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数学 高校生

解答解説の矢印の箇所が分からないです。 +‪αで方針と桁の指定の式の10ⁿ×Mところです。 よろしくお願いいたします。

重要 例題 6n桁の数の決定と二項定理 (1)次の数の下位5桁を求めよ。 (ア) 101100 におけ イ) 99100 ②) 2951を900で割ったときの余りを求めよ。 指針 00000 (類 [類 お茶の水大] 基本1 (1) これらをまともに計算することは手計算ではほとんど不可能であり,また,それ を要求されてもいない。 そこで、次のように 二項定理を利用すると、必要とされ る下位5桁を求めることができる。 (ア) 101100 = (1+100)100= (1+102) 100 これを二項定理により展開し、 各項に含ま れる 10" (nは自然数) に着目して,下位5桁に関係のある範囲を調べる。 (イ) 99100=(-1+100)’=(-1+102) 100 として, (1) と同様に考える。 - (2)(割られる数) = (割る数)×(商)+(余り)であるから, 291 を900で割ったと きの商をM, 余りを とすると, 等式 291= 900M+r (Mは整数, 0≦x<900) が成 り立つ。2951=(30-1)" であるから,二項定理を利用して,(30-1) を 900M+r の形に変形すればよい。 21 1 章 3次式の展開と因数分解、 二項定理 (1)(ア) 101100(1+100) TOTO= (1+102) 10 100 答 =1+100C1×102 + 100C2 ×10 +10°×N | 展開式の第4項以下をま =1+10000+495×105+106×N B とめて表した。 (Nは自然数 この計算結果の下位5桁は,第3項 第4項を除いて 10"×N (N, n は自然数, 5)の項は下位5桁の 計算では影響がない。 も変わらない。 よって, 下位5桁は 10001 (イ) 99'%=(-1+100)=(-1+102)100はちが =1-100C1×102+100C2×104 +10°×M =1-10000+49500000 +10°×M =49490001+10°×M (Mは自然数) この計算結果の下位5桁は,第2項を除いても変わら ない。 よって、下位5桁は90001 (2) 2951(30-1)51 =3051-51C1×3050+・... 展開式の第4項以下をま とめた。なお,99100 は 100 桁を超える非常に大 きい自然数である。 ことを示せ 【佐賀大) a & [ε] [f] SAKURAC900-302 -51C49×302+ 51C50×30-1 =302(3048-51C1 × 3048 +. -51C49) +51×30-1 =900(3048-51C1 ×304 +51C49) +1529 borg)-900 (3049-51C1×3048 +51C49+1)+629) ここで,30^-51C×30+-51 C 49+1は整数である J (-1) は rが奇数のとき -1-2 が偶数のとき 1 1529=900+629 [sp から 2951900で割った余りは 629 である。(0≦pl+ps [8]

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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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