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Mathematics Senior High

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重要 例題29 ユークリッドの互除法と1次不定方程式 (1) 不定方程式 161x+19y=1を満たす整数x,yの組の中で, xの絶対値が最| ①小のものはx=アイ,y=ウエである。 (2) 不定方程式 161x+19y=5 を満たす整数x,yの組の中で, xの絶対値が最 a 大量 小のものはx=オ,y=カキクである。 POINT ! 1次不定方程式の整数解の1組が容易に見つからない場合は, ユークリッドの互除法を用いる。 ( 51 参考) (2) (1) の等式の両辺を5倍すると 161(5x) +19(5y)=5 よって,(1) で見つけた整数解の1組をそれぞれ5倍したものは 161x+19y=5の整数解の1組である。 解答 (1) 161x+19y=1 161=19.8+9 19=9・2+1 この計算を逆にたどると 1=19-9・2 01- =19-(161-19・8)・2 =161・(-2)+ 19・17 ① とする。 移項すると 9161-19・8 移項すると 119-9・2 ...... (2-8-) (ar- したがって 161・(-2)+19・17=1 ① ② から 161(x+2)+19(y-17) = 0 161 と 19 は互いに素であるから、③より ...... (2) 161x+19y=5 ②から ④ - ⑤ から 161(x+10)+19(y-85)=0 161 19 は互いに素であるから, ⑥ より ..... (2) x+2=19k, y-17-161k (kは整数) よって x=19k-2, y=-161k+17 |x|が最小となるのはん=0のときであるから x=アイ- 2,y=ウェ17 ④ とする。 161・(-2.5)+19.(17・5)=5 ...... ⑤ ⑥ 1s)(3) ③ xの係数 161 とyの係数 19 にユークリッドの互除 法の計算を行う。 6518-5 x+10=19l, y-85-1617 (Zは整数) よって x=191-10, y=-161+85 |x|が最小となるのはl=1のときであるから x=オ9, y=カキクー76 ◆余りが1になったところ で,計算を逆にたどる。 0 ← ① を満たす 1組の解 01-x=-2,y=17 が得られる。 al- a I & meroun SHOR H.260 •②×5 とすると, ④ を満た す1組の解x=-10, |y=85 が得られる。

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English Senior High

34〜41の答えを教えてください。

A long email from Japan arrived in the computer of Bill Perkins, who worked in an office in London. The message was from a company in Tokyo that Bill's company had just sent a large order to. Bill read it once and then once (注1) named Steve to read. Steve read it and also looked again, looked puzzled, and then gave it to a colleague" confused. The letter began by praising the English company. () It then mentioned that some goods had been damaged during shipping (2) to Japan, and then the letter happily 34 (v) This kind of letter may work well in Japan, 35 it is not very successful as international communication. The letter 36 the reader to read between the lines to understand the problem and to sympathize with the company. (5) Of course, it also wanted Bill and Steve's company to rectify the trouble. But the letter did not spell out (4) that message very 37 . So Bill and Steve were thinking of just ignoring it. But then they received more correspondence from the Japanese company, this time with a specific request for action. It was an hour later when a second letter arrived that contained 38 for the first confusing letter. It also stated the intent of the Japanese company concerning the damaged goods. They wanted the replacement items shipped as soon (25) would foot as possible with no charges. Bill and Steve were happy once again because their insurance company the bill 16), and the goods would arrive in about ten days. (2) The Japanese company didn't follow the standard international business pattern in its communication. But the English company was 39 , too, because they hadn't realized that there was a deeper meaning to the letter. Bill and Steve had only looked at the communication's surface. It seems to me that both sides could benefit from a seminar on international understanding. (1) colleague: (2) shipping: (**) * (注3) rectify: 対応する (注4) spell out : 詳しく述べる (5) insurance company (注6) foot the bill: 費用を払う t (Terry O'Brien et al. Simply Reading, Simply Writing NAN'UN-DO) 6

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English Junior High

回答を解説含め教えて頂きたいです🙇‍♀️🙏

問題8【思考・判断・表現】 (2X4=8) 次の(ア) (エ)の各対話文の 3x0 選び、 番号を答えなさい。 HORS (7) Yuichi: Today is my grandmother's birthday. Mary: Yuichi: She's seventy. 1~4の中から一つずつ AXUCE OST) -NEER ŠPEJAT JSY uoy list of onion m'I wold ob alqosq ynom nint I Calplopori si bo od movs olish 1 Where does she live? 2 How old is she? 3 Who gave her a present? 4 ynoteid eti tuodo (S) What's her name? Why is chocolate mort trasllib ti stoloporls silm of oppo* sau ot batante osixeM (1) Satomi: Oh, you are carrying a big box. Are you all right? b slqos David: No. This is a little difficult. Satomi: Sure. EATONKON the first Japanese persoly siano ni siqos yobot stplooards saviensis isy DD snipibsm to brix o zow sqomus montslqosa boinsg ob3 silt erinud Snoqot of smoo tarit stolosorts bib woll 1 Will you help me? May I help you? 2 emixom 3 You won't help me. moz, bainqilis4 Do you want me to help you? sorls triguend tu8 bluos varit vllonit bad bror vsv bsint yanT noqot ni ti slom ot batnow bad stolosoris colate aviensqxs llite 20w ti pooltootroo* 9/02 1 Why do you want to go to the park? qua 2 3. How is the weather next Sunday? 4 () Steve: What are you going to do next Sunday, Hitoshi? Hitoshi: I'm going to play baseball with my friends in the park. Steve: I see. yab Hitoshi: Well, I'll do my homework at home. we amosad stolo Mr. Smith: Tomoko: Tomoko: Yes, Mr. Smith. We are going to ** in China. insianD (1) Mr. Smith: Tomoko, I hear you are going to visit China with your friends this summer. a junior high school ing to visit blow 9††A lay baseball? Loy When will you play What will you do if it rains? inain W 1 2 How many students are there in the school? Is it easy for your friends to speak Chinese? How will you go there? 3 4 Have you ever been there? It is my second time to visit the school, but it is the first time for my friends. I made a lot of Chinese friends last year. So I'm looking forward to seeing them again.

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