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IB MAI HL Calculus Topic 5.1 Differentiation (id: 95d4361a3)

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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]
Mustafa is an ice sculptor. Inmhyzytusht 9 b6a+:(9 a5 uw i:h)roidgocu:(+n ice and snow festival, he is about to build an ice tent in the shape of a cylinder with a cone of the same radius at the t:oh +)iu (dc:our5 gwiop. The total surface area of the tent is in $m^2$ and given by
A=$\frac{18\pi}{r}$ + $\pi r^2$ - 2
where r is the radius of the cylinder, in metres.

In order for his work to last as long as possible, Mustafa aims to reduce the evaporation rate and hence minimize the total surface area of the ice tent.
1.Find $\frac{dA}{dr}$=-$\frac{a\pi}{r^2}$ + b$\pi r$;
a=  , b=  .
2.Determine the value of r that minimizes the total surface area of the ice tent.
r≈  .08m.




参考答案:
空格1: 18空格2: 2空格3: 2


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