この問題の(3)の、 p,2p3p,…,まではわかったのですが、最後のp^n-1pが何を言っているのかよくわからないです わかりにくい質問で申し訳ありませんが教えて欲しいです🙇‍♀️🙇‍♀️

とする。このとき, 次の値を求めよ。ただし, pは素数とする。 1からnまでの自然数の中で, n と互いに素である目然数の個数を」。 Action》 互いに素である自然数の個数は, 互いに素でない自然数の個数からも二 正の整数 N を素因数分解して, N = が'g"r".… (p, 4, 7, 例題 236 互いに素である整数の個数 (2) F(b) (3) f(が) (1) f(100) 条件の言い換え nと互いに素一 nと1以外に公約数をもたない 補集合を考える Action》 互いに素である自然数の個数は,互いに素でない自然数の何称 開 (1) 100= 2° 5°であるから, 100 と互いに素でない自然 数は2または5の倍数である。 ここで,1から 100 までの自然数の中に 2の倍数は50個, 5 の倍数は 20個, 10 の倍数は 10個 よって,2または5の倍数は 50+20-10 = 60 (個) 例題 161 (1003D 2×50, 100 = 5×20, 100 = 10× 10 n(AUB) = mA) +mB- したがって f(100) = 100-60 = 40 (2) かは素数であるから, 1からかまでの自然数の中で pと互いに素でない自然数はpのみである。 したがって f(p) = p-1 (3) 1からがまでの が個の自然数に含まれるかの倍数は p, 2p, 3p, *, がカの が-1 個 1)と同様に =DXが 1個と考えても したがって f(p")= p"- p"-1 Point オイラー関数 き,1から Nまでの正の整数の中て は素数)と表される a(A) 田新は 思考のプロセス

答え合わせのため答えを教えて欲しいです

C Circle the correct form of the words in parentheses. 1. (Contributions/Contributors) from four continents write material for the travel blog. 2. If's (vital/ vitally) that you tell the police everything you witnessed. .na (collective/collectively) effort, management and labor came up with a plan to save the company. 4. Taking (legislative/legislate) action is a long process requiring thorougn analysis and deliberation. . Instead of placing blame, let's try to deal with the traffic problem (Constructive/constructively) and come up with a solution.

100 times moreは何と比較しているか教えください

of the hottest environmental issues abroad is bottled 1 When thinking about the environment, the Japanese should take time to reconsider their lifestyles. Today, one bottled [bá:tld] ds Ales os issue(s) [ju:(z)] industry[indastri] water. Not only does the bottled water industry cost tne deal [di:1] planet a great deal in energy and materials, it has beCome a symbol of First World excess. 5 excess [iksés] ironic [airá:nik] wealthy[welli] willing[wilig) 2 It is ironic that, although consumers in wealthy Countries have safe drinking water, they are willing to pay up to 100 times more for bottled water because of clever packaging and attractive names. All the development that o has brought drinkable tap water to everyone in Japan packaging [pékidzig) drinkable [drigkabl] tap [tep] seems somehow wasted. Why people prefer to buy small amounts of water in PET bottles remains a mystery.. 1ル 3 The bottled water industry makes large profits while mystery[místri] profit(s) [prá:fat(s)] refrigerated [rifridsarèitid] shelves [felvz] <shelf consuming, large amounts of energy. Vending machines 15 and refrigerated store shelves run 24 hours a day. PET bottles require costly disposal. Bottled water is an costly [ks:stli disposal [dispóuzl developed (divelapt] ecological [:kalá:dgikl] impact [impackt] example of how industries in developed countries increase consumer choice while ignoring the ecological impact of their actions. dran 20 oftesup 00 01 mov alte obesup boog 9. 100 times moreとは, 何と比較してですか。 ggy 6. *First World 11. *tap water btorio m yd moe 4. Not only does the bottled ~, (but) it has : not onlyが文頭に来た倒置 13. PET [pét] ポリエチレンテレフタレート 18. developed country → develonin

3番の①で答えはWhat do you think he did?なのですが、書き換えたときsayの要素がなくなるのはなぜですか？？

|3 Rewrite the following sentences using do ) 3. What (you, made, do, think, her, such, do, thing, a y? 2. In a few years' time, children (be, own, their, will, using, cl hat (you, made, dlo, thnk, her, such, do, thing, a Y? て Rewrite the following sentences using do think you 1. What did he say? 2. What was the reaction of the customers? 3. Who was she talking to? Focus on Form

