Mathematics, 30.10.2020 16:20, AriaMartinez
The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs nine times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials. (Let x, y, and z be the dimensions of the aquarium. Enter your answer in terms of V.) (x, y, z)
Answers: 2
![x=y = \sqrt[3]{\frac{2V}{9}} , z = \sqrt[3]{\frac{81V}{4}}](/tpl/images/0855/0861/4865b.png)
![Volume = xyz=(x)(x)(\frac{9x}{2})\\Volume V = \frac{9x}{2}x^3\\\sqrt[3]{\frac{2V}{9}}=x\\x=y=\sqrt[3]{\frac{2V}{9}}\\z=\frac{9(\sqrt[3]{\frac{2V}{9}})}{2}\\z=\sqrt[3]{\frac{81V}{4}}](/tpl/images/0855/0861/2975d.png)
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The base of an aquarium with given volume V is made of slate and the sides are made of glass. If sla...
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