Find the isosceles triangle of smallest area

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1. Find the isosceles triangle of smallest area (Figure) that circumscribes a circle of radius 1 (from Thomas Simpson's The Doctrine and Application of Fluxions, a calculus text that appeared in 1750).

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2. A box of volume 72 m³ with a square bottom and no top is constructed out of two different materials. The cost of the bottom is $40/m² and the cost of the sides is $30/m². Find the dimensions of the box that minimize total cost.

Reference no: EM131009551

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