题干

如图,点C是半圆O的半径OB上的动点,作PCAB于C.点D是半圆上位于PC左侧的点,连结BD交线段PC于E,且PD=PE.

(1) 求证:PD是⊙O的切线.
(2) 若⊙O的半径为43,PC=83,设OC=x,PD2=y
①求关于的函数关系式.
②当x=3时,求tanB的值.
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答案(点此获取答案解析)

解:(1)证明:连接OD.

∵OB=OD,
∴∠OBD=∠ODB.
∵PD=PE,
∴∠PDE=∠PED.
∠PDO=∠PDE+∠ODE
=∠PED+∠OBD
=∠BEC+∠OBD
=90°,
∴PD⊥OD.
∴PD是⊙O的切线.
(2)①连接OP.
在Rt△POC中,
OP<

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    Plants are flowering faster than scientists predicted(预测)in reaction to climate change, which could have long damaging effects on food chains and ecosystems.

    Global warming is having a great effect on hundreds of plant and animal species around the world, changing some living patterns, scientists say.

    Increased carbon dioxide(CO2)in the air from burning coal and oil can have an effect on how plants produce oxygen, while higher temperatures and changeable rainfall patterns can change their patterns of growth.

    “Predicting species' reaction to climate change is a major challenge in ecology,” said the researches of several U.S. universities. They said plants had been the key object of study because their reaction to climate change could have an effect on food chains and ecosystem services.

    The study, published on the Nature website, uses the findings from plant life cycle studies and experiments across four continents and 1,634 species. It found that some experiments had underestimated(低估)the speed of flowering by 8.5 times and leafing by 4 times.

    “Across all species, the experiments under-predicted the speed of the advance — for both leafing and flowering — that results from temperature increases,” the study said.

    The design of future experiments may need to be improved to better predict how plants will react to climate change, it said.

    Plants are necessary for life on the Earth. They are the base of the food chain, using photosynthesis(光合作用)to produce sugar from carbon dioxide and water. They let out oxygen which is needed by nearly every organism on the planet.

    Scientists believe the world's average temperature has risen by about 0.8℃ since 1900, and nearly 0.2℃ every ten years since 1979.

    So far, efforts to cut emissions(排放)of planet-warming greenhouse gases are not seen as enough to prevent the Earth heating up beyond 2℃ this century — a point scientists say will bring the danger of a changeable climate in which weather extremes are common, leading to drought, floods, crop failures and rising sea levels.

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