学年

質問の種類

数学 高校生

赤い四角の部分が何のために判別式を持ってきているのかわかりません。 3q^2+1 > 0 だから異なる2つの実数界解を持つのは分かりますが、なぜ④が異なる2つの実数解をもつ必要があるのですか? 教えていただけると嬉しいです。

頭出 例題21 楕円の2接線が直交する点の軌跡 +y=1…① に引いた2本の接線が直交すると 4 点P(p, q) から楕円 ア き,点Pの軌跡を求めよ。 軌跡の問題である。 山 軌跡を求める点PはP(b, q)とおかれている。 かのの関係式を求めたい。 P(b,の) 2 与えられた条件を式で表す。 未知のものを文字でおく 0 x 2本の接線の傾きを考える。 → 接線をyー9=m(x-p) ② の形でおく。 条件の言い換え 《CAction 直交する接線は, 重解条件と垂直条件を利用せよ のと2を連立した方程式を③とすると 例題 20 mの2次方程式 ① と②が接する → (③の判別式)= 0 条件の →のを満たす実数 m が2つある。 しm, ma とすると 条件 より mim2 = -1 (接線が2本ある 3 2の式からか, q以外の文字を消去して, か, qの式を導く。 4 除外点がないか調べる。 解(7) 点Pを通る直線 x=D b が楕円 に接するとき よって, 4点(2, 1), (2, -1), (-2, 1), (-2, -1) から, 直交 する楕円の接線 x = ±2, y= ±1 (複号任意) が引ける。 )pキ±2 のとき 接線はy軸と平行でないから, 点 点Pを通る直線は x = p または y-q= m(x-b) 頂点における接線 x= ±2, y= ±1(複号 任意)の交点である。 11 p= ±2 0 -1 P Pを通る直線は yーq= m(x-) y= m(x-b)+q とおける。 0, 2を連立すると x*+ 4{m(x-b)+qド=4 (4m°+ 1)x-8m(mp-9)x+4{(mp-q)°-1}=0…③ 楕円のと直線2が接するとき, 2次方程式 ③ の判別式 を D,とすると 0 x 14m°+1キ0 より, ③ は xの2次方程式である。 D、= 0 D、 - 16m° (mp-g)-4(4m° + 1){(mp-q)°-1} 4 思考のプロセス|

回答募集中 回答数: 0
英語 高校生

これについて意見を書かないといけないのですが、 意見の書き方教えてください。。🙇‍♀️🙇‍♀️

Date Reading TR 15-18 The solar system* is known to have eight planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Mars seems to be an especially interesting planet to the scientists who study planets. Robert Zubrin* is one of those scientists. There are two main reasons why he is so interested in Mars. の 5。 One reason is that Zubrin wants to determine if human beings will be able to live on Mars in the future. Though Mars is now a cold and dry planet, 。it is more similar to Earth の- than any other planet in the solar system. So there is a possibility that Mars is a place where human beings can live. In what ways are Mars and Earth alike? First, the soil and atmosphere of Mars is similar to those of Earth. Scientists found that the soil and 10 atmosphere of Mars contains many of the main elements* essential for human life. A Mars exploration rover* named Curiosity has been working on the surface of Mars to gather various scientific information about its environment. Second, the rotation* period of Mars is 24 hours and 39 minutes, which is very close to that of Earth. Third, there are seasons on Mars as there are on Earth. 15 等 The other reason is that, studying Mars, Zubrin thinks we can better predict the future of Earth. It is believed that there used to be a liquid like water on Mars a long time ago. If we can find out how and why Mars has changed into a (A) and (B) place, we may be able to better understand the Earth's future. Zubrin says, “We humans have changed the Earth's environment through our actions and activities. From our research on Mars, 20 we may be able to solve such problems as global warming. Mars may be the key to our survival on Earth." Not only Zubrin but also many other scientists are doing research on Mars. Studying Mars might not seem to be connected with our daily life, but actually it is. New discoveries can influence our future. We should remember that in that regard* Mars is a 25 very important planet for our future. (357 words) Robert Zubrin:ロバート·ズブリン main element:主要元素(人間の生命維持に必要な元素。窒素, 水素など) rotation:自転 (注) solar system: 太陽系 exploration rover : 探査車 in that regard:その点で

