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Mathematics Senior High

同じ文字の置き換えの問題です チャートの方は最後xの値まで求めていますが 文系の数学の方は最小値のみです xの値を求めるか求めないかの違い、見極め方を教えてください

10 置きかえの利用 MXFORES x が実数全体を変化するとき 関数y=(x2-2x)2 +4 (x2-2x) の最小値 を求めよ. (北海道工業大) [解答] y=(x2-2x)2+4(x2-2x) x2-2x=t とおくと、①より y=t² +4t =(t+2)2-4 ここで,t=x2-2xより, ...2 t=(x-1)2-1 となるから、 xが実数全体を変化するとき, tの範囲は t≧-1 である. t≧-1 において② のグラフは右のようになるから, t=-1のときにy は最小となり, 最小値は, (-1)²+4(-1)=-3 文系 数学の必勝ポイント・ JURN 0 FX 1 -2-1 t=x2xのとき t≧-1である ことがグラフから分かる 2次関数 t=x2-2x yy=(t+2)²-4 置きかえの注意 置きかえをしたら, 新しい文字のとり得る範囲を確認する 0 -3 -4 解説講義 関数を扱うときに,置きかえはよく行われる操作である. 本間は置きかえをするときの注 意事項を確認する問題である. ②のグラフの頂点に注目して 「最小値は-4」 と間違えた人 はいないだろうか? HANDS yはxを変数として①の式で定められている. ①をそのまま扱おうとすると4次関数になっ てしまうので, x2-2xが2ヶ所にあることに注目し, x2-2x=t と置きかえてyをtの2次関 9 で勉強したように、 関数の最大最小 数として扱う.しかし, ここに落とし穴がある! は 「正しい範囲で正しい関数を分析」 しなければならない.tの2次関数として扱うのであ れば、「正しいもの範囲』で②の関数を分析する必要がある. 問題文にはすべての実数をとっ て変化すると書いてあるが,tのとり得る範囲は書かれていない. したがって, t=(x-1)²-1 と変形してものとり得る範囲が≧-1 であることを求めて, この範囲で ② の関数の最小値を 求めなければならない. 式を見やすくしたりするために安易に置きかえを行うと痛い目にあう. 「置きかえをした ら、新しい文字のとり得る範囲を確認する」ということをつねに注意するようにしよう. -t 19

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English Senior High

九州大学英語2019年の英作文の添削をお願いします🙇‍♀️ 大問4が要約と英作文、5が和文英訳です!🙇‍♀️🙇‍♀️🙇‍♀️

〔4〕 九州大-理系前期 Read the following newspaper article and follow the instructions below. (36) 16 2019年度 英語 in Engligi taul" According to the Kanagawa Prefectural Police Station, a 20-year-old female university student caused a traffic death. The student was riding on a power- She moved off from an assisted bicycle when the accident happened. intersection and started riding on the sidewalk. At that moment, a 77-year-old lady was walking on the sidewalk and moved toward the bicyclist. The student hit the lady. The collision caused the lady to fall and strike her head. She was transported to hospital, but died of her injuries two days later. At the time of the incident, the student was apparently holding a smartphone in her left hand and a drink in her right while steering the power- assisted bike. Moreover, she had an earphone in her left ear. Therefore, police arrested the student for breaking the new law and riding recklessly. Police are investigating whether the student noticed that the old lady was walking toward her. They suspect that she was not paying sufficient attention because she was operating her smartphone right up until the collision. Her court appearance date has not been decided yet. The Mainichi, December 16, 2017 Instructions: Write two well-developed paragraphs in English. In the first paragraph, summarize the main points of the newspaper article above in lo approximately 100 words. Use different vocabulary and sentence structure from the original passage as much as possible. In the second paragraph, write your opinion about what should be done to reduce accidents like this in approximately 50 words. hosidinlong unich lor, condadnoah

