(2)なんですが、どうしてγが0から1の範囲にあると分かるのか教えて頂きたいです！

5 解で (1)実数係数の方程式が虚数 α を解にもつ 考え方 両 あることを利用する。 つけ,できるだけ未知数の少ない式を立てることは大切である。 (x++)+("ィ++ (S a月 Process よ 解答 3+V7i を解にもつ実数係数の方程式は, (1)複素数a= 共役な複素数aも解 3-V7iも解にもつから,これらを2解とする2次方程 2 Q= 報O (0+) 0%3Db+x+d+ 天野さ 式は 3-V7i)。 3+/7i )-3-7) = 0 D x一 2 したが : -3x+4=0 -2a (2)(1)より, x+ax'+bx+cはx-3x+4を因数にもつ から,与えられた3次方程式の実数解をyとおくと x°+ ax°+ bx+c==(x-y)(x°-3x+4) : +ax°+ bx+c=x°-(y+3)x°+(3y+4)x-4y と表せる。両辺の係数を比較して [a=-y-3 6=3y+4 dDr fr+ 虚数解 a,a と実数解 をもつ3次方程式を立 式 5 2 lc=-4y ここで,aは整数であるから, ①より yも整数であることが わかる。このことと0SyS1であることから 8+S-- -= J キ)=D++。 Y=0または1 したがって, 求める整数の組 (a, b, c)は①~③より (a, b, c)=(-3, 4, 0), (-4, 7, -4) 答 1S+S.S- 実数解yを求める 解説 実数係数の方程式 f(x)= anx"+an-1.2"-1 + …+a1x+ao=0 が虚数解aをもつとき,それと共役な複素数αも方程式(*)の解である。 これは次のように証明できる。 お Cる

左側が問題、右側が回答です。 四角3番の(1)②の回答の式変形で±の符号がどのように変化しているのかがわかりません。教えてくだい。

(2) のは,結論の方が式が立てやすいので, 対偶を証明するとラクである。 を有理数と仮定すると, /2 は既約分数(p. qは整数, pキ0) と表せる(とく より p, qは自然数としてよい)。 このとき p, qは互いに素であるから、このこと 第1章 数と式, 問題させ、 第1章 数と式,集合と論理 3背理法 Lv.★★★★V の 第1回 解答は12ページ 考え方 2 は既約分数 p は整数, pキ0)と表せる(と を証明す 1 Lv.★★★ れ=1 2 を有理数と仮定すると, 9 = 3 次の問いに答えよ。 (1)a+6°+c° =1をみたす複素数a, 6, cに対して, x=a+b+cとおく。 このとき, ab+ bc+caをxの2次式で表せ。 2) a°+6°+c°=1, α+が+c°=0, abc = 3をすべてみたす複素数aん cに対して, x=a+b+cとおく。このとき,xー3x の値を求めよ。 て矛盾を導こう。 よって、 対偶 Process 解答 (1) ① 12 が有理数であると仮定すると V2= (ただし, pとqは互いに素な自然数) (早稲田大) 「N2は有理 Y/0 2 Lv.★★★ 解答は13ページ p と表せ と表せる。両辺を2乗すると にあてはまるものを, x, yを実数とする。下の(1), (2 )の文中の 次の(ア),(イ), (ウ), (エ)の中から選べ。 2= が 「分子は開散。 右辺に →= 2が 右辺は偶数であるから, q° は偶数,すなわち, qgも偶数である。 よって、q=2q' (g'は自然数) とおけて 2p= (2g)°=→ が3D2q'° がは偶数であるから, pも偶数である。すなわち, pもqも 偶数となり,pと qは互いに素であることに矛盾する。 したがって,仮定は誤りで, V2 は無理数である。 (証終) 2 aが有理数であると仮定すると りuも (ア)必要条件ではあるが,十分条件ではない。 (イ)十分条件ではあるが,必要条件ではない。 (ウ)必要条件であり,かつ, 十分条件である。 (エ)必要条件でも, 十分条件でもない。 本 よっ 「分母は偶数」 は 「分子と分はなわ に矛盾 とに) (1)x+y?<1は, -1<x<1であるための (2) -1<x<1かつ-1<y<1は, +y°<1であるための し 「aは有理数 (関西大図) 『=+(ただし、 sとtは互いに素な自然数) 3 Lv.★★★ 20 と表せる。aは α+α+1=0をみたすから いと 解答は14ページ を背 (+)+キ+ ニ=ーts±) (複号同順) 背 1=0→ t 与式に代入 次の各設問に答えよ。 (1)0 V2 が無理数であることを証明せよ。 ② 実数αがα+α+1=0をみたすとき, aが無理数であることを 証明せよ。 (2)0 nを自然数とするとき, n°が3の倍数ならば, nは3の倍数に なることを証明せよ。 ② ¥3が無理数であることを証明せよ。 国のせ さ すそ 理数 右辺は整数であるから, 左辺も整数でなければならず, s, tは 互いに素な自然数であるから、 t=1である。 よって、(*)より 00 土s°土s+1=0 → s(s°+1)3D1 sは自然数なので, sZ1, s"+1>1であるから(左辺)>1 となり、(右辺)= ±1に矛盾する。 (複号同順) 式を変形し、 したがって、仮定は誤りで、 αは無理数である。 (2) 0 対偶 (明治大) (証終) 8 14

