Answer:
The problem is amenable to some simple complex number analysis (you have to work in radian measure, note that 45∘=π4).
Each step can be characterised as a vector in the complex plane. The first step is 1=1ei0, the second is 12eiπ4, and the nth step is 1nei(n−1)π4. The final position is the infinite sum of all of these complex numbers.
Let z=eiπ4.
Then define a series sum S(z)=1+12z+13z2+14z3+...
Note that zS(z)=z+12z2+13z3+14z4+...
And now observe: (zS(z))′=1+z+z2+z3+z4+...=11−z, where convergence is assured for complex |z|<1.
By integrating and rearranging, we find, S(z)=−1zln(1−z). (The constant of integration is easily shown to be zero).
Now find |S(eiπ4)|, which is the distance of the final position of the ant from the origin.
|S(eiπ4)|=|−e−iπ4ln(1−eiπ4)|
Since |z1z2|=|z1||z2|, the above is equal to |−e−iπ4||ln(1−eiπ4)|=|ln(1−eiπ4)|
(since |−e−iπ4|=1)
To find |ln(1−eiπ4)|, we first express 1−eiπ4 in the form reiθ.
1−eiπ4=1−cosπ4−isinπ4
Now r=(1−cosπ4)2+(sinπ4)2−−−−−−−−−−−−−−−−−−√=2−2cosπ4−−−−−−−−−√=2−2–√−−−−−−√
and θ=arctansinπ41−cosπ4=arctan(2–√+1)
and ln(reiθ)=lnr+iθ, giving:
|ln(1−eiπ4)|=|12ln(2−2–√)+iarctan(2–√+1)|=[arctan(2–√+1)]2+14[ln(2−2–√)]2−−−−−−−−−−−−−−−−−−−−−−−−−−−−√=1.20806...
Explanation:
SO EASY.
give one example of a life lesson you have learned
Answer:
To not trust the people that have hurt me before l m a o
Explanation:
As used in paragraphs 2, 3, and 4 of the passage, the word powers is closest in meaning to
a-abilities b-influence c-forcefulness d-authority
Answer:
A. abilities
Explanation:
The word "powers" as used in paragraphs 2, 3 and 4 actually means "abilities".
The passage reveals that some animals have "regenerative powers" that is "regenerative abilities". This means that those animals have abilities to regenerate some new from what was lost. The excerpt reveals that starfish have the regenerative ability to grow new arm when any of its arms is broken. It also reveals that even planaria that can be cut into pieces have the ability to grow into a new one from any of the pieces.
Regenerative power actually refer to the ability of restoring bringing something new out of something old. So, some animals that such abilities in them to do so.
How can social media shape an individual’s perception of beauty?
essay
Answer:
social media can shape an individuals perception of beauty in a positive and negative way. In a negative way, it can make people self conscious about their bodies or the way they look. People can also write mean comments under someone's picture and that could change their own perception. Recently on social media platforms like TikTok, there's been a trend in body positivity posts, encouraging people to love themselves and be proud of how they look.
Explanation:
Present Perfect
1 I...........(not/ do) the homework yet.2 They..........(study) very hard recently.
3 She..........( Promise) to help many times.
4 He........... (clean) the kitchen. Everything is speaking clean.
5 she...........(write) her essay and ...........(send) it to her professor.
6 He..........(see) the film 'The King's Speech' about six times.
7 We .............(paint) our living room. I think it looks a lot better.
8 She............(take) French lessons lately.
9 It...........(not/rain) for three hours! only about one hour.
10 Lucy....................(already/leave).
What act of the Roman Catholic clergy did Martin Luther most strongly criticize in his Ninety-Five Theses?
A. forcing young girls to become nuns B. receiving money for the remission of sins C. taking lovers and having illegitimate children D. getting involved in court politics and trade E. getting involved in religious wars and crusades
Answer:
receiving money for the remission of sins
Explanation:
The act that was criticized by Martin Luther is B. receiving money for the remission of sins.
It should be noted that indulgences was simply the commutation for money as a temporal penalty for sin. It was the practical satisfaction which was part of penance.
This was an act of the Roman Catholic clergy that Martin Luther most strongly criticized in his Ninety-Five Theses. He wasn't in support of receiving money for the remission of sins.
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what problem does the knight encounter during his quest?
