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IB MAI HL Calculus Topic 5.4 Differential Equations (id: 0287240ca)

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admin 发表于 2025-12-26 13:45:44 | 显示全部楼层 |阅读模式
本题目来源于试卷: IB MAI HL Calculus Topic 5.4 Differential Equations,类别为 IB数学

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An experiment is conducted on a gas conn7 -gmt9 0tsyya2v9/gsofhu8vbj1/bd w /bza6bo q66dvzdv/a3)55:esfiol fined in a container. The pressure P measureoslo6 ve66 f wb5qdz:5 /vdzabd/3ia)d in Pascals, and the volume V measured in \mathrm{cm}^{3} satisfy the differential equation

$\frac{\mathrm{d} P}{\mathrm{~d} V}=-\frac{P}{V}$


Initially, the gas has a pressure of 20000 Pascals and it is confined in a container with a volume of 100 $\mathrm{~cm}^{3}$ .
1. Solve the differential equation to show that

P=$\frac{2000000}{V}$

2. Calculate the pressure required to compress the gas to a different container that has a volume of 50 $\mathrm{~cm}^{3}$ .
P=   Pa.




参考答案: 40000


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