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Category: Coordinate Geometry

find-the-volume-of-the-solid-generated-by-the-region-bounded-by-y-x-0-x-1-and-X-axis-

Question Number 145780 by Engr_Jidda last updated on 08/Jul/21 $${find}\:{the}\:{volume}\:{of}\:{the}\:{solid}\: \\ $$$${generated}\:{by}\:{the}\:{region}\:{bounded}\:{by} \\ $$$${y}=\sqrt{{x}}\:,\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\:{X}−{axis} \\ $$ Answered by ArielVyny last updated on 08/Jul/21 $${V}=\pi\int_{\mathrm{0}} ^{\mathrm{1}}…

What-is-the-transformed-equation-of-a-parabola-given-by-y-2x-2-8-5-x-109-50-if-the-coordinate-axes-is-rotated-anticlockwise-by-tan-1-3-4-

Question Number 14664 by ajfour last updated on 03/Jun/17 $$\:{What}\:{is}\:{the}\:{transformed}\: \\ $$$${equation}\:{of}\:{a}\:{parabola}\:{given}\:{by} \\ $$$$\:\:\boldsymbol{{y}}=\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} +\frac{\mathrm{8}}{\mathrm{5}}\boldsymbol{{x}}−\frac{\mathrm{109}}{\mathrm{50}}\:,\:{if}\:{the} \\ $$$${coordinate}\:{axes}\:{is}\:{rotated}\: \\ $$$$\:{anticlockwise}\:{by}\:\:\boldsymbol{\alpha}=\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{3}}{\mathrm{4}}\:. \\ $$ Answered by mrW1…

etude-complete-de-la-courbe-d-equation-polaire-r-1-sin-2-symetrie-et-trace-

Question Number 144900 by ArielVyny last updated on 30/Jun/21 $${etude}\:{complete}\:{de}\:{la}\:{courbe}\:{d}'{equation} \\ $$$${polaire}\:{r}=\frac{\mathrm{1}}{{sin}\left(\mathrm{2}\theta\right)}\:\:\:\:\left({symetrie}\:{et}\:{trace}\right) \\ $$$$ \\ $$ Answered by qaz last updated on 30/Jun/21 $$\mathrm{2rsin}\:\theta\mathrm{cos}\:\theta=\mathrm{1} \\…

Question-144210

Question Number 144210 by bramlexs22 last updated on 23/Jun/21 Answered by liberty last updated on 23/Jun/21 $$\mathrm{shaded}\:\mathrm{area}\:=\:\left(\frac{\mathrm{6}+\mathrm{2}}{\mathrm{2}}\right).\mathrm{4}\sqrt{\mathrm{3}}−\frac{\pi}{\mathrm{6}}.\mathrm{36}−\frac{\pi}{\mathrm{3}}.\mathrm{4} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{16}\sqrt{\mathrm{3}}−\frac{\pi}{\mathrm{6}}\left(\mathrm{36}+\mathrm{8}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{16}\sqrt{\mathrm{3}}−\frac{\mathrm{44}\pi}{\mathrm{6}}\:=\:\mathrm{16}\sqrt{\mathrm{3}}−\frac{\mathrm{22}\pi}{\mathrm{3}}\: \\ $$ Terms of…