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English Senior High

合っているか確認していただきたいです。

1 各組の文がほぼ同じ意味になるように( )に適当な語を入れなさい. (1) They sell various kinds of fruits at that store. Various kinds of fruits (is) ( sold alcohol at this restaurant. (2) They don't serve Alcohol (ist ) (served ) at this restaurant. ) at that store. (3) Ken painted the doghouse blue. The doghouse (was ) ( painted) (blue) by Ken. (4) They say that many people died of the disease. (It) (is) (said ) that many people died of the disease. 2 日本文の意味に合うように( に適当な語を入れなさい. (1) 報告書が彼によってちょうど仕上げられた. The report (had ) just ( been ) by him. (2) 私たちの便の出発は濃霧で遅れた. The departure of our flight ( were ) (delayed) by the heavy fog. ) ( (5) ボブは学校の成績に満足している. Bob is (satisfied) ( with (3) 私たちは森の中でひどいにわか雨にあった。inow.banagged We were ) ( caught ) ( in the woods. (4) トイレは今清掃中です . quiber sib The restroom (s ) now ( being ) ( cleaned ). wento d ) a heavy shower in ) his record at school. (1 many young people. [受動態に] 3 各文を [ ]内の指示にしたがって書きかえなさい. (1) Did the musician write the song? [受動態に] Was The musician written the song? (2) This magazine is read by many young people. [文末に for many years を加えて現在完了形の受動態に] The magazine has been read (3) What did you name your daughter? What was name your daughter? (4) Our teacher's farewell party was given last Friday. [下線部を next Friday に置きかえ, will を使った文に] Our teacher's will be (5) These pictures were taken in Australia. [下線部を尋ねる疑問文に given farewell party next Friday. where were these pictures taken?

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Mathematics Senior High

EX76の問題を標問135の研究と同じ解き方で、3x+2y=6nを両辺6で割ってx/2+y/3=nになってx=2k、x=2k-1で場合分けして解くことはできますか。

無問 135 格子点の個数 I, y, z を整数とするとき, ry平面上の点(x,y) を2次元格子点, TYz 空 間内の点(x,y,z) を3次元格子点という.m,nを0以上の整数とすると き,次の問いに答えよ. (1) 2012/21/ysm をみたす 2次元格子点(x,y) の総数 + を求めよ. (2) x0,y0,z≧0かつ 1/3+1/13y+zan をみたす 3次元格子点 (x,y,z) の総数を求めよ. (名古屋市立大 ) ・精講 (1) 格子点をどう数えるかが問題で す。研究でx=(一定) となる直 線上の格子点を順次数えてみましたが, 大変です. そこで合同な三角形を付け足して長方形にしてみ たらどうでしょう. (2) z=(一定)となる平面による切り口を考え ると (1) が利用できます。 〈解答 (1) 0(0,0),A(3m, 0), B(3m, 5m),C(0, 5m) とおくと, 与えられた領域は △OACの周および内部である. △OAC≡△BCA であり,線分 AC 上には (0, 5m), (3, 5(m−1)), (6, 5(m-2)), ···, (3m, 0) のm+1個の格子点がある. =1/12 (15) 1 (2) ²/3x+//y+z<n & {√x+} {y≤n-z 求める2次元格子点の総数Sは, 長方形 OABC の周および 内部にある2次元格子点の総数を T, 対角線AC上の2次元格 子点の総数をLとおくと 0 S=1/12(T_L)+L=1/12(3m+1)(5m+1)-(m+1)}+(m+1) -(15m²+9m+2) 解法のプロセス (1) 三角形内の格子点の総数 ↓ 長方形を考える (2) z=(一定) 平面による切 り口を考える と変形する. z(z=n,n-1, n-2, ..., 0) を固定し, 303 3n x n y+ 5mm 0 -n-m B 3m HA IC 5n 第8章

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Mathematics Senior High

下線部の計算がよくわからないんですけどどういうことですか?

