解き方教えてください!!

Focus そのときの おいた文字の値の範囲と解の吟味に 練習 右の図のような直角三角形ABCにおいて, 辺BC 46 上の点Pから, 辺AB, ACに下ろした垂線とAB, AC の交点をそれぞれ Q, R とする. ▲BPQ と △CPRの面積の和が最小となるときのBPの長さ を求めよ. B 4 5 A AK P 3R C p.10712

分かりやすく解説お願いします🙇‍♀️🙇‍♀️

Check 例題265 りは素数nは正の整数 m,n を分母とする既約分数の総和を求めよ. 「解答 考え方 具体的な数で考えてみる。 たとえば,2と4の間 (2以上4以下) にあって、5を分母 とする数は、の順 既約分数の和比数列 He は正の整数でm<nとする、mとnの間にあってか (同志社大) BERSAN b. 5 つまり, 2,2 323 いる。項数は分子に着目して 11 (=20-10+1) 個である. これらの和を求めて、そのうち既約分数にならないもの(整数)を引くとよい. (=2), ₁ 1. 12. 13. 14. 15 (-3). 16, 17, 18, 19, 29 (-4) (20 5'5' 5' 5'5'5'5' 5 1 2+ (8-) X (82) S Focus m 以上以下でかを分母とする数は, mp+1 mp+2 mp (= m), (7J5 "(-))"81 2 差数列と等比数列 ..... 01-88 P P² P p つまり,初項m,公差 の等差数列となる.sat カー 項数np-mp+1,末項nであるから,その和 S」 は, Si= 12 (np-mp+1)(m+n)………① また,このうち,既約分数でない数は, m, m+1, m+2, n-1, n つまり,初項m, 公差1の等差数列となる. 項数n-m+1,末項nであるから,その和 S2 は, 10 2+ 5 となり,初項2、公差 1/3の等差数列になって (S2=1/12 (n-m+1)(m+n). ② (23. よって,求める和をSとすると, ①,②より, A 2 また=1/(m+n) np-1_np (= n) *** b²=ac (m+n)(np-mp+1-n+m-1) としてもよい. 分母が素数であるから, 既約分数でないものは mからnまでの整数に なる. S=1/12 (np-mp+1)(m+n)-1/12 (n-m+1)(m+n) 項数n(m-1) S1 から S2 を引けば、 まずはすべての分数の 和を求める. ¹2 公差 1 の等差数列 項数をんとすると, (0 &n=m+ (k-1) ²1 £5, =(n-m)p+1 だから, S₁=((nm)p+1} 469 具体例で検算s=Si-Se +n)(n-m)(n-1)具体例で検算 sobeda ÁHASEU ST-QUENE 具体的な数で調べて規則性をみつける x(m+n) 既約分数の総和となる.

放物線の準線、焦点の問題で解き方がわからないので、教えてほしいです。 ちなみにfocusは焦点の座標で Directrixが準線です。

Find the focus and directrix of the parabola. y = 31/12(x + 2)² focus: directrix: y = E https://4.file... ♦ |) Bor

放物線についての質問です。黒い丸で囲んだところがなぜ成り立つのかを教えて欲しいです。

9585b2f1981a9b1fc6895fb92a57852f.png 808x8957 Conic: Equation: Equation (Horizontal) Graph (Horizontal) Equation (Vertical) Graph (Vertical) Circle Center: (h, k) (x-h)²-(y-k)² = r Same Same To get r: Additional Information y==√√²-(x-h)² + k Parabola Vertex: (h, k) x= a(y-k)² +h or x-h=a(y-k)² or b(x-h)=(y-k)² (Positive Coefficient) D: x= V P P F y=a(x-h)² +k or y-k=a(x-h)² V 2p or b(y-k)=(x-h)² (Positive Coefficient) 2p D: y= For x-h=a(y-k): 1 1 a= p=40 4p For b(x-h)=(y-k)²: b b=4p; P=4 p=focal length Negative Coefficients: Flip parabola https://i.pinimg.com/originals/95/85/b2/9585b2f1981a9b1fc6895fb92a57852f.png Ellipse Center: (h, k) a always larger than b 今までの2次関数と同じ! y=2x² →x²=54 ?P=& (x-h)²(y-k)² +(x-k)² Horizontal: Focus (P/O) # y²4ex, XFP Vertral: focus (P₁0) (y=+x²) x²= Apy youp is directrix b² Co-V Co-V b C Co-V (x-h)²+(-k)=1 (x−h)²_(y-k)² a² C a directrix, a X V b =1 c²=a²-b² F Co-V Hyperbola Center: (h, k) a always before the "-" (x-h)²_(y-k)² a² (Diago) Asymptotes: Ty=-p 8/21/22 午後 5:24 q² y-k=±=(x-h) Co-V b² Co-V -=1 a Co-V (y-k)²_(x-h)² 6² Asymptotes: y-k=±(x-h) =1 c²=a² +6² Co-V 1/1ページ

