Liczba a przy dzieleniu przez 2 daje resztę 1. Wykaż, że kwadrat liczby a powiększony o 3 jest podzi.... Question from @fullspeed

October 2018 2 13 Report

Liczba a przy dzieleniu przez 2 daje resztę 1. Wykaż, że kwadrat liczby a powiększony o 3 jest podzielny przez 4.

Nie do końca ogarniam to zadanie, bo przecież tą liczbą a może być 3,7,9,11,13,15, ... 23 ...

Na pewno będzie to liczba nieparzysta a podniesienie liczby nieparzystej do potęgi daje liczbę nieparzystą, a gdy dodamy 3 to będzie wtedy parzysta.

Więc sama nie wiem jak to zrobić, dlatego proszę o pomoc :)

Kto mi wyjaśni jak zmieniają się kąty na pods. załamania i przejścia promienia świetlnego przez dwa ośrodki? Np. że w powietrzu jest więkjsza szybkość to kąt alfa jest większy, a w wodzie mniejsza to beta mniejszy. No własnie czy jak jest większa szybkość to ten kąt ma być mniejszy czy większy??? :)

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fullspeed October 2018 | 0 Replies

Wymień trzy dzielniki liczby 3 n+2 + 3 n różne od 1. Odpowiedź uzasadnij słownie lub rachunkowo.* n+2 i n są zapisane w formie potęgi :)

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fullspeed October 2018 | 0 Replies

Załóżmy, że x spełnia równanie x+1/x=√6.Oblicz x²+1/x², a następnie oblicz tym samym sposobem x(do potęgi czwartej)+1/x(do potęgi czwartej).

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fullspeed October 2018 | 0 Replies

Przetłumaczcie kilka zdań na niemiecki.Tutaj nie wolno było palić papierosów (w Prateritum)My jako uczniowie myślimy zawsze o szkole.Wy przynosiliście zawsze do szkoły książki (w Prateritum)

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fullspeed October 2018 | 0 Replies

O dwóch liczbach a i b wiadomo, że a+b=8 i a²+b²=39. Wyznacz wartośc iloczynu ab.

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fullspeed October 2018 | 0 Replies

Zamknięty pojemnik zawiera 9g tlenu i 22,4 g opiłków żelaza. Oblicz max. ilość tlenku żelaza (III), jaka może powstać w tym pojemniku. Który substrat został użyty w nadmiarze - odpowiedź uzasadnij obliczeniami.

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fullspeed October 2018 | 0 Replies

Uzasadnij, że liczba 5 (do potęgi 16) - 1 jest podzielna przez 24

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fullspeed October 2018 | 0 Replies

Uczestnicy konkursu matematycznego mieli do rozwiązania 20 zadań. Za każde zadanie rozwiązane poprawnie uczestnik otrzymywał 5p., za brak rozwiązania lub rozwiązanie błędne tracił 3p. W konkursie tym Adam uzyskał 76p. Ile zadań rozwiązał poprawnie?Jakoś nie ogarniam tego pytania. W ogóle jak mógł uzyskać 76p. skoro zadania były po 5p., wtedy musiałby zrobić 15,2 zadania No nie wiem jakieś to dziwne, pomóżcie :)

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fullspeed October 2018 | 0 Replies

