解いたけど、答えが分からないので教えてください🙇‍♀️ よろしくお願いします！

A 次の問1~5の英文の空所に入れるのに最も適当なものを,それぞれ下の1~4のうち から一つずつ選び, 番号で答えよ｡ 1 When I found out Ken could not come, I ( 1 had been waiting 2 3 waited 4 2 We() his violin performance that day. 1 satisfied 2 3 4 were satisfied 3 "Hurry up! We'll be late for the movie." "All right, how ( ) will it start?" 1 fast 2, long ) for him for over an hour. have been waiting was waiting satisfied with were satisfied with 2 Both 3 quickly 4 4 This new computer will ( ) you to check the data more easily. 1 enable 2 let 3 manage 4 take soon 5 () of the three participants in the speech contest from this school is likely to win a medal. 1 All 3 Each 4 Every

解答1の四角で囲んだ部分についてなのですが、なぜnは4以上の時になるのですか？ どなたかお願いします🙏

考え方 296 漸化式 an+1=f(n)・an =1,(n+3)an+1=nan で定義される数列{an}の一般項 αn を求めよ. 解答1 漸化式は an+1= 4 an+1=f(n)an となる. ここで, これをくり返すと, 解答 2 漸化式の両辺に(n+2)(n+1)を掛けると, (n+3)(n+2)(n+1)an+1=(n+2)(n+1)nan DOD bn=(n+2)(n+1) nan とおくと, この式はbn+1=0となる. 解答1 漸化式を変形して, このとき an= n n+gan と変形できて,f(n)=+3 とおくと, An+1=f(n)an=f(n){ƒ(n−1)an_1}=ƒ(n)ƒ(n − 1){ƒ(n−2)an-2} an+1=f(n)f(n-1) f(n-2)......f(1)a1 az= よって, an+1= n+2n+1 3 1 1+3a1² n n+3a 50=1/11 2 a3= 2+3 92= 4 のとき, ① をくり返し用いると, n-1.n-2.n-3.n-4 -an 2 2+3 1+391 10 2 ··1= n+2n+1n この式はn=1,2,3のときも成り立つ. よって, an= ・① 4321 n_n-1 F7654 6 n(n+1)(n+2) n(n+1)(n+2) SOURON 解答2 漸化式の両辺に(n+2) (n+1)を掛けると, (n+3)(n+2)(n+1)an+1=(n+2)(n+1) ここで,b=(1+2)(1+1) 16 より 16 bn=(n+2)(n+1) nan であるから, (n+2)(n+1)nan=6 -a an I and *** n-1 n+2 a₁=1 n-1n-2 n+2n+1 -an-1 nan REAVES (1) x(n+1) an+1 bn=(n+2)(n+1) nan とおくと, ② は bn+1=bn となり, =(n+2)(n+1)nan これはすべての自然数nに対して成り立つ. したがって, bn=bn-1=bn-2=......=b1 a=1 (n+3)(n+2) -an-2 6 an=n(n+1)(n+2) Testo At **R*12*10 (282,4)

高校生英語です。 ビジョンクエストとtry it out Lesson7がわからないので教えてください。

Try it out 1 Which word fits best? 1. (Encouraged / Encouraging ) by an American teacher, I applied to a college in the U.S. 2. ( Talk / Talking) with the international student, I found myself enjoying speaking English. 3. (Whether / Although) the pronunciation of the word was difficult, I made myself understood. 4. He was proud (to / that ) win the speech contest held last week. 5. ( Unfortunate / Unfortunately ), our group lost the debate about how to protect minority languages. 6. He was reading a newspaper with his legs ( crossing / crossed ). Lesson 7

3番の答えが×なのですが、どこが間違えているのかがよくわかりません😭どなたか教えて頂けませんか？

2. Kate runs the fastest in all the students. 3. She is one of the most famous actor in the world. 4. Tone River is the second longer river in Japan

黄色線の部分の構造について教えてください。

℗ Almost 2,000 times more particle pollution is produced by *tyre wear than is pumped out of the exhausts of modern cars, tests have shown. The tyre particles pollute air, SJE water and soil and contain a wide range of toxic organic compounds, including known carcinogens, the analysts say, suggesting tyre pollution could rapidly become a major issue for regulators. 60 2 Air pollution causes millions of early deaths a year globally. The requirement for better filters has meant particle emissions from tailpipes in developed countries are now much lower in new cars, with those in Europe far below the legal limit. However, the increasing weight of cars means more particles are being thrown off by tyres as they wear on the road. The tests also revealed that tyres produce more than one trillion ultrafine particles for each *kilometre driven, meaning particles smaller than 23 *nanometres. These are also emitted from exhausts and are (2 ) special concern to health professionals, as their size means they can enter organs via the bloodstream. Particles below 23 nm are hard to measure and are not currently regulated in either the EU or US.

