题库网 (tiku.one)

 找回密码
 立即注册

手机扫一扫,访问本页面

开启左侧

IB MAI HL Calculus Topic 5.2 Integration (id: c2816cd4c)

[复制链接]
admin 发表于 2024-3-22 14:10:48 | 显示全部楼层 |阅读模式
本题目来源于试卷: IB MAI HL Calculus Topic 5.2 Integration,类别为 IB数学

[填空题]
All lengths in this quesuaa+(7oem fa r w2bo)4tion a* 1 : j *w6knvbrcezw7mke:on1re in metres.
Consider the function $f(x)=\sqrt{\frac{16-4 x^{2}}{7}}$ , for $-2 \leq x \leq 2 $. In the following diagram, the shaded region is enclosed by the graph of f and the x -axis.

A rainwater collection tank can be modelled by revolving this region by $360^{\circ}$ about the x -axis.
1. Find the volume of the tank.
V=   m$^3$
Rainwater in the tank is used for drinking, cooking, bathing and other needs during the week.
The volume of rainwater in the tank is given by the function g(t) , for $ 0 \leq t \leq 7$ , where t is measured in days and g(t) is measured in $\mathrm{m}^{3}$ . The rate of change of the volume of rainwater in the tank is given by $g^{\prime}(t)=1.5-4 \cos \left(0.12 t^{2}\right)$ .
2. The volume of rainwater in the tank is increasing only when a 1. Find the value of a and the value of b .
2. During the interval a d=   m$^3$
When t=0 , the volume of rainwater in the tank is 8.2 $\mathrm{~m}^{3}$ . It is known that the tank is never completely full of rainwater during the 7 day period.
3. Find the minimum volume of empty space in the tank during the 7 day period.

V$_{min}$=  m$^3$




参考答案:
空格1: 19.1空格2: 11.1空格3: 6


本题详细解析:

微信扫一扫,分享更方便

帖子地址: 

回复

使用道具 举报

您需要登录后才可以回帖 登录 | 立即注册

本版积分规则

浏览记录|使用帮助|手机版|切到手机版|题库网 (https://tiku.one)

GMT+8, 2024-12-26 03:47 , Processed in 0.062027 second(s), 29 queries , Redis On.

搜索
快速回复 返回顶部 返回列表