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数学 高校生

242.1 tとおいたときにt≠0と条件をつけたのは 傾きを求める際にt=0だと分母が0になるからですよね??

370 基本例題 242 放物線と円が囲む面積 TROCS H ORHANSE 5 放物線L:y=x2 と点 R (0, 21 ) を中心とする円Cが異なる2点で接するとき 4 739 K 味 (1) 2つの接点の座標を求めよ。 (2) 2つの接点を両端とする円Cの短い方の弧とLとで囲まれる図形の面積S を求めよ。 [類 西南学院大 ] 基本 237 指針▷(1) 円と放物線が接する条件を p.156 重要例題102では接点重解で考えたが、 b+aps=d+op ここでは微分法を利用して,次のように考えてみよう。 LとCが点P で接する点Pで接線l を共有する ⇔ RP⊥ℓ LAO (②2) 円が関係してくる図形の面積を求める問題では,扇形の面積を利用することを考え ACT 1 ²0 21 するとるとよい。 半径が , 中心角が 0 (ラジアン)の扇形の面積は byd 解答 (1)y=x2 から y'=2x 果の LとCの接点Pのx座標をt (t=0) とし, この点での共通 の接線をl とすると, lの傾きは 2t 点と点P(t, t2) を通る直線の傾きは ② 放物線y=f(x)と2本の接線と 412-5-1 4t をそれ nens-s DAER RPi l から x2t. S=S+△RBA-(扇形RBA) 200+0x t2_ から -S(+4) √√3x + 2 2 √3 のゆえに、接点の座標は 2 t-0 よって t=± =(2+(-) (2) 右図のように,接点A,Bと点Cを定めると, x- 5 4 4t2-5 5 3 RC:AC=1:13 から ∠ORA=13. RA-2-(1-2)=1 4 4 (298+6) al L と直線 AB で囲まれた部分の面積をSとすると 2 √√3 2 2 2. 10 = √²+ ( ³3 - x³²) dx + 1/2 · 1² · sin ²/3 7-7.1. Ze π一 •1². /3 2 3 √3 4t $$8730<D √3 T 4 3 dx+ (0 √√3 1-(-1){ √ ³ - (- 1¹/3³ ) ² + √³-3- 2 2 4 R (x)) ゆえに f=22-x)(x+\=(xー(x) √√3 π 3√3 4 8+0 S 42-8 B 3 + 3/4 (33) (-33) 2 4 2 A O a)-(0-B $1 π B 132 YA 1-2 722 √3 R t² 5 5 4 540 VAL(y=x2) 4 R R A P 1 132 R

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英語 高校生

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ⅡI. 次の英文の空欄 ( 11 ) から ( 30 )に入る最も適切な語句を, a.〜d.の中から 1つ選びなさい。 解答は解答用紙1枚目 (マークシート方式)の所定の解答欄にマークし なさい。 Huy Fong Foods, the southern California company that produces 20 million bottles of sriracha (1) annually, has experienced a low ( 11 ) of red jalapeño chili peppers in recent years made worse by spring's crop failure. What is the cause? ( 12 ) weather and drought (2) conditions in Mexico. It's not (13) chili peppers. Mustard producers in France and Canada said extreme weather caused a 50% reduction in seed production last year, ( 14 ) to a shortage of the condiment on grocery store shelves. Blistering heat, stronger storms, droughts, floods, fires and changes in rainfall (15) are also affecting the cost and availability of staples, including wheat, corn, coffee, apples, chocolate and wine. The climate crisis is increasing the intensity and ( 16 ) of extreme weather events — and it's putting food production at risk. "Almost everything we grow and ( 17 ) in the US is facing some climatic stress," said Carolyn Dimitri, nutrition and food studies professor at NYU. Wheat and other grain crops are particularly ( 18 ). In the Great Plains region, (19) most of the US's wheat is harvested, drought depressed the winter crop. Farmers are abandoning farmland used for growing winter wheat in the US-primarily in Texas and Oklahoma - at the highest rate since 2002. Meanwhile in Montana, flooding is (20) grain crops. The impact of the climate crisis on grain crops ( 21 ) beyond the US. In India, a fierce heatwave damaged the wheat crop ( 22 ) record-setting temperatures throughout the spring and summer. As Delhi hit 49°℃ in May, the government placed a ( 23 ) on wheat exports, driving up prices even further than the rise following Russia's invasion of Ukraine. Food production is a driver of the climate crisis and a (24) of it. ( 25 ) the food system will require a wide variety of actions, including increasing crop diversity, delivering climate (26) to farmers around the world, expanding conservation programs and offering growers insurance that pays out when an index such as rain or wind speed falls above or below a fixed limit. The Biden administration is supporting research into "climate-smart" agriculture, an approach to managing cropland, forest, fisheries and cattle that attempts to address the intersecting challenges of the climate crisis and food ( 27 ). In May, the UN secretary general, António Guterres, said that climate-related disasters and extreme weather were a driver of global hunger and that 1.7 billion people ( 28 ) by the climate crisis over the last decade. Experts say (29) action is taken, we can expect to see increased food prices, decreased availability and conflict over water, which will primarily affect poorer countries and low-income Americans, (30) everything from school lunches to food aid programs. © Copyright Guardian News & Media Ltd 2023 (1) sriracha (2) drought かんばつ 世界中で人気のチリソース

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