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Mathematics Senior High

(2)どうしてa-bに置き換えて証明できるのかわかりません 教えてください🙇‍♀️

不等式の証明 (絶対値と不等式) 本 例題 29 次の不等式を証明せよ。 (1) |a+b|≤|a|+|b| CHART & THINKING 似た問題 1 結果を使う (1) 絶対値を含むので、このままでは差をとって考えにくい。 |A=A2 を利用すると,絶 対値の処理が容易になる。 よって, 平方の差を作ればよい。 (2) |a|-|6|≦|a-bl 2 方法をまねる (2) 証明したい不等式の左辺は負の場合もあるから,平方の差を作る方針は手間がかかり そうである (別解 参照)。 そこで, 不等式を変形すると |a|≦la-61+16 ← (1) と似た形になることに着目。 ① の方針で考えられそうだが,どのように文字をおき換えると (1) を利用できるだろうか? 解答 (1) (|a|+|6|-|a+b=(|a|+2|a||3|+|6)-(a+b)² =2(|abl-ab)≧0 =a²+2|ab|+62-(a²+2ab+b2) よって ...... よって la+b≤(al+|b|) ² |a+b≧0,|a|+|6|≧0であるから |a+6|≦|a|+|6| 別解 demo da -10|≧0≦|6| であるから lal≦a≦lal, 辺々を加えて -(al+161)≦a+b≧|a|+|6| |a|+|6|≧0であるから la +6|≦|a|+|6| (2) (1) の不等式の文字αを a-b におき換えて |(a−b)+b|≤la-b|+|b| p.42 基本事項 4. 基本 28 よって |a|sla-61+101 ゆえに |a|-|6|≦la-6| 別解 [1] [a|-|6|<0 すなわち |a|<|6| のとき ④の等号が成り立=2(−ab+lab)≧0 (|a|-|6|)2≦|a-6|2 4+ |a|-16|≧0,|a-b≧0であるから |a|-|b|≤la-bl inf. A≧0 のとき (1) |-|A|≦A=|A| 0 |-|A|=A<|A| であるから,一般に |-|A|A|A| 51 更に,これから |AI-A≧0,|A|+A≧0 30 1= x≤-c, c≤x |x|c 1章 c≧0 のとき -c≤x≤c |x|≤c ←②の方針 |a|-|6|が負 (左辺) <0, (右辺) > 0 であるから不等式は成り立つ。 の場合も考えられるの [2] |a|-|6|≧0 すなわち |a|≧|6|のときで,平方の差を作るには 場合分けが必要。 la-bl²-(lal-1b)²=(a−b)²(a²-2|ab|+6²) inf. 等号成立条件 (1) は(*)から, labl=a 4 等 すなわち, ab≧0のとき よって, (2) は (a-66 ゆえに (a-b≧0かつ または (a-b≦0かつb すなわち ab≧0 まな a≦b≧0のとき。

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English Senior High

空所2に入るものを選べ。 1.important 2.interesting 3.active 4.ambitious 答えは3なのですが、何故ですか? importantはダメですか?

If you are asked why you study, your obvious answer is that your studies will be useful because you will profit by the knowledge and the work habits that you acquire. You will apply the things you learn, not merely in making a success of your vocation, but also in all your thinking, talking, and writing, and in conduct of the most varied sorts. When you think through new problems or draw new conclusions, you are using your knowledge. ( 1).(when you give advice or information to or discuss issues with your friends and when you write, plan, or take action in social and political affairs in everything you do -you are using your knowledge. The one great aim of all your study is increased efficiency of thought and action through putting your knowledge and skill to use. Using knowledge is not only the aim of your studying; it is the very essence of the study process. Knowledge is not something that you can absorb and hold for later use. Knowledge is acquired only through thinking and doing. The material in books becomes part of your mental equipment only when you succeed in tying it to the rest of your knowledge and use your ideas in relation to one another. The common saying "We learn through doing" says it all. Learning is an (2) process. In order to acquire new ideas, you must react to them, put them to use, talk and write about them, and act upon them.

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English Senior High

4の解き方がわかりません。 例えば(a)で、続く文であくびを謝っていることも全て把握した上で、挨拶なのでpolitelyかと考えたのですが、なぜ誤りなのか教えていただきたいです。