The Friar's TaleThe Summoner and the DevilThere was a summoner and a friar on the pilgrimage to Canterbury.Summoners found people who did bad things. They took them to an important person in the church. People often paid summoners a lot of money to forget those bad things. A friar's job was different. He asked people for money for the church.The summoner and friar on the pilgrimage were not friends.The friar said to the pilgrims,' I'm going to tell you a story about summoners.'Then the summoner said, 'And I'm going to tell you a story about friars.''Well, I'm going to tell my story first,' said the friar.So the friar began.●There was an important man in the church who was very bad. He only wanted people's money. A summoner worked for this man. He watched people quietly. Then he caught them when they did bad things. 'You must leave the church,' he told them. 'But if you give me a lot of money, you can come into the church again.'●One day, the summoner was on his way to see an old woman. He thought that she was a bad woman. He wanted her to give him money.On the way he met a man. The man was wearing bright red clothes and riding a brown horse.' Where are you riding to ?' asked the man. Nobody liked the summoner, so he lied.'I'm just going to get some money from an old woman. She has to pay the money to my lord.'' Oh, so you're a bailiff,' said the man.A bailiff is a man who looks after land for rich lords. He takes money from the farmers who use the land.' Yes, that's right,' answered the summoner.' I'm a bailiff.' ' I've got a farm which I look after for a lord,' said the man. ' Oh, that's interesting,' said the summoner.' Tell me, how do you get your money from people ?'' I get it in many different ways,' said the man.' I like having a lot of money, but my lord doesn't pay me much.'' I've got my ways too,' said the summoner.' I don't mind if people are frightened of me or unhappy. I think we're the same, you and I.What's your name?'The man's answer gave the summoner a surprise. ' I'll tell you who I am. I'm a devil, and I live in hell!' he said. ' Oh, I thought you were an ordinary man like me,' said the summoner.' You look like a man.'' Devils can look like anything they want to,' laughed the devil. ' There are good reasons for this. Now, let's continue our journey.'●So the man and the devil rode along the road. After a short time, they saw a man with some horses. He was hitting the horses and shouting at them.' The devil can take you, you lazy animals!' he cried.'Did you hear that?' the summoner asked the devil. 'Go and take his horses. He says that the devil can take them!''You can't believe everything you hear,' answered the devil. 'Wait. Let's see what happens.'After a few minutes the tired horses started to walk a little faster.' Good horses!' shouted their owner.' Good Brock! Good old Scottie! God will save you all!'' What did I tell you ?' said the devil.' He said one thing but he meant another thing. There's nothing for me here. Let's continue.'●When the town was far behind them, the summoner said to the devil,' You didn't do very well with the man and his horses, did you? Now I'm going to get some money from this poor old woman. Watch carefully! You can see how I do it.'He went to the old woman's door.' Come out!' he shouted. ' I'm sure you're doing something bad in there!''Who's that?' cried the old woman, coming quickly out of her house.When she saw the summoner, she looked very frightened. ' Oh, it's you, sir,' she said.' People are saying some very bad things about you,' said the summoner in a serious voice.' If they're true, you'll have to go to the church. You'll have to pay them a lot of money.'When she heard this, the old woman began to cry.' Oh, sir, please be kind to me,' she said.' I'm ill and I can't get to church. Can I pay you the money ?'' Yes, but you must pay me now,' answered the summoner.' It will cost you twelve pennies. Quickly!'' Twelve pennies!' cried the old woman.' Oh, God help me! I haven't got twelve pennies! What can I do ?'' Give me your money!' shouted the summoner angrily.' But I haven't done anything bad,' said the poor woman.'Give me your money or I'll take your cooking pot. You were with a man who isn't your husband. You know you were!''No, I always loved my husband,' cried the old woman. 'I hope the blackest devil in hell carries you away! And the cooking pot too!'Then the devil spoke to the old woman.' Do you really mean what you're saying, madam ?'' Yes I do!' she answered. ' The devil can carry him away — clothes, cooking pot, everything.'The summoner was still shouting at her. He was very angry.' What ? Will I get no money from this stupid old woman ?''Why are you so angry?' asked the devil. 'You and the cooking pot are mine now. She gave you to me. Tonight you'll be in hell with me. You can learn about devils there and about how we do our work!'Suddenly the devil jumped on the summoner and caught him. Then he carried him down to hell. There's a place for summoners in hell, and it's always very full!●The friar finished his story and looked at all the pilgrims.'Think hard about my story,' he said. 'We must hope that God will keep us from the devil!'Then the summoner told his story about the friar. But it wasn't a very interesting story so I haven't put it in this book.Proszę o przetłumaczenie na polski. Bez translatora!

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fullspeed October 2018 | 0 Replies

