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数学 高校生

よってのあとの ここ❕と書いてあるところの式がよくわかりません 8はどこからきたのですか?

ユークリッドの互除法の利用 a=11, b=19 とおいて, [解] のように求めてもよい。 よって,(1)で求めた解を x3Dp、 yーq とすると、 x=5p, y-5q が(2) の解に 0) 11と19は互いに素である。まず, 等式 11.x+19y=1 のxの係数 Ⅱとyの 係数19に互除法法の計算を行う。 その際, 11<19 であるから、 11 を割る数。 19 次の等式を満たす整数x, yの組を1つ求めよ。 (2) xの係数とyの係数が (1)の等式と等しいから、 (1)を利用できる。 を割られる数として割り算の等式を作る。 例題 121 1次不定方程式の整数解 (11 425 (2) 11x+19y=5 077 11x+19y=1 ーズ り.423 基本事項 - 本 L.9 lOLUTION ART 1次不定方程式の整数解 12 スペー が 1+299 2+69 +23 マと966 の は23 (1)の等式の両辺を5倍すると 11(5x)+19(5y)=5 る。 なる。 2 1 667 ) 966 598 667 69 299 移項すると 移項すると 移項すると 移項すると 1=3-2-1 1=3-2-1=3-(8-3-2)-1 =8(-1)+3-3=8-(-1)+(1-8-1)-3 =11-3+8-(-4)==11·3+(19-11·1).(14) =11·7+19·(-4) 11-7+19-(-4)=1 8=19-11·1 3=11-8-1 2=8-3-2 (1) 4=11, b-19 とする。 8=19-111-6-a 19=11·1+8 11=8·1+3 8=3-2+2 15 レ版 3-11-8-1 3=2-1+1 =a-(b-a)-2aー6 2=8-3-2 =(b-a)-(2a-b)-2 1 2 0323 )884 238 646 85 238 よって そのまま ここ。 =ー5a+36 B/I ます 1=3-2-1 のの の =(2a-b)-(-5a+36)-1 =7a-4b すなわち ゆえに,求める整数x, yの組の1つは 能 など すなわち 7 1 11-7+19-(-4)3D1) よって、求める整数x, yの 組の1つは x=7, y=-4 19 ) 2077 6 1829 248 0の両辺に5を掛けると レッド対 11-(7-5)+19-((-4)·5}=5 11-35+19·(-20)=5 3 x=7, y=-4 すなわち よって,求める整数 x, yの組の1つは x=35, y=-20 (2)の整数解には x=-3, y=2 という簡単なものもあ る。このような解が最初に発見できるなら, それを答と してもよい。 ATICE … 121° 1 5-12- 2と変形し、 T0 19x+26y%=1 15(2) 19x+26y=-2 オークリッドの互継 Z

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数学 高校生

なぜ角dになるのかが分かりません 角TASです!

No. 362 OOO00 C 基本例題 図のように,大きい円に小さい円が点Tで接してい る。点Sで小さい円に接する接線と大きい円との 交点を A, Bとするとき, ZATS と ZBTSが等し いことを証明せよ。 ATAB の辺 直線 PT は 【神戸女学院大) CHART 接弦定 3点A, 弦である 定理の S B p.357 基本事項2 CHARTO 接線と弦には 接弦定理 OLUTION BT と小さい円との交点)を引くことによって, 接弦定理 を利用できる。 解答 APAT とA] PT°=PA·PE P 解答 点Tにおける接線を引き,図のように 点C, Dを定める。 また,線分 AT, BTと小さい円との 交点をそれぞれ P, Qとし,点Sと2 点P, Qを結ぶ。 ZASP=a, ZBSQ=6, ZCTP=c, ZDTQ=d とおく。 直線 AB は小さい円の接線であるから C D また よって P C ゆえに くd A したがって、 直線 PT は S a b B する。 ZATS=a, BTS=6 a+btc+d=180° *接弦定理 よって -3点C, T, Dは一直線 上にある。 直線 CD は小さい円, 大きい円の接線であるから ZTSP=c, ZTAS=d INFOR 全直線CDは2つの円の よって,ATASの内角の和を考えて この例是 共通接線。 ZT+ZA+ZS==a+d+(a+c) =2a+c+d=180° すなわ 0, ②から a=b 定理 ゆえに ZATS=ZBTS (日+1 8- PRACTICE… 82° 右の図のように,円0に内接する△ABC とAにおける接線 息がある。ただし, AC<BC とする。 辺 BC上に AD=BD となるように点Dをとり, 線分 AD の延長と円Oの交点をE, 線分 ECの延長と!の交点をFとする。 このとき, △ABC B と△AEF が相似であることを証明せよ。 PRAI C が 日 るJ 6.5.4 |20 (通り) (え21) かタ

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英語 高校生

この英文の()に入る言葉が全然分かりません。 分かるところだけでも大丈夫なので説明してほしいです!