どこか間違えてる部分ありますか？教えてください、お願いします。質問というか確認なのですがお願いしますm(_ _)m

10回 後は演気のため学校を欠度した。 He was absen1 from school because of his sickness . He was absent from schoo1 becanse of his sickness. 『リーはフラン入書がかなり進歩している。 Lily is moking geocd progress- with her French. Lily is making good progress with her French. 3 衆は立ろ工がって幸援を送った。 The audience st00d up andi cheered.. The audience stood up and cheered. 4 n1は 楽レみのためにはく読書します。 I often read I of+en read for pleasure. 5アンディは先生の言ってることに注参を払わなかった Andy hidnt A ndy didn't pay attention t円 6 れは完生にあなたに同意します I absolutely agree with you. I Absolutely agree with you. 9 私は調痛 がレたので年く床に着いた 2 for pleasure. fo what his teacher was saying. what his teacher Was saying pay attention to bed early because I had bed early because I had a headache . headache. went a I 8じのようにしてをの手故が起ったのか調査するべきだ We should exanine how the accident hoppened. We should examine how the accident happened. 9 彼は高 理想 を特つ指導者だった Weht t0 a leader with hghideals . a leader with high ideals. He was He Was 0.そのニュース教者は新しい発見 についてだった The news report was about a new dis covery. The news report was obout a new discovery.

（3）の問題の解き方がわかりません。 こういう問題を見た時の解き方のプロセス？みたいなのがあれば、それも教えてほしいです。

30 Lv.★★★ 解答は53ページ 複数の参加者がグー, チョキ, パーを出して勝敗を決めるジャンケンにつ いて, 以下の問いに答えよ。 ただし, 各参加者は,グー, チョキ, パーをそ れぞれらの確率で出すものとする。 1 い() (1)4人で一度だけジャンケンをするとき, 1人だけが勝つ確率,2人が 勝つ確率,3人が勝つ確率, 引き分けになる確率をそれぞれ求めよ。 (2)n人で一度だけジャンケンをするとき, r人が勝つ確率を nとrを用 いて表わせ。ただし, n>2, 1ハrくnとする。 n- (3)2Cr=2"-2が成り立つことを示し, n人でジャンケンをするとき, r=1 引き分けになる確率をnを用いて表わせ。ただし,n>2とする。 (大阪府立大)

