赤く丸をしたbの問題で解答の方に二階微分した後の式がなぜ(-1/4)(-1/4)(H-27)になるのか分かりません。教えてください🙇‍♀️

QA At time t = 0, a boiled potato is taken from a pot on a stove and left to cool in a kitchen. The internal temperature of the potato is 91 degrees Celsius (°C) at time t = 0, and the internal temperature of the potato is greater than 27°C for all times t > 0. The internal temperature of the potato at time t minutes can be modeled by the function H that satisfies the differential equation dH (H- (H-27), where H(t) is dt measured in degrees Celsius and H(0) = 91. (a) Write an equation for the line tangent to the graph of Hat t = 0. Use this equation to approximate the internal temperature of the potato at time t = 3. (b) Use 2017 APⓇ CALCULUS AB FREE-RESPONSE QUESTIONS (a) dH d²H dt² to determine whether your answer in part (a) is an underestimate or an overestimate of the internal temperature of the potato at time t = 3. (c) For t < 10, an alternate model for the internal temperature of the potato at time 7 minutes is the function -= − (G - 27)²/3, where G(t) is measured in degrees Celsius dG G that satisfies the differential equation dt and G(0) = 91. Find an expression for G(t). Based on this model, what is the internal temperature of the potato at time t = 3 ? 564 at (21-27) - == 2-16 To = - = (H(3)-27) 4 -64 = HB)-27 -37 = H (3) (b) _d²fi © 2017 The College Board. Visit the College Board on the Web: www.collegeboard.org. GO ON TO THE NEXT P

(７)の分詞構文の解説お願いしますｑ

1 Although 2 As long as 5 Whatsoever No matter how However (6) Susan has little money because she ( 2 always 1 almost 1 W (8) How much did the digital camera ( 1 charge (2) cost ) works regularly any longer. 4 mostly ほとんど~ない (7) ( ) started raining the day before, the picnic was postponed. 1 Having 2 It has 3 It having 4 It 3 hardly (12) The woman, ( 1 such as )? 3 pay 人が払う (9) ( ) with last year, statistics show a 15% reduction in burglary in this area. 1 Comparing 4 Compare Compared 3 Having compared 「○○と比較すると」の慣用表現 (10) ( ) Mariko studied hard for the final examination, she could not pass it. 1 Even 2 Although 3 Since 4 If (11) My friends hope you'll come back soon and ( 1 I do so 2 I too so 3 so I do 4 value ). so do I ) we believed was in her thirties, had three grandchildren. 2 what 4 whom 3 who (東洋大) (青山学院大) (6) The ans 1 prep (学習院大) (南山大改) (7) He's to 1 go (関西学院大 ) (日本女子大) (8) Do y 1h (9) His 1 (10) T 重要

・〔3〕の範囲のことで、赤線のsinの範囲でなぜ≦1なのか？ ・赤線から波線のところの過程が分からないので教えてくださると嬉しいです。お願いします

tが実数値をとって変化するとき, 次の関係式をみたす点 P(x, y) の軌跡を求め,図示せよ。 (1) (2) (3) |x=-t+2 ly=2t+1 x=1-sint y=1+cost ( 30°≦t≦120°) [x=1-|t| ly=t2-1

gをこのように求めるのは何故ですか？

(gt) Ves a Vaki00 No 0 Vicord V=0 $ B 2 Sind t= 1: Vostnd gsino 特に着目して考える AN -fusing V=Vo + of and 0 = (Vosink) — (Jsino) t ming cost # gsing 7+7+38 1=(株)・ 3g² V. pagcoo g + Vo Vo² g 3g 3g ・下敷きを斜めに立てて(一この下指きが)この 上で朝方投射する!! 200² サ ・下敷きの 方向は(-ganoで 等加速度運動中、水平方 月の力はないので、 方向は等速直線運針 時間を求めるから、 鈴方向にあgをこのように求める イメージするこ 由

この解答でも大丈夫ですか？

礎問 150 第5章 微分法 82 媒介変数で表された関数のグラフ xy平面上で媒介変数0を用いて 精講 π れる曲線C上の点Pにおける接線がx軸の正方向との角をなすとき, 6 ▲(2) 点Pの座標を求めよ. (1) Cのグラフをかけ. (1) 媒介変数で表された関数の微分については 64で学びました. ここでは,それを用いてグラフをかく練習をしましょう。最大の ヤマは増減表のかき方です。 解答の中では,スペースの関係上、 d'y (1) 08 <2πのとき, dx=1-cos, dy de do 64 で求めた are をそのまま (途中を省略して)使ってあります. 2 (2)直線とx軸の正方向とのなす角をaとすると (ただし、一<a< の直線の傾きは tan で表せます.(数学ⅡⅠ・B58 解答 1 また、 dx² (1-cos)² よって, グラフは上に凸. また, dy=0 -=0 より dx dy alim 0→+0 lim 0+0 dx (230 Ly=l-cose dy lim 0-2-0 dx x=0-sin0 = sin0 より = lim 1-cos0 >0 だから,増減は右表のよう になる.また, =lim sin 0(1+cos 0) 1-cos²0 (0≦0≦2π)で表さ 1+cos 0 0 _sin(2x+t) -0 1-cos (2π+t) dysino 0 6+0 sine 0-2=t とおくと, 02-0 のとき, t→-0 = dx 1-cose 71 sin0=0.0= (0<<2πより) 0 -=+∞ 20 I 0 dy dx 注参照 y 0 64 ... + K 150 (5) π π 0 2 : T 7 2π 2π 0