青印以降の構造が分からないです。どこがどこにかかっている(修飾されている)などを教えて頂きたいです。また、元の文に戻すとどうなりますか？？(カンマの挿入があるのでカンマを使わずに表した時にどうなるか知りたいです。)

Raks 1 Almost 2,000 times more particle pollution is produced by *tyre wear than is pumped out of the exhausts of modern cars, tests have shown. The tyre particles pollute air, water and soil and contain a wide range of toxic organic compounds, including known carcinogens, the analysts say, suggesting tyre pollution could rapidly become a major issue for regulators.

一文目の構造が分からないです。接続語が無いのに急に「,tests have shown.」と来てるのは何故ですか？

℗ Almost 2,000 times more particle pollution is produced by *tyre wear than is pumped out of the exhausts of modern cars, tests have shown. The tyre particles pollute air, UPNO MESSAGS water and soil and contain a wide range of toxic organic compounds, including known carcinogens, the analysts say, suggesting tyre pollution could rapidly become a major issue for regulators.

動名詞について質問です🙌🏻 ①Don’t worry about making mistakes. ②After the test, he left the classroom saying a word. この場合前置詞はあるでしょうか？ もしあるとしたら是非何が前置詞か... Read More

比較の問題です。 あっているか確認して頂きたいです。

SIS A 15 日本文の意味に合うように[ ]内の語句を並べかえなさい. (1)彼らはその子の治療のためにできるだけ多くのお金を集めた. 本星 1854 825.4 They raised [as, as, for, money, much, possible ] the child's 1 treatment. They raised · the child's treatment. (2) 小包は重ければ重いほど, 送るのにお金がかかる. vitaimado wom! siriqo2 The heavier the package is, [ it, more, is, expensive, the ] to send. The heavier the package is, the more expensive it is to send. (D) 20 much money as possible for (3) いたずらっぽいところはあるが,やはりリンは弟のことが好きだ. (3) p.267 (参考) edway to (bed) el nbdome f 「~だがやはり･･･・」 This naughtiness | Lin loves her brother [ the for, less, his naughtiness, none ]. (0) word 9d2 (a) Lin loves her brother hone the less for h (4) この公園は東京ドーム 40個分の広さだ。さ (5) (1) p.265 「できるだけ」 文 (4) 参 p.256 1 This park is [as, as, forty, large, times ] Tokyo Dome.med edT (1) だ」 This park is forty times as large as ti tialvy Tokyo Dome. Artilsup ai ano tsd (olnard) insqua ai notuqmos au (S) (2) p.266 ｢~すればするほど･･ (土) 日本文の意味に合うように英文を完成させなさい [list (19llet ori) ai roid W (2) (1) 彼は真面目なので、いっそう援助してあげたい。 L Ⅰ would like to help him all theml is earnest. (2) その作家は一生のうちに300冊もの本を書いた. aas 400) The writer wrote no less then three hundred books in his life. TEJV10AS somn testent sdi ei osM he more because Yasm) sved I (a) NGENASEBESS) ( 文本日 Sott (2) p. 268 LA(s) (3) その自転車は私が思っていたほど値段が高くなかった. 「AはBのX 1830 That bicycle was less expensive than I thought JPG 882.4 (2) ) bas ( asgal gabieiv is arehwot ** (s) aoqmi stom ei Plimns (3) p.258 注意 2. £ (€) (1) p.267 FOR COMMUNICAT salot hean faoyuoy 各対話文の( )に入る最も適当な語句をa~dから選びなさい. (1) A:How far is it from here to the bus stop?同志社 B: It is not far away it will take ( 1shlo) than fifteen minutes to get there.not ) stand red ned 19blo ai nave (5) a. few S b. little ob ano yino C. lessa-T aid) Ingued. more (2) AI hear that Tom is a great reader.) mt fide T eiry idgund Ⅰ B: Yes, he has read (ons) more books than I have, lidi H (E) a. much auoisenb. many ) ai ( c. a lot of isdi alaid. plenty of

VisionQuestの問題です お時間があれば日本語訳もお願いしたいです🙇‍♀️

Try it out! Thi 1 ( 内から適切な語を選んで、文を完成させましょう。 1. (Encouraged / Encouraging) by our teacher, I applied to a college in the U.S. 2. She has never been to Japan, but she speaks Japanese (fluent / fluently). 3. (Talk/Talking) with the international student, I found myself enjoying speaking English. 4. (Whether / Although) the exam was difficult, I did well on it. 5. He was proud (to / that) win the speech contest held last week. 6. (Unfortunate / Unfortunately ), our group lost the debate. 7. He was reading a newspaper with his legs ( crossing / crossed ).