数２の問題です！ practiceの置き換えをしてとく問題は 置き換えることでどのように証明しているのかを 分かりやすく教えてほしいです！！ よろしくおねがいします！🙇🏻‍♀️՞

本 例題 29 不等式の証明 (絶対値と不等式) 00000 51 次の不等式を証明せよ。 (1)|a+6|≦|a|+|6| (2)|a|-|6|≦|a-bl p.42 基本事項 4. 基本28 1章 CHART & THINKING 似た問題 1 結果を使う ② 方法をまねる TRAH (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=A' 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) 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+10 ← (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? 笑 解答 4 等式・不等式の証明 (1)|a|+|6|2-la+b1=(al+2|a||6|+|6|2)-(a+b)2 よって =a2+2|ab|+b2-(a2+2ab+62) =2(abl-ab)≥0...... (*) la+b=(al+16)2 |a+6|≧0,|a|+|6|≧0 であるから 別解 a+b=al+16 lal≦a≦lal, -660であるから 辺々を加えて -(lal+16)≦a+6≦|a|+|01 |a|+|6|≧0 であるから la+6|≦|a|+|6| (2)(1) 不等式の文字αを a b におき換えて | (a-b)+6|≦la-6|+|6| よって|a|≦la-6|+|6| ゆえに|a|-|6|≦|a-6| (別解 [1] |a|-|6|<0 すなわち |a|<|6|のとき (左辺) < 0, (右辺) > 0 であるから不等式は成り立つ。 [2] |a|-|6|≧0 すなわち a≧6 のとき |a-bp-(|a|-|6|)2=(a-b)2-(a-2|ab|+62) =2(-ab+labl≧0 よって (|a|-161)2≦|a-62 |a|-|6|≧0,|a-b≧0 であるから |a|-|6|≦|a-6| in A≧0 のとき -|A|≦A=|A| A<0 のとき -|A|=A<|A| であるから, 一般に -|A|≦A≦|A| 更に、これから JAI-AO |A|+A≧0 c≧0 のとき cxclxlsc x≤-c, c≤x xc ←②の方針。 |a|-|6|が負 の場合も考えられるの で, 平方の差を作るには 場合分けが必要。 inf. 等号成立条件 (1) は (*) から, lab=ab, すなわち, ab≧0 のとき。 よって, (2) は (a-b)6≧0 ゆえに (a-b≧0 かつ 6≧0) または (a-b≦0 かつ b≦0) すなわち ab≧0 または a≦b≦0 のとき。 PRACTICE 29 2 不等式 |a+6|≦|a|+|6| を利用して,次の不等式を証明せよ。 (1)|a-6|≦|a|+|6| (3)|a+b+cl≦|a|+|6|+|c| (2)|a-cl≦|a-6|+|6-c|

黄色のラインを引いたところなのですが、なぜこのようになるのかが分かりません💦

=(x+1)(x−1}\x˜+2) (3) 4a4-17a2b²+4b4=4(a²)2-17a2b2+4(62) 2 =(a²-4b²)(4a²-6²) =(a+2b)(a-2b)(2a+b)(2a-b) PRACTICE 13Ⓡ 切手の

2行目のallowはどういった使い方でしょうか...?allow A BでAをBに割り当てるという使い方と考えれば良いでしょうか...？

M The old must place their wisdom and experience at the service of 10 the young, yet allow the vitality, energy and enthusiasm of youth freedom of scope, while the young must respect and honor the achievements and practical sense of their elders and place their physical strength and vigor, while they still possess them, at the service of the continuing community.

写真 2枚目の３パラグラフ目の棒線部についてです。 和訳と照らし合わせたところ、 吐く　 というのが cought upの意味だと思い、調べてみましたが、出ませんでした 。そのような意味はcought upにあるんでしょうか？

erlode aids (0 英文を読み、下記の問いに答えなさい。 For most prey, ( 14 ) is over once they've been swallowed. But one species of beetle can escape from a toad's stomach nearly two hours after being eaten, according to a new study. Found in wooded areas on nearly every continent, bombardier beetles - a group that consists of more than 500 species - get their name from their signature defense mechanism: When threatened, they shoot a hot chemical spray from their rear end. In Japan, the insects have long been known as "the farting bug." Toads have been observed vomiting bombardier beetles after eating them, but no one knew exactly why, or ( 15 ) the beetles survived after their brush with digestion. あわや? bine To better understand the beetle's defenses, two biologists from Kobe University fed a species of bombardier beetle to two different species of toad collected from forests in central Japan. One toad species shared its natural habitat with that particular species of beetle, while the other was unlikely to encounter it in the wild. (16) After the beetles were swallowed, a small explosion could be heard inside each toad, indicating that the insects were firing their defenses. Overall, 43 percent of the toads vomited the beetles, taking anywhere

写真1枚目の 3 パラグラフめについてです。 棒線部のところの和訳が、 その甲虫が あわや消化されそうになった と書いてありますが、どこからあわやという表現が出たのか 、そして該当する英文中のbrush とらなんのことなんでしょうか？