Answer:
No two woman can agree on the answer
Explanation:
The wife of baths tale
Who is a modern day lecher/ licentious celebrity?
What makes you different from others?
Answer:
Everybody is different and unique in their own way. I am different from others because I have a heart condition and I am funny and weird in some cases, but I can be VERY ANNOYING... But I love myself, I am still making improvements with my body... but I am good:)
Explanation:
Hope this helped, can I please get brainliest!:)
Which concluding sentence best ties the ideas together and supports the paragraph’s compare-and-contrast text structure?
Some people do not use a board at all when they ride waves at the beach.
Waves have different strengths and sizes depending on the weather.
Two types of boards used to ride waves are the body board and the surfboard.
However, once the basics are learned, both are fun ways to enjoy the ocean
Answer:
d
Explanation:
hope this helps
The concluding sentence which best ties the ideas together and supports the paragraph compare-and-contrast text structure here is However, once the basics are learned, both are fun ways to enjoy the ocean.
In the sentence, it is seen that However is a phrase used for concluding a sentence and the sentence compares two things here.
Concluding sentencesA concluding sentence is the last sentence of a paragraph. It puts in summary the main idea of a paragraph.
Therefore, the correct answer is option D.
However, once the basics are learned, both ways are fun ways to enjoy the ocean.
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Which situation is most clearly ironic?
O A. A powerful vampire who is a strict vegetarian
B. A trade route between Asia Minor and Europe
O c. A train that connects Sendai, Tokyo, and Osaka
O D. A duel between two aristocrats over an insult
NEED HELP ASAP
The situation which is more ironic is -A powerful vampire who is a strict vegetarian.
Ironic wordsUsing ironic words is using words to convey a meaning that is the opposite of its literal meaning.
An ironic remarkAn ironic remark conveys a meaning that is the opposite of its literal meaning. So, in an ironic statement one thing is said, while another thing is meant. For example, if you were trying to be ironic on a stormy, dreary day, you might say, “What glorious weather!”
Thus, the situation which is more ironic is -A powerful vampire who is a strict vegetarian.
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Why we considered internet is the most dangerous place on the planet?
Because people are fake, rude, two-faced, and toxic. It's a place where people can get a chance to get their feelings out to a perosn behind the screen because they think they can get away with it. It's sickening.
We consider the internet the most dangerous place on the planet because it makes people full of fraud, abrupt, multi-faced, and venomous.
What are the disadvantages of the internet?The disadvantages of the internet are as follows:
It becomes an addiction, especially for youths.It is considered one of the most time waste mechanisms. It stimulates the process of distraction and lack of focus.It also involves some nonsense activities like bullying, trolls, and crime.According to the context of this question, the internet is a place where people can access an opportunity in order to mutually connect with one another over a large distance and receives their thoughts, emotions, and feelings that make you think and adjust yourself accordingly. In this way, people are distracted from the life of others. This is the most dangerous impact of the internet on people.
Therefore, the reasons why we considered the internet the most dangerous place on the planet are well described above.
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Which of the following do not affect the delivery of a speech? a. body language c. opinions b. articulation d. pronunciation
Answer:
Pronunciation
Explanation:
Based on the evidence in this text, what is the best inference about the genii’s motivation?
Answer:
Based on the evidence in this text, what is the best inference about the genii’s motivation?
Explanation:
Could you please add in a picture so that we know what your talking about? please and thank you! i'd totally legitimately answer but you know, i have no evidence. Thank you for your time.
Can someone help as soon as possible pease, ty!! (Will mark brainliest)
Which side of the polygon is exactly 6 units long? On a coordinate plane, point A is at (negative 4, 6), point B is at (2, 6), point C is at (4, negative 8), and point D is at (negative 6, negative 8). AB BC CD DA
Answer:
AB
Explanation:
I know its right it tells me the answer :) Hope this helps.
Answer:
AB
Explanation:
If you think of it and look at the numbers (-4,6) and (2,6)
this is how i look at it
6 and 6 dont worry about those look at -4 and 2
-4 + 2= 6 units
there is your answer AB because it is 6 units
hope this helps
How does Martin Luther king portray the appalling condition of negro community
Answer:
miserable, crippled and still limited.
Explanation:
In his speech "I Have a Dream", Martin Luther King portrays the condition of the negro community as miserable, crippled and still limited even after one hundred years after the emancipation proclamation.
