolling a six-sided die and event A is rolling an even number, and event B is rolling an odd number, these events are exhaustive because there are no other possible outcomes besides rolling an even or odd number.

In conclusion, events A and B are exhaustive if they cover all possible outcomes of an experiment or situation and the probability of either event occurring is equal to 1.

Keeping in mind, the definition of exhaustive mentioned in Question 3, events A and B are exhaustive, it is due to covering all outcomes of an experiment.

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Fluency is an ability to express yourself clearly and accurately. Select all of the characteristics that directly relate to strong fluency when reading.

expression
Format
pace
rate
accuracy
complex vocabulary
volume

Answers

Complex vocab
Expression
Pace
Volume
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what is meant by fundamental unit? write any two difference between mass and weight. Quorum sensing A. is a phenomenon in which bacteria monitor their own population density. B. depends on the sensing of signal protein molecules. C. plays an important role in formation of biofilms by Pseudomonas aeruginosa. D. All of the choices are correct. Pleaasee answer!!!!!!!!!!!!!!!!!!!! Which describes the standard deviation? Which of the following hormones is most responsible for signaling satiety as well as reducing food intake during a meal?A) GastrinB) AdipokinesC) Neuropeptide YD) Cholecystokinin Imagine that we are interested in studying genetic and environmental influences on psychedelic mushroom consumption. For a group of twins, pairwise concordance is defined as C/(C+D), where C is the number of concordant pairs and D is the number of discordant pairs. In a study of 50 MZ twin pairs: There are 2 pairs for which both twins have consumed mushrooms. There are 38 pairs for which neither twin has consumed mushrooms. There are 10 pairs for which only one of the twins has consumed mushrooms. Required:What is the MZ pairwise concordance rate? EXCERPT FROM 'A CHRISTMAS CAROL': MARLEY'S GHOSTScrooge is visited bya)his nephew who comes to implore Scrooge to be more festive.b)the two men who visited his office earlier.c)the spirit of a man whom he cannot recognize.d)the ghost of his old business partner, Jacob Marley. find the resultant resistance of the circuit At the 15 January 2019, the amount of Retained earnings reported by Moon Corporation is $2,500,000. During 2019, Moon Corporation uued common stocks of $750,000, declared and paid cash dividends of $140,000, and declared share dividends of $320,000. The amount of net income of 2019 reported by Moon Corporation $1,000,000 Moon Corporation was required to make a correction of understatement of depreciation expenses in price years of $430,000 (net of tax) Required: How much was the retained earnings reported on 31 December, 20197 (Show your calculations), 1/7*5/3 um i need help plese i only have 1 secont Molly wrote messages to her friends on the sidewalk. She used 1/4 of a piece of chalk that was 2 3/5 inches long. How many inches of chalk did she use? Which of the following statements is NOT true ? a defense mechanism by which unacceptable feelings are transferred from one person to another person is _____ Perewi Cor (Figure 1) shows the force needed to stretch a 20-m-long, 3.2mm-diameter wire Part A What is the strain when the wire has been stretched by 50 cm? Express your answer to two significant Mauren ? Vo] - 124,4 Submit Previous Answers Request Answer * Incorrect; Try Again: one attempt remaining Figure 101 1 Part 8 What is the stress when the wire has been stretched by 5.0 cm? Express your answer to two significant figures and include the appropriate units. F (N) 1500 HA ? 1000 500 Value Units 0 AL (cm) Submit Request Answer 0 1 2 3 4 5 OE Value Units Submit Request Answer Part C 1 of 1 > What is Young's modulus for this wire? Express your answer to two significant figures and include the appropriate units. ? Y = Value Units Submit Request Answer TAL (cm) 5 Provide Feedhack Which statement includes explicit information from the excerpt? Washington asked James Jay to invent a form of invisible ink. Washington only knew about invisible ink that required heating. James Jay was a doctor who had knowledge of chemistry. James Jay created an invisible ink system that required two chemicals. compared with other peer-to-peer networks, bittorrent takes advantage of the fact that broadband internet connections group of answer choices continue to drop in price. are immune from surveillance by the police. provide higher speeds for downloading than for uploading. have become the standard in most homes in the united states. all of these. 3. Express the following numbers in scientific notation, making sure there is only one nonzerodigit to the left of the decimal place. Do not discard any nonzero digits.a) 0.000890b) 35470 select the digit in the thousands place of 689,234 what is the answer Define a short story and what it includes and the importance of it. How can I find equations for these graphs using the standard polynomial equation?