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数学 高校生

(2)の1行目、なぜ0<=θ<π/2なんでしょうか? どなたか教えていただけませんか?

例題1(回転) (1) 楕円 4 =1 2 .① を原点Oを中心に 45° 回転して得られる曲線の方程式を求めよ (2) 2次曲線+2ふy-y'=D8 ② はどのような図形か 解答 (1) 2次曲線の上の点(x, y)を原点のまわりに回転した点を(X, Y)とする。 X+Yi=(r+ yi)| cos-+isin 4 より, x+yi= (X+Y)| cos 4 -isin 4 -であるから、 1 *= Xcos-+Y sin = X+ 4 . y=-Xsin-+Y cos 4 ニーーーX+ 4 *+2y=4より、 X+E =4 ゆえに,3x? - 2.XY +3y' =8 +2 -Y よって,求める曲線の方程式は, 3r° -2.ry+ 3y° = 8 (2) 点(x, y)が原点のまわりに6 (0s0<-)回転し, 2次曲線②上の点(X, Y)移ったとする。 X+Yi=(r+yi)(cos@+isin@)より, X=rcos@- ysin@, Y=xsin@+ycos@ x*+ 25xY -Y' =18より, (xcose -ysine) +2B(xcos@- ysin@)(xsin@ +ycose)-(xsin0+ycosé)' =8 これより、 (cos'e+ 2,5sin@cos9-sin'e}r"-{4sin@cos@-2B(cos°0 - sin'@)]}: + (sin°e-25sin@cos0-cos'e)v =8 (cos20 + 5in 28)r"ー2(sin 20 -Fcos2e).y-(cos20+ 5sin29)v" =8 sin20-3cos20 =0とすると, π cos 20 +0より, tan 20= 3 0s 20<πより, 20= π ゆえに,0=: 6 このとき,2.r-2y=8 よって,双曲線 ー=1を原点のまわりに30°回転させた図形 Notel 楕円のを30° 回転して得られる曲線の方程式は, S.r' - 2~3.y +7x°=16 π 2元 Note2 |2 Note3 (1) 等より、0=- ュ--1を原点のまわりに-60*1回転] 5 =1を原点のまわりに-60° 回転] 3 3 8.5 -S.5 -1

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数学 高校生

間違っているところありますか?

y 。 次の2次関数の最大値または最小値を求めよ。また、その時のxの2 次の関数の最大値と最小値を求めなさい。また、 その時のxの値 値を求めよ、 (1) y=x?-4x+7 を求めなさい。 (1) y=x?-8x+11 (3Sx57) = (x -4) -4° +1 最大値なし =(x -2)-4+7 =<x-2)+3 #マo7 = X 最小値3 こ 全?0E= X 4= (3 -4)-5 2 oL=X (2) y=ーx-3x+5 最大値4 x ==3のとき 最大値 14 最小値なし S-{1-)= S-1 ニ *= 4のとき 最小値 -5 S+ と+ - ミ bー= 3=(7-4) -5 =?0L= X (3) y=-2x?-4x+1 = -2 (x +2^)+1 S- (E) = 5-b = b= (2) y=-x?-2x-3 (0Sx<2) * = - |のとき 最大値3 ミ -2(々+1)。+2+1 ニ -2<a+)*+3 ミ- (»て+。x) ミ- 1-.(1+x) 最小値なし ー こ (4) y=3x?-2xー1 キ307 - X = 3 (ペー言の)-1 リ- ¥ とマ o 0 こX y=-(o+リ-2 最小値ない 1-。(チーと) e = X=すのとき 最大値 -等 最小値 -2 全?0 - = = 3(^-)-番 こ-.())- - こ-|- = JxAs_ E- = (5) y=x?+6x+2 =(«+3)-3°+2 =(x+3)-9+2 - (^+シ)ーク 年3 0て= X 4= -(2+1)^-2 最値なし ミ - <3)-2 最大値 -7 よス0E- =X こ- b- = 1- = X=号のとき 最大値- - (6) y=ーx?+x+1 (3) y=x?-3x+1 (-2<x<1) -(こ) まャき(-) = キ(チ)。 子ー=X 最大値 最小値なし 全?0Z- - X% 「*ー(子+) キキ子さ)- - まャ(チ**)- - D =?0 C- - > ミ= (-2-)-是 (7) y=-2x°+4x-3 = -2 (x*-2^)-3 = -2(x-1):-P -3 - -2 C^-1 )+2-3 X = |のとき 最大値 -) 最小値なし き -( )- チ-(そ)= キー-) き-() き-キ キーま

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数学 高校生

英語の長文ってどうやったら読めるようになりますか

1 次の英文を読んで、問 (1) ~ (5) に且本語で答えなさい。 Lobola is the African custom of paying fora bride. Although it is an old custom, not In fact, it is being debated in Botswana. everyone in African cultures is happy with it. Many people, including many women, support payment of lobola. They explain that in Tswana culture, a marriage means joining a family, not just marrying an individual. The idea of marrying into a family is very African. just the man.Through marriage, the young woman's family loses their daughter as she then becomes a part of her husband's family. Lobola is a way to show thanks. It is a form of generosity in African culture. In its traditional form, they also explain, the groom's family gave cattle to the bride's family. But it didn't matter whether the family owned cattle or not. A woman does not get married to A man only had to pay what he could afford if he had no cattle, he could give something else, even the smallest form of payment. The tradition of lobola was a matter of pride. Today, lobola is often given in cash. purchase of a bride. Lobola is meant to join two families together. They know that But its supporters say it is not about the some people abuse the custom. But they believe that the tradition should not be tossed out because it has many positive effects. Rather than get rid of it, many believe it should just be explained better. However, many others say this custom should be stopped. They think it has become commercialized. Families make lots of demands on the groom. They think this makes lobola look very bad. They argue that in Africa's past, a girl was an asset at home. and other household chores. She did the cooking When a family lost that child through marriage, it demanded payment. Today, they think that lobola has changed into a useless tradition. In this custom, a man is buying the right to control a woman. They say women are individuals with rights. In today's world, parents do not have to be paid for a bride because their male and female children are equal. They all work and make contributions to the household. They believe that paying lobola makes it seem like a man is buying a pair of shoes or a bicycle, instead of getting married. They also argue that it is often a financial burden for couples. It is too difficult for many people to pay the price asked. So, is lobola a rich tradition, bringing families together? Or is it an ugly custom of buying women? This debate continues in Botswana, as does the custom.

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