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Mathematics Senior High

三角比です 問題文に書いてあるのは比なのに辺の長さとして扱ってもいいんですか?

274 重要 例 168 三角形の面積の最小値 | 面積が1である △ABCの辺AB, BC, CA 上にそれぞれ点D,E,F を AD: DB=BE: EC=CF:FA=t: (1-t) (ただし, 0<t<1) となるように る。 (1) ADF の面積をtを用いて表せ。 (2) △DEF の面積をSとするとき, Sの最小値とそのときのtの値を求めよ。 指針 (1) 辺の長さや角の大きさが与えられていないが, △ABCの面積が1であることと、 △ABCと△ADF は ∠Aを共有していることに注目。 △ABC=1/AB・ACsinA(=1), 解答 (2) △DEF=△ABC-(△ADF+△BED+△CFE) として求める。 Sはもの2次式となるから,基本形 a(t-p)2 +αに直す。 ただしtの変域に要注意! (1) AD=tAB, AF=(1-t) AC であるから AADF=AD・AFsinA 1 AADF= -AD AF sin A AD 2 1-t 練習 1辺の - D =t(1-t)AB. AC sin A また, △ABC=1 ABACsin A であり, △ABC=1から AB.ACsin A=2 よって △ADF=12t(1-t).2=t (1-t) 2 ANS & (2)(1) と同様にして ABED=ACFE=t(1−t) よって S=△ABC-(△ADF+△BED+△CFE) A 08:08 12 = 3 ( +- ²1/-)² + · ゆえに, 0<t<1の範囲において,Sは 1-t BtE(1-t- B 2-114 S+S)+ MAI=1-3t(1−t)=3t²−3t+1 676 =3(1²-1)+1=3{1²-1+ ( 1 )²} − 3 ( 12 ) ² + 1 2 03 EGO C 晶検討 一般に MAAI t=1/2のとき最小値 をとる。 (D,E,F がそれぞれ辺 AB, BC, CA の中点のとき最小となる) △AB'C'__ ABAC △ABC AB-AC nico A B B' OXE +1 SA S-31-3t+ AC 0 C 最小

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English Senior High

なぜdに入るのが③なんですか?④ではないのですか?

Who was the first scientist? It wasn't Isaac Newton. Today, it is generally acknowledged that Newton never thought of himself as a scientist. He couldn't, for the word didn't exist in was not only a scientist, but the greatest scientist who ever lived, yet (Newton his time. Newton thought of himself as a "philosopher," a word that (a)dates back to the ancient Greek thinkers and that comes from Greek words (b)meaning "lover of wisdom." There are different kinds of wisdom we might love, of course. Some philosophers are concerned chiefly with the wisdom derived from the study of the world about us and the manner of its workings. The world { c ℗ about 2 be 3 can 4 referred 5 to 6 us as "nature," from the Latin word meaning “birth." Nature, in other words, is everything that has been created or that has come into being. Philosophers who deal primarily with nature are, therefore, "natural philosophers." Newton thought of himself as a natural philosopher, and the sort of thing he studied was natural philosophy. Thus, when he wrote the book (d) he carefully described his three laws of motion and his theory of universal gravitation—the greatest scientific book ever written-he called it (in Latin) Philosophiae Naturalis Principia Mathematica, which in English is The Mathematical Principles of Natural Philosophy. The Greek word for "natural" is physikos, which in English becomes physical. Natural philosophy might also be spoken of as "physical philosophy, which can be shortened to “physics.” on. Physics As natural philosophy grew and expanded, all kinds of special studies developed. People began to speak of chemistry, of geology, of physiology, and so was whatever was left over, so it didn't suit as a general overall word for natural philosophy. Yet you needed some such short word, for natural philosophy was a seven-syllable mouthful.

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