英文を読み, 下記の問いに答えなさい。 For most prey, ( 14 ) is over once they've been swallowed. But one species of beetle can escape from a toad's stomach nearly two hours after being eaten, according to a new study. Found in wooded areas on nearly every continent, bombardier beetles - a group that consists of more than 500 species- get their name from their signature defense mechanism: When threatened, they shoot a hot chemical spray from their rear end. In Japan, the insects have long been known as "the farting bug." Toads have been observed vomiting bombardier beetles after eating them, but no one knew exactly why, or ( 15 ) the beetles survived after their brush with digestion. ? To better understand the beetle's defenses, two biologists from Kobe University fed a species of bombardier beetle to two different species of toad collected from forests in central Japan. One toad species shared its natural habitat with that particular species of beetle, while the other was unlikely to encounter it in the wild. (16) After the beetles were swallowed, a small explosion could be heard inside each toad, indicating that the insects were firing their defenses. Overall, 43 percent of the toads vomited the beetles, taking anywhere

英作文の添削をお願いします！！ 字数数える関係で改行見ずらいです申し訳ないですm(_ _)m

TOPIC Is it beneficial for workers to change jobs often? POINTS .Career goals •Motivation EAM G . The economy bdtog of pandai baidliw 2 I abind or aworul vised sil2. I •Working conditions odebris dogmoun d be mo

問6の答えを教えてください、、。お願いします🙇‍♀️🙇‍♀️

26 Unit 4 長文問題≫ もしも時間を戻せたら? ) able to change the past? If you 1 Do you ever wish you (1)( had (2) that ability, maybe you would spend more time practicing soccer, learn the instrument that you always wanted to play, study harder for that big test, or try to save more money for the future. 2 What would you do if you had the ability to turn back the clock? This was a question which Mr. Woodall, a high school teacher in Philadelphia, asked his students. Mr. Woodall wanted to know what was important to his students but was pleasantly surprised to see the results. I think their answers will be very interesting to you, too. 3 which were connected to Mr. Woodall expected to see answers (v)) the own good of the students, but (3) he was wrong. The majority of the which he received from his students were for the good of answers (5) others. 4 A very common answer he found was, "If I could turn back the clock, I would take back some things that I said to a friend." Apparently, many of the students regretted saying something (5)( ) hurt their friends and wanted to change that. Surprisingly, close to 40% of the students answered this way. 5 Another common answer was about pets. "(6) If I were able to turn back the clock, I would spend more time with my dog," or "(I would be nicer to my cat," were some common answers. Almost 25% of the students missed their pet very much and wanted to show more love. These pets included dogs, cats, birds, rabbits and other animals. 6 There were other answers about reading more books, studying harder, or eating less junk food. However, Mr. Woodall was quite impressed with his students and their concern for others. He decided to share all of the answers with his students, and the students enjoyed hearing the different answers. Mr. Woodall decided to try this activity with his students every year. By asking, he felt he would learn a lot about his students. Target ①関係代名詞 ②仮定法・間接疑問 turn back (時計を) 巻き戻す 問1 (1) (C pleasantly 心地よく good 問2 問3 い。 問 expected to 〜するだろうと思う majority t F (4 take back 取り消す apparently どうやら~らしい close to ~近く be nice to 〜にやさしい junk food ジャンクフード concern for 〜への気遣い、配慮

Learning English can be challenging, but the more you practice, the better you'll become. この文章中のbutの働きがわからなくて全体の訳し方がわかりません。解説お願いします。🙇

3️⃣の（5）を教えて欲しいです🙇‍♀️

33 次の文を( )内の指示にしたがって書きかえなさい。 □ (1) Kana writes an e-mail. (「･･･しています」 という現在進行形の文に □(2) Ryoma practiced the piano yesterday. (否定文に) □(3) You are a baseball fan. (疑問文にかえて, No で答える文も) □(4) My brother has a guitar. (否定文に) 680 of now I new nombr □(5) Kota was cooking lunch. (下線部をたずねる疑問文に)

an+1とanと2nがそれぞれ表しているものを教えてください

化式 日本 例題 35 図形と漸化式(1) 「平面上にn個の円があって, それらのどの2個の円も互いに交わり,3個以 00000 上の円は同一の点では交わらない。 これらの円は平面をいくつの部分に分け るか。 CHART L & THINKING 漸化式を作成し、解く問題 (求める個数を αとする) 1a1, a2, a3, an とan+1 ･･を調べる(具体例で考える) の関係を考える (漸化式を作成) 1 まず, n=1, 2, 3 の場合について図をかくと、下のようになる。 この図を参考に、 平面の部分は何個増加するだろうか? n=1 基本 29 との式で表した漸化式を作ろう。 円を1個追加すると n=3 n=2 e ⑤ ⑥ ① ② ④ ③ 平面の部分は+2. (交点も+2) 平面の部分は +4 (交点も+4) 一答 AGA カ個の円によって平面が αn 個に分けられるとすると=2 分割された弧の数と同じだ ④ 平面上に条件を満たすn個の円があるとき,更に、条件を満け平面の部分が増える。 たす円を1個追加すると, n個の円とおのおの2点で交わる から交点が2n個できる。 この2n個の交点で, 追加した円 が 2n個の弧に分割される。 これらの弧によって, その弧が 含まれる平面の部分が2分割されるから,平面の部分は 2n 個だけ増加する。元や平面 ① 3 ② 0 ●よって +2n ゆえに an+1-an=2n よって,n≧2 のとき n-1 an=art 2k=2+2.12 (n-1)n=n-n+2 階差数列の一般項が2n k=1 =2であるから,この式は n=1のときにも成り立つ。 したがって, n個の円は平面を (n-n+2) 個の部分に分ける。 | n=1 とすると 12-1+2=2 PRACTICE 35 2 とする。 平面上にn個の円があって, それらのどの2個の円も互いに交わり, 3個以上の円は同一の点では交わらない。これらの円によって, 交点はいくつできる 3