Question Number 1611 by Rasheed Soomro last updated on 26/Aug/15 $$\mathrm{A}\:\mathrm{right}\:\mathrm{angled}\:\mathrm{triangle}\:\mathrm{has}\:\mathrm{fixed}\:\mathrm{hypotenuse}\:\mathrm{measuring} \\ $$$$\mathrm{h}\:\mathrm{units}.\:\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{measures}\:\:\mathrm{of}\:\mathrm{its}\:\mathrm{legs}, \\ $$$$\mathrm{for}\:\boldsymbol{\mathrm{maximum}}\:\boldsymbol{\mathrm{perimeter}}\:\mathrm{P}\:\mathrm{units}. \\ $$$$\mathrm{Will}\:\mathrm{the}\:\mathrm{area}\:\mathrm{be}\:\mathrm{also}\:\mathrm{maximum},\:\mathrm{when}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{be} \\ $$$$\mathrm{maximum}? \\ $$ Commented by Rasheed Soomro…
Question Number 1592 by Rasheed Soomro last updated on 23/Aug/15 $$\mathrm{I}\:\mathrm{have}\:\mathrm{a}\:\mathrm{loop}\:\mathrm{of}\:\mathrm{string}\:\mathrm{of}\:\mathrm{length}\left(\mathrm{perimeter}\right)\:\:\mathrm{p}\:\mathrm{units}.\: \\ $$$$\mathrm{I}\:\mathrm{want}\:\mathrm{to}\:\mathrm{make}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{of}\:\mathrm{largest}\:\mathrm{area}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{loop}.\:\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{dimensions}\:\mathrm{of}\:\mathrm{that}\:\mathrm{triangle}? \\ $$ Commented by 123456 last updated on 23/Aug/15 $${x}+{y}+{z}={p}…
Question Number 1581 by 112358 last updated on 21/Aug/15 $${Find}\:{a}\:{function}\:{f}\left({x}\right)\:{satisfying} \\ $$$${the}\:{following}\:{equation}. \\ $$$$\int_{{a}} ^{\:{b}} \left[\frac{\mathrm{1}}{\mathrm{2}}\left\{{f}\left({x}\right)\right\}^{\mathrm{2}} −\sqrt{\left\{{f}\left({x}\right)\right\}^{\mathrm{2}} +\left\{\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)\right\}^{\mathrm{2}} }\right]{dx}=\mathrm{0} \\ $$$${b}>\mathrm{0},{a}>\mathrm{0}\:,\:{b}\neq{a}.\:\: \\ $$ Commented by…
Question Number 67116 by TawaTawa last updated on 23/Aug/19 Commented by TawaTawa last updated on 23/Aug/19 $$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$ Answered by Kunal12588 last updated on…
Question Number 67102 by TawaTawa last updated on 22/Aug/19 Answered by mr W last updated on 23/Aug/19 Commented by mr W last updated on 23/Aug/19…
Question Number 67072 by TawaTawa last updated on 22/Aug/19 Answered by mr W last updated on 22/Aug/19 Commented by mr W last updated on 22/Aug/19…
Question Number 67071 by TawaTawa last updated on 22/Aug/19 Commented by Prithwish sen last updated on 22/Aug/19 $$\left.\mathrm{a}\right)\mathrm{The}\:\mathrm{eqn}.\:\mathrm{of}\:\boldsymbol{\mathrm{C}}\:\:\left(\mathrm{x}−\mathrm{8}\right)^{\mathrm{2}} +\left(\mathrm{y}−\mathrm{2}\right)^{\mathrm{2}} =\mathrm{r}^{\mathrm{2}} \\ $$$$\because\:\boldsymbol{\mathrm{L}}\:\mathrm{is}\:\mathrm{a}\:\mathrm{tangent} \\ $$$$\therefore\:\frac{\mathrm{k}.\mathrm{8}−\mathrm{5}.\mathrm{2}−\mathrm{21}}{\:\sqrt{\mathrm{k}^{\mathrm{2}} +\mathrm{25}}}\:=\:\mathrm{r}…
Question Number 67033 by TawaTawa last updated on 22/Aug/19 Commented by Tony Lin last updated on 22/Aug/19 $${let}\angle{DBM}=\angle{MBC}=\phi \\ $$$$\:\:\:\:\:\angle{ECM}=\angle{MCB}=\theta \\ $$$$\mathrm{2}\theta+\mathrm{2}\phi=\mathrm{90}° \\ $$$$\Rightarrow\theta=\mathrm{45}°−\phi \\…
Question Number 67026 by TawaTawa last updated on 21/Aug/19 Commented by Tony Lin last updated on 22/Aug/19 $$\because{slope}\:{of}\:{L}_{{BC}} ={tan}\mathrm{150}°=−\frac{\sqrt{\mathrm{3}}}{\mathrm{3}} \\ $$$$\therefore{L}_{{BC}} :\:{y}=−\frac{\sqrt{\mathrm{3}}}{\mathrm{3}}\left({x}+\mathrm{4}\right) \\ $$$$\because{L}_{{BC}} \bot{L}_{{AB}}…
Question Number 1395 by Rasheed Soomro last updated on 28/Jul/15 $$\:\:\:\:\:\:\:\:\:\:\mathrm{C}{onsider}\:\boldsymbol{\mathrm{quadrilateral}}\:\boldsymbol{\mathrm{ABCD}}\:\:{same}\:{as}\:{in}\:{Q}\:\mathrm{1378}\:{with}\: \\ $$$${same}\:{conditions}/{restrictions}\:\left({Pl}\:\:{refer}\:\:{the}\:{Question}\:{again}\right). \\ $$$$\:\:\:\:\:\:\:\:\:\:\bullet\:{What}\:{could}\:{be}\:{possible}\:\boldsymbol{\mathrm{minimum}}\:{and}\:\boldsymbol{\mathrm{maximum}}\:\boldsymbol{\mathrm{area}} \\ $$$${of}\:{the}\:{quadrilateral}? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\bullet{When}\:{qusdrilateral}\:{has}\:\boldsymbol{\mathrm{minimum}}\:\boldsymbol{\mathrm{area}}\:{what}\:{is}\:{the}\:{value}/{s} \\ $$$${of}\:\boldsymbol{{m}}\angle\boldsymbol{\mathrm{A}}?\:{Similarly}\:{what}\:{is}\:{value}/{s}\:\:{of}\:\boldsymbol{{m}}\angle\boldsymbol{\mathrm{A}}\:{in}\:{case}\:{of} \\ $$$$\boldsymbol{\mathrm{maximum}}\:\boldsymbol{\mathrm{area}}? \\ $$$$…