（2）θとおく、という考えの導き方を教えて欲しいです。 あと、θと置いた時、どうして（2）の解説の3行目のことが言えるか教えて欲しいです。

4/ 無限等比級数の図形への応用 (2)POQ=0 とおくと, (1) より 8 83 zy 平面上に, 2直線 y=xとl:y=2x とがある。 直線上の点P (1,1) を通りに垂 直な直線との交点をQ とし,点Q を通り に垂直な直線との交点をP とする. 以下同様に,上の点P を通りに垂直な 直線との交点をQnとし, Q を通りに垂 Y 12:y=2x ao sin= OP。 √10 √10 (0<<) Ly=x [PQncos0QnP+1 XpPo (1,1) ... 直な直線ととの交点をP+1として,直線上の点Po, Pi, Pz, ・・・お よび直線上の点Qo, Q1, Q2, を定め, PrQn=an (n=0, 1, ...) と おく.このとき,次の問いに答えよ. 10° (1) α を求めよ. なかも (2) an+1 を an で表せ. 次に,∠PQP+1=∠QnPn+1Q+1=0より QP+1 cos 0=Pn+1Qn+1 QnP+1 を消去して Pn+1Qn+1=cos20PQn an+1= cos20.an cos20=1-sin²0=1- an+1= an lim PQ すなわち lim n→∞k=0 だから, YA Q Q Pa Pa+1 1 9 0 = より 10 10 akは、 n→∞k=0 ( (3) lim PkQk * * D L . n→∞k=0 初項 店,公比 あるので 10 -1<- <<1 だから,収束して 10 9 の無限等比級数を表し (46ポイント) 精講 「以下同様に」という文言がポイントです. この文言があるときは、 漸化式をつくることになりますが、 1つだけコツがあります. それ は,初項を求めるための図とは別に, 漸化式をつくるための図をか くことです. 問題文の図を利用して(1)も(2)も解こうとすると,図がゴチャゴチ ャしてわかりにくくなります. 1 1 その和は, =2√5 √5 9 1 10 ポイント 点列ができる図形の問題では、 初項を求めるための図 と漸化式をつくるための図の2つをかく また,(3), limΣの形からもわかる通り、無限級数の和がテーマです. (46 解答 (1) Po(1,1) と直線 2x-y=0 の距離:y=2xc がα だから, 演習問題 47 h:y=x ao Po 1----- |2-1| 1 ao= 5 ことができ √22+(-1)2 (IIB ベク34点と直線の距離) To x 10 点P (n=0, 1, 2, …)をx座標が1/7(a>0)である放物線 y=x2上の点とする. 2点PとP+1 を結ぶ線分と放物線によっ て囲まれる部分の面積を An とするとき, 次の問いに答えよ. (1) A をαで表せ. (2) Anna で表せ. (3) Anaで表せ. n=0

（B）の英文、一回目のhave beenでは 〜された で訳してるけど、２回目の have been では 〜している で訳してるのはなぜですか？ ｢多くの動植物が狩られたり採集されたりしているので、消滅の危機にさらされている種もいる｣と訳したのですがだめですか？🙇‍♂️

2 公 threatening the health of the people who depend on them. So (B) many animals and plants have been hunted or collected that some species have been driven to the point of disappearance. 5

赤線を引いているところがよくわからないのですが、まず、 1、母と議論するのは難しかったとありますが、何についての議論か 2、最後の分の「彼女は首に巻いた〜合図であった」は何を意味しているのでしょうか できれば要約をお願いしたいです🙇

