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Mathematics Senior High

どう展開したら線部のひとつ前の式から線部の式になるのでしょうか?

360 第6章 微分法 Check 例題 考え方 練習 197 解 Flocus *** 曲線 y=x2 上の点P(α, α²) における法線と, この曲線との交点の うち, 点Pでない方を点Qとする.ただし, α = 0 とする. (2) 点Qの座標を求めよ. (1) 法線の方程式を求めよ. 197 接線に垂直な直線(法線) 接点で接線と垂直に交わる直線を法線と呼ぶ. (詳しくは数学Ⅲで学習) 点P(α, f (a)) における法線の傾きをmとすると, 接線の傾きが f'(a) 0 のとき, JA m·f'(a)=-1 つまり, m=-- 1 f'(a) f'(x)=2x (1) f(x)=x2 とおくと, より, 点Pにおける接線の傾きは, f'(a)=2a したがって,点Pにおける法線の傾きをmとすると, m・2a=-1より, 1 2a (a=0) よって, 点Pにおける法線の方程式は, m=- 2a, (2) 曲線 y=x2 と直線y=- を消去して、x=-2ax+1+1/12 x² = − 12 / 2x + a² + 1/1/2 より, (x-a)(x+a+ 1=0 となる. 1 y-a²=-2 (x-a) 2b, y=-2 / 4x + a² + 1 / 1 D, 2a 2 2/2x+a+1/1/2 の交点は,y +a²+· 1 2a 法線 1 (-a-2a² 4a² SLEI 1 S 注点(a, f(a)) における接線の傾きが0であった場合は, 右の図のように, 接線 y=f(a), 法線: x=α となる. まず,接線の傾きを 考える. (接線の傾き) × ( 法線の傾き) =-1 接線 したがって, x=a, -a- \2 x=-a- a121のとき、y=(-a-12/12)=a+1/+14 点Qのx座標は =x²+ 4a² 1 -a- よって, 点Qの座標は, 2a a²+ | 連立方程式を解いて 交点のx座標を求め る. 左辺に移項して因数 分解 点Pも交点の1つで あるから, x=a も 解になっている. 接線の傾き f'(a)(0) 法線の傾き 法線の傾き fla) f' V₂ (a,f(a)) y=f(a) x=a 曲線 y=x2-2x 上の点P(a, a²-2a) (a≠1) における法線の方程式を求め また、この法線と曲線との交点のうち点Pでない方の点Qの座標を求め よ. → p.361 8 Step I Cマークの問題 1 次 (1 S ←p.340 2 ←p. 341 S 3 ←p. 343 S C S 4 ←p.352 C 5 S ←p.35 c_ S ( ←p. →p. S C

Resolved Answers: 1
Mathematics Senior High

(2)が分かりません!なぜ①からグラフが上に凸と分かるのですか?もう1枚写真貼れませんでした💦解説お願いします🙇🏻‍♀️

数学ⅡⅠ・数学B 〔2〕 関数 を考える。 (1) (i) 関数 g(x) は2次関数であるとする。 y=g(x)のグラフの概形が図1であるとき, y=f(x)のグラフの概形は である。 y=g(x)のグラフの概形が図2であるとき, y=f(x)のグラフの概形は である。 f(x) = f*g(t) di ス シ (3 V x x軸と1点で接する 図 1 ス については,最も適当なものを、次の⑩~⑤のうちから一 つずつ選べ。 ただし, 同じものを繰り返し選んでもよい。 なお, x軸と軸は 省略しているが,x軸は右方向, y軸は上方向がそれぞれ正の方向である。 O ② - 26- x x軸と異なる2点で交わる 図2 (5) (数学ⅡⅠ・数学B 第2問は次ページに続く。) ()関数f(x) が3次関数であり, y=f(x)のグラフの概 形が図3であるとする。 次の⑩~⑤のうち、f(x) の式 として矛盾しないものは q,rは0でない実数とし, b, g, rはすべて異なるも である。 ただし,a,p, のとする。 +₂ の解答群 Oa(x-p)(x-g)(x-r) a(x-p)²(x-q) 3 ax(x-p)(x-q) 4ax(x-p)² β(α≦β) とすると ソ タ このとき, g(x) は2次関数であるから, 2次方程式 g(x)=0 の判別式をD とすると, である。このとき, 2次方程式 g(x)=0の二つの解をα, の解答群 D<0 t の解答群 ⑩0 <a <B ③0 <α=β タ である。 ① D = 0 ①/α < 0 <B ④ α =β=0 数学ⅡI・数学B - 27- yA AV. Xxx 図3 2 a(x-p)³ 5 ax²(x-p) 2 D>0 ② α<B<0 ⑤ α = β<0 (数学ⅡI・数学B 第2問は次ページに続く。)

