（4）について、 この面積がなぜ、△AP1Q1になるか教えて欲しいです！

= 〔II〕 nを自然数とする. 座標空間内に, ベクトル= (1,1,1) に平行 で原点 0 を通る直線l , ベクトル=(2,3,-1) に平行で点(0,1,-3) を通る直線がある。 n = 1,2,3,... に対して,直線ℓ上の点Pn と, 直線 m 上の点Qn を次のようにそれぞれ定める. 点P1 の座標は (5,5,5) である。点Pn が定まったとき, 直線上 の点Qnを条件 PQ1=0 により定める. 点Qn が定まったと き,直線l上の点Pn+1 を条件 QnPn+1=0 により定める. PnQn 点Pの座標をan, 点Qn の 座標を 6 とおく. 次の問いに答えよ. (1) 条件 PnQnd = 0 を使って, bn を an を用いて表せ. (2) 条件 QmPn+1 ← ← k=1 an+1 を n を用いて表せ. =0を使って, (3) anをnの式で表せ.また, α = lim an, β = lim bn とおくとき, a n→∞ n→∞ α, β の値を求めよ. さらに, 直線l上の点Pと直線上の点Q のx座標がそれぞれαとβのとき, 点Pと点 Q の座標を求めよ. (4) APQPn+1の面積を Sn とし, △QnPn+1Qn+1 の面積をTとす る。 lim (k + Tk) の値を求めよ. n 84x

出来れば全ての問題解説して欲しいです！ 分からない問題などある場合はわかるとこだけでも結構です！すみません至急お願いします🙇‍♀️

2 次の英文を完成するために最も適当な語句をa~d の中から選んで解答用紙にa~dで 記入しなさい。 (1) I wish they would ( a. leave (3) Let's go by taxi, ( a. will you (2) Can you give me a call when you ( a. will arrive b. arrived (4) I was ( a. said (5) He didn't know ( a. what (6) They enjoyed ( a. study (8) Weather ( a. permits b. put ) me alone. (10) I ( )? b. shall we a. shouldn't (7) Do you know what language is ( a. spoken b. to speak c. make b. where ) to by a foreigner at the airport. b. told c. spoken ) at the train station. c. are arrived c. won't you d.get ) to consult with when he was young. c. when ) in Brazil. c. speaking (9) The buses here are often late since the traffic is ( a. heavy b. much c. a lot d. arrive ) help crying whenever I hear that song. b. mustn't c. can't d. don't we ) with the students came from African countries. b. to study c. studying d. studied d. informed d. whom ), the final game will be held tomorrow morning. b. permitting c. to permit d. of speaking d. permitted ) during rush hour. d. slow d. won't

全ての解説出来ればよろしくお願いします🙇‍♀️ 分かるとこだけでも構いません😥基礎から出来ていないため丁寧に解説していただけると助かります よろしくお願いします、、！

2 次の英文を完成するために最も適当な語句をa~d の中から選んで解答用紙にa~dで 記入しなさい。 (1) I wish they would ( a. leave (3) Let's go by taxi, ( a. will you (2) Can you give me a call when you ( a. will arrive b. arrived (4) I was ( a. said (5) He didn't know ( a. what (6) They enjoyed ( a. study (8) Weather ( a. permits b. put ) me alone. (10) I ( )? b. shall we a. shouldn't (7) Do you know what language is ( a. spoken b. to speak c. make b. where ) to by a foreigner at the airport. b. told c. spoken ) at the train station. c. are arrived c. won't you ) to consult with when he was young. c. when ) in Brazil. c. speaking (9) The buses here are often late since the traffic is ( a. heavy b. much c. a lot d.get ) help crying whenever I hear that song. b. mustn't d. arrive ) with the students came from African countries. b. to study c. studying d. studied d. don't we c. can't d. informed d. whom ), the final game will be held tomorrow morning. b. permitting c. to permit d. of speaking d. permitted ) during rush hour. d. slow d. won't

教えてください🙏 あまり意味がわかってません、、

A〈分詞+名詞〉 次の各文の意味がとおるように( (1) There were many (アbreaking / イbroken) toys in the box. ・ )内からふさわしいものを選び、記号で選びなさい。 B (2) Do you know the (アsmiling /イ smiled) girl? (3) My father bought a (アusing / イused) car last year. (4) The box is filled with (ア collecting /イ collected) stamps. (5) Soccer is an (アexciting /イ excited) sport. B〈名詞+分詞+なにを・いつ･どこでなど〉 次の各文の意味がとおるように( (1) The girl (talk) with Ms. Green is my sister. (2) These are the books (give) by my uncle. (3) This is the picture (take) last year. (4) There were some students (wait) for a bus.com slom (5) I know the woman (sit) by the window. 現在分詞を使うか、過去分詞を使う ・現在分詞 名詞に「~している」 ● ・過去分詞 名詞に 「~されている )内の語を適する形にかえなさい。

