题干

如图①,小慧同学把一个正三角形纸片(即△OAB)放在直线l1上.OA边与直线l1重合,然后将三角形纸片绕着顶点A按顺吋针方向旋转120°,此时点O运动到了点O1处,点B运动到了点B1处;小慧又将三角形纸片AO1B1,绕点B1按顺吋针方向旋转 120°,此时点A运动到了点A1处,点O1运动到了点O2处(即顶点O经过上述两次旋转到达O2处).
小慧还发现:三角形纸片在上述两次旋转的过程中.顶点O运动所形成的图形是两段圆弧,即 OO1^O1O2^ ,顶点O所经过的路程是这两段圆弧的长度之和,并且这两段圆弧与直线l1围成的图形面积等于扇形A001的面积、△AO1B1的面积和扇形B1O1O2的面积之和.
小慧进行类比研究:如图②,她把边长为1的正方形纸片0ABC放在直线l2上,0A边与直线l2重合,然后将正方形纸片绕着顶点A按顺时针方向旋转90°,此时点O运动到了点O1处(即点B处),点C运动到了点C1处,点B运动到了点B2处,小慧又将正方形纸片 AO1C1B1绕顶点B1按顺时针方向旋转90°,….按上述方法经过若干次旋转后,她提出了如下问题:
问题①:若正方形纸片0ABC按上述方法经过3次旋转,求顶点0经过的路程,并求顶点O在此运动过程中所形成的图形与直线l2围成图形的面积;若正方形纸片OABC按上述方法经过5次旋转.求顶点O经过的路程;
问题②:正方形纸片OABC按上述方法经过多少次旋转,顶点0经过的路程是 4120
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上一题 下一题 0.0难度 选择题 更新时间:2013-09-23 07:57:10

答案(点此获取答案解析)

解:①如图所示,正方形纸片OABC经过3次旋转,顶点O运动所形成的图形是三段圆弧,
∴顶点O在此过程中经过的路程为: 90180
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    There might be as many as 10 million species of complex life on this planet today —— a huge number. But add up all of the complex species that ever lived and some biologists think the grand total would be about five billion. The estimate leads to an astonishing conclusion: a staggering 99% of species are not around any more. They have been driven to extinction.

    More species are joining the ranks of the extinct every year. Many scientists believe we are living through an episode of remarkably rapid extinction, on a scale that has been seen only five times in the last half a billion years.

    They call this current episode the sixth mass extinction —— a large, global decline in a wide variety of species over a relatively short period of time. And they tend to agree that humans are the main cause.

    Over-hunting, overfishing, and human-driven habitat loss are pushing many species to the brink. In fact, we have changed the planet so much that some geologists are now suggesting that we have entered a new phase in Earth's history; an epoch they call the "Anthropocene". By 2100, it is expected that humans will have caused the extinction of up to half of the world's current species.

    Because we are living through this extinction, it is relatively easy for us to study the driving forces behind it. But how do we determine what caused other mass die-offs that happened long ago? To do so we have to look at what archaeologists, palaeontologists, geologists and other scientists have concluded from the evidence they have gathered.

    The trouble is, those scientists do not always agree with one another —— even about the most recent extinction event. As well as the five-or six- mass extinctions, there have also been many smaller extinctions.

    One of these mini extinction events happened towards the end of the Pleistocene, a few tens of thousands of years ago. It is sometimes called the "megafaunal" extinction because many of the species it claimed were particularly large animals, weighing more than 97lb (44kg). However, its cause remains a debate amongst scientists.