Proszę,przetłumaczcie! :DThe Pardoner's TaleThree Men Look for DeathThe pardoner told his story next. But first, he told the other pilgrims about his job.' I speak to people in churches,' he said.' I always talk about the same thing. I tell people: " Love of money is a real problem. You do bad things, and bad things happen to you, because of it." And I sell pardons. I've got a lot of things that belonged to saints - bits of cloth and other old things. Well, they didn't really belong to saints, but people don't know that! If people buy these things, God will forgive them. And I make a lot of money. I don't like being poor. Oh no! I must have fine clothes and good food! The poor give me money and I have a good life. I sell them pardons and they're happy'The pardoner was a very bad man but his story was very good. The pilgrims were surprised that a bad man could tell a good tale.This is the story.●There were three young men who did many bad and stupid things.They drank too much and they did no work.One morning, they were drinking when they heard a noise outside. People were carrying the body of a dead man.They asked the boy who brought them more drink,' Whose body is that, boy ?''He was your friend,' answered the boy. 'He was killed last night while he was drinking here. He was killed by that quiet thief, Death. Death kills all the people in this country. He killed your friend and then went away. He's killed thousands and thousands of people. You should get ready to meet Death.''I'm not afraid to meet him!' cried one young man, and he quickly jumped up.'I'm going to find him! I'll look for him in every field and wood and town. Listen! Let's hold up our hands and promise to be brothers. Let's find Death and kill him!'' I'll come with you,' said the second man.'And me,' said the third. 'We'll kill this dangerous man, Death, before night comes.'So the three men went to find Death. They walked a little way and saw an old man with a long white beard. He was wearing a lot of old clothes and carrying a stick. When he saw the three men, he spoke to them kindly.' God be with you, rny young friends.'But the men shouted at him,' You stupid old man! Why are you wearing all those clothes ?''Because I'm very old,' answered the man. 'I feel the cold and I can never get warm.''Well, why have you lived for so long then, you ugly old man? You should die more quickly!' they shouted.The old man looked at them angrily.' I live like this because Death hasn't taken me. I travel up and down the country, looking for Death. I say to the ground under my feet: "Dear Mother Earth, let me in! Oh, Mother Earth, I want to lie down in you and sleep for ever!" But she isn't kind to me. That's why I'm old, young men.'One of the men laughed loudly. The old man turned to him and said quietly,' You've spoken very unkindly to me and now you're laughing at me. But I've done nothing to hurt you. You should speak more kindly to an old man. Now, I've got nothing more to say to you. I'm going to continue on my journey to meet Death.''No, you can't do that!' they shouted. 'He's killed all our friends in this country. We're going to find him and kill him. Quickly, tell us where he is'.'If you really want to find Death, I'll tell you,' answered the old man.' Can you see that little road? Go up there. Not long ago I saw him near a great tree in the wood. But you can't save men from Death. He won't be afraid of you. Go now. I hope God will help you to become better men.'Proszę o przetłumaczenie tego na polski, bez translatora :)

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greenfox453

a:2 = 1

a2 (do kwadratu)+3=(2a+3):4

2a:4 to a:2=1 X a:2=1 czyli wynik 1

1+3=4

wiec ta liczba jest podzielna przez 4

0 votes Thanks 0

platon1984

$a=2n+1\\ n\in Z\\ a^2=(2n+1)^2\\ 4n^2+4n+1\\ a^2+3=4n^2+4n+1+3=4n^2+4n+4\\ a^2+3=4(n^2+n+1)\\ \frac{a^2+3}{4}=n^2+n+1$

ponieważ n jest całkowite to kwadrat też jest całkowity i cała suma także samo...

co było do okazania

pozdrawiam

---------------
"non enim possumus quae vidimus et audivimus non loqui"

1 votes Thanks 0

Wymień trzy dzielniki liczby 3 n+2 + 3 n różne od 1. Odpowiedź uzasadnij słownie lub rachunkowo.* n+2 i n są zapisane w formie potęgi :)

Załóżmy, że x spełnia równanie x+1/x=√6.Oblicz x²+1/x², a następnie oblicz tym samym sposobem x(do potęgi czwartej)+1/x(do potęgi czwartej).

Przetłumaczcie kilka zdań na niemiecki.Tutaj nie wolno było palić papierosów (w Prateritum)My jako uczniowie myślimy zawsze o szkole.Wy przynosiliście zawsze do szkoły książki (w Prateritum)

O dwóch liczbach a i b wiadomo, że a+b=8 i a²+b²=39. Wyznacz wartośc iloczynu ab.

Zamknięty pojemnik zawiera 9g tlenu i 22,4 g opiłków żelaza. Oblicz max. ilość tlenku żelaza (III), jaka może powstać w tym pojemniku. Który substrat został użyty w nadmiarze - odpowiedź uzasadnij obliczeniami.

Uzasadnij, że liczba 5 (do potęgi 16) - 1 jest podzielna przez 24

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