テキストには写真の（2.13）と（2.15）より（2.15）式の右辺、左辺の定数項について求められるとしていますが、求め方が分かりません。どのように考えた場合定数項について求められるかを教えてください

}) (0) で .11) xx-th-1² tr 1 n-1 (2.12) Page bi age 171 EN (T 20 君のこと Page +1)= 172 l を上昇階乗ベキと呼ぶ。 この両者をあわせて, 階乗ベキと呼ぶことにする。 2.3 スターリング数 2.2節で学習したように、 階乗ベキは差分演算のなかで有効な計算手段 である。 ここでは,スターリング (Stirling *3) 数を利用して下降階乗ベ キュ”と単項式”の関係を学習する。 ここでnは2以上の自然数とし ておく。 実際には、下降階乗ベキを多項式で表すこと, 単項式を下降階 乗ベキの一次結合で表すことを問題意識とする。 まず、前者については x² = x² +Nn-1,nxn-1 +...+₁,nx = Σnj,n x² in (2.13) j=0 と表せる。ここで,Vn,n=1,70,n=0, さらにnjin=0,j>nであり, 7j,n は漸化式 In=zn+in-1,n n - njn+1=nj-1,n nnjin, 1≤j≤n x² (x-1) {[ (x-1) (x-2) * \\ { XL-{h+1) +2) (x −(n+1)+1) (2.14) を満たす。実際,zn+1=cℓ.(x-n) であるから、この式の両辺をライ プニッツの公式 *4 を利用して回微分すると, 積の微妙で、()は2階 (xn+¹)(i) = (x²)(i). (x − n) + j(x²)(i-1)³025 (2.15) を得る。2.13) から (215) の左辺の定数項は, j! 7jn+1 であり, (2.15) の右辺の定数項は-nj! nijn+j.(j-1)! nj-1 である。 したがって、 う! で割って比較することで, (2.14) が導かれる。 また,後者については, 第2章 差分法 | 37 n xn-¹ +...+ñ₁, x² = Σnk,n x² k=0 x. ?jn+の区間の生き残り処理する? (2.16) と表せる。 ここで, in,n=1,70,n=0, さらに ik,n=0,knであ り kn は漸化式 *3 James Stirling, 1692-1770, スコットランド, スターリングによって書かれた ものに [163] などがある。 *4 1.4.2の定理 1.4を参照のこと。 > (x^²+1) = x^² + Mn₁n₁₁ X²

一枚目　長文 二枚目　問題（ア） 三枚目　自分の答えand模範解答 付属の解説本が意味不明でした。解説お願いしたいです。

10 Life Reading 目標 20分 速読問題 次の英文を2.5分で読んで, 1. の問いに答えなさい。 Would you like to try to read a book that is 140 pages long every day! Many - are Japanese are surprised (2) to learn how long some American newspapers are. They a Slæom orll aneqsgewen to ancieev listipib ert asli orl not always 140 pages long, but they are usually at least 50 pages long. On Sundays 70198 ni olqooq odT C to 21697 0 1 qoq T some big city newspapers have hundreds of pages and *weigh almost a kilogram. gnibro biqs news, too. 37 There are lots of sections 5 (3) Of course, not everything in such a newspaper is news. m2 T raqaq zabavě s esi vis (1974-monib) 19m 16918 i 1996 about books, movies, travel, computers and hobbies, as well as star interviews and es, as well s boy arroqe bas zadintend comics in color. There are also many *advertisements, of course, but a lot of people ano ang m CECING OF COU vsbru² no,199sq ylisb niebimos atidhe bias Hold com bris flood, 25ñola bas find the advertisements very entertaining. Of course, the newspapers have a lot of he) {lind sdt ni snovievs ch the news Moky) zpililoq You may be surprised to find that (4)such large newspapers are (5)very cheap. They gaidyar are much cheaper than a newspaper in Japan. A large, heavy Sunday *edition of a vbodyas J Sunday edition of a Japanese newspaper. ding/ 4 weigh [wéi] : 重さが･･･である 11 edition [idífan] : (新聞の)… 版 1. smi ca ad te bear a newspaper in a big city may only cost about 350 yen, but it is 20 times bigger than the JR noilo92 smse sdt best a siqot amae ad juos at ziqot installib yasm tuds et 7 advertisement [ædvərtáizmənt]: 2 @ (171 words)