オレンジ色でマークしたところなんですけど、何故このようになるのかが分かりません、

例題112 軌跡(6)…反転 OP 上に OP·OQ =2 を満たす点Qをとるとき,点Qの軌跡を求めよ 例題109 《Action 動点Pに連動する点の軌跡は, P(s, t) とおいて s, tを消去せよ I 軌跡を求める点 → 点Q(X, Y) とおく。 それ以外の動点 →点P(s, t) 与えられた条件をX, Y, s, tの式で表す。 条件の言い換え とおく。 の Q(X, Y) 2 【P(s, t) 条件の → 2s+4t-1=0 [X = as (a> 0) 条件の →点Qは半直線 OP上にある [Y = at 条件の→?+ X°+Y° =2 3 2の式から, s, t, aを消去して, X, Y の式を導く。 4 除外点がないか調べる。 する です 解点P(s, t), 点Q(X, Y) とおく。 点Pは直線1上にあるから 点Qは0を端点とする半直線 OP上にあるから X= as, Y = at (a>0) 2s +4t -1=0 の ベクトル(数学B) を用 いると X S= Y t= a OQ= aOP(a>0) と表すことができる。 とおくと a' のに代入すると 2X 4Y -1=0 a a よって a=2X+4Y 3) OP-OQ =2 より V+X+Y"= 2を代入すると =D2 a よって X°+Y? = 2a =2 3を代入すると よって X° +Y? = 2a X°+Y? = 2(2X+4Y) (X-2)°+(Y-4)。 %3D20 ここで,(X, Y) キ (0, 0) であるか ら,求める軌跡は 円(x-2)+(y-4)° = 20 ただし,点(0, 0) を除く。 する ゆえに 半直線 OP上に点Qを OP·0Q = (一定) となるように定める。こ のとき点Pを点Qに対 応させることを反転と いう。 x 練習112 原点0と異なる点Pに対して, 0を端点とする半直線 OP 上に, OP-0Q=4 を満たす点Qをとる。点Pが直線 y==2 上を動くとき、点Qの軌跡を求のり 196 p.222 問題112 ン 思考のプロセス」

答えだけ教えてください🙇‍♀️🙏

Grammar Focus noun refers to something that cannot be counted (a mass), and so it does not use a plural form. When a noun is countable and it refers to only one person, place or thing, the singular form is used. If the noun refers to more than one, we use the plural form. Plurals are usually created by adding -s to a noun's When a noun is used, it is important to determine if it is countable or uncountable. If uncountable, the singular form, but the spelling of plurals varies and can be irregular. Nouns-Countable / Uncountable Complete each of the following sentences with an appropriate word or phrase. 1. Donating blood is a good way to savea life because patients often require ( to help treat a fatal disease. ) or platelets b. was blood a. a blood C. blood d. its 。Radiation, matter, gravitation, electric charge, and magnetism are all invisible physical a. a phenomenon b. phenomenon C. the phenomenons d. phenomena 3. If people have ( )lasting a week or longer, it may be caused by the flu. a. fever b.a fever C. fevers d. the fevers 4. The ( )are using the forensic science lab report to help them in the investigation. a. detective b. police officer C. polices d. police ) travels in straight lines, and transmits energy from one place to another. a. Light b. The lights C. A light d. Lights ) people think that smoking is healthy, some people do think that smoking is ) people never try to quit smoking. C. few, quite a few 6. Although ( arelaxing tool. Surprisingly, ( a. quite a little, little b. little, quitea few d. quite a few, little ) in the summer camp are interested in nature. a. Most of childs b. The most child c. Most of children d. Most of the children ) can be dangerous if you don't recognize an adverse reaction. b. a medicine 8. Taking a. medicine d. one medicine c. medicines lectronic data exchange via e-mail or the Web is more eco-friendly than using millions of d. sheets of papers a. a sheet of paper c. sheets of paper b. a sheet of papers 10. 7Of the employees in the company are contract workers. c. Number d. Majority a. Lot b. Half

【至急】高校一年生です。明日学校のコミュ英の授業でスピーチがあります。テーマは私の宝物についてです。当日その宝物を学校に持って行って見せながらスピーチします。翻訳アプリで訳してみましたが変な英文になってしまいました。なので次の文を英語にして欲しいです🙏🏻🙇🏼‍♀️ 今日は... Read More

赤い四角の部分が何のために判別式を持ってきているのかわかりません。 3q^2+1 > 0 だから異なる２つの実数界解を持つのは分かりますが、なぜ④が異なる２つの実数解をもつ必要があるのですか？ 教えていただけると嬉しいです。

