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Mathematics Senior High

・2)の証明の「同様に」以降はなぜr≠0とだけ仮定するのですか?0≦r<lの否定になるんですか? ・1)の証明の、「」が何を言っているかわからないです。2)の何をどう利用したんですか? 本当に理解できないので簡単めに解説をお願いしたいです。😢

446の会社数は無数 基本事項 ① 最大公約数と最小公倍数 (12) 24.…… 2つ以上の整数に共通な約数を,それらの整数の公約数といい、公約数のうち最大 のものを最大公約数という。 また,2つ以上の整数に共通な倍数を,それらの整数 の公倍数といい,公倍数のうち正で最小のものを最小公倍数という。 一般に、公約数は最大公約数の約数 公倍数は最小公倍数の倍数である。 TA 注意 最大公約数をG.C.D Createst Common Divisor) または G.C.M (Greatest Common Measure), 最小公倍数を L.C.M (Least Common Multiple) ともいう。 ② 互いに素 2つの整数αの最大公約数が1であるとき, a,bは互いに素であるという。 ③3 最大公約数 最小公倍数の性質 2つの自然数a,b の最大公約数をg, 最小公倍数を1とする。 aga, b=gb' である とすると,次のことが成り立つ。 a' と'は互いに素 gdg b 21=ga'b'=a'b=ab' 解説 <最大公約数、最小公倍数> 上の1) 2) を証明してみよう。 それには,まず2) から示す。 [2) の証明]a,b,c, ······ の最小公倍数を 任意の公倍数をとする。 kを1で割ったときの商を Q, 余りをrとすると a,bはgでひろいろ なかった素因数の あつまり ~ 1 Y = 77₂ 318 7 きずり h=qlty...... ①,0ょくし -0 もしもの倍数であるから, k=ak', l=gl' (k', I'は整数)と表され axsh Tabの任にかけた rkgl=g(k-ql ) より はαの倍数である。 ab=gl 同様に,b, G…. の倍数であるから、はa,b,c,….. の公倍 w z C 数である。 「ここで、y=0 と仮定すると、より小さい正の公倍数rが存 在することになるが,これはが最小公倍数であることに矛盾する。」 ゆえに = 0 よって, ① はん=ql となり, kは1の倍数である。 [1) の証明] α, b, c, ······ の最大公約数を g, 任意の公約数をmとする。 「1をgとmの最小公倍数とすると, はgとmの公倍数であるから 2) より αはもの倍数である。 同様に, b, c, ...... もの倍数である。 したがって は a, b, C....... の公約数である。 ここでgが最大の公約数であるから l≤g 12g ゆえに lg 一方, 1はgとmの最小公倍数であるから よって,gとmの最小公倍数がg に一致し, gはmの倍数である。 すなわち, 任意の公約数は最大公約数g の約数である。 大きい所どり! xy X² Yo X'Y = l この等式については、 次の 「§18 整数の割 り算と商および余り」 で詳しく学習する。 <背理法。 Fag (A)) 1) を示すにぼg と mの最小公倍数が であることを示せば よい。 ASB かつ A≧B ならば A=B この論法は整数の性 質に関する証明でよ

