Question: Question #3 (optimization). We have an empty cone of height 10 m. Any point on the surface of the cone is given by its

Question #3 (optimization). We have an empty cone of height 10 m. Any point on the surface of the cone is given by its co-ordinates (x, y, z) such that z=10-2(x+ y), 0 z 10. A tiny cube of sugar is placed at the inside surface of the cone at A = (-3, 4, 0). An ant and a fly are sitting inside the cone at B = (1.5, 2, 5). They wish to go for the tiny cube of sugar at A. (a) Verify that the points A and B lie on the inner surface of the cone. (b) How do the ant/fly determine which way to move/fly? (c) What is the minimum distance the ant must travel before it gets to the sugar? (d) How about the fly?

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a To affirm that the factors A 340 and B 15 2 5 lie on the internal surface of the cone we can repla... View full answer

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