King claims that the lives of the negro community have not changed much as they still live in poverty and corners of the American society although the world and the country has prospered so much. He wanted to address this appalling condition which was still prevalent in American society.
Which word is an antonym for the word wholehearted
In the article “Survival is Your Own Responsibility,” whats the authors purpose?
Answer:
you have to be prepared to have responsibility
Explanation:
Choose the word that best fits the provided statement:
1. Which word means - to replace; to usurp
sheathe
grieve
supplant
mark
supplant means to replace
Read the following excerpt from “Raymond’s Run” and answer the question.
The big kids call me Mercury cause I’m the swiftest thing in the neighborhood. Everybody knows that—except two people who know better, my father and me. He can beat me to Amsterdam Avenue with me having a two-fire-hydrant headstart and him running with his hands in his pockets whistling.
What can you infer about Squeaky’s father from the information presented in this passage?
Squeaky’s father helps her to train for her races.
Squeaky’s father was a runner in high school.
Squeaky hopes that no one learns that her father is a faster runner.
Squeaky is proud that her father is a fast runner.
Answer:
i'm pretty sure it's "Squeaky is proud that her father is a fast runner."
Explanation:
i did this last quarter lol
Answer:
d
Explanation:
(the book is Pax.)
What do the details in Chapter 2 show about Peter’s father?
A. He feels bad for leaving his son to join the military.
B. He loves animals as much as his son does.
C. He is fond of sharing childhood memories with his son.
D. He is often angry and sometimes harmful toward his son.
Answer: Pax and Peter’s story begins when Peter and his father drop Pax off in the woods near an abandoned rope mine. Peter had chosen that spot because he believed his friend would be safe there. Pax soon meets the other foxes who live in the area. Bristle, a female fox, hates humans and blames them for the destruction of her family.
Explanation: pls mark branliest
The details in Chapter 2 show about Peter’s father is He feels bad for leaving his son to join the military. Thus the correct option is A.
What is the summary of pax?A summary reflects young readers in the thoughts of a 5-year-old fox. Pax is adopted by Peter, a youngster whose mother passed away, after being dumped as a kit. Pax must be released into the wild for the first time after Peter's father reunites in the military.
After dropping Peter off at his grandfather's house, Peter's father departs to join the military. Peter's grandfather provides some initial assistance before turning him free.
He is hesitant to deal with his father's anger, but he is also afraid. In order to locate Pax and save his friend, Peter starts on a search mission. Through his search, he gains the ability to recognize and embrace his own feelings of anger.
Therefore, option A is appropriate.
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HELP PLS!!!! DOES ANYBODY KNOW A EXAMPLE OF THE WORD RESOLUTE IN THE BOOK CHARLES????????
Read the excerpt from "Thomas Edison: The Master of Improvement.”
Its glow was produced by electricity passing through a filament, or tiny piece of material. The inside of the glass bulb was a vacuum.
Based on context clues, what is the meaning of the word filament?
a place where electricity is made
a very small piece of material
the inside of a lightbulb
the vacuum inside a bulb
Answer:
the answer is b..
Explanation:
got it right 2020 on edge..
1) Does john kill lenina?
Teen siblings send cards to tell health care workers they're heroes
Answer:
that's so cool i might do this
Explanation:
Need answer ASAP) What are the differences and similarities between information in a chart and information presented in a paragraph? In an image? Why is it important to recognize the differences in how information is presented? ( Brainliest Answer).
ggggggggggggggggggggggggggg
This is due at 12 can someone help me I can’t think of anything
Answer: ok i gotchu i’m answering now so you’re not left hanging ok :)
first person to type the alphabet like this aAbBcC all the way to zZ gets braillest good luck
AaBbCcDdEeFfGgHhIiJjKkLlMmNnOoPpQqRrSsTtUuVvWwXxYyZz
The National Restaurant Education Foundation provides educational and awareness programs, particularly in
O food safety and restaurant management
O sanitation
O finance
O regulation awareness
the answer is food safety and restaurant management
(both...and) (either...or) (not only...but also) (Neither...nor)
7. ___ I will come there ___ you will come here.
8. ___ you ___ your friend are old enough to enter.
Answer:
7. Either Or
8. Both And