7行目のasなんですか？whenでは？

diesel Adventure Part 2 After test-driving Vasco-5 in Japan, I sailer across the iic Ocean to North America.n Th。 first city Iisited was Vancouver, Canada. I askei for waste oil in many restaurants and hotels there However, my requests were often refused becaus. people knew little about biodiesel fuel. That made G-2) whena希名れ t] me feel disappointed. Still, as people heard abou そ47 Aラ後少る my project, they started bringing me waste oil fron their homes. It took mea few days to process the il into biodiesel fuel. After the process was finished, was able to start on my journey again. When I ran of fuel, I stopped and asked people for waste oil again

教えてほしいです！！お願いします！！

問題は【1】~【4】まである。答えは各問題の指示に従って別紙の解答用紙に書きなさい。 【1】次の英文を読んで設問に答えなさい。 Headaches are a big problem. Each year, millions of people suffer from severe headaches that affect their enjoyment of life, (1) not to mention their productivity at work. estimate, headaches cost individuals and businesses more than (2) $50 billion each year! (3) This is one of the reasons research into headaches has become a worldwide effort. Although he did not know much about how headaches work, Hippocrates was the first doctor to find a way to treat them. By 400 BC, Hippocrates had discovered that the *bark from willow trees was useful in treating pain. He made a white powder from the tree's bark and gave it to his patients. Hippocrates did not know it, but he was actually prescribing a natural chemical in willow bark called salicin. Whena person eats salicin, the chemical is changed inside his or her body into (4) salicylic acid. It turns out that salicylic acid is good for stopping pain, including headache pain, but it is bad for a person's stomach. In the 1800s, a chemist in Germany slightly changed easier for people to take. commonly known as aspirin. Aspirin was used throughout most of the 1900s to treat headaches, but doctors had little idea about what really caused headaches. When doctors can *diagnose the cause of a disease, they can find better ways to treat it. Therefore, as medical technology developed, doctors began to use it to learn more about the human brain and about headaches. In fact, according to one m to make it This new form of the chemical was called acetylsalicylic acid, now acid's Now doctors classify headaches ( A ) two general types: primary and secondary. A primary headache is a condition ( B) as only the headache itself. one caused by another physiological condition, such as an *infection or a *tumor. For primary headaches, doctors have determined three possible causes. headache is caused by stress. characteristically felt on both sides of the head as a dull, steady pain. Another kind of primary headache is the *migraine headache. Exactly what causes these headaches is not well understood, but many experts believe it could be abnormal brain activity causing changes in the brain's chemistry and blood flow. For many people, migraines are caused by certain (5) stimuli, such as poor sleep or particular foods or smells. A sufferer usually feels intense pain on one side of the head and becomes sensitive to light and noise. If the migraine is severe, the sufferer may *vomit repeatedly. The third kind of primary headache is known as the cluster headache. Cluster headaches typically occur around the same time each day for weeks or months at a time. The person ( C)from this kind of headache usually feels pain on one side of her or his head, and the pain is centered around one of the eyes. Doctors do not know much (6) at present about cluster headaches, but they seem to be more common among men and could be related to alcohol or other things that affect a person's blood flow. Using computers and more advanced medical equipment, doctors continue to learn more about what happens in the brain before and during headaches. Especially in the case of migraines, some doctors believe they have found the part of the brain that sets off the reaction for severe attacks. With these insights into brain processes, doctors hope new ways will be discovered to stop headaches before they begin. On the other hand, a secondary headache is One kind of primary Doctors usually call these tension headaches, and they are 注: bark 樹皮 diagnose ~を診断する、~を突き止める 感染症·伝染病 migraine (headache) 偏頭痛 infection tumor 腫場 vomit 食べたものを吐く (出典:READING FOR THE REAL WORLD 3rd edition, Compass Publishing より)

(3)の問題がf(θ)のtについての関数式を作ってから 何をしてるのかわかりません 詳しい解説お願いします！

する 解答は75ページ 44 Lv.★★★ 関数f(0)= a(W3 sin0+cos0)+ sin0(sin0+V3 cos 0) について,次の各 問に答えよ。ただし, 0<0<πとする。 (1)t=V3 sin0+ cos0 のグラフをかけ。 (2) sin0(sin0+V3 cos0) をtを用いてあらわせ。 7(3) 方程式f(0)=0が相異なる3つの解をもつときのaの値の範囲を求 めよ。 20)が (島根大)

