コーシーシュワルツの不等式の一般化したもの？の証明がわかりません

2,…, [2] (1) 右辺を展開すると, a,b,' (i = 1, 2,...,n;j= 1, 2,......,n)の和にな るから, してもよい。 (a'+and+....+α)(b^2+b2++6円) n 2 n i++ =Σa²b²+Σa²b² +Σab² = Σab²+(ab²+a‚²³b;²) i=1 i<j i>j i=1 i<j ただし, Σa' by は 1≤i<j≤nなる整数 i, j に対する a'b の総和を表すもの 2 2 i<j 04 とする. Σaby も同様. +do i>j n Apdo (2)(a,b) i=1 (a,b,+azbz+…+a)(b)+2 Σ (a,b) (ajb;) i<j .. 右辺一左辺 = Σ (a²b²+a²b² −2a,b,a,b) = Σ (a,b,a,b,)² ≥ 0 (ab+ab-2a,b;a;b;) ≥0 ∴. 左辺 ≦ 右辺 i<j i<j (注1) この不等式はコーシー・シュワルツの不等式と呼ばれる (注2) 等号成立の条件は aibj = a,b, (1≦i<j≦n) であるが,これは, b a1 a2 = = b₁ b2 an bn と書ける(ただし, 分母子の一方が0のときは他方も0とする.) 2 (2) A = R= [SPORT]

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DIALOG 引き続きエイミーと拓が話しています。OR A: Amy T: Taku T: What sport did you play in your country? A: I played tennis in Australia. T: Oh, did you? Were the practices hard? A: Not at all! I enjoyed it very much with my friends. 拓 エイミーは母国で どんなスポーツをしていたの? エイミー: オーストラリアでは テニスをしていたよ。 拓: そうなんだ。 練習は厳しかったの? エイミー: 全然! 友だちと 楽しんでやっていたわ。 Less が聞こえました。 場合には, be動 1.I used 2. A long time ago, people 昔, 人々は羽根をペンとして使っていました。 3. There Were many people in the park yesterday. 昨日公園には多くの人がいました。 be / meet / use EXERCISES ① もっとも適する語を下から選び、形を変えて空所に入れましょう。 met Tomoko at the station this morning. 私は今朝、駅で智子に会いました。 (Hints 否定文、疑問文の作り方 ● be動詞 I was not hungry. Were you hungry? ●一般動詞 I didn't play soccer. Ryo didn't like math. Did you play soccer? Did Ryo like math? feathers as pens. wol 2 日本語の意味に合うように,( )内の語句を並べかえましょう。 nada pad cold last Weer した。 縄を訪れました。 1. John (bad / a / cold / had / last week), but he's well now. ジョンは先週ひどい風邪をひいていましたが, 今はよくなっています。 2. My mother (books/me/read/to) in bed when I was a child. me read books to 私が子どものとき, 母はベッドで読み聞かせをしてくれました。 buta 3. After the long rain, ( there / rise/a/was) in the price of vegetables. there was a rise 長雨のあと, 野菜の値段が上がりました。 3 右の絵を見て、空所に入る語を考えましょう。 In Columbus' days, people believed that Vivian du the earth was flat. Hint 昔, 地球は平らだったと考えられていました。 D 中学校時代の部活動について, 発表しましょう。 ▶ Useful Words & Expressions p.78-A PERFORM loem b 003 Inom oble 例 I was a member of the basketball team when I was a junior high school student. The practices were so hard, but I tried my best. I had a good time with my teammates.