わからないので答えを教えてもらいたいです。

英語 Amy: Hey Jake, I was thinking about online shopping this weekend. Do you shop online often? Jake: Yeah, I do it quite a bit. It's so ( house and you can ( ) almost anything online. That's true. I love the convenience, too, especially with a busy schedule. But I've heard there are some downsides to it. What do you think? Well, one obvious downside is not being able to ( ) or try the product before buying. Sometimes, what you see on the website isn't exactly what you get. Amy: Yeah, that's a good point. I've had a couple of instances where the color or size was ) from what I expected. ( Another thing is the shipping time. Even with express shipping, you might have to ( ) a few days for your stuff to arrive. It's not great if you need Amy: Jake: Jake: Amy: Amy: Jake: Jake: Jake: something urgently. True, waiting can be frustrating. But what about the ( that sometimes the prices are higher online. It depends. I've found some great deals online, especially during sales. But you're right; in some cases, the prices can be a bit inflated, and you might end up paying more than if you bought it in-store. Amy: And returns can be a hassle, too. I had to return a shirt once, and the process took forever. It's not as easy as just going to a store and returning it on the spot. Yeah, returns can be a pain. Also, there's the whole security issue. You must be careful about where you're buying from to avoid scams or stealing your ( ). Amy: Oh, definitely. I always make sure the website is secure before entering any payment details. 日本語 L ), you know? No need to leave the On the bright side, online ( ) can be super helpful. I always check them before making a purchase. It gives you an idea of the product's quality and whether it's worth the money. Amy: That's a good point. I do the same. It's like having the opinions of a bunch of friends who've already ( ) the product. Jake: Exactly. So, while there are some drawbacks, I think the ( ) of online shopping, like the convenience and variety, outweigh the ( ) for me. Yeah, I agree. It's all about finding a balance and being cautious about where and what you're buying. )? I've heard

至急です。明日提出のためどなたかわかる方手伝っていただけたら嬉しいです。

【1】 次の英文の空欄に最も適したものを選び、 英文を完成さ せなさい。 (2点×20) (1) What time will you ( come 2 happen 3 (2) Why don't you ( (4) You ( coming. lie 2 lay 3 send 4 sleep (3) All of the guests missed you. You ( the party. *miss〜 : 〜 の不在を寂しがる must 2 should 3 would 4 will to not (5) I haven't decided ( ) go out tonight because another typhoon is ought not 2 hadn't better 3 had better not had 4 to where going (6) He is good at ( *employee ) the mountain cabin? reach 4 arrive ) on the sofa and have a nap? ) on vacation yet. where going 2 going where 3 where to go motivation 2 to motivate ) his employees. (9) The Bible might be ( 4 motivating (7) I tried counting the number of languages ( world. 1 speaking 2 have spoken 3 to speak 4 spoken (8) A truck crashed into a group of carpenters ( the park. ) have attended (10) Our boss said we had to work ( motivate to working worked 3 who works that working ) useful book of all. much 2 better 3 the more 4 the most (12) This is the house we ( (14) Stop chatting, ( Das hard 2 more hard 3 harder 4 so hard (11) This is a cave ( * Neanderthal man : ネアンデルタール人 which 2 that 3 where 4 why lived 2 live 3 lived in 4 live (13) You must hand in the paper ( *hand in : 提出する until 2 for 3 till 4 by and 2 but 3 or 4 so ) in the ) Neanderthal man lived. ) as we could. (15) John is ( 1 taken took 3 taking 4 take ) in ) when we were children. ) the professor will get angry. (1 shower now. Please call later. ) eleven o'clock

数Ⅰ 二次関数 この問題の解説をして欲しいです🙏 これ以降の①－②？の計算方法がわかりません

問題7 変数の2次関数f(x)の最小値は12であり、f(1)=3かつf(2)=3 とします。 f(x)の値を表すの2次式を求めなさい。 結果はの降べきの順に整理しなさい.

