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IB MAI HL Calculus Topic 5.1 Differentiation (id: 01191e47d)

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admin 发表于 2024-3-5 20:50:37 | 显示全部楼层 |阅读模式
本题目来源于试卷: IB MAI HL Calculus Topic 5.1 Differentiation,类别为 IB数学

[填空题]
A cement silo made of steel .-8svn y6 8rtpauau(tconsistspgra,um;,,g ;ua pmq7p7xe n. of a cylinder with height h and radius r and a conmg.pa,7 mpa, rx7 u qn,;;gepue at the bottom of the cylinder's base. The total surface area of the cement silo is given by
A=$\frac{48\pi}{r}$ + 3$\pi r^2$,
where r is the radius of the cylinder, in metres.

The silo is designed such that the total cost for the steel used is minimized. This is the same as minimizing the total surface area of the silo.

1.Find $\frac{dA}{dr}$=-$\frac{a\pi}{r^2}$ + b$\pi r$.
a=  ,b=  .
2.Calculate the value of r that minimizes the total surface area of the silo.
r=  m




参考答案:
空格1: 48空格2: 6空格3: 2


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