学年

質問の種類

数学 高校生

図形と漸化式の範囲です。 やり方がわからないので教えて欲しいです。

図形と漸化式 (1) 本例題 35 「上の円は同一の点では交わらない。これらの円は平面をいくつの部分に分け 平面上にn個の円があって, それらのどの2個の円も互いに交わり、3個以 00000 るか。 & THINKING CHART 漸化式を作成し, 解く問題 (求める個数を αとする) 1 ai, a α3, ・・・・・・を調べる (具体例で考える) 2 an ① まず, n=1, 2, 3 の場合について図をかくと、 下のようになる。 この図を参考に、 2 平面の部分は何個増加するだろうか? n=2 とみ+1の関係を考える (漸化式を作成)・ n=1 an+1 を anとnの式で表した漸化式を作ろう。 円を1個追加すると、 ① 平面の部分は+2 (交点も+2 ) ゆえに n=3 Tran ① 5 (2) 平面の部分は +4 (交点も+4) n個の円によって平面が個に分けられるとすると」=2 平面上に条件を満たすn個の円があるとき,更に,条件を満 たす円を1個追加すると, n個の円とおのおの2点で交わる から交点が2個できる。 この2n個の交点で,追加した円 がn個の弧に分割される。これらの弧によって, その弧が 含まれる平面の部分が2分割されるから,平面の部分は 2n 個だけ増加する。 よって an+1=an+2n よって, n ≧2のとき an+1=an=2n an=a₁ + Z2k=2+2• 1² (n−1)n=n²_n+2 k=1 =2であるから, この式はn=1のときにも成り立つ。 したがって, n個の円は平面を (n²-n+2) 個の部分に分ける。 • RACTICE 35 ⑧⑨ 6 3 ⑦ 4 基本 29 ① 分割された弧の数と同じだ け平面の部分が増える。 403 ② 1歳 4 新化式 階差数列の一般項が2n n=1 とすると 1²-1+2=2 n≧2 とする。 平面上にn個の円があって,それらのどの2個の円も互いに交わり, ENE 3個以上の円は同一の点では交わらない。これらの円によって,交点はいくつできる

回答募集中 回答数: 0
英語 中学生

緑の線を引いているところの意味がわかりません。 その前のTwo girls were swimming in the lake.とその後のOne was the ...からは分かるのですがこの部分だけ日訳わ簡単なものの文脈が理解できません。この話自体ニュージーランド民話ら... 続きを読む

1 ウエヌクが出会った少女 [大阪教育大附高平野 制限時間 1回目: 20分 / 2回目(英文のみ) : 7分 This is the story of "Ue-nuku. Early one morning, before the sun was up, Ue-nuku was walking in the forest. He came to a lake. Two girls were swimming in the lake. They were girls of the sky. They were on earth for a little while. One _)( ) was the Rain-girl. 5 was the "Mist-girl, and ( Ue-nuku did not know who they were, but he knew that they were beautiful. They were so beautiful that 2[ he / how / know / marry / to /to/ wanted] one of them. But while he was watching, the sun came up. When the girls saw it was day, they were frightened. "We must 10 go!" they cried. "We are girls of the mist and rain. If the sun shines on us, we will die." While Ue-nuku watched, the two girls went slowly and softly back up to the sky. That night, Ue-nuku sat alone in his house. He said to himself, "Will I ever see the two girls again? They were so beautiful. I want to 15 marry one of them!" While he was thinking, the door of this house opened and the Mist-girl came in. “Ue-nuku, I have come to stay with you," she said. "But I can only stay at nighttime. When day comes, I must go back up to the sky. If the sun shines on me, I will die." The Mist-girl stayed all that night. Before the sun came up, she said 20 goodbye to Ue-nuku and went to her home in the sky. Ue-nuku did not like this. 4[ he/her/him / stay / to / wanted with all the time. One day, he said to himself, "I will put "mats over the door and window of my house. The Mist-girl will not know day has come. 25 She will think it is still night, and she will stay with me." That night, there were mats over the door and window of the house. "Day has not yet come," said Ue-nuku. "Stay with me." The Mist- )! I'm sure it is day by girl said, "What a 5 ( ) ( now." Ue-nuku said again, "Day has not yet come. Stay with me." Time passed, and the Mist-girl said a third time, "This night is too long. I'm sure it is day now." Before Ue-nuku could stop her, she

解決済み 回答数: 1