解説に赤線を引いた部分は何のために示しているのですか？書き込みで見にくくなっていてすみません。

19 Lv. ★★ 解答は189ページ 関数f(x) = a-cosx が,0<x<今の範囲で極大値をもつように, 定数 a+ sin x 2 aの値の範囲を定めよ。 また,その極大値が2となるときのaの値を求めよ。 (福島県立医科大)

英文4段落目3文目のno paintを塗られていないとなくしてしまいました、塗られていないだとしたらno paintedでしょうか？？ またno paintは完全否定なんでしょうか、、？？

第4問 次の問い(A· B)に答えよ。 (配点 33) will shrink considerably over time.、This shrinkage is caused by moisture not change size too much. But wood from a tree that has just been cut down (water) within the wood escaping into the atmosphere. The drying process of Wood used in the construction of homes must be stable. That is, it must A 次の文章と図およびグラフを読み,下の問い(問1~3)に対する答えとして 2012年度 本試験 15 roo に入れるのに最も適当なものを,それぞれ下の①~④のうち 37 35 fnnu yileub から一つずつ選べ。 19unolli bomisa odt bas boow boi basg es 9120m lo . known as “seasoning. There are actually two ways to season wood. r is to allow the natural drying process to occur. The other is to put it . cnecial oven called a kiln. Kiln drying is much faster than the natural method. During the seasoning process, water is removed from the wood until the moisture content of the wood is approximately equal to the humidity of the air around it. These changes in size due to shrinkage are not uniform because changes depend on the kinds of trees, the way trees are cut, and the surrounding conditions. It is also important to note that even after seasoning, there will always be Some small changes in size due to changes in the humidity of the surrounding air. For example, last year, I used a 230 mm wide piece of eastern white pine WOod to makea cabinet door. It changed in width across the grain (Figure 1), Shrinking by 2 mm from the original in the winter and expanding by 3 mm Ine moisture content of wood changes according to the seasons even niw= from the original in the summer. um volbsoH 8. -409

答えが無くて分からないので教えて欲しいです

SIMなし合 22:01 Cop 【1】次の英文を読んで, 設問 1~12に答えなさい。 なお, *印の語(句)には文末に注 がついています。 Modern examinations of working conditions in British and U.S. industry in the nineteenth and early twentieth centuries concentrate mainly on the experiences, Complaints, and overall difficulties of working-class laborers. The first complaint that a majority of industrial workers had was that their workdays* were too long. The average (ア) of hours in a shift varied from industry to industry, from place to place, and from era to era. Workers in British and American textile mills* in the early to middle 1800s generally worked twelve to fifteen hours, six days a week, ( イ) only Sundays off. Their average workweek* was seventy-eight hours. In contrast were the hours of workers who labored in American steel mills in the late 1800s. The length of their shifts was determined by the fact that the blast furnaces* they tended almost always operated twenty-four hours a day. Thus, (oit became customary* for steel mills to have two twelve-hour shifts. However, many of the steel workers labored seven days a week. (a)That gave them a workweek of sighty-four hours. Moreover, sometimes they had to work extra hours on top of this demanding schedule. (オ )the minor differences in the length of workweeks from one industry to another, the average worker put in twelve-to fourteen-hour days at least six days a week, This harsh schedule remained more ( カ) less standard well into the twentieth century. It was not until 1920 that a fifty-hour workweek was introduced in the United States. Anda forty-hour week did not become the rule in most industries until 1938. Low wages was another common complaint of industrial workers. In 1851, the average wage earned by American industrial workers in general was seven to ten dollars per week. That same year New York's Daily Tribune* reported that a worker's family of five required just over ten dollars a week just for basics such as rent, food, and fuel. Most ordinary workers could not afford many simple comforts that middle-class workers enjoyed. (o This miserable situation lasted in America for decades and improved only slowly. As late as 1912, a study found that only 15