頭出 例題21 楕円の2接線が直交する点の軌跡 +y=1…① に引いた2本の接線が直交すると 4 点P(p, q) から楕円 ア き,点Pの軌跡を求めよ。 軌跡の問題である。 山 軌跡を求める点PはP(b, q)とおかれている。 かのの関係式を求めたい。 P(b,の) 2 与えられた条件を式で表す。 未知のものを文字でおく 0 x 2本の接線の傾きを考える。 → 接線をyー9=m(x-p) ② の形でおく。 条件の言い換え 《CAction 直交する接線は, 重解条件と垂直条件を利用せよ のと2を連立した方程式を③とすると 例題 20 mの2次方程式 ① と②が接する → (③の判別式)= 0 条件の →のを満たす実数 m が2つある。 しm, ma とすると 条件 より mim2 = -1 (接線が2本ある 3 2の式からか, q以外の文字を消去して, か, qの式を導く。 4 除外点がないか調べる。 解(7) 点Pを通る直線 x=D b が楕円 に接するとき よって, 4点(2, 1), (2, -1), (-2, 1), (-2, -1) から, 直交 する楕円の接線 x = ±2, y= ±1 (複号任意) が引ける。 )pキ±2 のとき 接線はy軸と平行でないから, 点 点Pを通る直線は x = p または y-q= m(x-b) 頂点における接線 x= ±2, y= ±1(複号 任意)の交点である。 11 p= ±2 0 -1 P Pを通る直線は yーq= m(x-) y= m(x-b)+q とおける。 0, 2を連立すると x*+ 4{m(x-b)+qド=4 (4m°+ 1)x-8m(mp-9)x+4{(mp-q)°-1}=0…③ 楕円のと直線2が接するとき, 2次方程式 ③ の判別式 を D,とすると 0 x 14m°+1キ0 より, ③ は xの2次方程式である。 D、= 0 D、 - 16m° (mp-g)-4(4m° + 1){(mp-q)°-1} 4 思考のプロセス|

これについて意見を書かないといけないのですが、 意見の書き方教えてください。。🙇‍♀️🙇‍♀️

Date Reading TR 15-18 The solar system* is known to have eight planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Mars seems to be an especially interesting planet to the scientists who study planets. Robert Zubrin* is one of those scientists. There are two main reasons why he is so interested in Mars. の 5。 One reason is that Zubrin wants to determine if human beings will be able to live on Mars in the future. Though Mars is now a cold and dry planet, 。it is more similar to Earth の- than any other planet in the solar system. So there is a possibility that Mars is a place where human beings can live. In what ways are Mars and Earth alike? First, the soil and atmosphere of Mars is similar to those of Earth. Scientists found that the soil and 10 atmosphere of Mars contains many of the main elements* essential for human life. A Mars exploration rover* named Curiosity has been working on the surface of Mars to gather various scientific information about its environment. Second, the rotation* period of Mars is 24 hours and 39 minutes, which is very close to that of Earth. Third, there are seasons on Mars as there are on Earth. 15 等 The other reason is that, studying Mars, Zubrin thinks we can better predict the future of Earth. It is believed that there used to be a liquid like water on Mars a long time ago. If we can find out how and why Mars has changed into a (A) and (B) place, we may be able to better understand the Earth's future. Zubrin says, “We humans have changed the Earth's environment through our actions and activities. From our research on Mars, 20 we may be able to solve such problems as global warming. Mars may be the key to our survival on Earth." Not only Zubrin but also many other scientists are doing research on Mars. Studying Mars might not seem to be connected with our daily life, but actually it is. New discoveries can influence our future. We should remember that in that regard* Mars is a 25 very important planet for our future. (357 words) Robert Zubrin:ロバート·ズブリン main element:主要元素(人間の生命維持に必要な元素。窒素, 水素など) rotation:自転 (注) solar system: 太陽系 exploration rover : 探査車 in that regard:その点で

要約(日本語で)お願いします🙇‍♀️🙏急ぎです💧 できる範囲で大丈夫です。

Reading 88点 Grammar 30 Writing 10点 100点 Conversation 10 Listening 12点 Reading TR. 15-18 C C 6 The solar system* is known to have eight planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Mars seems to be an especially interesting planet to the scientists who study planets. Robert Zubrin* is one of _those scientists. There are の two main reasons why he is so interested in Mars. の 5 One reason is that Zubrin wants to determine if human beings will be able to live on Mars in the future. Though Mars is nowa cold and dry planet, it is more similar to Earth than any other planet in the solar system. So there is a possibility that Mars is a place where human beings can live. In what ways are Mars and Earth alike? First, the soil and atmosphere of Mars is similar to those of Earth. Scientists found that the soil and 10 atmosphere of Mars contains many of the main elements* essential for human life. A Mars exploration rover* named Curiosity has been working on the surface of Mars to gather various scientific information about its environment. Second, the rotation* period of Mars is 24 hours and 39 minutes, which is very close to that of Earth. Third, there are seasons on Mars as there are on Earth. The other reason is that, by studying Mars, Zubrin thinks we can better predict the 15 future of Earth. It is believed that there used to be a liquid like water on Mars a long time ago. If we can find out how and why Mars has changed into a (A) and (B) place, we may be able to better understand the Earth's future. Zubrin says, “We humans have changed the Earth's environment through our actions and activities. From our research on Mars. 20 we may be able to solve such problems as global warming. Mars may be the key to our survival on Earth." Not only Zubrin but also many other scientists are doing research on Mars. Studying Mars might not seem to be connected with our daily life, but actually it is. New discoveries can influence our future. We should remember that in that regard* Mars is a 25 very important planet for our future. (357 words) (注)solar system: 太陽系 main element:主要元素 (人間の生命維持に必要な元素。 窒素, 水素など) exploration rover: 探査車 Robert Zubrin : ロバート ズブリン rotation:自転 in that regard :その点で