(21)の答えが3になるのがなんでか少し分からないです…わかる方いますか？？

(21) (22) (23) Any Change? Long ago, humans did not use money. Because they often could not produce everything that they needed, they traded some of their goods for goods made by others. Gradually, the goods that they exchanged were replaced by cash. For hundreds of years, metal coins and paper bills that can be exchanged for goods and services have been produced. Cash is convenient for many people because it is easy to carry. At the same time, though, it ( 21 ). Another disadvantage is that criminals have been able to produce fake coins and bills. In the middle of the 20th century, plastic credit cards were introduced. They had security features to prevent them from being used by anyone except their owners. At first, their use was limited to wealthy people. Over time, however, they became ( 22 ). In the last few years, apps for smartphones that can be used in the same way as credit cards have also become popular. Because of this, some people are suggesting that we may soon see the end of cash. Supporters of a "cashless" society in which all payments are made electronically argue that it would have several benefits. For example, people would not have to worry about keeping their wallets safe. However, some people are concerned that they might be unable to pay for the things they need because of a software error or a broken smartphone. Moreover, some people do not have bank accounts or credit cards, so their only option is to use coins and bills. ( 23 ), it seems as though societies will continue to use cash. 1 can be lost or stolen can be recycled 1 thinner and lighter 3 harder to use 1 For now 2 Until then 2 4 2 4 3 is used for shopping online is understood by almost everyone more colorful and exciting more widely available With luck 4 By contrast

文構造について質問です！ catch a picture で「姿をとらえる」ですか？？ これってどういうイメージで覚えればいいんでしょうか？？

第6段落 ¹Awareness of touch can bring a new feeling to the most commonplace experiences. 2“I have just touched my dog," wrote the young Helen Keller in her diary. 3"He was rolling on the grass with pleasure in every muscle and limb. 4I wanted to catch a picture of him in my fingers, and I touched him lightly as I would cobwebs. 5But, to my surprise, his body turned towards me and moved into a sitting position, and his tongue gave my hand a lick. He pressed close to me as if he intended to put himself into my hand. He loved it with his tail, with his paw, with his tongue. If he could speak I believe he would say with me that paradise is attained by touch."

答えはawareなのですが、understandにして私たちを理解させたという風にはならないのでしょうか？

173 The instructor made us ( 1 aware 2 familiar 174 noitdaigami to Towoq edi (Biyebobe\Juoritiw \on\ns) ) of the dangers of mountain climbing. 3 known 4 understand OVERC 17

3行目のdealの訳し方がわかりません

It's hard for them to wait for the good things in their lives, too. For children, holidays are jor events that they look forward to, and (5) they seem to take forever to come! However, their anticipation of the event can be used to help them learn a great deal about the passage of time, and the meaning of a day, a week, a month. We can help them enjoy the waiting すぎ period and learn from it, too. Studying the calendar will help them begin to understand how time is represented graphically, and will give them a rudimentary* awareness of the relative VT --- funita of time.

2文目の下線部5からのところで訳が それはいつまでたっても来ないように思えるのだ！ と書いてあるのですが否定になってるのはどうしてですか？

It's hard for them to wait for the good things in their lives, too. For children, holidays are major events that they look forward to, and (5) they seem to take forever to come! However, their anticipation of the event can be used to help them learn a great deal about the passage of time, and the meaning of a day, a week, a month. We can help them enjoy the waiting period and learn from it, too. Studying the calendar will help them begin to understand how time is represented graphically, and will give them a rudimentary* awareness of the relative V₁ 6 本

会話文でのsay人to人意味を教えてください 117行目のハーリーアップの後ろのやつです ちなみに四角3に入る言葉は副詞なので無視していいです

115 says peers dubiously at the usual motley collection of night bus riders. A man with bulbous eyes looks up at us and hunches his plastic hood over his [60shut. The shar engine. The nois head. "Is this safe?" thumping up th again. "You sound like my grandpa! Of course it's safe. It goes to the end of my road." "Hurry up!" says the driver 3 to Jack. "If I can fe corners, but I'm you haven't got the money, get off." "I have an American Express card," says 120 Jack, feeling in his pocket. 165 going. Until a familiar sights at my street. I and totter along Suddenly "You can't pay a bus fare with American Express!" I say. "Don't you know anything? And anyway"-I stare at my travel card for a few (and I grab for seconds-"I think maybe we should call it an myself. Why are 125 evening. I'm pretty tired." window, thinkin having to walk, We're in m the aware of t me. The old-fasl I'm not really tired. But somehow I want to be alone. I want to clear my head and start again. "I see," says Jack in a more serious voice. "I 195* T7 0033 th bo driver And now w I hurry dow