(1)の、青い波線部分がなぜこのようになるのか分かりません。教えていただきたいです。

T 2 56 (1) 等式 So f (sinx)dx = f(cosx)dx を証明せよ。 √² 0 0 (2) 定積分I= =-S₁² sin x o sin x + cos x (1) [解]x=1/2 a -七とおくと、dx=-dt sinx = sin (-1) = cost 1/10 -dx を求めよ。 また、x10→ t A 290 A £₂². So f(sinx) dx よって、So =) = f (cos x)

問題)底辺と辺VAの間の角度を求めなさい。 この解き方を教えてください。 底辺は8×8cmの正方形です。 解答は60.5cmです。 ※計算機いると思います

(6 LED Ac² = 82 +82 AC = 11.31 11.49cm MB=5、66 VB² = 10² +5.66² VB = 11.49 10 cm 11.31. ´M. 5-66 ai 8 cm B The diagram shows a pyramid with a square base ABCD of side length 8 cm. The diagonals of the square, AC and BD, intersect at M. Vis vertically above M and VM = 10 cm. Calculate the angle between VA and the base. 8em cos 0 = NOT TO SCALE 64 2 0.35 = 69.627 11.492 +8²-11.492 2x8x11.49 183-84 69.63° x [4] [Total: 4]

(b)の解き方を教えてください。辺ACを求める問題です。解答は13.4 or 13.38... です。 ※計算機いると思います

2 42° = 16×23 chy (a) Calculate the value of x. 101.48 cos 2 = 5.3² +11²-6192 2x 5.3 x 11 116.6 29.50 54° 5.3 cm to The diagram shows triangle ABC with point G inside. CB = 11 cm, CG= 5.3 cm and BG = 6.9 cm. Angle CAB = 42° and angle ACG = 54°. 29.500 G 6.9 cm 11 cm x = NOT TO SCALE 96.50 B 29.50° [4]

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拓殖大〕 松山大〕 [洋大〕 科 大 [] ant 【験] 大] 改] 5 ()内に入る最も適切な語句を, ①~④のうちから一つ選びなさい。 I want to visit. 1. Ghibli Museum is a place ( ① where ③ to which 2. ( ) seemed easy at first turned out to be very difficult. ② That ③ Which ② to where ① It 3. I'll give you () toy you like. ① where ② whom 2 what 3 it 5. That's the only suggestion from my father () is really useful. ① what ② who ③ which 6. She is the last person ( ) would do it. ① that ② which ③ whom 7. Without American influences, Japanese culture would not be ( ① that 2 what 3 when ③ whomever (4) whichever 4. The bus arrived just when I got to the bus stop, () was very lucky as it runs only three times a day. 〔東京国際大〕 ① that ④ which agreement. 3. The girl whom Hiroshi is going to marry are my best friend. ① 2 4 ④ What ④ whose ) it is today. ④ which ③3 日本語に合うように,( )内に適語を入れなさい。 1. そのことについて心配するのは愚かだと考えている人たちもいました。 There were some ( 2 誤っている箇所を, 下線部 ① ~ ④ のうちから一つ選び、 ○で囲みなさい。 1. Donna said she was very sick, ③ what was not true. ① 3 4 ④ which 2. あなたがパーティーでジョンに言ったことは,まったく失礼だったよ。 ) you said to John at the party ( ) totally rude. ④ whom 3. ナンシーは無事に家に戻った。 彼女の両親はそのことを喜んだ。 Nancy returned home safely, ( ) ( ) her parents. [杏林大〕 〔獨協大〕 〔駒澤大〕 〔大手前大一改] 2. The head of the opposition party is the one ③ whom holds the key to reaching an ① 〔西南学院大一改〕 〔摂南大〕 〔拓殖大〕 〔関西学院大〕 〔京都光華女子大一改〕 ) thought it was stupid to be concerned about the matter. [京都女子大一改] [ 大同大一改〕 [専修大一改〕

that day は過去の表現じゃなくて過去完了の表現ということですか？解説がよく分からないので教えて欲しいです🙇‍♀️💦

87 XXX If I ( ) him that day, my life would be totally different now. 1 didn't meet 3 don't meet RINGONK 2 would meetdolhat (4) hadn't met MED STA & bluow $ lliw <芝浦工大