の 指針 (1) αti= (2) α+iの絶対値に注目すること 解答 (1) a=cos- (3) 39 で表すことは難しい。 そこで, α=cos 基本6 1+(1/2+1); であるが,これをか.20 基本例題6と同じようにして極形式 π π i=cos Atisinn +isin 2 練習 (2) a+i= π arti= (cos ++cos)+ (sina+sin / 絶対値はどもに1である。 →積の公式を利用するとうまくいく。 ここで, 三角関数の和 sinA+sinB=2sin A+B COS cos A+cos B=2 cos- 2 (2) α+iは極形式,a+biの形の2通りに表される。その絶対値を等しいとおく。 a+i=(cos+isin π satisinicostisin / から 17)+(cos+isin) =(cos+cos 7)+i(sin+sin) 3 =2coscos 8 a+i=2 cos A-B A+B 2 1 π π cos + cos=2 cos(+7))}cos ( 12 ( = − 4 )} COS 2 2 π 8 COS COS COS π 8 sinosin=2sin{1/(1/4)} cos {1/(-4)} // π -2.sing rcos o であるから 8 8 COS + (cosmo/2rtisin/13) 8 8 π 8 8 π 2cos /> 0 から, ① がα+iの極形式で偏角は ...... ① 9 √2 |a+i|=- √ 12+(1+√2)^=√2+√2 √√2 (1) から |α+i| =2cos π 8 YA 1 √2 -(1+i)+i=- {1+(1+√2)}であるから /2 = α π 04 2π 1 √2 COS πの値を求めよ。 注目すると x (1) a=212 (√3+i) とするとき,α-1 を極形式で表せ。 5 (2) (1) の結果を利用して, cos/1/270 1 O 別解 図で考える。 y₁ O cos 01 01 cosit 1 √2 0₁ 1 A-B 2 n 2014 求める偏角は (11) π よって 2cos- √2+√2 から cos- gati. \+i 1 π 4 √2 から a 18 -= x K/000/00 = 章2 複素数の極形式と乗法・除法 π 4 +0.1-28 -+0₁= 3 極形式 r(cos Otisine) では, > 0 となる必要がある。 このことを確認している。 R 8th √2+√2 2 or Op.28 EX10

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English Senior High

これといてください。至急です お願いします 英語分かるかた

2010 解答用紙を6/1(木)に提出 解説は英語でします。 【1】 次の英文を読んで、後の設問に答えよ。 (配点 50) A few years ago, a certain famous university in Japan asked a unique question as its entrance examination in English. The question was this: Write a reply in English to a junior high school student who doesn't like studying. He says he has no intention of going abroad, so he doesn't think he needs to study English. Nor does he want to get a job in which the knowledge of math or science is required. He, therefore, insists that he cannot understand the reason he is forced every day to study subjects he is not interested in. As an entrance examination, it's not very difficult to write an answer to this question. (2) you take it seriously, however, it touches on such a profound aspect of human nature that it is worth thinking about. Fundamentally, why do you have to study? What is learning for? Would you still like to study even if there were no schools or examinations in the world? In my opinion, it is possible to answer such questions from a practical and essential point of view. First, it is not rare for anyone to find changes in their own preferences or desires over time. Sometimes we find ourselves possessing no interest in what we thought to be precious before. Sometimes we are surprised to realize that what we thought to be of little value is so important. So it is quite hard, especially for young people, to predict actually what one will want in the future, say, ten years from now. That's why it is highly desirable for students to prepare for their future by increasing their knowledge and improving their intelligence. Whatever job one may get, it is quite (4) that knowledge or intelligence gets in the way. This can be demonstrated partly by many adults confessing that they should have studied harder. ( 5 ), it's only while one is young that one has a good memory and can absorb and retain a vivid impression of what one has learned. Next, I would like to talk about a more subtle viewpoint. Essentially, no human beings can be satisfied with what they already have, and everyone has, at 1921 the bottom of their heart, the desire for a better existence. Please do not interpret (67 INT this only in terms of materialism or religious belief. Of course, food, clothing. and housing are important. Still, ( 7 ). Also, in the present age, it is difficulí to feel there is anything in the belief that God will come to help you have a better existence some day. Even if all of your basic needs are met, without one important thing, you cannot feel that your life is meaningful. This one thing is the ambition to improve yourself. When you learn something you didn't know before, you will surely feel the satisfaction that no other element in life can give. In this sense, learning will enable you to broaden your world, giving you the joy of knowing. In short, learning is an important way to make your own life richer. (A) 下線 (1) (3) を和訳せよ。 (B) 空所 (2) ( 5 )に入れるのに最も適切なものを、それぞれ次のア~エ の中から1つずつ選び、 その記号を記せ。 (2) 7 Because If (5) 7 For example In conclusion Though In addition What is worse (C) 空所 (4) に入れるのに最も適切な 同じ段落の中から抜き出して、 解答欄に記入せよ。 下線部)が表す内容を、 本文に即して70字以内の日本語で説明せよ。 1931 1. Unless

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