「」の部分の文の構成がわかりません。 このthatはNew York. までの関係代名詞ですか？

101) The Fun of the Hunt Fox hunting is a well-known sport typically associated with England A group of people on horseback follow dogs called foxhounds that chase a fox and sometimes kill it. Supporters of fox hunting say that it helps control fox populations. Many other people, however, say that the sport is cruel. This feeling ( 4 ) fox hunting in the United Kingdom in 2004. A kinder but similar sport that has become popular as far away as New York is called beagling. Beagling utilizes beagles* instead of foxhounds, the people taking part do not ride on horseback, and the dogs chase rabbits more often than foxes. The events rarely end in the catching of a rabbit, let alone the killing of one. ( 5 ), the game is over as soon as the rabbit disappears into a hole in the ground. Beagling participants range from the very young, who are simply attempting to learn to manage the dogs, to former fox hunters who are too old to ride horseback. They all enjoy dressing up in old English

当てはまらないもの、あるいは、全て当てはまるかを選択する難しい問題です😥 わかる方教えて欲しいです🙏

The old bridge, ( ) for more than a century, is now being considered for preservation as a cultural landmark. A which has supported local transportation B which has been admired by many travelers C which was built using traditional methods D which is planning to renovate itself soon E ALL CORRECT

Basketball is the most interesting of all sports.をBasketball is the most interesting sports of all ．にしたんですが、意味は変わりますか？正解になりますか?

訳を教えてください

Whoever 2 You may go ((3) However goes abroad must carry a passport. wherever) you want to go, but come back by seven. far my dog wanders, he is sure to come home. my 歩き回る (4) (Whatever) reasons you may have, you must not use violence. 暴力

英作文の問題です。添削お願いします!

5 I like playing sports. I have two reasons. First, I can play sports with my friends and family. Second, I can exciting. I my play it outside. It is

数を聞く問題で、答え方がこれと、もうひとつあるらしいのですが、なにか教えて欲しいです🙇‍♀️③

40c (青森) 73 次の英文はケンタ (Kenta)のスピーチである。これを読んで、あとの質問に英語で答えなさい。 I get up at six thirty and have breakfast every morning. But a week ago, I got up at seven forty because I finished my homework and went to bed very late. I didn't have time to have breakfast and came to school without it I was hungry during class and became *sleepy in the morning. I usually play volleyball well in *PE but I couldn't play it well that day. I thought having breakfast was very important, so I asked my *classmates some questions about breakfast. There are forty students in our class. Thirty-six classmates had breakfast. Three of them had only milk for breakfast. Two of them had *snacks for breakfast. There four classmates who didn't have breakfast. They felt bad and tired. were When we have breakfast, we can study harder and play sports better at school. Let's have it every morning and enjoy our school lives. 〔注〕 sleepy : 眠い PE: # classmate(s): 1 What time does Kenta get up every morning? He gets up at six thirty. Diag 2 Why was Kenta hungry during class? snacks: Because he didn't have time to have breakfast to school without it. 3 How many students are there in Kenta's class? There are forty students in his class TO and Came

これの解答例おしえていただきたいです🙇‍♀️

A: I seé: We'll get the red one. エ 9 次の英文は、あなたと留学生のブライアン (Brian) との対話です。 これを読んで,あとの(1), (2)の問いに答えなさい。 あなた: I went to Tokyo last month. Brian: That's good. Tokyo is the capital of Japan, right? あなた : Yes, it is. My aunt lives there and I sometimes visit her. Brian : Do you want to live in Tokyo in the future? あなた : ① Brian : Why do you think so? あなた : (I) 質問に対する答えとなるように,文中の ①に入る適当な英語を, 3語以上で書きなさい。 (3点) (2)質問に対する答えとなるように、文中の②に入る適当な英語を,8語以上で書きなさい。 ただし,文の数は1文または2文で書きなさい。 (4点)

この問題の回答で Yes,I do.It is good for them to play overseas.If they play abroad,they get a lot of money.Playing abroad makes them strong.Many... Read More

4 次の英文を読んで,下線部の質問に対するあなたの考えを,その理由が伝わるように,〔記入上の 注意〕に従って 40語以上 50語程度の英語で書きなさい。(10点) Today, many professional Japanese athletes play overseas. And some of them are achieving agreat success in various sports. Do you think that in the future, more and more professional Japanese athletes will play overseas?