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英語 中学生

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あと 次は,中学生のタケシ ( Takeshi) が書いたスピーチの原稿 の1~6の問いに答えなさい。 I am going to talk about my interesting experience. I went to London during this summer vacation with my family. This was my first trip to a foreign country. I wanted to know about London, so I looked for information about it on the Internet. I was able to see many famous things on the Internet before the trip. In London, we went to some popular places, for example, Buckingham Palace and Tower Bridge. I already saw them on the Internet, but they looked bigger and more beautiful to me when I saw them directly. I was ( )! When I walked around, I saw a lot of people from different countries, too. Then, we went to a restaurant to eat local dishes. They were very new to me, but I enjoyed them. When we finished our dinner and left the restaurant at about nine in the evening, I found 2one strange thing. It was not dark outside! I was very surprised. In Fukuoka, it is dark at nine in July, but it is not in London! This was the most interesting thing to me. I enjoyed this trip very much because I was able to discover new things. After the summer vacation, I told my classmates about my trip to London in an English class. Many of them liked my story and I was glad. After school, one of my classmates came to me and said, "I really enjoyed your story. I love Harry Potter, and I'm very interested in London. Can you tell me more about your trip ?" In fact, 3 was surprised when she came to talk to me. Before that, we didn't talk, and I though she was not interested in foreign countries. But that was not right. She knew a lo about London. We talked about my trip and Harry Potter. When we were talking she said to me, "Going abroad is a good way to study, but I have ( ) to Foreign country. I was glad to talk with you." I discovered new things about her o hat day. ) ( 4 You can get information about many things on TV and the Internet, and you ofte hink you know about people around you before talking to them. But you can discove ew things when you experience something directly. I want to remember this idea ar xperience a lot of things in the future. 主) foreign: 外国の Buckingham Palace: バッキンガム宮殿 Tower Bridge: タワーブリッジ directly : 直接に local dishes : その土地の料理 outside: 外で discover : 発見する Harry Potter: ハリー・ポッター

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数学 高校生

数IIです お願いします🙏

72 610 00000 基本例題 244- 面積の最大 最小 (1) 作用と飲作はソード"で囲まれる図形の面積をSとする 小値を求めよ。 指針点 (1,2) を通る直線の方程式は, その傾きをm とすると, y=m(x-1)+2と表される まず, この直線と放物線が異なる2点で交わるとき, 交点のx座標α, BSを表す が利用できる。 このとき,公式f'(x-a)(x-B)dx=1/(a-α) 6 更に,S を m の関数で表し,mの2次関数の最小値の問題に帰着させる。 解答 点 (1, 2) を通る傾きmの直線の方程式は y=m(x-1)+2 ....... ① と表される。 直線 ① と放物線y=x2の共有点のx座標は, 方程式 x2=m(x-1)+2 すなわち x-mx+m-2=0 の実数解である。 この2次方程式の判別式をDとすると D=(-m)²-4(m-2)=m²-4m+8=(m−2)²+4 常に D > 0 であるから, 直線①と放物線y=x2は常に異なる 2点で交わる。 その2つの交点のx座標をα, β (a <β) とすると s=Sm {m(x-1)+2-x2}dx=- =-f(xーmx+m-2)dx =-f(x-a)(x-B)dx=1/(B-α) _m+ √D _m-√D = √D=√ (m−2)²+4 2 また B-α=- したがって, 正の数β-α は, m=2のとき最小で,このとき (B-u)も最小であり,Sの最小値は 1/12 (14)=1/3 x2-mx+m-2=0の2つの解をα, β とすると よって (B-α)²=(a+B)2-4aß=m²-4(m-2)=(m−2)²+4 a YA y=x² (1,2), x= IS 点(1,2)を通り軸に垂 な直線と放物線y=x"で まれる図形はない。よって 軸に垂直な直線は考えなく てよい。 y=ms-1 <α, βは2次方程式 検討 β-αに解と係数の関係を利用 S=12 (B-α) において, (B-α)の計算は 解と係数の関係 を使ってもよい。 =1/(B- a+β=m, aβ=m-2 B x2-mx+m-2=0の解で »*1²=__=_s=—=— (B-a)² = — _ ((B-a)²³)³ = = = {(m − 2)² + 4)}²} ≥ 1/1 •4 ² = 1 {3} S= m± √√m²-4m+8 2 m²4m+8=D 練習 ③244 きが 2x+mであるという。 放物線y=f(x) と放物線y=-x²+4x+5で囲まれる mは定数とする。 放物線y=f(x) は原点を通り, 点 (x, f(x)) における接線の 図形の面積をSとする。 Sの最小値を求めよ。 p.382 EX19

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