题目
题目
单项选择题

Water is flowing into a large spherical tank at a constant rate (e.g. 1 gallon per minute). Let 𝐻 ( 𝑡 ) be the height of the water in the tank. Which of the following is true about 𝑑 𝐻 𝑑 𝑡 ?

选项
A.𝑑 𝐻 𝑑 𝑡 < 0 and 𝑑 𝐻 𝑑 𝑡 is constant.
B.𝑑 𝐻 𝑑 𝑡 < 0 and 𝑑 𝐻 𝑑 𝑡 is not constant.
C.𝑑 𝐻 𝑑 𝑡 = 0   and 𝑑 𝐻 𝑑 𝑡 is constant.
D.𝑑 𝐻 𝑑 𝑡 = 0   and 𝑑 𝐻 𝑑 𝑡 is not constant.
E.𝑑 𝐻 𝑑 𝑡 > 0   and 𝑑 𝐻 𝑑 𝑡 is not constant.
F.𝑑 𝐻 𝑑 𝑡 > 0   and 𝑑 𝐻 𝑑 𝑡 is constant.
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标准答案
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思路分析
Consider the situation: water is pouring into a large spherical tank at a constant volumetric rate, so the volume flow rate dV/dt is a fixed value. Option 1: dH/dt < 0 and dH/dt is constant. This would imply the water height is decreasing, which cannot happen when water is being added to the tank; the height increases, not decreases. Additionally, even if the height were increasing, the rate would n......Login to view full explanation

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