问题详情
用长为12m的栅栏围成一个长方形花圃，花圃ABCD的一边AD靠墙(墙足够长)，设AB长为xm，长方形ABCD的面积为Sm2．
(1)用函数表达式表示：S＝________；
(2)用表格表示：
(3)用图像表示；
(4)根据以上三种表示方式回答下列问题．
①自变量x的取值范围是什么？
②图像的对称轴和顶点坐标分别是什么？
③如何描述S随x的变化而变化的情况？
④当x取何值时，长方形的面积最大？它的最大面积是多少？
【回答】
*：解析：
(1)S＝－2x2＋12x (2)从左向右依次填10,16,18,16,10,0 (3)略 (4)①0＜x＜6;②对称轴直线x＝3 顶点坐标(3，18);③当0＜x＜3时S随x的增大而增大；当3＜x＜6时S随x的增大而减小;④当x＝3时，长方形面积最大;最大面积为18m2 |
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A People all over the world eat rice. Millions of people in Asia, Africa and South America live on it. Some people eat almost nothing but rice. Rice is a kind of grass. There are more than 7,000 kinds of rice. Most kindsare water plants. Farmers grow rice in many countries, even in the south of the United States and in eastern Australia. China is the world's largest rice-growing country. In 2003, China grew 166 million tons of rice. But it is noteasy to feed the world's largest population. In the 1960s, thousands of Chinese died because they didn't haveenough food to eat. In the 1970s, Yuan Longping, a Chinese scientist, grew a new kind of rice called hybrid rice. It makes 20% more rice than any other kind. Hybrid rice is a stronger plant, unlike ordinary (普通的) rice.It can grow in lots of water or in not much water. It doesn't easily get diseases or worms. Today, half of China's rice plants are Yuan's special hybrid rice. China uses Yuan's hybrid rice to grow much more rice than before. Yuan is known as the Father of Hybrid Rice. He won the World Food Prize for his work to help feed so many people.
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A People all over the world eat rice. Millions of people in Asia, Africa and South America live on it. Some people eat almost nothing but rice. Rice is a kind of grass. There are more than 7,000 kinds of rice. Most kindsare water plants. Farmers grow rice in many countries, even in the south of the United States and in eastern Australia. China is the world's largest rice-growing country. In 2003, China grew 166 million tons of rice. But it is noteasy to feed the world's largest population. In the 1960s, thousands of Chinese died because they didn't haveenough food to eat. In the 1970s, Yuan Longping, a Chinese scientist, grew a new kind of rice called hybrid rice. It makes 20% more rice than any other kind. Hybrid rice is a stronger plant, unlike ordinary (普通的) rice.It can grow in lots of water or in not much water. It doesn't easily get diseases or worms. Today, half of China's rice plants are Yuan's special hybrid rice. China uses Yuan's hybrid rice to grow much more rice than before. Yuan is known as the Father of Hybrid Rice. He won the World Food Prize for his work to help feed so many people.
根据短文内容判断正（T）误（F）。 ( )1. Rice is grown in almost every country. ( )2. Yuan Longping's hybrid rice can grow without water. ( )3. Yuan's hybrid rice can make more rice. ( )4. The Chinese scientist, Yuan Longping, is famous for his hybrid rice. ( )5. The hybrid rice can feed all the Chinese people.
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如图，在Rt△ABC中，∠ACB=90°，AB=4，BC=2，将△ABC绕点B顺时针方向旋转到△A′BC′的位置，此时点A′恰好在CB的延长线上，则图中*影部分的面积为 （结果保留π）．
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