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数学 高校生

(2)の別解のやり方が使えるのってどんな時ですか?

C2-164 (512) 第6章 式と曲線 Think 例題 C2.74 曲線の媒介変数表示 (2) **** 次の媒介変数表示は,どのような曲線を表すか. (tは媒介変数) 2(1-12) x= ++ x=- 1+t 2t y=t t 1+12 (筑波大) [考え方 媒介変数を消去する. 分数式を含む場合は,t=(x,y の式)やf=(xy の式)に変形する他に、両辺を2 することなどを考えてみよう. www. また、含まない点がある場合があるので、その変域に注意しよう. 解答 (1)x=2(1+1+1)より、1+1=08-1 t+ (1) t うまくを y=t-11より、 t 消していく。 ①+② より, ②より, ①,②'の辺々を掛けて, 4 = (リージ 2 -y” より, ①を変形すると、ピー = 2t=1+y ・①、 2 x t 2 l-y _(x-2)2y2 1= 16 4 (2) D₁=(-1)-4=- t+1=0 より 判別 式をD, とすると, x2 x-3≧0 より x≤-2, 6≤x 相加相でも x,yの変域を調べる. 与えられた媒介変数表示 より,それぞれについ て整理する. 判別式を用いて実数解を もつ条件を調べる. y4 また、②を変形すると, いける。 t-yt-1=0 より, 判別式をD2 とすると, D2=y'+4>0 したがって,yはすべての実数値をとる. よって、与えられた媒介変数表示は, 双曲線 (x-2)^y' 16 x=- -=1 を表す. 4 より, 2 (1-t2) 1+t =2-x x+2 (x-2) ①を代入して整理すると, 2t y=- 1+12 t= 2y x+2 2y 2-x ②①に代入して, \x+2, x+2 (x+2)t=2-x x=2のとき, (右辺) 0 より x 2 | y(1+ 2-x =2t より、 x+2 4y x+2 -=2t YA 4y2=(x+2) (2-x) 4y=-x2+4

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英語 中学生

英文読解です。左が文章、右が問題です。写真が見にくいかもしれませんが、お願いします。

How Much Is a Tree Worth? It is easy to measure the value of most things that people own. If you want to sell your house or car, for example, an expert will be able to tell you how much money it is worth. However, it's much harder to decide how much things in nature are worth. What is the value, for example, of a tree? One way to measure the value of a tree could simply be in terms of how much money could be made from cutting it down and selling the wood. A tree might be worth more, however, if it isn't cut down. In the case of a fruit tree, for example, we would have to ask how much money could be made by selling the fruit that the tree produces over its lifetime. Furthermore, what about the seeds that tree produces that can grow into new trees that will produce their own fruit? Do these elements add to the value of the original tree? In assessing its value, we might also look beyond the tree itself to the other creatures that live in it. For example, insects, birds, and other animals could not survive without the tree. These creatures use the tree for both food and shelter. Does the fact that the tree supports all these other lives add to the value of the tree itself? Trees also offer non-monetary benefits to people. For example, a tree gives us shelter on a sunny day or provides refuge from heavy rain. How much are these things worth? And what about the beauty of trees that can calm us when we are feeling stressed and that even inspires poetry. How do these kinds of benefits add to the value of the tree? If placing a value on a tree is such a difficult task, placing a value on nature itself is likely impossible. The natural world is an irreplaceable wonder that not only provides humans with many of our basic needs but also inspires us. How do we place value on such a resource? Before You Read Vocabulary CANTON Look at the definitions below. Can you find words that match the definition in the word grid? Some letters have been given to you as clues. Match the words with their definitions below. Definitions worth (n) The importance of an item Reading for Gist Scan the article "How Much Is a Tree Worth?". How many paragraphs are there? Now match each paragraph with the best heading below. There are more headings than you will need. Paragraph 1. Paragraph 2. Paragraph 3. Paragraph 4 produce (v) A person with special skills/knowledge about a subject Paragraph 5. Paragraph 6. value (n) • How much money something should cost creature (n) A small, hard object produced by a plant from which a new plant can grow seed (n) To make or create something Trees add to the beauty of nature. It's impossible to say how much nature itself is worth. How much is a tree worth if we don't cut it down? Different trees offer different kinds of benefits to people. Do the non-monetary benefits that a tree offers add to its value? . Can a tree's value be measured in terms of the wood it provides? Deciding the value of things in nature is a difficult task. Do the creatures that live in a tree add to its value? Reading for Detail Now read the article again in more detail and answer the questions below. According to the article, are the following statements true (T) or false (F)? Underline the part of the text in which you find the answer. monetary (adj) . An animal, especially a nonhuman a. An expert can easily tell you the value of a tree. T/F b. The fruits and seeds that a tree produces might add to its value. T/F c. Many creatures need trees in order to be able to live. T/F d. Trees are only important in terms of the money that they are worth. T/F e. It would be difficult to say how much money nature is worth. T/F expert (n) . Of or relating to money 75 Unit 5: Economics JPREP Empower Vol.76

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物理 高校生

(1)なぜFを力分解せずに、重力を分解しているんですか? Fsin30=mgにしました

基本例題18 仕事 [知識] 図のような、 水平となす角が30°のなめらかな斜面 ACがある。質量40kgの物体を斜面上でゆっくりと AからCまで引き上げた。 重力加速度の大きさを9.8 ms"として、次の各問に答えよ。 (1) 物体を引き上げる力Fの大きさは何Nか。 (2) 力Fがした仕事は何Jか。 3 物体にはたらく重力がした仕事は何Jか。 (1) 「ゆっくりと引き上げた」とは、 力がつりあったままの状態で、 物体を引き上げ たことを意味する。 斜面に平行な方向の力のつ りあいの式を立て、Fの大きさを求める。 (2) (3) 力の向きと移動の向きの関係に注意して、 「W=Fx」 を用いる。 解説 (1) 物体にはたらく力は、図のよ うになる。 斜面に平行な方向の力のつりあいか mg sin30° (3) N -40×9.8× =1.96×102N mgsin30° mgcos30° 2.0×102N 30° 30° mg 130° 10m 基本問題 147 C B (2)物体は、力Fの向きに10m移動しているの で、仕事は、 W=(1.96×102)×10=1.96×103J 2.0×10J (3) 重力の斜面に平行な方向の成分はFの大き さと同じで、物体が移動する向きと逆向きにな る。 重力がする仕事 W' は、 W'=-(1.96×102) ×10 =-1.96×10 J - 2.0×10°J 別解 (3) 重力は保存力であり、その仕 事は、重力による位置エネルギーの差から求め られる。 点Aを高さの基準とすると、点Cの高 さは10sin30°=5.0mであり、 仕事 W' は、 W'=0-mgh=0-40×9.8×5.0 =-1.96×103J - 2.0×10

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