わかりません

Step 2 1 次の各文の 1. Tom |内に入れるのに最も適当なものを、一つずつ選びなさい。 be living in London now; he moved to Tokyo two months ago. ② would 3 can 4 cannot (愛知工大) ① ought to 2. After a lot of practice he was ① able ② easy 3. Under the circumstances it ① might to understand spoken English. 3 good ④ possible ought 4. I promised that I would lose weight, so I ① don't have to ② must ③ have You must not ③ No, you have to 7. Miki and her family no answer. ① could go be best to wait for a few weeks. needed ④ seemed 5. The room is full of gas, so you ① didn't ② needn't 6. A: Do I have to finish this work today? B: must be strike a match. ③ couldn't ③ should go eat snacks between meals. ④ mustn't ④ mustn't (センター試験) would be ② No, you may not ④ No, you don't have to lout of town. I have called several times, but there is (東京経大) 10. 彼女は長い間歩いておなかがすいているにちがいない。 She (be / after/ hungry/must/ walking) for a long time. (芝浦工大) (日本大) Notes, 8. performance 「演技,芸当 」 3. under the circumstances ｢そういう状況では｣ 9. unlike ... 9. in time 「間に合って (治療が可能な段階で)」 「…..と違って」 (近畿大) 2 ► ( 内に与えられた語句を並べかえて文を完成させなさい。 8. Monkeys learn tricks (give great performances / they will / that / be able to / so easily) in a short time. (名古屋工大) (南山大) 9. 他の病気とは異なり,ガンは適時に適切な手当てをしても治るとは限らない。 Unlike other (be/by/cancer / cured / diseases / may / not / proper) treatment in time. (金沢工大 ) Par 1 ( 大阪学院大 ) 文法編 7

２２８の問題と和訳です 別荘を買うのと晩年を過ごすの時勢について 晩年を過ごすのほうが後の事だと思うのですが、これは時制のズレを考えて過去完了を使ったりしないのですか？

228 229 230 |231 He bought a cottage in the countryside, ( ) he spent the last days of his life. 1 which where Tom has three daughters, all ( 1 of who 3 who when why He le surp th W They spoke only English and French, neither of ( ) she understood. 1 what 3 whose 2 of whom 4 whom 2 which 4 that ) live in different cities in Japan. speak fluent J ONI (明治大) only one ye <金城学院大

186. このような記述でも問題ないですよね？ またこの類の問題ではほとんどの場合互いに素を用いるように思うので、互いに素を使いたい、そして有理数の性質（m/nでm,nは整数でn≠0）よりこのような証明方法になるということですよね？ また、有理数であることを仮定してから、「... Read More

演習 例題186 指数方程式の有理数解 (1) 3*=5 を満たす xは無理数であることを示せ。 (②2) 35-2y=53-6 を満たす有理数x,yを求めよ。 m (m,nは整数,n≠0) と表される数を有理数といい, 有理数でない n 指針 実数において, ものを無理数 という｡ (1) 無理数であることの証明では, 有理数であると仮定して, 矛盾を導く (背理法)。 (2) 方程式1つに変数がx,yの2つ。 有理数という条件で解くから, (1) が利用できそう。 底が3,5であるから, 3' =5 [(1)] の形にはならないことを用いる。 解答 (1) 3=5を満たすxはただ1つ存在する。 そのxが有理数であると仮定すると, 3*=5>1 であるから m CHART 無理数であることの証明 (有理数) とおいて、 (1) n 背理法 事柄が成り立たないと仮定し て矛盾を導き, それによって m x>0で,x=- (m,n は正の整数)と表される。 =(a+事柄が成り立つとする証明法 (数学Ⅰ)。 n m 37=5 よって 両辺をn乗すると 3m=5n ① ここで,①の左辺は3の倍数であり,右辺は3の倍数ではな いから,矛盾。 よって, xは有理数ではないから、無理数である。… 3x-y+6=5x+2y (2)等式から 2) spol x+2y=0 と仮定すると, ② から x-y+6 3x+2y = 5 練習 ③ 186 x,yを有理数とすると, x-y+6, x+2y はともに有理数で x-y+6 x+2y ...... ゆえに このとき, ② から よって x-y+6=0 ④,⑤を連立して解くと も有理数となり, (1) により③は成り立たない Gram x+2y=0 000 3x-y+6=1 基本 167 x=-4, y=2 等式 20x10y+1 を満たす有理数x,yを求めよ。 3と5は1以外の公約数を もたない。 このとき,3と 5は互いに素 という。 3÷36=5÷5-2y 3x-(y-6)=5x-(-2y) ②から3-y+6)x+2y X = (5x+2y)x+2y (1) で3'=5を満たすは 無理数であることを証明し ている。 KH ④: x+2y=0 と仮定して, 矛盾が生じたから, x+2y=0 である。｣< 40 T810 Op.294 EX120 53