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Category: Coordinate Geometry

proof-that-volume-of-frustum-of-circular-cone-is-1-3-h-A1-A2-A1A2-A-1-and-A-2-are-areas-of-base-

Question Number 220257 by abbb last updated on 10/May/25 $${proof}\:{that}\:{volume}\:{of}\:{frustum}\:{of} \\ $$$$\:{circular}\:{cone}\:{is}\:\frac{\mathrm{1}}{\mathrm{3}}{h}\left[{A}\mathrm{1}+{A}\mathrm{2}+\sqrt{{A}\mathrm{1}{A}\mathrm{2}}\right. \\ $$$${A}_{\mathrm{1}} {and}\:{A}_{\mathrm{2}} \:{are}\:\:{areas}\:{of}\:{base} \\ $$ Answered by MrGaster last updated on 10/May/25…

Question-219685

Question Number 219685 by alcohol last updated on 30/Apr/25 Answered by SdC355 last updated on 01/May/25 $$\kappa=\frac{\mathrm{2}}{\:\sqrt{\left(\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} \right)^{\mathrm{3}} }}\:\:\:\left(\mathrm{curvature}\:\kappa=\frac{\mid\mid{y}^{\left(\mathrm{2}\right)} \left({t}\right)\mid\mid}{\:\sqrt{\left(\mathrm{1}+\left({y}^{\left(\mathrm{1}\right)} \left({t}\right)\right)^{\mathrm{2}} \right)^{\mathrm{3}} }}\:\right) \\ $$$${r}=\frac{\mathrm{1}}{\kappa}=\frac{\sqrt{\left(\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}}…

Question-218384

Question Number 218384 by Spillover last updated on 08/Apr/25 Answered by Nicholas666 last updated on 09/Apr/25 $${percentage}\:{of}\:{red}\:{area}: \\ $$$$\frac{\mathrm{15}\pi\sqrt{\mathrm{3}}}{\mathrm{32}.\mathrm{3}}.\mathrm{100\%}=\frac{\mathrm{5}\pi\sqrt{\mathrm{3}}}{\mathrm{32}}=\mathrm{100\%} \\ $$$$=\frac{\mathrm{5}.\pi.\mathrm{1},\mathrm{732}}{\mathrm{32}}.\mathrm{100\%}=\frac{\mathrm{27},\mathrm{206}}{\mathrm{32}}.\mathrm{100\%}=\mathrm{85},\mathrm{02\%} \\ $$$$ \\ $$…