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English Senior High

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knew that whene Tn the fifth grade、we were notin the same class, but at lunch Sat in nearby assigned seats and turned around to talk to each othex were always blocking the aisle、talking too oudly and not (a)Ceat ) our lunches、but we didn't care. The teachers knew we were best friends, but we were also a disturbance.(b)Our big mouths got US { 15 ltrouble, and we were warned that we would never be in the sameclass again ifwe kept this up. 7 That summer, Molly and her brother were at my house quite often. We went swimming, played outside and practiced playing Our flutes. Summer went 【[ 16 lvery quickly, and middle school began. As the teachers had warned us、we were not in the same class. We still talked on the ph went over to each other's house, sang in the choir and Practiced < together in the band. ( c )could destroy this friendship. The seventh grade started and, again, We were not in the same class and could not sit near each other at lunch.It(d)(7.we イ.puttoatest ウ .being E.were オ.seemed カ.as if ). We both made new friends. Molly started to hang out with a new grTOUuD of people and was groWing Very popular. We spent( e ) time together and we rarely talked on the phone. At school, I would try to talk to her, but she would just ignore me. When we did take a minute to talk, one of her more popular friends would come up and Molly would just walk away with her, leaving me in the dust. It (0hurt. 1 was so confused.Tm sure she didnt know[ 17 ]thetime how badly 1 felt、 I met Erin、who was also a friend of Molly's、She was in the same gituation I was【[ 18 ]Molly.She and Molly had been close friends。and lately Molly had been treating Erin and me the same way- We decided to talk to her. The phone call was not easy. (g)Talking toherandsaving how Ifeltwas .⑩ ( 5 It was fanny, ⑪though.Whenitwasjust thetwoofus again.It w he_old

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Mathematics Senior High

この-4はどこから出てきたのですか

148 人 WW の 放物線と円の共有上 ・接 放物線 yニエzs+o と円 デキアー16 に 4 この放物線と円が接すると まきの 2) 4 個の共有点をもつよう な定数の (uasr@還oronron 放物線と円 4(ッーo)エパテ16 の実数解, なお, 放物線と円が 接する の をもつときで, この問題の場合 2 次のものを求めよ。 場合と 1 点で接する場合がある aiscaaaiise 2 2 ーーーー ーー ーー EE に デェ』 三 る if <=4 のとき,⑨は の 0 9ー2Tg から ダー4ウーの の 9 2 夫 9 すなわち ①ー$①+$=( なだし20 2 ら から. ッー4(間。 =86送 | 上 で重解をもたない。 ① を 9+yー16 に代入して ッっユ再 も 4(ッーの)二ー16 しかし, FE 臣 人hるな アキ4ッー4g一16ニ0 …③ ィ<?キー16 放物線と円が2 点で接する場合 2 次方程式 ③ は重解をもつ。 ⑧ の判別式をのとすると 革ーグー(-4g16)=4g20 の=0 から デー5 このとき, ③ の重解は yッテー2 であるから ②⑫ に適する。 [2] 放物線と円が1 点で接する場合 図から, 点(0, 4, (0, 一4) で接する場合で 因, [2] から, 求めるZの値は gw=ュ4, 5 (2) 放物線と円が4 個の共有点をもつのは, 上の図から, 放物 株の頂点が, 点 (0, 5) と点 (0, 4) を結ぶ 除く) にあるときである。 線分上 (端点を よって, 求める定数の値の範囲は 四 l 土4 2 ー5くgwマーー4 連立方程式で, y を消す ると デキは4) = 整理して ァX(x2T48)ニ0 講 この 4 次方程式は。2生 ァー0 をもつから, 点(0 9 で接していることがわお2。 同様に (<=-4 とき* についての4 災亡程式 本と ッ※ー16**ー0 すなわち 。Z*(=16)=0 から, ァニ0 (2重鍋3 | をもつから, 点(0⑩ 9で "96 3? 放物線 = と円 の交点が 4 個となる ヶの範囲を求めよ †(①ゅ-4"=ニァ* (ヶ>0) がある。 放物線と 接していることがわかる。

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