|1| The conversation begins with a British professor talking to a Japanese professor about a lesson he had conducted with his Japanese students. He explains how one of his students ( ① ) him by referring to one of the colors of traffic lights as blue 及する 指角する ( 2 ) of green. The Japanese professor points out that in the Japanese language some objects that are usually thought of as green in many languages are ((3 ) using a Japanese word for blue. The British professor then describes similar ( ④ ) in other languages and cultures, such as that of the Berinmo in Papua New Guinea. They also discuss how Japanese and other languages also have ( ⑤ ) words for light blue and blue. 特称もべろ 2| This leads to a discussion about whether Japanese people are( ⑥ ) different things when they look at objects, or whether they are just ( ⑦ ) different terms to describe them. The British professor then brings up a study that investigated how bilingual speakers of Greek and English ( ③ ) different shades of blue. He notes that the conclusion of the study was that those people who spent more time in the UK were ( 9 ) likely to describe the shades of light blue and blue as very different from each other. 3 The Japanese professor continues the conversation by bringing up a second study that further examines the idea that language can( 10 ) the way we think. This study involved Japanese and English speakers and found that the Japanese speakers judged shades of light blue and blue to be further apart. Both professors conclude the discussion by noting the ( ① ) in interpreting the results of these studies, with the Japanese professor observing that language could be influencing thought or that other ( 2 ) factors could be at work. (D) separate (B) cultural (F) effect (A) assessed (C) characteristics (G) society (H) in contrast (E) less (K) disagreeing (O) surprised (S) designed (W) seeing (L) more (1) using (J) instead (N) mistakes (P) dificulty (M) felt (T) critical (X) increasing (Q) need (R) affect (U) reinforce (V) referred )6(W) へ の( )の( C ) ⑤ ( の( 9

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数学 高校生

数3です!無理方程式・不等式のグラフを用いるときと用いないときの違いはなんですか?

30 0OO000 基本例題 81 無理方程式·不等式 (2) 次の方程式,不等式を解け。 (1) V10-x=x+2 738 v2x+6>x+1 (2) Vx+2Sx 命題 基本0 る。 CHARTO グラフを用いない無理方程式· 不等式の解法 2乗して をはずす /A20, A20 に注意 方程式の場合(1) A=B→ A'=B° は成り立つが, 逆は成り立たない。 「をはずして得た解が最初の方程式を満たすかどうか確認する。 不等式の場合(2), (3) AZ0, B20 ならば A>B→ A°>B° が成り立っ 両辺を2乗する前に条件を確認する。必要に応じて場合分け。 OLUTION ば 解答 (1) 方程式の両辺を2乗して 整理すると x?+2x-3=0 10-x=(x+2)? ゆえに(x-1)(x+3)30 - 2x+4x-6=0 よって x=1, -3 x=-3 は与えられた方程式を満たさないから (2) x+220 であるから また, x2Vx+220 から このとき,不等式の両辺はともに0以上であるから, 両辺を 2乗して x=-3 を代入すると (左辺)=1, (右辺)=-1\ x=1 x2-2 の x20 x+2<x° ゆえに (x+1)(x-2)20 よって xS-1, 2<x 求める解は,O, ②, ③ の共通範囲であるから 2② x22 あケ精のて2 -1.0 2 (3) 2x+620 であるから [1] x+120 すなわち x>-1 不等式の両辺はともに0以上であるから, 両辺を2乗して x2-3 ②のとき 囲 ③ 整理すると x<5 これを解いて 0, 2, ③ の共通範囲を求めて [2] x+1<0 すなわち x<-1 のとき V2.x+620, x+1<0 であるから, 不等式は常に成り立つ。 このとき, ① との共通範囲は 求める解は, ④, ⑤ を合わせた範囲であるから -3Sxく/5 -1Sx</5 -3-15- 4) 15* -3<x<-1 5 []または [2] を満たす 範囲。 乗ば

