2018岡山理科大学 下線部の変形が分かりません教えてください🙏

7 [2018 岡山理科大] 関数P (x) == sinx+sin" (x+a)+sin"(x-a) について,次の問いに答えよ。 Sac であり, n=1,2,3とする。 (1) すべてのxに対してP(x)=0となるの値を求めよ。 (2) を (1) で求めた値とするとき, Pa(x) が定数になることを示せ。 また、その値を 求めよ。 (3) を (1) で求めた値とするとき, Px) = 0 となるようなxの値を求めよ。 税 (1) P(x) =sinx+sin(x+a) +sin(x-a) 0≦x≦* を満たすすべてのxでP{(x)=0となるので、x=1でも成立する必要が + +. 1 ある。よって、P(12) in // sin(+α) + sin (一) =1+cosa + cosa =1+2cosa 1 1+2cosa=0より, cos4= 2 逆にこのとき, 2 P(x)=sin x + sin(x+3)+sin(-) = sinx +(sinxcosf* + coussin for)+(sin.xcos for - cosxsin-2a) - +(1/2sin+cosx)+(1/2sing x √ cosx)=0となり成立 よって、a=1/23 (2) as / 木のとき Pa(x)=sin*x + sin(x+3)+sin(x-3) =sinx + sinx + cosx + sinx - cosx) 3 =122 (sinx+cos'x)=2/2 したがって,a=1/2のときP2(x)は定数であり (3)a=1/2のとき P₂(x)=sin'x + sin(x+x)+sin(x-3) P2(x)=1/2/2 =sin'x +(1/2sinx + 2 -COS X ✓ cos x)+(-2½ sin x - ✓ cos.x)" √3 3 sin'xosinaco's =24sin' xsinx(1-sin'x) =2sinx (4 ) = sinx(4sinx – 3) よって, P3(x)=0のとき sinx=0, ± √字 02xから x=0,3 T, 2 2

なぜ、suggesting になるのかがわかりません💦

英語 About seven years ago I started learning how to paint as a hobby: I was pretty terrible. Everything looked flat, I did not have the right proportions, and my colors were totally off. My friends and colleagues suggested that I stop wasting my time (a ) something I wasn't good at. "Focus on your day job," they said. I kept at it practicing, taking classes, finding the right teachers who could teach and challenge me Over five years, painting started to become intuitive", and surprisingly, I am now considered "good." Today, the same friends say I was born with this talent. "You're in the wrong profession," one said recently. The same thing happened when I started piano and singing lessons a couple of years ago. Comments shifted from. "Stop wasting your time and focus on what you know," to "You've got a musical talent." (A These comments originate from long-held beliefs that growth is largely not possible for adults. Even when there is evidence of learning, it can be caused by talent from birth, like the comments that I received suggested. Most scientific studies on adulthood focus on cognitive maintenance or decline, rather than growth. (b) that even scientists may think that development is severely limited in adulthood. The prevailing" mentality is represented by proverbs, such as "use it or lose it," or worse, "old dogs can't learn new tricks." A few recent studies, such as ones by Arne May and Denise Park, ( C ) suggest that learning new skills, such as juggling or photography, for even three months may strengthen brain functioning in adults. (B) I would take these studies one step further to argue that an important cause of cognitive

なんでonじゃだめなんですか？

) the south of Asia. (3) on 695 Singapore is ( 1 to 2 in 696 What is the difference w and that? 4 for

145番で、なんでsinとcosが出てきてるのか教えて欲しいです🙏

ly=3t-5 145 次の曲線の媒介変数表示を求めよ。 ly=2t-1 15 (1)円 (x-1)+(y+ 2) = 9 (2) 楕円 x2 +4y2 = 4

まーかーでひいたところについて質問です。 muchは形容詞、副詞の比較級を修飾するのだとしたら、much good(形容詞の原級)の語順が納得いかないので、解説お願いしたいです

Line Much good design evolves: the design is tested, problem area discovered and modified, and then it is continually retested remodified until time, energy, and resources run out. This n design process is characteristic of products built by craftspe 5 especially folk objects. With handmade products such as pottery, hand tools, or furniture, each new product can be m slightly from the previous one, eliminating small problems, r small improvements or testing new ideas. Over time, this p results in functional, aesthetically pleasing products. 10 Rutouch J