13 Lucy is a British schoolgirl who lives in Oxford. She is talking to her father, Fred, in the kitchen of their home. Read the conversation below and answer the following questions. Lucy: (a) Good morning, Dad. Oh, sorry for yawning. What are you doing with that microwave oven? It looks heavy. Do you need a hand with moving it? Fred: I think I'll be OK, Lucy. I'm just going to put it in the car and take it to the city dump. Lucy: Couldn't you send it away to be repaired? Fred: It's ten years old and well out of warranty now, so I very much doubt that the manufacturer would do it. They probably don't even carry the spare parts anymore. Lucy: That's a shame. Oh, I know what! Why not take it to the Repair Café near my school? Fred: What's that? I've never heard of it. Lucy: It's brilliant! We visited it as part of our environmental science course recently. It's a meeting place where people can get together to mend broken items cooperatively. And have a chat and a cup of coffee! Fred: I'm all ears. Tell me more. Lucy: Well, the first Repair Café was started by a Dutch woman called Martine Postma in Amsterdam in 2009. (1) 彼女は,使い捨て文化で環境が破壊されて, ゴミの量が地球規模で増えることを心配してたん . She wanted to find a local solution to this global problem. Fred: That's what they call "thinking globally, acting locally," isn't it? Lucy: Exactly. She also wanted to address the decline in community spirit amongst urban dwellers and do something about people's loss of practical skills and ingenuity. Fred: And the idea (2) caught on? Lucy: Very much so. The concept has grown into a global movement. The one in Oxford started about four years ago. Fred: Impressive! What kind of things do they repair? Lucy: Oh, all sorts. Electrical appliances, clothes, furniture, crockery, bicycles, and even toys. Fred: How successful are they at repairing things? Lucy: Well, of course, they cannot guarantee to fix every item brought to them, but they have a fairly good success rate. One study found that on average 60 to 70 percent of items were repaired. The rate is higher for some items such as bicycles and clothes but lower for things like laptop computers. Fred: I can understand that. Just between you and me, I think some electronics manufacturers deliberately make products in such a way that you cannot disassemble them and repair them unless you have specialized tools and equipment. Lucy: Yes, and that's where Repair Cafés can help. But these cafés are not just about repairing things for people. They are places where we can meet others, share ideas, and be inspired. The volunteer repairers are very keen to involve the visitors in thinking about the repair and actually carrying out the repair themselves. They also encourage people to think about living together in more sustainable communities. Fred: I suppose you could say they are about repairing our minds, not just our things. Lucy: Quite so, although often the two are very closely related. Many people attach (3)sentimental value to old things that might, for example, be part of their family history. Fred: I see what you mean. It almost sounds too good to be true. (a)Is there a catch? For example, how much does it cost? Lucy: Advice and help from the repairers is free, but people who use the café are invited to make a donation. That money is used to cover the costs involved in running the café. If specific spare parts are needed, the repairers will advise you on how to obtain them. Fred: Well, that's marvelous! (e)Then I'll take this old microwave there. Are they open today? Lucy: Yes, and I'll come with you. I've got a pair of jeans that are badly in need of some attention. QUESTIONS 1. Translate the underlined part after (1) into English. 2. What does the underlined phrase after (2) mean? Select the most appropriate expression from the list below. (A) became popular (B) hit a dead end (C) occurred to you (D) played a significant role (E) worked in practice 3. The underlined phrase after (3) means the value of an object which is derived from personal or emotional association rather than its material worth. Give ONE object that has "sentimental value" for you and explain why it has such value. Your answer should be between 15 and 20 English words in length. (Indicate the number of words you have written at the end of your answer.)

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English Senior High

一枚目の写真で、this coming Sundayとあるんですが、comingの訳が、今度のという意味なので、thisがいらないと思うんですけど、誰かわかりますか? 二枚目、1番のto find は何に修飾しているんですか? to不定詞は、〜するために、の副詞的用法か、... Read More

50 ブスピーカーたちが名詞に対して行う 新婚夫婦のケリーとタクマ。 2人の新居にタクマの両親が訪ねてくることになったようですよ。 Takuma: Kelly, my parents are 'coming over for dinne on Sunday. This coming Sunday? We have to clean up th カ Kelly: Kelly: Japartment. Takuma: I'll help. Let's go shopping tomorrow. What are we going to serve? Kelly: Takuma: I was thinking of Italian food. We need som 2 too much. Takuma: OK. And a few bottles of red wine. 1 I didn't know your parents liked wine. olive oil and onions. Don't put in too much onion. You usually us Kelly: Takuma: They drink wine every weekend. up 日本語訳例 タクマ:ケリー、 僕の両親が日曜日、 一緒に夕食を食べに来るんだ。 ケリー: 今度の日曜日に? アパートをきれいに片づけなくちゃ。 タクマ : 僕も手伝うよ。 明日、買い物に行こう。 全 そ di ケリー: 食事は何を出そうかしら? タクマ: イタリア料理にしようと思っていたんだ。 オリーブオイルとタマネギが必要だね。 ケリー: タマネギをあまりたくさん入れないでね。 あなたはいつも使いすぎるから。 タクマ:わかった。 それから赤ワインを数本。 ケリー: あなたのご両親がワイン好きだったなんて知らなかったわ。 タクマ: 2人は週末になるといつも飲んでいるよ。

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English Senior High

今回の共通テストで、納得いってないんですが、4の答えは④なんですけど、本文を見ていると、どのキャンプコースでも、他の生徒の前で、発表する という趣旨のことが書いていますが、見る側の立場にも立てば、お互いのパフォーマンスにアクセスしてる、という①がバツと言える理由が分かりません

You are a senior high school student interested in improving your English during the summer vacation. You find a website for an intensive English summer camp run by an international school. B GIS Intensive English Summer Camp Galley International School (GIS) has provided intensive English summer camps for senior high school students in Japan since 1989. Spend two weeks in an all-English environment! Dates: August 1-14, 2023 Location: Lake Kawaguchi Youth Lodge, Yamanashi Prefecture Cost: 120,000 yen, including food and accommodation (additional fees for optional activities such as kayaking and canoeing) Courses Offered ng i FOREST: You'll master basic grammar structures, make short speeches on it sdt trods a simple topics, and get pronunciation tips. Your instructors have taught English for over 20 years in several countries. On the final day of the camp, you'll take part in a speech contest while all the other campers listen. MOUNTAIN: You'll work in a group to write and perform a skit in English. Instructors for this course have worked at theater schools in New York City, London, and Sydney. You'll perform your skit for all the campers to enjoy on August 14. SKY: You'll learn debating skills and critical thinking in this course. Your instructors have been to many countries to coach debate teams and some have published best-selling textbooks on the subject. You'll do a short debate in front of all the other campers on the last day. with an advanced level of English will be accepted.) (Note: Only those (2610

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