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英語 中学生

答えがない高校の過去問です。 回答確認のために教えてほしいです。

【2】次の英文を読んで, 下の(1)~ (5)の英文の( を書きなさい。 )に当てはまる最も適当なものを, それぞれア~エの中から1つずつ選び, その記号 *Ogasawara Islands are a group of islands in *the Pacific Ocean, about. 1000 kilometers south of Tbkyo. There are more than 30 islands, and about 3000 people live on the two largest islands. They are sometimes called “Tolyo's *Hidden Islands' or **the Galapagos of the East". When Ogasawara people go to Tbkyo, they have to take a ferryboat for 24 hours because there is no airport. Ogasawara Islands are far from the main islands, so there are many kinds of *unique plants and animals.They are called *endemic species. Thirty - six percent of the plants on the islands'are endemic species. We can see those plants only in Ogasawara Islands. Because only plants and animals that have *adapted to Ogasawara *environment could *survive, unique *ecosystems were developed. This is a story about people who saved two kinds of animals on Ogasawara Islands. One is a red-headed wood pigeon, Karasu Bato".: This is one of the endemic species on Ogasawara Islands. Birds usually live on trees and *protect themselves from their *enemies. But red-headed wood pigeons on the islands have no enemies, so they live on the ground. Their living environment has changed since people brought cats to the islands as pets. Some of them *went wild and became *stray cats. Amother cat usually has about 20 babies a year, so the number of the stray cats *kept increasing and a lot of pigeons were eaten by them. In 2002, the number of the pigeons was only about 40. People began to think they should do something to protect this endemic species and natural environment on Ogasawara Islands. In 2008, people on the islands, Japanese and *overseas researchers, *public officials and animal doctors met together and started a project to save the pigeons. At thé meeting, they decided to *get rid of the stray cats, but they didn't know what to do. So after the meeting, they asked *the Tbkyo Veterinary Medical Association for advice. Animal doctors in this association *cooperated with a lot of volunteers and started a project to save the stray cats. They said, “The pigeons can't survive outside the islands, but cats can live in Tokyo. We want to save both kinds of animals,” The stray cats were *caught and carried to Tbkyo by ship. Animal doctors and volunteers took care of them and looked for their new fanmilies. From 2008 to 2018, about 800 stray cats were sent to Tokyo to start their new ife. Also, the number of pigeons has increased to about 400 now. This story shows that people may have a bad *influence on the natural environment, but we can protect and make it better by cooperating with each other. A person who took part in this project said, “It is important for us to think how we can keep the natural environment for the future." “Aka-gashira *the Pacific Ocean 太平洋 *unique 独特の *environment 環境 *went wild 野生化した *Hidden 隠された *endemic species 固有種 *ecosystems 生態係 (注) *Ogasawara Islands 小笠原諸島 *the Galapagos ofthe East 東洋のガラパゴス *adapted adapt 「適応する」 の過去形·過去分詞 *protect~ ~を守る *kept increasing 増え続けた *get rid of ~ *suIvive 生き残る *stray cats ノラネコ *public officials 公務員 *enemies 敵 *overseas researchers 海外の研究者 *c0operated 協力した ~を駆除する *caught catch 「~をつかまえる」の過去形·過去分詞 *the Tokyo Veterinary Medical Association 東京都獣医師会 *influence 影響

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英語 中学生

答えがない高校の過去問です。 回答確認のために教えてほしいです。

【2】次の英文を読んで, 下の(1)~ (5)の英文の( を書きなさい。 )に当てはまる最も適当なものを, それぞれア~エの中から1つずつ選び, その記号 *Ogasawara Islands are a group of islands in *the Pacific Ocean, about. 1000 kilometers south of Tbkyo. There are more than 30 islands, and about 3000 people live on the two largest islands. They are sometimes called “Tolyo's *Hidden Islands' or **the Galapagos of the East". When Ogasawara people go to Tbkyo, they have to take a ferryboat for 24 hours because there is no airport. Ogasawara Islands are far from the main islands, so there are many kinds of *unique plants and animals.They are called *endemic species. Thirty - six percent of the plants on the islands'are endemic species. We can see those plants only in Ogasawara Islands. Because only plants and animals that have *adapted to Ogasawara *environment could *survive, unique *ecosystems were developed. This is a story about people who saved two kinds of animals on Ogasawara Islands. One is a red-headed wood pigeon, Karasu Bato".: This is one of the endemic species on Ogasawara Islands. Birds usually live on trees and *protect themselves from their *enemies. But red-headed wood pigeons on the islands have no enemies, so they live on the ground. Their living environment has changed since people brought cats to the islands as pets. Some of them *went wild and became *stray cats. Amother cat usually has about 20 babies a year, so the number of the stray cats *kept increasing and a lot of pigeons were eaten by them. In 2002, the number of the pigeons was only about 40. People began to think they should do something to protect this endemic species and natural environment on Ogasawara Islands. In 2008, people on the islands, Japanese and *overseas researchers, *public officials and animal doctors met together and started a project to save the pigeons. At thé meeting, they decided to *get rid of the stray cats, but they didn't know what to do. So after the meeting, they asked *the Tbkyo Veterinary Medical Association for advice. Animal doctors in this association *cooperated with a lot of volunteers and started a project to save the stray cats. They said, “The pigeons can't survive outside the islands, but cats can live in Tokyo. We want to save both kinds of animals,” The stray cats were *caught and carried to Tbkyo by ship. Animal doctors and volunteers took care of them and looked for their new fanmilies. From 2008 to 2018, about 800 stray cats were sent to Tokyo to start their new ife. Also, the number of pigeons has increased to about 400 now. This story shows that people may have a bad *influence on the natural environment, but we can protect and make it better by cooperating with each other. A person who took part in this project said, “It is important for us to think how we can keep the natural environment for the future." “Aka-gashira *the Pacific Ocean 太平洋 *unique 独特の *environment 環境 *went wild 野生化した *Hidden 隠された *endemic species 固有種 *ecosystems 生態係 (注) *Ogasawara Islands 小笠原諸島 *the Galapagos ofthe East 東洋のガラパゴス *adapted adapt 「適応する」 の過去形·過去分詞 *protect~ ~を守る *kept increasing 増え続けた *get rid of ~ *suIvive 生き残る *stray cats ノラネコ *public officials 公務員 *enemies 敵 *overseas researchers 海外の研究者 *c0operated 協力した ~を駆除する *caught catch 「~をつかまえる」の過去形·過去分詞 *the Tokyo Veterinary Medical Association 東京都獣医師会 *influence 影響

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