なんでこうなるのかが理解できません

Focus ** 練習 20 a² /\ α3 a 1 1 a² + ½ = (a ² ÷-_— ;) ( a ² + —- )-(a + 1) Q5 =7・18-3=123 a5=a² a³, (1) x2+ 1 2 x² (40) 注>> α=x, 1 =y とおくと,x+y=a+1=3,xy=a1=1 となり、x,yの対称式と同 a 様に考えることができる. + 1 x=3のとき, 次の式の値を求めよ. x (3)x3+ (2) x + α°= (x²)=(α3)2 のように,次数を下げて考える +a+- tatio より. 1 x 1 =(x+y)(x-xy+y^) を利用してもよい。 3 x (4) x5+ 1 x³ (5) x + 6

高校1年生の問題です。 この赤丸のところで質問なんですが、なぜマイナスになるんですか？

解答 Focus (2) Aが文字式の場合も, ) VA=A={-A(A<0のとき) たとえば, A=α+1 のときは, <√(a+1)=la+1={_(a+b)(a+1<0 つまり, a <1のと (a +1≧0 つまり, a≧-1のと (1)(ア)|a-3|={ a-3 (a≧3) -a+3 (a<3) VI AZ(S- (1) 12a-41={_2a+4 (a<2) 5->2 J XJ (ウ) (-1≦a<2) |a-2|+|a+1|=-(a-2)+(a+1) って (a<-1) -(α-2)-(a+1) 2a-1 (2≦a) √a² = |a|={_a - =3 (a−2)+(a+1) (2≦a) (1)a=2 -2a+1 (-1≤a<2) OSS (a<-1) (2) √a²+2a+1+√a²-4a+4=√(a+1)² +√(a−2)² =a+1|+|a-2| ここで,-1<a<2のとき, (1) の (ウ)より, (与式)=(a+1)-(α-2) ((S) =a +1-a+2=3 (a≧0のとき) (a<0のとき) (SO What ||内 練習 (1) |2a-1|+|2a+3| を絶対値の記号を用いずに表せ. 30 (2) 1<a<2のとき =* ころ mm 界に 2a- を簡単にせよ。 (a-1)²-√(a−2)² (3) x=a²+1 のとき, √x+2a+√x-2a を簡単にせよ. (S-) A (x) 11 450, #12S+xJ0²XJ A la-2 分け la-2< a+1< ✓ -(a-

写真の赤丸⭕️の部分が、いつもプラスにするのかマイナスにするのかあやふやになります、、、 どうやって見分けるのか分かりやすく教えてください🙏🙇‍♀️

84 第2章 2 次 Think 例題 33 練習 ** 33 平行移動(②2) (1) 放物線y=-x+4x+1 は放物線y=-x2-6x+7 をどのように 平行移動したものか. (2) ある放物線Cを,x軸方向に2,y 軸方向に1だけ平行移動すると、 飲物線 y=2x-3x+4 になった。 放物線Cの方程式を求めすると 考え方 (1) 頂点の移動を考える. どちらをどちらに平行移動するのかを、しっかりおさえ (2) 放物線y=2x-3x+4 を逆に, x軸方向に -2,y 軸方向に1だけ平行移動 WALL ると, 放物線Cが得られる. Focus 解答 (1)y=x2+4x+1=-(x-2)2+5 より,頂点は点 (25) y=−x²−6x+7= −(x+3)²+1651 より,頂点は点(-3, 16) 頂点(-3.16) が点(2.5)に移動するから x 軸方向に, 2-(-3)=5 5-16=-11 (2) 放物線y=2x2-3x+4... ① を逆に, x軸方向に ―2 y軸方向に -1) だけ平行移動したものが, 放物線Cである. y軸方向に だけ平行移動している. よって,x軸方向に5,y 軸方向に-11y=2x²3x+4 よって, y=2x2+5x+5 逆の移動を考える 605061 放物線C つめる。 よって、①のxをx+2, y を y+1 におき換えて, _y+1=2(x+2)2-3(x+2)+4 STOS CASERT y=2(x²+4x+4)=3x-6+3 (8) 「x軸方向にか 軸方向に g [x軸方向に 頂点の座標をます JEAN- (移動した分) (後(前) ちなよ! 軸方向に-g VJ 頂点の移動で考えて もよい. C 放物線 C' (1) 放物線y=2x²-4x-1 をどのように平行移動すると, 放物線 y=2x2+8x- になるか. (2) ある放物線Cを,x軸方向に2,y 軸方向に3だけ平行移動すると, 線y=-x²+2x+3 になった. 放物線Cの方程式を求めよ. 放物 p.92 Cor <グ 対 たすあて とす であ ので 点 京 とな