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English Senior High

日本語訳をお願いしたいです!!お願いします

次の英文を読んで、設問に答えなさい。 Everybody wants to eat delicious and safe food. However, exposure to different cultures reveals 2 how people's attitudes towards food safety and taste are not all innate or biological. Assumptions and practices regarding the preparation and presentation of food highlight the influence of culture on what and how people eat. For example, in one culture, some kinds of fresh ingredients might be considered edible (a), that is, without any kind of preparation like washing, peeling or heating. Yet in another culture, the same foodstuff may require some kind of preparation before it can be eaten. It is often difficult for people from the same culture to view such activities and beliefs objectively, and so witnessing the food practices of other cultures can be surprising. Sashimi is a great example of this. While sashimi may be the result of several steps of preparation from cleaning and cutting, to a particular style of presentation - heating is not one of these steps. (2)Japanese consumers take it for granted Cultures, the conventional belief may be that real and fish require some sort of cooking, such as baking or frying, (3) in order (b) them to be considered edible. In these cultures, sashimi is not thought of as raw, delicious and safe to eat, but rather as uncooked, and therefore possibly unsafe to eat, regardless of how it may taste. Fresh chicken eggs are another raw foodstuff commonly eaten in Japan — as a topping for rice, or as a dipping sauce for sukiyaki, for example but most people in the UK or the USA believe that chicken eggs require some kind of heating before they are fit for human consumption. However, the ways in which people from other cultural backgrounds eat certain foods might be considered equally unconventional by many Japanese. For example, few Japanese would eat the skin of apples or grapes. In this case, the difference involved in the preparation of the food is not the use of heat, but the removal of part of the foodstuff. People in much of the world eat apples and grapes without peeling them. A European might think, What could be more healthy and delicious than picking an apple from the tree and eating it?' But this way of thinking is not shared by a large number of Japanese. (4) It is clear that different cultures have different conventions regarding the preparation of particular foods, and different beliefs about what is considered delicious. However, there is no question that some common food preparation practices - or sometimes a lack of certain food preparation processes - are unsafe from a scientific point of view. However delicious they may be, raw meat and fish can contain the eggs of harmful parasites like tapeworms, which are often undetectable. If chicken eggs are not properly stored, and are left unconsumed for a long time, they can easily produce bacteria like salmonella. The poisoning caused by salmonella does not usually require hospitalization, but it can be very dangerous for young children and elderly people. In addition, while eating the skin of apples and grapes may be a good source of dietary fiber, one also runs the risk of consuming insecticides, the poisons that are used to protect many non-organically farmed fruits from insects. So, while there may be 'no accounting for taste' beyond culture, safety is a different issue, and (5) we should always be aware of the risks involved with culturally accepted methods of food production and consumption. 問1 下線部 (1)で,空欄 ( a )に入る最も適切な語句を, (A)~(D)から選び, 記号で答えなさい。 (A) as is clear (B) as is fresh (C) as they are (D) as unclean 問2 問3 問4 問5 下線部(2)を日本語に訳しなさい。 下線部 (3)の空欄(b)に入る語(1語) を書きなさい。 下線部(4) を日本語に訳しなさい。 下線部 (5)の理由として最も適切なものを, (A)~(D) から選び,記号で答えなさい。 (A) Eating raw chicken eggs or unpeeled fruits can be dangerous in certain conditions because of harmful bacteria or pesticides. (B) Eating unpeeled apples or grapes may cause weight gain. (C) Only young children and elderly people are vulnerable to particular bacteria. (D) Beliefs about what is considered delicious actually come from better understanding of food preparation. 問6 本文の内容と一致するものを, (A)~(G)から3つ選び,記号で答えなさい。 (A) By food preparation processes, the author exclusively means the use of heat. (B) Culturally established ways of consuming food may conflict with scientific principles of food safety. (C) In some food cultures outside Japan, fish in its raw state is not categorized as an edible foodstuff. (D) People having little contact with other cultures tend to view their own food-related conventions as natural and standard. (E) Repeated exercise is required for the mastery of any food preparation. (F) Instinct alone determines what and how people eat. (G) All cultures around the world consider it natural to eat unpeeled fruit.

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