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English Junior High

どうしてもお願いしたいです。お願いします。こう言う文全然わからないんです。答えをお願いします。できれば解説もあるとありがたいです。

2 次の中学生の敏夫 (Toshio)と雅子 (Masako)と留学生のボビー(Bobby) の夏休み中の会話文を読ん で、あとの問いに答えなさい。 Bobby: Hi, Toshio. Our city has the Himawari Festival for three days every August, right? Masako told me about it. That's right. I go to the festival every year. Toshio: Bobby: Toshio: Bobby: Toshio: That's nice. So, you went to the festival on August 21, right? (B) Right. Bobby: So, the festival won't start on Toshio's birthday this year. Masako: Right. I will go with my brother on the second day this year. The music club in our city will have a concert. They will play music from 10:40 to 11:00 in the morning. Their performances are wonderful. My brother and I enjoy their concert at the festival every year. We love music. I play the flute, and he plays the guitar. Bobby: Sounds nice! I love music, too! Toshio: Bobby, you play the piano very well. Last Thursday, I listened to your piano performance at your house. I really enjoyed it. And your brother plays the violin, right? Yes. My father plays the violin, too. And my mother plays the piano. Everyone in my family loves music. Then, let's go to the Himawari Festival together and enjoy the concert! Can your family come? Bobby: (C) How about you, Toshio? Toshio: Well, the second day is Saturday this year. You know, I'm on the school baseball team. We have practice every Saturday, so I can't go with you. I'm sorry. I will go to the festival with my parents and my sister on the first day. Bobby: Masako: Who do you usually go to the festival with? (A) With my parents and my sister. Every year, we join the festival on the first day. Last year, it was on my birthday, so my sister bought a nice bag for me at the festival. Masako: OK. Bobby: Well, can we enjoy any food at the festival? Toshio: Sure. You can eat your favorite food there.. Bobby: My favorite food? Do you mean my favorite Japanese food? Toshio: Yes. Guess what. Bobby: Toshio: (D) Well, is it sushi or sukiyaki? No. Masako, you said that you had it with your family last Sunday. Masako: Oh, I had yakisoba for lunch and oden for dinner that day, but we can't eat oden at the festival. We can eat () at the festival, right? Right! You can enjoy it at the festival! Bobby: Toshio: 5 10 15 25

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English Senior High

英単語教えて欲しいです。 間違えてるところあったら教えて欲しいのと、分からないところが沢山あるのでこの文章の中に書かれている単語で右の空欄教えて欲しいです。お願いします。

20 25 20 35 15 STEP 3 DEAR (1年7月改) 回 目標 IGG 登場人物の心情を想像しながら読み進めよう。 次の英文を読んで,あとの問いに答えよ。 取り組み日 A 日 得点 /18 目標時間 17分 tell Sara was annoyed/when her mom told her the news. from Japan/to live with her family//Their two-bedroom apartment/was(already crowded/ with her mom, dad and her.// While her mom was from Japan/Sara (7)/She knew only a few Japanese words. 5 Her mom told her about Sara's Grandpa)//He studied English (in college, but Sara and Grandpa had never spoken (in English.) When she went to Japan every summer, the most. they said to each other was "Ohayo" in Japanese. Grandpa didn't talk much. A month had passed since Grandpa moved in/With the new family member in her home, Sara spent more time alone in her room working on her favorite hobby drawing 10 comic strips./She hardly showed these drawings to anyone.) Her parents thought it was a waste of time. They hoped she would spend more time on her schoolwork.)// Sara had been working for months on a 16-page comic book about a teenage girl with magic powers. She hoped to enter it in a comic book contest the next month but was struggling with how to draw the hero with invisible magic powers// One afternoon, she got so frustrated that she crushed almost all the pages she had drawn and threw them in the wastebasket) She didn't know why but her eyes were full of tears. //Her Her grandfather was moving She grabbed her jacket and went into the living room. Grandpa was reading a book (on the sofa. She said, "Please tell my mom that I went for a walk. Grandpa said. “Itterasshai" to her but she walked out of the room. When she came home, Sara was still upset, but more disappointed. a comic book that she could hand in for the contest. del pr Then she saw her desk. Her drawings were put back on the desk//They were laid flat and attached with small sticky notes all over the pages.// Sara(1-0)Who had gone through her wastebasket? //This was her room.//No one came in without telling her.)// The handwriting on the sticky notes) was really easy to read//She (quickly) realized they were from Grandpa. 'here wouldn't be "Sara, you have a gift for art," the first note said. The second note was longer/"When 30 I was your age. I also wanted to be a comic artist."// The other notes gave to her face."Finally, someone understands my passion I Sara advice on improving her comic strips. Sara felt a smile coming to never imagined Grandpa would ()do that!" She started writing a card to Grandpa "Dear Grandpa /Thank you so much for your kind comments! I want to finish my comic book so I can enter it in the contest next month//Please be my advisor!/Love, Sara"// Grandpa was watching TV with her parents in the living room but looked at Sara/as she walked up to him.// Sara (1-2), so she handed him the card without a word. She wondered if Grandpa 40 would accept it. When he read the card, he smiled but did not say anything, either. Sara quickly went into her room. Her parents were wondering what had just happened. (1) She went straight back to the desk/and started working on her comic book //She only had a month. She couldn't wait to show Grandpa her next draft for more advice. (567W) 内 () ORIGINAL MATERIAL

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English Senior High

英語和訳です! toの用法の単元なんですが、このピンクでマーカー引いたところがどんな用法でどうしてこう訳されるのかがわからないです! よろしくお願いします!