軌跡を求める問題なのですが 例題の解答によれば 十分性の確認をしてないようなのですが 答え方としてはそれでもいいのでしょうか？

200 第3章 図形と方程式 Check (1) P(t+2, 2t²-3) (2) 放物線y=x²-2(t+1)x+t+1 がx軸と異なる2点で交わると tが実数値をとって変化するとき, 次の点Pはどのような図形を描くれ の頂点P 例題 108 媒介変数と軌跡 考え方 (1), (2)で用いられている変数t を 媒介変数 (パラメータ) という. の満たす方程式を導く. 点Pの座標を(x, y) とおいて, x, yをそれぞれで表し, t を消去することで Focus 解答 P(x,y) とおく. [x=t+2 (1) ….………. ① ly=2t2-3... ② ①より, t=x-2 これを②に代入して, y=2(x-2)2-3 よって, 求める軌跡は, 放物線y=2(x-2)2-3 (2)y=x²-2(t+1)x+t+1 ={x-(t+1)}2-(t+1)+t+1 = {x-(t+1)}²-t²-t より, 頂点Pの座標は, (t+1, -t²-t) x=t+1 ......1 したがって, ly=-t-t... ② 放物線 y=-x2+xの x<0, 1<xの部分 YA x=(tの式) y=(tの式) O ① ② より, y=-(x-1)2-(x-1)=-x2+x ここで, 放物線はx軸と異なる2点で交わるので、 3310 D 20 y=-t-t<0 t(t+1)>0 より, t <-1,0 <t ① から, x-1<-1,0<x-1 より, x<0, 1<x よって, 求める軌跡は, 練習 108 (1) P(2t-2, 3t²+1) ** (2) 円x2+y2-2tx+4t -3-- tを消去 YA 2 1 4 0 1 1-2 XC 1\x (x,y)=(t+2.20 ① ② からを る. Cab 平方完成する。 Check 例題 (1) tがすべての実 とるときも の実数値をとる。 放物線y=2x- でもよい。 (x,y)=(t+1,6 ①より、 t=x-1 これを②に代入 x軸と異なる2点 わるという条件から tの範囲に制限がつ (頂点のy座標 ) < 0 x,yの方程式 (x,yの範囲に注意 tが実数値をとって変化するとき、次の点Pはどのような図形を描くか. (2) 考え方 解答 7 S

この問題の答えを教えてください🙏

【ⅢI】 次の(A), (B)の設問に答えよ。 (A)14点,(B) 6点) (A) 次の英文を読んで下の設問に最も適切な解答をせよ。 特に指示のない選択式の設問は記 号を1つ選んで答え, "You may choose more than one option." と指示のある設問に対して複 数の記号を選ぶ場合は, アイウエオ順に解答すること｡ Mike: Hello Alex, long time no see! Alex: Hi, it's been almost two years since we last met each other! How were you doing? Mike: Until recently, I was frustrated that I could not meet my friends at university, but I was able to spend more time with my family, so I was okay. By the way, how did you like the online classes? Alex: Personally, I did not like them. It was difficult for me to maintain my concentration at home. Also, I could not resist the temptation of using my smartphone, because there was no supervisor at home who checked whether I was working hard or not. Mike: If you use your phone during class, the professor will definitely tell you off! Mo Alex: Another reason why I prefer in-person classes is that I can ask questions or have discussions with my friends. In the Pre-covid-19 era, when I had questions, I went up to my friend Thomas, one of the best students in our faculty and he taught me everything that I did not understand. Mike: That was a huge issue for me as well. If I have questions piled up, then I am more likely to dislike the subject and have more anxiety towards it. So, my friends and I decided to have meetings online on a regular basis and this helped me to worry less about online learning. Alex: That was really ( 1 ) of you, I should have done that! So, are you in favor of online learning? Mike: Yes, although I have less face-to-face interaction with friends, I like online learning more because I do not have to spend a lot of time commuting to school. I live far away from university and it takes two hours for me to get here by train. B(A) Alex: Really! I did not know that, what time do you wake up? Mike: I usually wake up at 5 am. Alex: That's so early! What do you do on the train? Mike: I just do netsurfing and I do not feel that I use my time productively on the train. If we can continue to take online classes wherever we want, we can get more flexibility in our schedules, We won't have take the time to commute to the university to attend classes, or if we like it, we may even be able to watch lecture videos on our phones while traveling by train. Alex: I understand your opinion, but didn't you have any technical problems? Mike: I only had a few. Besides, most of the professors posted recorded videos of lectures after class. So, I watched the recordings when I missed some parts. Furthermore, I could study at my own pace and the videos allowed me to digest what I had learned. Alex: That's a good point, but it had an adverse effect on my learning. Mike: How? Alex: I started skipping my online classes because I thought I could just watch those recorded videos later. So, just before exams, I had so many videos to watch. Mike: Maybe, traditional classroom settings might be better for people like you. Alex: I think so. Oh, it's time to go to class. Mike: Oh, yeah, have a good day. Alex: You too! 問1 NOTES Topic of the conversation: (2) Standpoint Basis Mike (3) (5) Choose the best one to complete blank 1. 7 because cruel clever I kind 2 Choose the best title to complete blank 2. 7 How to get good results at university Technical issues in online classes Safe remote learning at home I Online learning or learning face to face Alex (4) (6) -11-