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English Senior High

九州大学英語2019年の英作文の添削をお願いします🙇‍♀️ 大問4が要約と英作文、5が和文英訳です!🙇‍♀️🙇‍♀️🙇‍♀️

〔4〕 九州大-理系前期 Read the following newspaper article and follow the instructions below. (36) 16 2019年度 英語 in Engligi taul" According to the Kanagawa Prefectural Police Station, a 20-year-old female university student caused a traffic death. The student was riding on a power- She moved off from an assisted bicycle when the accident happened. intersection and started riding on the sidewalk. At that moment, a 77-year-old lady was walking on the sidewalk and moved toward the bicyclist. The student hit the lady. The collision caused the lady to fall and strike her head. She was transported to hospital, but died of her injuries two days later. At the time of the incident, the student was apparently holding a smartphone in her left hand and a drink in her right while steering the power- assisted bike. Moreover, she had an earphone in her left ear. Therefore, police arrested the student for breaking the new law and riding recklessly. Police are investigating whether the student noticed that the old lady was walking toward her. They suspect that she was not paying sufficient attention because she was operating her smartphone right up until the collision. Her court appearance date has not been decided yet. The Mainichi, December 16, 2017 Instructions: Write two well-developed paragraphs in English. In the first paragraph, summarize the main points of the newspaper article above in lo approximately 100 words. Use different vocabulary and sentence structure from the original passage as much as possible. In the second paragraph, write your opinion about what should be done to reduce accidents like this in approximately 50 words. hosidinlong unich lor, condadnoah

Solved Answers: 1
English Senior High

2を教えてほしいです💦お願いします🙇

英語 ( 70分) 1 次の文章を読んで 1~7の問いに英語で答えなさい。 It's Christmas Eve, December 24, 1914. The night is clear and cold/ Moonlight illuminates the snow/covered land separating the British and German trenches outside a small town in northern France. British military command feeling nervous sends a message to the front lines: it is thought possible the enemy may attack during Christmas or New Year. Extra caution will be maintained during this period. The military command has no idea what's really about to happen. Around seven for eight in the evening/ British soldier Albert Moren blinks in disbelief What's that on the other side? Lights flicker on./ one by one. Lanterns. he sees, and torches, and... Christmas trees? /"Stille Nacht, That's when he hears it - soldiers singing in German/" heilige Nacht." Never before had the Christmas music sounded so beautiful. I shall never forget it," Moren says later. It was one of the highlights of my life. Then, in response, the British soldiers start singing The First Noel." The Germans applaud, and counter by singing "O Tannenbaum." They go back-and-forth for a while, until finally the two enemy camps sing "O Come, All Ye Faithful" in Latin, together. "This was really a most extraordinary thing." soldier Graham Williams later recalled, "two nations both singing the same Christmas music in the middle of a war." Events just north of a small town in western Belgium go further still. From the enemy trenches, Corporal John Ferguson hears Someone call out, asking if they want some tobacco. "Come towards the light," shouts the German. So Ferguson walks out into no-man's land into the field between both armies. "We were soon speaking as if we had known each other for years." he later wrote. "What a sight little groups of Germans and British talking together almost as far as the eye can seel Out of the darkness we could hear laughter and see lighted matches.... Here we were laughing and chatting to men who only a few hours before we were trying to kill!" The next morning. Christmas Day, the bravest of the soldiers again climb out of the trenches. Walking past the barbed wire, they go over to shake hands with the enemy. Then they wave "come on!" to those who'd stayed behind. "We all cheered." remembered soldier Leslie Washington of the Queen's Westminster Rifles. "and then we all came out together like a football crowd." (A Gifts are exchanged. The British offer chocolate, tea and cakes: and the Germans share cigars, sauerkraut and schnapps. They make jokes and take group photographs as though it's a big./happy reunion/ More than one game of football is played./using helmets for goal posts. One match goes 3-2 to the Germans, another goes to the British, 4-1. In northern France/the opposing sides hold a joint burial service. "The Germans formed up on one side." Lieutenant Arthur Pelham- Burn later wrote./"the English on the other, the military officers standing in front, helmets off, heads bowed in respect. As their friends are laid to rest friends killed by enemy bullets - they sing in English "The Lord is My Shepherd" and the same song in German mein Hirt" their voices in unison. "Der Herr That evening, there are Christmas dinner parties up and down the lines. One English soldier finds himself invited into the German held zone to a wine cellar, where he and a soldier from southern Germany pop open a bottle of 1909 French champagne. The men exchange

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