至急！！！この問題が分かりません！ わかる人教えください！問1から問10までお願いします🙏

Unit 2 長文問題Ⅱ ミツバチは女社会? 1 Have you ever experienced a bee sting? If you have, you may (1) not be fond of bees. However, they are very interesting and honeybee society is very similar to ours. Let's look at some interesting facts about it. 2 Honeybees live together in groups of 20,000-80,000 in a beehive. This group is call] a colony and the bees in the hive can be categorized into three types: a single queen, tens of thousands of worker bees and hundreds of drones. 3 A queen bee's job is to lay eggs all her life. Each day the queen bee lays around 2,000 eggs. The average lifespan of a queen is three to four years. Does the queen "rule" the colony? No. Her duty is simply egg- laying. In fact, the queen bee has a smaller brain than a worker bee. Target ①現在完了形 現在完了進行形 ② 名詞・冠詞 人称代名詞 ③ 受け身 (6) sting 刺すこと,~を刺す be fond of lifts honeybee ミツバチ be similar to ~に似ている beehive ハチの巣 colony コロニー categorize ~を分類する tens of thousands of 何万もの〜 drone 雄バチ lay eggs 卵を産む lifespan (5) 4 The worker bees are the largest population in the hive. They are all female bees but can't lay eggs. A worker bee's life is rather short. They live around 40 days. Their job is to keep the queen bee happy. They do all the work but change jobs as they grow. For about a week after birth, they mainly clean the hive. Sometime between five to sixteen days after birth, they usually take care of the babies and help to build the hive. When they become twelve to eighteen days old, they carry food. After that, they guard the hive entrance. When they are three weeks old, they fly out the hive, pollinate plants and collect food. If you're a drone bee, life is hard. You're [ bear ], live for a month or two, and then die. During that time, you're not a productive member of the hive-you can't collect pollen or help to look after eggs, like worker bees-and you can't even sting anyone. Drone bees live with one thing in mind: mating with a queen. When they're lucky, they (7) can, but they die soon after that. 5 (8) 6 Every bee in the hive has a part to play in the survival and success of their kind. Bees have been living like this for ages. They work together and live in harmony. rule ~を統治する duty. female 雌の rather かなり as ~につれて guard 守る pollinate 授粉する productive pollen E Poj (2) C (7) in mind 考えて mate with ~と交尾する success, ** in harmony 問 1 調和して、仲良く PLE (4 (E

わけわかめなので教えてください

標準 3 図形 右の図のように, 2辺の長さがそれぞれ5cmと9cm の長方形 ABCD がある。 辺AB上に BE = 3cm となる 点Eをとり、頂点CがEと重なるように折ったときの 折れ線をPQ, 頂点Dが移った点をFとする。 また, EFAQ の交点をG とする。 (1) BP の長さを求めよ。 (2) AG: GQ QD の比を求めよ。 : 応用 - (3) 四角形 EPQGの面積を求めよ。 応用 A E 5cm B G F P -9cm D C

至急お願いします🙇‍♀️すみません💦 問1から問10まで分かりません😓 教えてくれると嬉しいです！ 解説あると助かります🙇‍♀️

Unit 2 長文問題 Ⅱ ミツバチは女社会? 1 (1) Have è you ever experienced a bee sting? If you (2)have, you may not be fond of bees. However, they are very interesting and honeybee society is very similar to (3) Ours. Let's look at some interesting facts about it. 2 Honeybees live together in groups of 20,000-80,000 in a beehive. This group is [call ] a colony and the bees in the hive can be categorized into three types: a single queen, tens of thousands of worker bees and hundreds of drones. Target ①現在完了形 現在完了進行 ② 名詞･冠詞 人称代名詞 ③受け身 queen bee 3 A queen bee's job is to lay eggs all her life. Each day the lays around 2,000 eggs. The average lifespan of a queen is three to four years. Does the queen "rule" the colony? No. Her duty is simply egg- laying. In fact, the queen bee has a smaller brain than a worker bee. 4 The worker bees are the largest population in the hive. They are all female bees but can't lay eggs. A worker bee's life is rather short. They live around 40 days. Their job is to keep the queen bee happy. They do all the work but change jobs as they grow. For about a week after birth, they mainly clean the hive. Sometime between five to sixteen days after birth, they usually take care of the babies and help to build the hive. When they become twelve to eighteen days old, they carry food. After that, they guard the hive entrance. When they are three weeks old, they fly out the hive, pollinate plants and collect food. 5 If you're a drone bee, life is hard. You're [ bear ], live for a month or two, and then die. During that time, you're not a productive member of the hive-you can't collect pollen or help to look after eggs, like worker bees-and you can't even sting anyone. Drone bees live with one thing in mind: mating with a queen. When (7) can, but they die soon after that. (5) they're lucky, they (6) 6 sting 刺すこと､~を刺す be fond of ~を好む honeybee ミツバチ be similar to 「~に似ている beehive ハチの巣 colony コロニー categorize ~を分類する tens of thousands of 何万もの〜 drone 雄バチ lay eggs 卵を産む lifespan Every bee in the hive has a part to play in the survival and success of their kind. Bees have been living like this for ages. They work together and live in harmony. rule ~を統治する duty. female 雌の rather かなり as 〜につれて guard 守る pollinate 授粉する productive 生産的な pollen E 問 1 in mind 考えて mate with ~と交尾する in harmony (2) ( (7) C success ** 問: 調和して、仲良く 問 Pa (4) (6) あ