(1)の問題について質問です。 1番右の画像のように解いたのですが、なぜ答えと違ってしまうのでしょうか🙏

16 ド・モアブルの定理(I) 次の問いに答えよ. (1)(3)の値を求めよ. (2) 00200)=(1) (2)(3)の値を求めよ。そ SA

マーカー部分が何故なのか分かりません。 対称性に注目してなぜ、Pが第一象限にあるとわかるんですか？

35 150 基本 88 曲の接線の長さに関する証明問題 00000 曲線x+2y=(a>0)上の点Pにおける接線がx軸, y軸と交わる点を それぞれA,Bとするとき, 線分ABの長さはPの位置に関係なく一定である ことを示せ。 ただし, Pは座標軸上にないものとする。 (類岐阜 指針 まず 曲線の対称性に注目 すると (p.178 参照), 点P は第1象限にあるつまり P.1(2010)としてよりは基本83 (1) C同様にして点 における 接線の方程式を求め,点A,Bの座標を求める。様の長さがPの位置に関係 <一定であることを示すには,AB' が定数 (8,1に無関係な式)で表されることを祈 √√x²+√√y²=√√a² (a>0) ・・・... ① とする。 解答 ① は x を -x に, y を -y におき換えても成り立つから, 曲線①はx軸, y 軸, 原点に関して対称である。 どこから 58739 よって、点Pは第1象限の点としてよいから, P(s, t) (s>0, t>0) とする。 また,s = p,t=g(p>0,g>0) とおく。 ...... (*) y B P a 0 a A (xacosif ー x>0,y>0のとき,①の両辺をxについて微分すると 2 + 2y' 33√x 3√y -=0 ゆえに よって、点Pにおける接線の方程式は Ly=asing (*) 累乗根の形では表記 が紛れやすくなるので 文字をおき換えるとよい。 y-t=- (x- ゆえに y=- = ——— ( x − p³) +q³ .. @Ty=0¿¢b¿_x=p³+pq² :. A(p(p²+q²), 0) <s=p, t=q3 40=-(x-p³)+q³ 両辺にを掛けて 0=-gx+qp3+pq^ ゆえに x=p+pq^ x=0 とするとy=pq+g° ∴ B(0,g('+q2)) よって AB²={p(p²+q²)}²+{q(p²+q²)}² =(p²+q²)(p²+q²)²=(p²+q²)³ =(2s2+2/+2)=(ya²)=α² したがって, 線分ABの長さはαであり,一定である。 <a>0 曲線x2+y^2=(a>0) ① は媒介変数 0 を用いて る。この曲線を アステロイドという。アステロイドはx軸, y 軸, 原点に関して対称である。 なお, アステロイドは, サイクロイド (p.137の検討) に関連した曲線である。 その他のサイクロ イドに関する曲線について, p.638 で扱っている。 x=acos'0 y=asin'0 ②と表され 練習曲線√x+y=√a (a>0) 上の点P (座標軸上にはない)における接線が,x軸 ③ 88 y 軸と交わる点をそれぞれA, B とするとき, 原点0からの距離の和 OA+OBは 一定であることを示せ。 p.153 EX85

一番最後の文で、make OCが使われていると思ったんですが、at以下ってどういう構造でどう訳せばいいんですか(T . T)

38 音楽と人の感情 (7) [人間] Q. Which group got the best scores? iw 1155000 izum s a. The first group. b. The second group. C. The third group. The first and second groups had about the same test alemine al scores. But surprisingly, the third group who listened to 1 Mozart got much better scores than them. Their Ustant average 2 was a whole ten percent higher than the other groups. bas basd aid qu blad Torba 3 U 52 Now, here is an important question: did Mozart's music make them smarter? The answer is no. Listening to no spivbs 101 BOY das of s Q. a D Mozart's music did not immediately make them better at 5 getting high scores on tests. [い] (70 words) 第2 の 2

赤線引いているところなのですが、「had taught」ではなくなぜ「had been teaching」なのですか？ (ご飯も食べずに寝ずに)ずっと英語を教え続けている訳ないと思うのです。

5 〈完了進行形〉 次の英文を日本文になおしなさい。 (1) She has been playing the piano since she came home. (2) He had been teaching English before he became a singer. had taught

不適切なものを選ぶ問題です 解答の根拠を教えていただきたいです。 答えは上から順に、1.3.3.1.3.2.2.1.4.4.です。

(1) Judge from the circumstances of the case, the robber must have visited the jewelry shop 1 in advance. 4 11 3 (2) Dreams mostly happen during the state of asleep characterized by rapid eye movement, or REM. 12 2 3 (3) The database contains hundreds of thousands of article, but that does not make it science. 4 T 13 2 3 (4) I fond of my boyfriend, but he often turns up late for a date. Other than that, I have nothing 1 to complain about. 14 2 3 (5) Climate, soil type, and availability of water are the most critical factors than choosing the best type of grass for a lawn. 1 15 2 3 (6) Mary Quant is one of the most popular British designer of the 1960s, whose daisy motif T 2 16 has attracted the attention of younger generations in Japan. 3 (7) After so long a basketball game, I am such exhausted to write my essay, which is due on Monday. 17 2 (8) The music professor strongly advised that Emily goes to the Royal Albert Hall during her stay in London, where a globally known summer concert series is held. 18 1 2 3 (9) In the tea industry, tea leaves are graded in quality according to size, color, and appear. 19 2 3 (10) Some fish use their sense of smell as a guide when return to a spawning river. 1 2 3 20