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英語 中学生

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5 10 15 20 25 30 The Olympics were held in Tokyo in 1964. A few years ago before the Olympics, Japan had a big problem. It was a problem of communication. Many foreign people didn't visit Japan, and we had only, Japanese signs. For example, words like "i" or "" were on toilet doors. These signs were not understood by many foreign people. Japanese people at that time needed to make signs in many different languages for foreign people. But when they put many words on one sign, the "letters became too small. They could not easily read the sign. They had to think of ) signs for foreign people. Mr. Masaru Katsumi, a leader of a design team for the Olympics, had a great idea. everyone /to/ was easy / thought / understand he forit pictures. He wanted to make picture signs. These signs are called *pictograms and are used in many places now. Picture 1 Picture 2 Picture 3 Look at these pictures. Picture 1 shows a shower. Picture 2, shows a toilet. Picture 3 shows a restaurant. Foreign people can easily understand what each picture shows. They had to make pictograms which everyone could understand without any trouble. When they started to make them, one of the pictograms was a shower. Many Japanese people didn't know about showers at that time and didn't have one at home. One of the designers didn't even know the word "shower." One officer had to explain how to use it with a photo of a shower. The designer made the pictograms through the officer's words. With a lot of trouble and hard work, twelve designers needed three months and made pictograms for the Olympics. When the last pictogram was finished, Mr. Katsumi said to all the designers, "You did a great job, but this work is not for us. We did it for all Japanese people. Please write your names on this paper." The paper said that they'd like to give up the *copyright to the pictograms. They wrote their names on the paper. They gave up the copyright. One of the designers said, "Mr. Katsumi hopes that many people in many places will use the pictograms in the future. Money from the copyright is not important to Mr. Katsumi. He is proud that he is one of the members who worked for the Tokyo Olympics." In 2020, we are going to have the Olympics in Tokyo. Our life will change a lot. What kinds of new signs or pictograms will we see around us? (E) letter pictogram ピクトグラム(絵文字) designer www. デザイナー officer 役人 copyright 著作権

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数学 高校生

xy平面上に2つの放物線 C1:y=8, C2:y=ーx^2ー4x+aがある. C1上の点P(t、t^2)(t>0)におけるC1の接線をlとする. (1)lの方程式をtを用いて表せ. (2)lがC2に接するとする。このとき、aをtを用いて表せ、また、lとC2の接点の... 続きを読む

■ 解答 とおく. f(x)=x2, g(x)=-x2-4x+α C:y=f(x) y P(t, t2) XxC (i) s=S__(h(x)-g(x)}dx =S__2(x+t+2)dx = -(x+t+: =1/(1+2). (Ⅱ) 直線 PQ の傾きは P²-a-1-4- t-0 -t-2 (ただし, a= -2t2-4t-4.) したがって, 直線 PQ の方程式は y=(1-1)x+a. t C2:y=g(x) (1) f'(x) = 2x より,P(t, f2) における Cの 接線の方程式は, よって, y-t=f(t)(x-t). y-t=2t(x-t). y=2tx-t². T = [ " [ f ( x ) = { (t − q ) x + a}]dx T= - {x² - (-)x−a}ax -lt- = =1/3/3-2/31 a 2 t- -ax (2) ① の右辺をh(x) とおく. y=h(x) と y=g(x) を連立し,yを消去すると, h(x)=g(x). 2tx-f=-x2-4x+a. x2+2(t+2)x-t-a=0. l が C2 に接する条件は, ②が重解をもつこ とであるから,②の判別式をDとすると, 01=(z+2)-1 (−f-a)=0. これより, a=-2t-4t-4. また、このとき②は重解 x= -(t+2) =-t-2 をもつ. 2 ---at 2 =-11³ -- 1/1/1at 6 =-11³-(-212-41-4)t 6 =cof+2t+2t. したがって, S-T=1/2(t+2)-(qt+2t+2t) そこで, 8 =-1713³ + 2 + 31315 F(t)=1/213+2t+10/23 == (3) よって, l と C2 の接点のx座標は, -t-2. とおくと, C:y=f(x) y l:y=h(x) F'(t) = - 3³t² +2 2tx-t² 2 2 -t-2 P(t, t2) t+ t- 2 √3 x 0 T よって, t>0 における F(t) の増減は次 のようになる. C2:y=g(x) S Q(0, a) 2 t (0) ... 3 F'(t) + 0 F(t) 7 極大 -16- 無断転載複製禁止/著作権法が認める範囲で利用してください。

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