この問題の答えを教えてください🙇‍♀️

【Ⅲ】 次の(A), (B)の設問に答えよ。 ((A)14点,(B)6点) (A) 次の英文を読んで,下の設問に最も適切な解答をせよ。 特に指示のない選択式の設問は記 号を1つ選んで答え, "You may choose more than one option." と指示のある設問に対して複 数の記号を選ぶ場合は、 アイウエオ順に解答すること。 Mike: Hello Alex, long time no see! Alex: Hi, it's been almost two years since we last met each other! How were you doing? Mike: Until recently, I was frustrated that I could not meet my friends at university, but I was able to spend more time with my family, so I was okay. By the way, how did you like the online classes? Alex: Personally, I did not like them. It was difficult for me to maintain my concentration at home. Also, I could not resist the temptation of using my smartphone, because there was no supervisor at home who checked whether I was working hard or not. Mike: If you use your phone during class, the professor will definitely tell you off! Hot Alex: Another reason why I prefer in-person classes is that I can ask questions or have discussions with my friends. In the Pre-covid-19 era, when I had questions, I went up to my friend Thomas, one of the best students in our faculty and he taught me everything that I did not understand. Mike: That was a huge issue for me as well. If I have questions piled up, then I am more likely to dislike the subject and have more anxiety towards it. So, my friends and I decided to have meetings online on a regular basis and this helped me to worry less about online learning. Alex: That was really (1) of you, I should have done that! So, are you in favor of online learning? Mike: Yes, although I have less face-to-face interaction with friends, I like online learning more. because I do not have to spend a lot of time commuting to school. I live far away from university and it takes two hours for me to get here by train. Alex: Really! I did not know that, what time do you wake up? Mike: I usually wake up at 5 am. ant mo Alex: That's so early! What do you do on the train? Mike: I just do netsurfing and I do not feel that I use my time productively on the train. If we can continue to take online classes wherever we want, we can get more flexibility in our schedules, We won't have to take the time to commute to the university to attend classes, or if we like it, we may even be able to watch lecture videos on our phones while traveling by train. Alex: I understand your opinion, but didn't you have any technical problems? Mike: I only had a few. Besides, most of the professors posted recorded videos of lectures after class. So, I watched the recordings when I missed some parts. Furthermore, I could study at my own pace and the videos allowed me to digest what I had learned. Alex: That's a good point, but it had an adverse effect on my learning. Mike: How? Alex: I started skipping my online classes because I thought I could just watch those recorded videos later. So, just before exams, I had so many videos to watch. Mike: Maybe, traditional classroom settings might be better for people like you. Alex: I think so. Oh, it's time to go to class. Mike: Oh, yeah, have a good day. Alex: You too! 問1 NOTES Topic of the conversation: ( 2 ) Standpoint Basis Mike (3) (5) Choose the best one to complete blank 1. 7 because cruel clever I kind 2 Choose the best title to complete blank 2. 7 How to get good results at university Technical issues in online classes Safe remote learning at home I Online learning or learning face to face Alex ( 4 ) (6) -11- 18