<英文構造> Thomas Alva Edison is said to have led the world into the age of technology. He invented 完了不定詞 lead ~ into... 「~を・・・へ導く」 many of the technologies vital to the modern world. Although he patented over 1,100 technologies を修飾 inventions, many were improvements / to the inventions of others. A lot of invention ↑ many of his inventions nowadays improves existing products and processes to make them a little bit more effective. V 0 to 不定詞の副詞用法 And Edison started all that off. 3 不定詞 (2) ↑前文の 「既存の製品と製法を改良すること」を指す FOCUS 不定詞(2) Thomas Alva Edison is said to have led the world into the age of technology. : A is said to do 〜 「A は〜すると言われている」 のto不定詞が, to have+過去分詞の完了不定 詞の形になっている。 to 不定詞の内容が、 主節の動詞 (ここではis) よりも前のことを表してい るので, is said to have led the world into 〜を 「世界を~へと導いたと言われている」と訳す。 voltraph (→ 重要構文9 ) ◆l.2 the technologies vital to ~ : vital は前の technologies を修飾。 形容詞が後ろから前の名詞を修飾 するのは, 形容詞が修飾語句を伴う (ここでは vital は to the modern world を伴っている)場合 lineである。 l.4 make them a little bit more effective: make +0 +C「~を… にする」 の表現。 them は前述の existing products and processes を指す→ 「既存の製品や (製造) 過程をもう少し効果的なものに する」。 Vocabulary Check □ technology 「(科学技術」 □ invent 「~を発明する」 □ vital 「きわめて重要な」 □ improvement 「改良 (したもの)」 process (S) PET 20001. [訳] トーマス・アルバ・エジソンは、世界を科学技術の時代へと導いたと言われている。 彼は現代世界にとっ てきわめて重要な技術の多くを発明した。 彼は 1,100を超える発明品の特許権をとったが、 多くは他人の 発明品を改良したものだった。 今日では多くの発明は、もう少し効果的なものにするために既存の製品と(製 造) 過程を改良している。 そして, エジソンがそういったことをすべて始めたのである。 af yoludsoov ortner 「物を作り出すための) 過程」 Vocabulary Plust □ existing product □ effective □ start off / start off ~ 「既存の 現存する」 「製品」agene 「効果的な」 「~を始める」 font istnatoa 13

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English Senior High

この誤り箇所指摘の問題が分からないのでよろしくお願いします。

【4】 次の1~10について, 誤った英語表現を含んだ部分がある場合には(a)~(d)から誤り を一つ選び,誤りがない場合には (e) を選んでマーク解答用紙にマークせよ。 1. In (a) classical Islamic history there could be no clash between since the caliph, the titular head of the Islamic state and community, (b) combined in pope and emperor, himself both (c) political or religious-though (a) not spiritual-authority. NO ERROR 2. The years (a) immediately following the end of the Cold War offered (ú) a tantalizing glimpse of a new kind of international order, with nation-states growing together or disappearing, ideological conflicts (c) melting away, cultures intermingling, and free commerce and communications (a) increasing. NO ERROR 3. Despite the growth of the economy, or perhaps (a) in part because of it, and because, as well, (b) the vast rural exodus owing to both (c) population growth and increasing agricultural productivity, workers (a) crowded into urban slums. NO ERR 4. Malthus, Ricardo, Marx, and (a) many others had been talking about inequalities for decades without citing any sources (b) whatsoever or any methods for (c) comparison NO ERROR one era with (a) another. 5. The religious differences between Europe and the United States are (a) typically described in terms of (b) beliefs and practices: Europeans are (c) far less likely than Americans (a) join and attend houses of worship or to believe in heaven and hell. NO ERROR

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