3〜6番と18番の答えお願いします。答えがないので教えて欲しいです。早めにお願いしたいです。

英単語/句動詞 (26点) 1. She decided to her career goals. A) turn down B) turn up C) turn around D) turn out the job offer because it wasn't the right fit for 2. When baking the cake, she accidentally an important ingredient. A) leave off B) leave for C) leave up to D) leave out 3. His strong leadership skills will A) make for B) make out C) make up for D) make up his mind 4 the success of the project. 4. While exploring the old library, she dusty shelf. A) come up with B) come around C) come across D) come about a rare book hidden behind a the bad weather, the team continued to play their best. 5. A) Due to B) Because of C) Despite D) Owing to the difficulties they faced, they still managed to finish the project 6. on time. A) Nonetheless B) However C) Though D) Therefore 7. Before making a decision, it is important to A) disregard B) consider C) neglect D) overlook 8. She decided to A) buy B) sell C) trade D) return the dress she had been eyeing for weeks. all the available options. 9. The company experienced a high rate of due to the stressful environment. in their workforce

不特定多数だからlanguagesになるのか...?? だとしても解釈の仕方が分かりません。どのようにしたら複数形の意味になるのかを教えてほしいです。

次の日本文に合う英文になるように語句を並べかえなさ い。ただし、不要な語句が含まれている場合がありま す。また,文頭にくる文字も小文字で示してあります。 ブラジルでは何語が話されていますか。 (1語不要) ウ ア エ 正解! イ オ what languages are spoken in Brazil ? カ

鉄壁初心者です。 下記のenlighten のenの意味が分かりませんでした。 ＋鉄壁を勉強する際　「何周もする」以外に 意識すべきポイント等あれば教えて頂きたいです。

564 ●単に知識を供給するだけが教育ではありません。 教育の真の目的は、人を 「啓蒙・啓 「発する」 (enlighten) ことだとも言えます。 「啓蒙」 という日本語は難しいですが、この enlighten という動詞のスペルに注目してください。 無知でぼんやりとした頭の中に 「光」 (light) を与え, 教え導くという意味なのです。 また inspire は ｢息をする｣ という語源 から「息=意気を吹き込む」 → 「行動・創作の意欲をかき立てる」 という意味が生まれ ます。 incentive は, 「やる気をおこさせるもの」 という意味の名詞です。 「テストで良い 点を取ったら**を買ってあげよう」という約束も一種の incentive です。 啓蒙・啓発・意欲 855□enlighten [enlártn] * 他~を啓蒙・啓発する, に知らせる ★en- + light → 「光 (light) を与える」 lighten the public 「大衆を啓蒙する」 e government launched a campaign to enlighten teenagers on the dangers surrounding AIDS. 「政府は若者たちにエイズの危険を知ら 1856 ill minoto* せるための運動を起こした。｣ □enlightenment* 名啓蒙・啓発 [enlártnmant] ・(明照) (enlighten II alanifu) Fe 12 RI 10歳 Sonc

間違ってる所の解説お願いします🙇‍♂️

✓1. The powerful hurricane caused widespread damage to the city, destroying ( 1 ) more buildings than the previous storm. b. any a. few much many Because my sister did not like the style of the dress; she asked the store clerk to show her ( 2 ). a. each b. other another c. either 3. The construction plans for the new park have to win ( 3 ) from the local residents. a. approve b approval c. approved d. approving 4. The sign warns swimmers not ( 4 ) too far out from the beach. a. go going 5. We should provide (5) information travel safely in Japan. a. several b. a lot d. a number of The outdoor concert was canceled ( 6 ) it started to rain more suddenly. a. due to to go d. to have gone 験パスナビ 過去問ライブラリー nsha Co.,Ltd. to foreign visitors on how to b as c. although d. regardless 7. Many students find it ( 7 ) to ask the teacher questions in class. a. embarrass b. embarrassed embarrassing d. embarrassment 8. (8) were your teachers like when you were in high school? a. How c. When -8- Why What 2232100106

どんな問題だったか忘れてしまい、どんな感じかわかる方いませんか😭教えてください😭

8 = 問題1 1 9 ? =D13- F13- H13 に答えてく D5 + F5-H5 X 2 - 07* F7-H7 3 ÷ X =D9 / F9 * H 9 4 = DII * FII * H(l 5 6 = D15+ F15 - H15 7 D17-F17 *H17 =D19* F19/H19 D₂l + F21 +421 FD23/F23 + H23 10 X = * ( 1² lt 3 ) =/(わる) 問題2 2 合計 最初 =SUM (C6: 3 = 4 平均 SUM (C7: = 5 最大 AVERAGE 8 £ MAX (C6 6 最低 MIN (DE =MAX(C1₂ MIN(CI 9 こうんと数字 COUNT( 10 文字・数字 =COUNTA SUM ( AVERAG MAX MIN