AR Paraboloid

Paraboloid
[img]data:image/png;base64,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[/img][br]where [math]r[/math] = radius at top, [math]h[/math] = height, [math]r(x)[/math] = radius as function of [math]x[/math].[br][img]data:image/png;base64,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[/img]
[u][color=#0000ff]https://www.geogebra.org/classic/tgyhrh2p[/color][/u]

Información: AR Paraboloid