③で模範解答と違うのですが間違ってるとこがあるか教えてください！

Ame ◆ 解答 「別冊｣p.4 p.14 原則2~が少ない ・ 少しある ③ 幸福が身近なところにあることに気づいている人は少ない。 ○ パソコンを持っている人は多いが、 十分に活用する方法を知っ ている人はきわめて少ない。 31.90 yeud ai eda To ed nedw neve 学 3 (十片岡

これはなぜ受け身のような意味にはならないのですか??

beauave of 意識する

この問題の緑の線の部分についてです。 なぜ上に凸の放物線になるのでしょうか？ ()の直前のaに➖がなければ下に凸という認識だったのですが、、

(2)関数 y=2cos0 - asin' (aは定数)において, 0 が0≧0≦ 2 の範囲で動くとき, y の最小値を求めよ. ただし, a<0 とする. (立命館大改) 解説を見る (2) 与えられた式に sin'0=1-cos' を代入すると, y=2 cos 0-a(1-cos²0) = acos²0 +2cos 0 - a cos0=t とおくと.00= 2/27より。12ts であり、 y=at2+2t-a f(t) = at'+2t-a とすると, a≠0 より f(t)= a(t+1)²-12-a 関数 y=f(t) のグラフは,軸の方程式が 上に凸の放物線である. - — (>0) <. で, また、tの変域 -1/sts1の中央は、t=12/2 である。 文字でおくときは,そ の文字のとる値の範囲 に注意する. 移動 戻す やり直す 血 全消し 蛍光ペン 太き選択 色選択 × WARE

なぜan≠0を確認するのですか？0だと成り立たないのはわかりますが、なぜ初めにそれを確認しようという考えになるんですか？

考え方 Check 例題292 分数型の漸化式 ( 1 ) a=- Focus で定義される数列{an}の一般項an を求めよ. EUDO MALWARE 1 an+1= 2 9 ○ an の逆数 フェン [an] (s) + Dg=+D THR An 2-an これまでに学んだ漸化式の解法が利用できないか考える。ここ では,漸化式の両辺の逆数をとって考える. ここで,(bm- 1 - をbn とおくと, 与えられた漸化式は,例題285 +29 an (p.505) のタイプ (an+1= pan+g) となる よって, 解 an+1=0 と仮定すると, これをくり返すと, an-1=An-2=・・・・・・=α1=0 1 となり, α= -≠0 と矛盾するので, an 0 (n≥1) 与えられた漸化式の両辺の逆数をとると, 1 2-an 2 an+1 an an 1 an = an= 3 漸化式と数学的帰納法 *** an=0 1 2-1+1 --1 n=1のとき, α= ASTERKE (南山大) ituto Ce *********** とおくと, bn+1−1=2(6n-1),bx-1=1 したがって,数列{bm-1} は初項1,公比2の等比数列だから、 bn-1=1・2n-1 より, bn=27-1+1 SCD &+s+an+ an+1= &+as+ bn+1=26-1,b1=-=2 a1 となり,n=k+1 のときも成り立つ. よって、すべてのに対して, an≠ 0 が成り立つ. 421 5 (1 -$+187 HEJN の逆数 2-an より, an=0 のとき, αk=0 と仮定すると,n=k+1 のとき,k+1=- an :=0 α=2α-1 より, a=1 1=27-1+1 より, an= 分数型の漸化式は逆数で考える 10.3 例題292 で an≠0 は,これから学ぶ数学的帰納法 (p.532〜) を用いた証明もでき 104030 る. <an=0 の数学的帰納法による証明> 1/12/3=1 -≠0 トキノを確認するときとの ちがいは? (- 1 2-1+1 HOHES - C ak 2-ak *0 513 + CES また、分数型の漸化式は,例題292のように逆数を考える方法だけでなく,例題 293 (p.516) のように特性方程式を利用する解き方もある。 SET 8 数 列