回答募集中 回答数: 0
英語 高校生

要約(日本語で)お願いします🙇‍♀️🙏急ぎです💧 できる範囲で大丈夫です。

Reading 88点 Grammar 30 Writing 10点 100点 Conversation 10 Listening 12点 Reading TR. 15-18 C C 6 The solar system* is known to have eight planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Mars seems to be an especially interesting planet to the scientists who study planets. Robert Zubrin* is one of _those scientists. There are の two main reasons why he is so interested in Mars. の 5 One reason is that Zubrin wants to determine if human beings will be able to live on Mars in the future. Though Mars is nowa cold and dry planet, it is more similar to Earth than any other planet in the solar system. So there is a possibility that Mars is a place where human beings can live. In what ways are Mars and Earth alike? First, the soil and atmosphere of Mars is similar to those of Earth. Scientists found that the soil and 10 atmosphere of Mars contains many of the main elements* essential for human life. A Mars exploration rover* named Curiosity has been working on the surface of Mars to gather various scientific information about its environment. Second, the rotation* period of Mars is 24 hours and 39 minutes, which is very close to that of Earth. Third, there are seasons on Mars as there are on Earth. The other reason is that, by studying Mars, Zubrin thinks we can better predict the 15 future of Earth. It is believed that there used to be a liquid like water on Mars a long time ago. If we can find out how and why Mars has changed into a (A) and (B) place, we may be able to better understand the Earth's future. Zubrin says, “We humans have changed the Earth's environment through our actions and activities. From our research on Mars. 20 we may be able to solve such problems as global warming. Mars may be the key to our survival on Earth." Not only Zubrin but also many other scientists are doing research on Mars. Studying Mars might not seem to be connected with our daily life, but actually it is. New discoveries can influence our future. We should remember that in that regard* Mars is a 25 very important planet for our future. (357 words) (注)solar system: 太陽系 main element:主要元素 (人間の生命維持に必要な元素。 窒素, 水素など) exploration rover: 探査車 Robert Zubrin : ロバート ズブリン rotation:自転 in that regard :その点で

回答募集中 回答数: 0
英語 高校生

§18-1の下線部のorは何と何を並立してますか? §18-2(2)の,andのandは何と何を並立してますか? 教えてください。

共通関係一何と何が並んでいるの? 以下の英文を読み, 下線部を和訳しなさい。b indeed when my friend Peggy Hughes first suggested to me that d yno ai. bptnsg 0 b In the last decades of the eighteenth century, and in the first half of the nineteenth century, a number of words, which are now of capital importance, came for the first time into Common English use, or where they had already been generally There is in facta general pattern of change in these words, and it is possible to look at the wider changes in life and thought to 5 used in the language, acquired new and important meanings. thought at first of making these letters and notes into a book, and Icould and should do so, the idea seemed impossible and absurd. 42 o benti S 18 9on9brgg 1916W no) ny re G 5 O990 G200L0B tcione which the changes in language evidently refer. The destruction of (法政大) m s dependence on the m In 1960, when I first began writing notes about Lisa, I did 2 not think of myself as collecting data, or doing research, or getting ready to write a book. I was a charmed and delighted adult with(like Mrs. Bissex)“an inclination toward writing 5 things down," in the form of letters to friends or notes to mysell, of which I sometimes later sent copies to friends,/ (2 au thought at first of making these letters and notes into a boOK, e declo ard people who are diferst (協大) as and ies y mutual tudenstanding

解決済み 回答数: 1
数学 高校生

ここの式変形が分からないので途中式含め教えていただきたいです!(2)です!

(1) 関数 f(x) = (x+a)e*" が, f'(0) =D 3, f"(0) = -2 を満たすとき、 (2) y=e-"cosbx のとき, y"+ 2ay' + (α°+6)y = 0 を示せ。 例題 155 第2次導関数 定数a, bの値を求めよ。 (式変形)… = 0を示す。 , y”を計算して, (__の左辺) y、=-ae" cos bx -be 見方を変える 三** (2) 素直に考えると… もう1度微分するのは大安 一 'sin bx これはもう1度微分しやす。 =ーay-be-a"sin bx ←- =yであるから Action》 第2次導関数f"(x) は, f(x) をxで微分せよ f(x), f"(x)を求める。 (eoxy = bee 闇(1) f(x) = 1·e + (x+a)·bex = (bx+ab+1)e*x f"(x) =D b·eo* +(bx+ab+1)·bebx = 6(bx +ab+2)ebt f(0) = ab+1==3 f"(0) = b(ab+2) = -2 mitni よって 0より ab= 2 これを2に代入すると 6=- 2 16(2+2) = -2 これより a= -4 したがって a= -4, 6= - 2 (2) y=e-ax cosbx 0とする。 y=-ae ax . cosbx+e-ax. (-bsinbx) これに0を代入して整理すると y= -ay-be-a" sinbx 2の両辺をxで微分すると さらにxで微分して をxの式で表し、ゾ- を与えられた等式に して証明してもよい 計算が複雑である。 hol …2 y= -ay' +abe ax . sinbx-be-ax. bcosbx …3 ここで,2より be-ax sinbx = -y-ay これと0を3に代入して整理すると y"=-ay' +a(-yーay)-ピッ したがって y"+2ay' + (α°+6°)y= 0 考のプロセス

回答募集中 回答数: 0