14 第6問 次の文章を読み、下の問いに答えよ。 標準解答時間 9分 depressed. It was not the exam that made her feel that Christine came out of her last examination, feeling way, but the fact that it was the last one; it meant the end of the school year. She dropped in at the coffee 5 as usual, then went home early because there didn't 10 seem to be anything else to do. shop "Is that you, dear?" her mother called from the living room. She must have heard the front door close. Christine went in and sat on the sofa. "How was your exam, dear?" her mother asked. "Fine," said Christine flatly. It had been fine; she had passed. She was not a brilliant student, she knew, but she was hard-working. Her professors always wrote things like "A serious attempt" and "Well thought out but 15 perhaps lacking in energy" on her term papers; they gave her Bs, the occasional B*. She was taking Political Science and Economics, and hoped to get a job with the government after she graduated; with her father's connections she had a good chance. 20 "That's nice." Christine felt, bitterly, that her mother had only a vague idea of what an exam was. She was arranging roses in a vase; she had rubber gloves on to protect her hands as she always did when engaged in what she 25 called 'housework.' As far as Christine could tell, her housework consisted of arranging flowers in vases. Sometimes she cooked elegantly, but she thought of it as a hobby. It was hard, anyway, to argue with her mother. She was so easily upset that it was better to avoid 30 arguing with her.

このthenの使い方間違ってますか？？

V (B I think that food loss. during processing because a lot of food we can eat are wasted A Love dirtyc -1 might happen At the time then -1 out of the food, even if it is a

食品ロスについて私たちができることについての英作文です。添削してください！！😖 I think we can do two things to reduce the amount of food waste. First, we can avoid buying ... 続きを読む

英語が得意な方、この答えを全て教えてください。よろしくお願いします。

2 Word Definitions Match the words with the definitions. 1. favorite ( a C d a stage in the history of a family to say that you will not accept an offer what is left after everything else has gone to have something in your hands or arms liked more than others of the same kind 2. hold ( ) b 3. generation ( ) 4. refuse ( ) 5. rest ( ) e 3 Complete the Sentences Fill in the blanks using the words shown above. color. 1. Orange is my 2. Peter ate the of the pizza. 3. Could you this puppy for me? 4. People of my grandfather's hardworking. are 4 Words in Context Circle the appropriate answer. 1. Bill was named after his father. His father is (also not) called Bill. 2. These pillows were very soft, so I ( had / didn't have) a good sleep. 3. My sister and I hug each other every day. We are (not / very) close. 4. David was popular at school. Everyone (liked / hated) him. 7

分詞について質問です。補語になる分詞と（叙述用法）と教科書に書いてあるのですが、よく意味がわかりません。どなたか教えてくださると嬉しいです。

B 補語になる分詞 (叙述用法) F105 7. The mall will remain closed until Thursday. S V 8. He came running to us. S C (現在分詞) C (過去分詞) 9. She kept me waiting for an hour. V 0 C (現在分詞)* 10. Keep the door locked at night. V O C (過去分詞) →S is CO. The mall is closed. →S is CO. He was running. → O is CO. I was waiting. O is CO. The door is locked. 3 7. remain/stay, keep, look, feel, seem/appear などの補語を伴う自動詞がこの形をとる。 8. come, walk, sit, stand, lie などは 「~しながら」 の意味で分詞を補語として続ける。 9.10.0とC(分詞) の間に, 意味上のSVの関係が成り立つ。 keep, leave, find, want, catch など。

この問題の解き方がわからないので教えてください。

021 Scarcely ( ) in the office knew what they were supposed to do when the alarm went off. 1 everyone (3 anyone (2 no one 4 all of them 1824 <学習院大

写真の問題教えて欲しいです.

Which country did Kate go on vacation? How often does the big mirror appear? 質問1 7 イ Brazil. Bolivia. ウ Peru. It always appears. イ It rarely appears. 3 How was the weather when Kate visited the flat? It never appears. 質問4 ア It was sunny. イ It was rainy. It was cloudy. Was Kate able to see the mirror? Yes, she was. 1 No, she wasn't.

Its appearance is such a huge event that it inspired invasions by William I in 1066 and Genghis Khan in 1222. ハレー彗星の出現は、1066年のウィリアム1世による ... 続きを読む