Question Number 87939 by ajfour last updated on 07/Apr/20 Commented by naka3546 last updated on 07/Apr/20 $${what}'{s}\:\:{the}\:\:{question}\:,\:{sir}\:? \\ $$ Commented by ajfour last updated on…
Question Number 87911 by jagoll last updated on 07/Apr/20 Commented by jagoll last updated on 07/Apr/20 $$\mathrm{dear}\:\mathrm{mr}\:\mathrm{W}. \\ $$$$\mathrm{i}\:\mathrm{forgot}\:\mathrm{your}\:\mathrm{method}. \\ $$$$\mathrm{please}\:\mathrm{remember}\:\mathrm{me}\:\mathrm{for}\:\mathrm{this}\: \\ $$$$\mathrm{question} \\ $$…
Question Number 87803 by ajfour last updated on 06/Apr/20 Commented by ajfour last updated on 06/Apr/20 $${Nice}\:{question}\:{this}\:{is},\:{posted}\:{by} \\ $$$${Moth}…\left({I}\:{haven}'{t}\:{tried}\:{but}\:{no}\right. \\ $$$$\left.{one}\:{else},\:{either}\right)\:{mrW}\:{Sir}\:{shall} \\ $$$${you},\:{please}?\:{Area}\:{of}\:{green}\:\bigtriangleup=? \\ $$…
Question Number 22232 by tapan das last updated on 13/Oct/17 $$\mathrm{find}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\mathrm{where}\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{x}}{\mathrm{y}}\right)=\mathrm{x}+\mathrm{y} \\ $$ Answered by ajfour last updated on 13/Oct/17 $$\:\:\:\:\:{x}={y}\mathrm{sin}\:\left({x}+{y}\right) \\ $$$$\:\:\:\:\mathrm{1}=\frac{{dy}}{{dx}}\mathrm{sin}\:\left({x}+{y}\right)+{y}\left(\mathrm{1}+\frac{{dy}}{{dx}}\right)\mathrm{cos}\:\left({x}+{y}\right) \\…
Question Number 87648 by john santu last updated on 05/Apr/20 $$\mathrm{the}\:\mathrm{sequence}\:\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} ,\mathrm{a}_{\mathrm{3}} ,\:…\:\mathrm{satisfies} \\ $$$$\mathrm{the}\:\mathrm{relation}\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:=\:\mathrm{a}_{\mathrm{n}} +\mathrm{a}_{\mathrm{n}−\mathrm{1}} \:,\:\mathrm{for} \\ $$$$\mathrm{n}>\mathrm{1}.\:\mathrm{given}\:\mathrm{that}\:\mathrm{a}_{\mathrm{20}} \:=\:\mathrm{6765}\:\mathrm{and} \\ $$$$\mathrm{a}_{\mathrm{18}} \:=\:\mathrm{2584}\:\mathrm{what}\:\mathrm{is}\:\mathrm{a}_{\mathrm{16}}…
Question Number 153108 by peter frank last updated on 04/Sep/21 $$\int\frac{\mathrm{d}\theta}{\mathrm{sin}\:^{\mathrm{2}} \theta\left(\mathrm{3}−\mathrm{sin}\:\theta\right)} \\ $$ Answered by MJS_new last updated on 05/Sep/21 $$\int\frac{{d}\theta}{\left(\mathrm{3}−\mathrm{sin}\:\theta\right)\mathrm{sin}^{\mathrm{2}} \:\theta}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:\frac{\theta}{\mathrm{2}}\:\rightarrow\:{d}\theta=\frac{\mathrm{2}{dt}}{{t}^{\mathrm{2}}…
Question Number 152985 by ajfour last updated on 03/Sep/21 Commented by mr W last updated on 03/Sep/21 $${area}\:{in}\:{first}\:{quadrant}\: \\ $$$$+\:{area}\:{in}\:{second}\:{quadrant}\: \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\:{of}\:{rectangle}\:=\:{constant} \\ $$$${i}.{e}.\:{when}\:{area}\:{in}\:{first}\:{quadrant}\:{is} \\…
Question Number 152829 by liberty last updated on 01/Sep/21 Answered by MJS_new last updated on 02/Sep/21 $${z}^{\mathrm{2}} =\mathrm{1}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \\ $$$$\Rightarrow\:{f}\left({x},\:{y},\:{z}\right)={x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{x}+\mathrm{2}{y}−\mathrm{1} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{obviously}\:{x}\geqslant\mathrm{0}\wedge{y}\geqslant\mathrm{0}\:\mathrm{to}\:\mathrm{get}\:\mathrm{a}\:\mathrm{maximum}…
Question Number 87285 by ajfour last updated on 03/Apr/20 Commented by ajfour last updated on 03/Apr/20 $${If}\:{regions}\:{A}\:{and}\:{B}\:{have}\:{equal} \\ $$$${areas},\:{determine}\:{R}/{r}\:. \\ $$ Answered by mr W…